The Effects of Concentration, Relative Permittivity and Temperature on the Transport Properties of Sodium Polystyrenesulphonate in MethanolYWater Mixed Solvent Media Ajaya Bhattarai, Prabir Nandi and Bijan Das * Department of Chemistry, North Bengal University, Darjeeling 734 013, India (*Author for correspondence; E-mail: bijan_dasus@yahoo.com) Received 17 March 2006; accepted in revised form 26 June 2006; published online 18 August 2006 Key words: mixed solvents, electrical conductivity, sodium polystyrenesulphonate, Manning theory, counterion condensation Abstract Precise measurements on the electrical conductivity of solutions of sodium polystyrenesulphonate in methanolYwater mixed solvent media containing 8, 16, 25, and 34 wt.% of methanol at 308.15, 313.15, 318.15, and 323.15 K are reported. The degree of substitution of sodium polystyrenesulphonate used was 1, and the concentrations were varied from õ2.0  10 j4 to õ4.0  10 j3 monomol l j1 . The results showed a slight and monotonous increase in the equivalent conductivity with decreasing polyelectrolyte concentration. The applicability of the Manning_s theory for salt-free polyelectrolyte solution was examined and a major discrepancy against the theory was observed. The calculated values of the equivalent conductivity deduced on the basis of this theory were found to be lower than the experimental ones. Possible reasons for this discrepancy have been discussed. The effects of the temperature and relative permittivity of the medium on the equivalent conductivity were also investigated. Estimation of the fractions of uncondensed counterions provides important insight regarding the solution behavior of the polyelectrolyte in methanolYwater mixtures. Introduction Polyelectrolytes are polymers having ionizable groups, which in polar solvents, can dissociate into charged polymer chains (macroion) and small counterions of opposite charge [1, 2]. Solution properties of polyelectrolytes, both in the presence and in the absence of added salt, differ consid- erably from those of neutral macromolecular solutions or those of simple electrolytes. The origin of this specificity lies in the combination of properties derived from long- chain molecules with those derived from charge interac- tions. The high charge density on the macroion produces a strong ionic field which attracts counterions. This strong ionic interaction is the source of the characteristic properties of polyelectrolytes. Current interest in charged polymer solutions, in particular in high-molecular weight ionic macromolecules, is supported by the needs of biophysics since biopolymers are usually charged under physiological conditions and many of their biological functions are governed by the polyelectrolyte behavior [3]. In accounting for the solution behavior of biological and synthetic polyelectrolytes, elucidation of the interac- tions between counterions and charged groups on the polyion are of essential importance. Polyelectrolyte effect includes both deviations from the behavior of neutral polymers caused by the existence of charges along the polymer chain and deviations from the behavior of the electrolytes caused by the fixation of one sort of charges on the polymer chain. Therefore, in addition to the method of macromolecular characterization, electrochemical tech- niques have also been applied to investigate the solution behavior of polyelectrolytes. The specific conductance and the equivalent conductivity, L, are experimentally deter- mined parameters which are suitable to describe the electrolytic transport properties of polyelectrolyte solutions because these properties take into account the movement of any charged entity present in the system under the influence of an externally applied electric field. In spite of various attempts by different investigators, a completely satisfactory theory to describe the electrolytic conductivity of polyelectrolyte solutions has not yet been developed [4Y6]. However, the description of different electrical proper- ties of polyions in aqueous solutions and of their interactions with counterions is generally based on the Manning counterion condensation theory [7Y10] that, under some aspects, can be considered equivalent to the PoissonYBoltzmann cylindrical cell model [11Y15]. Within this model, the polyion is represented as an infinitely long charged line, small ions (counterions) are assumed to form an ionic atmosphere whose density depends on the frame Journal of Polymer Research (2006) 13: 475Y482 # Springer 2006 DOI:10.1007/s10965-006-9070-x