Molecular Interpretation of Dynamic Birefringence and Viscoelasticity of Amorphous Polymers

Abstract

Published data of dynamic birefringence and viscoelasticity of amorphous polymers were compared with the molecular expression of stress proposed by Gao and Weiner. The theory states that the stress is composed of contributions from the chain orientation (orientation term), the monomer orientation around the chain axis (rotation term), and the fluctuation of the local stress tensor (fluctuation term); the birefringence is composed of only two terms corresponding to the first two of the stress. The experimental data indicate that in the glassy zone and the high-frequency region of the glass-to-rubber transition zone the stress is attributable to the rotation and the fluctuation terms and the degrees of contribution vary with polymer species. For polymers with flat units (like polycarbonate), the fluctuation term is negligible and the relaxation spectrum in the glassy zone is low. For polymers with thin axisymmetric units (like polyisobutylene) or bulky irregular units (like poly(2-vinylnaphthalene)), the relaxation spectrum in the glassy zone is enhanced by the fluctuation term. It is also argued that, for polymers with thin axisymmetric units, the relaxation spectrum for the rotation term resembles that of a dilute solution; the role of rotational barrier along the chain is relatively enhanced since the rotational barrier from the surrounding is low because of the symmetry of the unit and because of the high fluctuation of the local stress. Some experiments are proposed to verify the statements. IntroductionThe strain-induced birefringence of polymers is related to the stress. In the rubbery and terminal flow zones of the stress relaxation or dynamic mechanical measurements, the deviatoric component of the refractive index tensor, An, is proportional to that of the stress tensor, u.

Birefringence of Polymers in the Softening Zone

“…The virial stress formulation, whereby vector forces are summed to yield the system stress, is often used in molecular dynamic simulations of polymers, 18 and it has been taken as justification for eq 5. 7,8 However, simulations can be analyzed using alternative conservation laws, for example, summation of the local strains. [19][20][21] Creep/recovery experiments on a polymer melt enable the assumption underlying eq 4 to be assessed directly.…”

Multiple Representation of Linear Dielectric Response

“…This situation is again similar to the situation for the viscoelastic response, the preference of G*(w) for materials obeying the stress-optical rule. [2][3][4][5] In this article, we first start from the most fundamental linear stimuli-response framework to re-visit the above duality in the representation of the dielectric response. Then, we focus on the relaxation functions involved in this framework and examine, for some model cases, molecular expressions of these functions that naturally results in the preference of e*.…”

Molecular Cooperativity in Large Deformation and Subsequent Structural Relaxation for Epoxy Glass

“…[13][14][15][16][17][18][19][20][21][22] The MSOR is considered to be a powerful tool also for epoxy glass to study its plastic deformation mechanism.…”

“…The MSOR states that stress σ can be divided into two components σ R and σ G , and that these stress components contribute to the change in birefringence Δn as follows: 14,19) where, C R and C G are materials constants designated as stressoptical coefficients. Stress component σ R was ascribed to the entropic elasticity of orientation motion of main chains, and σ G was ascribed to torsion or rotational motion of structure units around a main chain.…”

“…Stress component σ R was ascribed to the entropic elasticity of orientation motion of main chains, and σ G was ascribed to torsion or rotational motion of structure units around a main chain. [13][14][15][16][17] In the case of dynamic measurements, the complex modulus E * is related to the complex strain-optical coefficient O * as follows:…”