“Raindrop” Coalescence of Polymer Chains during Coil–Globule Transition (original) (raw)
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The coil–globule transition for a polymer chain confined in a tube: A Monte Carlo simulation
Journal of Chemical Physics, 2000
The behavior of a grafted polymer chain confined in a tube is investigated within a scaling theory substantiated with biased Monte Carlo simulations of a self-avoiding walk ͑SAW͒ on a cubic lattice. All the statistical and thermodynamic properties of the chain follow from the knowledge of the joint distribution P(z,m) giving the probability to observe a length z and a number of contacts m, in a model where the energy of the chain in a given configuration is proportional to m. The analysis is based on the factorization of P(z,m) into the a priori distribution P(z) and the conditional probability P(m͉z) of finding m contacts given that the chain length is z. P(m͉z) is well-approximated by a Gaussian distribution. Taking the variance ͗m 2 ͘Ϫm 2 of this distribution into account, we obtain a nonmean-field expression for the free energy of the confined chain. We show that the coil-globule transition of the confined chain is independent of its size but depends on the pore diameter. Contrary to free, unconfined chains, it is always a continuous transition.
Simulation of Phase Transitions of Single Polymer Chains: Recent Advances
Macromolecular Symposia, 2006
The behaviour of a flexible polymer chain in solvents of variable quality in dilute solution is discussed both in the bulk and in the presence of an adsorbing wall. Monte Carlo simulations of coarse-grained bead-spring models and of the bond fluctuation model are presented and interpreted in terms of phenomenological theories and scaling concepts. Particular attention is paid to the behaviour of the polymer chain when the temperature of the polymer solution gets lower than the Theta temperature. It is argued that the adsorption transition line at the Theta temperature splits into lines of wetting and drying transitions of polymer globules attached to the wall. In addition, it is shown that the coil-globule transition is followed by a second transition, which in the bond fluctuation model is a crystallization into a regular lattice structure. Performing a finite size scaling analysis on the two transitions it is shown that (for the chosen model) both transitions coincide in the thermodynamic limit, corresponding to a direct collapse of the random coil into the crystal without intermediate coil-globule transition. The implications of this result for the standard mean field or tricritical theory of the coil-globule transition based on a truncated virial expansion are discussed.
Physical Review E, 1998
A discrete-to-continuum approach is introduced to study the static and dynamic properties of polymer chain systems with a bead-spring chain model in two dimensions. A finitely extensible nonlinear elastic potential is used for the bond between the consecutive beads with the Lennard-Jones ͑LJ͒ potential with smaller (R c ϭ2 1/6 ϭ0.95) and larger (R c ϭ2.5ϭ2.1) values of the upper cutoff for the nonbonding interaction among the neighboring beads. We find that chains segregate at temperature Tϭ1.0 with R c ϭ2.1 and remain desegregated with R c ϭ0.95. At low temperature (Tϭ0.2), chains become folded, in a ribbonlike conformation, unlike random and self-avoiding walk conformations at Tϭ1.0. The power-law dependence of the rms displacements of the center of mass (R c.m.) of the chains and their center node (R cn) with time are nonuniversal, with the range of exponents 1 Ӎ0.45Ϫ0.25 and 2 Ӎ0.30Ϫ0.10, respectively. Both radius of gyration (R g) and average bond length (͗l͘) decrease on increasing the range of interaction (R c), consistent with the extended state in good solvent to collapsed state in poor solvent description of the polymer chains. Analysis of the radial distribution function supports these observations. ͓S1063-651X͑98͒11205-9͔
Mechanical Model of Globular Transition in Polymers
ChemPlusChem, 2014
Understanding polymers in solution, in a wide range of environments-from DNA and proteins in cells to long chain polymers in gels-is important throughout science. In complex, multicomponent systems, polymers often undergo phase transitions between distinct conformations; examples include the folding of proteins, or the coil-to-globule transition of homo-and heteropolymers. This paper demonstrates a millimeter-scale granular model of coil-to-globule transitions: one "polymer" chain-a cylinders-on-a-string "pearl necklace"-and many spheres, all shaken on a horizontal surface. This model includes short-and long-range interactions and is more complex than most granular models of molecular systems. It is possible to describe the behavior of this granular system using formalisms generally used in statistical physics of polymers, i.e. first and second order coil-to-globule transitions. This designed granular system represents another kind of approach to the study of polymer phase transitions and might inspire future designs of polymer-like mesoscale systems.
In this note, a novel cluster analysis algorithm recently applied in simple Molecular Dynamics simulations of systems that tend to phase separate, was employed in the study of polymer coil to globule transition via single chain Monte Carlo simulations. The method has been described in detail in http://arxiv.org/abs/1306.3460\. Findings tend to favour a two-stage model of collapse kinetics, although the existence of an intermediate fuzzy phase is also observed, when looking at the details of cluster formation along the backbone chain.
Coil-globule transition of a single short polymer chain: An exact enumeration study
The Journal of Chemical Physics, 2007
The authors present an exact enumeration study of short self-avoiding walks in two as well as in three dimensions that addresses the question, “what is the shortest walk for which the existence of all the three scaling regimes—coil, globule, and the theta—could be demonstrated.” Even though they could easily demonstrate the coil and the globule phase from free energy considerations, they could demonstrate the existence of a theta temperature only by using a scaling form for the distribution of gyration radius. That even such short walks have a scaling behavior is an unexpected result of this work.
Phase transitions of a single polymer chain: A Wang–Landau simulation study
The Journal of Chemical Physics, 2009
A single flexible homopolymer chain can assume a variety of conformations which can be broadly classified as expanded coil, collapsed globule, and compact crystallite. Here we study transitions between these conformational states for an interaction-site polymer chain comprised of N = 128 square-well-sphere monomers with hard-sphere diameter and square-well diameter. Wang-Landau sampling with bond-rebridging Monte Carlo moves is used to compute the density of states for this chain and both canonical and microcanonical analyses are used to identify and characterize phase transitions in this finite size system. The temperature-interaction range ͑i.e., T-͒ phase diagram is constructed for Յ1.30. Chains assume an expanded coil conformation at high temperatures and a crystallite structure at low temperatures. For Ͼ1.06 these two states are separated by an intervening collapsed globule phase and thus, with decreasing temperature a chain undergoes a continuous coil-globule ͑collapse͒ transition followed by a discontinuous globule-crystal ͑freezing͒ transition. For well diameters Ͻ1.06 the collapse transition is preempted by the freezing transition and thus there is a direct first-order coil-crystal phase transition. These results confirm the recent prediction, based on a lattice polymer model, that a collapsed globule state is unstable with respect to a solid phase for flexible polymers with sufficiently short-range monomer-monomer interactions.
Kinetics of Loop Formation in Polymer Chains †
The Journal of Physical Chemistry B, 2008
We investigate the kinetics of loop formation in flexible ideal polymer chains (Rouse model), and polymers in good and poor solvents. We show for the Rouse model, using a modification of the theory of Szabo, Schulten, and Schulten, that the time scale for cyclization is τc ∼ τ0N 2 (where τ0 is a microscopic time scale and N is the number of monomers), provided the coupling between the relaxation dynamics of the end-to-end vector and the looping dynamics is taken into account. The resulting analytic expression fits the simulation results accurately when a, the capture radius for contact formation, exceeds b, the average distance between two connected beads. Simulations also show that, when a < b, τc ∼ N ατ , where 1.5 < ατ ≤ 2 in the range 7 < N < 200 used in the simulations. By using a diffusion coefficient that is dependent on the length scales a and b (with a < b), which captures the two-stage mechanism by which looping occurs when a < b, we obtain an analytic expression for τc that fits the simulation results well. The kinetics of contact formation between the ends of the chain are profoundly affected when interactions between monomers are taken into account. Remarkably, for N < 100 the values of τc decrease by more than two orders of magnitude when the solvent quality changes from good to poor. Fits of the simulation data for τc to a power law in N (τc ∼ N ατ ) show that ατ varies from about 2.4 in a good solvent to about 1.0 in poor solvents. The effective exponent ατ decreases as the strength of the attractive monomer-monomer interactions increases. Loop formation in poor solvents, in which the polymer adopts dense, compact globular conformations, occurs by a reptation-like mechanism of the ends of the chain. The time for contact formation between beads that are interior to the chain in good solvents changes non-monotonically as loop length varies. In contrast, the variation is monotonic in poor solvents. The implications of our results for contact formation in polypeptide chains, RNA, and single stranded DNA are briefly outlined. arXiv:0708.2077v2 [cond-mat.soft]