On the reliability of mean-field methods in polymer statistical mechanics

The reliability of the mean-field approach to polymer statistical mechanics is investigated by comparing results from a recently developed lattice mean-field theory (LMFT) method to statistically exact results from two independent numerical Monte Carlo simulations for the problems of a polymer chain moving in a spherical cavity and a polymer chain partitioning between two confining spheres of different radii. It is shown that in some cases the agreement between the LMFT and the simulation results is excellent, while in others, such as the case of strongly fluctuating monomer repulsion fields, the LMFT results agree with the simulations only qualitatively. Various approximations of the LMFT method are systematically estimated, and the quantitative discrepancy between the two sets of results is explained with the diminished accuracy of the saddle-point approximation, implicit in the mean-field method, in the case of strongly fluctuating fields.Comment: 27 pages, 9 figure

Novi kopolimerni zwitterionski matriksi za polagano oslobađanje verapamil hidroklorida

Stable co-polymer [vinyl acetate-co-3-dimethyl(methacryloyloxyethyl)ammonium propane sulfоnate, p(VA-co-DMAPS)] latex of different compositions has been synthesized for the first time by emulsifier-free emulsion copolymerization. The unusual “overshooting” behavior of the co-polymer tablets has been explained by the formation of specific clusters from the opposite oriented dipoles zwitterionic species. The change of their concentration with the DMAPS unit fraction (mDMAPS), pH and ionic strength has been considered responsible for the differences observed in the swelling kinetics. The results obtained prove that mDMAPS and ionic strength could be used to control the swelling degree of the p(VA-co-DMAPS) matrices. In this way, p(VA-co-DMAPS) matrices could be effectively used to control the sustained release of drugs with basic properties like verapamil hydrochloride from model tablets.Metodom emulzijske polimerizacije sintetiziran je novi stabilni kopolimer [vinil acetat-ko-3-dimetil(metakriloiloksietill)amonijev propan sulfоnat, p(VA-co-DMAPS)] lateks promjenjivog sastava. Neobično “overshooting” ponašanje tableta pripravljenih iz tog kopolimera objašnjava se stvaranjem specifičnih klastera suprotno rijentiranih dipola zwitterionskih specija. Proučavan je utjecaj udjela DMAPS jedinica (mDMAPS), pH i ionske jakosti na kinetiku bubrenja. Dobiveni rezultati dokazuju da se promjenom mDMAPS i ionske jakosti može kontrolirati stupanj bubrenja p(VA-co-DMAPS) matriksa i oslobađanje verapamil hidroklorida iz tableta pa se ti matriksi mogu upotrijebiti za polagano oslobađanje bazičnih lijekova srodnih verapamilu

Real-Space Mesh Techniques in Density Functional Theory

This review discusses progress in efficient solvers which have as their foundation a representation in real space, either through finite-difference or finite-element formulations. The relationship of real-space approaches to linear-scaling electrostatics and electronic structure methods is first discussed. Then the basic aspects of real-space representations are presented. Multigrid techniques for solving the discretized problems are covered; these numerical schemes allow for highly efficient solution of the grid-based equations. Applications to problems in electrostatics are discussed, in particular numerical solutions of Poisson and Poisson-Boltzmann equations. Next, methods for solving self-consistent eigenvalue problems in real space are presented; these techniques have been extensively applied to solutions of the Hartree-Fock and Kohn-Sham equations of electronic structure, and to eigenvalue problems arising in semiconductor and polymer physics. Finally, real-space methods have found recent application in computations of optical response and excited states in time-dependent density functional theory, and these computational developments are summarized. Multiscale solvers are competitive with the most efficient available plane-wave techniques in terms of the number of self-consistency steps required to reach the ground state, and they require less work in each self-consistency update on a uniform grid. Besides excellent efficiencies, the decided advantages of the real-space multiscale approach are 1) the near-locality of each function update, 2) the ability to handle global eigenfunction constraints and potential updates on coarse levels, and 3) the ability to incorporate adaptive local mesh refinements without loss of optimal multigrid efficiencies.Comment: 70 pages, 11 figures. To be published in Reviews of Modern Physic