Lin Y-H, Das A K
Department of Applied Chemistry, National Chiao Tung University, Hsinchu 30050, Taiwan.
J Chem Phys. 2007 Feb 21;126(7):074903. doi: 10.1063/1.2431649.
The nonlinear viscoelastic behavior of the Fraenkel-chain model is studied with respect to the constitutive equation of the Rouse model. Distinctly different from the results of the Rouse model, the Fraenkel-chain model gives the following characteristic nonlinear behavior: (a) The two distinct dynamic modes in the relaxation modulus GS(t,lambda)--as observed in the linear region reported in Paper I [Y.-H. Lin and A. K. Das, J. Chem. Phys. 126, 074902 (2007), preceding paper]--or in the first normal-stress difference function GPsi1(t,lambda) are shown to have different strain dependences: strain hardening for the fast mode and strain softening for the slow mode. (b) The Lodge-Meissner relation GS(t,lambda)=GPsi1(t,lambda) holds over the whole time range, which has been shown both analytically and by simulation. (c) The second normal-stress difference is nonzero, being positive in the fast-mode region and negative in the slow-mode region. The comparisons between orientation and stress for all tensor components consistently confirm the strong correlation of the slow mode as well as its entropic nature with the segmental-orientation anisotropy as shown in the linear region studied in Paper I. A consequence of this correlation is the applicability of the stress-optical rule in the slow-mode region. This also leads to the expectation that the damping function h(lambda)=G(S)(t,lambda)/G(S)(t,lambda-->0) and the ratio between the first and second normal-stress differences, N2(t,lambda)/N1(t,lambda), are described by the orientation tensor which has the same form as that given by Doi and Edwards [J. Chem. Soc. Faraday Trans. 2 74, 1789 (1978); 74, 1802 (1978)] with independent-alignment approximation for an entangled system. The similarity between the slow mode of an entanglement-free Fraenkel-chain system and the terminal mode of an entangled polymer system as observed in the comparison of theory, simulation, and experiment suggests that the close correlation of the entropic nature of the mode with the orientation anisotropy--as of the Fraenkel segment or the primitive step in the Doi-Edwards theory--is a generally valid physical concept in polymer viscoelasticity.
针对劳斯模型的本构方程，研究了弗伦克尔链模型的非线性粘弹性行为。与劳斯模型的结果明显不同，弗伦克尔链模型呈现出以下特征性的非线性行为：(a) 在弛豫模量GS(t,λ) 中观察到的两种不同的动态模式——如在论文I [Y.-H. 林和A.K. 达斯，《化学物理杂志》126, 074902 (2007)，前文] 报道的线性区域中，或在第一法向应力差函数GPsi1(t,λ) 中——显示出具有不同的应变依赖性：快速模式为应变硬化，慢速模式为应变软化。(b) 洛奇-迈斯纳关系GS(t,λ)=GPsi1(t,λ) 在整个时间范围内成立，这已通过解析和模拟得到证明。(c) 第二法向应力差不为零，在快速模式区域为正，在慢速模式区域为负。对所有张量分量的取向和应力之间的比较一致地证实了慢速模式及其熵性质与论文I中研究的线性区域中链段取向各向异性的强相关性。这种相关性的一个结果是应力-光学规则在慢速模式区域的适用性。这也导致人们期望阻尼函数h(λ)=G(S)(t,λ)/G(S)(t,λ→0) 以及第一和第二法向应力差之比N2(t,λ)/N1(t,λ) 由取向张量描述，该取向张量具有与Doi和Edwards [《化学学会法拉第会刊》2 74, 1789 (1978); 74, 1802 (1978)] 给出的形式相同，对于缠结系统采用独立排列近似。在理论、模拟和实验的比较中观察到的无缠结弗伦克尔链系统的慢速模式与缠结聚合物系统的末端模式之间的相似性表明，该模式的熵性质与取向各向异性（如弗伦克尔链段或Doi-Edwards理论中的原步）的紧密相关性是聚合物粘弹性中一个普遍有效的物理概念。
