E. G. Timoshenko

Kinetics at the collapse transition of homopolymers and random copolymers

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 ...

Kinetic laws at the collapse transition of a homopolymer

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 discu...

Conformations of dendrimers in dilute solution

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 method and Monte Carlo 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 analyzed. It is also confirmed that while smaller dendrimers have a dense core, larger ones develop a hollow domain at some separation from the center.

Kinetics at the collapse transition Gaussian self‐consistent approach

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 ar...

On the conformational structure of a stiff homopolymer

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 the 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.

Equilibrium and kinetic phenomena in a stiff homopolymer and possible applications to DNA

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.

Conformations of Amphiphilic Diblock Star Copolymers

Full Paper: We study conformations assumed by single diblock star copolymers in a poor solvent by means of the Gaussian variational theory and Monte Carlo simulation in continuous space. Cases of stars with internal and external hydrophobic blocks are analysed. While in the former case the collapsed state has an obvious micellar shape, the latter case exhibits two nontrivial conformational structures. Apart from the equilibrium state of a globular hydrophobic core with hydrophilic daisy loops, one also finds here a metastable state of outstretched hydrophilic blocks with hydrophobic subglobules at their ends. Such a state appears to be rather long-lived during the kinetics of collapse of a swollen star. The plots of monomer densities and other observables computed by means of both techniques are found to be in good agreement with each other.

Formation of mesoglobules from phase separation in dilute polymer solutions: a study in experiment, theory, and applications

The appearance of spherical particles resulting from heating beyond the phase separation temperature in dilute solutions of poly(N-isopropylacrylamide) has been observed by dynamic light scattering (DLS). They have a relatively narrow size distribution. The size of particles increases with increasing concentration of polymer, and decreasing heating speed. Electron microscopy confirms the existence of spherical particles with size and polydispersity in agreement with DLS. We develop a theory based on the Gaussian self-consistent method for study of the equilibrium and kinetics of conformational transitions in homopolymer solutions. The theory leads to a natural interpretation of the mesoglobules as a very long-lived metastable state. Finally, we mention the potential for these mesoglobules to find applications.

Intrachain correlation functions and shapes of homopolymers with different architectures in dilute solution

We present results of Monte Carlo study of the monomer–monomer correlation functions, static structure factor, and asphericity characteristics of a single homopolymer in the coil and globular states for three distinct architectures of the chain: ring, open, and star. To rationalize the results we introduce the dimensionless correlation functions rescaled via the corresponding mean-squared distances between monomers. For flexible chains with some architectures these functions exhibit a large degree of universality by falling onto a single or several distinct master curves. In the repulsive regime, where a stretched exponential times a power law form (de Cloizeaux scaling) can be applied, the corresponding exponents δ and θ have been obtained. The exponent δ=1/ν is found to be universal for flexible strongly repulsive coils and in agreement with the theoretical prediction from improved higher-order Borel-resummed renormalization group calculations. The short-distance exponents θv of an open flexible chain a...

Analysis of stability of macromolecular clusters in dilute heteropolymer solutions

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.