T.Vuletić ¹ , R. Žaja ¹ , ² , M. Vukelić ¹ , S.Tomić ¹ and I. Sondi ²

1. Low-frequency dielectric spectroscopy of aqueous solutions ¹ , Zagreb, Croatia ² Institut Ruđer Bošković, Zagreb, Croatia • T.Vuletić ¹, R. Žaja¹,², M. Vukelić ¹, S.Tomić ¹ and I. Sondi ² tvuletic@ifs.hr ; www.ifs.hr/real_science MOTIVATION  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 propertiesand 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

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

3. chamber Pt steel casing LOW-FREQUENCY DIELECTRIC SPECTROSCOPY Precision impedance analyzer Agilent 4294A: 40 Hz-110 MHz Temperature control unit: 0° to 60°C Stability: ±10 mK Conductivity chamber for aqueoussamples: 1.5- 2000mS/cm; volume 50-200 mL Reproducibility 1%, Long term (2 h) 2% Agilent BNCs Pt

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

5. ∞ generalized Debye function FITS to a sum of two generalized Debye functions Results: Two Relaxation Modes in 1 kHz – 10 MHz range LF mode: De 100-1000 1-a 0.8-0.95 HF mode: De 2-20 1-a 0.85-1  relaxation process strength  = (0) - ∞ 0 – central relaxation time  symmetric broadening of the relaxation time distribution 1 -  S. Havriliak and S. Negami, J.Polym.Sci.C 14, 99 (1966).

6. LHF=k-1 LLF=2R Electro-kinetics of Electrical Double Layer  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 k-1on 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: k-1- Debye-Hückel length & contour length of particle (~diameter, 2R) two types of dielectric dispersion, two dielectric modes S.S.Dukhin et al, Adv.Coll. Interface Sci. 13, 153 (1980) R.W.O’Brian, J. Coll. Interface Sci 113, 81 (1986). Counterions move diffusively:Length scale, L is related to the characteristic relaxation time, tof the dielectric modeL= (t∙D)1/2

7. Origin of dielectric dispersion in DNA solutions - Na+, Cl- - - - - - L - k-1 - Lp - LHF 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 M. Sakamoto et al., Biopolymers 18, 2769 (1979) S.Takashima, J.Phys.Chem.70, 1372 (1966) 1) Contour length; n0< 1 kHz 2) LF mode: 1 kHz <n0 < 70 kHz Persistence length, lP: 50nm and higher 5-45nm 3) HF mode: 0.1 MHz <n0 < 15 MHz ? Mesh size LHF c-0.5 ? Debye-Hückel length LHF= k-1I-0.5

9. Results: Two Relaxation Modes in 10 kHz – 10 MHz range HF mode: De 10, 1-a 0.8 LF mode:De 100, 1-a 0.8

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

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

12. Results: Characteristic length scales & counterion species  LHF,LF= (tHF.LFD)1/2 tHF,LF from experimentsD(Na+) = 1.5 ·10-9 m2/sD(H+) = 9 ·10-9 m2/s (Diffusion constants from: CRC Handbook) LLF:particle diameter –Characteristic length scale of the low-frequency modeCounterions: H+ LHF:Debye-Hückel screening length – k-1Characteristic length scale of the high-frequency mode s– conductivity of latex solution I - ionic strength of equivalent electrolyte solution L - molar conductivityof equivalent NaCl electrolyte solution=12 S/Mm k-1– Debye Hückel length for a given ionic strength