T.Vuletić T.Vuletić ¹¹,, R. Žaja R. Žaja ¹¹,,²², M. Vukelić , M. Vukelić ¹¹, S.Tomić , S.Tomić ¹¹ and I. Sondi and I. Sondi ²²

tvuletic@ifs.hrtvuletic@ifs.hr ; www.ifs.hr/real_science ; www.ifs.hr/real_science

Low-frequency dielectric spectroscopy Low-frequency dielectric spectroscopy of aqueous solutionsof aqueous solutions

¹¹ , Zagreb, Croatia , Zagreb, Croatia

²² Institut Ruđer Bošković, Zagreb, Croatia Institut Ruđer Bošković, Zagreb, Croatia

Worldwide motivation: Worldwide motivation: Transport of electrical signals in bio-materials Transport of electrical signals in bio-materials on a molecular scale is of fundamental interest in the life scienceson a molecular scale is of fundamental interest in the life sciences

Our motivation: Our motivation: Counterion atmospheres condensed onto charged Counterion atmospheres condensed onto charged biopolymers strongly affect their physical propertiesbiopolymers strongly affect their physical propertiesand biological functions, but have been difficult to quantify and biological functions, but have been difficult to quantify experimentally.experimentally.

Our aim: Our aim: investigating dielectric relaxation in charged systems, investigating dielectric relaxation in charged systems, polyions and colloids, in aqueous environment of varying ionic strength polyions and colloids, in aqueous environment of varying ionic strength and pH and pH

MOTIVATION

POLYSTYRENE LATEX POLYSTYRENE LATEX Serva inc. & Interfacial Dynamics Co.

nominal particle sizes and concentrations: nominal particle sizes and concentrations: 178nm (5% vol.) 178nm (5% vol.) 196nm (10% vol.) 196nm (10% vol.) 820nm (10% vol.)820nm (10% vol.)

SAMPLES & MATERIALS

MODEL COLLOIDAL SYSTEM

Polystyrene particles are almost perfectly sphericalPolystyrene particles are almost perfectly spherical

latex is monodisperselatex is monodisperse

well-determined polarization responsewell-determined polarization response

TEM image:TEM image:latex sphereslatex spheres

Precision impedance analyzerPrecision impedance analyzer

Agilent 4294A: 40 Hz-110 MHzAgilent 4294A: 40 Hz-110 MHz

AgilentBNCs

Conductivity chamber for Conductivity chamber for aqueousaqueous samples:samples:

1.5- 20001.5- 2000S/cm; volume 50-200 S/cm; volume 50-200 LL

Reproducibility 1%, Long term (2 h) 2%Reproducibility 1%, Long term (2 h) 2%

Temperature Temperature

control unitcontrol unit::

00°° to 60 to 60°°CC

Stability: Stability:

±±10 mK10 mK

Pt

cham

ber

steelcasing

Pt

LOW-FREQUENCY DIELECTRIC SPECTROSCOPY

GN

aCl (

mS

)

0.01

0.1

1

10

100

f (Hz)101 102 103 104 105 106 107 108

CN

aCl (

pF)

100

101

102

103

104

105

10mM NaCl

0.05mM NaCl

empty chamber

• We measure complex conductivity components We measure complex conductivity components G(G() and ) and BB(()=)=CC(())**

=’()+i’’()

Y()= G()+iB()

From complex conductance to complex dielectric function

B.Saif et al., Biopolymers 31, 1171 (1991)

Resulting (G-GResulting (G-GNaClNaCl, C-C, C-CNaClNaCl) are converted ) are converted into complex dielectric functioninto complex dielectric function

0

'B

S

l

0

'' corrG Gl

S

•These are These are subtracted for (G, C) subtracted for (G, C) of background of background (reference) (reference) NaCl solution of NaCl solution of matching matching conductivity (conductivity (i.e.i.e. ionic strength)ionic strength)

(Hz)

102 103 104 105 106 107 108

''

10

100

1000 25 oCpolystyrene

latex820nm (10%vol.)

196nm (10%vol.)

178nm (5%vol.)

1

01

1

iHF∞

relaxation process strength = (0) - ∞

0 – central relaxation time

symmetric broadening of the relaxation time

distribution 1 -

generalized Debye function

FITS to a sum of two generalized Debye functions

HF mode: 2-20

1- 0.85-1

LF mode: 100-10001- 0.8-0.95

Results: Two Relaxation Modes in 1 kHz – 10 MHz range

820nm (10%vol.)

f (Hz)101 102 103 104 105 106 107 108

Gla

tex

- G

NaC

l ( S

)

0.1

1

10

100

1000

196nm (10%vol.)

178nm (5%vol.)

25 oCpolystyrene

latex

S. Havriliak and S. Negami, J.Polym.Sci.C 14, 99 (1966).

Electro-kinetics of Electrical Double Layer

S.S.Dukhin et al, Adv.Coll. Interface Sci. 13, 153 (1980)

R.W.O’Brian, J. Coll. Interface Sci 113, 81 (1986).

Counterions (Counterions (e.g. e.g. NaNa++, H, H++) after dissociation from functional groups are) after dissociation from functional groups are redistributed in the vicinity of redistributed in the vicinity of particle surface, screening the surface chargeparticle surface, screening the surface charge

ions from the electrolyte create eions from the electrolyte create electrical double layer with thickness lectrical double layer with thickness -1-1 on on the particle surfacethe particle surface

Under applied ac field Under applied ac field Counter-ion atmosphere around the particle Counter-ion atmosphere around the particle oscillates with the fieldoscillates with the field

Oscillations can be expected along two characteristic length scales: Oscillations can be expected along two characteristic length scales: -1-1 - Debye-H- Debye-Hüückel length & contour length of particle (~diameter, 2R)ckel length & contour length of particle (~diameter, 2R) two types of dielectric dispersion, two dielectric modes two types of dielectric dispersion, two dielectric modes

Counterions move diffusively:Counterions move diffusively:

Length scale, Length scale, LL is related to the is related to the

characteristic relaxation time, characteristic relaxation time,

of the dielectric modeof the dielectric mode

L= (L= (∙∙ D)D)1/21/2

LLF=2R

LHF=-1

2) LF mode: 1 kHz <0 < 70 kHz

DNA chain segments of random lengths placed in counter-ion atmosphere

Under applied ac field: broad relaxation modes due to oscillating counter-ions at different length and time scales

Persistence length, lP: 50nm and higher

1) Contour length; 0 < 1 kHz M. Sakamoto et al., Biopolymers 18, 2769 (1979)S.Takashima, J.Phys.Chem.70, 1372 (1966)

3) HF mode: 0.1 MHz <0 < 15 MHz

? Mesh size LHF c-0.5L

-1

Na+, Cl-

Lp

LHF

--

-

--

- - -

-

Origin of dielectric dispersion in DNA solutions

? Debye-Hückel length LHF = -1 I-0.5

5-45nm

HF mode: 10, 1- 0.8

LF mode: 100, 1- 0.8

Results: Two Relaxation Modes in 10 kHz – 10 MHz range

Worldwide motivation: Worldwide motivation: Transport of electrical signals in Transport of electrical signals in bio-materials on a molecular bio-materials on a molecular scale is of fundamental interest scale is of fundamental interest in the life sciencesin the life sciences

Our motivation: Our motivation: Counterion Counterion atmospheres condensed onto atmospheres condensed onto charged biopolymers strongly charged biopolymers strongly affect their physical propertiesaffect their physical propertiesand biological functions, but and biological functions, but have been difficult to quantify have been difficult to quantify experimentally.experimentally.

Our aim: Our aim: investigating investigating dielectric relaxation in charged dielectric relaxation in charged systems, polyions and colloids, systems, polyions and colloids, in aqueous environment of in aqueous environment of varying ionic strength and pH varying ionic strength and pH

MOTIVATION Experimental characterization of the Experimental characterization of the counter-ion atmospheres counter-ion atmospheres around around macromolecules/colloidal macromolecules/colloidal particlesparticles in in aqueous environmentaqueous environment is is essential essential

Low frequency dielectric spectroscopy Low frequency dielectric spectroscopy (LFDS) (LFDS) studies: studies: application specific and non-destructive application specific and non-destructive technique allowing detection and technique allowing detection and quantification of polarization response quantification of polarization response of charged systems in polar and non-of charged systems in polar and non-polar solvents. polar solvents.

LFDS is also well established in the LFDS is also well established in the solid state, for investigations of the solid state, for investigations of the collective electronic response in the collective electronic response in the low-dimensional synthetic materialslow-dimensional synthetic materials

N.Nandi et al., Chem.Rev.100, 2013 (2000)M. Sakamoto et al., Biopolymers 18, 2769 (1979)S.Bone et al., Biochymica et Biophysica Acta 1306, 93 (1996)R. Roldán-Toro and J.D. Solier J.Colloid & Interface Sci. 274, 76 (2004)

R.Das et al.,Phys.Rev.Lett.90, 188103 (2003)

R. Pethig “Dielectric & Electronic Properties of Biological Materials”,

Wiley & Sons, NY (1979).

A. K. Jonscher “Dielectric Relaxation in Solids”, Chelsea Dielectrics Press, London (1983);M. Pinteric et al., EPJB, (2001).

testing LFDS:testing LFDS: our technique is operable in 1kHz – 50 MHz range, due to our technique is operable in 1kHz – 50 MHz range, due to succesful removal of measurement artifacts, both at low and high succesful removal of measurement artifacts, both at low and high frequenciesfrequencies

CONCLUSIONS

latex – model system:latex – model system: we observed both we observed both theoretically expected dielectric modes theoretically expected dielectric modes

Future prospects

LFDS:LFDS: low-frequency limit should be lowered. Electrode polarization low-frequency limit should be lowered. Electrode polarization phenomenon could be suppressed in several known ways.phenomenon could be suppressed in several known ways.

Systems:Systems: Alongside systems with spherical Alongside systems with spherical geometry, systems of longitudinal geometry may geometry, systems of longitudinal geometry may be investigated – bio-polymers like DNA can be be investigated – bio-polymers like DNA can be characterized by several length scalescharacterized by several length scales

LLHFHF:: Debye-HDebye-Hüückelckel screening lengthscreening length – – -1-1

Characteristic length Characteristic length scale of the scale of the high-frequency modehigh-frequency mode

LLHF,LFHF,LF= (= (HF.LFHF.LFD)D)1/21/2 HF,LFHF,LF from experiments from experiments

D(D(NaNa++) = 1.5 ·10) = 1.5 ·10-9 -9 mm22/s/s

D(H+) = 9 ·10-9 m2/s

LLLLFF:: particle diameter –particle diameter –Characteristic length Characteristic length scale of the scale of the low-frequency modelow-frequency mode

Counterions: HCounterions: H++

(Diffusion constants from: CRC Handbook)

size [nm]

vol.% LF 0 LF

[s]

1- L [nm]

LLF [nm]

HF 0 HF

[s]

1- LHF [nm]

178 5% 100 3 0.78 70 165 22 0.011 0.85 10

196 10% 160 2.5 0.91 60 150 5 0.08 0.9 28

820 10% 2625 37.5 0.94 240 600 6 0.09 1 26

Results: Characteristic length scales & counterion species

size [nm]

vol.% S/cm

I= m

-1

[nm]

178 5% 40 0.33 17

196 10% 80 0.65 13

820 10% 54 0.45 15

– conductivity of latex solutionII - ionic strength of equivalent electrolyte solution - molar conductivityof equivalent NaCl electrolyte solution=12 S/Mm-1-1 – Debye Hückel length for a given ionic strength 1 10 /nm I mM