We consider an osmotic equilibrium between bulk solutions of polyelectrolyte bounded by semi-permeable membranes and separated by a thin film of salt-free liquid. Although the membranes are neutral, the counter-ions of the polyelectrolyte molecules permeate into the gap and lead to a steric charge separation. This gives rise to a distance-dependent membrane potential, which translates into a repulsive electrostatic disjoining pressure. From the solution of the nonlinear Poisson-Boltzmann equation, we obtain the distribution of the potential and of ions. We then derive an explicit formula for the pressure exerted on the membranes and show that it deviates from the classical van't Hoff expression for the osmotic pressure. This difference is interpreted in terms of a repulsive electrostatic disjoining pressure originating from the overlap of counterion clouds inside the gap. We also develop a simplified theory based on a linearized Poisson-Boltzmann approach. A comparison with simulation of a primitive model for the electrolyte is provided and does confirm the validity of the theoretical predictions. Beyond the fundamental result that the neutral surfaces can repel, this mechanism not only helps to control the adhesion and long-range interactions of living cells, bacteria, and vesicles, but also allows us to argue that electrostatic interactions should play enormous role in determining behavior and functions of systems bounded by semi-permeable membranes.

We study the ionic equilibria and interactions of neutral semi-permeable spherical shells immersed in electrolyte solutions, including polyions. Although the shells are uncharged, only one type of ions of the electrolyte can permeate them, thus leading to a steric charge separation in the system. This gives rise to a charge accumulation inside the shell and a build up of concentrationdependent shell potential, which converts into a disjoining pressure between the neighboring shells. These are quantified by using the Poisson-Boltzmann and integral equations theory. In particular, we show that in case of low valency electrolytes, interactions between shells are repulsive and can be sufficiently strong to stabilize the shell dispersion. In contrast, the charge correlation effects in solutions of polyvalent ions result in attractions between the shells, with can lead to their aggregation.

The phenomenological Landau theory of phase transitions can be employed for the description of the thermodynamic behavior of an equilibrium system, provided the coefficients of the expansion of the Landau free energy of this system in powers of the order parameters are known. These coefficients, referred to as the vertex functions, under the consideration of spatially periodic mesophases, depend on the momenta. An algorithm for finding the vertex function for any term of the Landau free energy expansion is introduced. This algorithm provides a possibility to obtain the explicit expressions for the vertex functions describing a compressible melt of polydisperse multiblock copolymer composed of any number of types of blocks with arbitrary distributions for lengths. Under theoretical consideration of block copolymers, the solution of the problem of finding of the vertex functions in such a general formulation has not been reported in literature so far.

The penultimate model of copolymerization taking into account the dependence of the reactivity of a macroradical on the type of the unit preceding the ultimate one is well-known in polymer chemistry. All types of chemical structure of multiblock copolymers capable to form during copolymerization processes described by such a model are revealed in the present work. Phase diagrams of copolymers of all these types specifying the regions of thermodynamic stability of spatially periodic mesophases differing in morphology are constructed in the framework of the weak segregation theory. Besides, the periods and amplitudes of the variation of different type densities of units in mesophases as well as volume fractions of these latter within the regions of their coexistence are calculated.