Persistence length excluded volume interactions

In this paper, a molecular thermodynamic approach is developed to predict the structural and compositional characteristics of microemulsions. The theory can be applied not only to oil-in-water and water-in-cil droplet-type microemulsions but also to bicontinuous microemulsions. This treatment constitutes an extension of our earlier approaches to micelles, mixed micelles, and solubilization but also takes into account the self-association of alcohol in the oil phase and the excluded-volume interactions among the droplets. Illustrative results are presented for an anionic surfactant (SDS) pentanol cyclohexane water NaCl system. Microstructur al features including the droplet radius, the thickness of the surfactant layer at the interface, the number of molecules of various species in a droplet, the size and composition dispersions of the droplets, and the distribution of the surfactant, oil, alcohol, and water molecules in the various microdomains are calculated. Further, the model allows the identification of the transition from a two-phase droplet-type microemulsion system to a three-phase microemulsion system involving a bicontinuous microemulsion. The persistence length of the bicontinuous microemulsion is also predicted by the model. Finally, the model permits the calculation of the interfacial tension between a microemulsion and the coexisting phase. 

These theoretical considerations have led to the following view on a nematic solution, in particular of a solution of a para-aromatic polyamide in sulfuric acid [38]. In a quiescent solution of a lyotropic polymer the chains are more or less aligned parallel inside domains of microscopic size, see Fig. 3. The degree of orientation inside the domain, as represented by the order parameter (Pj), is determined by the concentration and temperature. The excluded volume entropy term leads to the formation of oriented blobs with a size of the order of Lp, the persistence length. These blobs line up due to their anisotropic polarizability, which implies that the formation of the anisotropic phase is governed by a dipole-dipole type of interaction, immediately leading to the Maier-Saupe mean-field potential. The entropy or excluded volume interaction merely tells us... 

In a melt of homopolymers, the excluded volume interaction is effectively screened. There is no tendency for a chain to swell beyond the ideal random-walk dimension. Only the prefactor, or more precisely the persistence length, is governed by the very local monomer-monomer interactions. The mean-square end-to-end distance of a chain of length N has the form... 

Equation [118] can be considered as a self-consistent eqrration for the effective chain s persistence length /p". Note that by using the relationship between a chain s persistence length and chain size Rp = 2blp N, one can rewrite eqn [118] in a form similar to the Floty-like expression for a chain size. " It is important to point out that for the case of the weak electrostatic interactions, their contribution to the effective monomeric second virial coeffident has to be supplemented by the second virial coeffident due to excluded volume (hard core) interactions, Bq. 

In all these studies, ACM allowed, with the massive data provided, the behavior of the polyelectrolyte conformational and interaction parameters to be followed at a level of detail previously unobtainable by manual gathering of individual data points. Correlations were made between experimental data and of electrostatic persistence length and electrostatic excluded volume theories, with no adjustable parameters. 

An investigation on the effect of added electrolyte valence and species on polyelectrolytes studied using ACM was made in Reference [46], First-order differences in polyelectrolyte conformations, interactions, and hydrodynamics were reported by the authors when electrolytes of different valence and symmetry were added to the polyelectrolyte solution. Each relevant characteristic, however, followed the same scaling relationship to ionic strength but the prefactors were different. Electrostatic persistence length/electrostatic excluded volume calculations without adjustable parameters suggested that the effective linear charge density is considerably lower in the presence of divalent ions than monovalent ions. Consideration of the... 

---