Random heteropolymer dynamics (original) (raw)
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Phase Diagram of Random Heteropolymers
Physical Review Letters, 2004
We propose a new analytic approach to study the phase diagram of random heteropolymers, based on the cavity method. For copolymers we analyze the nature and phenomenology of the glass transition as a function of sequence correlations. Depending on these correlations, we find that two different scenarios for the glass transition can occur. We show that, beside the much studied possibility of an abrupt freezing transition at low temperature, the system can exhibit, upon cooling, a first transition to a soft glass phase with fully broken replica symmetry and a continuously growing degree of freezing as the temperature is lowered. PACS numbers: 81.05.Lg, 64.70.Pf, 36.20.Ey
Embedding a native state into a random heteropolymer model: the dynamic approach
Physical review. E, Statistical, nonlinear, and soft matter physics, 2003
We study a random heteropolymer model with Langevin dynamics, in the supersymmetric formulation. Employing a procedure similar to one that has been used in static calculations, we construct an ensemble in which the affinity of the system for a native state is controlled by a "selection temperature" T0. In the limit of high T0, the model reduces to a random heteropolymer, while for T0-->0 the system is forced into the native state. Within the Gaussian variational approach that we employed previously for the random heteropolymer, we explore the phases of the system for high and low T0. For high T0, the system exhibits a (dynamical) spin-glass phase, like that found for the random heteropolymer, below a temperature T(g). For low T0, we find an ordered phase, characterized by a nonzero overlap with the native state, below a temperature T(n) proportional to 1/T(0)>T(g). However, the random-globule phase remains locally stable below T(n), down to the dynamical glass transi...
Glassy phases in random heteropolymers with correlated sequences
The Journal of Chemical Physics, 2004
We develop a new analytic approach for the study of lattice heteropolymers, and apply it to copolymers with correlated Markovian sequences. According to our analysis, heteropolymers present three different dense phases depending upon the temperature, the nature of the monomer interactions, and the sequence correlations: (i) a liquid phase, (ii) a "soft glass" phase, and (iii) a "frozen glass" phase. The presence of the new intermediate "soft glass" phase is predicted for instance in the case of polyampholytes with sequences that favor the alternation of monomers.
Dynamic Properties of Random Heteropolymer with Correlations in Sequence
The some dynamic properties of a random heteropolymer in the condensed state are studied in the mode coupling approximation. In agreement with recent report a dynamic friction increasing is predicted for the random heteropolymer with power-law correlations in comparison with exponential correlations. In the case of strong power-law correlations the dynamic friction function diverge in the thermodynamic limit. The qualitative explanation is given for the monomer's dynamics slowing down and diverged energetic barrier between the frozen and random coil states. The possible relations with protein's function and evolution are discussed.
Field-theoretic simulations of random copolymers with structural rigidity
Soft Matter, 2017
Copolymers play an important role in a range of soft-materials applications and biological phenomena. Prevalent works on block copolymer phase behavior use flexible chain models and incorporate interactions using a mean-field approximation. However, when phase separation takes place on length scales comparable to a few monomers, the structural rigidity of the monomers becomes important. In addition, concentration fluctuations become significant at short length scales, rendering the mean-field approximation invalid. In this work, we use simulation to address the role of finite monomer rigidity and concentration fluctuations in microphase segregation of random copolymers. Using a field-theoretic Monte-Carlo simulation of semiflexible polymers with random chemical sequences, we generate phase diagrams for random copolymers. We find that the melt morphology of random copolymers strongly depends on chain flexibility and chemical sequence correlation. Chemically anti-correlated copolymers undergo first-order phase transitions to local lamellar structures. With increasing degree of chemical correlation, this first-order phase transition is softened, and melts form microphases with irregular shaped domains. Our simulations in the homogeneous phase exhibit agreement with the density-density correlation from mean-field theory. However, conditions near a phase transition result in deviations between simulation and mean-field theory for the density-density correlation and the critical wavemode. Chain rigidity and sequence randomness lead to frustration in the segregated phase, introducing heterogeneity in the resulting morphologies.
A general model of random copolymers in an athermal solution
Macromolecules, 1995
It is shown that a general model of athermal random copolymers in an equilibrium state is related to an appropriately generalized n-0 spin vector model, with each spin having 2n components. By adjusting various coupling constants in the model, one can control various densities such as bond densities of each type and copolymer density, average copolymer size, average block size, etc. The model is solved in a mean-field approximation to study the complete phase diagram and to calculate the free energy and the entropy and the entropy of mixing of copolymers in an athermal solution.
Hamiltonian dynamics of homopolymer chain models
Physical Review E, 2006
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of observables numerically computed along dynamical trajectories are found to reproduce results given by the statistical mechanics of homopolymer models. The dynamical treatment, however, indicates a nontrivial transition between regimes of slow and fast phase space mixing. Such a transition is inaccessible to a statistical mechanical treatment and reflects a bimodality in the relaxation of time averages to corresponding ensemble averages. It is also found that a change in the energy dependence of the largest Lyapunov exponent indicates the theta-transition between filamentary and globular polymer configurations, clearly detecting the transition even for a finite number of particles.
Stochastic lattice models for the dynamics of linear polymers
Physics Reports, 2009
Linear polymers are represented as chains of hopping reptons and their motion is described as a stochastic process on a lattice. This admittedly crude approximation still catches essential physics of polymer motion, i.e. the universal properties as function of polymer length. More than the static properties, the dynamics depends on the rules of motion. Small changes in the hopping probabilities can result in different universal behavior. In particular the cross-over between Rouse dynamics and reptation is controlled by the types and strength of the hoppings that are allowed.
Journal of Statistical Mechanics: Theory and Experiment, 2010
Any first course on polymer physics teaches that the dynamics of a tagged monomer of a polymer is anomalously subdiffusive, i.e., the mean-square displacement of a tagged monomer increases as t α for some α < 1 until the terminal relaxation time τ of the polymer. Beyond time τ the motion of the tagged monomer becomes diffusive. Classical examples of anomalous dynamics in polymer physics are single polymeric systems, such as phantom Rouse, self-avoiding Rouse, self-avoiding Zimm, reptation, translocation through a narrow pore in a membrane, and many-polymeric systems such as polymer melts. In this pedagogical paper I report that all these instances of anomalous dynamics in polymeric systems are robustly characterized by power-law memory kernels within a unified Generalized Langevin Equation (GLE) scheme, and therefore, are non-Markovian. The exponents of the power-law memory kernels are related to the relaxation response of the polymers to local strains, and are derived from the equilibrium statistical physics of polymers. The anomalous dynamics of a tagged monomer of a polymer in these systems is then reproduced from the powerlaw memory kernels of the GLE via the fluctuation-dissipation theorem (FDT). Using this GLE formulation I further show that the characteristics of the drifts caused by a (weak) applied field on these polymeric systems are also obtained from the corresponding memory kernels. PACS numbers: 05.40.-a, 02.50.Ey, 36.20.-r, 82.35.Lr
Dynamics of a polymer in a quenched random medium: A Monte Carlo investigation
Europhysics Letters (EPL), 2004
We use an off-lattice bead-spring model of a self-avoiding polymer chain immersed in a 3-dimensional quenched random medium to study chain dynamics by means of a Monte-Carlo (MC) simulation. The chain center of mass mean-squared displacement as a function of time reveals two crossovers which depend both on chain length N and on the degree of Gaussian disorder ∆. The first one from normal to anomalous diffusion regime is found at short time τ1 and observed to vanish rapidly as τ1 ∝ ∆ −11 with growing disorder. The second crossover back to normal diffusion, τ2, scales as τ2 ∝ N 2ν+1 f (N 2−3ν ∆) with f being some scaling function. The diffusion coefficient DN depends strongly on disorder and drops dramatically at a critical dispersion ∆c ∝ N −2+3ν of the disorder potential so that for ∆ > ∆c the chain center of mass is practically frozen. The time-dependent Rouse modes correlation function Cp(t) reveals a characteristic plateau at ∆ > ∆c which is the hallmark of a non-ergodic regime. These findings agree well with our recent theoretical predictions.