Two-component solutions biopolymer solvent

We first consider the case of a two-component solution (biopolymer + solvent) over a moderately low range of biopolymer concentrations, i.e., C 20 % wt/wt. The quantities pm x in the equations for the chemical potentials of solvent and biopolymer may be expressed as a power series in the biopolymer concentration, with some restriction on the required number of terms, depending on the steepness of the series convergence and the desired accuracy of the calculations (Prigogine and Defay, 1954). This approach is based on simplified equations for the chemical potentials of both components as a virial series in biopolymer concentration, as developed by Ogston (1962) at the level of approximation of just pairwise molecular interactions  

p and m are the standard chemical potential and concentration (molal scale) of the /-component (z = 1 for solvent, z = 2 for biopolymer) A2 is the second virial coefficient (in molal scale units of cm /mol, i.e., taking the polymer molar mass into account) and m° is the standard-state molality for the polymer. 

Following on from equation (3.5), we note that it is the value of the second virial coefficient A2 that determines the osmotic pressure of the biopolymer solution  

the quantities jn ° and ji are, respectively, the chemical potentials of pure solvent and of the solvent at a certain biopolymer concentration V is the molar volume of the solvent and n is the biopolymer number density, defined as n C/M, where C is the biopolymer concentration (% wt/wt) and M is the number-averaged molar weight of the biopolymer. The second virial coefficient has (weight-scale) units of cm mol g. Hence, the more positive the second virial coefficient, the larger is the osmotic pressure in the bulk of the biopolymer solution. This has consequences for the fluctuations in the biopolymer concentration in solution, which affects the solubility of the biopolymer in the solvent, and also the stability of colloidal systems, as will be discussed later on in this chapter. 

It is essential to take note here of the relationship between concentrations expressed in molal and weight units (Wells, 1984)  

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