Segmental versus chain dynamics of linear polymers

Segmental dynamics of relatively short linear polymers are discussed in terms of two distinct contributions, one related to the local segmental motion (alpha relaxation) and the other to polymer-specific effects that reflect Brownian dynamics of the polymer under chain connectivity constraints (Rouse relaxation modes). These two aspects of polymer dynamics are reflected, though differently, in relaxation spectra of different experimental techniques. Two contrasting cases of the (collective) dipolar response (dielectric techniques) versus the individual segmental response (e.g., NMR spin-lattice relaxation spectroscopy) are considered. The second-rank orientational correlation function of an elementary (Kuhn) segment, directly related to NMR observables, is derived in terms of Rouse normal modes. The effect of alpha dynamics is estimated under the assumption of a separation of time scales which, as it is argued, is a necessary precondition of the Rouse approach. The relative magnitude of the polymer-related dynamics is expressed through the number of elementary Rouse units in the chain and the number of Kuhn segments in a Rouse unit. The results are discussed in the context of recent literature.     

Apparent glassy dynamics of an adsorbed polymer chain in the bond-fluctuation model

The dynamics of a single homopolymer chain strongly adsorbed on a flat surface is investigated by Monte Carlo simulation using the bond-fluctuation model. Previously observed anomalous glassy dynamics at low temperatures [Phys. Rev. E 49 , 5420 (1994)] is revisited in detail. We also study the dynamics of a polymer chain confined in a narrow slit of width of a monomer and a modified bond-fluctuation model in three dimensions to include more relevant bond vectors. We show that the previously observed glassy dynamics is due to an artifact of the bond-fluctuation model in three dimensions in that it does not cross-over to the two dimensional bond-fluctuation model with the correct Rouse dynamics. With the proper inclusion of the extra bond vectors P(2,2,0) and P(3,2,0), no glassy behavior appears for the strongly adsorbed chain.     

Local and chain dynamics in miscible polymer blends: A Monte Carlo simulation study

Local chain structure and local environment play an important role in the dynamics of polymer chains in miscible blends. In general, the friction coefficients that describe the segmental dynamics of the two components in a blend differ from each other and from those of the pure melts. In this work, we investigate polymer blend dynamics with Monte Carlo simulations of a generalized bond fluctuation model, where differences in the interaction energies between nonbonded nearest neighbors distinguish the two components of a blend. Simulations employing only local moves and respecting a no bond crossing condition were carried out for blends with a range of compositions, densities, and chain lengths. The blends investigated here have long time dynamics in the crossover region between Rouse and entangled behavior. In order to investigate the scaling of the self-diffusion coefficients, characteristic chain lengths N(c) are calculated from the packing length of the chains. These are combined with a local mobility mu determined from the acceptance rate and the effective bond length to yield characteristic self-diffusion coefficients D(c)=muN(c). We find that the data for both melts and blends collapse onto a common line in a graph of reduced diffusion coefficients DD(c) as a function of reduced chain length NN(c). The composition dependence of dynamic properties is investigated in detail for melts and blends with chains of length N=20 at three different densities. For these blends, we calculate friction coefficients from the local mobilities and consider their composition and pressure dependence. The friction coefficients determined in this way show many of the characteristics observed in experiments on miscible blends.     

Monte Carlo simulations of polymer dynamics: Recent advances

A brief review is given of applications of Monte Carlo simulations to study the dynamical properties of coarse-grained models of polymer melts, emphasizing the crossover from the Rouse model toward reptation, and the glass transition. The extent to which Monte Carlo algorithms can mimic the actual chain dynamics is critically examined, and the need for the use of coarse-grained rather than fully atomistic models for such simulations is explained. It is shown that various lattice and continuum models yield qualitatively similar results, and the behavior agrees with the findings of corresponding molecular dynamics simulations and experiments, where available. It is argued that these simulations significantly enhance our understanding of the theoretical concepts on the dynamics of dense macromolecular systems. © 1997 John Wiley & Sons, Inc.     

Polymer crystallization: Simulation with entropic barrier model and application to specific polymers

The growth of polymer single crystals has been simulated on the basis of a simple two-dimensional ‘entropic barrier’ model. The chain is described by a sequence of growth units. Their additions and removals are determined by rate constants obeying detailed balance. The crystallization is then simulated by a kinetic Monte Carlo algorithm. An application of the model to specific crystallizable polymers (polyethylene, isotactic polystyrene, isotactic polypropylene, polyhydroxybuterate and polypivalolactone) is presented. Input parameter values for the model are derived from the respective surface free energies, bulk enthalpies, melting points and crystallographic repeat lengths. The only free parameter is the length of a polymer growth unit. This is set to half the lamellar crystal thickness at large undercooling. The lamellar thicknesses calculated on this basis are in good agreement with experimental data. An analysis of the growth unit lengths of the different polymers indicates a scaling with the chain persistence length in the melt.     

二维三角格子上高分子动态 Monte Carlo模拟的协同运动算法

在动态Monte Carlo模拟的协同运动算法中,几个相邻的链节可以同时运动,这可以理解为高分子链中张力的作用引起的协同运动。将这一算法用于二维三角格子模型上RW链和SAW链的模拟。结果表明RW链的动力学行为符合Rouse理论,说明说明该算法可以用于高分子动力学研究,其优点是不需要使用键长涨落模型。     

Transitions of tethered polymer chains: a simulation study with the bond fluctuation lattice model

A polymer chain tethered to a surface may be compact or extended, adsorbed or desorbed, depending on interactions with the surface and the surrounding solvent. This leads to a rich phase diagram with a variety of transitions. To investigate these transitions we have performed Monte Carlo simulations of a bond fluctuation model with Wang-Landau and umbrella sampling algorithms in a two-dimensional state space. The simulations' density-of-states results have been evaluated for interaction parameters spanning the range from good- to poor-solvent conditions and from repulsive to strongly attractive surfaces. In this work, we describe the simulation method and present results for the overall phase behavior and for some of the transitions. For adsorption in good solvent, we compare with Metropolis Monte Carlo data for the same model and find good agreement between the results. For the collapse transition, which occurs when the solvent quality changes from good to poor, we consider two situations corresponding to three-dimensional (hard surface) and two-dimensional (very attractive surface) chain conformations, respectively. For the hard surface, we compare tethered chains with free chains and find very similar behavior for both types of chains. For the very attractive surface, we find the two-dimensional chain collapse to be a two-step transition with the same sequence of transitions that is observed for three-dimensional chains: a coil-globule transition that changes the overall chain size is followed by a local rearrangement of chain segments.     

A Monte Carlo study of a tethered polymer chain in a uniform field

We study the non‐uniform stretching and relaxation of a long flexible end‐anchored polymer chain of N monomers (32 ≤ N ≤ 1 024) in a uniform field B by means of an off‐lattice bead‐spring Monte Carlo model. Our simulational results for the case of a Rouse‐like polymer in the good solvent regime confirm the existence of “trumpet”‐ and “flower”‐type chain conformations, predicted recently by scaling analysis based on the notion of Pincus tensile blobs. The observed elongation of the chain and the critical fields, separating three different regimes of chain deformation, are found to obey the predicted scaling behavior. The segment density distribution matches that of a DNA molecule pulled from one end at constant velocity in a good solvent. As expected, the relaxation of the stretch to coil transition of the polymer of length N is determined by the typical Rouse time τ ∝ N^2ν+1.     

Monte carlo study of the dynamics of star-branched polymers

A uniform star-branched polymer model with f = 3 arms based on a simple cubic lattice was studied by means of the dynamic Monte Carlo method. The model chain is athermal with excluded-volume interactions and it is flexible. A new type of local micromodification was introduced to make the branching point movable. Static properties of the star polymer are in accordance with other theoretical predictions and experimental evidence. Scaling of the self diffusion constant and the terminal relaxation times is close to those of the Rouse theory and to simulation results of linear chains.     

高分子动态Monte Carlo模拟的协同运动算法

在高分子动力学的研究中 ,动态 Monte Carlo模拟发挥了重要的作用 [1] .动态 Monte Carlo模拟的关键是选择具有物理真实性的高分子运动算法 .目前广为采用的算法是经 Hilhorst和 Deutch[2 ] 修正的 Verdier- Stockmayer算法 [3] 以及 Carmesin和 Kremer等的键长涨落算法 [4 ] ,陆建明和杨玉良曾提出一种高分子动态算法 [5] ,在他们的算法中很长一段链节可能作蛇行运动 ,但是冯捷等 [6 ] 指出这种运动模式不满足微观可逆性条件 .本文对该运动模式进行修正 ,得到一种协同运动算法 ,并对其动力学行为进行检验 .1　算　法在平面正方形格子…     

A simple model for finitely extensible polymers

A simple model for the calculation of configurational and rheological properties of finitely extensible polymers in flow is introduced. The finite extensibility of the chain is incorporated into the common Rouse model by varying the spring constant such that a constant contour length is maintained for every flow strength. For elongational flow, a comparison with Monte Carlo simulations of a bead-rod chain with 100 links yields qualitative agreement. For shear flow, this model predicts non-Newtonian flow behaviour.     

Dynamics of Bond‐Fluctuation Model Chains in Good and Theta Solvents

The dynamic Monte Carlo algorithm is employed to explore the dynamics of flexible linear chains. The chains are represented by the bond‐fluctuation model with and without attractions between non‐bonded units placed at close distances. This mimics the behavior of real chains in the good and poorer solvents. We obtain the chain sizes, diffusion coefficients, Rouse modes, and their relaxation times. We also evaluate the time correlation function of the end‐to‐end vector at different concentrations. Subsequently, we compare the dependence of the simulation results on chain length, solvent quality, concentration, and mode order with the corresponding theoretical predictions. We observe a retardation of diffusion for non‐dilute systems close to the theta state. This retardation is too high to be exclusively attributed to the increase of global friction and can be caused by temporary adherence of the chains to transient clusters.     

Interchain coupled chain dynamics of poly(ethylene oxide) in blends with poly(methyl methacrylate): coupling model analysis

Quasielastic neutron scattering and molecular dynamics simulation data from poly(ethylene oxide) (PEO)/poly(methyl methacrylate) (PMMA) blends found that for short times the self-dynamics of PEO chain follows the Rouse model, but at longer times past t(c) = 1-2 ns it becomes slower and departs from the Rouse model in dependences on time, momentum transfer, and temperature. To explain the anomalies, others had proposed the random Rouse model (RRM) in which each monomer has different mobility taken from a broad log-normal distribution. Despite the success of the RRM, Diddens et al. [Eur. Phys. Lett. 95, 56003 (2011)] extracted the distribution of friction coefficients from the MD simulations of a PEO/PMMA blend and found that the distribution is much narrower than expected from the RRM. We propose a simpler alternative explanation of the data by utilizing alone the observed crossover of PEO chain dynamics at t(c). The present problem is just a special case of a general property of relaxation in interacting systems, which is the crossover from independent relaxation to coupled many-body relaxation at some t(c) determined by the interaction potential and intermolecular coupling/constraints. The generality is brought out vividly by pointing out that the crossover also had been observed by neutron scattering from entangled chains relaxation in monodisperse homopolymers, and from the segmental α-relaxation of PEO in blends with PMMA. The properties of all the relaxation processes in connection with the crossover are similar, despite the length scales of the relaxation in these systems are widely different.     

An ellipsoid-chain model for conjugated polymer solutions

We propose an ellipsoid-chain model which may be routinely parameterized to capture large-scale properties of semiflexible, amphiphilic conjugated polymers in various solvent media. The model naturally utilizes the defect locations as pivotal centers connecting adjacent ellipsoids (each currently representing ten monomer units), and a variant umbrella-sampling scheme is employed to construct the potentials of mean force (PMF) for specific solvent media using atomistic dynamics data and simplex optimization. The performances, both efficacy and efficiency, of the model are thoroughly evaluated by comparing the simulation results on long, single-chain (i.e., 300-mer) structures with those from two existing, finer-grained models for a standard conjugated polymer (i.e., poly(2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylenevinylene) or MEH-PPV) in two distinct solvents (i.e., chloroform or toluene) as well as a hybrid, binary-solvent medium (i.e., chloroform/toluene = 1:1 in number density). The coarse-grained Monte Carlo (CGMC) simulation of the ellipsoid-chain model is shown to be the most efficient--about 300 times faster than the coarse-grained molecular dynamics (CGMD) simulation of the finest CG model that employs explicit solvents--in capturing elementary single-chain structures for both single-solvent media, and is a few times faster than the coarse-grained Langevin dynamics (CGLD) simulation of another implicit-solvent polymer model with a slightly greater coarse-graining level than in the CGMD simulation. For the binary-solvent system considered, however, both of the two implicit-solvent schemes (i.e., CGMC and CGLD) fail to capture the effects of conspicuous concentration fluctuations near the polymer-solvent interface, arising from a pronounced coupling between the solvent molecules and different parts of the polymer. Essential physical implications are elaborated on the success as well as the failure of the two implicit-solvent CG schemes under varying solvent conditions. Within the ellipsoid-chain model, the impact of synthesized defects on local segmental ordering as well as bulk chain conformation is also scrutinized, and essential consequences in practical applications discussed. In future perspectives, we remark on strategy that takes advantage of the coordination among various CG models and simulation schemes to warrant computational efficiency and accuracy, with the anticipated capability of simulating larger-scale, many-chain aggregate systems.     

Sequence design of biomimetic copolymers: modeling of membrane proteins and globular proteins with active enzymatic center

The biomimetic approach to the sequence design of synthetic AB‐copolymers has been developed further by means of new series of Monte Carlo computer simulation. The approach is based on using of some particular conformation of a homopolymer chain for “coloring” of monomeric units into two “colors” (or types) A and B depending on the spatial position of particular monomeric unit. We present recent data of our Monte Carlo computer simulation studies of properties of designed AB‐copolymers which mimic membrane proteins, and designed ABC‐copolymers which mimic proteins with active enzymatic center. We have found further evidences for the fact that designed copolymer chain preserves the “memory” about its “parent” spatial conformation and shows the well‐pronounced tendency to restore main features of the “parent” conformation.     

A Monte Carlo algorithm to study polymer translocation through nanopores. II. Scaling laws

In the first paper of this series, we developed a new one-dimensional Monte Carlo approach for the study of flexible chains that are translocating through a small channel. We also presented a numerical scheme that can be used to obtain exact values for both the escape times and the escape probabilities given an initial pore-polymer configuration. We now present and discuss the fundamental scaling behaviors predicted by this Monte Carlo method. Our most important result is the fact that, in the presence of an external bias E, we observe a change in the scaling law for the translocation time tau as function of the polymer length N: In the general expression tau approximately N(beta)E, the exponent changes from beta=1 for moderately long chains to beta=1+nu or beta=2nu for very large values of N (for Rouse and Zimm dynamics, respectively). We also observe an increase in the effective diffusion coefficient due to the presence of entropic pulling on unbiased polymer chains.     

Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular pair correlation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. For strictly symmetric blends the Flory‐Huggins theory becomes quantitatively correct in the long chain length limit, when the χ parameter is identified via the intermolecular pair correlation function. For small chain lengths composition fluctuations are important. They manifest themselves in 3D Ising behavior at the critical point and an upward parabolic curvature of the χ parameter from small‐angle neutron scattering close to the critical point. The ratio between the mean field estimate and the true critical temperature decreases like √χ/(ρb³) for long chain lengths. The chain conformations in the minority phase of a symmetric blend shrink as to reduce the number of energeticaly unfavorable interactions. Scaling arguments, detailed self‐consistent field calculations and Monte Carlo simulations of chains with up to 512 effective segments agree that the conformational changes decrease around the critical point like 1/√N. Other mechanisms for a composition dependence of the single chain conformations in asymmetric blends are discussed. If the constituents of the blends have non‐additive monomer shapes, one has a large positive chain‐length‐independent entropic contribution to the χ parameter. In this case the blend phase separates upon heating at a lower critical solution temperature. Upon increasing the chain length the critical temperature approaches a finite value from above. For blends with a stiffness disparity an entropic contribution of the χ parameter of the order 10^–3 is measured with high accuracy. Also the enthalpic contribution increases, because a back folding of the stiffer component is suppressed and the stiffer chains possess more intermolecular contacts. Two aspects of the single chain dynamics in blends are discussed: (a) The dynamics of short non‐entangled chains in a binary blend are studied via dynamic Monte Carlo simulations. There is hardly any coupling between the chain dynamics and the thermodynamic state of the mixture. Above the critical temperatures both the translational diffusion and the relaxation of the chain conformations are independent of the temperature. (b) Irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface in a symmetric binary polymer blend are investigated. End‐functionalized homopolymers of different species react at the interface instantaneously and irreversibly to form diblock copolymers. The initial reaction rate for small reactant concentrations is time dependent and larger than expected from theory. At later times there is a depletion of the reactive chains at the interface and the reaction is determined by the flux of the chains to the interface. Pertinent off‐lattice simulations and analytical theories are briefly discussed.     

Structural modes of a polymer in the repton model

Using extensive computer simulations, the behavior of the structural modes-more precisely, the eigenmodes of a phantom Rouse polymer-are characterized for a polymer in the three-dimensional repton model and are used to study the polymer dynamics at time scales well before the tube renewal. Although these modes are not the eigenmodes for a polymer in the repton model, we show that numerically the modes maintain a high degree of statistical independence. The correlations in the mode amplitudes decay exponentially with (p∕N)(2)A(t), in which p is the mode number, N is the polymer length, and A(t) is a single function shared by all modes. In time, the quantity A(t) causes an exponential decay for the mode amplitude correlation functions for times <1; a stretched exponential with an exponent 1∕2 between times 1 and τ(R) ～ N(2), the time-scale for diffusion of tagged reptons along the contour of the polymer; and again an exponential decay for times t > τ(R). Having assumed statistical independence and the validity of a single function A(t) for all modes, we compute the temporal behavior of three structural quantities: the vectorial distance between the positions of the middle monomer and the center-of-mass, the end-to-end vector, and the vector connecting two nearby reptons around the middle of the polymer. Furthermore, we study the mean-squared displacement of the center-of-mass and the middle repton, and their relation with the temporal behavior of the modes.