Void Microstructuring in Lamellar Phase of Amphiphilic Macromolecules

The free volume (voids) distribution in the lamellae of the conventional symmetric and amphiphilic diblock copolymers is studied via Monte–Carlo simulation based on the standard bond fluctuation model. Both in the conventional and amphiphilic block copolymers the voids are found to concentrate on the interfaces between the incompatible units, the magnitude of the effect being unexpectedly significant. A crystalline‐like ordering of voids with increase of the incompatibility between the different repeated units in amphiphilic copolymers is first reported and implications of this peculiarity for the morphology and mechanical properties of the amphiphilic copolymers are discussed.

     

Statistical thermodynamics of the formation of an infinite cluster of thermally reversible chemical bonds

A systematic “mean-field” treatment of the thermodynamic equilibrium formation of an infinite cluster of bonds in a system of identical monomers capable of forming from n=0 to n>2 reversible chemical bonds with one another is proposed within the Cayley-tree approximation. For this purpose the difference between the symmetry of the monomers appearing in “point-to-point” and closed bond paths, respectively, is taken into account on the basis of an analysis of the structure of the infinite cluster. Minimization with respect to the distribution of such monomers yields a nontrivial solution corresponding to a lower free energy than the classical solution, which does not allow for the symmetry difference indicated. In addition, it is shown that the classical solution corresponds to the free-energy maximum when the infinite cluster is formed and that the formation of the infinite cluster is a first-order phase transition. The possible form of the phase diagrams of the systems considered is analyzed. Zh. éksp. Teor. Fiz. 115, 979–990 (March 1999)     

Interdiffusion in polymer blends: The effect of compressibility

The polymer/polymer interdiffusion in a binary compressible blend consisting of long and short chains is investigated within the framework of the dynamic random phase approximation (RPA). The relative contributions of two (fast and slow) stages into the total relaxation of compositional heterogeneities are explicitly shown to be strongly dependent on the initial conditions and the degree of asymmetry of the blend. Special emphasis is given to the influence of the initial distribution of free volume on the apparent rate of the composition relaxation. The evolution of the dynamic struture factor is described as well. It is shown that most of the peculiarities usually ascribed to the “fast‐mode” behavior can be derived within the RPA approach.     

Equilibrium nano-structures in poor solvent polymer solutions near glass transition temperature

Poor solvent polymer solutions near the glass transition temperature are considered on the basis of the nonlocal entropy model which allows the possibility of microphase separation transition. The dependence of the magnitude of nonlocal entropy and nonlocality radius on the temperature are explicitly taken into account. It is shown that accounting for nonlocal entropy can lead to i) the solubility enhancement in the vicinity of glass transition temperature, ii) microphase separation transition. Microphase separation transition is studied in the weak segregation limit. Phase diagrams containing the regions of stability of different microdomain structures, as well as the regions of macroscopic phase separation, are obtained.     

Microphase separation in poor-solvent polyelectrolyte solutions: Phase diagram

Microphase separation in solutions of weakly charged polyelectrolytes in poor solvents is studied in the weak segregation limit within the framework of the mean field approximation using a method first developed by Leibler. As a result a complete phase diagram of the solution near the critical point is obtained. The regions of the stability of the disordered, homogeneous phase and of body-centered cubic (bcc), triangular and lamellar microdomain structures, as well as the phase separation regions are determined. The most striking difference in comparison with the corresponding diagram for block-copolymer melts is the existence of broad phase separation regions even for monodisperse systems. As the quality of solvent becomes poorer, the triangular microdomain structure remains the most stable among microdomain phases of other symmetry.     

Phase diagram for microphase separation transition in poor solvent polymer solutions

In the present paper, we consider the possibility of microphase separation transition in poor solvent polymer solutions. It is shown that this phenomenon can take place if the following two conditions are fulfilled: i) there is a large entropic contribution to the entropy of polymer/solvent mixing, i.e., solvent acts like a plastisizer; ii) this entropic contribution is nonlocal. Both conditions are met below the glass transition temperature for the pure polymer near the so-called Berghmans point when the glass transition curve intersects the liquid-liquid phase separation curve for polymer solutions. The phase diagram for the microphase separation transition is calculated within the framework of weak segregation approximation first proposed by Leibler for block-copolymer systems. The regions of stability of different microdomain structures (lamellar, triangular, body-centered-cubic) are obtained. It is shown that under certain conditions the phase diagram can have two critical points related to the macro- and microphase separation respectively.This paper is dedicated to Prof. E. W. Fischer on the occasion of his 65th Birthday.This work was done in the course of the Humboldt Research Award stay of A.R. Khokhlov at the Max-Planck-Institute for Polymer Research in Mainz. During this stay A.R.K. greatly benefited from numerous discussions with Professor E.W. Fischer who introduced him to the fascinating field of glass transition in polymer systems and formulated several new directions for future research.     

Nonconventional morphologies in two-length scale block copolymer systems beyond the weak segregation theory

The order-disorder and order-order transitions (ODT and OOT) in the linear multiblock copolymers with two-length scale architecture A(fmN)(B(N2)A(N2))(n)B((1-f)mN) are studied under intermediate cooling below the ODT critical point where a nonconventional sequence of the OOTs was predicted previously [Smirnova et al., J. Chem. Phys. 124, 054907 (2006)] within the weak segregation theory (WST). To describe the ordered morphologies appearing in block copolymers (BCs) under cooling, we use the pseudospectral version of the self-consistent field theory (SCFT) with some modifications providing a good convergence speed and a high precision of the solution due to using the Ng iterations [J. Chem. Phys. 61, 2680 (1974)] and a reasonable choice of the predefined symmetries of the computation cell as well as initial guess for the iterations. The WST predicted sequence of the phase transitions is found to hold if the tails of the BCs under consideration are symmetric enough (mid R:0.5-fmid R:0.05, a large region of the face-centered cubic phase stability is found (up to our knowledge, first within the SCFT framework) inside of the body-centered cubic phase stability region. Occurrence of the two-dimensional and three-dimensional phases with the micelles formed, unlike the conventional diblock copolymers, by the longer (rather than shorter) tails, and its relationship to the BC architecture is first described in detail. The calculated spectra of the ordered phases show that nonmonotonous temperature dependence of the secondary peak scattering intensities accompanied by their vanishing and reappearance is rather a rule than exception.     

Depletion of ideal polymer chains near a spherical colloid particle beyond the Dirichlet boundary conditions

We reconsider the depletion interaction of an ideal polymer chain, characterized by the gyration radius R_G and bond length a , and an impenetrable spherical colloid particle of radius R . Forbidding the polymer-colloid penetration explicitly (by the use of Mayer functions) without any other requirement we derive and solve analytically an integral equation for the chain partition function of a long ideal polymer chain for the spherical geometry. We find that the correction to the solution of the Dirichlet problem depends on the ratios R/R _G and R/a . The correction vanishes for the continuous chain model (i.e. in the limit R/R _G → 0 and R/a → ∞ but stays finite (even for an infinite chain) for the discrete chain model. The correction can become substantial in the case of nano-colloids (the so-called protein limit).