Igor I. Potemkin

Associating polyelectrolytes: Finite size cluster stabilization versus physical gel formation

The theory of phase equilibria in the solutions of associating polyelectrolyte telechelic chains proposed earlier is generalized to take into account the possibility of existence in the solutions of finite size thermodynamically stable clusters in addition to the formation of macroscopic physical gel. It is shown that in some region of polymer concentrations and energies of attraction between the end groups of the chain (stickers) the size distribution of chain clusters has a maximum, i.e., the solution is dominated by the clusters of optimum size. The stabilization of such a cluster is due to the interplay between the energy of attraction of stickers, on the one hand, and the Coulomb interaction together with the contribution from the translational entropy of counter ions, on the other hand. For small enough optimum clusters direct Coulomb interactions are more important, while for large optimum clusters the main reason for stabilization is connected with the translational entropy. This type of stabiliza...

Hollow and Core–Shell Microgels at Oil–Water Interfaces: Spreading of Soft Particles Reduces the Compressibility of the Monolayer

We investigate the influence of a solid core and of the cross-link density on the compression of microgel particles at oil-water interfaces by means of compression isotherms and computer simulations. We investigate particles with different morphology, namely core-shell particles containing a solid silica core surrounded by a cross-linked polymer shell of poly(N-isopropylacrylamide), and the corresponding hollow microgels where the core was dissolved. The polymer shell contains different amounts of cross-linker. The compression isotherms show that the removal of the core leads to an increase of the surface pressure at low compression, and the same effect can be observed when the polymer cross-link density is decreased. Low cross-link density and a missing core thus facilitate spreading of the polymer chains at the interface and, at high compression, hinder the transition to close hexagonal packing. Furthermore, the compression modulus only depends on the cross-link density at low compression, and no difference can be observed between the core-shell particles and the corresponding hollow microgels. It is especially remarkable that a low cross-link density leads to a high compression modulus at low compression, while this behavior is reversed at high compression. Thus, the core does not influence the particle behavior until the polymer shell is highly compressed and the core is directly exposed to the pressure. This is related to an enhanced spreading of polymer chains at the interface and thus high adsorption energy. These conclusions are fully supported by computer simulations which show that the cross-link density of the polymer shell defines the degree of deformation at the interface. Additionally, the core restricts the spreading of polymer chains at the interface. These results illustrate the special behavior of soft microgels at liquid interfaces.

Associating polyelectrolyte solutions: Normal and anomalous reversible gelation

An equilibrium mean-field theory for dilute polyelectrolyte solution with many associating groups per chain is presented. We have shown that in addition to physical gel formation, the aggregation of polyelectrolyte chains in dilute solution can lead to the formation of optimum size clusters. The physical reason for the stabilization of such clusters is discussed. Intramolecular optimum cluster formation (necklace conformation) becomes possible for long or charged enough chains. The study of influence of the number of stickers on phase behavior of associating polyelectrolyte solution enabled us to predict a rather unusual counterintuitive effect: The physical gel formation can be induced by the decrease of the number of stickers (anomalous physical gelation). This effect has pure polyelectrolyte nature and is connected with the translational entropy of mobile counterions.

Multi-Shell Hollow Nanogels with Responsive Shell Permeability

We report on hollow shell-shell nanogels with two polymer shells that have different volume phase transition temperatures. By means of small angle neutron scattering (SANS) employing contrast variation and molecular dynamics (MD) simulations we show that hollow shell-shell nanocontainers are ideal systems for controlled drug delivery: The temperature responsive swelling of the inner shell controls the uptake and release, while the thermoresponsive swelling of the outer shell controls the size of the void and the colloidal stability. At temperatures between 32 °C < T < 42 °C, the hollow nanocontainers provide a significant void, which is even larger than the initial core size of the template, and they possess a high colloidal stability due to the steric stabilization of the swollen outer shell. Computer simulations showed, that temperature induced switching of the permeability of the inner shell allows for the encapsulation in and release of molecules from the cavity.

When Colloidal Particles Become Polymer Coils

This work concerns interfacial adsorption and attachment of swollen microgel with low- to medium-level cross-linking density. Compared to colloids that form a second, dispersed phase, the suspended swollen microgel particles are ultrahigh molecular weight molecules, which are dissolved like a linear polymer, so that solvent and solute constitute only one phase. In contrast to recent literature in which microgels are treated as particles with a distinct surface, we consider solvent-solute interaction as well as interfacial adsorption based on the chain segments that can form trains of adsorbed segments and loops protruding from the surface into the solvent. We point out experimental results that support this discrimination between particles and microgels. The time needed for swollen microgels to adsorb at the air/water interface can be 3 orders of magnitude shorter than that for dispersed particles and decreases with decreasing cross-linking density. Detailed analysis of the microgels deformation, in the dry state, at a solid surface enabled discrimination particle like microgel in which case spreading was controlled predominantly by the elasticity and molecule like adsorption characterized by a significant overstreching, ultimately leading to chain scission of microgel strands. Dissipative particle dynamics simulations confirms the experimental findings on the interfacial activity and spreading of microgel at liquid/air interface.

Microphase separation in solutions of associating polyelectrolytes: Strong segregation approximation

Strong segregation theory of microphase separation in dilute solutions of associating polyelectrolytes is developed. The driving force of the separation is shown to be a competition between a short-range attraction of associating groups and long-range repulsion of charged groups. We predict that with the increase of polymer concentration single chains first aggregate into spherical clusters of optimum size which can be disordered in space or arranged with the symmetry of the bcc lattice. Further increase of polymer concentration can result in the formation of hexagonal and lamellar structures which precede the physical gelation. The hexagonal and lamellar structures are stable at very small fractions of charged groups on the chains.

Elasticity driven spontaneous curvature of a 2D comb-like polymer with repulsive interactions in the side chains

Abstract.We have shown that the rectilinear conformation of a 2D comb-like polymer with symmetrical left-right distribution of the side chains relative to the backbone is thermodynamically unstable. The minimum of the free energy of the comb molecule per unit of its length is attained at asymmetrical distribution of the side chains accompanied by the bending of the backbone. The curved conformation is characterized by a lower elastic energy of the side chains.

Effect of grafting density of the side chains on spontaneous curvature and persistence length of two-dimensional comblike macromolecules

We develop a theory that predicts the response of a two-dimensional (2D) comblike macromolecule (brush) to the bending which is accompanied by redistribution of the side chains with respect to the backbone. The brush is considered under poor solvent conditions, i.e., monomer units of the side chains and of the backbone attract each other. The line tension is explicitly taken into account. It is shown that densely grafted brushes (or brushes with long side chains) demonstrate spontaneous curvature. This curvature is induced by elasticity of the side chains: asymmetrically distributed side chains forming curved segments of the brush possess smaller elastic free energy than symmetrically distributed ones forming rectilinear segments of the brush. Sparsely grafted brushes (or brushes with short enough side chains) exhibit elastic response to the bending. In this case, a role of the elasticity of the side chains diminishes and main contributions to the elastic response of the brush come from the mixing entropy of the side chains and from the line tension. It is shown that persistence length of the sparsely grafted brushes lambda as a function of the number of segments in the side chain M can be approximated by a power function, lambda=const x M(alpha), with the exponent alpha<or=2. This persistence length is much smaller than that of the 2D brush with fixed distribution of the side chains. Our theoretical predictions are consistent with computer simulations.

Nematic Ordering of Polymers in Confined Geometry Applied to DNA Packaging in Viral Capsids.

A density functional theory of the spatial distribution and biaxial nematic order of polymers of arbitrary length and rigidity inside a spherical cavity is proposed. The local order of different chain segments is considered as an alignment to a spatially varying director field of cylindrical symmetry. The steric interactions are taken into account in the second virial approximation. Polymer density and orientational order distributions inside the spherically cavity are the principal results. It was found that short and flexible polymers were located at the center of the sphere and were orientationaly disordered. Upon increasing polymer length and/or polymer rigidity, the location of the polymer was continuously shifted toward the surface of the spherical cavity and the polymer segments became gradually more aligned. Parameters have been selected to model the behavior of genomes in spherical viral capsids.

Influence of the counterion size on swelling and collapse of polyelectrolyte gel

A theory that predicts the effect of the counterion size on the swelling and collapse of a weakly charged polyelectrolyte gel was developed. In addition to excluded-volume interactions between monomer units of the gel, the theory involves the counterion-monomer unit and counterion-counterion interactions in terms of the virial approximation. The character of interactions between different units in the system varies from repulsion to attraction depending on the type of solvent, counterion, and dielectric permittivity of the solvent. For solvents with a low permittivity, the effect of condensation of counterions resulting in the formation of ion pairs is taken into account.