The competition between chain entropy and bending rigidity in compact polymers can be addressed within a lattice model introduced by Flory in 1956 [Proc. R. Soc. London A 234, 60 (1956)]]. It exhibits a transition between an entropy dominated disordered phase and an energetically favored crystalline phase. The nature of this order-disorder transition has been debated ever since the introduction...

The Flory-Huggins theory of flexible polymers mixtures @P. J. Flory, Principles of Polymer Chemistry ~Cornell University Press, Ithaca, 1953!# and the Lebwohl-Lasher model of nematogens @G. Lasher, Phys. Rev. A 5, 1350 ~1972!; P. A. Lebwohl and G. Lasher, ibid. 6, 426 ~1972!# are combined to understand the phase behaviors of mixtures of flexible polymers ~coils! and small molecular liquid cryst...

Using the path integral approach, we obtain characteristic functions of gyration radius distributions for Gaussian star and rosette macromolecules. We derive analytical expressions cumulants both distributions. Applying steepest descent method, estimate probability distribution in limit a large number arms two limiting regimes: strongly expanded collapsed show that cases, regime relative to its...

The conflict between classical and modern theories of criticality is resolved by recognising that both theories work with approximate models, whose relative merits can be assessed by their response to efforts to refine them. Contrary to many claims, critical exponents are not tools fitted to discriminate between different models. True, Riemannian theory which characterises analytic functions in...

The contribution of neutral polymer brush to the curvature elasticity of the grafting surface is investigated theoretically. Using self-consistent field theory, we accurately evaluate the dependence of bending modulus on parameters including chain length, Flory-Huggins parameter and grafting density and reveal the importance of solvent. The results show that the brush-induced bending modulus fo...