T.Vuletić ¹, R. Žaja ¹, ², M. Vukelić ¹, S.Tomić ¹ and I. Sondi ² ; Low-frequency dielectric spectroscopy of aqueous solutions ¹, Zagreb, Croatia ² Institut Ruđer Bošković, Zagreb, Croatia  Worldwide motivation: Transport of electrical signals in bio-materials on a molecular scale is of fundamental interest in the life sciences  Our motivation: Counterion atmospheres condensed onto charged biopolymers strongly affect their physical properties and biological functions, but have been difficult to quantify experimentally.  Our aim: investigating dielectric relaxation in charged systems, polyions and colloids, in aqueous environment of varying ionic strength and pH MOTIVATION

POLYSTYRENE LATEX nominal particle sizes and concentrations: 178nm (5% vol.) 196nm (10% vol.) 820nm (10% vol.) POLYSTYRENE LATEX Serva inc. & Interfacial Dynamics Co. nominal particle sizes and concentrations: 178nm (5% vol.) 196nm (10% vol.) 820nm (10% vol.) SAMPLES & MATERIALS MODEL COLLOIDAL SYSTEM  Polystyrene particles are almost perfectly spherical  latex is monodisperse  well-determined polarization response TEM image: latex spheres

Precision impedance analyzer Agilent 4294A: 40 Hz-110 MHz Agilent BNCs Conductivity chamber for aqueous samples: S/cm; volume L Reproducibility 1%, Long term (2 h) 2% Temperature control unit: 0° to 60°C Stability: ± 10 mK Pt chamber steel casing Pt LOW-FREQUENCY DIELECTRIC SPECTROSCOPY

We measure complex conductivity components G() and B()=C()* We measure complex conductivity components G() and B()=C()* =’()+i’’() Y()= G()+iB() From complex conductance to complex dielectric function B.Saif et al., Biopolymers 31, 1171 (1991) Resulting (G-G NaCl, C-C NaCl ) are converted into complex dielectric function These are subtracted for (G, C) of background (reference)These are subtracted for (G, C) of background (reference) NaCl solution of matching conductivity (i.e. ionic strength)

∞   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:     LF mode:     Results: Two Relaxation Modes in 1 kHz – 10 MHz range 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 (e.g. Na +, H + ) after dissociation from functional groups are redistributed in the vicinity of particle surface, screening the surface charge  ions from the electrolyte create electrical double layer with thickness  -1 on the particle surface  Under applied ac field  Counter-ion atmosphere around the particle oscillates with the field  Oscillations can be expected along two characteristic length scales:  -1 - Debye-Hückel length & contour length of particle (~diameter, 2R)  two types of dielectric dispersion, two dielectric modes Counterions move diffusively: Length scale, L is related to the characteristic relaxation time,  of the dielectric mode L= ( ∙ D) 1/2 L LF =2R L HF = -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, l P : 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 L HF  c L  -1 Na +, Cl - LpLp L HF Origin of dielectric dispersion in DNA solutions ? Debye-Hückel length L HF =  -1  I nm

HF mode:   10, 1-   0.8 LF mode:   100, 1-   0.8 Results: Two Relaxation Modes in 10 kHz – 10 MHz range

 Worldwide motivation: Transport of electrical signals in bio-materials on a molecular scale is of fundamental interest in the life sciences  Our motivation: Counterion atmospheres condensed onto charged biopolymers strongly affect their physical properties and biological functions, but have been difficult to quantify experimentally.  Our aim: investigating dielectric relaxation in charged systems, polyions and colloids, in aqueous environment of varying ionic strength and pH MOTIVATION  Experimental characterization of the counter-ion atmospheres around macromolecules/colloidal particles in aqueous environment is essential  Low frequency dielectric spectroscopy (LFDS) studies: application specific and non-destructive technique allowing detection and quantification of polarization response of charged systems in polar and non- polar solvents.  LFDS is also well established in the solid state, for investigations of the collective electronic response in the low-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, (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: our technique is operable in 1kHz – 50 MHz range, due to succesful removal of measurement artifacts, both at low and high frequencies CONCLUSIONS latex – model system: we observed both theoretically expected dielectric modes Future prospects LFDS: low-frequency limit should be lowered. Electrode polarization phenomenon could be suppressed in several known ways. Systems: Alongside systems with spherical geometry, systems of longitudinal geometry may be investigated – bio-polymers like DNA can be characterized by several length scales

L HF : Debye-Hückel screening length –  -1 Characteristic length scale of the high-frequency mode  L HF,LF = ( HF.LF D) 1/2   HF,LF from experiments D(Na + ) = 1.5 ·10 -9 m 2 /s  L HF,LF = ( HF.LF D) 1/2   HF,LF from experiments D(Na + ) = 1.5 ·10 -9 m 2 /s D(H + ) = 9 ·10 -9 m 2 /s L LF : particle diameter – Characteristic length scale of the low-frequency mode Counterions: H + (Diffusion constants from : CRC Handbook ) size [nm] vol.%  LF  0 LF [  s] 1-  L [nm] L LF [nm]  HF  0 HF [  s] 1-  L HF [nm] 1785%5% % % Results: Characteristic length scales & counterion species size [nm] vol.%   S/cm I=   m   -1 [nm] 1785%5% % %   – conductivity of latex solution I I - 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