TUNABLE MECHANICAL PROPERTIES OF SELF-ASSEMBLED SWNTPOLYMER NANOCOMPOSITE FILMS FOR MEMS

D Zhang and T Cui Department of Mechanical Engineering University of Minnesota Minneapolis Minnesota USA

ABSTRACT

This paper presents layer-by-layer (LbL) self-assembled single-walled carbon nanotube (SWNT) polymer nanocomposite films with a large range of tunable mechanical properties characterized by a combinative approach of piezoelectric excitation and laser vibrometer measurement The Youngrsquos modulus of SWNTpolymer nanocomposites is tunable from hundreds to tens of GPa as a function of the SWNT volume fraction This tunability can serve as a benchmark to tailor the nanocomposite thin films for potential applications to MEMS and NEMS devices such as nanoswitches nanoresonators and biosensors INTRODUCTION

Single-walled carbon nanotubes (SWNTs) have been extensively investigated owing to their exceptional mechanical electrical optical thermal and chemical properties [1-2] SWNTs demonstrate remarkable Youngrsquos modulus of 1 TPa and tensile strength of over 60 GPa applicable to the design and reinforcement of SWNTpolymer nanocomposites [3] Recent advance revealed that the nanotube-reinforced polymer composites opened a pathway for versatile engineering materials to combine the desirable properties of SWNTs and polymers [4] However the poor dispersion of pristine SWNTs and the absence of structural property constitute the main obstacles for device applications [5] An alternative cost-effective approach layer-by-layer (LbL) self-assembly allows a sequential adsorption of nanometer monolayers of oppositely charged polyelectrolytes and nanoparticles to form a heterogeneous hierarchical membrane with a molecular-level control over the architecture It was very successful to form the cross-linked films with interfacial interactions between SWNTs and polymers through dense covalent bonding and polymer chains stiffening [6] Therefore the LbL assembly approach offers a promising way to yield excellent mechanical properties in nanotube-reinfoced polymer nanocomposites

To achieve the full potential this paper presents LbL self assembly of SWNTpolymer films with a variation of SWNT volume fraction to obtain a well-dispersed large volume fraction of functionalized SWNTs The solution-based sequential deposition process of the nanocomposite membranes was characterized using QCM technique from which the thickness and SWNT fractions were predicted The substrate a circular poly(vinylidene fluoride) (PVDF) film was actuated by a piezoelectric excitation A laser vibrometer was utilized to determine the vibration frequency shift due to the adsorption of SWNTpolymer films The Youngrsquos modulus was derived from the measured resonant frequencies in virtue of vibration model established for a

circular membrane Through experimental vibration testing and theoretical verification a large-scale tunability in Youngrsquos modulus of SWNTpolymer composite from several hundreds to tens of GPa as a function of the SWNT volume fraction was observed The measurement results show a very large magnitude reinforcement in Youngrsquos modulus much higher than other SWNTpolymer composites due to the layered structure and the high SWNT volume fraction This observed tunability can serve as a benchmark to tailor the design of nanocomposite thin films for potential applications to MEMS and NEMS devices

FABRICATION OF SELF-ASSEMBLED FILMS

Pristine SWNTs (50 microm long 11 nm in diameter and 21 gcm3 in density) were chemically functionalized with the concentrated acid (31 for 98 wt H2SO4 70 wt HNO3) at 110oC and stirred at 140 rmp for 1 hour followed by micropore membrane filtering and several rinsing by de-ionized water (DI water) The chemically treated SWNTs were negatively charged by carboxylic groups facilitating the uniformly dispersion of SWNTs into DI water Polyelectrolytes used for LbL assembly were 15 wt poly(diallylimethyammonium chloride) [PDDA (Sigma-Aldrich Inc) molecular weight (MW) of 200K-350K polycation] and 03 wt poly(sodium 4-styrenesulfonate) [PSS (Sigma-Aldrich Inc) MW of 70K polyanion] with 05 M NaCl in both for enhancing the ionic strength and polyions adsorption The substrate a circular poly(vinylidene fluoride) (PVDF) piezoelectric film was firmly bonded to a flat poly(methy1 methacrylate) (PMMA) supporting block for a free-standing membrane followed by hydrolyzing with 6 M NaOH aqueous solution for 20 min at 50oC After rinsing with DI water and drying in nitrogen blow (N2) two bi-layers of PDDAPSS were LbL self-assembled as precursor layers on the both sides of PVDF substrate for charge enhancement Followed by the alternative sequence of the immersion [(PDDAPSS)m(PDDASWNT)]n for double-side deposition where m represents the number of (PDDAPSS) bi-layers and n represents the number of iterative stacked (PDDAPSS)m(PDDASWNT) sub-layers Hereby m was designed for modulating the volume ratio between polymer and SWNT and n was designed for iterative stacked deposition of SWNTpolymer nanocomposites Schematic of the LbL self-assembly process of the multilayer film of [(PDDAPSS)m(PDDASWNT)]n is illustrated in Fig 1 and the sketch of double-side LbL assembled SWNTpolymer nanocomposite films together with the piezoelectric testing scheme is shown in Fig 2

978-1-4244-9634-111$2600 copy2011 IEEE 497 MEMS 2011 Cancun MEXICO January 23-27 2011

Fig1 Fabrication process of multilayer film [(PDDAPSS)m(PDDASWNT)]n

Fig 2 Sketch of LbL assembled SWNTpolymer nano- composite films along with the piezoelectric testing scheme STRUCTURE CHARACTERIZATION

The self-assembly process was characterized using a quartz crystal microbalance (QCM) which was extremely sensitive to capture the mass adsorption Gold-coated polished AT-cut quartz crystal with a fundamental frequency of 9 M Hz and an active oscillation area of 034 cm2 was used The self-assembled SWNT polymer multilayer films on the QCM crystal exploited the similar procedure as shown in Fig 1 First immerse the crystal into PDDA and PSS solution for two cycles to pre-charge the crystal surface followed by an alternative immersion of [(PDDAPSS)m(PDDASWNT)]n for given periods of time

The mass increased for LbL adsorption can be estimated from the frequency shift by using the Sauerbrey equation In our system a frequency decrease of 1 Hz corresponds to a mass increase of 188 ng The thickness (d in nm) of an adsorbed film on the crystal is given by

)()()()( 312 cmgngcmHzC

Hzfnmdf ρminussdotsdot

Δminus= (1)

where fC = 0181 Hzcm2ng-1 is the sensitivity factor of the

used crystal fΔ is the frequency shift from QCM ρ is the density of deposited film The volume fraction of SWNTs in the multilayer films can be calculated as

polyswnt

swntswntf tt

tV

Vv

+== (2)

where is the volume fraction and is the thickness of SWNT and polymer layers respectively

fv swntt polyt

Fig 3 illustrates the calculated thickness of polymeric multilayer of (PDDAPSS)mPDDA and SWNT layer in the self-assembled film of [(PDDAPSS)m (PDDASWNT)]n The average thickness of each stacked sub-layers of (PDDAPSS)m(PDDASWNT) and the SWNT volume fraction as a function of m are plotted in Fig 4 The error bars represent a standard deviation of experimental data and the solid line is a fit to the points measured Film thickness and SWNT volume fraction variation can be precisely modulated by adjusting the cycle number m of polymer bi-layers PDDAPSS

Fig3 Film thickness for [(PDDAPSS)m (PDDASWNT)]n with varied cycle numbers n

498

Fig4 Average thickness (a) and SWNT volume fraction (b) of each stacked sub-layers [(PDDAPSS)m( PDDASWNT)] with varying m

CHARACTERIZATION OF YOUNGrsquoS MODULUS

The governing equations of a circular diaphragm clamped at the boundary under the stiffness-tension (ST) effect is given by [7]

0)11()11( 2

2

2

2

22

22

2

2

22

2

=partpart

+partpart

+partpart

+partpart

minuspartpart

+partpart

+partpart

twhw

rrrrTw

rrrrD ρ

θθ (3)

where is the bending stiffness T is the pre-tension and E

)]1(12[ 23 vEhD minus=v h ρ are the Youngrsquos modulus

Poissonrsquos ratio thickness and density of the membrane respectively w is the transverse deflection t is the time and )( θr are polar coordinates

Considering the contribution of stiffness-tension (ST) to the resonance frequencies we defined ST ratio as λ=TR2(1468D) and the natural frequency f is obtained as

)1(341

21

2

2

22

2

2

vEh

RTD

RhRf m

p

minus=

⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

ρπκα

αρπ

(4)

where αp and αm are the vibration constants of a plate and a membrane respectively and the frequency coefficient κ is represented through the least-square polynomial fitting (LSPF) as

22104617512403-2106417892-04584 2345 +++= λλλλλκ (5) The effective Youngrsquos modulus of the composite

diaphragms with SWNTpolymer nanocomposites on both sides are derived from the resonant frequencies using

22

2222

)()1(3)4(

hvfRE

λκρπ minussdot

= (6)

where hhh sspp )( ρρρ += sp hhh += pρ and are the

density and thickness of PVDF film sh

sρ and are the density and thickness of SWNTpolymer composites The Youngrsquos modulus of SWNTpolymer nanocomposites are determined by the empirical mixing rule [8] as

sh

)2()( dnhEEhE pps minus= (7) where and are the effective Youngrsquos modulus of

PVDF film and SWNTpolymer composites pE sE

d and are

the average thickness and cycle numbers of stacked sub-layers for the SWNTpolymer films

n

A highly sensitive laser vibrometer was utilized to determine the resonance frequency shift from the deposition of SWNTpolymer film The experimental setup consisting of a piezoelectric exciter and a laser-scanning vibrometer is shown in Fig5 A sinusoidal harmonic excitation was applied to drive the PVDF film actuator and the wavelength of He-Ne laser used 633 nm The vibration magnitude was optically captured by the photodetector and transformed into an electrical signal for the processing of computer data-acquisition system Through experimental vibration testing and theoretical verification the Youngrsquos modulus determined for a series of SWNTpolymer nanocomposite films with a variation of SWNT volume fraction is illustrated in Fig6 A large-scale tunability in Youngrsquos modulus of SWNTpolymer nanocomposite films from 46156 plusmn 7278 to 3576 plusmn555 GPa along with the SWNT volume fraction decreased from 7235 plusmn 814 to 1478 plusmn 089 is observed It clearly shows a significant dependency of the large-scale tunable Youngrsquos modulus of SWNT-based nanocomposites on the SWNT volume fraction

Fig5 Schematic diagram of experiment setup for the measurement of frequency response

Fig6 Youngrsquos modulus of SWNTpolymer nanocomposites as a function of an SWNT volume fraction

499

RESULTS AND DISCUSSION

To probe the structure-property relationship of layered nanotube-reinforced nanocomposite conventional mixture models such as Cox and Halpin-Tsai models are applied to results discussion For non-aligned short fibers-reinforced composite the matrix-fiber stress transfer mechanism is relatively well described by Cox [9] as

)1( ntmntntloc vEvEE minus+= ηη (8)

ntnt

ntntl dla

dla

)tanh(1sdotsdot

minus=η (9)

)ln(23

ntnt

m

vEEa minus

= (10)

where cE ntE and represent the Youngrsquos modulus of the composite SWNT and polymer matrix respectively and is the SWNT volume fraction The Youngrsquos modulus of SWNTs has been previously measured of 1 TPa and hereby take of 4000 is the aspect ratio for the nanotubes

mE

ntv

mnt EE ntnt dl

oη and lη are the orientation and length efficiency factors respectively In our case the length efficiency factor

lη is very close to 1 for a high aspect ratio of SWNTs (gt100) Based on this model orientation efficiency factor oη of 024-064 were determined

For Halpin-Tsai model the composite modulus with SWNT randomly oriented in polymer matrix is given by [10]

⎥⎦

⎤⎢⎣

⎡minus+

+minus

+=

ntt

ntt

ntl

ntlntntmc V

VV

VdlEE

ηη

ηη

121

85

1)(21

83 (11)

)(2)(1)(

ntntmnt

mntl dlEE

EE+

minus=η (12)

2)(1)(

+minus

=mnt

mntt EE

EEη (13)

As cE ntE and mE ntv are known in this model the aspect ratio of the reinforcing nanotubes can be obtained by model fitting The theoretical curve for Cox model and Halpin-Tsai model are plotted by the dotted and dashed lines in Fig 7 respectively It shows that the Cox model and H-T model can fit some data well at low volume fractions but fail to explain the structure-property regime in nanoscale at a high SWNT fraction ratio Using a third-order parametric model for composite modulus in the form

ntnt dl

)1()135510716904006( 2ntmntntntntc vEvEvvE minus++minus= (14)

where is named as reinforcement efficiency factor The model fitting curve with the solid line is shown in Fig 7 The curve fit validates the the proposed model A third-order reinforcement efficiency factor is associated with nonlinear behavior in length and orientation of the SWNTs as reinforcing fibers

2135510716904006 ntnt vv +minus=h

CONCLUSION

Nanotube-reinforced polymer is currently the subject of extensive research worldwide The layer-by-layer self

assembly offers a way for nanocomposite materials to realize their true potential for MEMS and NEMS The Youngrsquos modulus of the self-assembled SWNTpolymer composite films was characterized using a combinative approach of piezoelectric excitation together with laser measurement A large-scale tunability in Youngrsquos modulus of SWNTpolymer nanocomposite as a function of the SWNT volume fraction was observed Such significant enhancement results from an effective loading of SWNTs to the polymeric matrix SWNT-polymer reinforcement through dense bondingand the polymer chains stiffening Conventional mixture model such as Cox and Halpin-Tsai model fail to explain the structure-property regime in nanoscale at a high volume fraction ratio of SWNTpolymer This observed large tunability in Youngrsquos modulus can serve as a benchmark to tailor the design of MEMS and NEMS devices such as nanoswitches nanoresonators and biosensors

ACKNOWLEDGEMENT

This work was partially supported by the Minnesota Partnership Program and the Joint Doctoral Training Program at South China University of Technology sponsored by China Scholarship Council REFERENCES [1] R H Baughman A A Zakhidov W A de Heer

ldquoCarbon Nanotubes-the Route toward Applicationsrdquo Science vol 279 pp 787-792 2002

[2] H D Wagner ldquoNanocomposites Paving the Way to Stronger Materialsrdquo Nat Nanotechnol vol 2 pp 742-744 2007

[3] J N Coleman U Khan Y K Gunrsquoko ldquoMechanical Reinforcement of Polymers Using Carbon Nanotubesrdquo Adv Mater vol 18 pp 689-706 2006

[4] A CBalaza T Emrick T P Russell ldquoNanoparticle Polymer Composites Where Two Small Worlds Meetrdquo Science vol 314 pp 1107-1110 2006

[5] P Podsiadlo A K Kaushik E M Arruda et al ldquoUltrastrong and Stiff Layered Polymer Nanocompositesrdquo Science vol 318 pp 80-83 2007

[6] J H Rouse P T Lillehei ldquoElectrostatic Assembly of PolymerSingle Walled Carbon Nanotube Multilayer Filmsrdquo Nano Lett vol 3 pp 59-62 2003

[7] T wah Vibration of Circular Plates J Acoust Soc Am vol 34 pp 275-281 1962

[8] Q M Wang L E Cross ldquoDetermination of Youngrsquos Modulus of the Reduced Layer of A Piezoelectric Rainbow Actuatorrdquo J Appl Phys vol 83 pp 5358-5363 1998

[9] H L Cox ldquoThe Elasticity and Strength of Paper and Other Fibrous Materialsrdquo Brit J appl Phys vol 3 pp 72-79 1952

[10] D Qian E C Dickey R Andrews T Rantell ldquoLoad transfer and deformation mechanisms in carbon nanotube-polystyrene compositesrdquo Appl Phys Lett vol76 pp 2868-2870 2000

500

Fig1 Fabrication process of multilayer film [(PDDAPSS)m(PDDASWNT)]n

Fig 2 Sketch of LbL assembled SWNTpolymer nano- composite films along with the piezoelectric testing scheme STRUCTURE CHARACTERIZATION

The self-assembly process was characterized using a quartz crystal microbalance (QCM) which was extremely sensitive to capture the mass adsorption Gold-coated polished AT-cut quartz crystal with a fundamental frequency of 9 M Hz and an active oscillation area of 034 cm2 was used The self-assembled SWNT polymer multilayer films on the QCM crystal exploited the similar procedure as shown in Fig 1 First immerse the crystal into PDDA and PSS solution for two cycles to pre-charge the crystal surface followed by an alternative immersion of [(PDDAPSS)m(PDDASWNT)]n for given periods of time

The mass increased for LbL adsorption can be estimated from the frequency shift by using the Sauerbrey equation In our system a frequency decrease of 1 Hz corresponds to a mass increase of 188 ng The thickness (d in nm) of an adsorbed film on the crystal is given by

)()()()( 312 cmgngcmHzC

Hzfnmdf ρminussdotsdot

Δminus= (1)

where fC = 0181 Hzcm2ng-1 is the sensitivity factor of the

used crystal fΔ is the frequency shift from QCM ρ is the density of deposited film The volume fraction of SWNTs in the multilayer films can be calculated as

polyswnt

swntswntf tt

tV

Vv

+== (2)

where is the volume fraction and is the thickness of SWNT and polymer layers respectively

fv swntt polyt

Fig 3 illustrates the calculated thickness of polymeric multilayer of (PDDAPSS)mPDDA and SWNT layer in the self-assembled film of [(PDDAPSS)m (PDDASWNT)]n The average thickness of each stacked sub-layers of (PDDAPSS)m(PDDASWNT) and the SWNT volume fraction as a function of m are plotted in Fig 4 The error bars represent a standard deviation of experimental data and the solid line is a fit to the points measured Film thickness and SWNT volume fraction variation can be precisely modulated by adjusting the cycle number m of polymer bi-layers PDDAPSS

Fig3 Film thickness for [(PDDAPSS)m (PDDASWNT)]n with varied cycle numbers n

498

Fig4 Average thickness (a) and SWNT volume fraction (b) of each stacked sub-layers [(PDDAPSS)m( PDDASWNT)] with varying m

CHARACTERIZATION OF YOUNGrsquoS MODULUS

The governing equations of a circular diaphragm clamped at the boundary under the stiffness-tension (ST) effect is given by [7]

0)11()11( 2

2

2

2

22

22

2

2

22

2

=partpart

+partpart

+partpart

+partpart

minuspartpart

+partpart

+partpart

twhw

rrrrTw

rrrrD ρ

θθ (3)

where is the bending stiffness T is the pre-tension and E

)]1(12[ 23 vEhD minus=v h ρ are the Youngrsquos modulus

Poissonrsquos ratio thickness and density of the membrane respectively w is the transverse deflection t is the time and )( θr are polar coordinates

Considering the contribution of stiffness-tension (ST) to the resonance frequencies we defined ST ratio as λ=TR2(1468D) and the natural frequency f is obtained as

)1(341

21

2

2

22

2

2

vEh

RTD

RhRf m

p

minus=

⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

ρπκα

αρπ

(4)

where αp and αm are the vibration constants of a plate and a membrane respectively and the frequency coefficient κ is represented through the least-square polynomial fitting (LSPF) as

22104617512403-2106417892-04584 2345 +++= λλλλλκ (5) The effective Youngrsquos modulus of the composite

diaphragms with SWNTpolymer nanocomposites on both sides are derived from the resonant frequencies using

22

2222

)()1(3)4(

hvfRE

λκρπ minussdot

= (6)

where hhh sspp )( ρρρ += sp hhh += pρ and are the

density and thickness of PVDF film sh

sρ and are the density and thickness of SWNTpolymer composites The Youngrsquos modulus of SWNTpolymer nanocomposites are determined by the empirical mixing rule [8] as

sh

)2()( dnhEEhE pps minus= (7) where and are the effective Youngrsquos modulus of

PVDF film and SWNTpolymer composites pE sE

d and are

the average thickness and cycle numbers of stacked sub-layers for the SWNTpolymer films

n

A highly sensitive laser vibrometer was utilized to determine the resonance frequency shift from the deposition of SWNTpolymer film The experimental setup consisting of a piezoelectric exciter and a laser-scanning vibrometer is shown in Fig5 A sinusoidal harmonic excitation was applied to drive the PVDF film actuator and the wavelength of He-Ne laser used 633 nm The vibration magnitude was optically captured by the photodetector and transformed into an electrical signal for the processing of computer data-acquisition system Through experimental vibration testing and theoretical verification the Youngrsquos modulus determined for a series of SWNTpolymer nanocomposite films with a variation of SWNT volume fraction is illustrated in Fig6 A large-scale tunability in Youngrsquos modulus of SWNTpolymer nanocomposite films from 46156 plusmn 7278 to 3576 plusmn555 GPa along with the SWNT volume fraction decreased from 7235 plusmn 814 to 1478 plusmn 089 is observed It clearly shows a significant dependency of the large-scale tunable Youngrsquos modulus of SWNT-based nanocomposites on the SWNT volume fraction

Fig5 Schematic diagram of experiment setup for the measurement of frequency response

Fig6 Youngrsquos modulus of SWNTpolymer nanocomposites as a function of an SWNT volume fraction

499

RESULTS AND DISCUSSION

To probe the structure-property relationship of layered nanotube-reinforced nanocomposite conventional mixture models such as Cox and Halpin-Tsai models are applied to results discussion For non-aligned short fibers-reinforced composite the matrix-fiber stress transfer mechanism is relatively well described by Cox [9] as

)1( ntmntntloc vEvEE minus+= ηη (8)

ntnt

ntntl dla

dla

)tanh(1sdotsdot

minus=η (9)

)ln(23

ntnt

m

vEEa minus

= (10)

where cE ntE and represent the Youngrsquos modulus of the composite SWNT and polymer matrix respectively and is the SWNT volume fraction The Youngrsquos modulus of SWNTs has been previously measured of 1 TPa and hereby take of 4000 is the aspect ratio for the nanotubes

mE

ntv

mnt EE ntnt dl

oη and lη are the orientation and length efficiency factors respectively In our case the length efficiency factor

lη is very close to 1 for a high aspect ratio of SWNTs (gt100) Based on this model orientation efficiency factor oη of 024-064 were determined

For Halpin-Tsai model the composite modulus with SWNT randomly oriented in polymer matrix is given by [10]

⎥⎦

⎤⎢⎣

⎡minus+

+minus

+=

ntt

ntt

ntl

ntlntntmc V

VV

VdlEE

ηη

ηη

121

85

1)(21

83 (11)

)(2)(1)(

ntntmnt

mntl dlEE

EE+

minus=η (12)

2)(1)(

+minus

=mnt

mntt EE

EEη (13)

As cE ntE and mE ntv are known in this model the aspect ratio of the reinforcing nanotubes can be obtained by model fitting The theoretical curve for Cox model and Halpin-Tsai model are plotted by the dotted and dashed lines in Fig 7 respectively It shows that the Cox model and H-T model can fit some data well at low volume fractions but fail to explain the structure-property regime in nanoscale at a high SWNT fraction ratio Using a third-order parametric model for composite modulus in the form

ntnt dl

)1()135510716904006( 2ntmntntntntc vEvEvvE minus++minus= (14)

where is named as reinforcement efficiency factor The model fitting curve with the solid line is shown in Fig 7 The curve fit validates the the proposed model A third-order reinforcement efficiency factor is associated with nonlinear behavior in length and orientation of the SWNTs as reinforcing fibers

2135510716904006 ntnt vv +minus=h

CONCLUSION

Nanotube-reinforced polymer is currently the subject of extensive research worldwide The layer-by-layer self

assembly offers a way for nanocomposite materials to realize their true potential for MEMS and NEMS The Youngrsquos modulus of the self-assembled SWNTpolymer composite films was characterized using a combinative approach of piezoelectric excitation together with laser measurement A large-scale tunability in Youngrsquos modulus of SWNTpolymer nanocomposite as a function of the SWNT volume fraction was observed Such significant enhancement results from an effective loading of SWNTs to the polymeric matrix SWNT-polymer reinforcement through dense bondingand the polymer chains stiffening Conventional mixture model such as Cox and Halpin-Tsai model fail to explain the structure-property regime in nanoscale at a high volume fraction ratio of SWNTpolymer This observed large tunability in Youngrsquos modulus can serve as a benchmark to tailor the design of MEMS and NEMS devices such as nanoswitches nanoresonators and biosensors

ACKNOWLEDGEMENT

This work was partially supported by the Minnesota Partnership Program and the Joint Doctoral Training Program at South China University of Technology sponsored by China Scholarship Council REFERENCES [1] R H Baughman A A Zakhidov W A de Heer

ldquoCarbon Nanotubes-the Route toward Applicationsrdquo Science vol 279 pp 787-792 2002

[2] H D Wagner ldquoNanocomposites Paving the Way to Stronger Materialsrdquo Nat Nanotechnol vol 2 pp 742-744 2007

[3] J N Coleman U Khan Y K Gunrsquoko ldquoMechanical Reinforcement of Polymers Using Carbon Nanotubesrdquo Adv Mater vol 18 pp 689-706 2006

[4] A CBalaza T Emrick T P Russell ldquoNanoparticle Polymer Composites Where Two Small Worlds Meetrdquo Science vol 314 pp 1107-1110 2006

[5] P Podsiadlo A K Kaushik E M Arruda et al ldquoUltrastrong and Stiff Layered Polymer Nanocompositesrdquo Science vol 318 pp 80-83 2007

[6] J H Rouse P T Lillehei ldquoElectrostatic Assembly of PolymerSingle Walled Carbon Nanotube Multilayer Filmsrdquo Nano Lett vol 3 pp 59-62 2003

[7] T wah Vibration of Circular Plates J Acoust Soc Am vol 34 pp 275-281 1962

[8] Q M Wang L E Cross ldquoDetermination of Youngrsquos Modulus of the Reduced Layer of A Piezoelectric Rainbow Actuatorrdquo J Appl Phys vol 83 pp 5358-5363 1998

[9] H L Cox ldquoThe Elasticity and Strength of Paper and Other Fibrous Materialsrdquo Brit J appl Phys vol 3 pp 72-79 1952

[10] D Qian E C Dickey R Andrews T Rantell ldquoLoad transfer and deformation mechanisms in carbon nanotube-polystyrene compositesrdquo Appl Phys Lett vol76 pp 2868-2870 2000

500

Fig4 Average thickness (a) and SWNT volume fraction (b) of each stacked sub-layers [(PDDAPSS)m( PDDASWNT)] with varying m

CHARACTERIZATION OF YOUNGrsquoS MODULUS

The governing equations of a circular diaphragm clamped at the boundary under the stiffness-tension (ST) effect is given by [7]

0)11()11( 2

2

2

2

22

22

2

2

22

2

=partpart

+partpart

+partpart

+partpart

minuspartpart

+partpart

+partpart

twhw

rrrrTw

rrrrD ρ

θθ (3)

where is the bending stiffness T is the pre-tension and E

)]1(12[ 23 vEhD minus=v h ρ are the Youngrsquos modulus

Poissonrsquos ratio thickness and density of the membrane respectively w is the transverse deflection t is the time and )( θr are polar coordinates

Considering the contribution of stiffness-tension (ST) to the resonance frequencies we defined ST ratio as λ=TR2(1468D) and the natural frequency f is obtained as

)1(341

21

2

2

22

2

2

vEh

RTD

RhRf m

p

minus=

⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

ρπκα

αρπ

(4)

where αp and αm are the vibration constants of a plate and a membrane respectively and the frequency coefficient κ is represented through the least-square polynomial fitting (LSPF) as

22104617512403-2106417892-04584 2345 +++= λλλλλκ (5) The effective Youngrsquos modulus of the composite

diaphragms with SWNTpolymer nanocomposites on both sides are derived from the resonant frequencies using

22

2222

)()1(3)4(

hvfRE

λκρπ minussdot

= (6)

where hhh sspp )( ρρρ += sp hhh += pρ and are the

density and thickness of PVDF film sh

sρ and are the density and thickness of SWNTpolymer composites The Youngrsquos modulus of SWNTpolymer nanocomposites are determined by the empirical mixing rule [8] as

sh

)2()( dnhEEhE pps minus= (7) where and are the effective Youngrsquos modulus of

PVDF film and SWNTpolymer composites pE sE

d and are

the average thickness and cycle numbers of stacked sub-layers for the SWNTpolymer films

n

A highly sensitive laser vibrometer was utilized to determine the resonance frequency shift from the deposition of SWNTpolymer film The experimental setup consisting of a piezoelectric exciter and a laser-scanning vibrometer is shown in Fig5 A sinusoidal harmonic excitation was applied to drive the PVDF film actuator and the wavelength of He-Ne laser used 633 nm The vibration magnitude was optically captured by the photodetector and transformed into an electrical signal for the processing of computer data-acquisition system Through experimental vibration testing and theoretical verification the Youngrsquos modulus determined for a series of SWNTpolymer nanocomposite films with a variation of SWNT volume fraction is illustrated in Fig6 A large-scale tunability in Youngrsquos modulus of SWNTpolymer nanocomposite films from 46156 plusmn 7278 to 3576 plusmn555 GPa along with the SWNT volume fraction decreased from 7235 plusmn 814 to 1478 plusmn 089 is observed It clearly shows a significant dependency of the large-scale tunable Youngrsquos modulus of SWNT-based nanocomposites on the SWNT volume fraction

Fig5 Schematic diagram of experiment setup for the measurement of frequency response

Fig6 Youngrsquos modulus of SWNTpolymer nanocomposites as a function of an SWNT volume fraction

499

RESULTS AND DISCUSSION

To probe the structure-property relationship of layered nanotube-reinforced nanocomposite conventional mixture models such as Cox and Halpin-Tsai models are applied to results discussion For non-aligned short fibers-reinforced composite the matrix-fiber stress transfer mechanism is relatively well described by Cox [9] as

)1( ntmntntloc vEvEE minus+= ηη (8)

ntnt

ntntl dla

dla

)tanh(1sdotsdot

minus=η (9)

)ln(23

ntnt

m

vEEa minus

= (10)

where cE ntE and represent the Youngrsquos modulus of the composite SWNT and polymer matrix respectively and is the SWNT volume fraction The Youngrsquos modulus of SWNTs has been previously measured of 1 TPa and hereby take of 4000 is the aspect ratio for the nanotubes

mE

ntv

mnt EE ntnt dl

oη and lη are the orientation and length efficiency factors respectively In our case the length efficiency factor

lη is very close to 1 for a high aspect ratio of SWNTs (gt100) Based on this model orientation efficiency factor oη of 024-064 were determined

For Halpin-Tsai model the composite modulus with SWNT randomly oriented in polymer matrix is given by [10]

⎥⎦

⎤⎢⎣

⎡minus+

+minus

+=

ntt

ntt

ntl

ntlntntmc V

VV

VdlEE

ηη

ηη

121

85

1)(21

83 (11)

)(2)(1)(

ntntmnt

mntl dlEE

EE+

minus=η (12)

2)(1)(

+minus

=mnt

mntt EE

EEη (13)

As cE ntE and mE ntv are known in this model the aspect ratio of the reinforcing nanotubes can be obtained by model fitting The theoretical curve for Cox model and Halpin-Tsai model are plotted by the dotted and dashed lines in Fig 7 respectively It shows that the Cox model and H-T model can fit some data well at low volume fractions but fail to explain the structure-property regime in nanoscale at a high SWNT fraction ratio Using a third-order parametric model for composite modulus in the form

ntnt dl

)1()135510716904006( 2ntmntntntntc vEvEvvE minus++minus= (14)

where is named as reinforcement efficiency factor The model fitting curve with the solid line is shown in Fig 7 The curve fit validates the the proposed model A third-order reinforcement efficiency factor is associated with nonlinear behavior in length and orientation of the SWNTs as reinforcing fibers

2135510716904006 ntnt vv +minus=h

CONCLUSION

Nanotube-reinforced polymer is currently the subject of extensive research worldwide The layer-by-layer self

assembly offers a way for nanocomposite materials to realize their true potential for MEMS and NEMS The Youngrsquos modulus of the self-assembled SWNTpolymer composite films was characterized using a combinative approach of piezoelectric excitation together with laser measurement A large-scale tunability in Youngrsquos modulus of SWNTpolymer nanocomposite as a function of the SWNT volume fraction was observed Such significant enhancement results from an effective loading of SWNTs to the polymeric matrix SWNT-polymer reinforcement through dense bondingand the polymer chains stiffening Conventional mixture model such as Cox and Halpin-Tsai model fail to explain the structure-property regime in nanoscale at a high volume fraction ratio of SWNTpolymer This observed large tunability in Youngrsquos modulus can serve as a benchmark to tailor the design of MEMS and NEMS devices such as nanoswitches nanoresonators and biosensors

ACKNOWLEDGEMENT

This work was partially supported by the Minnesota Partnership Program and the Joint Doctoral Training Program at South China University of Technology sponsored by China Scholarship Council REFERENCES [1] R H Baughman A A Zakhidov W A de Heer

ldquoCarbon Nanotubes-the Route toward Applicationsrdquo Science vol 279 pp 787-792 2002

[2] H D Wagner ldquoNanocomposites Paving the Way to Stronger Materialsrdquo Nat Nanotechnol vol 2 pp 742-744 2007

[3] J N Coleman U Khan Y K Gunrsquoko ldquoMechanical Reinforcement of Polymers Using Carbon Nanotubesrdquo Adv Mater vol 18 pp 689-706 2006

[4] A CBalaza T Emrick T P Russell ldquoNanoparticle Polymer Composites Where Two Small Worlds Meetrdquo Science vol 314 pp 1107-1110 2006

[5] P Podsiadlo A K Kaushik E M Arruda et al ldquoUltrastrong and Stiff Layered Polymer Nanocompositesrdquo Science vol 318 pp 80-83 2007

[6] J H Rouse P T Lillehei ldquoElectrostatic Assembly of PolymerSingle Walled Carbon Nanotube Multilayer Filmsrdquo Nano Lett vol 3 pp 59-62 2003

[7] T wah Vibration of Circular Plates J Acoust Soc Am vol 34 pp 275-281 1962

[8] Q M Wang L E Cross ldquoDetermination of Youngrsquos Modulus of the Reduced Layer of A Piezoelectric Rainbow Actuatorrdquo J Appl Phys vol 83 pp 5358-5363 1998

[9] H L Cox ldquoThe Elasticity and Strength of Paper and Other Fibrous Materialsrdquo Brit J appl Phys vol 3 pp 72-79 1952

[10] D Qian E C Dickey R Andrews T Rantell ldquoLoad transfer and deformation mechanisms in carbon nanotube-polystyrene compositesrdquo Appl Phys Lett vol76 pp 2868-2870 2000

500

RESULTS AND DISCUSSION

To probe the structure-property relationship of layered nanotube-reinforced nanocomposite conventional mixture models such as Cox and Halpin-Tsai models are applied to results discussion For non-aligned short fibers-reinforced composite the matrix-fiber stress transfer mechanism is relatively well described by Cox [9] as

)1( ntmntntloc vEvEE minus+= ηη (8)

ntnt

ntntl dla

dla

)tanh(1sdotsdot

minus=η (9)

)ln(23

ntnt

m

vEEa minus

= (10)

where cE ntE and represent the Youngrsquos modulus of the composite SWNT and polymer matrix respectively and is the SWNT volume fraction The Youngrsquos modulus of SWNTs has been previously measured of 1 TPa and hereby take of 4000 is the aspect ratio for the nanotubes

mE

ntv

mnt EE ntnt dl

oη and lη are the orientation and length efficiency factors respectively In our case the length efficiency factor

lη is very close to 1 for a high aspect ratio of SWNTs (gt100) Based on this model orientation efficiency factor oη of 024-064 were determined

For Halpin-Tsai model the composite modulus with SWNT randomly oriented in polymer matrix is given by [10]

⎥⎦

⎤⎢⎣

⎡minus+

+minus

+=

ntt

ntt

ntl

ntlntntmc V

VV

VdlEE

ηη

ηη

121

85

1)(21

83 (11)

)(2)(1)(

ntntmnt

mntl dlEE

EE+

minus=η (12)

2)(1)(

+minus

=mnt

mntt EE

EEη (13)

As cE ntE and mE ntv are known in this model the aspect ratio of the reinforcing nanotubes can be obtained by model fitting The theoretical curve for Cox model and Halpin-Tsai model are plotted by the dotted and dashed lines in Fig 7 respectively It shows that the Cox model and H-T model can fit some data well at low volume fractions but fail to explain the structure-property regime in nanoscale at a high SWNT fraction ratio Using a third-order parametric model for composite modulus in the form

ntnt dl

)1()135510716904006( 2ntmntntntntc vEvEvvE minus++minus= (14)

where is named as reinforcement efficiency factor The model fitting curve with the solid line is shown in Fig 7 The curve fit validates the the proposed model A third-order reinforcement efficiency factor is associated with nonlinear behavior in length and orientation of the SWNTs as reinforcing fibers

2135510716904006 ntnt vv +minus=h

CONCLUSION

Nanotube-reinforced polymer is currently the subject of extensive research worldwide The layer-by-layer self

assembly offers a way for nanocomposite materials to realize their true potential for MEMS and NEMS The Youngrsquos modulus of the self-assembled SWNTpolymer composite films was characterized using a combinative approach of piezoelectric excitation together with laser measurement A large-scale tunability in Youngrsquos modulus of SWNTpolymer nanocomposite as a function of the SWNT volume fraction was observed Such significant enhancement results from an effective loading of SWNTs to the polymeric matrix SWNT-polymer reinforcement through dense bondingand the polymer chains stiffening Conventional mixture model such as Cox and Halpin-Tsai model fail to explain the structure-property regime in nanoscale at a high volume fraction ratio of SWNTpolymer This observed large tunability in Youngrsquos modulus can serve as a benchmark to tailor the design of MEMS and NEMS devices such as nanoswitches nanoresonators and biosensors

ACKNOWLEDGEMENT

This work was partially supported by the Minnesota Partnership Program and the Joint Doctoral Training Program at South China University of Technology sponsored by China Scholarship Council REFERENCES [1] R H Baughman A A Zakhidov W A de Heer

ldquoCarbon Nanotubes-the Route toward Applicationsrdquo Science vol 279 pp 787-792 2002

[2] H D Wagner ldquoNanocomposites Paving the Way to Stronger Materialsrdquo Nat Nanotechnol vol 2 pp 742-744 2007

[3] J N Coleman U Khan Y K Gunrsquoko ldquoMechanical Reinforcement of Polymers Using Carbon Nanotubesrdquo Adv Mater vol 18 pp 689-706 2006

[4] A CBalaza T Emrick T P Russell ldquoNanoparticle Polymer Composites Where Two Small Worlds Meetrdquo Science vol 314 pp 1107-1110 2006

[5] P Podsiadlo A K Kaushik E M Arruda et al ldquoUltrastrong and Stiff Layered Polymer Nanocompositesrdquo Science vol 318 pp 80-83 2007

[6] J H Rouse P T Lillehei ldquoElectrostatic Assembly of PolymerSingle Walled Carbon Nanotube Multilayer Filmsrdquo Nano Lett vol 3 pp 59-62 2003

[7] T wah Vibration of Circular Plates J Acoust Soc Am vol 34 pp 275-281 1962

[8] Q M Wang L E Cross ldquoDetermination of Youngrsquos Modulus of the Reduced Layer of A Piezoelectric Rainbow Actuatorrdquo J Appl Phys vol 83 pp 5358-5363 1998

[9] H L Cox ldquoThe Elasticity and Strength of Paper and Other Fibrous Materialsrdquo Brit J appl Phys vol 3 pp 72-79 1952

[10] D Qian E C Dickey R Andrews T Rantell ldquoLoad transfer and deformation mechanisms in carbon nanotube-polystyrene compositesrdquo Appl Phys Lett vol76 pp 2868-2870 2000

500