We identify the mechanism behind a rapid entropy drop in the metastable (ML) polymer liquid and clarify the significance of the Kauzmann paradox. We also establish a thermodynamic basis for an apparent critical mode-coupling transition between supercooled (SCL) and ML polymer liquids, and for the ideal glass transition but only in ML. The latter need not ever form an equilibrium phase. The crystal can have higher entropy than ML or SCL polymer liquids.

A lattice model of semiflexible linear chains (with equilibrium polydispersity) containing free volume is solved exactly on a Husimi cactus. A metastable liquid (ML) is discovered to exist only at low temperatures and is distinct (and may be disjoint) from the supercooled liquid (SCL) that exists only at high temperatures. The free volume plays a significant role in that the spinodals of the ML and SCL merge and then disappear as the free volume is reduced. The Kauzmann temperature T(K) occurs in the ML without any singularity. At T(MC)>T(K), the ML specific heat has a peak. For infinitely long polymers, the peak height diverges and the free volume vanishes at T(MC), resulting in a continuous liquid-liquid transition. Contrary to the conventional wisdom, both T(K) and T(MC) occur in the ML and not in the SCL.

We investigate the localization of a hydrophobic-polar regular copolymer at a selective solvent-solvent interface with emphasis on the impact of block length M on the copolymer behavior. The considerations are based on simple scaling arguments and use the mapping of the problem onto a homopolymer adsorption problem. The resulting scaling relations treat the gyration radius of the copolymer chain perpendicular and parallel to the interface in terms of chain length N and block size M, as well as the selectivity parameter chi. The scaling relations differ for the case of weak and strong localization. In the strong localization limit a scaling relation for the lateral diffusion coefficient D( parallel) is also derived. We implement a dynamic off-lattice Monte Carlo model to verify these scaling predictions. For chain lengths in a wide range (32

We investigate an extension of the lattice model of melting of semiflexible polymers originally proposed by Flory. Along with a bending penalty epsilon, present in the original model and involving three sites of the lattice, we introduce an interaction energy epsilon (p), corresponding to the presence of a pair of parallel bonds and an interaction energy epsilon (h), associated with a hairpin turn. Both these new terms represent four-site interactions. The model is solved exactly on a Husimi cactus, which approximates a square lattice. We study the phase diagram of the system as a function of the energies. For a proper choice of the interaction energies, the model exhibits a first-order melting transition between a liquid and a crystalline phase at a temperature T(M). The continuation of the liquid phase below T(M) gives rise to a supercooled liquid, which turns continuously into a new low-temperature phase, called metastable liquid, at T(MC)

We propose a simple scaling theory describing the variation of the mean first passage time (MFPT) τ (N, M ) of a regular block copolymer of chain length N and block size M which is dragged through a selective liquid-liquid interface by an external field B. The theory predicts a non-Arrhenian τ vs. B relationship which depends strongly on the size of the blocks, M , and rather weakly on the total polymer length, N . The overall behavior is strongly influenced by the degree of selectivity between the two solvents χ.The variation of τ (N, M ) with N and M in the regimes of weak and strong selectivity of the interface is also studied by means of computer simulations using a dynamic Monte Carlo coarse-grained model. Good qualitative agreement with theoretical predictions is found. The MFPT distribution is found to be well described by a Γ -distribution. Transition dynamics of ring-and telechelic polymers is also examined and compared to that of the linear chains.The strong sensitivity of the "capture" time τ (N, M ) with respect to block length M suggests a possible application as a new type of chromatography designed to separate and purify complex mixtures with different block sizes of the individual macromolecules.

The localization kinetics of a regular block-copolymer of total length N and block size M at a selective liquid-liquid interface is studied in the limit of strong segregation between hydrophobic and polar segments in the chain. We propose a simple analytic theory based on scaling arguments which describes the relaxation of the initial coil into a flat-shaped layer for the cases of both Rouse and Zimm dynamics. For Rouse dynamics the characteristic times for attaining equilibrium values of the gyration radius components perpendicular and parallel to the interface are predicted to scale with block length M and chain length N as τ ⊥ ∝ M 1+2ν (here ν ≈ 0.6 is the Flory exponent) and as τ ∝ N 2 , although initially the characteristic coil flattening time is predicted to scale with block size as ∝ M . Since typically N ≫ M for multiblock copolymers, our results suggest that the flattening dynamics proceeds faster perpendicular rather than parallel to the interface, in contrast to the case of Zimm dynamics where the two components relax with comparable rate, and proceed considerably slower than in the Rouse case.We also demonstrate that, in the case of Rouse dynamics, these scaling predictions agree well with the results of Monte Carlo simulations of the localization dynamics. A comparison to the localization dynamics of random copolymers is also carried out.

We consider the adsorption kinetics of a regular block-copolymer of total length N and block size M at a selective liquid-liquid interface in the limit of strong localization. We propose a simple analytic theory based on scaling considerations which describes the relaxation of the initial coil into a flat-shaped layer. The characteristic times for attaining equilibrium values of the gyration radius components perpendicular and parallel to the interface are predicted to scale with chain length N and block length M as τ ⊥ ∝ M 1+2ν (here ν ≈ 0.6 is the Flory exponent) and as τ ∝ N 2 , although initially the rate of coil flattening is expected to decrease with block size as ∝ M −1 . Since typically N ≫ M for multiblock copolymers, our results suggest that the flattening dynamics proceeds faster perpendicular rather than parallel to the interface. We also demonstrate that these scaling predictions agree well with the results of extensive Monte Carlo simulations of the localization dynamics. PACS numbers: 36.20.-r, 68.05.-n, 07.05.Tp

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