A new theory is introduced to model the lipid membrane structure and stability both above and below the gel to liquid phase transition temperature. Recently, we elaborated a self-consistent-field (SCF) theory, in which the full set of conformations was generated in a rotational isomeric state scheme and Boltzmann statistics was used to determine the statistical weight per conformation. In the present paper we also take into account that the anisotropic distribution of the molecules on the lattice induce a self-consistent anisotropic molecular field. This field, which is a function of the bond orientations, leads to an extra factor in the statistical weight of each conformation and is based on a generalization of Flory’s and Di Marzio’s analysis of systems with rigid rods. This elegant refinement follows from elementary statistics, is free of new adjustable parameters, and significantly improves details of the structure of the model membranes. To examine the properties of the SCAF (self-consistent anisotropic field) theory we use a model membrane built up by lecithin-like molecules composed of apolar and polar segments. The model has three nearest-neighbor interaction parameters of the Flory–Huggins type, namely for the interaction between apolar segments and water, that between polar segments and water, and that between polar and apolar segments. A fourth parameter is the dihedral trans/gauche energy difference. The theory predicts a first order gel to liquid phase transition for the model membranes. Depending on the membrane concentration, both an intercalated (in the dilute regime) and a nonintercalated (in the concentrated regime) gel phase are observed. Detailed information on the various membrane phases is obtained. Order parameter and segment density profiles are given.
Abstract The parabolic approximation for self‐consistent molecular potential is widely used for theoretical analysis of conformational and thermodynamic properties of polymer brushes formed by linear or branched macromolecules. The architecture‐dependent parameter of the potential (topological coefficient) can be calculated for arbitrary branched polymer architecture from the condition of elastic stress balance in all the branching points. However, the calculation routine for the topological coefficient does not allow unambiguously identifying the range of applicability and the accuracy of the parabolic approximation. Here the limits of applicability of parabolic approximation are explored by means of numerical self‐consistent field method for brushes formed by Y‐shaped and comb‐like polymers. It is demonstrated that violation of the potential parabolic shape can be evidenced by appearance of multimodal distribution of the end monomer unit in the longest elastic path of the macromolecule. The asymmetry of branching of Y‐shaped polymers does not disturb the parabolic shape of the potential as long as the degree of polymerization of the root segment remains sufficiently large. The same applies to comb‐shape polymers with sufficiently long main chain and large number of branching points. For short comb‐like polymers multiple modes in the distribution of the end monomer unit of the main chain are observed and related to deviation from the parabolic shape of the potential.
The presence of multivalent ions in polymer-flooding produced water (PFPW) hampers its recycling mainly because i) they increase the risk of scaling and reservoir souring (sulfate), ii) they interfere with the viscosifying effect of the fresh polyelectrolyte. It is desirable to achieve the removal of most multivalent ions without completely desalting the stream. With the adequate process conditions, electrodialysis could help to achieve this goal, so this work focused on evaluating the removal of divalent ions from synthetic PFPW through varying operational conditions. The experimental work consisted on batch experiments run in an electrodialysis-stack composed of strong Neosepta ion-exchange membranes. Synthetic PFPW solutions containing a mixture of monovalent and divalent ions were desalted at four different current densities, and three different temperatures. Additionally, the effect of the dissolved polymer on the removal was assessed by performing half of the experiments on polymer-containing solutions and half of them on solutions without it. Our results demonstrate that it is possible to achieve preferential removal of divalent cations (calcium and magnesium) through electrodialysis, especially when employing low current densities (24 A/m2) and high temperature (40 °C). The removal of sulfate, a divalent anion, is also accelerated in these conditions. The presence of polyelectrolyte did not significantly affect the removal rate of divalent ions. Thus, it is concluded that meticulous application of ED to minimize concentrations of divalent ions in PFPW is a potential effective way for water and polymer recycling in enhanced oil recovery situations, as an alternative to the use of other non-selective desalination technologies.
We study the curvature dependence of the liquid-liquid (liquid-gas) interface using the well-known mean field lattice model to estimate its rigidity parameters. The gaussian or saddle-splay modulus is found by evaluating the curvature energy of an interface onto which a saddle shape is imposed as this occurs in an Im3m cubic phase. The resulting values are consistent with those found by the classical indirect route, wherein the gaussian bending modulus results from combining the curvature dependences of the interfacial tension in cylindrical and spherical geometries.
