V. V. Vasilevskaya

Conformational transitions in polymer gels: Theory and experiment

We present a review of theoretical and experimental results on the swelling behavior and collapse transition in polymer gels obtained by our group at Moscow State University. The main attention is paid to polyelectrolyte networks where the most important factor is additional osmotic pressure created by mobile counter ions. The influence of other factors such as condensation of counter ions, external mechanical force, the mixed nature of low-molecular solvents, interaction of network chains with linear macromolecules and surfactants etc. is also taken into account. Experimental results demonstrate a good correlation with theoretical analysis.

Structure of collapsed persistent macromolecule: Toroid vs. spherical globule

We studied theoretically the behavior of a collapsed persistent macromolecule in poor solvent as a model of collapse transition of single double-stranded DNA chain, and constructed the diagram of states in the variables with contour length of a macromolecule and quality of the solvent. We found that the state of toroidal globule exists as an intermediate state between the states of elongated coil state and the spherical globule. Our theoretical result suggests that a single linear macromolecule with a high degree of polymerization can form a toroidal globule. However, the range in which the toroidal structure is stable decreases as the macromolecule length increases. Experimental observation with transmission electron microscopy has been performed to study the globular structure of single DNA chain (bacteriophage T4 DNA, λ-DNA) collapsed by hexammine cobalt (III) at different concentrations. We found that an extremely long chain of T4 DNA (166 kbp), with a contour length of 56 μm, actually forms a toroidal globule, and that isotropic spherical globule appears at higher hexammine cobalt concentration.

Structures of stiff macromolecules of finite chain length near the coil-globule transition: A Monte Carlo simulation

Using a coarse-grained model of a semiflexible macromolecule, the equilibrium shapes of the chain have been studied varying both the temperature and the chain stiffness. We have applied Monte Carlo techniques using the bond fluctuation model for a chain length of N = 80 effective monomers, and two different types of interactions: a potential depending on the angle between successive bonds along the chain to control the chain stiffness, and an attractive interaction between non-bonded effective monomers to model variable solvent quality. In a diagram of states where chain stiffness and inverse temperature and used as variables, we find regions where the chain exists as coil, as spherical globule, and as toroidal globule, respectively. Some of these regions are not limited by sharply defined boundaries, but rather wide two-state coexistence regions occur in between them, where also intermediate metastable structures (such as rods and disks) occur. Recording histograms of energy, orientational order parameters, etc., which exhibit a two peak structure in the two-state coexistence regions, we perform a subensemble analysis of the individual structures corresponding to these peaks.

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...

Semiflexible amphiphilic polymers: Cylindrical-shaped, collagenlike, and toroidal structures

A coarse-grained model is used to study the conformational properties of semiflexible polymers with amphiphilic monomer units containing both hydrophilic and hydrophobic interaction sites. The hydrophobically driven conformational transitions are studied using molecular dynamics simulations for the chains of varying stiffness, as characterized by intrinsic Kuhn segment lengths that vary over a decade. It is shown that the energy of hydrophobic attraction required for the realization of the coil-to-globule transition increases with increasing chain stiffness. For rather stiff backbone, the coil-to-globule transition corresponds to a first order phase transition. We find that depending on the chain stiffness, a variety of thermodynamically stable anisometric chain morphologies are possible in a solvent selectively poor for hydrophobic sites of amphiphilic monomer units. For flexible chains, the amphiphilic polymer forms a cylindrical globule having blob structure with nearly spherical blobs. With increasing stiffness, the number of blobs composing the globule decreases and the shape of blobs transforms into elongated cylinder. Further increase in stiffness leads to compaction of macromolecules into a collagenlike structure when the chain folds itself several times and different strands wind round each other. In this state, the collagenlike structures coexist with toroidal globules, both conformations having approximately equal energies.

Computer simulation of macromolecular systems with amphiphilic monomer units: Biomimetic models

The review presents the basic models used to analyze the self-assembly of protein macromolecules and the main results of studying the self-organization of macromolecules in terms of the concepts of amphiphilicity of an individual monomer unit. The features of the coil-globule transition of these macro-molecules in solutions with different concentrations are described in terms of the statistics of the distribution of monomer units and chain rigidity. It is shown that this model is efficient for interpreting and analyzing experimental data for the study of synthetic and biological macromolecules.

Conformation of a polymer chain near the solvent critical region. I. The integral equation theory

Using the polymer reference interaction site model (PRISM) approximation and hybrid self-consistent MC/RISM method which combines the traditional Monte Carlo (MC) simulation with the numerical solution of the site–site Ornstein–Zernike-type (RISM) integral equation, we study solvent–mediated interactions and the conformational behavior of a single flexible-chain polymer immersed in a monoatomic solvent. The PRISM theory and the self-consistent MC/RISM method predict that in the vicinity of the solvent critical point there is an effective intrachain attraction between monomeric units of the chain. However, the strongly fluctuating solvent can induce significant conformational changes only if there is rather strong attraction between polymer segments and solvent particles. At such conditions, the collapse transition of long chains is possible near the solvent critical point. The equilibrium microstructure of the chain is modulated as a result of the competition between the intrachain short-range excluded vo...

Swelling and collapse of Swiss-cheese polyelectrolyte gels in salt solutions

A simple theory of swelling of microporous Swiss-cheese polyelectrolyte gels (i.e., polyelectrolyte gels containing water voids) in the solution of 1-1 low-molecular-weight salt is developed. Due to the Donnan effect the overall concentration of salt within porous Swiss-cheese gel can be significantly higher than that within the corresponding homogeneous gel due to the effective absorption of salt by the embedded voids. The degree of this absorption increases with the increase of average size of the voids and of their concentration. In the case of relatively large water voids with radii of about few μm the salt concentration within the water voids is approximately equal to that in the external solution, while the salt concentration in the polymer matrix can be much lower. It is thought that polyelectrolyte Swiss-cheese gels are promising for use as suitable media for microreactors for nanotechnology.

Conformational properties of rigid-chain amphiphilic macromolecules: The phase diagram

The coil-globule transition in rigid-chain amphiphilic macromolecules was studied by means of computer simulation, and the phase diagrams for such molecules in the solvent quality-persistence length coordinates were constructed. It was shown that the type of phase diagram depends to a substantial extent on the degree of polymerization of a macromolecule. Relatively short amphiphilic macromolecules in the poor-solvent region always form a spherical globule, with the transition to this globule involving one or two intermediate conformations. These are the disk globule if the Kuhn segment is relatively large and the string of spherical micelles or the disk globule in the case of relative flexible chains. The phase diagram of a long rodlike amphiphilic chain turned out to be even more complex. Namely, three characteristic regions were distinguished in the region of a poor solvent, depending on the chain rigidity: the region of a cylindrical globule without certain order in the main chain, the region of the cylindrical globule with blobs having the collagen ordering of the chain, and the region of coexistence of collagen-like and toroidal globules. In the intermediate transitional region, not only conformations of strings of spherical micelle beads but also the necklace conformations in which the polymer chain in each bead has collagen ordering can occur in this case.

Amphiphilic Comb Macromolecules with Different Distribution Statistics of Side-Chain Grafting Sites : Mathematical Modeling

The influence of the distribution statistics of side-chain grafting sites on the conformational properties of amphiphilic comblike macromolecules immersed in a solvent that is poor for the main chain and good for the side chains was studied. It was shown that the coil-globule transition for macromolecules with the protein-like distribution of side-chain grafting sites occurs at higher temperatures, wherein the size of the proteinlike macromolecules is generally smaller than that of the corresponding regular macromolecules. Regardless of distribution statistics of side-chain grafting sites, the coil-globule transition of comb macromolecules passes through the step of the formation of the beads-on-a-string conformation composed of micelle-like beads. The temperature dependence curves of the heat capacity exhibit at least two maximums associated with the coil-globule transition per se and the coalescence of the beads into a single globule. The coil-globule transition temperature is slightly dependent upon the degree of polymerization of the main chain and drops with a decrease in the degree of polymerization of the side chains. It was found that comb macromolecules can form spherical, disklike, or cylindrical globules, depending on the structural parameters.