This review article focuses on the transport phenomena of entangled polymeric liquids. The study of transport phenomena is one of the fundamental fields in chemical engineering, which addresses the transport of mass, momentum, and energy. For simple transport cases, such as the flow of a Newtonian fluid, the methodology of transport phenomena has been established. However, for an entangled polymeric liquid, which is an example of a viscoelastic liquid, various problems remain due to the various time and length scales involved. In this review article, we summarize studies of entangled polymeric liquids for problems on different time and length scales and multiscale problems that connect different scales.
Foams have a large number of applications in our daily life. Their stability depends on the thin liquid film, which consists of an aqueous phase bound by two air-water interfaces. During its processing, foam is exposed to a large deformation. Therefore, the study of the air-water interface under large amplitude oscillatory shear (LAOS) flow is highly relevant for foam stability. In this article, the LAOS behavior of the air-water interface was investigated. The interface was formed by 0.1 mol m−3 hexadecyltrimethylammonium bromide and 0.5% w/v silica nanoparticles. The LAOS study was performed by analyzing the intracycle stress waveforms and Lissajous-Bowditch curves. The Fourier transform rheology and Chebyshev polynomial approaches were used to describe the LAOS flow of the interface. The air-water interface exhibited intracycle strain-hardening and shear thickening behavior under the LAOS flow. However, at very large strain amplitude (i.e. 45%), the interface displayed intracycle shear thinning behavior.
Theoretical analysis was made for dielectric relaxation of model chains, linear Rouse chains having type-A dipoles and being end-adsorbed (tethered) and desorbed at equilibrium, with an attempt to find a clue for investigation of the adsorbed chain dynamics in polymer nanocomposites. Expanding the bond vector of those chains with respect to the Rouse eigenfunctions, we obtained analytical expressions of the normalized complex dielectric permittivity and the first-moment average relaxation time of those chains. The adsorbed and desorbed chains, respectively, were found to exhibit retarded and accelerated relaxation due to motional coupling activated by their mutual conformation transfer.
For the entangled polymer dynamics, in addition to reptation and contour length fluctuation (CLF), constraint release (CR) has been widely accepted as an essential relaxation mechanism. However, although conceptually established, the nature of CR has not been fully clarified yet. In this study, entangled polymer dynamics were observed via primitive chain network simulations in the melt, and in a matrix where CR is suppressed. The viscoelastic and end-to-end relaxation times, the diffusion constant, and the apparent plateau modulus were obtained as functions of molecular weight. All the obtained results are reasonably consistent with experimental data in the literature. In the results, CR accelerates the relaxation and the diffusion as expected, and the acceleration factor decreases as an increase of the molecular weight. Consequently, the power-law exponent for the molecular weight dependence of the relaxation time is affected by CR. Meanwhile, the plateau modulus is not affected by CR, yet the molecular weight dependence is consistent with the literature. These results explain the time-stress discrepancy, which has been reported as inconsistency between the relaxation time and the modulus.
Using the primitive chain network model, we have simulated the startup of steady planar elongation of a moderately entangled polymer melt at several elongation rates. The time dependence of the first normal stress growth coefficient, η+p1, was similar to that under startup uniaxial elongation, η+u, and exhibited significant strain hardening when the Rouse Weissenberg number, WiR ≳ 1. Analysis of the chain conformation revealed that planar elongation resulted in the loss of fewer entanglements and in a lower orientation anisotropy compared to uniaxial elongation, and these two effects nearly compensated each other resulting in the qualitative similarity between η+p1 and η+u. The second normal stress growth coefficient, η+p2, showed only strain softening and resembled startup shear including the appearance of a stress maximum. Independent of the strain rate, this stress maximum occurred at approximately half the strain at the stress maximum under startup shear. The time dependence of the segment orientation revealed that the molecular origin of the stress maximum can be attributed to the maximum in the corresponding orientation anisotropy, in direct analogy to the behavior under shear.
Linear viscoelastic behavior has been examined for the mixtures of a transient network and entangled linear polymers in aqueous solutions. We have found that the aqueous blends of hydrophobically ethoxylated urethane (HEUR) and sodium polyacrylate (PAANa) become transparent solutions and look homogeneous. To examine the molecular level homogeneity of this mixture, we analyze the linear viscoelastic spectra as functions of the volume fraction of PAANa, ϕP, at fixed HEUR concentrations, especially focusing on the plateau modulus, GN,mix of the mixtures. The increase in GN,mix by increasing ϕP is assumed to be due to the formation of the hetero-entanglement between HEUR and PAANa, and the contribution of the hetero-entanglement on the plateau modulus, G0N,H−P, can be estimated by using the Wu’s model. We have obtained the result that all the data can be explained in terms of a single G0N,H−P value, strongly supporting the view that the HEUR and PAANa chains are homogeneously mixed and interpenetrated each other in the mixed aqueous solutions.