Static and dynamic properties of grafted ring polymer: Molecular dynamics simulation

The static and dynamic properties of a system of end-grafted flexible ring polymer chains grafted to a flat substrate and exposed to a good solvent are studied by using a molecular dynamics method. The monomers are described by a coarse-grained bead-spring model. Varying the grafting density ρ and the degree of polymerization or chain length N, we obtain the density profiles of monomers, study the structural properties of the chain (radius of gyration, bond orientational parameters, etc.), and also present the dynamic characteristics such as chain energy and bond force. Compared with a linear polymer brush, the ring polymer brush exhibits different static and dynamic properties for moderate or short chain length, while it behaves like linear polymer brush in the regime of long chain length.     

Entropic and conformational study of isolated double-tethered chains by three-dimensional lattice simulations

Double-tethered polymers are a kind of linear polymer with a peculiar topological constraint; that is, both of its end-points are attached to a plane which the polymer segments cannot penetrate. The effects of the constraint on the polymer's configurational and entropic properties were investigated by means of a three-dimensional lattice simulation that combined a previously proposed idea with a very efficient chain generation algorithm. In particular, the value of a topology-dependent critical exponent was estimated for the double-tethered configurations. This data is the first report on isolated and double-tethered chains. Also, two optional types of tethered-polymer were investigated as asymptotes of the double- and single-tethered configurations.     

Ring polymers in melts and solutions: scaling and crossover

We propose a simple mean-field theory for the structure of ring polymer melts. By combining the notion of topological volume fraction and a classical van der Waals theory of fluids, we take into account many-body effects of topological origin in dense systems. We predict that although the compact statistics with the Flory exponent ν=1/3 is realized for very long chains, most practical cases fall into the crossover regime with the apparent exponent ν?2/5 during which the system evolves toward a topological dense-packed limit.     

Dewetting as an investigative tool for studying properties of thin polymer films

Employing mass conservation, time-resolved dewetting experiments of thin polymer films allow to determine in real time the dynamic contact angle and the slippage length. Moreover, based on a systematic variation of interfacial properties of a polymer brush, dewetting makes it possible to calculate the force it needs to extract a single polymer chain from its own melt. In the visco-elastic regime close to the glass transition, the temperature and molecular weight dependence of the relaxation time of residual stresses resulting from film preparation by spin-coating can be obtained from the evolution of the shape of the dewetting rim. The presented examples demonstrate that dewetting represents a powerful approach for a sensitive characterization of rheological, frictional and interfacial properties of thin polymer films.     

Non-linear osmotic brush regime: Simulations and mean-field theory

We investigate polyelectrolyte brushes in the osmotic regime using both theoretical analysis and molecular dynamics simulation techniques. In the simulations at moderate Bjerrum length, we observe that the brush height varies weakly with grafting density, in contrast to the accepted scaling law, which predicts a brush thickness independent of the grafting density. We show that such behavior can be explained by considering lateral electrostatic effects (within the non-linear Poisson-Boltzmann theory) combined with the coupling between lateral and longitudinal degrees of freedom due to the conserved polymer volume (which are neglected in scaling arguments). We also take the non-linear elasticity of polyelectrolyte chains into consideration, which makes significant effects as chains are almost fully stretched in the osmotic regime. It is shown that all these factors lead to a non-monotonic behavior for the brush height as a function of the grafting density. At large grafting densities, the brush height increases with increasing the grafting density due to the volume constraint. At small grafting densities, we obtain a re-stretching of the chains for decreasing grafting density, which is caused by lateral electrostatic contributions and is controlled by the counterion-condensation process around polyelectrolyte chains. These results are obtained assuming all counterions to be trapped within the brush, which is valid for sufficiently long chains of large charge fraction.Received: 14 May 2003, Published online: 11 November 2003PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 36.20.-r Macromolecules and polymer molecules - 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc.     

The segregation of poly(styrene-b-isoprene) diblock copolymers to the surface of a polystyrene melt: the effect of the ratio of block lengths

The effect of the ratio of block lengths on the interfacial partitioning of poly(styrene-block-1,4 isoprene) diblock copolymers from their mixtures with polystyrene homopolymer melt is investigated utilizing a series of copolymers with almost constant molecular weight but different compositions. The concentration profile of the copolymer is measured directly using the nuclear reaction analysis technique; a segregation of the diblock is found at both the air/polymer surface, due to the lower surface energy of polyisoprene, and at the substrate/polymer interface. No significant effect of the block length ratio on the free-surface excess was observed. The block molecular weights have apparently led to dangling chain conformations in the non-overlapping mushroom and in the overlapping mushroom regimes whereas the brush regime was not accessible; no indications of a real border between the two former regimes was found. Received: 20 July 1998 / Received in final form and Accepted: 11 September 1998     

Polymer brushes near the crystallization density

In this paper, polymer brushes are studied via molecular-dynamics simulations at very high grafting densities, where the crossover between the brush regime and the polymer-crystal regime is taking place. This crossover is directly observed with the structure factor and pair-correlation function. With increasing grafting density, this crystallization is progressing from the core layer of the brush towards the surface layer. The same process is analyzed using the lateral fluctuations of the monomers as a signature of their diminishing mobility. Additionally, bond forces and the chain excess free energy indicate a transition from the brush regime to the overstretched regime, which is in agreement with predictions of a modified self-consistent field theory.     

New dynamic scaling in increasing systems

We report a new dynamic scaling ansatz for systems whose system size is increasing with time. We apply this new hypothesis in the Eden model in two geometries. In strip geometry, we impose the system to increase with a power law, L ∼ h ^a . In increasing linear clusters, if a < 1/z, where z is the dynamic exponent, the correlation length reaches the whole system, and we find two regimes: the first, where the interface fluctuations initially grow with an exponent β = 0.3, and the second, where a crossover comes out and fluctuations evolve as h ^aα . If a = 1/z, there is not a crossover and fluctuations keep on growing in a unique regimen with the same exponent β. In particular, in circular geometry, a = 1, we find this kind of regime and in consequence, a unique regime holds.      

Effects of counterion fluctuations in a polyelectrolyte brush

We investigate the effect of counterion fluctuations in a single polyelectrolyte brush in the absence of added salt by systematically expanding the counterion free energy about Poisson-Boltzmann mean-field theory. We find that for strongly charged brushes, there is a collapse regime in which the brush height decreases with increasing charge on the polyelectrolyte chains. The transition to this collapsed regime is similar to the liquid-gas transition, which has a first-order line terminating at a critical point. We find that, for monovalent counterions, the transition is discontinuous in theta solvent, while for multivalent counterions, the transition is generally continuous. For collapsed brushes, the brush height is not independent of grafting density as it is for osmotic brushes, but scales linear with it.Received: 26 November 2003, Published online: 11 May 2004PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc.     

Effect of geometrical constraint on conformational properties of a polymer chain

In this article, we analyse the effect of geometrical constraint on the conformational properties of an infinitely long linear semiflexible polymer chain confined in-between two constraints under good solvent condition in two dimensions. The constraints are two impenetrable stair shaped surface and for two-dimensional space, the surface is a one-dimensional line. The semiflexibility of the chain is accounted by introducing a Boltzmann weight of bending energy required to produce each turn in the chain and good solvent condition was accounted by using self-avoiding walk model of the chain. We have calculated exact critical value of step fugacity required for polymerization of an infinitely long polymer chain confined in-between the constraints for different values of separation between the constraints for directed version of the model. We have also calculated possible maximum, minimum values of the persistent length for such chains and the maximum value of bending energy required for each turn in the chain for few values of separation between the constraints.     

Stretching of polymer chains by fluctuating flow fields

We investigate polymer stretching by fluctuating flow fields via numerical solutions of the Brownian dynamics of multibead polymer chains taking into account nonlinear elasticity, hydrodynamic interactions and good solvent, excluded volume interaction effects. By varying the scaling exponent of the energy spectrum whilst keeping the same Reynolds and Deborah numbers, as well as microscale length and turnover times, we show that steeper spectra are associated with stronger stretching. We compute the probability density functions of chain length, and explain their main features by examining explicit molecular histories. We quantify the interaction between strain rate tensor structure and chain geometry as a means of understanding better the different stretching mechanisms in mild, moderate and strong polymer stretching regimes.     

动力学淬火过程中的不动点及衍生拓扑现象

本文对近两年来有关淬火动力学过程中拓扑现象的研究做简要综述.这些动力学拓扑现象被动力学过程中的衍生拓扑不变量保护,与淬火前后体系的拓扑性质有密切关系.基于人工量子模拟平台的高度可控性,已在诸如超冷原子、超导量子比特、核磁共振、线性光学等众多物理体系中,通过对人工拓扑体系动力学过程的调控,观测到如动力学涡旋、动量-时间域的Hopf映射及环绕数、拓扑保护的自旋环结构、动力学量子相变、动量-时间斯格明子等诸多动力学拓扑现象.其中某些拓扑结构还可以在非幺正动力学淬火过程中稳定存在.这些研究将人们对拓扑物相的认识和研究从平衡态推广到非平衡动力学领域,具有重要的科学价值.     

Free energy change of crystallisation in single copolymers

ABSTRACT

We performed dynamic Monte Carlo simulations to calculate the free energy change of crystallisation in single linear and ring polymers containing one or more non-crystallisable sequence defects (comonomers) along the chain. We found that, similar to chain ends, the numbers of comonomers bring only a thermodynamic effect to the free energy barrier and shift down the melting points of single copolymers by following Flory’s thermodynamic equation. Furthermore, there exists a critical comonomer number (or sequence length) for the success of crystallisation, which explains the segregation of sequence lengths upon crystallisation in statistical copolymers. Our observations shed light onto the kinetic suppression of crystallinity for polymers containing various chemical, geometrical or stereo-optical sequence defects, as well as for protein molecules containing specific sequences.     

A dynamic rheological model for thin-film lubrication

In this study, the effects of the non-Newtonian rheological properties of the lubricant in a thin-film lubrication regime between smooth surfaces were investigated. The thin-film lubrication regime typically appears in Stribeck curves with a clearly observable minimum coefficient of friction (COF) and a low-COF region, which is desired for its lower energy dissipation. A dynamic rheology of the lubricant from the hydrodynamic lubrication regime to the thin-film lubrication regime was proposed based on the convected Maxwell constitutive equation. This rheology model includes the increased relaxation time and the yield stress of the confined lubricant thin film, as well as their dependences on the lubricant film thickness. The Deborah number (De number) was adopted to describe the liquid-solid transition of the confined lubricant thin film under shearing. Then a series of Stribeck curves were calculated based on Tichy's extended lubrication equations with a perturbation of the De number. The results show that the minimum COF points in the Stribeck curve correspond to a critical De number of 1.0, indicating a liquid-to-solid transition of the confined lubricant film. Furthermore, the two proposed parameters in the dynamic rheological model, namely negative slipping length b (indicating the lubricant interfacial effect) and the characteristic relaxation time λ 0 , were found to determine the minimum COF and the width of the low-COF region, both of which were required to optimize the shape of the Stribeck curve. The developed dynamic rheological model interprets the correlation between the rheological and interfacial properties of lubricant and its lubrication behavior in the thin-film regime.     

Short-time dynamic behaviour of critical XY systems

Using Monte Carlo methods, the short-time dynamic scaling behaviour of two-dimensional critical XY systems is investigated. Our results for the XY model show that there exists universal scaling behaviour already in the short-time regime, but the values of the dynamic exponent z differ for different initial conditions. For the fully frustrated XY model, power law scaling behaviour is also observed in the short-time regime. However, a violation of the standard scaling relation between the exponents is detected.     

Phase behaviour of polyethylene knotted ring chains

The phase behaviour of polyethylene knotted ring chains is investigated by using molecular dynamics simulations. In this paper, we focus on the collapse of the polyethylene knotted ring chain, and also present the results of linear and ring chains for comparison. At high temperatures, a fully extensive knot structure is observed. The mean-square radius of gyration per bond ² / (Nb²) and the shape factor <δ^*> depend on not only the chain length but also the knot type. With temperature decreasing, chain collapse is observed, and the collapse temperature decreases with the chain length increasing. The actual collapse transition can be determined by the specific heat capacity C_v, and the knotted ring chain undergoes gas-liquid-solid-like transition directly. The phase transition of a knotted ring chain is only one-stage collapse, which is different from the polyethylene linear and ring chains. This investigation can provide some insights into the statistical properties of knotted polymer chains.     

Turbulent dynamics of polymer solutions

We study properties of dilute polymer solutions. The probability density function (PDF) of polymer end-to-end extensions R in turbulent flows is examined. We show that if the value of the Lyapunov exponent lambda is smaller than the inverse molecular relaxation time 1/tau then the PDF has a strong peak at the equilibrium size R0 and a power tail at R>R0. This confirms and extends the results of J. L. Lumley [Symp. Math. 9, 315 (1972)]. There is no essential influence of polymers on the flow in this regime. At lambdatau>1 the majority of molecules is stretched to the linear size R(op)>R0, which can be much smaller than the maximal length of the molecules due to their back reaction.     

Relationship between dynamic mechanical property and thermodynamic interaction parameter of concentrated polymer solutions

The use of concentrated polymer solutions is one of the basic techniques in the application of polymers. They may be coating materials, plasticized polymers, and oil-extended rubber. In these applications the solubility relation is one of the key requirements. The polymer-solvent interaction is expected to influence the mechanical property of the mixture. It is the intent of this study to explore how the dynamic mechanical property is affected by the change of thermodynamic interaction parameter in concentrated polymer solutions. The theoretical development is based on several assumptions: (1) a polymer chain in the amorphous state and in its own environment assumes unperturbed configuration; (2) a polymer chain in a good solvent (poor) is expanded (contracted) relative to the unperturbed dimension; (3) the expanded (contracted) chain configuration results in the higher (lower) entanglement density; (4) both expanded and contracted chains store an elastic energy, the magnitude of which may be estimated; (5) the elastic energy of the deformed chain is balanced by the thermodynamic energy of interaction. The paper focuses on the development of a theory. Also, limited examples of the application of the theory are presented.     

Dynamics of a polymer chain in an array of obstacles

On the basis of the model “polymer chain in an array of obstacles” the influence of the topology effects on the dynamics of concentrated polymer systems is investigated theoretically. The 1/z-expansion (where z is the coordinational number of the lattice of obstacles) is proposed for this problem. By means of this expansion the diffusion coefficient of a linear unclosed polymer chain is calculated. The equilibrium properties of linear closed chain (i.e. ring) unentangled with either of the edges of the lattice are investigated in detail. In particular, it is shown that the diffusion coefficient D of the center of mass of closed chain consisting of N links is proportional to N^−5/2.