Sir Samuel Edwards: A sketch on the background of scientific revolution

The scientific contribution of late Professor Sir Sam Edwards and its relationship to the scientific revolution in polymer physics as well as some characteristic features of Sir Edwards as a great scientific character are shortly described and discussed.     

Gyroid symmetry and phase diagram of weak crystallization

The phase diagram in the (τ-δ) plane, where τ is the reduced temperature and δ is a parameter characterizing the anisotropy of the fourth vertex of the effective Hamiltonian, is constructed on the basis of the standard mean-field approximation of the theory of weak crystallization. It is shown that the region of the gyroid phase dominates the phase diagram for intermediate values of the parameters τ and δ. An expression is obtained for the free energy of the gyroid phase. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 436–440 (25 March 1996)     

The global phase behavior of the two-component systems with intracomponent association: Flory approach

Within the Flory approach we study the phase diagrams of two-component fluids, the molecules of each component A(f(A)), B(f(B)) bearing f(A) (f(B)) functional groups capable of forming thermoreversible A-A and B-B bonds. We develop a general procedure to classify these diagrams depending on the values of four governing parameters -- entropies and normalized energies of A-A and B-B bonds, and give full topological classification of phase diagrams with f(A,B)> or =3. We show that these phase diagrams can have immiscibility loops and up to four critical points.     

Microphase separation in multiblock copolymer melts: Nonconventional morphologies and two-length-scale switching

The phase behavior of AfmN(BN2AN2)B(1-fmN) multiblock copolymer melts is studied within the weak segregation theory. The interplay between ordering on different length scales is shown to cause dramatic changes both in the ordered phase symmetry and periodicity upon small variation of the architectural parameters of the macromolecules. Phase diagrams are presented in the (f,chiN) plane (chi is the Flory-Huggins parameter) for various values of the architecture parameters n and m. Near the critical surface, i.e., for (f-0.5)2<1, such nonconventional cubic phases as the face-centered cubic (FCC), simple cubic (SC), (double) gyroid, and the so-called BCC(2) (single gyroid) are found to be stable. The lamellar morphology is shown to be replaced by BCC2, FCC, or SC (depending on the structural parameters) as the most stable low-temperature phase.     

Phase Behavior of Solutions of Polymers with Multiply Aggregating Groups

We have theoretically investigated phase diagrams of solutions of aggregating polymers. In our model all polymer chains in the solution carry a certain number of aggregating groups (“stickers”), capable of the formation of thermoreversible aggregates, each assumed to consist of exactly m stickers. The treatment of aggregation corresponds to the Flory‐like theory of gelation. We have studied the dependence of the phase diagram on the parameters of aggregation, such as its strength (fraction of monomeric units carrying stickers and aggregation constant) and cooperativity (aggregation number). In the considered system of homopolymer chains the stickers have been found to always promote phase separation. The value of aggregation number m is crucial for the topology of the phase diagram: for m ≥ 5 the triple point may appear in the phase diagram. Conditions on the properties of the system ensuring the appearance of this feature have been obtained. The interrelation between gelation and phase separation for different values of parameters is elucidated.     

Stabilization of polymer blend structure by diblock copolymers

The stabilizing (emulsifying) effect of a symmetric diblock copolymer in the mixture of two immiscible homopolymers is considered. The equilibrium value of the interfacial area per copolymer chain is calculated via minimization of the free energy of the mixture for a fixed number of copolymer chains adsorbed to the interface. The size and concentration of droplets of the minor component are determined for the equilibrium state. The particles' radius is shown to be inversely proportional to the copolymer concentration, the coefficient of proportionality being dependent on the Flory-Huggins parameter and chain length. The penetration of homopolymer segments into the copolymer layer on the interface is taken into account and proved to be important for stabilization of the droplets by symmetric copolymers. The conditions of the validity of the presented approach are discussed in detail.     

Phase equilibrium and charge fractionation in polyelectrolyte solutions

A new type of phase separation in the polyelectrolyte solutions consisting of several types of charged macromolecules differing in their degree of ionization is presented. Via a general thermodynamic consideration we show that even a small difference in the degree of ionization of otherwise equivalent high‐molecular components results in their spatial separation occurring upon decreasing the temperature much earlier than precipitation of any of the pure components from the solution. Some implications of charge fractionation are discussed, including the separation of DNA (or RNA) strands interacting with different proteins and the appearance of heterogeneities in polyelectrolyte solutions of partially charged hydrophobic chains with polydispersed charge distributions such as sodium polystyrene sulfonate. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3003–3009, 2007     

Contribution to the statistical theory of solutions of polymers in a critical solvent

The thermodynamics of high polymers in equilibrium with a low-molecular solvent with a large correlation radius (super-and near-critical solvent) is studied. Special attention is devoted to the analysis of typical phase diagrams describing the conditions of solubility of a polymer in such a solvent. The nature of these diagrams is determined by the existence of long-range multiparticle attraction between the monomers, which increases as the critical point of the solvent is approached. At the critical point the contribution of this attraction to the free energy of the system is nonanalytic with respect to the polymer concentration. It is shown that the nontrivial dependences of the polymer-polymer and polymer-solvent coupling constants, which appear in the phenomenological analysis, on the pressure and temperature of the solvent play an important role in the quantitative analysis of the phase diagrams of the solubility of the polymer. These dependences are found in explicit form under the assumption that in the absence of intermonomer bonds the system can be described as a compressible two-component lattice alloy. The partition function of the system under study is represented as a functional integral over two coupled, strongly fluctuating fields, one of which, describing the fluctuations of the polymer density, is the 0 component. By virtue of the specific nature of the problem, the effective temperature corresponding to the 0-component of the field cannot be specified independently, but can be determined by minimizing the total free energy of the system. Zh. éksp. Teor. Fiz. 114, 910–929 (September 1998)