A COMPARATIVE STUDY OF CHAIN DYNAMICS OF DI-AND TRI-BLOCK COPOLYMERS IN SEMIDILUTE SOLUTION IN A NON-SELECTIVE SOLVENT

The chain dynamics of a pair of diblock poly(styrene-b-butadiene) (PS210-b-PB960) and triblock poly(styrene-b-butadiene-b-styrene) (PS200-b-PB1815-b-PS200) copolymers in both dilute and semidilute toluene solutions has been comparatively studied by dynamic laser light scattering. As expected, the mutual diffusion of individual chain changes into a fast cooperative diffusion of the chain segments (“blobs“) between two neighboring entanglement points for both the copolymers as the solution changes from dilute to semidilute. Further increases of the concentration lead to a second slow relaxation mode. For the triblock chains, there exists an additional middle relaxation between the fast and the slow modes.with 0.33 ＜α＜ 0.44, much smaller than 0.75 predicted or 0.72 observed for linear homopolymer chains in good solvent. It implies that the solvent quality of toluene for PB might not be as good as that for PS. Due to such a difference in solubility, it is reasonable to speculate that the PB and PS blocks are transiently segregated in semidilute solution. The relaxation of these transient PB and PS richer domains leads to the observed slow relaxation. Such a speculation is supported by the appearance of an additional slow relaxation mode in the study of polyisoprene-b-polystyrene-b-polyisoprene in semidilute solution in cyclohexane, a non-selective solvent, in which we alternated the solubility difference by a variation of the solution temperature.     

Study of tetrabutylammonium perfluorooctanoate aqueous solutions with two cloud points by dielectric relaxation spectroscopy

Dielectric relaxation spectra of tetrabutylammonium perfluorooctanoate (TBPFO), an anionic fluorocarbon surfactant with two cloud points in aqueous solution, were investigated in the frequency range from 40 Hz to 110 MHz. Striking dielectric relaxations were observed when both the temperature-dependent and concentration-dependent phase transitions in TBPFO aqueous solution occurred. The changes in dielectric relaxation and the distribution of dielectric parameters were consistent with the phase boundaries of the phase diagram. In the first homogeneous phase region, two relaxations of rodlike micelles appeared at about 100 kHz and 5 MHz, which originated from the diffusion of the free counterions in the directions of the long axis and the short axis of rodlike micelles, respectively. With increasing temperature, two relaxations gradually turned to one as a result of the formation of connected or entanglement points between the wormlike micelles. The lengths of the long half-axis and the short half-axis of the rodlike micelles, as well as the average distance of the connected or entanglement points of the wormlike micelles, were evaluated by the obtained relaxation times.     

分子量分布对双烯聚合物粘弹性能的影响—Ⅱ.顺-1,4-聚异戊二烯的粘弹性能对分子量及其分布的依赖关系

本文利用凝胶渗透色谱和应力松弛方法研究了顺-1,4-聚异戊二烯的粘弹性能对分子量及分布的依赖性。实验结果表明,生胶的松弛模量和最长松弛时间与分子量和分子量分布都有依赖关系,主要是改变τ_m=KM_w^β关系中的K值,对β值的影响甚小。由于本体聚合物的链缠结而导致的非牛顿效应使生胶的τ_m与KM_w的关系偏离3.4法则,这可用缠结网络密度来校正。探讨了生胶的应力松弛过程是橡胶分子链的滑移和解缠结兼有的两种运动。低分子量级份对链缠结网络有显著影响,起稀释剂作用,使网络的临界缠结分子量增高。     

Chain contraction and nonlinear stress damping in primitive chain network simulations

Doi and Edwards (DE) proposed that the relaxation of entangled linear polymers under large deformation occurs in two steps: the fast chain contraction (via the longitudinal Rouse mode of the chain backbone) and the slow orientational relaxation (due to reptation). The DE model assumes these relaxation processes to be independent and decoupled. However, this decoupling is invalid for a generalized convective constraint release (CCR) mechanism that releases the entanglement on every occasion of the contraction of surrounding chains. Indeed, the decoupling does not occur in the sliplink models where the entanglement is represented by the binary interaction (hooking) of chains. Thus, we conducted primitive chain network simulations based on a multichain sliplink model to investigate the chain contraction under step shear. The simulation quantitatively reproduced experimental features of the nonlinear relaxation modulus G(t,γ). Namely, G(t,γ) was cast in the time-strain separable form, G(t,γ)=h(γ)G(t) with h(γ)=damping function and G(t)=linear modulus, but this rigorous separability was valid only at times t comparable to the terminal relaxation time, although a deviation from this form was rather small (within ±10%) at t>τ(R) (longest Rouse relaxation time). A molecular origin of this delicate failure of time-strain separability at t～τ(R) was examined for the chain contour length, subchain length, and subchain stretch. These quantities were found to relax in three steps, the fast, intermediate, and terminal steps, governed by the local force balance between the subchains, the longitudinal Rouse relaxation, and the reptation, respectively. The contributions of the terminal reptative mode to the chain length relaxation as well as the subchain length/stretch relaxation, not considered in the original DE model, emerged because the sliplinks (entanglement) were removed via the generalized CCR mechanism explained above and the reformation of the sliplinks was slow at around the chain center compared to the more rapidly fluctuating chain end. The number of monomers in the subchain were kept larger at the chain center than at the chain end because of the slow entanglement reformation at the center, thereby reducing the tension of the stretched subchain at the chain center compared to the DE prediction. This reduction of the tension at the chain center prevented completion of the length equilibration of subchains at t～τ(R) (which contradicts to the DE prediction), and it forces the equilibration to complete through the reptative mode at t?τ(R). The delicate failure of time-strain separability seen for G(t,γ) at t～τ(R) reflects this retarded length equilibration.     

Why is understanding glassy polymer mechanics so difficult?

In this Perspective, I describe recent work on systems in which the traditional distinctions between (i) unentangled versus well‐entangled systems and (ii) melts versus glasses seem least useful, and argue for the broader use in glassy polymer mechanics of two more dichotomies: systems which possess (iii) unary versus binary and (iv) cooperative versus noncooperative relaxation dynamics. I discuss the applicability of (iii–iv) to understanding the functional form of strain hardening. Results from molecular dynamics simulations show that the “dramatic” hardening observed in densely entangled systems is associated with a crossover from unary, noncooperative to binary, cooperative relaxation as strain increases; chains stretch between entanglement points, altering the character of local plasticity. Promising approaches for future research along these lines are discussed. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Pulsed NMR study of network formation in the course of bulk polymerization of methyl acrylate.

The proton spin-spin relaxation time (T2) during the bulk polymerization of methyl acrylate was measured as a function of the reaction time at various temperatures. Three kinds of T2 (T2L (long), T2S (short) and T2M (intermediate)) were obtained as the polymerization proceeded. The fraction of T2S (FS) increased sigmoidally at a certain reaction time, while that of T2L (FL) decreased reciprocally. The former corresponded to the amount of a polymer whose molecular weight was sufficiently high enough to cause a tight entanglement that produced a transient network structure; the latter reflected a decrease in the mixture of the monomer and the low molecular weight of the polymer. T2M is considered to arise from a relatively mobile region of the entanglement. The relationship between the fractions of T2S + T2M and the polymer yield was found to be linear, which led us to monitor the polymer yield in real time during the polymerization in a non-distractive manner. 13C DD (dipolar decoupling)/MAS (magic angle spinning) NMR spectra were also measured to monitor the polymerization process in terms of the molecular motions between the main chain and the side chain in the formation of a network structure. The 13C DD/MAS NMR spectra show that the side chain motion became restricted as well as the main chain when the "Trommosdorff effect" (gel effect) was observed, and a part of the monomers were trapped in the network structure.     

Mesoscopic simulation of the crossing dynamics at an entanglement point of surfactant threadlike micelles

The crossing dynamics at an entanglement point of surfactant threadlike micelles in an aqueous solution was studied using a mesoscopic simulation method, dissipative particle dynamics, with a coarse-grained surfactant model. The possibility of a phantom crossing, which is the relaxation mechanism for the pronounced viscoelastic behavior of surfactant threadlike micellar solution, was investigated. When two threadlike micelles were encountered at an entanglement point under the condition close to thermal equilibrium, they fused to form a four-armed branch point. Then, a phantom crossing reaction occurred occasionally, or one micelle was cut down at the branch point. Increasing the repulsive forces between hydrophilic parts of the surfactants, fusion occurred less and the threadlike micelle was frequently broken down at an entanglement point. In these three schemes (a phantom crossing cut down at the branch point, and break down at the entanglement point), the breakage occurs at somewhere along the threadlike micelle. The breakage is considered as an essential process in the relaxation mechanism, and a phantom crossing can be seen as a special case of these processes. To explain the experimental evidence that a terminal of threadlike micelles is scarcely observed, a mechanism was also proposed where the generated terminal merges into the connected micelle part between two entanglement points due to the thermal motion.     

Local chain mobility of gellan in aqueous systems studied by fluorescence depolarization

The local chain mobility of a gellan, an electrolyte polysaccharide, in aqueous systems was examined with respect to the effect of the temperature, the concentration of gellan (c(G)), and the concentration of added salt (c(S)). The relaxation time of local motion was estimated for fluorescein isothiocyanate (FITC)-labeled-gellan by the fluorescence depolarization technique, and the chain mobility was discussed. The relaxation time increased with decreasing temperature, in particular when accompanying the coil-helix transition due to the great difference in chain mobility between the coil and the helical conformations. The effect of c(G) was observed for gellan solutions even below the critical concentration of chain entanglement (2 wt.-%) for well-expanded nonelectrolyte polymers with size similar to that of the gellan. This suggests that the actual excluded volume of gellan is larger than that of nonelectrolyte polymers due to the electrostatic repulsion between segments. The relaxation time for 0.2 wt.-% systems of gellan in coil conformation is independent of c(S), whereas a c(S) dependence of the relaxation time is clearly observed for 0.5 wt.-% systems. The degree of expansion of the gellan chain is independent of the shielding effect of cations on the electrostatic repulsion between gellan segments due to the stiffness of gellan chain. On the other hand, the c(G) as well as the c(S) dependence of the chain mobility is clearly observed for gellan in the helical conformation, examined over the concentration range, probably due to the partial aggregation of helices induced by the attractive interaction between gellan segments.     

Interactions between Hydrophobically Modified Associating Polyacrylamide and Cationic Surfactant at the Water‐Octane Interface: Interfacial Dilational Viscoelasticity and Relaxation Processes

The interfacial dilational viscoelastic properties of hydrophobically associating block copolymer composed of acrylamide (AM) and a low amount of 2‐ethylhexyl acrylate (EHA) (<1.0 mol%) with a hydrolyzed degree of about 1.5–2.0% at the octane‐water interfaces were investigated by means of two methods: the interfacial tension response to sinusoidal area variations (oscillating barriers method) and the relaxation of an applied stress (interfacial tension relaxation method) respectively. The influence of cationic surfactant cetyl trimethylammonium bromide (CTAB) on the dilational viscoelastic properties was studied. The results obtained by oscillating barriers method showed that dilational modulus decreased moderately with the increase of CTAB concentration. The results obtained by interfacial tension relaxation measurements showed that two main relaxation processes exist in the interface at 7,000 ppm polymer concentration: one is the fast process involving the exchange of hydrophobic blocks between the proximal region and distal region in the interface; the other is the slow relaxation process involving conformational changes of polymer chain in the interface. By adding CTAB, the slow process changed obviously due to the strong electrostatic interaction between oppositely charged surfactant and hydrolyzed part of polymer chain. Only when the CTAB concentration was close to the “equal charge point,” the associations formed mainly by the hydrophobic interaction like that in SDS/polymer system appeared and the characteristic time of fast process decreased obviously. The information of relaxation processes obtained from interfacial tension relaxation measurements can explain the results from dilational viscoelasticity measurements very well.     

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.     

Tube relaxation: A quantitative molecular model for the viscoelastic plateau of entangled polymeric media

The relaxation of an entangled polymeric medium in the viscoelastic plateau is investigated theoretically by using the slip-link representation of topological constraints. In addition to the chain retraction process introduced by Daoudi and investigated theoretically by Doi, we show that two processes contribute significantly to the relaxation: The first, “equilibration across slip-links,” is a longitudinal reequilibration between parts of the chain which have been differently extended or compressed, depending on their initial orientation relatively to the strain tensor. The second, “tube relaxation,” is a mean-field representation of the loss of topological constraints on one chain due to the retraction of the others. Closed analytical expressions for the stress accounting for these three processes are derived and compared with previous theories: the relaxation should be much more progressive than previously predicted, and the terminal time for retraction is reduced significantly by tube relaxation.     

Effect of chain entanglements on plastic deformation behavior of ultra‐high molecular weight polyethylene

Samples of ultra‐high molecular weight polyethylene, in which the chain topology within the amorphous component was altered using two‐stage processing, including crystallization at high pressure in the first step, were produced and their deformation behavior in the plane‐strain compression was studied. Deformation and recovery experiments demonstrated that the state of the molecular network governed by entanglement density is one of the primary parameters controlling the response of the material on the imposed strain, especially at moderate and high strains. Any change in the concentration of entanglements markedly influences the shape of the true stress–true strain curve. The strain hardening modulus decreases while the onset of strain hardening increases with a decrease of the entanglement density within the amorphous component. Density of entanglements also influences the amount of rubber‐like recoverable deformation and permanent plastic flow. In material of the reduced concentration of entanglements permanent flow appears easier and sets in earlier than in the material with a higher entanglement density, becoming a favorable deformation mechanism at moderate strains. As a result, strong strain hardening is postponed to higher strain when compared with the samples of equilibrium entanglement density. In the samples of an increased entanglement density the molecular network becomes stiffer, with a reduced ability of strain induced disentangling of chains. Consequently, there is a less permanent flow and strain hardening begins earlier than in the reference material of an unaltered chain topology. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 276–285, 2010     

溶液中尼龙11的NMR弛豫研究

用 2DNMR(HMQC)技术归属了溶液中尼龙 11分子的主要1H和13 C NMR共振信号 ,并通过变温和变浓度 1H NMR弛豫时间的测定 ,得到了尼龙 11溶液中氢键结构变化的动力学信息 .结果表明 ,溶液中尼龙 11分子的弛豫行为与一般高聚物不同 ,随着温度升高 ,尼龙链间相互作用逐渐减弱 ,尼龙分子与溶剂小分子间相互作用逐渐增强 ,尼龙链间氢键逐渐离解 ,而离解出来的自由NH和CO基团又与溶剂小分子间生成氢键 .尼龙 11链卷曲堆积成无规线团状 ,一部分溶剂被包裹在内部并和α CO质子成为一个整体而一起运动 .变浓度实验弛豫过程呈现双指数特性 ,快弛豫部分随体系浓度增加而增多 ,表明聚合物溶液中凝聚缠结含量的增大 ,这种凝聚缠结是由溶液中氢键引起分子链物理交联成网而形成的 .随着浓度增加 ,溶液逐渐变成局部粘度较大的类似软固体     

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.     

Significance of cross correlations in the stress relaxation of polymer melts

According to linear response theory, all relaxation functions in the linear regime can be obtained using time correlation functions calculated under equilibrium. In this paper, we demonstrate that the cross correlations make a significant contribution to the partial stress relaxation functions in polymer melts. We present two illustrations in the context of polymer rheology using (1) Brownian dynamics simulations of a single chain model for entangled polymers, the slip-spring model, and (2) molecular dynamics simulations of a multichain model. Using the single chain model, we analyze the contribution of the confining potential to the stress relaxation and the plateau modulus. Although the idea is illustrated with a particular model, it applies to any single chain model that uses a potential to confine the motion of the chains. This leads us to question some of the assumptions behind the tube theory, especially the meaning of the entanglement molecular weight obtained from the plateau modulus. To shed some light on this issue, we study the contribution of the nonbonded excluded-volume interactions to the stress relaxation using the multichain model. The proportionality of the bonded/nonbonded contributions to the total stress relaxation (after a density dependent "colloidal" relaxation time) provides some insight into the success of the tube theory in spite of using questionable assumptions. The proportionality indicates that the shape of the relaxation spectrum can indeed be reproduced using the tube theory and the problem is reduced to that of finding the correct prefactor.     

Stress relaxation upon cessation of steady flow and the overshoot effect of polymer solutions

The basis for obtaining the steady-state compliance from stress relaxation upon cessation of steady flow (SRUCSF) data is derived. Measurements on three polymer solutions of differing molecular weight, polydispersity, and degree of entanglement coupling show good agreement between results from SRUCSF and creep-recovery experiments in both linear and nonlinear viscoelastic regions. The stress overshoot phenomenon is interpreted in terms of a change in entanglement spacing upon imposition of a shearing field. The phenomenon is analyzed in terms of a relaxation time for re-entanglement, which is found to be much longer than the relaxation time of the shear stress upon cessation of steady flow.     

受限状态聚合物熔体的分子动力学模拟

用粗粒化的分子动力学(MD)模拟方法从分子层次研究了受限于粗糙壁内的聚合物熔体的动力学性质. 结果表明, 对于链长较短的受限聚合物熔体体系, 随着膜厚的增加, 体系内部高分子链的松弛时间逐渐减少; 然而对于链长较长的受限体系, 聚合物链的松弛时间随着膜厚的增加先减少后增加. 推测这种由于链长的变化所引起的动力学性质的差异源自受限熔体内聚合物链聚集状态的改变, 并且通过考察交叠参数对这种改变进行了分析. 结果表明, 在膜厚增加的过程中, 决定受限状态高分子长链松弛机理的因素逐渐从受限效应转变成为链间的缠结效应.     

Viscoelastic properties of entangled polymers. II. The interchain–intrachain entanglement model

Our earlier model of entangled chain dynamics represented the elastic effects at entanglement points as a coupling with the surrounding medium, which was propagated weakly to every other entanglement site on the parent chain. In this way, a great variety of linear viscoelastic phenomena could be successfully predicted, with the only significant deficiency being a quantitative failure in curve fitting the local minimum in dynamic loss modulus G″(ω). Here we introduce the “intrachain entanglement,” or the “internal entanglement,” in which the parent chain entangles directly with itself. Elastic forces between pairs of internal entanglements are assumed to be stronger than those with the medium (“external entanglement”). Predictions of the new model are compared with rheological data on monodisperse polystyrene. Good agreement is obtained between theory and experiment, including G″(ω).     

Strain hardening of polymer glasses: Effect of entanglement density,temperature, and rate

The strain hardening behavior of model polymer glasses is studied with simulations over a wide range of entanglement densities, temperatures, strain rates, and chain lengths. Entangled polymers deform affinely at scales larger than the entanglement length as assumed in entropic network models of strain hardening. The dependence of strain hardening on strain and entanglement density is also consistent with these models, but the temperature dependence has the opposite trend. The dependence on temperature, rate, and interaction strength can instead be understood as reflecting changes in the flow stress. Microscopic analysis of local rearrangements and the primitive paths between entanglements is used to test models of strain hardening. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3487–3500, 2006