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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. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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 αi=9/11 (7/11) with (without) hydrodynamics. We find the scaling laws of the characteristic time of the coarsening stage, τm∼Nγm, and the final relaxation time, τf∼Nγf, as a function of the degree of polymerization N. These exponents are equal to γm=3/2, γf=1 in the regime of strong hydrodynamic interaction, and γm=2, γf=5/3 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. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present results of Monte Carlo simulations of a homopolymer with three-body interactions on a lattice. At equilibrium we find three collapsed phases with different orientational order. The first one may be described as a conventional phase with effective three-body attraction. Two other phases are observed in the region of the phase diagram corresponding to three-body repulsion. The second phase is characterized by local orientational order within the globule. The third one possesses global orientational order and it appears to be analogous to nematic phase of a liquid crystal. Kinetics of the collapse transition to the phase III is crucially different from that of phase I and II due to formation of clusters with different orientations at the intermediate stage. This is the origin of a metastable long-lived state in kinetics. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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: R2g(t)=R2g(0)-At7/11 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∝t1/2, where S is the average number of Kuhn units per cluster, and the final relaxation stage is described by the law R2g(t)=R2g(∞)+A1(1)e-t/τ1(1) with τ1(1)∝N2. 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 na. 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 χc(na)∝na-2/3. In the kinetics we see unusual phenomena such as the appearance of a metastable long-lived states with few clusters and nontrivial loop structure. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We introduce an approximation to the Langevin equation that can be used to study the nonequilibrium dynamics and kinetics of polymer conformational transitions in dilute solution. The approach we describe involves the introduction of a time-dependent effective potential, ΔVq(t), and effective friction ζq. The potential is used to generate a time-dependent Gaussian ensemble and we derive time-dependent self-consistent equations that can be analyzed numerically, or by asymptotic methods. We work out various examples of the homopolymer kinetics, including relaxation of a Flory coil and the collapse transition. For the latter we argue that there are various characteristic regimes after a fast quench that carry us from the Flory to collapsed state. We have explicitly worked out the early stage kinetics where we find a process rather like spinodal decomposition, but where the degrees of freedom are confined to the internal metric of the polymer chain. The chain evolves to produce a chain with a near-periodic arrangement of locally collapsed blobs, which is then believed to coarsen, and we have discussed this phenomenon elsewhere. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Three-dimensional discrete tensor wavelets are applied to calculate wave functions of excess electrons solvated in polar liquids. Starting from the Hartree–Fock approximation for the electron wave functions and from the linear response to the solute charge for the solvent, we have derived the approximate free energy functional for the excess electrons. The orthogonal Coifman basis set is used to minimize the free energy functional and to approximate the electron wave functions. The scheme is applied to the calculation of the properties of the solvated electron and the singlet bipolaron formation. The obtained results indicate that the proposed algorithm is fast and rather efficient for calculating the electronic structure of the solvated molecular solutes. [ABSTRACT FROM AUTHOR]

We study the formation of clusters consisting of several chains in dilute solutions of amphiphilic heteropolymers. By means of the Gaussian variational theory we show that in a region of the phase diagram within the conventional two-phase coexistence region mesoglobules of equal size possess the lowest free energy. Monte Carlo simulation confirms that the mesoglobules are stabilized due to microphase separation, which introduces a preferred length scale. The very existence of such mesoscopic structures is related to a delicate balance of the energetic and entropic terms under the connectivity constraints. The issue of size monodispersity and fluctuations for mesoglobules is investigated. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Discrete wavelets are applied to the parametrization of the intrachain two-point correlation functions of homopolymers in dilute solutions obtained from Monte Carlo simulations. Several orthogonal and biorthogonal basis sets have been investigated for use in the truncated wavelet approximation. The quality of the approximation has been assessed by calculation of the scaling exponents obtained from the des Cloizeaux ansatz for the correlation functions of homopolymers with different connectivities in a good solvent. The resulting exponents are in better agreement with those from recent renormalization group calculations as compared to the data without the wavelet denoising. We also discuss how the wavelet treatment improves the quality of data for correlation functions from simulations of homopolymers at varied solvent conditions and of heteropolymers.