Primitive chain network simulations for asymmetric star polymers

For branched polymers, the curvilinear motion of the branch point along the backbone is a significant relaxation source but details of this motion have not been well understood. This study conducts multi-chain sliplink simulations to examine effects of the spatial fluctuation and curvilinear hopping of the branch point on the viscoelastic relaxation. The simulation is based on the primitive chain network model that allows the spatial fluctuations of sliplink and branch point and the chain sliding along the backbone according to the subchain tension, chemical potential gradients, drag force against medium, and random force. The sliplinks are created and∕or disrupted through the motion of chain ends. The curvilinear hopping of the branch point along the backbone is allowed to occur when all sliplinks on a branched arm are lost. The simulations considering the fluctuation and the hopping of the branch point described well the viscoelastic data for symmetric and asymmetric star polymers with a parameter set common to the linear polymer. On the other hand, the simulations without the branch point motion predicted unreasonably slow relaxation for asymmetric star polymers. For asymmetric star polymers, further tests with and without the branch point hopping revealed that the hopping is much less important compared to the branch point fluctuation when the lengths of the short and long backbone arms are not very different and the waiting time for the branch point hopping (time for removal of all sliplinks on the short arm) is larger than the backbone relaxation time. Although this waiting time changes with the hopping condition, the above results suggest a significance of the branch point fluctuation in the actual relaxation of branch polymers.     

Pre-Averaged Sampling On the Entanglement Kinetics for Polymer Dynamics

A new model for entangled polymer dynamics based on pre-averaged sampling of the entanglement structure is proposed. Although it has been reported that sliplink simulations are powerful and promising to predict entangled polymer dynamics, it is still unpractical to calculate polymers with many entanglements. In the present study, a possible approach to achieve fast calculation is proposed by pre-averaged sampling of entanglement structure with skipping detail kinetics of entanglements dominated by chain ends in conventional sliplink models. To achieve time development of the chain conformation and entanglement structure, i) number of entanglement per chain and number of monomers for each segment are randomly obtained from the equilibrium distribution proposed by Schieber [J. Chem. Phys. 2003 , 118, 5162] and ii) the renewed entanglement structure is mechanically equilibrated. The established power-laws on molecular weight dependence of chain dimension, the longest relaxation time and self-diffusion coefficient were reasonably reproduced. Comparison on linear viscoelastic response is also discussed.     

Theory of relaxation properties of two‐dimensional polymer networks, 2. Local dynamic characteristics

Using normal mode transformation obtained in Part 1 of this series^[1], the exact analytical expressions for the mean‐square displacements of junctions and non‐junction beads, the autocorrelation functions of the end‐to‐end chain vectors between neighboring junctions, and those of subchain vectors of a two‐dimensional regular network consisting of "bead and spring" Rouse chains are obtained. Contributions of intra‐ and interchain relaxation processes to the local dynamic characteristics considered are compared. The time behavior of dynamic quantities obtained is estimated for different scales of motions. The possibility of describing long‐time relaxation of a two‐dimensional network by a simplified coarse‐grained network model is demonstrated. It is shown that the local relaxation properties of a two‐dimensional polymer network (as well as a three‐dimensional network) on scales smaller than the average distance between cross‐links are very close to those of a single Rouse chain. The large‐scale collective relaxation of the polymer networks having a two‐dimensional connectivity differs considerably from that of the three‐dimensional networks.     

Molecular rheology of concentrated polymer systems. I

The primitive chain model of Doi and Edwards is generalized to include the short-time relaxation process. Stress relaxation after a sudden imposition of strain is studied in detail. It is shown that in the linear region (small strain) stress relaxation occurs in two steps, the relaxation of chain segments between the fixed entanglement points, and the relaxation of the entanglement points, in accordance with the conventional picture, whereas in the nonlinear region (large strain) there appears a new relaxation process between the above two. The characteristic time of this process is the Rouse relaxation time which the entire chain would have if there were no entanglements, and increases with the square of the molecular weight. This result is consistent with experimental observations.     

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.     

Statics and dynamics of dense polymer systems studied by monte carlo simulation

Monte Carlo simulations of coarse–grained models of macromolecules offer a unique tool to study the interplay between coil conformations, thermodynamic properties, and chain configurational relaxation and diffusion. Two examples are discussed where the chain conformation strongly differs from a gaussian coil: (i) collapsed chains in a bad solvent, where anomalous diffusion occurs in the Rouse limit and the relaxation time increases at least with the third power of chain length. (ii) Expulsion of a chain from a semidilute polymer brush. The initially stretched chain contracts to a gaussian coil and the center of mass moves outward with constant velocity until it reaches the region of the “last blob” where crossover to diffusive behavior occurs.     

Mechanical Spectral Hole Burning in polymer solutions

Mechanical Spectral Hole Burning (MSHB) was previously developed to investigate dynamic heterogeneity for polymeric materials, which exhibit relatively weak dielectric responses. In our previous work, MSHB was applied to a densely entangled block copolymer and successfully distinguishes the heterogeneous from the homogeneous states. Here, a series of polystyrene (PS) solutions was chosen to further investigate the effect of different types of heterogeneity on mechanical spectral hole burning. The three types of heterogeneity of interest include the entanglement spacing, the entanglement density (or number of entanglements per chain), and chain end density. The heterogeneity was varied by changing either solution concentration or molecular weight of the PS. Different types of dynamics from close to the Rouse regime into the terminal region were also examined. Our results are consistent with a heterogeneous dynamics over the time scales from close to Rouse regime into the rubbery plateau regime and the rubbery plateau‐to‐terminal flow transition regime. Terminal relaxation dynamics, on the other hand, were found to be homogeneous for the PS/diethyl phthalate solutions investigated. The results also indicate the hole properties are dominated by the type of dynamics rather than the length scale of heterogeneity. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2047–2062, 2009     

Effect of bending and torsion rigidity on self-diffusion in polymer melts: a molecular-dynamics study

Extensive molecular-dynamics simulations have been performed to study the effect of chain conformational rigidity, controlled by bending and torsion potentials, on self-diffusion in polymer melts. The polymer model employs a novel torsion potential that avoids computational singularities without the need to impose rigid constraints on the bending angles. Two power laws are traditionally used to characterize the dependence of the self-diffusion coefficient on polymer length: D proportional to N(-nu) with nu=1 for NNe (reptation regime), Ne being the entanglement length. Our simulations, at constant temperature and density, up to N=250 reveal that, as the chain rigidity increases, the exponent nu gradually increases towards nu=2.0 for NNe. The value of Ne is slightly increased from 70 for flexible chains, up to the point where the crossover becomes undefined. This behavior is confirmed also by an analysis of the bead mean-square displacement. Subsequent investigations of the Rouse modes, dynamical structure factor, and chain trajectories indicate that the pre-reptation regime, for short stiff chains, is a modified Rouse regime rather than reptation.     

A time-integrated estimate of the entanglement mass in polymer melts in agreement with the one determined by time-resolved measurements

We make a critical examination of how the entanglement molecular mass Me is determined from various measurable quantities. We are guided by reptation theory, where it is assumed that characteristic relaxations abruptly change and become equal to those of a chain moving in a Gaussian tube, as soon as the corresponding length scales surpass the tube diameter d or similarly as soon as the corresponding mass surpasses a critical value. Taking this critical mass as a definition of the "reptational" entanglement mass, we observe that all methods based on time-resolved quantities, such as the single-chain dynamic structure factor S(q,t) and the zero-shear relaxation modulus G(t), give the same result. We observe that such a value differs, beyond error bars, from that obtained from the plateau modulus, which is a time-integrated quantity. We have investigated an alternative definition of entanglement mass in terms of time-integrated quantities and observe that the value of this specific entanglement mass is consistent with that obtained from the time-resolved observables. We comment on possible reasons for the plateau modulus discrepancy.     

Linear viscoelastic properties of transient networks formed by associating polymers with multiple stickers

We have developed a single-chain theory that describes dynamics of associating polymer chains carrying multiple associative groups (or stickers) in the transient network formed by themselves and studied linear viscoelastic properties of this network. It is shown that if the average number N of stickers associated with the network junction per chain is large, the terminal relaxation time τ(A) that is proportional to τ(X)N(2) appears. The time τ(X) is the interval during which an associated sticker goes back to its equilibrium position by one or more dissociation steps. In this lower frequency regime ω<1/τ(X), the moduli are well described in terms of the Rouse model with the longest relaxation time τ(A). The large value of N is realized for chains carrying many stickers whose rate of association with the network junction is much larger than the dissociation rate. This associative Rouse behavior stems from the association/dissociation processes of stickers and is different from the ordinary Rouse behavior in the higher frequency regime, which is originated from the thermal segmental motion between stickers. If N is not large, the dynamic shear moduli are well described in terms of the Maxwell model characterized by a single relaxation time τ(X) in the moderate and lower frequency regimes. Thus, the transition occurs in the viscoelastic relaxation behavior from the Maxwell-type to the Rouse-type in ω<1/τ(X) as N increases. All these results are obtained under the affine deformation assumption for junction points. We also studied the effect of the junction fluctuations from the affine motion on the plateau modulus by introducing the virtual spring for bound stickers. It is shown that the plateau modulus is not affected by the junction fluctuations.     

混合离子液体对聚甲基丙烯酸甲酯分子链缠结及松弛行为的影响

首先通过两步法合成了具有双咪唑环阳离子结构的离子液体(DIL),并将其与单咪唑环离子液体(MIL)进行混合以调控黏度变化,混合离子液体(ILs)的黏度符合对数混合规则且随温度变化呈现Arrhenius型流体行为.进一步通过动态流变、示差扫描量热(DSC)、电化学测试等方法研究了混合离子液体中DIL比例对聚甲基丙烯酸甲酯(PMMA)链缠结和松弛行为的影响,并讨论了PMMA/ILs体系热稳定性、玻璃化转变及离子电导率等的变化.结果表明,DIL独特的双咪唑环结构可与PMMA分子形成更多相互作用位点,从而导致凝聚缠结的形成,很大程度上限制了PMMA分子链的运动和松弛.随DIL含量增加,PMMA/ILs体系的松弛时间、热分解温度、玻璃化转变温度等参数均呈增大趋势,但其离子电导率有所损失,这与DIL较大的分子尺寸和运动能力有关.     

Dielectric and Viscoelastic Study of Entanglement Dynamics: A Review of Recent Findings

This article gives a review of the results of recent dielectric and viscoelastic studies for entangled binary blends of linear cis-polyisoprenes to explain the current understanding of the equilibrium entanglement dynamics on the basis of the molecular picture of dynamic tube dilation (DTD). Comparison of dielectric and viscoelastic properties reveals that the full-DTD picture regarding the relaxed portions of the chains as a solvent fails for the high molecular weight component chain in the blends at intermediate times. This failure is related to insufficient constraint release (CR) equilibration of the entanglement segments of this chain. A partial-DTD picture properly considering this CR equilibration successfully describes the linear relaxation behavior of the blends. The dielectric and viscoelastic properties of PI under fast flow, being affected by the flow-activated CR/DTD mechanism, are also presented in order to demonstrate the usefulness of the comparison of these properties in both equilibrium and non-equilibrium states.     

Crossover behavior in crystal growth rate from n‐alkane to polyethylene

A crystal growth rate equation, parameterized from molecular dynamics simulations of n‐alkanes, is compared to recent experiments on growth rates for polyethylene at high undercooling. The analysis reveals that the growth rate of alkanes and polyethylene can both be described by the same relationship. The appropriate relaxation time is used to describe the kinetic barrier to crystallization. For chains shorter than the entanglement length, this is the Rouse time. For chains longer than the entanglement molecular weight, kinetic limitations are modeled by the local relaxation of an entangled segment at the interface. This model supports a different mechanism for fast crystal growth at high undercooling than that usually inferred from slow growth data near the melting temperature. Use of the crystal growth rate model is illustrated for polyethylene crystallizing under conditions of slow cooling and fast cooling. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2468–2473, 2005     

Dissipative particle dynamics simulations of polymer melts. I. Building potential of mean force for polyethylene and cis-polybutadiene

We present the derivation of coarse-grained force fields for two types of polymers, polyethylene (PE), and cis-polybutadiene (cis-PB), using the concept of potential of mean force. Coarse-grained force fields were obtained from microscopic simulations for several coarse-graining levels, i.e., different number of monomers lambda per mesoscopic unit called "bead." These force fields are then used in dissipative particle dynamics (DPD) simulations to study structural and dynamical properties of polymer melts of PE and cis-PB. The radial distribution functions g(R), the end-to-end distance R0, the end-to-end vector relaxation time tau, and the chain center of mass self-diffusion D(CM), are computed for different chain lengths at different coarse-graining factor lambda. Scaling laws typical of the Rouse regime are obtained for both polymers for chain lengths ranging from 6 to 50 beads. It is found that the end-to-end distance R0 obtained from DPD simulations agree well with values obtained from both microscopic simulations and experiments. The dependence of the friction coefficient used in DPD simulations versus the coarse-graining level is discussed in view of the overall scaling of the dynamical properties.     

Influence of polyethylene oxide on the rheological properties of semidilute, wormlike micellar solutions of hexadecyltrimethylammonium chloride and sodium salicylate

The influence of polyethylene oxide (PEO) on the rheological properties of equimolar wormlike micellar solutions of hexadecyltrimethylammonium chloride (HTAC) and sodium salicylate (NaSal) is investigated, above the concentration where a micellar entanglement network is formed. PEO is known to have a temperature-dependent binding affinity for HTAC micelles. The influence of temperature, PEO concentration, and HTAC concentration is explored. Within the concentration and temperature range examined (25-100 mM HTAC and 25-50 degrees C), HTAC/NaSal solutions exhibit rheological characteristics of an entanglement network. Application of transient network theory provides information in the form of the plateau modulus, G(infinity)', the terminal viscoelastic relaxation time, tau(R), the reptation time, tau(rep), the micellar breaking time, tau(br), the mean micellar length, L , and the entanglement length, l(e). Consistent with literature data, increase of HTAC concentration results in an evolution from slow-breaking to fast-breaking behavior, accompanied by an increase in G(infinity)' and tau(rep), and decreases in tau(R), and tau(br), l(e) and L . Addition of PEO results in a substantial decrease in G(infinity)' (increase in l(e)), and corresponding increases in tau(R) and L . These observations are consistent with the idea that binding of HTAC micelles to PEO in aqueous solution decreases the number of surfactant molecules available to contribute to the entanglement network of wormlike micelles.     

Scaling of mesoscale simulations of polymer melts with the bare friction coefficient

Both the Rouse and reptation model predict that the dynamics of a polymer melt scale inversely proportional with the Langevin friction coefficient xi. Mesoscale Brownian dynamics simulations of polyethylene validate these scaling predictions, providing the reptational friction xi(R)=xi+xi(C) is used, where xi(C) reflects the fundamental difference between a deterministic and a stochastic propagator even in the limit of xi to zero. The simulations have been performed with Langevin background friction and with pairwise friction, as in dissipative particle dynamics. Both simulation methods lead to equal scaling behavior with xi(C) having almost the same value in both cases. The scaling is tested for the diffusion g(t), the shear relaxation modulus G(t), and the Rouse mode autocorrelations of melts of C(120)H(242), C(400)H(802), and C(1000)H(2002). The derived dynamical scaling procedure is very useful to reduce run-time in mesoscale computer simulations, especially if pairwise friction is applied.     

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.     

Length-scale dependent relaxation shear modulus and viscoelastic hydrodynamic interactions in polymer liquids

A quantitative theory of hydrodynamic interactions in unentangled polymer melts and concentrated solutions is presented. The study is focussed on the pre-Rouse transient time regimes (t < τ(R), the Rouse relaxation time) where the hydrodynamic response is governed mainly by the viscoelastic effects. It is shown that transient viscoelastic hydrodynamic interactions are not suppressed (screened) at large distances and are virtually independent of polymer molecular mass. A number of transient regimes of unusual and qualitatively different behavior of isotropic and anisotropic hydrodynamic response functions are elucidated. The regimes are characterized in terms of two main length-scale dependent characteristic times: momentum spreading time τ(i) ∝ r(4∕3) and viscoelastic time τ(?) ∝ r(4). It is shown that for t > τ(i) the viscoelastic hydrodynamic interactions can be described in terms of the time or length scale dependent effective viscosity which, for t < τ(R) and/or for r < R(coil), turns out to be much lower than the macroscopic "polymer" viscosity η(m). The theory also involves a quantitative analysis of the length-scale dependent stress relaxation in polymer melts. The general predictions for hydrodynamic interactions in thermostated systems with Langevin friction are obtained as well.