A Chain Model for Polyelectrolytes. I

Abstract

The various theories of polyelectrolyte behavior are examined and the nature of the approximations inherent in each are discussed. A new model of the polyion in solution is proposed and an outline is described for the evaluation of the free energy of the polyelectrolyte solution, including the effects of dissociation, binding and entropy of distribution of the unionized groups, ions and bound ion pairs. The binding of counter ions by the polymer is related to the pH, and comparison with experimental data of the theoretical relationship gives indications as to the nature of the binding process. The entropy of distribution among charged and uncharged sites on the polymer chain is evaluated, considering interaction between nearest neighboring sites, and is found to decrease markedly from its value for a random distribution, especially at intermediate degrees of neutralization. This large decrease in entropy as the degree of neutralization increases is responsible for the extensive binding of counter ions which is experimentally observed. These manifestations of non-ideal behavior make it impossible to use the previously accepted relationship between the pH of the solution and the thermodynamic properties of the polyion.

X-ray grazing incidence diffraction from alkylsiloxane monolayers on silicon wafers

“…The morphology of hydrocarbon chain monolayers has been studied theoretically in several molecular-dynamics (MD) calculations in which the head group was either free to move in the plane of the surface, as is the case for Langmuir films on water, [18][19][20][21] or fixed at specific lattice sites, as found for alkanethiol monolayers on gold. 22 These calculations provide explicit predictions of the atomic positions, from which scattering cross sections have been calculated.…”

Numerical Techniques to Study Complex Liquids

“…In this scheme, the chain molecule is built up step-by-step. The method of Kumar et al resembles the 'gradual insertion scheme' to measure excess chemical potentials that was Rice [73] and Siepmann [74] showed how to compute the chemical potential of chain molecules with discrete conformations using an algorithm to generate polymer conformations due to Rosenbluth and Rosenbluth [69]. A generalization to continuously deformable molecules was proposed by Frenkel, Smit and Mooij [75,76] and by de Pablo et a/.…”

“…The special case of chain molecules on a lattice was studied by Mooij and Frenkel [80,81] who found that, using the techniques that are described in section 5.2, the calculation of the chemical potential can even be made 2-3 orders of magnitude more efficient than the original scheme of refs. [73,74] which, in turn, is many orders of magnitude more efficient than the 'brute force' particle insertion method. In what follows I denote the chain in the absence of the 'external' interactions as the ideal chain.…”

“…[113]). Here I shall focus on the Configurational Bias Monte Carlo (CBMC) scheme [73,114,76,115]. This is a relatively recent simulation technique that is of particular use in cases where it is not possible to change the conformation of a macromolecule by successive small steps.…”

“…As before, we only consider the expression for one of the segments, to keep the equations simple. E;`,=1 exp(-Ouest(f )) (73) In order to compute the acceptance probability of this move, we have to consider what happens in the reverse move Then we start from conformation j and generate a set of k trial directions that includes i. When computing the acceptance probability of the forward move, we have to impose detailed balance.…”