LANGMUIR-SCHAEFER FILMS OF A FERROELECTRIC COPOLYMERFOR INFRARED IMAGING APPLICATIONS

A thesis submitted toKent State University in partial

fulfillment of the requirements for thedegree of Master of Science

by

Revathy Durairaj

May, 2012

Thesis written by

Revathy Durairaj

B.Sc., Bharathidasan University, 2001

M. Sc., Bharathidasan University, 2003

Approved by

Dr. Elizabeth K. Mann, Advisor

Dr. Jim Gleeson, Chair, Department of Physics

Dr. John R.D. Stalvey, Dean, College of Arts and Sciences

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Table of Contents

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Ferroelectrics and their properties . . . . . . . . . . . . . . . . . . . . . . . 6

1.1.1 Ferroelectric polymers . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.1.2 Structure of PVDF in 3d . . . . . . . . . . . . . . . . . . . . . . . . 9

1.1.3 Structure of PVDF-TrFE . . . . . . . . . . . . . . . . . . . . . . . . 11

1.2 Langmuir Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.2.1 The Pressure - Area Isotherm . . . . . . . . . . . . . . . . . . . . . 13

1.3 Langmuir-Blodgett films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.4 Pyroelectricity of PVDF-TrFE . . . . . . . . . . . . . . . . . . . . . . . . . 16

2 The Brewster Angle Microscopy and other experimental methods for

Langmuir films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.1 Interaction of Light with Air-Water interface . . . . . . . . . . . . . . . . . 20

2.2 Interaction of Light with Air-Thin film-Water interfaces . . . . . . . . . . . 23

2.3 The Brewster Angle Microscope . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.4 Surface Tension and Free energy . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.1 Liquid-liquid interface . . . . . . . . . . . . . . . . . . . . . . . . . . 29

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2.4.2 Solid-liquid interface . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.4.3 Surface pressure Measurement - Wilhelmy Plate Method . . . . . . . 32

3 Experimental methods of Langmuir and Langmuir-Schaefer films . . . . 35

3.1 Langmuir trough and other components . . . . . . . . . . . . . . . . . . . . 35

3.2 Cleaning procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Experiment: How to make a Langmuir film . . . . . . . . . . . . . . . . . . 37

3.4 Langmuir-Schaefer Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4 Langmuir and Langmuir-Schaefer films of PVDF-TrFE . . . . . . . . . . 42

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2 Polymer monolayer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.3 Surface pressure - Area isotherm . . . . . . . . . . . . . . . . . . . . . . . . 45

4.3.1 Comparison with Isotherms in the Literature . . . . . . . . . . . . . 50

4.3.2 Effect of sample concentration . . . . . . . . . . . . . . . . . . . . . 51

4.3.3 Effect of subphase temperature . . . . . . . . . . . . . . . . . . . . . 53

4.4 BAM images of PVDF-TrFE . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.5 Atomic Force Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.7 Suggestions for Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5 Numerical simulation of linear plasmonic photodetector . . . . . . . . . . 70

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.2 Surface plasmons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.3 Results of numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

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6 Conclusions and Recommendations . . . . . . . . . . . . . . . . . . . . . . . 79

6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

A Reflectivity for Langmuir Monolayers . . . . . . . . . . . . . . . . . . . . . 87

B Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

B.1 Molecular weight of PVDF-TrFE . . . . . . . . . . . . . . . . . . . . . . . . 93

B.2 Concentration of the sample in weight percentage . . . . . . . . . . . . . . . 93

B.3 Calculation of Molecular area per structural unit . . . . . . . . . . . . . . . 94

B.4 Calculation of thickness of LB films . . . . . . . . . . . . . . . . . . . . . . . 94

C MATLAB program for calculating Rs and Rp . . . . . . . . . . . . . . . . . 96

D MATLAB program for plotting dispersion curves of anti-symmetric

MDM waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

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List of Figures

1.1 Types of polarization. (Left)Linear polarization: The two orthogonal electric

field components have the same magnitude and same phase, (Middle) Circu-

lar polarization: The electric field components are the same magnitude, but

900 out of phase and (Right) Elliptical polarization: The field components

differ in both magnitude and phase.4 . . . . . . . . . . . . . . . . . . . . . . 2

1.2 (a) Visible picture of two trucks in the shade (b) Long-wave IR intensity

image (c) Long-wave IR polarimetric image. The two trucks in the shade is

very clear in the Polarimetric image because of the strong contrast.3 . . . . 3

1.3 SEM images of the wire grid polarizers that allow (a) vertical (b) horizontal

and (c) 450 linearly polarized light. The polarization images of a static scene

is shown at the bottom panel. Images (e), (f) and (g) are S0, S1 and S2

respectively.8 The S0 image is equivalent to typical IR image. Compared

with S0 image, things are more apparent in the S1 image. The image contrast

is enhanced in this case. But this depends on the orientation of the surfaces

with respect to the polarizer as shown in the S2 image, the two halves of the

building’s roof is clearly visible. . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 (a)Classification of crystals based on their crystallographic symmetry15 (b)The

relation between piezoelectric, pyroelectric and ferroelectric materials.16 . . 7

1.5 Typical Dielectric hysteresis loop of a Ferroelectric crystal. Here Pr is the

remanent polarization, Ps is the spontaneous polarization and Ec is the co-

ercive electric filed required for zero polarization.17 . . . . . . . . . . . . . . 8

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1.6 Structure of PVDF; (a) Structure of the all-trans conformation, called β

phase, showing the planer carbon backbone with attached fluorine and hy-

drogen atoms; The arrow shows the direction of dipole moment when viewed

along the chain axis. Drawn using Chem3D software. . . . . . . . . . . . . . 10

1.7 Ball and stick model of all-trans β conformation PVDF-TrFE (70:30). 30%

of the VDF units have been replaced randomly by TrFE units. The arrow

shows the net dipole moment fluorine to hydrogen.27 . . . . . . . . . . . . . 13

1.8 (A)Typical isotherm of a Langmuir monolayer. When compressing the dilute

gas, the area per molecule decreases and the monolayer undergoes several

phase transitions from Gas (G) to liquid-disordered (LD) to liquid-ordered

(LO) and finally to solid phase (S) in which the molecules are closely packed.

The isotherm is taken from the book Interfacial Science: An Introduction29

and modified. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.9 Techniques for depositing a monolayer on a solid substrate (a) Langmuir-

Blodgett method - Vertical deposition on a hydrophilic substrate (b) Langmuir-

Schaefer method - Horizontal deposition (Modified from KSV website: http :

//www.ksvnima.com/langmuir − and− langmuir − blodgett− troughs) . 15

1.10 (a) Temperature cycle and the corresponding pyroelctric current. A negative

current flows through the circuit when the temperature increases and when

the temperature decreases, the pyroelectric current is positive. (b) Plot of

pyroelectric current vs temperature shows the maximum pyroelectric current

near the Curie temperature. (c) Hysteresis of the effective piezoelectric coef-

ficient and the pyroelectric current as the applied dc electric field was cycled

at room temperature.36 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

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2.1 Reflection and transmission at the interface between two media. (a) In s-

polarization, the electric field is perpendicular to the plane of incidence and

(b)in p-polarization, the electric field is parallel to the plane of incidence5 . 21

2.2 The total reflectivity Rp goes to zero at Brewster Angle . . . . . . . . . . . 23

2.3 Reflection and transmission of light when there are two or more interfaces . 24

2.4 s-polarization reflectivity curves for a flim of the copolymer PVDF-TrFE at

the air-water interface for different values of thickness. The refractive indices

are: n1 = 1.000, n2 = 1.420 and n1 = 1.333 for air, PVDF-TrFE and water

respectively. There is no significant variation of reflectivity with changes in

the film thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.5 p-polarization reflectivity curves for a flim of the copolymer PVDF-TrFE at

the air-water interface for different values of thickness. The refractive indices

are n1 = 1.000, n2 = 1.420 and n1 = 1.333 for air, PVDF-TrFE and water

respectively. The reflectivity goes to zero at the Brewster angle when there is

no film on the water surface, which corresponds to 0nm curve (Black). The

blue bordered box is zoomed out and shown in the bottom panel to show the

difference in reflectivity between a 0.45nm (Red) film of PVDF-TrFE and a

clean water surface (Black). . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.6 A photograph of the Brewster angle microscopy set up in our lab. . . . . . . 29

2.7 (a)Π − σ isotherms of low concentration sample at different temperatures.

Isotherms shift towards left as the temperature increases. (b)Gibbs free en-

ergy calculated from the isotherms is plotted against temperature for different

surface pressures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.8 A liquid drop on solid surface . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.9 Forces acting on Wilhelmy plate . . . . . . . . . . . . . . . . . . . . . . . . 33

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3.1 A photograph of the Langmuir trough used in this work with its components,

two barriers and beam dump. . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2 Arrangement of the Langmuir trough with beam dump inside the dipping

hole and the barriers are kept symmetrically on the trough which will be

controlled by the motor. The photograph at the bottom shows the Langmuir

trough, Wilhelmy plate for surface pressure measurement. The laser light

falls on the monolayer film at the air-water interface at the Brewster angle

and the reflected beam is directed to the CCD. . . . . . . . . . . . . . . . . 38

3.3 Three steps involved in Inverse Langmuir-Schaefer technique. The solid sub-

strate is held by tweezers44 . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.1 STM image of a single monolayer film on graphite.45 . . . . . . . . . . . . . 42

4.2 Schematic diagram of polymer molecules on water surface during compres-

sion. (a) Initially polymer molecules may take a random coil shape. (b)

and (c) Note the surface concentration, as in the number of molecules per

unit area, is unchanged. Coil untangles and the polymer molecules fills the

water surface and hence the surface coverage increases. (d) When the area

is decreased by the barriers, polymer chains are closely packed. (e) and (f)

On compression, polymer chains overlap on each other and move away from

water surface. (b) and (c) are after the presentation [49] . . . . . . . . . . . 45

4.3 Surface pressure Π - Area σ isotherm of PVDF-TrFE at 25 C. Here σ0 is

limiting surface area for close packing of molecules. This can be found by

extrapolating to Π = 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.4 log Π - log σ plot (black) from the surface pressure-area isotherm. The slope

of the linear fit (green) gives the value of scaling exponent ν as 4.97. Choosing

another region for the linear fit, the value of ν was found to be 6.55. . . . . 48

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4.5 The elasticity of the Langmuir film calculated from the Π − σ isotherm.

The elasticity increases with decreasing mean molecular area. At σϵ−max ∼

0.0045nm2, elasticity reach a maximum which may mean that the monolayer

begins to collapse out of the surface. . . . . . . . . . . . . . . . . . . . . . . 49

4.6 Comparison of isotherms of the present work with the previously published

isotherms. The main difference is that the coarea in the present case is almost

10 times lesser than the coarea found from the isotherm published for the

first time in 1995. In fact, all studies since the initial isotherm shown in red

find much smaller coareas; a typical example is shown in the middle curve.

A. Cavalli et al. suggests that the smaller coarea is due to the dissolution

of the copolymer into the water. Published isotherms were scanned and the

values are extracted by the free software PlotDigitizer. . . . . . . . . . . . 50

4.7 (a)Comparison of isotherms of different sample concentrations. (b)The coarea

vs sample concentration is shown; σ01 and σ02 are coareas found from two

different tangent lines drawn on the isotherms and extrapolated for Π = 0.

These values for each isotherm gives the uncertainty in the calculation of

coarea. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.8 Elasticity of different concentration samples calculated from Π−σ isotherms

shown in Figure[4.6]. The shift in elasticity may be because of difference in

polymer configurations on water surface and its surface concentration of the

polymer. Beginning of film collapse and rearrangement of polymer molecules

may be the reason for the fluctuations of elasticity at the higher surface

pressures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

x

4.9 (a) Π − σ isotherms of low concentration sample at different temperatures.

Isotherms shift towards left as the temperature increases for which the reason

may be the balance between adhesive and cohesive properties of the copoly-

mer. (b) Gibbs free energy calculated from the isotherms using equation [4.3]

is plotted against temperature for different surface pressures. . . . . . . . . 55

4.10 : A schematic diagram of behaviour of polymer molecules on the water surface

for increasing temperature. As the temperature increases, monomers will be

more soluble in water, so that more segments leave the surface (upper two

figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.11 (a)BAM image of the water subphase without any film on it. The reflec-

tivity of p-polarized light is nearly zero at the Brewster’s angle. This cre-

ates the background for BAM imaging. (b)Typical BAM image of PVDF-

TrFE(70:30) at room temperature taken at very low surface pressure (less

than 1mN/m). The brighter regions characterizes the thicker film while the

darker region is for film with lesser thickness. The bottom right corner of

this image is simply water and it is dark. . . . . . . . . . . . . . . . . . . . 58

4.12 BAM images of PVDF-TrFE of 0.158mg/ml at low and high surface pres-

sures are shown in left and right columns respectively. (a) and (b) At low

temperature, small bright spots are clear, especially at high pressure. The

small circular patterns observed in both high and low surface pressures are

similar particles which are out of focus because of the incident angle: only a

line perpendicular to the plane of incidence, parallel to the horizontal azis on

the figures, is in focus. (c) and (d) Near room temperature, there are more

spots (out of focus here) at both pressures. (e) and (f) At high temperature,

Again many bright, probably 3-d particles are observed. . . . . . . . . . . . 59

xi

4.13 BAM images of PVDF-TrFE of 1.38 mg/ml at low and high surface pressures

are shown in left and right columns respectively. (a) and (b) Low tempera-

ture BAM images show that even at very low surface pressures, the polymer

molecules completely covered the water surface with only occasional dark

areas. Further compression results in overlapping of polymer chains and that

can be seen in brighter region of (b). At room temperature, (c) show that

the polymer film is very thick and nonhomogeneous. In figure (d) we can see

that the film is about to collapse. At high temperature, the films seem much

more uniform with few bright particles. Moreover, we can see some domains

with fine boundaries. From the Table [4.2], we can note that the value of σ0

is less for the all the three temperatures. As recommended before in Section

[4.3.3], we can try BAM imaging for deposition of polymer solution at low

temperature and compression of the film at high temperature . . . . . . . . 65

4.14 AFM images of 0.2% high concentration sample are shown. Top left 2D AFM

image represents the LS film of PVDF-TrFE prepared at 250C at low surface

pressure, 5mN/m. The scan size is 2µm × 2µm. Top right 2D AFM image

is for the same concentration sample, but prepared at low temperature 120C

at 5mN/m. The scan size is 1µm× 1µm. Their 3D images are shown in the

bottom panel. The blue box indicates a void, that will be enlarged in Figure

[4.15]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.15 Enlarged image of void (blue box) drawn in Figure [4.9]. The height profiles

of lines 1 and 2 show that the film is not homogeneous. . . . . . . . . . . . 66

4.16 Comparison of height profiles of the two films prepared at room temperature

and low temperature. For comparison the height profiles are drawn only for

the length of blue lines drawn on the images. . . . . . . . . . . . . . . . . . 67

xii

4.17 Comparison of roughness of two films is shown here. Lower the area under

the curve, the better the smoothness. Therefore, the film prepared at room

temperature shows more smoothness compared to the one prepared at low

temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.18 AFM picture of the same low concentration sample prepared at room tem-

perature, low surface pressure. The area of blue box is enlarged to show that

the void exists in low concentration samples also. The height profile is also

shown below corresponding to the blue line. . . . . . . . . . . . . . . . . . . 68

4.19 (a)Comparison of roughness of low (green curve) and high concentration (red

curve) samples. This shows that the LS film of high concentration sample

has more roughness. (b)Roughness of low concentration film is compared

with that of simple Silicon substrate without any film on it. The roughness

of both the film and Silicon substrate looks similar. The green curve implies

that there may be a very thin layer of polymer molecule is formed on Si

substrate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.20 2D and 3D AFM images of the LS film of low concentration sample prepared

at room temperature at 5mN/m is shown on the left side. We observed some

triangular patterns. The reason is now known and this needs further inves-

tigation. The right side AFM image is for simple Silicon substrate without

any film on it. From these images it is clear that the Silicon substrate itself

is not smooth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

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5.1 (a) Schematic illustration of electromagnetic wave and surface charges at the

interface between the metal and the dielectric material,(b) the locally electric

field component is enhanced near the surface and decay exponentially with

distance in a direction normal to the interface and (c) Dispersion curve of

a SP wave; kSP and k are the wavevectors of SP and light wavevectors,

respectively. This shows that the momentum of the SP wave is larger than

that of the light photon in free space for the same frequency (ω).67 . . . . . 72

5.2 Side view of the linear plasmonic photodetector with periodicity d = 1300,

slit width a = 400nm and height h = 100nm. The dielectric medium is a

copolymer PVDF-TrFE polarization of which changes when it absorbs infra-

red radiation. The thickness of the polymer layer is 20nm. . . . . . . . . . . 73

5.3 (a) Real and (b) imaginary values of dielectric permittivity of the copoly-

mer PVDF-TrFE shows that the polymer is anisotropic as these values are

different in parallel and perpendicular directions of the polymer surface.40 . 74

5.4 Snap shot of the total electric field at ω = 20THz. . . . . . . . . . . . . . . 75

5.5 Snap shot of the total electric field at resonant ω = 43.64THz. . . . . . . . 76

5.6 Snap shot of the total electric field at ω = 60THz. . . . . . . . . . . . . . . 77

5.7 (a) Dispersion curves of anti-symmetric mode in metal-dielectric-metal waveg-

uide in the infra-red region and (b) The propagation length of SP wave along

x-direction. A MATLAB program for solving the dispersion equations is

given in Appendix D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.8 The ratio of the z components of electric fields obtained from simulations

with x- and y- polarized incident light demonstrating the detection of x-

polarized light. The peak corresponds to the resonant frequency between SP

and incident light. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

A.1 Reflectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

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A.2 Reflectivity for the tilt angle t = 450 and different polarizer angles α =

00, 300, 600 and 900 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.3 Reflectivity for the tilt angle t = 900 and different polarizer angles α =

00, 300, 600 and 900 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

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List of Tables

4.1 Concentration of different samples studied . . . . . . . . . . . . . . . . . . . 52

4.2 Langmuir film parameters derived from the Π−σ isotherms of three samples

are shown. Two different determinations of the coarea, σ01 and σ01, values

provide the uncertainty in the coarea calculation. The different values of

scaling factor ν show that the slope of the slope of the isotherm in each case is

different. Moreover, the water surface is a good solvent environment in some

experiments as ν values are closer to 3 which is the good solvent condition.

The coarea corresponds to maximum elasticity ϵmax decreases with increasing

temperature showing the isotherm shift towards left for higher temperatures. 57

xvi

Acknowledgements

First of all, I owe my deepest gratitude to my advisor, Dr. Elizabeth Mann. She

accepted me as her student immediately without any hesitation. She always explained

the concepts in very simple words with more patience which helped me to gain knowledge

efficiently and quickly. I learned a lot from her, especially during the preparation of the

thesis and defense presentation. In spite of her busy schedule, she reviewed my thesis and

gave valuable suggestions. I cant say thank you enough for her understanding, guidance

and encouragement.

I am also extremely indebted to my coadvisor, Dr. Qi-Huo Wei for giving me an oppor-

tunity to work on such a new innovative project. I feel motivated and inspired every time

I attend his group meeting.

My special thanks goes to Dr. David Allendar for his careful review and important

comments on my thesis.

I must thank my seniors, Fanindra Bhatta and Pritam Mandal for sharing their knowl-

edge and ideas with me. Particularly, I thank Pritam for his cooperation on scheduling

BAM usage. I extend my sincere thanks to Feng Wang for his support at the last minute

to complete the simulation part.

Thanks must also go to my classmates Prashanth, Piotr, Pengtao and Xinyi for cheering

me up all the time. In particular, I appreciate Piotr’s help to understand pyroelectricity

and its relation with symmetry group. Many thanks are due to Xinyi for listening to me

patiently at the time of practice sessions.

This list would be incomplete, if I do not mention our graduate secretary Loretta for

her constant and valuable support through out my time in KSU. Thank you, Loretta for

all your help!

xvii

Next, I want to thank my parents for all their support, love, blessings and encourage-

ment. I am grateful to my parents for taking good care of my daughter for the past two

years. I thank my sisters, Mano and Nirmal, for being with me all the way. Finally, I would

like to thank my husband, Siva, for his patience throughout.

xviii

Abstract

Poly vinlydene flouride (PVDF) and its random copolymers with trifluoroethylene [P(VDF-

TrFE)] and tetrafluoroethylene [P(VDF-TFE)] have many technological applications due to

their strong ferroelectric, piezoelectric and pyroelectric properties. All of these are related

to the spontaneous polarization property of this ferroelectric copolymer. We are particu-

larly interested in the pyroelectric property that is the change in polarization states due to

the change in temperature.

The pyroelectricity depends strongly on the degree of structural order of the polymer

film. We use the Langmuir-Blodgett technique to make such ordered films by transferring

the polymer monolayer at the water surface onto a solid substrate. The goal of this work is to

determine the transfer condition to maximize the film organization and thus its pyroelectric

response. In the first part of this work, we study the formation and characterization of

PVDF-TrFE(70:30) copolymer by variations in the Langmuir-Blodgett technique. These

films are first made by depositing the P(VDF-TrFE) copolymer in a solution at the air-

water surface. The self-assembly of the copolymer film is controlled by changing the area

of the film by means of two barriers. We apply Brewster Angle Microscopy (BAM) imaging

technique to monitor the Langmuir film formation. In the next step, we transfer this film

onto a solid substrate (for example, Silicon). Finally, the film characterization is done using

Atomic Force Microscopy (AFM).

The Langmuir-Blodgett films of PVDF-TrFE can be used as a dielectric sensitive to

Infra-red radiation in metal-dielectric-metal (MDM) waveguides. A simple metallic grating

nano structure, called a linear plasmonic photodector, is designed. Numerical simulations

of this structure are done for two linear polarization states to show how the photodetector

recognizes different linear polarization states of the incoming light. For this purpose, CST

xix

Microwave studio software which is used to solve Maxwell’s equation numerically.

xx

Chapter 1

Introduction

Recently, the Infrared Polarimetric Imaging technique has been exploited for remote

sensing and military applications1,2 . Typical IR imaging sensors give us information about

the intensity of infrared light reflected or emitted by objects in a scene. But IR polarimetric

imaging sensors measure the polarization states of light coming from all points in a scene.3

The polarization state of light is characterized by the phase and amplitude relationships

between any two perpendicular components of the electric field vectors. For reflected light

these components are conveniently chosen with respect to the incident plane, which is the

plane defined by the direction of incidence and the normal to the surface. Since light is a

transverse electromagnetic wave, the electric fields oscillate perpendicular to the direction

of propagation as shown in Figure [1.1]. If the two electric components have same amplitude

but with 900 phase difference, then it is called circular polarized light. If both amplitude

and phase are different between the two electric field components then it is called elliptically

polarized light.4

The polarization state of reflected light strongly depends on the type of reflecting surface,

i.e., the refractive index of the medium and its surface structure as well as the polarization

of the light that illuminates the surface. For example, man-made objects have very smooth

surfaces which reflect more light than natural objects such as grass, trees and sand. Reflec-

tion from the objects changes the phase and amplitude of the electric field components and

thus the polarization. In fact, if light with its electric field vibrating in the plane of inci-

dence falls on an optically smooth surface at the incident angle called the Brewster angle,

1

2

the reflection is zero. Thus light reflecting off a smooth surface at this angle becomes per-

fectly linearly polarized perpendicular to the incident plane. The reflected light is partially

polarized in a wide range of angles around the Brewster angle.5 Therefore, polarimetry

imaging offers good contrast sufficient to identify different materials in a scene or objects

with different surface structures or at different orientations. Figure[1.2] shows the color

(visible region) image of two trucks in the shade, along with long-wave IR intensity and

polarization images. It can be easily seen from the figure that the polarimetry image has

more contrast than the IR intensity image (Figure 1.2 (b)) which helps us to see the two

trucks in the shade.

Figure 1.1: Types of polarization. (Left)Linear polarization: The two orthogonal electric fieldcomponents have the same magnitude and same phase, (Middle) Circular polarization: The electricfield components are the same magnitude, but 900 out of phase and (Right) Elliptical polarization:The field components differ in both magnitude and phase.4

Ideally, polarimetry completely characterizes the polarization of the light. However,

one rarely measures the electric field, but rather the intensity (in a vacuum, the squared

magnitude of the field), so that the phase information is lost. One means of completely

characterizing the polarization of light through intensity measurements is by the four Stokes

3

parameters:6

S =

S0

S1

S2

S3

=

⟨E2x + E2

y⟩

⟨E2x − E2

y⟩

⟨2ExEycosδ⟩

⟨2ExEysinδ⟩

∝

I0 + I90

I0 − I90

I45 − I135

IL − IR

(1.1)

Here, S0 is the total intensity of the light, S1 is the difference between horizontal and

vertical polarizations, S2 is the difference between linear +450 and −450 polarization, and

S3 is the difference between right and left circular polarization; δ is the phase difference

between the two electric field components. The measurements of the first three parameters

are simple using a simple linear polarizer. But measurement of S3 involves practical dif-

ficulties as the circular polarization is typically measured by using both a linear polarizer

at 450 and a waveplate.7 In 1999, Nordin et al.8 and in 2008 Zhi Wu et al.,9 fabricated

Figure 1.2: (a) Visible picture of two trucks in the shade (b) Long-wave IR intensity image (c)Long-wave IR polarimetric image. The two trucks in the shade is very clear in the Polarimetricimage because of the strong contrast.3

4

a wiregrid micropolarizer array that permits the measurement of the first three Stokes

vector components in each pixel of an imaging polarimeter . The SEM images of the mi-

cropolarizer and the polarization images from these publications are shown in Figure [1.3].

However, these are only sensitive to linear polarization states and thus do not contain com-

plete polarization information. The fourth Stokes parameter which characterizes an object’s

circular polarization should also be detected for improved imaging sensitivity. Monolithic

photodetectors which can distinguish the status of both circularly and linearly polarized

light, though highly desired, do not currently exist. For measuring all the four Stokes pa-

rameters, Professor Qi-Huo Wei from the Liquid Crystal Institute proposed a design he calls

”Plasmonic Metal-Dielectric-Metal (MDM) Photodetectors” that can distinguish intensity

and the status of both linearly and circularly polarized light.

Figure 1.3: SEM images of the wire grid polarizers that allow (a) vertical (b) horizontal and (c)450 linearly polarized light. The polarization images of a static scene is shown at the bottom panel.Images (e), (f) and (g) are S0, S1 and S2 respectively.8 The S0 image is equivalent to typical IRimage. Compared with S0 image, things are more apparent in the S1 image. The image contrastis enhanced in this case. But this depends on the orientation of the surfaces with respect to thepolarizer as shown in the S2 image, the two halves of the building’s roof is clearly visible.

This photodetector uses nanostructures to differentiate between the different polariza-

tion states, with an underlying infrared-sensitive film. P(VDF-TrFE 70:30), a copolymer

of 70% vinylidene fluoride (VDF), and 30% trifluoroethylene (TrFE) is a natural choice for

5

this layer because of its strong pyroelectric properties, which makes it sensitive to IR light.

The structure and the properties of this copolymer are discussed in Section [1.1.2].

Pyroelectricity originates in the change of the net polarization of a sample under an

electric field with an increase in temperature. It depends strongly on the degeree of order

in the polymer.10 The Langmuir-Blodgett (LB) technique allows one to produce thin highly

ordered organic films by first organizing a monomolecular layer at the water surface, as a

so-called Langmuir layer, and then repeated transfer of this layer onto a solid substrate.11

Therefore, the polymer layer for the proposed super pixel is made by using the LB technique.

The first step of LB deposition method is the formation of a well-defined monolayer at

the air-water interface. To form a good Langmuir monolayer, the layer molecules should

be amphiphilic, i.e., possess both hydrophilic and hydrophobic groups, and be insoluble in

water. The experimental details are given in section [3.3] titled How to make a Langmuir

film. The LB technique is one of the most promising techniques for preparing this organic

thin film as it enables (i) the precise control of the monolayer thickness, (ii) homogeneous

deposition of the monolayer over large areas, (iii) multilayer structures with varying layer

composition and (iv) deposition on almost any kind of solid substrate.12

PVDF and its copolymers are not good amphiphiles and hence, it can be difficult for

them to form well-organized monolayers.13 In that case, a complete monolayer characteri-

zation is required in order to optimize conditions for making LB films of PVDF-TrFE. This

optimization is the focus of this thesis.

In this chapter, we present an overview of the ferroelectric properties of ferroelectric

polymers and copolymers. Also, the phase transition behaviour and the electrical properties

of these polymers are discussed briefly. Then, we introduce about Langmuir films along with

the Langmuir-Blodgett and Langmuir-Schaefer techniques used for transferring thin films

onto a solid surface.

6

1.1 Ferroelectrics and their properties

In 1921, Valasek observed dielectric hysteresis in sodium potasium tartrate tetrahydrate,

usually called Rochelle salt, which was analogous to the magnetic hysteresis in the case of

iron.14 Ferroelectricity owes its name because of this analogy with ferromagnetism. Ba-

sically, ferroelectric is defined as a material with a spontaneous electric polarization that

can be reversed by an applied electric field. The general properties of ferroelectric mate-

rials include crystal symmetry, spontaneous polarization, ferroelectric domains, dielectric

hysteresis loop and a phase transition at the Curie point. We summarize these properties

in the following sections.

It is well-known that crystals are classified into 32 classes based on their symmetry with

respect to a point. Among these 32 classes, eleven are centrosymmetric and the remaining

21 are non-centrosymmetric. Crystals which have a center of symmetry are non-polar and

behave like normal dielectric materials. Twenty out of the 21 non-centrosymmetric crystals

show the piezoelectric effect. These crystals develop electrical polarity when subject to

stress. They show the converse effect as well, i.e., an external electric field changes the length

of the dipole moments resulting in structural deformation. Ten out of these 20 piezoelectric

crystals have a unique polar axis whereby the whole crystal is polarized. The spontaneous

polarization in these polar crystals depends on temperature. Thus if the temperature of the

crystal is changed, a change in polarization occurs. This is called the pyroelectric effect.

Therefore, the ten polar classes are also called pyroelectric crystals.

Hence, it is clear that all pyroelectrics are piezoelectrics but the reverse is not true.

For example, quartz crystal is a piezoelectric material but not pyroelectric. In addition,

all ferroelectrics are piezoelectric and pyroelectric, but not vice versa. Although they have

spontaneous polarization like ferroelectrics, the polarization can not be reversed in all pyro-

electric and piezoelectric materials by applying electric field. The relationship between the

piezoelectric, pyroelectric and ferroelectric materials is shown graphically in Figure [1.4].

7

Figure 1.4: (a)Classification of crystals based on their crystallographic symmetry15 (b)The relationbetween piezoelectric, pyroelectric and ferroelectric materials.16

Usually, the ferroelectric materials acquire domains in which the dipoles are all aligned

in one particular direction. There are many domains in a single ferroelectric crystal sep-

arated by domain walls. The direction of the polarization vector is different in different

domains. These domains are visible under polarized light. Polarization reversal, the main

characteristic of any ferroelectric crystal can be seen in the hysteresis loop. This loop can be

obtained by plotting the change in polarization P with respect to the applied field E. Let us

say that the polarization vectors in the domains are randomly oriented before the applica-

tion of an electric field. In other words, the vector sum of dipole moments of the individual

domains vanishes and hence the net polarization is zero in the crystal initially. When the

electric field is increased in the positive direction, the domains start aligning parallel to the

field which increases the polarization. This is given by the curve OA in the hysteresis loop

(Figure 1.5). If the electric field is increased further, the domain walls disappears at B and

the crystal has only one domain. This means that all the dipole moments are now parallel

8

to the E. Now, if we decrease the electric field through CBD, the polarization decreases

but does not go to zero when E is completely removed. Instead it takes the value D which

is called the remanent polarization Pr. In the case of a completely polarized crystal, Ps is

the spontaneous polarization obtained by extrapolating the curve BC onto the polarization

axis.The negative electric field required to make this polarization zero is called the coercive

field Ec which is represented by F in the Figure. A further increase in electric field in the

negative direction results in polarization reversal at the point G in Figure [1.5].

Most ferroelectrics have a transition temperature called the Curie temperature Tc above

which they act like a non-polar, normal dielectric (or paraelectric) material. As said before,

the spontaneous polarization Ps is temperature dependent. It decreases as temperature

increases and disappears at Tc.. The ferroelectric phase transition is a structural phase

transition.

Figure 1.5: Typical Dielectric hysteresis loop of a Ferroelectric crystal. Here Pr is the remanentpolarization, Ps is the spontaneous polarization and Ec is the coercive electric filed required for zeropolarization.17

In summary, ferroelectric materials have the following properties:18,19

9

• They lack centrosymmetry and hence belong to one of the 10 polar class crystals.

• They exhibit spontaneous polarization which makes one side of the crystal positive

and the opposite side negative.

• The spontaneous polarization decreases with increase in temperature and vanishes at

the Curie Temperature.

• They possess a dielectric hysteresis loop which shows that the polarization is reversible

by the application of external electric field.

• The hysteresis will disappear at the Curie Temperature.

• They have domain structure, which can be visible in polarized light.

1.1.1 Ferroelectric polymers

In the 1970s, ferroelectric properties were found in liquid crystals and in polymers.20 The

most familiar ferroelectric polymer, poly(vinlydine fluoride) (PVDF), was first known for

its large dielectric constant. But it was experimentally proved that PVDF is a ferroelectric

polymer by Furukawa, Date and Fukada in 1980 and Furukawa and Johnson in 1981.

1.1.2 Structure of PVDF in 3d

The structure of one monomer unit of PVDF is -(CH2-CF2)- with a dipole moment

pointing from negative fluorine to positive hydrogen atoms. These dipoles are strongly

attached to the main-chain carbons; thus the orientation depends on the conformation

and packing of molecules. The two most common conformations are (i) all-trans TTTT

conformation and (ii) alternate trans-gauche TGTG conformations. When compact the

chains pack into different crystalline structure, one of the most common structure for the

all trans conformation is called the β phase. The lattice constants are a = 0.858nm, b =

0.491nm, and c = 0.256nm. The dipoles in all-trans conformation lie in a zig-zag plane; they

10

are perpendicular to the chain axis. Since the size of the fluorine atom (0.270nm) is slightly

greater than the distance between the two carbon atoms along the c-axis, overlapping of

two the fluorine atoms occurs. To avoid this overlapping, the CF2 groups are deflected

to right and left of the zig-zag plane in the all-trans phase.20 In the other major crystal

structure (α phase) the chain has alternate trans/gauche bonds and no net dipole moment.

The molecular conformation of β phase is shown in Figure [1.6].

From the previous section, we know that a crystal structure should be polar for it to

be ferroelectric. But it is mainly the instability of this polar structure which leads to

polarization reversal and the phase transition from ferroelectric to paraelectric. Only the α

phase is non-polar: it is paraelectric. The other phases are polar structures. However, the

β phase has spontaneous polarization double than that of other phases, because the dipoles

are oriented in one direction. Using an external electric field this polarization was shown

to be switchable and hence, the β phase is ferroelectric.

Figure 1.6: Structure of PVDF; (a) Structure of the all-trans conformation, called β phase, showingthe planer carbon backbone with attached fluorine and hydrogen atoms; The arrow shows thedirection of dipole moment when viewed along the chain axis. Drawn using Chem3D software.

The Curie temperature of PVDF is higher than its melting point. Therefore, the fer-

roelectric properties are mainly studied in its copoymer called Poly(vinylidene fluoride-

trifluoroethylene),PVDF-TrFE. In 1980, PVDF-TrFE copolymer was synthesized by Yagi

et al. with different compositions of PVDF and TrFE. In this PVDF-TrFE copolymer, VDF

and TrFE units are randomly distributed and so that it is called a random copolymer. The

11

hydrogen atoms of PVDF are replaced by bigger fluorine atoms; again, fluorine-fluorine

overlapping happens, in the α phase. Because of this the PVDF-TrFE copolymer takes

the β phase. The structure and properties of this copolymer is discussed in the following

section.

In general, ferroelectric materials undergo two types of transitions (called the displacive

transition and the order-disorder transition) based on whether the transition is due to the

displacement of ions or the ordering of permanent dipoles. The phase transition in the

PVDF-TrFE copolymer is a first order, order-disorder transition with a structural transfor-

mation from all-trans chains to a mixtures of trans-gauche bonds.

1.1.3 Structure of PVDF-TrFE

The chemical formula of PVDF-TrFE is ((CF2CH2)x(CF2CHF)1x)n. The VDF and TrFE

units are randomly distributed along the molecular chain to form a random copolymer

(Figure [1.7]). The copolymers of PVDF like PVDF-TrFE and PVDF-TeFE have great

advantages over VDF homopolymer for the following reasons:

• Introduction of a small amount of TrFE or TeFE into PVDF induces direct crys-

tallization of β phase from the melt. Therefore, ferroelectric films can be directly

produced from the melt. But PVDF takes many polymorphic structures which needs

to be treated electrically or thermally to yield the β phase.

• PVDF-TrFe shows higher crystallinity (∼ 90%) whereas the crystallinity of PVDF is

only 50%.21

• The dielectric hysteresis loops of PVDF-TrFE copolymer are sharper than those for

various crystalline phases of the PVDF homopolymer. This means, that only a small

amount of field is required for polarization reversal. The reason for this difference

12

is that in the copolymer, the addition of trifluoroethylene expands the crystal struc-

ture and hence reduces the steric hindrance to chain rotations. Therefore, dipole

reorientation occurs at lower fields.

• PVDF does not have a Curie point below its melting temperature, which is estimated

as 195−197C,22 which is less than its hypothetical Curie point. This means that the

melting of the ferroelectric phase of PVDF and the ferroelectric to paraelectric tran-

sition happens in the same temperature range. In the case of copolymers with TrFE

or TeFE with 50 − 80% VDF, the temperature of the phase transition is lower than

in PVDF..23 This is due to the fact that the unit cell of copolymer is larger than that

of PVDF polymer because fluorine atoms are bigger than hydrogen atoms. Because

of this PVDF-TrFe copolymer is less stable than the pure PVDF. This instability is

responsible for the ferroelectric to paraelectric transition on heating at lower Curie

temperature. A. V. Bune et al.24 found that the surface ferroelectric transition at

200C is distinct from the bulk ferroelectric to paraelectric phase transition at about

800C.24,25

At the same time, the spontaneous polarization of PVDF will be reduced when it forms

PVDF-TrFE copolymer. Because some hydrogen atoms are replaced by fluorine atoms that

reduces the dipole moment. The pyroelectricity of the copolymer depends on many factors

like temperature, crystallinity, thickness, impurities and composition.

Therefore, structurally-ordered polar thin films are required to achieve maximum pyro-

electricity. The Langmuir-Blodgett technique can be used to prepare such films with high

degree of order perpendicular to the plane.26 In plane-order can be introduced by compress

the film on water before transfer. All these considerations refer to bulk structure. A Lang-

muir film is, ideally, a single quasi-2d layer. The appropriate symmetry groups are the 2d

ones. However, the asymmetry of the surface introduced a preferred dipole direction if, for

13

example, the fluorine groups are preferentially directed towards the water. In the following

sections, we explain about the LB technique in more detail.

Figure 1.7: Ball and stick model of all-trans β conformation PVDF-TrFE (70:30). 30% of theVDF units have been replaced randomly by TrFE units. The arrow shows the net dipole momentfluorine to hydrogen.27

1.2 Langmuir Films

A Langmuir film is defined as a molecularly thin layer trapped at the gas-fluid inter-

face.28 Generally, it is air-water interface and the molecules that make a Langmuir film

are amphiphilic. A amphiphile molecule consists of two parts, a hydrophilic (water-loving)

head-group and a hydrophobic (water-fearing) hydrocarbon chain. Therefore, at the air-

water interface the head groups are immersed in the water surface and the tail groups point

away from water.

1.2.1 The Pressure - Area Isotherm

In a typical experiment , the sample of interest is dissolved in a volatile solvent and

drops of this solution are spread on water. The solvent evaporates and leaves a monolayer of

molecules on the water surface. More details of how to make monolayers are given in Chapter

3. The amount of sample to be spread should be calculated to make a monomolecular layer.

At this stage, the monolayer is in a gas phase as the molecules are far apart and there is

no interaction between them. Hence, the surface pressure is low. While the monolayer is

compressed by a movable barrier, the surface pressure and the area per molecule is recorded.

14

Figure 1.8: (A)Typical isotherm of a Langmuir monolayer. When compressing the dilute gas, thearea per molecule decreases and the monolayer undergoes several phase transitions from Gas (G) toliquid-disordered (LD) to liquid-ordered (LO) and finally to solid phase (S) in which the moleculesare closely packed. The isotherm is taken from the book Interfacial Science: An Introduction29 andmodified.

The surface pressure Π = γ0 − γ is defined as the difference between the surface tension of

pure water (γ0) and that of surface with the monolayer (γ). We already know the number

of molecules spread on the surface and the total area of the monolayer. Therefore, we can

calculate the area per molecule and plot Π as a function of area per molecule. The whole

experiment is done at constant temperature and hence, the Π−A plot is called as isotherm.

The Π−A isotherm is very important because it has information about the stability of the

monolayer at the air-water interface, and about phase transitions.

A typical surface pressure - area isotherm is shown in Figure [1.8]. If the monolayer is

further compressed, it changes from gaseous phase to liquid phase. There are two liquid

phases called liquid disordered and liquid ordered phases. In the liquid disordered phase

the chains are disordered whereas in liquid ordered phases the chains are fully extended

and uniformly oriented. Now a small reduction in area leads to phase transition from liquid

condensed to solid phase. This phase is characterized by steep linear isotherm at low area

per molecule. In the solid phase all the molecules are closely packed. Further compression

of the monolayer leads to monolayer collapse because the molecules are forced out of the

15

surface and form multilayers.

1.3 Langmuir-Blodgett films

The transfer of Langmuir films from the air-water interface to a solid substrate is known

as Langmuir-Blodgett-style deposition.30,31 The deposition process depends on the hy-

drophilicity or hydrophobicity of the solid substrate. For example, if the solid substrate is

hydrophilic, then the monolayer is transferred by an upward movement through the water

and the Langmuir layer, and if it is hydrophobic the transfer is done by downward movement

through the layer. Usually, the substrate is placed in the subphase before the monolayer is

spread. The transfer of monolayer onto a solid substrate can be done in two methods called

the Langmuir-Blodgett (LB) and Langmuir-Schaefer (LS) methods. In the LB method,

Figure 1.9: Techniques for depositing a monolayer on a solid substrate (a) Langmuir-Blodgettmethod - Vertical deposition on a hydrophilic substrate (b) Langmuir-Schaefer method - Horizontaldeposition (Modified from KSV website: http : //www.ksvnima.com/langmuir−and− langmuir−blodgett− troughs)

the solid substrate moves vertically while transferring the monolayer from the air-water

interface. There are many reports related to the arrangement of molecules on the solid

substrate after deposition.31 In some instances, such as highly viscous monolayers, the clas-

sic vertical deposition does not yield favorable results and alternate methods are required.

16

Langmuir and Schaefer found that for highly viscous monolayers a horizontal depostion

process was suitable.32 In the LS method, the solid substrate is placed horizontally on the

monolayer film and then lifted up. This method is mainly useful for the deposition of very

rigid films, for example, monolayers of protein and polymers.31,32 The floating monolayer

will be less disturbed in LS technique than in the LB method.11 In the present work, we

use the Langmuir-Schaefer method, as explained in Chapter 3, for monolayer transfer.

1.4 Pyroelectricity of PVDF-TrFE

In the present work, we are most interested in the pyroelectricity of the copolymer

PVDF-TrFE, with the goal of using Langmuir-Blodgett films of this polymer for infra-red

photodetectors. Therefore, in this section we discuss the pyroelectric effect of the copolymer.

As said before, a material is pyroelectric if each unit cell has an electric dipole. These

dipoles are produced because the center of the positive and that of negative charges do not

coincide. If these electric dipoles orient in such a way that they do not cancel each other,

then the material has spontaneous polarization. When there is a change in temperature of

the material, there will be a change in the atomic positions or interatomic bonding which

affects the spontaneous polarization. This change in spontaneous polarization due to a

change in temperature is called the pyroelectric effect.

The spontaneous polarization can be written in the form,

Ps =1

V

∫µdV (1.2)

where µ is the dipole moment per unit volume. From this equation, it is clear that for Ps

to be non-zero, the dipole moment should be non-zero. In order to satisfy this criteria, the

crystal should have a non-centrosymmetric unit cell and should show no axis of rotational

symmetry. As discussed in Section[1.1], only 10 out of 32 crystal classes obey the symmetry

requirements of pyroelectricity.

The derivative of spontaneous polarization with respect to temperature at constant

17

stress and electric field gives the pyroelectric coefficient:

p =

(∂Ps

∂T

)E

(1.3)

The following physical properties of pyroelectric materials are required for a good IR

detector:33

1. Large Pyroelectric Coefficient (p): Since the detector response is directly proportional

to the pyroelectric coefficient, large p values are required.

2. High Curie Temperature (Tc): The pyroelectric detector is used below Tc, because

they have large p value below that temperature. Tc of the detector is preferred to be

much over room temperature because p is not constant around room temperature.

3. Small Dielectric constant (ϵ): Small dielectric constant corresponds to small electric

capacity of the detector. Therefore, the voltage across the detector, i.e., the pyroelec-

tric response will be better for small dielectric value.

4. Small Heat capacity (Cs): Small heat capacity is required for maximum pyroelectric

response so that a small amount of IR absorption is sufficient to change the temper-

ature of the detector. The heat capacity can be reduced by using a thinner film since

it is an extensive property of the system.

These properties are satisfied by PVDF-TrFE copolymer and hence it is a very good

material for IR detection. The pyroelectric coefficient of the PVDF-TrFE copolymer is

significantly larger than that of the PVDF homopolymer. For example, the pyroelectric

coefficient for PVDF (β phase) is 1.8 × 10−9C/cm2K but for the copolymer with ratio

65:35, it is 2.9 × 10−9C/cm2K. The benefit of using pyroelectric polymers are: Very thin

films can be easily fabricated, their cost is low and they are flexible to conform to a curved

surface.

18

In 1995, crystalline films of ferroelectric P(VDFTrFE) copolymers were formed by the

LangmuirBlodgett method.34,35 These films possess ferroelectric properties close to those

of bulky films, including switching and a first-order ferroelectric phase transition. In the

best studied copolymers, the VDF:TrFE ratio is about 70:30. The pyroelectric properties of

Langmuir-Blodgett films of PVDF-TrFE(70:30) were studied by A. V. Bune et al. in 1999.36

Figure [1.10(a)] shows the typical temperature profile and the corresponding pyroelectric

current. The pyroelectric current vanishes at temperature greater than Tc which shows

the ferroelectric behaviour of the copolymer LB film (Figure [1.10(b)]). The hysteresis

behaviour of the pyroelectric and piezoelectric responses show a low polarizing voltage. In

this way, LB ferroelectric films are more advantageous than the traditional films.

Figure 1.10: (a) Temperature cycle and the corresponding pyroelctric current. A negative currentflows through the circuit when the temperature increases and when the temperature decreases, thepyroelectric current is positive. (b) Plot of pyroelectric current vs temperature shows the maximumpyroelectric current near the Curie temperature. (c) Hysteresis of the effective piezoelectric coeffi-cient and the pyroelectric current as the applied dc electric field was cycled at room temperature.36

19

In this thesis I will focus on optimizing the order within a single LS film of the P(VDF-

TrFE) copolymer, inspired by the earlier work. We will characterize the originating Lang-

muir films at the air/water interface through Brewster angle microscopy (discussed in chap-

ter 2) and surface pressure isotherms (discussed in chapter 3) as a function of deposition

conditions and temperature. The results will be discussed in chapter 4. Next, we will

optimize the dimensions of the metal-dielectric-metal photodetector using a commercial

software called Computer Simulation Technology (CST) for identifying the linear polariza-

tion state of the incoming light. The details of the simulation and the results are discussed

in chapter 5. In the end, concluding remarks and recommendations for future work are

given in Chapter 6.

Chapter 2

The Brewster Angle Microscopy and other experimental methods for

Langmuir films

Brewster angle microscopy uses the special condition of the light reflecting off a surface

at the Brewster angle to image films as thin as 0.5 nm thick. This chapter starts with

the overall concept of light propagation through different interfaces between two or three

homogeneous media. Then it discusses about the basic theory behind Brewster Angle

Microscope (BAM), along with the conditions necessary for good sensitivity of our films.

Also, we give details of the Wilhelmy plate method which is used to measure the surface

pressure of Langmuir films.

2.1 Interaction of Light with Air-Water interface

In general, when light travels from one medium to another medium, reflection and

refraction occur at the interface between the two media.5,37 Consider a light wave with

electric field Ei incident on the surface at angle θi. It will be partially reflected from the

surface and partially transmitted through the medium as shown in Figure [2.1]. Now, there

are two main equations that relate the angle of incidence θi to the angle of reflection θr and

the angle of refraction θt. The first one is called the law of reflection which can be written

as

θi = θr (2.1)

The second law, called law of refraction or Snell’s law, can be given as

n1sinθi = n2sinθt (2.2)

20

21

where n1 and n2 are refractive indices of the two isotropic media. From this law, it is clear

that when n1 is less than n2, i.e., when light travels from low refractive index medium to

high refractive index medium, θi > θt and therefore the transmitted light is closer to the

normal and vice-versa.

Conventionally, the direction of the electric field vector is taken as the direction of

polarization. The plane in which the electric field vector lies is called plane of polarization.

In Figure [2.1], the electric fields of reflected and transmitted light waves are represented

as Er and Et and their direction of propagation is given by propagation vectors, kr and

kt respectively. It can be noted that the propagation vectors of incident, reflected and

transmitted light waves are all in the same plane called the plane of incidence. Depending

on the direction of the electric field vector of the incident light, there are two types of

polarization (1) p- polarization if the electric field is in the plane of incidence and (2) s-

polarization if the electric field is perpendicular to the plane of incidence.

Figure 2.1: Reflection and transmission at the interface between two media. (a) In s-polarization,the electric field is perpendicular to the plane of incidence and (b)in p-polarization, the electric fieldis parallel to the plane of incidence5

According to the Fresnel equations, the amplitude of the reflection coefficient (which is

the ratio of the tangential component of the reflected wave electric field and that of incident

22

wave electric field) for p-polarization can be written as,5

rp =n2cosθi − n1cosθtn1cosθt + n2cosθi

. (2.3)

Similarly for s-polarization, the reflection coefficient will be,

rs =n1cosθi − n2cosθtn1cosθi + n2cosθt

(2.4)

Then, the total reflectivity can be calculated as

Rp = |rp|2 and Rs = |rs|2 (2.5)

for p- and s- polarized incident light wave respectively.

The total reflectivity Rp and Rs for light incident on an air-water interface has been

plotted using equation (2.5) with n1 = 1 for air and n2 = 1.333 for water. It can be

seen from the Figure [2.2] that the total reflectivity Rp is equal to zero when the incident

angle θi = 53.1230. This angle of incidence is called Brewster’s angle. This means that

when unpolarized light falls on an interface at the Brewster angle, then the light wave with

electric field perpendicular to the plane of incidence (rs) will only be reflected and hence

the light becomes polarized. The Brewster angle can also be derived from equation (2.3) as

follows:

rp =n2cosθi − n1cosθtn1cosθt + n2cosθi

= 0 (2.6)

If θi + θt = 900, then the above equation will become,

1− n1n2tanθi = 0 (2.7)

and

θB = θi = tan−1

(n2n1

)(2.8)

Therefore, the Brewster angle can be determined if we know the refractive indices of the two

media which makes the interface. In the next section, we will derive the total reflectivity

for light travelling through two interfaces.

23

Figure 2.2: The total reflectivity Rp goes to zero at Brewster Angle

2.2 Interaction of Light with Air-Thin film-Water interfaces

I will want to form polymer films only a monomer thick. In principle, we should consider

reflectivity at the molecular scale. However, for reasonably smooth films, it has been found

that the resulting reflectivity is very close to that of a uniform thin film.38 Therefore we will

approximate our films as uniform thin films for the purposes of estimating the reflectivity

and contrast we can expect with the Brewster angle microscope. The reflectivity from

a uniform thin film has been treated in several standard references; here we follow the

treatment of reference.5,39 Consider a thin film of thickness d on a substrate. This system

actually forms two interfaces:(i)the boundary between the air and the thin film and (ii) the

boundary between the thin film and the substrate. Let us say that the refractive indices of

air, thin film and the substrate are n1, n2 and n3 in that order. Now, if an incident light hits

the thin film at angle θ1, as explained in the previous section, it will be partially reflected

and partially transmitted at the air-thin film interface. The transmitted light reaches the

substrate and at the line between thin film and the substrate, it will be again reflected

24

back to the surface of the thin film and transmitted if the substrate is not opaque. In this

way, multiple reflections occur at the surface of the thin film as shown in the Figure [2.3].

Clearly, we can see that the second reflected wave travels more distance A-B-C than the

Figure 2.3: Reflection and transmission of light when there are two or more interfaces

first reflected wave. The difference in optical path length Λ between the first and the second

reflected rays can be written as,

Λ = n2(AB +BC

)− n1

(AD

)(2.9)

Then, from the traingle ABC we can write,

AB = BC =d

cosθ2(2.10)

and

AC = 2dtanθ2 (2.11)

where θ2 is the angle of refraction. Now, the distance travelled by first ray AD can be

calculated from the traingle ADC as,

AD = ACsinθ1 (2.12)

25

Next substituting equation (2.10) and (2.12) in equation (2.9) and along with Snell’s Law

(2.2), the optical path length difference can be derived in terms of known quantities as given

below:

Λ =2n2d

cosθ2− 2n2dsinθ2tanθ2 = 2n2dcosθ2 (2.13)

Consequently, the difference in phase angles, called the phase difference δ, between the first

and second reflected waves will become

δ = kΛ (2.14)

Here, k is the magnitude of the propagation vector which is equal to 2πλ . λ is the wavelength

of the incident light wave. On the whole, if the light falls on a multi-layered system, the

total reflection can be written as,

rsum = r12 + t12r13t12e−iδ + t12r23r21r23t21e

−2iδ + . . . (2.15)

where r and t are the reflection and transmission coefficients. The representation r12 means

that the light travels across the interface between medium 1 and medium 2 and r21 represents

that the light travels across the same interface but this time from the medium 2 to medium

1. In the same way, the transmission coefficients are also represented . On simplifying the

above equation we will get the amplitude of total reflection as

rsum = r12 +t12r23t21e

−iδ

1− r21r23e−iδ(2.16)

However, we know that r12 = −r21 from Fresnel equations which means that the light travels

in the same direction either way from the low dense medium to high or from high dense

medium to low. Therefore, using the other properties of Fresnel equations, like, r + t = 1

and t12t21 = 1− r212 , the above equation will become

rsum =r12 + r23e

−iδ

1 + r12r23e−iδ(2.17)

26

Consequently, the total reflectivity can be written as

R = |rsum|2 = | r12 + r23e−iδ

1 + r12r23e−iδ|2 = r212 + r223 + 2r12r23cosδ

1 + r212r223 + 2r12r23cosδ

(2.18)

Let us consider a thin film of the copolymer PVDF-TrFE at the air-water interface. The

refractive indices are: n1 = 1.000, n2 = 1.420 and n1 = 1.333 for air, PVDF-TrFE and

water respectively.40 Using Equation[2.18], the total reflectivity R can then be plotted for

s-polarization and p-polarization for different values of thickness d. They are shown in

Figures [2.4] and [2.5]. we assumed that the air-water interface is an ideal Fresnel interface.

But practically, the reflectance of the water surface is not zero because of surface roughness.

As can be seen from Figure [2.4], Rs increases with increasing angle of incidence. Also, it is

Figure 2.4: s-polarization reflectivity curves for a flim of the copolymer PVDF-TrFE at the air-water interface for different values of thickness. The refractive indices are: n1 = 1.000, n2 = 1.420and n1 = 1.333 for air, PVDF-TrFE and water respectively. There is no significant variation ofreflectivity with changes in the film thickness.

hard to differentiate between different thickness values. The p-polarization reflectivity, Rp

(Figure[2.5]) is sensitive to the film thickness near the Brewster angle (θB ∼ 53.120). The

reflectivity is large away from the Brewster angle. Therefore, the imaging of a monolayer

should be done close to Brewster angle with p-polarization since at this angle there exists a

27

good contrast between the films of different thickness. For example, the difference between

the p-reflectivities of water surface(0nm) and 0.45nm film is large near the Brewster angle.

Therefore, collimation of the incident beam is very important. From the zoomed out bottom

panel of Figure [2.5], we say that the collimation of laser beam should be within 0.0150.

Moreover, Figure[2.5] shows the values of p-reflectivity is very small (∼ 10−8). Therefore,

intense incident light and a high sensitive camera is required for imaging the small reflection

from the thin film.

Figure 2.5: p-polarization reflectivity curves for a flim of the copolymer PVDF-TrFE at the air-water interface for different values of thickness. The refractive indices are n1 = 1.000, n2 = 1.420and n1 = 1.333 for air, PVDF-TrFE and water respectively. The reflectivity goes to zero at theBrewster angle when there is no film on the water surface, which corresponds to 0nm curve (Black).The blue bordered box is zoomed out and shown in the bottom panel to show the difference inreflectivity between a 0.45nm (Red) film of PVDF-TrFE and a clean water surface (Black).

2.3 The Brewster Angle Microscope

The Brewster Angle Microscope (BAM) is based on the following principle: When p-

polarized light falls on a perfectly flat abrupt Fresnel interface, the intensity of the reflected

light goes to zero at a certain angle of incidence called the Brewster angle. Physically, it

means that the induced dipole moments in the medium oscillate in a direction parallel to

28

the propagation vector of the reflected light wave and hence, there is no dipole radiation

along this direction. The air/water interface is typically the best possible approximation to

a Fresnel interface and sets the dark background of the image. In practice, water surface

is not a perfect Fresnel interface, because it has a natural roughness of about 0.3nm due

to thermal fluctuations. So, the reflectivity is slightly greater than zero at the Brewster

angle. This gives a small brightness in the background image. Now, when we have a

monolayer with a refractive index different from that of water, it acts like a third optical

medium. Reflection occurs at the two interfaces and the total reflectivity can be calculated

as explained in the beginning of this chapter. Therefore, the change in the refractive index

of the system and the corresponding change in the reflectivity leads to high contrast images

that help us to visualize the monolayer on the water surface.

BAM consists of, on one side, a laser light source (λ = 488nm), a collimator, a polarizer

for illuminating the sample with a p-polarized light and on the other side, a converging

lens with a CCD camera on the imaging plane for the detection of reflected light. In order

to study the anisotropy of the monolayer film, an analyzer should be added at the detec-

tion side. The optical components associated with each side are attached to goniometers

equipped with adjustable mounts which can be used to set the incident and detection angles

close to the Brewster angle. Additionally, the set-up can be moved in all the three directions

easily using a translational x-y-z stage.

The monolayer formation is imaged by a CCD camera at the rate of 30 frames per

second. Then the images are extracted from the video file using Ulead VideoStudio 6.0

software. To facilitate high quality of imaging, the whole system is placed on a isolation

vibration table to minimize any mechanical vibrations. This is important not only for the

BAM imaging; the surface pressure measurement (discussed at the end of this chapter), is

also sensitive to mechanical vibrations.

29

Figure 2.6: A photograph of the Brewster angle microscopy set up in our lab.

2.4 Surface Tension and Free energy

Consider a film formed in a system with a movable barrier of length L. Now, the film

experiences some inward force on all the boundaries as shown in the Figure [7(a) (a)]. Let

us say that the barrier is moved by a small distance dx by an external force F . Then, if we

define the surface tension γ as the force acting perpendicular to the boundary of the frame

per unit length, then the work done to expand the film will be41

dW = −Fdx = −γLdx (2.19)

Here, Ldx is the change in area of the film dA. Hence, the work done on the system will

now become,

dW = −γdA (2.20)

This equation implies that the surface tension has dimensions of force per unit length,

Nm−1.

2.4.1 Liquid-liquid interface

Suppose two homogeneous surfaces, pure water surface denoted by α and a thin film on

water surface denoted by β, are divided by a movable barrier as seen in the Figure [7(a)(b)].

30

(a) (b)

Figure 2.7: (a)Π − σ isotherms of low concentration sample at different temperatures. Isothermsshift towards left as the temperature increases. (b)Gibbs free energy calculated from the isothermsis plotted against temperature for different surface pressures.

For this system, the total change in the Gibbs free energy can be written as,42,28

dG = dGα + dGβ + dGs (2.21)

where dGs is the change corresponding to interface region. If the barrier is moved by an

area dA at constant pressure, then the above equation can be rewritten as

dG = −SαdT − SβdT + γ0dA0 + γdA (2.22)

Since dA0 = −dA, we can write,

dG = − (Sα + Sβ) dT + (γ0 − γ) dA = − (Sα + Sβ) dT + πdA (2.23)

As we see in the above equation, the surface pressure is defined as the difference between

two surface tensions,

π = γ0 − γ (2.24)

Therefore, for constant temperature, equation can be written as

Π =

(∂G

∂A

)T

(2.25)

In this way, surface tension can also be considered as change in free energy per unit area.

31

Figure 2.8: A liquid drop on solid surface

2.4.2 Solid-liquid interface

In practice, the surface tension of a gas/liquid interface is determined by exploiting the

solid/liquid/gas interface. In our experiment this is done via the Wilhelmy plate, discussed

in this section. Like the liquid-liquid interface, the solid-liquid interface will also have its

surface free energy. If a liquid drop is placed on a solid surface, it would change its shape

to attain minimum surface free energy. As we can see from the Figure [2.8], there are

three interfaces in this system (a) solid-vapour interface, (b) solid-liquid interface and (c)

liquid-vapour interface. We can also observe that the liquid-vapour interface makes an

angle θ with the solid surface. This angle is called the contact angle, the characteristic

of a particular solid-liquid-vapour system. If we consider the small changes in areas as

dALV , dASL and dASV of the vapour-liquid interface corresponding to the solid-liquid and

solid-vapour regions respectively, then the change in Gibbs free energy can be written as,

dG = γLV dALV + γSLdASL + γSV dASV (2.26)

32

Also, we can write dASL = −dASV and therefore,

dG = γLV dALV + (γSL − γSV ) dASL (2.27)

At equilibrium, the relation between the surface tensions can be written by minimizing the

above equation as43

γSV = γSL + γLV cos θ (2.28)

Here, we assume that dALV = dASL. This equation, called Young’s equation, shows that

the contact angle of a particular system depends on the surface tensions between different

phases present in the system. At this point, we can think of three cases as explained below:

When θ > 900, the surface tension at solid-liquid interface is equal to the sum of the

surface tensions of the separate liquid-vapour and solid-vapour systems. Hence, we

can write γLS ≈ γLV + γSV and the liquid drop takes spherical shape at equilibrium.

The degree of wetting is very less.

If θ = 900, then γSL = γSV which means that the liquid molecules behave as if they

are in bulk phase. In this case, the shape of the liquid drop will be a hemisphere.

And if θ < 900 and if γLV < γSV then the solid-liquid interaction will be large to

minimize the free energy which leads to high degree of wetting. For θ = 0, the liquid

drop perfectly wets the solid surface.

2.4.3 Surface pressure Measurement - Wilhelmy Plate Method

In this method, the surface pressure is measured by measuring the change in the force

acting on a thin platinum plate because of the change in surface tension. Typically the

plate it is suspended in such a way that one third of it is below the liquid surface. The

various forces involved in this system are: (i) the downward gravitational force due to the

weight of the plate, FG, (ii) the buoyancy force acting upward due to capillary rise FBand

33

Figure 2.9: Forces acting on Wilhelmy plate

(iii) the surface tensions at different interfaces denoted as γSL, γSV and γLV (Figure [2.9]).

Therefore, the total force will be

F = FG − FB + 2 (t+ w) (γSL + γLV cos θ − γSV ) (2.29)

where t is the thickness and w is the width of the Wilhelmy plate. The contact angle θ must

be zero for complete wetting which is critical in this experiment because if cos θ < 1, then

the measured surface tension is less and the corresponding surface pressure will be larger

than the actual value. Now, if we represent the density of the plate and the density of the

liquid as ρp and ρl respectively, then the total force in equation for complete wetting can

be rewritten as

F = ρpglwt+ 2 (t+ w) γLV − ρlgtwh (2.30)

Therefore, the change in surface tension which is called as surface pressure will be

Π = −∆γ =∆F

2 (t+ w)(2.31)

In other words, the gravity and the buoyancy terms are independent of surface area changes

and they are ruled out. So the surface pressure depends only on changes in surface tensions

34

normal to the perimeter of the plate. The plate used in our lab has dimentions:(t + w) =

19.62mm. For t << w, the surface pressure is calculated as,

Π = −∆F

2w(2.32)

The change in force is measured by the electro-balance to which the platinum plate is

attached.

In this chapter we have discussed about the theory of BAM and surface pressure measure-

ments. Next, we will present the experimental methods of making Langmuir and Langmuir-

Schaefer films of the pyroelectric copolymer PVDF-TrFE.

Chapter 3

Experimental methods of Langmuir and Langmuir-Schaefer films

This chapter discusses experimental methods used for the present work. A step wise

procedure for making Langmuir films is given at this time. In particular, it will focus

on various means of transferring the Langmuir films of pyroelectric polymer on to a solid

substrate using the Langmuir-Schaefer method.

3.1 Langmuir trough and other components

A Langmuir trough is a shallow rectangular trough made up of Teflon. It is used to

make monolayers of amphiphilic molecules. Because Teflon is a hydrophobic material, it

is easy to clean the trough after every experiment. The dimensions of the trough, made

by KSV inc., measure 364 × 75mm. This trough is mounted on an aluminum base which

is used to control the temperature of the subphase (water) by means of circulating water.

Two symmetrically movable barriers are used to control the surface area. They are made

of Delrin which is a hydrophilic material. The hydrophobic Teflon trough and hydrophilic

Delrin barriers system provides good contact with water so as to prevent the leakage of the

materials on the surface across the barriers. This can be experimentally verified by keeping

the surface area constant and observing the change in surface pressure. If a surface pressure

does not decrease in time, it is sure that material is not leaking across the barrier. The

rate of compression and expansion can be controlled by the user through KSV Software

provided with the trough by KSV. There is a dipping well of 70mm depth at the center of

the trough as shown in the Figure. This hole is generally used for transferring the film on

to a solid substrate which is explained in Section [3.4].

35

36

Light that falls on the air-water interface is reflected not only from the surface but also

from the bottom of the trough. In order to avoid this back scattering, a beam dump was

designed by previous graduate students Zou Lu and Ji Wang.38,44 This beam dump has

two components: a cylinder and a cone attached to a disk as shown in Figure [3.1]. Both

of theese are made of Delrin and hence, cleaning is relatively easy.

As explained in Section [2.4.3], the surface pressure is measured by a Whilhelmy plate.

The whole Langmuir trough system is attached to the Brewster angle microscope set up for

imaging the monolayer as seen in Figure [3.2].

Figure 3.1: A photograph of the Langmuir trough used in this work with its components, twobarriers and beam dump.

3.2 Cleaning procedure

In our lab, we use pure water from the PurelabPlus/UV system (with resistivity 18.2MΩ/cm),

for cleaning the trough, barriers, Whilhelmy plate and beam dump. Not only for cleaning,

this pure water is also used as the subphase when we make Langmuir films. To confirm

that there is minimal water contamination, we do a shake test before filling the Langmuir

trough. To do this, we first half-fill the round bottom flask with pure water and then swirl

thoroughly. We can observe many bubbles coming to the surface of water and break. If

they do not break immediately, then we can say that the water is contaminated by some

37

surface-active material.

We follow a certain procedure for cleaning all the materials mentioned above.

1. Prepare soap solution by mixing 30ml of ExtranTM with 1000ml of water.

2. Clean the trough, barriers and beam dump with the prepared soap solution.

3. Rinse thoroughly with cold water first and then with hot water.

4. Then use deionized water and finally ultra-pure water from Purelab plus for further

cleaning.

5. The Wilhelmy plate is usually cleaned with chloroform and then with pure water.

One should take so much care while cleaning this plate as it is delicate such that a

small torque developed by the heavy flow of water along the sides of the plate will

cause damage to the plate.

3.3 Experiment: How to make a Langmuir film

The copolymer used in my experiment called poly(vinylidene Fluoride-Trifluoroethylene)

was purchased from Kunshan Hisense Electronics Co., Ltd., China, in powder form and it

was used without any further purification. From the literature45 I found that the PVDF and

its copolymers do not dissolve in volatile and water-immiscible solvents, such as chloroform

and hexane, which are frequently used in making Langmuir films. They are soluble in polar

solvents, such as acetone and dimethyl sulfoxide (DMSO). At the same time, we know that

DMSO is highly toxic and for safety reasons we preferred not use it. Also, it is known that

DMSO tends to leave traces in the Langmuir layer.46 Therefore, we decided to use acetone

(purchased from Sigma-Aldrich) for sample preparation. The concentration of the sample

ranged between 0.063 mg/ml and 1.58 mg/ml; the lower value is equivalent to a 0.01 weight

percent. The weight percentage calculation is given in Appendix B. The process of making

Langmuir film has following important steps:

38

Figure 3.2: Arrangement of the Langmuir trough with beam dump inside the dipping hole and thebarriers are kept symmetrically on the trough which will be controlled by the motor. The photographat the bottom shows the Langmuir trough, Wilhelmy plate for surface pressure measurement. Thelaser light falls on the monolayer film at the air-water interface at the Brewster angle and thereflected beam is directed to the CCD.

• The first step is to prepare the polymer solution of the desired concentration (e.g.

0.6mg/ml) by carefully weighing a certain amount of the copolymer and mixing it

with the solvent Acetone. We prepared samples of different concentrations which will

be discussed in the next section. For all the measurements discussed here, I used the

solution for 3 weeks. Longer storage leads to different isotherms.

• Before each experiment, the trough and barriers should be cleaned by using the

method in the previous section.

• Assemble the Langmuir trough system as shown in Figure [3.2(a)] and place it in the

Brewster angle microscope set-up.

• Fill the trough with ultra pure water in such a way that the surface of the water is

two or three millimeters above the trough.

39

• Attach the Wilhelmy plate to the KSV electrobalance. Usually, one third of the plate

will be immersed in the plate.

• Using the vacuum-system aspirator tip, empty the trough from the surface at least

two times. For the third time, we let the barriers move inwards and run the tip of

the pipette everywhere on the surface of the water to remove any contamination. A

contamination check can also be done by observing the change in the surface pressure

with changing area. A significant change in the surface pressure indicates a surfactant

on the water surface.

• Fill a syringe with the prepared copolymer solution. We use a gas-tight Hamilton

syringe for depositing the sample on water surface.

• Gently push on the syringe to produce a droplet at the end of the needle and then

touch the surface. We should not let the drop fall from the needle onto the subphase,

as some of the sample might be lost in the subphase by diffusion.

• Wait for approximately 15 min for the solvent to evaporate, after which the surface

pressure measurement can start. The surface pressure is measured by the forces acting

on the Wilhelmy plate.

3.4 Langmuir-Schaefer Method

As mentioned in Chapter 1, we use the Langmuir-Schaefer method of deposition for

transferring the Langmuir film on to a solid substrate. Because our copolymer forms very

stiff films on air-water interface; the film may not bend if we choose vertical deposition (LB)

technique. In our experiment, we use silicon (Si) as the solid substrate. The Si was cut

into small pieces of dimension 1 × 1mm which is a convenient size for taking atomic force

microscopy (AFM) images. Like other components used in this experiment, the cleaning

of Si is also important. I used the same cleaning procedure explained in Section [3.2] for

40

cleaning this Si plate. After that, it was cleaned with isopropyl alcohol (IPA) and then

with Acetone and finally blown dry with clean nitrogen gas.

Figure 3.3: Three steps involved in Inverse Langmuir-Schaefer technique. The solid substrate isheld by tweezers44

In the Langmuir-Schaefer method, I tried three types of deposition.

• METHOD 1: First, the Si substrate was kept under the water before the sample is

spread on water. Once the Langmuir layer is formed, the Silicon substrate was taken

out of the water. I found some disadvantages of this method. The monolayer was

disturbed by the tweezers when I tried to take out the Si substrate. Also, there may

be a water layer on the Si substrate along with the monolayer. Hence, this method

is not suitable for making good quality films.

• METHOD 2: In this case, I touch the monolayer film by one side of the substrate

from top of the water surface and took it out. Here, the problem was that water was

dripping off the substrate when I tried to turn the substrate back for drying.

• METHOD 3: This technique called as Inverse Langmuir-Schaefer method was used

by the previous graduate student Ji Wang. She found this method as the better one

41

among other methods she tried. In the first step, we held the solid substrate using

tweezers and it was dipped into the monolayer at a small angle. Then it was taken

out carefully by rotating the tweezers, lifting the solid substrate upward out of the

monolayer. Then, it is kept for drying as shown as step 3 in Figure [3.3]. In this

method, the tweezers do not disturb the monolayer as in the Method 1 explained

above.

Chapter 4

Langmuir and Langmuir-Schaefer films of PVDF-TrFE

4.1 Introduction

Langmuir-Blodgett films of PVDF and its copolymers have been studied for many years,

at least since 1995. Especially, S. Ducharme and his group from the University of Nebraska-

Lincoln have been studying various structural, electrical and optical properties of LB films

of PVDF-TrFE(70/30) random copolymer in collaboration with researchers from the Rus-

sian Academy of Sciences. They made high quality films as shown by scanning tunnelling

microscopy (STM) picture [4.1] of a transferred film from a single Langmuir layer onto on

graphite. However, they found that the average thickness of single film was three times the

molecular diameter. Another group, in Japan, did extensive studies of different copolymer

ratios. They conclude that the range 50-80% PVDF gave the best crystallinity. However,

they also found that the Langmuir films appeared thicker than a single monolayer.

Figure 4.1: STM image of a single monolayer film on graphite.45

With the aim of preparing high quality Langmuir-Schaefer (LS) films of PVDF-TrFE

42

43

copolymer, I searched for suitable experimental conditions. I have tried to reproduce earlier

work, and improve the order in the layers. The results are discussed in this chapter. I made

Langmuir films following the same process explained in Chapter 3. I used Acetone rather

than DMSO for the solvent, both for increased laboratory safety and because DMSO is

known to stay in the surface layer. I also varied the temperature and the concentration in

the spreading solution. As a first step, it is essential to study the properties of the polymer

molecules on water surface to make highly ordered structure of LS films. The films are

characterized by their surface tension and elasticity isotherms as a function of apparent

molecular area. The transferred films will be characterized by atomic force microscopy

(AFM).

4.2 Polymer monolayer

Unlike low molecular weight substances, strong amphiphilic character is not strictly

required for polymers; macromolecules without pronounced amphiphility, and even water-

soluble polymers, can form a distinct surface layer on liquids.47 The reason for this is

essentially that even a small decrease in free energy for each monomer adsorbed to the

surface can, over many monomers, lead to a substantial free energy advantage for the

adsorbtion. Not all polymers produce true Langmuir monolayers, where the entire polymer

chain lies flat at the airwater interface; segments many monomers thick may extend partially

into the water.48 If the monomers are sufficiently surface-active, then they are all tethered to

the surface, and the configuration is effectively two-dimensional. It is this constraint at the

asymmetric interface, forcing the organization of monomers there, that makes Langmuir

and Langmuir-Blodgett films a powerful technique for increasing the organization of the

films.

A flexible polymer in a dilute three-dimensional solvent, like the original acetone for

PVDF-TrFE, will be in a random-coil configuration: in a poor solvent the configuration

44

will be compact, for a good solvent the configuration will be extended; for the intermediate

θ solvent the statistics of the polymer path exactly follow a random walk. Therefore, the

polymer, deposited on the surface in the spreading solvent, will be in a 3-dimensional random

coil configuration, as indicated in figure [4.2a]. The configuration the polymer takes at the

surface as the spreading solvent evaporates depends on the balance of interactions between

the polymer monomers and between the monomers and the water solution, specifically the

water surface. If the monomers are sufficiently amphiphilic, then in equilibrium they will

all be tethered to the surface. The flexible polymer will be in either a compact 2-d coil or a

more stretched out configuration, depending on whether the water surface acts as a poor or

good ”solvent” for the 2-d polymer, in direct analogy to polymer behavior in a 3-d solvent.

For short molecules, the equilibrium can be reached quite quickly, but for a polymer, the

process can be much slower, particularly if the affinity for the water surface is less strong.

Thus, the polymer configuration may evolve with time from a more 3-d configuration as

shown in figure [4.2a] to a more 2-d configuration as shown in [4.2b]. During this process, the

polymers will fill more of the surface. Also, depending on the surface coverage and the type

of effective solvent, the individual molecules may remain well-isolated in an approximately

2-d gas or they may phase-separate into a gas and a 2-d condensed liquid or solid phase.

Moving the barriers (Figure [4.2c]) inward slowly compresses the polymer monolayer, until

the gas phase is squeezed out and all of the individual polymer chains must interact with

each other, and the pressure begins to increase rapidly. This is the critical molecular area

per polymer unit (σ0). This more compressed layer is shown in Figure [4.2c] and [4.2d].

The later suggests that compression may force the polymer to organize in a crystalline or

near-crystalline form.

Higher pressure creates bending of the polymer chain away from the water surface due

to fewer adsorption sites on water surface (Figure 4.2e). Finally, if compressed more the

number of loops increases and the polymer film collapses and thus the surface pressure

45

Figure 4.2: Schematic diagram of polymer molecules on water surface during compression. (a)Initially polymer molecules may take a random coil shape. (b) and (c) Note the surface concentration,as in the number of molecules per unit area, is unchanged. Coil untangles and the polymer moleculesfills the water surface and hence the surface coverage increases. (d) When the area is decreased bythe barriers, polymer chains are closely packed. (e) and (f) On compression, polymer chains overlapon each other and move away from water surface. (b) and (c) are after the presentation [49]

goes down (Figure 4.2f). Note that the coil structure, the untangling of coils and the

overlapping of polymer chains depend on physical properties of the particular polymer,

including its interactions with the water and the air/water interface.

4.3 Surface pressure - Area isotherm

As mentioned in Chapter 1, the copolymer used in this present work, PVDF-TrFE is

not a good amphiphile. However, it can be dispersed on top of the water subphase to form

a sufficiently stable Langmuir layer.45

The typical surface pressure, Π - area σ isotherm of PVDF-TrFE is given in Figure

[4.3]. In general, the isotherm shows a smooth increase from low to high pressures without

obvious kinks or plateaus indicating phase transitions. This is common for the condensed

films of most polymeric materials on a water surface.42 At very large areas, the polymer

molecules are so far apart that there are negligible interactions between them. As the

46

Figure 4.3: Surface pressure Π - Area σ isotherm of PVDF-TrFE at 25 C. Here σ0 is limitingsurface area for close packing of molecules. This can be found by extrapolating to Π = 0.

barriers compress the monolayer, the surface pressure increases very slowly as the density

is low at these regions. On further compression, the surface pressure will display a sharp

increase because the molecules are closely packed. The highest pressure is reached when the

barriers are at the closest attainable distance (∼ 40mm). The limiting area per structural

unit, σ0, corresponding to close packing can be found by extrapolating the isotherm from

the linear region to zero pressure. The value of σ0 obtained from the isotherm is 0.0073

nm2 which is small compared to the expected value of 0.057 nm2 from the molecular model

given in.34 Here, the area per structural unit27 is assumed as 0.259 × 0.22nm2 according

the molecular model shown in Figure [1.7]. The calculation of mean molecular area is given

in Appendix B. I also calculated the surface concentration Γ = 1/σ corresponding to the

limiting area assuming that the entire mass of the spread polymer remains on the surface

without any diffusion into the water subphase. It is equal to 137 mol/nm2 (almost 8 times

larger than the expected value).

47

The critical area per molecule σ0 is thus much less than the expected value from molec-

ular models of close packed, completely untangled polymer chains. This may be due to the

dissolution of polymer molecules into the water subphase, with perhaps deposition on one

of the other trough surfaces. Another possible reason may be that in our experiment, the

polymer chains may be looped perpendicular to the water surface well before the critical

molecular area. The factors that determine the polymer configuration at the surface, and

thus the coarea may be: (1) The concentration of the polymer sample solution, (2) the

temperature of the subphase (3) atoms present in the polymer backbone, and (4) the di-

mensions of the polymer chain (Radius of gyration, correlation length, etc.). Points (1) and

(2),the effect of concentration and temperature on the copolymer monolayer, are explored

in the following sections.

In practice, the deposition process itself may have a large effect on the initial configura-

tion. Ideally the spreading solvent simply spreads on the surface carrying the polymer with

it. However, solvents of this polymer are also miscible with water, so particular care must

taken while spreading the sample to avoid penetration of solvent into the water subphase.

Thus, the size and speed of a drop of sample solution as it approaches the surface may be

important factors. However, some of the polymer may have penetrated into the solution,

and either remain there or deposit on other surfaces. Thus, when I give the mean molec-

ular area σ, we must always keep in mind that this an apparent value, assuming that all

of the polymer stays at the air/water interface. Thus, the absolute values of the surface

concentration may be off by a constant factor. However, the shape of the isotherm should

be characteristic of the polymer. This shape can be analyzed in two major ways: by looking

for power law relationships between pi and sigma and by calculating the elasticity of the

monolayer.

Often at moderate pressures, a power law relationship exists between Π and σ for a

polymer monolayer at the air-water interface.50,51,52 The scaling behaviour of polymer

48

monolayers is given below:

Π ∼ σ−ν ∼ Γν (4.1)

where ν is the scaling exponent. The value of ν can be found from a log(Π)− log(σ) plot of

the semi-dilute region (small molecular area region) as shown in Figure [4.4]. The curve is

clearly not linear in the high σ, low Π region, where the uncertainties in the Π measurement

dominate. Further, at high pressure the monolayer is expected to collapse, and the slope

decrease. In the intermediate pressure region, the curve appears approximately linear.

Taking two different regions, we found values of ν = 5.0 and 6.5. The theoretical prediction

of ν for a flexible polymer in two dimensions is 3 for good solvent. For poor and theta

solvents ν is greater than 3.50,53,54 In general, the value of this exponent indicates how

good the solvent environment is for the two dimensional polymer film. The exponents we

find for the copolymer PVDF-TrFE are typical of a poor solvent.

Figure 4.4: log Π - log σ plot (black) from the surface pressure-area isotherm. The slope of thelinear fit (green) gives the value of scaling exponent ν as 4.97. Choosing another region for the linearfit, the value of ν was found to be 6.55.

Another parameter for characterization of polymer monolayer is elasticity ϵ which can

49

also be found from the Π− σ isotherm by using the following equation,

ϵ = −σ(∂Π

∂σ

)T

(4.2)

I used Origin software to perform the differentiation in the above equation, averaging over

60 points. The result is shown in Figure [4.4]. From the figure, we observed that the

elasticity of the monolayer increases as the area decreases. This implies that the monolayer

is less compressible in the condensed state. The elasticity reaches the maximum value at

σϵ−max =∼ 0.0045nm2. The decrease in the elasticity curve near high surface pressures

probably indicates some type of collapse out of surface. At high surface pressures (Π ∼

16mN/m), the values of elasticity become small. These correspond to non-equilibrium

polymer configuration and domain collapse of the monolayer.

Figure 4.5: The elasticity of the Langmuir film calculated from the Π−σ isotherm. The elasticityincreases with decreasing mean molecular area. At σϵ−max ∼ 0.0045nm2, elasticity reach a maximumwhich may mean that the monolayer begins to collapse out of the surface.

50

Figure 4.6: Comparison of isotherms of the present work with the previously published isotherms.The main difference is that the coarea in the present case is almost 10 times lesser than the coareafound from the isotherm published for the first time in 1995. In fact, all studies since the initialisotherm shown in red find much smaller coareas; a typical example is shown in the middle curve.A. Cavalli et al. suggests that the smaller coarea is due to the dissolution of the copolymer intothe water. Published isotherms were scanned and the values are extracted by the free softwarePlotDigitizer.

4.3.1 Comparison with Isotherms in the Literature

Figure [4.6] compares the isotherm of the copolymer PVDF-TrFE with the published

isotherms in Ref.[55]. These include the first isotherm found in the literature as well as typi-

cal isotherms in more recent publications. In both case, the authors prepared the Langmuir

film of this polymer by dissolving it in a 0.01% solution of dimethyl sulfoxide (DMSO). In

the present work, we made a 0.01% sample solution with acetone. The isotherms are similar

except for the different coarea. The coarea calculated from our isotherm, σ0 = 0.0073nm2,

is almost 10 times less than σ0 = 0.0073nm2 from the first isotherm published in the litera-

ture. There are many factors that affects the isotherm as discussed in the previous section.

However, the one possibility is that much of the polymer is not deposited on the water

surface; it may be dissolved in water or remain in an emulsion with the solvent there or

51

deposit eventually on solid surfaces within the trough. Indeed, the literature isotherms since

the 1995 paper (including those by the same group) show isotherms much closer to the one

we find. For example, A. Cavalli et al. studied the Langmuir monolayer of the copoly-

mer PVDF-TrFE by dissolving it into DMSO in the concentration range from 0.008% to

0.5%.13 and also reported the small apparent molecular area (σ0 ∼ 0.015nm2) compared

to the expected value.

In 2005, Stephen Ducharme45 and his group found that the copolymer PVDF-TrFE

tends to produce (3 times) thicker films on water surface than a monolayer; it is not a good

amphiphile. They mentioned that the polar solvents, DMSO and acetone are water miscible

due to which most of the polymer molecules may go under water surface along with the

solvent. They suggested that only about 10% of the copolymer stays on the surface.

The comparison of our isotherm with the isotherms published before suggests that the

copolymer PVDF-TrFE solutions prepared using acetone also produce similar results. As

mentioned in Chapter 3, DMSO is toxic and hence, it is safer to use acetone. Further,

DMSO is known to remain in the monolayer, so other solvents are preferable both for the

monolayer and for the experimenter.

4.3.2 Effect of sample concentration

How well the sample is deposited on the surface may depend on many factors. The most

important one, besides the nature of the spreading solvent, is the concentration of the sample

in the spreading solution. In order to study how the concentration of the spreading solution

affects the coarea, I prepared three different samples of different concentrations given in

Table [4.1]. The surface pressure measurements were done at room temperature (∼ 250C)

for all the samples. The comparison of isotherms are shown in Figure [7(a)]. The coarea

shifts lower as the concentration of the solution decreases. To understand this better, the

coarea for these three concentrations are plotted against spreading solution concentration.

52

The coareas are significantly greater when the sample concentration is approximately equal

to 0.01%, indicating a greater fraction of the monomers at the surface. The reason may

be that the smaller initial surface concentration allows the polymer chain to untangle from

random coil without overlapping with other chains.

Concentration Sample#1 Sample#2 Sample#3

Mole Fraction % 0.010 0.077 0.174mg/ml 0.063 0.606 1.380

Table 4.1: Concentration of different samples studied

(a) (b)

Figure 4.7: (a)Comparison of isotherms of different sample concentrations. (b)The coarea vssample concentration is shown; σ01 and σ02 are coareas found from two different tangent lines drawnon the isotherms and extrapolated for Π = 0. These values for each isotherm gives the uncertaintyin the calculation of coarea.

The corresponding elasticities are also calculated for three samples using the same

method explained in Section [4.3]. They are shown in Figure [4.8]. Two main things

can be observed from this figure: (i) Overall the elasticity of the film shifts towards higher

apparent molecular area and (ii) the maximum elasticity is less in the case of low sample

concentration compared to high concentrations. The third small observation may be that

53

at higher surface pressure, the elasticity fluctuates more in the case of high and lowest

concentration, whereas for the medium concentration the elasticity is very smooth; Such

instability may be due to the stability of the layer, but in may also be due to the mechanical

stability of the tensiometer making the surface pressure measurements. Since we see no clear

trend with solution or monolayer concentration in the instability, the latter (instrumental)

instability is more likely. Observation (i) may simply be due to the possibility that the

true surface concentration is less with higher solution concentrations. However, observation

(ii) suggests that there may be a real dependence of the configuration of the polymer at

the surface on the initial spreading solution concentration. We can say that the Langmuir

film of higher concentrations are less compressible. Thus, the high elasticity value at higher

solution concentrations may be due to the compression of polymer chains which are trapped

in a more 3-d configuration. But at the lowest concentration, the polymer chains may be

well separated and further compression will lead to rearrangement of molecules on surface

in a more 2-d configuration.

4.3.3 Effect of subphase temperature

The subphase temperature is very important when we study Langmuir monolayer sys-

tems as it affects the interaction (cohesive force) between the molecules that form the film

and between the film molecules and the subphase molecules (adhesive force). We studied the

Langmuir monolayer of the copolymer PVDF-TrFE at three temperatures, 120C,250C,400.

The isotherms are plotted together and shown in Figure [9(a)]. The concentration of the

sample used for this study is 0.158mg/ml and the amount of deposition is 250µl. As can

be seen, the isotherms shift towards lower molecular area as the temperature of the water

subphase increases. Polymer molecules may be more soluble in water as the temperature

increases. In other words, the solubility of this copolymer may increase with temperature

which leaves very few molecules on the surface of the water. This is shown schematically in

54

Figure 4.8: Elasticity of different concentration samples calculated from Π−σ isotherms shown inFigure[4.6]. The shift in elasticity may be because of difference in polymer configurations on watersurface and its surface concentration of the polymer. Beginning of film collapse and rearrangement ofpolymer molecules may be the reason for the fluctuations of elasticity at the higher surface pressures.

Figure [4.10]. So at high temperatures, the coarea is very less.

The temperature experiments were done in the following way: First fill the trough with

Ultra pure water. Then by using a temperature bath, the water subphase temperature

was set to the desired temperature, the polymer solution was dispersed at constant surface

area (the barriers are fixed at the end of the trough). I then waited for ten minutes for

equilibration of polymer molecules on the water surface. Finally, the barriers were set to

move inwards for compression. After compression, the trough and other components were

cleaned completely. Then the next experiment was set up for another desired temperature.

In the future, it might be interesting to try this experiment in a different way to sepa-

rate the effect of subphase temperature on the initial spreading and on the isotherms. For

that, the subphase temperature should be set to the required lower temperature and then

55

(a) (b)

Figure 4.9: (a) Π− σ isotherms of low concentration sample at different temperatures. Isothermsshift towards left as the temperature increases for which the reason may be the balance between ad-hesive and cohesive properties of the copolymer. (b) Gibbs free energy calculated from the isothermsusing equation [4.3] is plotted against temperature for different surface pressures.

deposit the polymer solution. Then the temperature can be increased to a particular high

temperature. Remember polymer is on the water subphase while temperature is rising. Af-

ter attaining high temperature, we can start the compression and measure surface pressure.

I recommend this experiment.

The Gibbs free energy is an important parameter to study the dependence of the surface

pressure with temperature. The change in Gibbs free energy at constant temperature can

be expressed as,

∆G = NA

∫ Π

0σdΠ (4.3)

where NA = 6.023 × 1023mol−1 is Avagadro’s number. This can be calculated from the

measured Π − σ isotherms. first I plotted σ vs Π and then the area under the curve was

found by integration option in Origin software. Finally, the integration value was multiplied

with NA to express ∆G in Nm/mol or J/mol.

The change in Gibbs free energy was calculated for different surface pressures for each

56

Figure 4.10: : A schematic diagram of behaviour of polymer molecules on the water surface forincreasing temperature. As the temperature increases, monomers will be more soluble in water, sothat more segments leave the surface (upper two figures)

isotherm and represented in Figure [9(b)]. It can be observed that the change in Gibbs free

energy decreases with increasing temperature except at the lowest surface pressure 1mN/m.

At the lowest surface pressure, the value of the Gibbs free energy is higher at 250C than

at 120C and 400C. There is no discontinuity observed at higher surface pressures. This

indicates that there is no phase transition occurs in the temperature range from 120C to

400C with surface pressure greater than 5mN/m.

These curves also give information on another important thermodynamic quantity which

is entropy. This is defined as

S = −(∂∆G

∂T

)Π

(4.4)

Therefore, the negative of the slope of the Gibbs free energy curves will give the value

of the entropy. Entropy is a measure of disorder. The higher the entropy the higher

the disorder. In Figure [9(b)], the change in Gibbs free energy with temperature gives a

negative slope, which in turn makes entropy a positive value. It can also be noted that the

slope increases for higher surface pressures. Therefore the entropy increases and the order

decreases at higher pressure. At lowest surface pressure, Gibbs free energy seems peaked

at intermediate temperatures ∼ 250C and hence, entropy is negative for lower temperature

57

below 250C and positive at higher ones. The reason may be that at low surface pressure the

system undergoes a transition from an ordered to disordered state due to rearrangement of

molecules on surface. For making Langmuir-Schaefer films of PVDF-TrFE, it is important

to find the right surface pressure that corresponds to close packing of copolymer molecules

on the water surface. Therefore, lower surface pressure, nearly 5mN/m, which seems to

have higher order is suggested for making LS film of the copolymer PVDF-TrFE.

Table [4.2] gives the summary of different parameters studied in the present work.

Sample Concentration Temperature σ01 σ02 ν ϵmax σϵmax

(mg/ml) (0C) (nm2) (nm2) (mN/m) (nm2)

0.15812 0.01042 0.01559 3.66 67.85 0.0069825 0.00644 0.00861 6.06 32.21 0.0044440 0.01110 0.01532 2.56 6.77 0.00354

0.60612 0.00833 0.01067 6.24 84.74 0.0058725 0.00497 0.00653 5.49 65.22 0.0032640 0.00218 0.00340 3.44 25.73 0.00125

1.3812 0.00470 0.00586 3.68 60.90 0.0031725 0.00296 0.00430 3.21 68.44 0.0021240 0.00266 0.00387 3.06 24.61 0.00145

Table 4.2: Langmuir film parameters derived from the Π−σ isotherms of three samples are shown.Two different determinations of the coarea, σ01 and σ01, values provide the uncertainty in the coareacalculation. The different values of scaling factor ν show that the slope of the slope of the isotherm ineach case is different. Moreover, the water surface is a good solvent environment in some experimentsas ν values are closer to 3 which is the good solvent condition. The coarea corresponds to maximumelasticity ϵmax decreases with increasing temperature showing the isotherm shift towards left forhigher temperatures.

4.4 BAM images of PVDF-TrFE

Brewster angle microscopy is used to visualize the morphology of the Langmuir film

formed on the air-water interface. The principle of working of BAM is discussed in Chapter

2. In short, when p-polarized light falls on the water surface, the reflectivity is nearly zero

at the Brewster’s angle. The low reflectivity is captured by our CCD and shown in Figure

[11(a)]. The introduction of polymer film on top of water surface increases the reflected light.

For example, the image of the polymer film when the barriers are far apart, corresponding

58

(a) (b)

Figure 4.11: (a)BAM image of the water subphase without any film on it. The reflectivity ofp-polarized light is nearly zero at the Brewster’s angle. This creates the background for BAMimaging. (b)Typical BAM image of PVDF-TrFE(70:30) at room temperature taken at very lowsurface pressure (less than 1mN/m). The brighter regions characterizes the thicker film while thedarker region is for film with lesser thickness. The bottom right corner of this image is simply waterand it is dark.

to zero surface pressure, is shown in Figure [11(b)]. The image size is 720 pixels x 480 pixels.

The brighter regions corresponds to high molecular density (high thickness) whereas darker

regions represents low density (small thickness). In general, we observe concentric circular

patterns in the BAM image of PVDF-TrFE. These indicate diffraction. Such diffraction is

seen from 3-d particles, but also when the surface is out of focus. Further experiments are

needed to determine the cause of these diffraction circles.

A series of BAM images of the Langmuir film of PVDF-TrFE for high and low con-

centrations are presented in this section. The barriers were stopped at desired surface

pressures and a short video of the film was taken at the rate of 30 frames per second. Then

the video was converted into images of size 720 x 480 pixels using software called Ulead.

Finally, a scaling factor of 7.45µm/pixel is used to express the size of the image in terms

of millimeters. In all the images shown in this section, the scale bar is 1mm.

Generally, the films are visibly inhomogenoeous, and the strong diffraction circles suggest

3-d material. The films at higher temperatures appear more uniform. It may be initially

form the films at higher temperature, and perhaps cool these films to attempt to increase

59

the order in the formed films.

(a) Π ∼ 5mN/m, T ∼ 120C (b) Π ∼ 15mN/m, T ∼ 120C

(c) Π ∼ 5mN/m, T ∼ 250C (d) Π ∼ 15mN/m, T ∼ 250C

(e) Π ∼ 5mN/m, T ∼ 400C (f) Π ∼ 15mN/m, T ∼ 400C

Figure 4.12: BAM images of PVDF-TrFE of 0.158mg/ml at low and high surface pressures areshown in left and right columns respectively. (a) and (b) At low temperature, small bright spotsare clear, especially at high pressure. The small circular patterns observed in both high and lowsurface pressures are similar particles which are out of focus because of the incident angle: only aline perpendicular to the plane of incidence, parallel to the horizontal azis on the figures, is in focus.(c) and (d) Near room temperature, there are more spots (out of focus here) at both pressures. (e)and (f) At high temperature, Again many bright, probably 3-d particles are observed.

4.5 Atomic Force Microscopy

BAM characterizes the macroscopic uniformity of the initial film on the water surface.

The pyroelectric behavior of interest will depend on the molecular organization of the film

after transfer to a solid. In the present work, we used Atomic Force Microscopy (AFM) for

60

LB film characterization at the intermediate mesoscopic. AFM is an instrument used for

studying surface properties of materials at the atomic level. The basic principle the AFM

is to measure the forces between a sharp tip mounted on a flexible cantilever and a sample

surface. Forces between the tip and the sample typically range from 10−11 to 10−6N.56

AFM produces images by scanning the sample with respect to the tip and measuring the

deflection of the cantilever as a function of lateral position.

In the earlier stage of the present work, high concentration sample (0.2%) was used for

preparing Langmuir-Schaefer films. Films were prepared at different conditions as given

below:

1. Two LS films prepared at low temperature (∼ 110C) using Method 1 and Method 3

explained in Section [3.4].

2. Two LS films prepared at high temperature (∼ 400C) using Mehtod 1 and Method 3.

3. Two LS films prepared at high (∼ 15mN/m) and low surface pressures (∼ 5mN/m)

at room temperature.

4. Two LS films prepared at high and low surface pressures in room temperature with

additional cleaning of silicon substrates done at LCI.

The AFM images of these films were taken using Veeco Dimension Icon AFM instrument

at Michigan State University. Due to time constraints, we could not take images of all the

samples. Here, the images of items (1) and (4) are presented in Figure [4.14]. Both the

films are prepared at ∼ 5mN/m, the left side image represents the film prepared at room

temperature and the image on right side represents the film prepared at low temperature.

The corresponding three dimensional images are given in the bottom panel. It can be

observed there are small voids (black spots) on both the images, but on the left one more

black spots are seen. One of the voids is zoomed-out from the left image and shown in

61

Figure [4.15] along with height profiles. A comparison of height profiles along the blue

line are given in Figure [4.16]. They merely show different height profiles ranging from 0

nm to 12 nm. In order to extract more information from these images by using the AFM

software, I plotted the roughness profiles and the comparison is shown in Figure [4.17]. This

shows that the film prepared at room temperature is more smooth than the film prepared

at low temperature. However, to make a general conclusion on roughness of samples made

at different temperatures AFM images of at least two more samples have to be compared.

The thickness of the film can be calculated approximately by assuming the density of the

polymer as 1g/cc. The thickness calculation is given in Appendix [B.4]. If we use the value

of σ0 corresponding to the spreading solution concentration 1.38mg/ml given in Table [4.2],

we found the thickness is ∼ 30nm. This shows that the film on silicon substrate is several

times more than the thickness (= 0.6nm) of one single monolayer.45,57

In the later stage of the present work, LS films of low concentration (0.01%) samples

were prepared. The AFM images of these samples were taken using NanoScope III Atomic

Force Microscope at the Liquid Crystal Institute of Kent State University by Ms. Liou

Qiu. The AFM image of low concentration sample transferred on to Si substrate at room

temperature, is shown in top left panel of Figure [4.20]. We observed triangular shaped

patterns which are oriented towards right. I suggested that in future one should track both

compression direction and the substrate dipping direction while making LS films, since the

orientation of these patterns may depend on either of these. The roughness of this low

concentration sample (0.01%, Green curve) is compared with that of high concentration

sample (0.2%, Red curve) in Figure [7(a)]. The two peaks in the green curve are due to

steps made by triangular patterns as can be clearly seen in the equivalent three dimensional

image. Although the maximum height of low concentration sample is smaller (4.21nm) than

that (6.06nm) of high concentration, the thickness of low concentration film is still larger

than the expected film thickness of 0.5nm. Then, AFM image of silicon substrate (without

62

any film) was taken which is shown in right side panel of Figure [4.20]. It is clear from the

two and three dimensional image that Silicon substrate itself has roughness with maximum

height of ∼ 4nm. Other AFM images of the same sample is given in Figure [4.18]. The

blue boxed area is enlarged and shown next to it. The height profile is drawn along the

diagonal line. This image also shows void as seen before in the image of high concentration

LS film. Now, what can be the source of these voids? Are those triangular patterns due to

the roughness of Silicon plate used for making LS films? To answer these type of questions,

it is suggested to make LS films of the low concentration solution on different substrates,

for example, mica and glass.

4.6 Conclusion

The properties of the PVDF-TrFE Langmuir and Langmuir-Schaefer films depended

strongly on the deposition conditions. In particular, they depended on both the concentra-

tion of the copolymer in the spreading solution and on the temperature at which film was

formed. We found that the apparent coarea, corresponding to the close packing of polymer

molecules on the water surface, is smaller for the lowest spreading solution concentration of

0.0632 mg/ml (0.01% mol fraction). However, this coarea is almost five times smaller than

the expected value of 0.57nm2, which would correspond to a layer 25 times thicker than a

nominal monolayer. This descrepency could be due to the formation of true multilayers,

but it could also be due to the dissolution of the polymer molecules into the water so that

the true coarea is much larger, or to polymer chain overlapping or folding. Furthermore,

the scaling exponent found from the isotherm is greater than 3. This shows that the water

surface does not serve as a good solvent for this copolymer. This may also be a reason

for multilayer configuration of polymer molecules on water surface a smaller. More recent

results published in literature, which also demonstrate that PVDF-TrFE polymer does not

form a monolayer on the air-water interface.

63

Subsequently, we studied the influence of subphase temperature on Langmuir films of the

copolymer. The Gibbs free energy was calculated from the isotherms and plotted against

temperature. Based on this plot, we conclude that the surface pressure equal or lower than

5mNm−1 is appropriate for making Langmuir-Schaefer films since the entropy increases

for higher surface pressures. Nevertheless, these experiments can be repeated for other

intermediate temperatures so as to ensure any discontinuity in the Gibbs free energy in the

temperature range 120C - 400C.

Brewster angle microscopy images of low concentration sample taken at different tem-

peratures show a homogeneous film only at the highest temperatures, ∼ 400C. However,

the order within these films may also be less. It would be interesting to compress the films

at higher temperature and then decrease the temperature, to see if the greater spreading of

the films at higher temperatures is maintained in a more ordered film.

Langmuir-Schaefer films of PVDF-TrFE were prepared on silicon substrates at different

temperatures for films made with high concentration spreading solutions. AFM images of

high concentrated sample show a uniformly bumpy film surface at room temperature. AFM

images of low concentrated sample needs further investigation as they show some strange

triangular patterns. I will discuss some ideas for improving this film quality in the next

section.

4.7 Suggestions for Future Work

Various properties of Langmuir-Blodgett films of PVDF-TrFE(70:30) copolymer were

studied and reported in many publications. As we know, the making a good Langmuir

film is the first step in the process of making good quality Langmuir-Blodgett films or

Langmuir-Schaefer films. Hence, it is necessary to study the basic physical properties of the

Langmuir film of this copolymer. For example, the thermodynamic properties, like Gibbs

free energy, entropy and order parameter can be investigated further. As of my knowledge,

64

these properties are not studied before. Furthermore, the visoelastic properties, like, static

and dynamic elasticities can be studied using surface light scattering (SLS) experiment

which is also not studied for this polymer before.

Apart from that, there are many other experiments suggested based on the present work:

• Temperature experiment: In all the temperature experiments studied in the present

work, I first heated the water subphase to the desired temperature and then I dis-

persed the polymer solution. These experiments can be done in a different way to

study the effect of subphase temperature on the monolayer. That is first deposit poly-

mer solution on water surface and start heating the subphase. This will change the

monolayer temperature slowly and we can study the change in the isotherm compared

to the isotherms plotted in the present work.

• Langmuir-Schaefer films can be prepared on mica substrate and compare the rough-

ness of the films that were prepared on Silicon substrate.

All these experiments may be considered as a complete study of PVDF-TrFE using

BAM instrument.

65

(a) Π ∼ 5mN/m, T ∼ 120C (b) Π ∼ 15mN/m, T ∼ 120C

(c) Π ∼ 5mN/m, T ∼ 250C (d) Π ∼ 15mN/m, T ∼ 250C

(e) Π ∼ 5mN/m, T ∼ 400C (f) Π ∼ 15mN/m, T ∼ 400C

Figure 4.13: BAM images of PVDF-TrFE of 1.38 mg/ml at low and high surface pressures areshown in left and right columns respectively. (a) and (b) Low temperature BAM images show thateven at very low surface pressures, the polymer molecules completely covered the water surface withonly occasional dark areas. Further compression results in overlapping of polymer chains and thatcan be seen in brighter region of (b). At room temperature, (c) show that the polymer film is verythick and nonhomogeneous. In figure (d) we can see that the film is about to collapse. At hightemperature, the films seem much more uniform with few bright particles. Moreover, we can seesome domains with fine boundaries. From the Table [4.2], we can note that the value of σ0 is lessfor the all the three temperatures. As recommended before in Section [4.3.3], we can try BAMimaging for deposition of polymer solution at low temperature and compression of the film at hightemperature

66

Figure 4.14: AFM images of 0.2% high concentration sample are shown. Top left 2D AFM imagerepresents the LS film of PVDF-TrFE prepared at 250C at low surface pressure, 5mN/m. The scansize is 2µm × 2µm. Top right 2D AFM image is for the same concentration sample, but preparedat low temperature 120C at 5mN/m. The scan size is 1µm× 1µm. Their 3D images are shown inthe bottom panel. The blue box indicates a void, that will be enlarged in Figure [4.15].

Figure 4.15: Enlarged image of void (blue box) drawn in Figure [4.9]. The height profiles of lines1 and 2 show that the film is not homogeneous.

67

Figure 4.16: Comparison of height profiles of the two films prepared at room temperature and lowtemperature. For comparison the height profiles are drawn only for the length of blue lines drawnon the images.

Figure 4.17: Comparison of roughness of two films is shown here. Lower the area under thecurve, the better the smoothness. Therefore, the film prepared at room temperature shows moresmoothness compared to the one prepared at low temperature.

68

Figure 4.18: AFM picture of the same low concentration sample prepared at room temperature, lowsurface pressure. The area of blue box is enlarged to show that the void exists in low concentrationsamples also. The height profile is also shown below corresponding to the blue line.

(a) (b)

Figure 4.19: (a)Comparison of roughness of low (green curve) and high concentration (redcurve) samples. This shows that the LS film of high concentration sample has more roughness.(b)Roughness of low concentration film is compared with that of simple Silicon substrate withoutany film on it. The roughness of both the film and Silicon substrate looks similar. The green curveimplies that there may be a very thin layer of polymer molecule is formed on Si substrate.

69

Figure 4.20: 2D and 3D AFM images of the LS film of low concentration sample prepared atroom temperature at 5mN/m is shown on the left side. We observed some triangular patterns. Thereason is now known and this needs further investigation. The right side AFM image is for simpleSilicon substrate without any film on it. From these images it is clear that the Silicon substrateitself is not smooth.

Chapter 5

Numerical simulation of linear plasmonic photodetector

5.1 Introduction

In the literature, it has been pointed out that a metal grating with period smaller than

the wavelength of the incident light acts like a linear polarizer as it transmits only one

polarization which is perpendicular to the grating slit.58,59,44 Recently, in 2008, Zhi Wu

et al. reported a metal wiregrid micropolarizer array, that has different transmission axes

within a group of pixel, for IR imaging polarimetry.60 They also mentioned that a focal

plane array detector integrated with metal wire grid polarizer array can be used to extract

the full Stokes parameters in polarimetric imaging applications. However, integrating focal

plane array and the plasmonic polarizer array may have practical difficulties. For example,

the distance between the focal plane array and the polarizer array is critical for imaging

since the loss increases with propagation distance.61

The new design not only identifies the polarization state of the incoming IR light, it can

also be used to measure the intensity of the incoming light since the dielectric medium is

a pyroelectric copolymer PVDF-TrFE. A simple plasmonic structure is taken for numerical

study to explain how the structure recognizes two different linear polarized states. Basically,

the geometrical dimensions of the linear plasmonic photodetector (hereafter called as linear

polarizer) can be optimized by the numerical simulation. For this purpose, the commercial

software package CST Microwave Studio (MWS)62 is used. This software applies finite-

difference time domain (FDTD) method for solving Maxwell’s equations for which Yee’s

algorithm is used.63 It first divides the physical system into small space grids and solve two

curl Maxwell’s equations at each point in the grid along with suitable boundary conditions.

70

71

This algorithm basically uses two numerical techniques: (1) central difference technique for

space derivatives and (2) Leapfrog technique for time derivatives. Electric field components

are first solved at constant volume space and then magnetic field components are find at

next instant of time for the same volume of space.64

Here, the goal is to distinguish electric field vibrations along the x and y directions of

the incident p-polarized light in infra-red range. This chapter summarizes the results of

numerical simulation of the linear polarizer. To begin with, I give a short introduction to

surface plasmons (SP) and go on with results of the numerical simulation.

5.2 Surface plasmons

Surface plasmons are collective charge oscillations that occur at the metal-dielectric

interface. They are basically a combined oscillation of the electromagnetic field and the

surface charges of the metal.65 The properties of surface plasmons, as depicted in Fig-

ure[5.1], are: (i)SPs are p-polarized called transverse magnetic (TM), i.e., the magnetic

field is parallel to the interface (Figure[5.1 (a)]). (ii) Only p-polarized light can be coupled

to SP mode, because only then does the electric field in this case has a component normal

to the surface and hence generate surface charges on the metal surface. (iii) The electric

field component perpendicular to the surface decays exponentially into both the medium

(Figure[5.1(b)]). (iv) The dispersion relation for the surface plasmons can be written as:66

ksp = k0

√ϵmϵdϵm + ϵd

(5.1)

where ϵm and ϵd are permittivity of metal and dielectric respectively. Usually, the Drude

model is used to calculate the permittivity ϵm of metals. It is given by,

ϵ(ω) = ϵ∞ −ω2p

ω(ω − iδ)(5.2)

Here, ϵ∞ is the high-frequency bulk permittivity, ωp is the bulk plasmon frequency and δ

is the electron collision frequency.

72

Figure 5.1: (a) Schematic illustration of electromagnetic wave and surface charges at the interfacebetween the metal and the dielectric material,(b) the locally electric field component is enhancednear the surface and decay exponentially with distance in a direction normal to the interface and(c) Dispersion curve of a SP wave; kSP and k are the wavevectors of SP and light wavevectors,respectively. This shows that the momentum of the SP wave is larger than that of the light photonin free space for the same frequency (ω).67

The dispersion curve for SP is shown in Figure[5.1]. It shows that at the same frequency,

ω , the SP wavevector ksp is greater than the wavevector of light k0. This frequency

is called the surface plasmon resonant frequency ωsp.68 SPs have optical frequencies (∼

1015Hz) but the wavelength is in the x-ray region (1nm). It is this property of SP which

is utilized to overcome the diffraction limit that light cannot be transmitted through a

sub-wavelength aperture if its wavelength is greater than two times the diameter of the

aperture.69 Moreover, in order to satisfy momentum conservation between the incident

light and the surface plasmon, a grating structure with periodicity Λ is introduced on the

metal surface. When light falls on the metal surface ,the wavevector of the surface plasmon

will become ksp = 2π/Λ at resonance. This should be matched with ksp given in Equation

[5.1] to find the resonant wavelength of excitation.

5.3 Results of numerical simulation

The schematic side view of the structure used for numerical simulation is shown in Figure

[5.2]. Here, a and h are the width and height of the slit; d is the period of the grating.

73

These are the key parameters for making this structure to excite surface plasmons and

hence enhanced transmission of light into the polymer layer which is sandwiched between

top and bottom gold layers.

Figure 5.2: Side view of the linear plasmonic photodetector with periodicity d = 1300, slit widtha = 400nm and height h = 100nm. The dielectric medium is a copolymer PVDF-TrFE polarizationof which changes when it absorbs infra-red radiation. The thickness of the polymer layer is 20nm.

For the simulation, we take a = 400nm, h = 100nm and d = 1300nm. The plane wave

falling on this structure is in −z direction. The dielectric parameters of gold can be calcu-

lated from the Drude model given in Equation [5.2] with ϵ∞ = 3.5, ωp = 1.3 × 1016rad/s,

and δ = 6 × 1013Hz. The refractive indices parallel (nx) and perpendicular to the surface

(ny) and the corresponding attenuation constants kx and ky of the copolymer were obtained

from Dr. Mengjun Bai from University of Nebraska-Lincoln who studied Infrared spectro-

scopic ellipsometry study of vinylidene fluoride (70%)-trifluoroethylene (30%) copolymer

LangmuirBlodgett films.40 The real and imaginary parts of the principal components of the

dielectric tensor for the copolymer are calculated by using the relation,

ϵ(ω) = ϵ′ + iϵ′′ = (n+ ik)2 (5.3)

They are shown in Figure [5.3].

74

(a) (b)

Figure 5.3: (a) Real and (b) imaginary values of dielectric permittivity of the copolymer PVDF-TrFE shows that the polymer is anisotropic as these values are different in parallel and perpendiculardirections of the polymer surface.40

When light falls on the structure, surface charges are excited at each metal-dielectric

interface and develops local electric field along z-direction. If the two interfaces are brought

together, by adjusting the slit width, then coupling between the two electric fields occurs by

constructive and destructive interference. This gives rise to symmetric and anti-symmetric

modes.70,71,72 Two simulations are done for incident plane waves polarized (1) along the

x-direction perpendicular to the grating slit and (2) along the y-direction parallel to the

grating slits. The frequency of the incident radiation is set from 20THz to 80THz. For

the x-polarized incident radiation, we observed that the resonance occurs at 48.7 THz. In

other words, the surface plasmon is excited and propagates along the interface between the

metal and polymer on either side of the slit. The snap shots of the electric field inside the

gap at resonant frequency (43.64THz) and at frequencies away from resonance (20THz and

60THz) are shown in Figure [5.4 - 5.6]. From these electric field distributions, we first

observed that the incident x-polarized light excites surface plasmons and the y-polarized

75

Figure 5.4: Snap shot of the total electric field at ω = 20THz.

light does not since it does not induce surface charges. Therefore, this plasmonic structure

can be used to detect linear polarization. Secondly, we can see that the magnitude of the

z-component of the electric field decreases as it propagates along the x-direction which is

generally due to the absorption property of metals. At last, the simulation results show that

anti-symmetric mode exists for this nanostructure with Ez oscillating in opposite directions

at the interface and they have minimum at the center of the slit. This is because the x-

component of incident light induce positive charges on one side of slit and negative charges

on the other side. The dispersion relation for anti-symmetric mode can be written as:73

tanh(2kdd) =

−2

[(ϵxxϵyykd

η

)2+

(kmϵm

)2] [

kmϵxxϵyykdϵmη

][kmϵxxϵyykd

ϵmη

]2+

[(ϵxxϵyykd

η

)2+

(kmϵm

)2]2 (5.4)

where

km =

√β2 − ϵm

ω2

c2

kd =

√β2ζ

ϵyyϵxx−(ωc

)2 η

ϵyyϵxx

η = ϵxxϵyyϵzz − ϵxzϵyyϵzx

76

Figure 5.5: Snap shot of the total electric field at resonant ω = 43.64THz.

and

ζ = ϵxxϵzz − ϵzxϵxz

The dispersion curves plotted using the above set of equations, for different slit widths

ranging from d = 20nm to d = 100nm, are shown in Figure[5.5(a)]. Here we take ϵxx = ϵyy

for a uniaxial material. The imaginary values of kx give propagation length as shown in

Figure[5.5(b)]. The propagation length decreases with increasing frequency of incident light.

The simulation was repeated for the structure with the same dimensions as before, but

the incident light polarization was changed to y-direction. The ratio between Ez of x-

polarization and y-polarization is plotted in Figure[5.6]. This clearly shows that the Ez for

x-polarization is nearly 108 times greater than that of y-polarization.

5.4 Conclusions

The numerical simulation of new plasmonic design shows a clear difference between

x- and y- polarized light. However, these design is not get optimized. One can run the

simulations for varying slit width and hence the periodicity of the grating. The dielectric

thickness can also be varied for another set of simulations and study how it affects the

77

Figure 5.6: Snap shot of the total electric field at ω = 60THz.

propagation length of the surface plasmons at metal-dielectric interface.

78

(a) (b)

Figure 5.7: (a) Dispersion curves of anti-symmetric mode in metal-dielectric-metal waveguide inthe infra-red region and (b) The propagation length of SP wave along x-direction. A MATLABprogram for solving the dispersion equations is given in Appendix D.

Figure 5.8: The ratio of the z components of electric fields obtained from simulations with x- andy- polarized incident light demonstrating the detection of x-polarized light. The peak correspondsto the resonant frequency between SP and incident light.

Chapter 6

Conclusions and Recommendations

6.1 Conclusions

From this work, we learned that a monolayer of PVDF-TrFE is difficult to form on

the water surface. However, I have made progress towards making good quality Langmuir-

Schaefer films of the copolymer PVDF-TrFE by carefully choosing the subphase temperature

and the concentration of the polymer in the spreading solution. The film thickness and the

order of polymer molecules in the thin film determines the quality of the film. Suggestions

for further imporving the film properties are given in chapter 4.

The final test of film-quality would be to measure the pyroelectricity of the LS films. This

could be done by LangmuirSchaefer deposition on a glass substrate covered by aluminium or

ITO.36 The top electrode for electrical measurements can be prepared by evaporating alu-

minium on top of the polymer film. There are two types of pyroelectric measurements: The

light absorption method called Chynoweth method74 and the heating/cooling method.75 In

the Chynoweth method the sample was heated by a laser light, its polarization changes and

the corresponding pyroelectric current is measured by an electrometer. In the heating/cool-

ing method, the sample is mounted on a cyrostat for heating or cooling the sample.

Next, I have shown by simulation that a simple nanostructure grating as part of a metal-

dielectric-metal waveguide can determine the linear polarization states of the incident light.

The structure period is optimized for focussing the light onto the polymer layer through

surface plasmon excitation. We found that the electric field enhancement is about 7 times

that of the incident light. Also, the electric field of one linear polarization state is ∼ 108

times greater than that of other linear polarization. The structure can further be optimized

79

80

to yield a resonance curve with a narrow width. The structure of the device can be modified

to select circular polarized light and then be optimized by simulation.76

The next important step would be to calculate the device sensitivity which is the min-

imum change in temperature required to produce a detectable pyroelectric current. This

depends on many different physical properties of the copolymer, including the pyroelectric

coefficient, the dielectric constant and the specific heat capacity.

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Appendix A

Reflectivity for Langmuir Monolayers

Consider a Lagmuir monolayer on water substrate as shown in Figure. The coordinate

system is chosen in such a way that the air-thin film interface is in xy plane and the

properties of the medium in the three layer system changes along z direction. Suppose a

plane wave described by the following equations

E = E0ei(k.r−ωt) (A.1a)

H = H0ei(k.r−ωt) (A.1b)

falls on an interface between air and thin film. Here, the plane of incidence is taken as x-z

plane and hence ky = 0. The Maxwell’s equations are:

∇ × H =∂D

∂t(A.2)

∇ × E = −∂B∂t

(A.3)

where

D = ϵ0ϵ(z)E (A.4)

and

B = µ0H (A.5)

The solution of these equations can be found using a standard method called, 4 x 4 ma-

trix method which has been discussed in the text by Azzam and Bashara39 and in other

publications.77,78,79 The derivation of reflectivity is given here with the help of references

mentioned above.

87

88

Figure A.1: Reflectivity

If we choose the coordinate system such that the x-y plane is the plane of incidence and

the origin is taken at the air-monolayer interface, then two Maxwell’s equations[A.1a and

A.1b] can be rewritten as one differential equation as

∂

∂zψ = i

ω

cTψ (A.6)

where

ψ =

√ε0Ex

√ε0Ey

õ0Hx

õ0Hy

(A.7)

and

T =

∆11 ∆12 ∆13 0

∆21 ∆11 ∆23 0

0 0 0 ∆34

∆23 ∆13 ∆43 0

(A.8)

89

∆11 =−∆ε sin t cos t cosϕ

ε33η

∆12 = 1− η2

ε33

∆13 =∆ε sin t cos t sinϕ

∆33η

∆21 = ε⊥ +ε⊥∆ε sin

2 t cos2 ϕ

ε33

∆23 =ε⊥∆ε sin

2 t sinϕ cosϕ

ε33

∆34 = 1

∆43 = ε⊥ +ε⊥∆ε sin

2 t sin2 ϕ

ε33− η2

ε33 = ε⊥ +∆ε cos2 t

η = sin θB

For a monolayer film of thickness h << λ, the solution of the Maxwell’s equation can be

approximately written as,

ψ(h) =

(I + i

2πh

λT

)ψ(0) ≡ P (δ)ψ(0) (A.9)

where δ =2πh

λ. Also, we can see from the figure that above the monolayer,we have only

contributions from the incident and the reflected light and therefore, ψ(z) = ψi(z) +ψr(z).

At the same time, below it is just the transmitted light represented by ψt. Hence, the above

equation will become

ψt(h) = P (δ)(ψi(0) + ψr(0)

)(A.10)

In terms of Electric fields, we can write as

√ε0E

tx

√ε0E

ty

−n cos θt√ε0E

ty

ncos θt

√ε0E

tx

= P (δ)

√ε0

(Ei

x + Erx

)√ε0

(Ei

y + Ery

)− cos θi

√ε0

(Ei

y − Ery

)1

cos θi

√ε0

(Ei

x − Erx

)

(A.11)

90

Here, the following relations between the electric and the magnetic fields were used:

√µ0Hx = −kz

k

√ε0εEy

and

õ0Hy =

kzk

√ε0εEx

Finally, the reflectivity of the Langmuir monolayer was derived as:Er∥

Er⊥

=

rpp rps

rsp rss

Ei

∥

Ei⊥

(A.12)

For the p-polarized incident light, Ei⊥ = 0 and hence, we can writeEr

∥

Er⊥

=

rppEi∥

rspEi∥

(A.13)

Here,

rpp =ikh∆21 cos

2 θB − ikh∆12

2 cos θB

and

rsp = (−ikh∆23 − ikh∆13) cosθB

Suppose the polarization of the reflected light from the monolayer is changed by using an

analyzer, then the intensity of the reflected light can be written in terms of the analyzer

angle α as,

Iα = |E|2 = |Er∥ cosα+ Er

∥ sinα|2 (A.14)

With these equations, the reflectivity equation will now take the following form

R =1

4cos2 θB(kh)

2cosα 1

cos2 θB

[−(ε⊥ +

ε⊥∆ε sin2 t cos2 ϕ

ε⊥ +∆ε cos2 t

)cos2 θB + 1− sin2 θB

ε⊥ +∆ϵ cos2 t

]+ sinα

2∆ε sin t sinϕ

ε⊥ +∆ε cos2 t(cos t sin θB + ε⊥ sin t cosϕ cos θB)2 (A.15)

91

Figure A.2: Reflectivity for the tilt angle t = 450 and different polarizer angles α = 00, 300, 600

and 900

Figure A.3: Reflectivity for the tilt angle t = 900 and different polarizer angles α = 00, 300, 600

and 900

92

The reflectivity R vs. the domain orientation ϕ for different tilt angle t and the analyzer

angle α, for a monolayer of thickness, h = 50nm for example, is shown in Figure [A.2 and

A.3]. The dielectric constants for the P(VDF-TrFE) copolymer ε⊥ = 2.06 and ε∥ = 1.99,

corresponding to the wavelength of light λ = 500nm, were adopted from the University

of Nebraska-Lincoln. So, this model can be used to study any anisotropy present in the

monolayer film. In other words, we can find the tilt angle and the refractive index anisotropy

by measuring the domain reflectivity.

Appendix B

Calculations

There are some calculations required before and after the experiments. They are given

in this Appendix.

B.1 Molecular weight of PVDF-TrFE

The molecular weight of one structural unit of the copolymer PVDF-TrFE(70:30) is

calculated by substituting the atomic weights of Hydrogen (H), Fluorine (F) and Carbon

(C) atoms in the chemical formula of VDF and TrFE polymers.

Atomic weight of H = 1.00794 Atomic weight of F = 18.9984 Atomic weight of C =

12.01

The chemical formula of VDF is CF2 − CH2. Therefore,

= 12.01 + 18.99842 + 12.01 + 1.007942 = 64.03268

Similarly, the chemical formula of TrFE is CF2 − CHF and hence

= 12.01 + 18.99842 + 12.01 + 1.00794 + 18.9984 = 82.02314

For the copolymer PVDF-TrFE (70:30), the molecular weight will be,

Mw = 64.03268 ∗ 0.7 + 82.02314 ∗ 0.3 = 69.42g

mol(B.1)

B.2 Concentration of the sample in weight percentage

The concentration of the sample in weight percentage can be calculated using the fol-

lowing formula:

W% =MPV DF−TrFE

MPV DF−TrFE +MAcetone(B.2)

93

94

We know that the density of Acetone is

ρ =MAcetone

25mL= 0.791

g

cm3(B.3)

Therefore,

MAcetone = 0.791g

cm3× 25mL (B.4)

Since, 1cm3 = 1mL, we can write

MAcetone = 19.755g (B.5)

The mass of the P(VDF-TrFE) can me measured using a normal weighing balance and

substituting it in the equation [B.2], we get the concentration of the sample in weight

percentage.

B.3 Calculation of Molecular area per structural unit

To plot the π − σ isotherm, we first have to calculate the area per structural unit

(monomer) of the copolymer.

Molecular weight per monomer Mw = 69.4 gmol

Area of the Langmuir trough at the time of sample deposition A = 30× 7.5cm2

Volume of the sample deposited V = 900µl

Concentration of the sample C = 0.0632mgml

Now, the area per structural unit can be written as

σ =Mw

NACV≃ 0.041nm2 (B.6)

The above equation can also be used to calculate the spreading volume V for a desired area

per molecule.

B.4 Calculation of thickness of LB films

Suppose we deposit M grams of polymer material of bulk density ρ on a water surface

to prepare a Langmuir film of thickness t. If A is the area of between the two barriers and

95

V is the volume of the film, then the average thickness of the film can be given by

t =V

A(B.7)

As we know,

M = V ρ = Atρ =⇒ t =M

Aρ(B.8)

From the calculation of Mean Molecular Area [B.3], we can write

M

A=

1

σ

Mw

NA(B.9)

Therefore,

t =Mw

σρNA(B.10)

Substituting the numerical values, we get for σ = 0.01nm2

mol

t =69.4 g

mol(0.01nm2

mol

)×

(1gcc

)× 6.023× 1023

≃ 10nm (B.11)

Appendix C

MATLAB program for calculating Rs and Rp

c l e a r a l l

c l o s e a l l

c l c

n1=1;

n2=1.42;

n3=1.333;

a=1;

f o r inc =52 :0 .05 :54

b=1;

f o r t =2 :2 : 8 ;

s t2=(n1 . / n2 ) . ∗ s ind ( inc ) ;

s t3=(n2 . / n3 ) . ∗ s t2 ;

ct2=sq r t (1− s t2 ˆ 2 ) ;

ct3=sq r t (1− s t3 ˆ 2 ) ;

r12=(n2 .∗ cosd ( inc )−n1 .∗ ct2 ) . / ( n2 .∗ cosd ( inc )+n1 .∗ ct2 ) ;

r23=(n3 .∗ ct2−n2 .∗ ct3 ) . / ( n3 .∗ ct2+n2 .∗ ct3 ) ;

l =500;

beta =4.∗180.∗n2 . ∗ ( t . / l ) . ∗ ct2 ;

Rp(a , b)=(( r12 ˆ2)+(2.∗ r12 .∗ r23 .∗ cosd ( beta ./2))+ r23 ˆ2 ) . /

(1+(2.∗ r12 .∗ r23 .∗ cosd ( beta . /2 ) )+( ( r23 ˆ 2 ) . ∗ ( r12 ˆ 2 ) ) ) ;

b=b+1;

96

97

end

a=a+1;

end

c=1;

f o r inc =52 :0 .05 :54

d=1;

f o r t =2 :2 : 8 ;

s t2=(n1 . / n2 ) . ∗ s ind ( inc ) ;

s t3=(n2 . / n3 ) . ∗ s t2 ;

ct2=sq r t (1− s t2 ˆ 2 ) ;

ct3=sq r t (1− s t3 ˆ 2 ) ;

r12=(n1 .∗ cosd ( inc )−n2 .∗ ct2 ) . / ( n1 .∗ cosd ( inc )+n2 .∗ ct2 ) ;

r23=(n2 .∗ ct2−n3 .∗ ct3 ) . / ( n2 .∗ ct2+n3 .∗ ct3 ) ;

l =500;

beta =4.∗180.∗n2 . ∗ ( t . / l ) . ∗ ct2 ;

Rs( c , d)=(( r12 ˆ2)+(2.∗ r12 .∗ r23 .∗ cosd ( beta ./2))+ r23 ˆ2 ) . /

(1+(2.∗ r12 .∗ r23 .∗ cosd ( beta . /2 ) )+( ( r23 ˆ 2 ) . ∗ ( r12 ˆ 2 ) ) ) ;

d=d+1;

end

c=c+1;

end

Appendix D

MATLAB program for plotting dispersion curves of anti-symmetric MDM

waveguide

c l e a r a l l

c l o s e a l l

c=3e17 ;

d=80;

x=ze ro s ( 1055 , 1 ) ;

y=ze ro s ( 1055 , 1 ) ;

omega=x l s r e ad ( ’D:\ Users \Revathy\Documents\MATLAB

\ eps . x lsx ’ , ’ Sheet1 ’ , ’ a2 : a2100 ’ ) ;

% omega=omega .∗ ( 1 e12 ) ;

epsxdp=x l s r e ad ( ’D:\ Users \Revathy\Documents\MATLAB

\ eps . x lsx ’ , ’ Sheet1 ’ , ’ b2 : b2100 ’ ) ;

epsxdpp=x l s r ead ( ’D:\ Users \Revathy\Documents\MATLAB

\ eps . x lsx ’ , ’ Sheet1 ’ , ’ e2 : e2100 ’ ) ;

epsxd=epsxdp+i .∗ epsxdpp ;

epszdp=x l s r ead ( ’D:\ Users \Revathy\Documents\MATLAB

\ eps . x lsx ’ , ’ Sheet1 ’ , ’ c2 : c2100 ’ ) ;

epszdpp=x l s r ead ( ’D:\ Users \Revathy\Documents\MATLAB

\ eps . x lsx ’ , ’ Sheet1 ’ , ’ f 2 : f2100 ’ ) ;

epszd=epszdp+i .∗ epszdpp ;

%c a l c u l a t i o n o f k0

98

99

k0=omega . / c ;

%k0=k0 ’ ;

%c a l c u l a t i o n o f eps meta l

% ep s i n f =3.5 ;

% omegap=1.3 e16 ;

% omegac=6e13 ;

e p s i n f =3.5 ;

omegap=1.3 e4 ;

omegac=6e1 ;

epsm=eps in f −((omegap ˆ2 ) . / ( omega . ∗ ( omega−i .∗ omegac ) ) ) ;

opt i ons = opt imset ( ’ Algorithm ’ , ’ Levenberg−Marquardt ’ ,

’ LargeScale ’ , ’ on ’ , ’ TolX ’ , 1 e−6);

%so l v i n g equat ion f o r c a l c u l a t i n g k wg

f o r n=1:2099

f=@(x ) tanh (2∗ s q r t ( ( ( ( x ˆ2 ) .∗ epszd (n ) ) . / ( epsxd (n ) ) )

−(( epszd (n ) . ∗ omega . ˆ 2 ) . / ( c ˆ 2 ) ) ) . ∗ d ) . . .

+(2 .∗ ( ( ( ( s q r t ( ( ( ( x ˆ2 ) .∗ epszd (n ) ) . / ( epsxd (n ) ) )

−(( epszd (n ) . ∗ omega . ˆ 2 ) . / ( c ˆ 2 ) ) ) . / epszd (n )) .ˆ2)+

( sq r t ( ( xˆ2−((omega . ˆ 2 ) . ∗ epsm(n ) )

. / ( c ˆ 2 ) ) ) . / epsm(n ) ) . ˆ 2 ) . . .

. ∗ ( ( ( s q r t ( ( xˆ2−((omega . ˆ 2 ) . ∗ epsm(n ) )

. / ( c ˆ 2 ) ) ) ) . ∗ ( s q r t ( ( ( ( x ˆ2 ) .∗ epszd (n ) )

. / ( epsxd (n)))−(( epszd (n ) . ∗ omega . ˆ 2 )

. / ( c ˆ 2 ) ) ) ) ) . / ( epsm(n ) . ∗ epszd (n ) ) ) ) . . .

. / ( ( ( ( ( s q r t ( ( xˆ2−((omega . ˆ 2 ) . ∗ epsm(n ) )

100

. / ( c ˆ 2 ) ) ) ) . ∗ ( s q r t ( ( ( ( x ˆ2 ) .∗ epszd (n ) )

. / ( epsxd (n)))−(( epszd (n ) . ∗ omega . ˆ 2 )

. / ( c ˆ 2 ) ) ) ) ) . / ( epsm(n ) . ∗ epszd (n ) ) ) . ˆ 2 ) . . .

+((( sq r t ( ( ( ( x ˆ2 ) .∗ epszd (n ) ) . / ( epsxd (n ) ) )

−(( epszd (n ) . ∗ omega . ˆ 2 ) . / ( c ˆ2 ) ) )

. / epszd (n ) ) . ˆ2 )+( sq r t ( ( xˆ2−((omega . ˆ 2 ) . ∗ epsm(n ) )

. / ( c ˆ 2 ) ) ) . / epsm(n ) ) . ˆ 2 ) . ˆ 2 ) ) ;

x (n)= f s o l v e ( f , 1 e−4, opt ions ) ;

% y(n)= f e v a l ( f , x (n ) ) ;

end

%ca l c u l a t i n g km and kd

%x=x ’ ;

% km=( sq r t ( epsm . ∗ ( k0 .ˆ2)−x . ˆ 2 ) ) ;

% kd=( sq r t ( epsd . ∗ ( k0 .ˆ2)−x . ˆ 2 ) ) ;

%P lo t t i ng d i s p e r s i o n curve and propagat ion l ength

x r e a l=r e a l ( x ) ;

y1=r e a l ( x ) . / r e a l ( k0 ) ;

p l o t ( r e a l ( y1 ) , omega ) ;

% y2=imag (x ) . / k0 ;

lp=abs ( 1 . / ( 2 . ∗ imag (x ) ) ) ;

p l o t ( lp , omega ) ;