The swelling of cellulose xanthate gels in dilute salt solutions

A theory is developed which connects the degree of swelling of a polymer network bearing ionogenic groups with the electrolyte concentration in the swelling medium. It is based on the assumption of an electrolyte distribution according to a Donnan equilibrium between the gel and the surrounding liquid on the one hand, and on the application of a modified Flory‐Rehner equation to the dependence of the free energy of dilution on the degree of swelling on the other hand. This theory is applied to the swelling of cellulose xanthate gels in neutral salt solutions. The following conclusions are reached. The theoretical relation between the degree of swelling q and the electrolyte concentration c has the form q 5/3 = B/βλ c + (1‐ K )/2 β, where B, β and K are constants related to fundamental physical properties of the swollen network; λ is a valency factor of the electrolyte studied. In agreement with this formula the experimental q 5/3 ‐ 1/λ c plots are linear at moderate degrees of swelling and fairly independent of the electrolyte used. An explanation is given for deviations from linearity observed in highly swollen systems. From the slope of the experimental swelling curves it is concluded that the network consists of short chains. Apart from the influence of the valency of the ions there exists also a lyotropic influence of the ions on the swelling of the gel. The strong dependence of swelling on the xanthate ratio of the gel is in quantitative agreement with the effect predicted by theory.