Summary: We have shown that the components of Cartesian rotation vectors can be used successfully as generalized coordinates describing angular orientation in Brownian dynamics simulations of non‐spherical nanoparticles. For this particular choice of generalized coordinates, we rigorously derived the conformation‐space diffusion equations from kinetic theory for both free nanoparticles and nanoparticles interconnected by springs or holonomic constraints into polymer chains. The equivalent stochastic differential equations were used as a foundation for the Brownian dynamics algorithms. These new algorithms contain singularities only for points in the conformation‐space where both the probability density and its first coordinate derivative equal zero (weak singularities). In addition, the coordinate values after a single Brownian dynamics time step are throughout the conformation‐space equal to the old coordinate values plus the respective increments. For some parts of the conformation‐space these features represent a major improvement compared to the situation when Eulerian angles describe rotational dynamics. The presented simulation results of the equilibrium probability density for free nanoparticles are in perfect agreement with the results from kinetic theory.
Simulation of p(eq)(Φ) for free nanoparticles. 相似文献
We study the interactions between polymer-grafted nanoparticles immersed in a chemically identical polymer melt using a numerical implementation of polymer mean-field theory. We focus on the interpenetration width between the grafted and free chains and its relationship to the polymer-mediated interparticle interactions. To this end, we quantify the interpenetration width as a function of particle curvature, grafting density, and the relative molecular weights of the grafted and free chains. We show the onset of wetting and dewetting as a function of these quantities and explain our results through simple scaling arguments to include the effects of curvature. Subsequently, we show that the interparticle potentials correlate quantitatively with the trends displayed by the interpenetration widths. 相似文献
In striking contrast to simple polymer physics theory, which does not account for solvent effects, we find that physical confinement of solvated biopolymers decreases solvent entropy, which in turn leads to a reduction in the organized structural content of the polymer. Since our theory is based on a fundamental property of water-protein statistical mechanics, we expect it to have broad implications in many biological and material science contexts. 相似文献
The aim of this work is to provide a physical model to relate the polarizability per unit cell of oligomers to that of their corresponding infinite polymer chains. For this we propose an extrapolation method for the polarizability per unit cell of oligomers by fitting them to a physical model describing the dielectric properties of polymer chains. This physical model is based on the concept of a dielectric needle in which we assume a polymer chain to be well described by a cylindrically shaped nonconducting rod with a radius much smaller than its length. With this model we study in which way the polarizability per unit cell approaches the limit of the infinite chain. We show that within this model the macroscopic contribution of the induced electric field to the macroscopic electric field vanishes in the limit of an infinite polymer chain, i.e., there is no macroscopic screening. The macroscopic electric field becomes equal to the external electric field in this limit. We show that this identification leads to a relation between the polarizability per unit cell and the electric susceptibility of the infinite polymer chain. We test our dielectric needle model on the polarizability per unit cell of oligomers of the hydrogen chain and polyacetylene obtained earlier using time-dependent current-density-functional theory in the adiabatic local-density approximation and with the Vignale-Kohn functional. We also perform calculations using the same theory on truly infinite polymer chains by employing periodic boundary conditions. We show that by extrapolating the oligomer results according to our dielectric needle model we get good agreement with our results from calculations on the corresponding infinite polymer chains. 相似文献
Transport properties of polymer solutions at finite concentration are derived in the partial draining case by formulating a static version of the theory given by Freed and Edwards (FE) for unentangled concentrated polymer solution. The method follows the Kirkwood—Riseman theory for infinitely dilute solutions: the dynamics of the polymer are ignored apart from the overall rotation or translation of the chain and the solvent velocity is given by the Navier—Stokes equations perturbed by point friction forces. The concentration dependence of viscosity and translational friction coefficient of finite chains obtained by numerical calculations are compared with the results of the FE closed-form solution. It is shown that the screening of the hydrodynamic interaction approximately follows Debye-like behavior in the entire range of concentration. The progressive balancing of the increasing intramolecular hydrodynamic interaction with its reduction due to the screening effects, as the molecular weight increases, is well evidenced by comparing results obtained at constant number concentration for different chain lengths. 相似文献
Translocation of biopolymers through pores is implicated in many biological phenomena. Confinement within a pore often breaks ergodicity on experimental and/or biological time scales by creating large entropic barriers to conformational rearrangements of the chain. Here, we study one example of such hindered rearrangement, in which the chain reverses its direction inside a long pore. Our goal is twofold. First, we study the dependence of the time scale of polymer reversal on the pore size and on the polymer length. Second, we examine the ability of simple one-dimensional theories to quantitatively describe a transition in a system with a complex energy landscape by comparing them with the exact rate constant obtained using brute-force simulations and the forward flux sampling method. We find that one-dimensional transition state theory (TST) using the polymer extension along the pore axis as the reaction coordinate adequately accounts for the exponentially strong dependence of the reversal rate constant on the pore radius r and the polymer length N, while the transmission factor, i.e., the ratio of the exact rate and the TST approximation, has a much weaker power law r and N dependence. We have further attempted to estimate the transmission factor from Kramer's theory, which assumes the reaction coordinate dynamics to be governed by a Langevin equation. However, such an approximation was found to be inadequate. Finally, we examine the scaling behavior of the reversal rate constant with N and r and show that finite size effects are important even for chains with N up to several hundreds. 相似文献
Taking into account the well known correspondence between the field theoretical ?(4) O(n)-vector model in the limit n → 0 and the behavior of long flexible polymer chains in a good solvent, the universal density-force relation is analyzed and the corresponding universal amplitude ratio B(real) is obtained using the massive field theory approach in fixed space dimensions d < 4. The monomer density profiles of ideal chains and real polymer chains with excluded volume interaction in a good solvent between two parallel repulsive walls, one repulsive and one inert wall, are obtained in the framework of the massive field theory approach up to one-loop order. Besides, the monomer density profiles for the dilute polymer solution confined in semi-infinite space containing mesoscopic spherical particle of big radius are calculated. The obtained results are in qualitative agreement with previous theoretical investigations and with the results of Monte Carlo simulations. 相似文献
We study the dynamics of long chain polymer molecules tethered to a plane wall and subjected to a stagnation point flow. Using a combination of theory and numerical techniques, including Brownian dynamics (BD), we demonstrate that a chain conformation hysteresis exists even for freely draining (FD) chains. Hydrodynamic interactions (HI) between the polymer and the wall are included in the BD simulations. We find qualitative agreement between the FD and HI simulations, with both exhibiting simultaneous coiled and stretched states for a wide range of fixed flow strengths. The range of state coexistence is understood by considering an equivalent projected equilibrium problem of a two state reaction. Using this formalism, we construct Kramers rate theory (from the inverse mean first passage time for a Markov process) for the hopping transition from coil to stretch and stretch to coil. The activation energy for this rate is found to scale proportionally to chain length or Kuhn step number. Thus, in the limit of infinite chain size the hopping rates at a fixed value of the suitably defined Deborah number approach zero and the states are "frozen." We present the results that demonstrate this "ergodicity breaking." 相似文献
This work studies surface instabilities in switchable homopolymer brushes where the minority chain differs in length from the brush chains. Both off-lattice numerical self-consistent field theory and classical density functional theory are employed. It is found that the two methods agree well with each other as long as the same equation of state for the polymer chains is used. 相似文献
Chemically modified nanopores show a strong and nontrivial coupling between ion current and the structure of the immobilized species. In this work we study theoretically the conductance and structure in polymer modified nanopores and explicitly address the problem of the coupling between ion transport and molecular organization. Our approach is based on a nonequilibrium molecular theory that couples ion conductivity with the conformational degrees of freedom of the polymer and the electrostatic and nonelectrostatic interactions among polyelectrolyte chains, ions, and solvent. We apply the theory to study a cylindrical nanopore between two reservoirs as a function of pore diameter and length, the length of the polyelectrolyte chains, their grafting density, and whether they are present or not on the outer reservoir walls. In the very low applied potential regime, where the distribution of polyelectrolyte and ions is similar to that in equilibrium, we present a simple analytical model based on the combination of the different resistances in the system that describes the conductance in excellent agreement with the calculations of the full nonequilibrium molecular theory. On the other hand, for a large applied potential bias, the theory predicts a dramatic reorganization of the polyelectrolyte chains and the ions. This reorganization results from the global optimization of the different interactions in the system under nonequilibrium conditions. For nanopores modified with long chains, this reorganization leads to two interesting physical phenomena: (i) control of polyelectrolyte morphology by the direction and magnitude of ion-fluxes and (ii) an unexpected decrease in system resistance with the applied potential bias for long chains due to the coupling between polyelectrolyte segment distribution and ion currents. 相似文献
By using a classical density functional theory (interfacial statistical associating fluid theory), we investigate the structure and effective forces in nonadsorbing polymer-colloid mixtures. The theory is tested under a wide range of conditions and performs very well in comparison to simulation data. A comprehensive study is conducted characterizing the role of polymer concentration, particle/polymer-segment size ratio, and polymer chain length on the structure, polymer induced depletion forces, and the colloid-colloid osmotic second virial coefficient. The theory correctly captures a depletion layer on two different length scales, one on the order of the segment diameter (semidilute regime) and the other on the order of the polymer radius of gyration (dilute regime). The particle/polymer-segment size ratio is demonstrated to play a significant role on the polymer structure near the particle surface at low polymer concentrations, but this effect diminishes at higher polymer concentrations. Results for the polymer-mediated mean force between colloidal particles show that increasing the concentration of the polymer solution encourages particle-particle attraction, while decreasing the range of depletion attraction. At intermediate to high concentrations, depletion attraction can be coupled to a midrange repulsion, especially for colloids in solutions of short chains. Colloid-colloid second virial coefficient calculations indicate that the net repulsion between colloids at low polymer densities gives way to net attraction at higher densities, in agreement with available simulation data. Furthermore, the results indicate a higher tendency toward colloidal aggregation for larger colloids in solutions of longer chains. 相似文献
The statistical–mechanical problem of the transition between crystalline and columnar phases in a main-chain liquid–crystalline polymer is treated in a simple model in which only longitudinal motions of the polymer chains are permitted. A mean-field approximation for the interchain potential is used to obtain a self-consistent equation for the crystalcolumnar transition temperature. When applied to typical homopolymers this theory correctly predicts transition temperatures above the degradation temperature; when applied to a crude model of a random copolymer a temperature in the observed range is predicted. 相似文献
Enthalpy of mixing of polymer with solvent has been evaluated by the new polymer/solvent theory proposed by the authors in a previous article. The new theory was based on the excess Gibbs function limit of hard sphere mixtures with infinite size difference. The calculated enthalpy of mixing for polymer/solvent mixtures by the new theory, agreed with experimental data with good accuracy and indicated that the theory is capable to produce the enthalpy of mixing in the whole concentration range of polymer compared with Flory–Huggins theory. Also the calculations provided information on the studied polymer chains and the molecular interaction effects which were consistent with the properties of polymers and solvents used in the mixtures. 相似文献