Mesoscopic theory of the viscoelasticity of polymers

We have advanced our previous static theory of polymer entanglement involving an extended Cahn-Hilliard functional, to include time-dependent dynamics. We go beyond the Gaussian approximation, to the one-loop level, to compute the frequency dependent storage and loss moduli of the system. The three parameters in our theory are obtained by fitting to available experimental data on polystyrene melts of various chain lengths. This provides a physical representation of the parameters in terms of the chain length of the system. We discuss the importance of the various terms in our energy functional with respect to their contribution to the viscoelastic response of the polymeric system.Comment: Submitted to Phys. Rev.

The effect of annealing on the nonlinear viscoelastic response of isotactic polypropylene

Three series of tensile relaxation tests are performed on isotactic polypropylene at room temperature in the vicinity of the yield point. In the first series of experiments, injection-molded samples are used without thermal pre-treatment. In the second and third series, prior to testing the specimens are annealed at 130 C for 4 and 24 hours, respectively. Constitutive equations are derived for the time-dependent response of semicrystalline polymers at isothermal loading. A polymer is treated as an equivalent temporary network of macromolecules bridged by junctions (physical cross-links, entanglements and crystalline lamellae). Under loading, junctions slip with respect to their positions in the bulk material (which reflects the viscoplastic behavior), whereas chains separate from their junctions and merge with new ones at random times (which reflects the viscoelastic response). The network is thought of as an ensemble of meso-regions (MR) with various activation energies for detachment of chains from temporary nodes. Adjustable parameters in the stress-strain relations are found by fitting observations. Experimental data demonstrate that the shape of the relaxation spectrum (characterized by the distribution of MRs with various potential energies) is independent of mechanical factors, but is altered at annealing. For specimens not subjected to thermal treatment, the growth of longitudinal strain does not affect the volume fraction of active MRs and the attempt rate for detachment of chains from their junctons. For annealed samples, the concentration of active MRs increases and the attempt rate decreases with strain. These changes in the time-dependent response are attributed to broadening of the distribution of strengths of crystalline lamellae at annealing.Comment: 30 pages, 13 figure

Engineering polymer informatics: Towards the computer-aided design of polymers

The computer-aided design of polymers is one of the holy grails of modern chemical informatics and of significant interest for a number of communities in polymer science. The paper outlines a vision for the in silico design of polymers and presents an information model for polymers based on modern semantic web technologies, thus laying the foundations for achieving the vision

Cure versus Flow in Dispersed Chip-Underfill Materials

The relative stability of chip-underfill composite materials was modeled as a function of glass filler concentration between 10 and 70 wt.-%, filler particle size (between 5 and 25 microns), and the curing temperature of the resin (150 vs. 180 °C), yielding different dynamic viscosity profiles. The stability was gauged using a modified sigmoidal chemorheology model for the dynamic viscosity, and incorporating the time-dependent viscosity into a model for Stokes' law of sedimentation. We also incorporated a hindered sedimentation term, due to filler concentration due to the higher loadings. Several important findings were observed. First, it appears to be the high concentration of filler that is maintaining the stability of these dispersions during cure. Smaller concentrations of the same particles were predicted to have a larger sedimentation velocity leading to stratification in the resin with time. Second, higher cure temperatures led to a shorter period of sedimentation in a pre-cured state and resulted in less sedimentation, even though there was probably a slightly smaller viscosity in the pre-cured condition. While these process models adequately describe the physics of the competitive processes of cure and sedimentation, a full picture may be incomplete without a larger determination of how this also affects polymerization shrinkage and residual shear stress upon cure.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/61220/1/828_ftp.pd

Topological character of hydrodynamic screening in suspensions of hard spheres: an example of universal phenomenon

Although in the case of polymer solutions the existence of hydrodynamic screening is considered as established, use of the same methods for suspensions of hard spheres so far have failed to produce similar results. In this work we reconsider this problem. Using superposition of topological, combinatorial and London-style qualitative arguments, we prove the existence of screening in suspensions. We show that the nature of hydrodynamic screening in suspensions is analogous to that known for the Meissner effect in superconductors. The extent of screening depends on volume fraction of hard spheres. The zero volume fraction limit corresponds to the normal state. The case of finite volume fractions-to the mixed state typical for superconductors of the second kind. Such a state is becoming fully "superconducting" at some critical volume fraction for which the (zero frequency) relative viscosity diverges. Our analytical results describing this divergence are in accord with known scaling results obtained by Brady and Bicerano et al which are well supported by experimental data. We provide theoretical explanation of the divergence of relative viscosity in terms of a topological-type transition which mathematically can be made isomorphic to the more familiar Bose-Einstein condensation transition. Because of this, the methods developed in this work are not limited to suspensions only. In concluding section we mention other applications of the developed formalism ranging from turbulence and magnetohydrodynamics to high temperature superconductors, QCD, string models, etc.Comment: 49 page

Time scale analysis for fluidizedbedmeltgranulation-II: binder spreading rate

The spreading time of liquid binder droplet on the surface a primary particle is analyzed for Fluidized Bed Melt Granulation (FBMG). As discussed in the first paper of this series (Chua et al., in press) the droplet spreading rate has been identified as one of the important parameters affecting the probability of particles aggregation in FBMG. In this paper, the binder droplet spreading time has been estimated using Computational Fluid Dynamic modeling (CFD) based on Volume of Fluid approach (VOF). A simplified analytical solution has been developed and tested to explore its validity for predicting the spreading time. For the purpose of models validation, the droplet spreading evolution was recorded using a high speed video camera. Based on the validated model, a generalized correlative equation for binder spreading time is proposed. For the operating conditions considered here, the spreading time for Polyethylene Glycol (PEG1500) binder was found to fall within the range of 10-2 to 10-5 s. The study also included a number of other common binders used in FBMG. The results obtained here will be further used in paper III, where the binder solidification rate is discussed