The dimensions of charged long chain molecules in solutions containing electrolytes

Abstract If a long chain molecule in a solution carries electric charges, the statistical coil is inflated, and the average square of the distance between the ends of the chain is larger than in the uncharged state. For a number of properties the determining factor is the value of ∑ k (r 2 k )av, where r k is the distance between the k'th link in the molecule and the centre of gravity. This quantity is proportional to the square of the effective radius and is related to the square of the distance between the ends by a simple formula (section 2), provided the radius of the coil is small compared with the length of the extended chain. In section 3 the electrical free energy of the molecule is derived as a function of effective radius on the assumption that no electrolytes are present. This free energy determines in its turn the average dimensions of the coil. In section 4 a similar theory is developed for charged polymer molecules in the presence of electrolytes. The change of the effective radius with the charge on the polymer and the concentration of the electrolytes is calculated. In the limit of high electrolyte content the equilibrium between the interior and the exterior of the polymer coil may be considered as a Donnan equilibrium.