We describe the results of Monte Carlo simulations for kinetics at the collapse transition of a homopolymer in a lattice model. We find the kinetic laws corresponding to the three kinetic stages of the process: R g 2 (t)ϭR g 2 (0)ϪAt 7/11 at the early stage corresponding to formation and growth of locally collapsed clusters, the coarsening stage is characterized by growth of clusters according to the law S ϰ t 1/2 , where S is the average number of Kuhn units per cluster, and the final relaxation stage is described by the law R g 2 (t)ϭR g 2 (ϱ)ϩA 1 (1) e Ϫt/ 1(1) with 1 (1) ϰ N 2 . We also present preliminary results on the equilibrium properties and ''collapse'' transition of a random copolymer. The transition curve is determined as a function of hydrophobic bead concentration n a . We discuss the different collapsed copolymer states as a function of the composition. At low hydrophilicity we believe the critical value of the interaction parameter is governed by the law c (n a ) ϰ n a Ϫ2/3 . In the kinetics we see unusual phenomena such as the appearance of a metastable long-lived states with few clusters and nontrivial loop structure.

Conformations of isolated homo-dendrimers of G = 1 − 7 generations with D = 1 − 6 spacers have been studied in the good and poor solvents, as well as across the coil-to-globule transition, by means of a version of the Gaussian self-consistent (GSC) method and Monte Carlo (MC) simulation in continuous space based on the same coarse-grained model. The latter includes harmonic springs between connected monomers and the pair-wise Lennard-Jones potential with a hard core repulsion. The scaling law for the dendrimer size, the degrees of bond stretching and steric congestion, as well as the radial density, static structure factor, and asphericity have been analysed. It is also confirmed that while smaller dendrimers have a dense core, larger ones develop a hollow domain at some separation from the centre.PACS numbers: 36.20.Ey, 61.25.Hq

Single-chain simulations of densely branched comb polymers, or "molecular bottle-brushes" with side-chains attached to every (or every second) backbone monomer, were carried out by off-lattice Monte Carlo technique. A coarse-grained model, described by hard spheres connected by harmonic springs, was employed. Backbone lengths of up to 100 units were considered, and compared with the corresponding linear chains. The backbone molecular size was investigated as a function of its length at fixed arm size, and as a function of the arm size at fixed backbone length. The apparent swelling exponents obtained by a power-law fit were found to be larger than those for the corresponding linear polymers, indicative of stiffening of the comb backbone. The probability distribution function for the backbone end-to-end distance was also investigated for different backbone lengths and arm sizes. Analysis of this function yielded the critical exponents, which revealed an increase in the swelling exponent consistent with values found from the molecular size. The apparent persistence length of the backbone was also determined, and was found to increase with increasing branching density. Finally, the static structure factors of the whole bottle-brushes and of their backbones are discussed, which provides another consistent estimate of the swelling exponents.

We present results from numerical analysis of the equations derived in the Gaussian self-consistent method for kinetics at the collapse transition of a homopolymer in dilute solution. The kinetic laws are obtained with and without hydrodynamics for different quench depths and viscosities of the solvent. Some of our earlier analytical estimates are confirmed, and new ones generated. Thus the first kinetic stage for small quenches is described by a power law decrease in time of the squared radius of gyration with the universal exponent ␣ i ϭ9/11 ͑7/11͒ with ͑without͒ hydrodynamics. We find the scaling laws of the characteristic time of the coarsening stage, m ϳN ␥m , and the final relaxation time, f ϳN ␥ f , as a function of the degree of polymerization N. These exponents are equal to ␥ m ϭ3/2, ␥ f ϭ1 in the regime of strong hydrodynamic interaction, and ␥ m ϭ2, ␥ f ϭ5/3 without hydrodynamics. We regard this paper as the completion of our work on the collapse kinetics of a bead and spring model of a homopolymer, but discuss the possibility of studying more complex systems.

Single-chain Monte Carlo simulations were carried out, in continuous space, of polymers with various topologies (branched and linear) in the good solvent. Using an inherently flexible beadand-spring model, the backbone of linear polymers with either linear or dendritic side-groups attached was found to be elongated, indicative of an induced stiffness. This "topological stiffness" was compared to the "intrinsic stiffness" of semiflexible linear polymers in terms of various observables. Semiflexible comb polymers, which contained both types of stiffness, were also considered.

In this paper we complete the study of the phase diagram and conformational states of a stiff homopolymer. It is known that folding of a sufficiently stiff chain results in formation of a torus. We find that the phase diagram obtained from the Gaussian variational treatment actually contains not one, but several distinct toroidal states distinguished by the winding number. Such states are separated by first order transition curves terminating in critical points at low values of the stiffness. These findings are further supported by off-lattice Monte Carlo simulation. Moreover, the simulation shows that the kinetics of folding of a stiff chain passes through various metastable states corresponding to hairpin conformations with abrupt U-turns.Comment: 9 pages, 16 PS figures. Journal of Chemical Physics, in pres

In this paper we extend the Gaussian self-consistent method to permit study of the equilibrium and kinetics of conformational transitions for heteropolymers with any given primary sequence. The kinetic equations earlier derived by us are transformed to a form containing only the mean squared distances between pairs of monomers. These equations are further expressed in terms of instantaneous gradients of the variational free energy. The method allowed us to study exhaustively the stability and conformational structure of some periodic and random aperiodic sequences. A typical phase diagram of a fairly long amphiphilic heteropolymer chain is found to contain phases of the extended coil, the homogeneous globule, the micro-phase separated globule, and a large number of frustrated states, which result in conformational phases of the random coil and the frozen globule. We have also found that for a certain class of sequences the frustrated phases are suppressed. The kinetics of folding from the extended coil to the globule proceeds through non-equilibrium states possessing locally compacted, but partially misfolded and frustrated, structure. This results in a rather complicated multistep kinetic process typical of glassy systems.Comment: 15 pages, RevTeX, 20 ps figures, accepted for publication in Phys. Rev.

We study the bead-and-spring model of a stiff chain using a self-consistent mean-field approach. For high stiffness parameter the system may undergo a transition to the phase in which the globule acquires a toruslike shape. The phase diagram of the model contains one second- and two first-order transitions meeting at a bicritical point. The stability of the toroidal conformation and scalings of the torus geometry are analyzed. We investigate different kinetic regimes after an instantaneous quench between the extended coil, torus and the spherical globule phases. The kinetic laws that govern these conformational changes are obtained.