Meng-Bo Luo

Depinning and creep motion in glass States of flux lines.

Using dynamical computer simulation, we investigate vortex matter in glass states. A genuine continuous depinning transition is observed at zero temperature, which also governs the low-temperature creep motion. With the notion of scaling, we evaluate in high accuracy critical exponents and scaling functions; we observe a non-Arrhenius creep motion for weak collective pinning where the Bragg glass is stabilized at equilibrium, while for strong pinning, the well-known Arrhenius law is recovered. In both cases, a sharp crossover takes place between depinning and creep at low temperatures.

The critical adsorption point of self-avoiding walks: A finite-size scaling approach

The critical adsorption of self-avoiding polymer chain in a simple cubic lattice onto a flat surface is studied with Monte Carlo simulations. The dependence of number of surface contacts M on chain length N and polymer-surface interaction epsilon is investigated by a finite-size scaling approach. We estimate the critical adsorption point epsilon(c)=0.291+/-0.002 and the exponent phi=0.54+/-0.01. The asymptotic behaviors M proportional variant N for epsilon>>epsilon(c) and M proportional variant N(0) for epsilon<<epsilon(c) are also obtained from the finite-size scaling relation. We have also estimated the critical adsorption point by using Binders cumulant method as well as configurational properties.

Simulation study on the translocation of polymer chains through nanopores

The translocation of polymer chains through nanopores is simulated by dynamical Monte Carlo method. The free energy landscape for the translocation of polymer is calculated by scanning method. The dependence of the free energy barrier Fb and the chemical difference Deltamu on the concentration of chains can explain the behavior of polymer translocation at low and high concentration limits. The relationship between Deltamu and the escaping time tau(2) is in good agreement with the theoretical conclusions obtained by Muthukumar [J. Chem. Phys. 111, 10371 (1999)]. Our simulation results show that the relaxation time is mainly dominated by Fb, while the escaping time is mainly dominated by Deltamu.

Monte Carlo simulation on polymer translocation in crowded environment.

The effect of crowded environment with static obstacles on the translocation of a three-dimensional self-avoiding polymer through a small pore is studied using dynamic Monte Carlo simulation. The translocation time τ is dependent on polymer-obstacle interaction and obstacle concentration. The influence of obstacles on the polymer translocation is explained qualitatively by the free energy landscape. There exists a special polymer-obstacle interaction at which the translocation time is roughly independent of the obstacle concentration at low obstacle concentration, and the strength of the special interaction is roughly independent of chain length N. Scaling relation τ ~ N(1.25) is observed for strong driving translocations. The diffusion property of polymer chain is also influenced by obstacles. Normal diffusion is only observed in dilute solution without obstacles or in a crowded environment with weak polymer-obstacle attraction. Otherwise, subdiffusion behavior of polymer is observed.

Monte Carlo simulation of polymer chain with ferromagnetic Ising interaction

We consider a self-avoiding walking polymer chain with nearest-neighbor ferromagnetic Ising interaction (J>0) on the simple cubic lattice. The magnetic and conformational properties are simulated using Monte Carlo technique with bond-fluctuation model. Spontaneous magnetization is observed at low temperature. We estimate the critical temperature Tc=1.37±0.05(J/kB) and the critical exponents α≈0.42 and ν≈0.80 based on the finite-size scaling law. The values of α and ν are different from those of two- or three-dimensional Ising models, indicating that the phase transition in the Ising polymer chain model belongs to a different universality class. Near Tc, the chain also undergoes a collapse transition from random coil at T>Tc to compacted globule at T<Tc. We conclude that the phase transitions in the Ising polymer chain model result from the cooperation of configurational movement and the ferromagnetic Ising interaction.

Free energy landscape for the translocation of polymer through an interacting pore.

Free energy landscapes for polymer chain translocating through an interacting pore are calculated by using exact enumeration method. A potential barrier exists at weak attractive or repulsive polymer-pore interaction and it changes to a potential well with the increase in the attraction. The result reveals that there is a free translocation point where polymer is free of energy barrier. Using the free energy landscape, the translocation time tau for polymer worming through the pore and the migration time tau(m) for polymer migrating from cis side to trans side are calculated with the Fokker-Plank equation. It shows that a moderate attractive polymer-pore interaction accelerates the migration of polymer from cis side to trans side.

Dissipative Particle Dynamics Simulation on a Ternary System with Nanoparticles, Double-Hydrophilic Block Copolymers, and Solvent

Dissipative particle dynamics (DPD) simulations are performed to study the aggregation of hydrophobic nanoparticles in the presence of double-hydrophilic block copolymer (DHBC). A single compact spherical nanoparticle aggregate is formed in the absence of DHBC. The response of the aggregate to a continuous increase in the concentration of DHBC has been investigated in detail. We observe the evolvement from single spherical aggregate, through single ellipsoidal aggregate, single platelike aggregate, single long and curly rod, dispersed aggregates, then to hexagonally packed cylinders, and ultimately to ordered lamellar structures upon slow addition of DHBC chains. However, when nanoparticles and DHBCs are added into the system simultaneously at the beginning of simulation, we only obtain single spherical aggregate, dispersed aggregates, hexagonally packed cylinders, and ordered lamellar structures at different concentrations of DHBC. Phase diagrams of structures against concentration of DHBC are presented for these two methods, and the stabilities of structures obtained with the two methods are compared.

Effect of attractive polymer-pore interactions on translocation dynamics

The effect of attractive polymer-pore interaction on the translocation of polymer chain through a nanopore under electric field is studied by using dynamical Monte Carlo method. The translocation dynamics is remarkably influenced by the interaction. The translocation time for chain moving through nanopore is strongly dependent on the interaction. It reaches minimum at a moderate interaction which is found to be roughly independent of electric field as well as chain length. At weak interaction region, chain spends long time to overcome the barrier of the pore entrance, i.e., the chain is trapped at the entrance. While at strong interaction region, chain is difficult to leave the nanopore, that is, the chain is trapped at the exit of nanopore. The phenomenon is discussed from the view of free energy landscape.

Polymer translocation through a gradient channel

The translocation of polymer through a channel with a gradient interaction between the polymer and the channel is studied. The interaction is expressed by E = E0 + kx, where E0 is the initial potential energy at the entrance, x is the position of the monomer inside the channel, and k is the energy gradient. The mean first passage time τ is calculated by using Fokker-Planck equation for two cases (1) N > L and (2) N < L under the assumption that the diffusion rate D is a constant, here N is the polymer length and L is the length of channel. Results show that there is a minimum of τ at k = k(c) for both cases, and the value kc is dependent on E0 and driving force f. At large f, the scaling relation τ ∼ N is observed for long polymer chains. But the scaling relation is dependent on the energy gradient k for an unforced driving translocation.

Escape of polymer chains from an attractive channel under electrical force

The escape of polymer chains from an attractive channel under external electrical field is studied using dynamical Monte Carlo method. Though the escaping process is nonequilibrium in nature, results show that the one-dimensional diffusion theoretical model based on the equilibrium assumption can describe the dependence of the average escaping time (τ(0)) on the polymer-channel interaction (ɛ), the electrical field (E), the chain length (n), and the channel length (L), qualitatively. Results indicate that both ɛ and E play very important roles in the escaping dynamics. For small ɛ, the polymer chain moves out of the channel continuously and quickly. While for large ɛ, the polymer chain is difficult to move out of long channels as it is trapped for a long time (τ(trap)) when the end segment is near the critical point x(C). These results are consistent with the theoretical results for the free energy profiles at small ɛ and large ɛ, respectively. The dependence of x(C) and τ(trap) on ɛ and E are discussed, and specific relations are obtained. The configurational properties of polymer chain are also investigated during the escaping process.