Session T17: Focus Session: Dynamics of Polymers and Complex Fluids I

Importance of the difference between maximum and average tube length fluctuations of entangled polymers

Classical analysis of tube length fluctuations (TLF) in entangled polymer solutions and melts includes only mean fluctuations and strongly underestimates the effect of TLF. We show that maximum fluctuations lead to additional logarithmic time dependence of stress relaxation function $\mu(t)$ that varies with time $t$ at $t<\tau_R$ as $\mu(t)\sim t^{1/4}\log t$ instead of $\mu(t)\sim t^{1/4}$, where $\tau_R$ is Rouse time. At $\tau_R [Preview Abstract]

How Entangled Polymer Chains Relax

It will be shown through a series of experiments with selectively deuterated model polymers that stress relaxation occurs through a mechanical percolation process which permits large clusters of entangled polymers to stress relax before their conformations are fully relaxed. We find that: (a) Reptating homopolymer chains with molecular weight M $>>$ M$_{c}$ appear to be non-Reptating as their ends and centers relax at the same rate in a Rouse-like manner during percolation. (b) The mechanical relaxation time .$\tau $(M) is related to the Reptation time T$_{r}\sim $ M$^{3}$ by .$\tau $(M) = T$_{r}$[(1-M$_{c}$/M) M$_{e}$/M$_{c}$]$^{2}$, which is the origin of the viscosity behaving as .$\eta \sim $M$^{3.4}$ (c) During stress relaxation, the random coil dimensions R$_{g}$(//) and R$_{g}$(.$\bot )$ are significantly not relaxed when the stress and birefringence relax to zero. (d) Matrix molecular weight P effects on relaxation time .$\tau $(M) of the probe chain M are as follows: When the probe chain M$>>$P, the matrix P-chains percolate and Rouse-like dynamics is observed for the M-Reptating chains with .$\tau $(M) $\sim $ P$^{1}$M$^{2}$. (e) When the matrix P$>>$M, percolation does not occur for the M-chain and the relaxation time of the probe chain .$\tau $(M) $\sim $ P$^{o}$M$^{3}$ is in accord with DeGennes Reptation theory. These results clearly suggest that current notions of polymer rheology involving chain end fluctuation and constraint release need to be reconsidered. .   

Dynamics in a polymeric melt: coupling the standard model to a slip-link model

We present a coarse grain approach to simulate the chain dynamics in a polymeric melt. The starting point is a particle-based implementation of the standard model of polymers, where chains are represented by a collection of beads interacting through soft pairwise potentials. A Langevin dynamics provides a realistic description for the behavior of short, unentangled polymers. To take into account at a coarse-grained level the entanglements that are important at high molecular weight, the model is supplemented with slip-links. We describe the specifics of our implementation, which, in contrast to some previous works, induces coupling between different chains. For the simple case of a homopolymeric melt, we characterize the motions of slip-links, the dynamics of the chain and the relaxation of stresses. The approach is also tested on diblock copolymers.   

Unconcatenated ring polymer melts: Molecular dynamics study of the static and dynamic properties

Molecular dynamics simulations were conducted to investigate the dynamic and structural properties of unconcatenated ring polymer melts in comparison to linear polymer melts. Systems were composed of 200--2500 polymer chains at a reduced temperature and density of 1.0 $\epsilon$ and 0.85 $\sigma^{-3}$, respectively. With $N$ denoting the number of monomers per chain, simulations were conducted with $N$ = 100, 200, 400 and 800. For the ring polymers an additional simulation was conducted with $N$ = 1600. The standard polymer melt model was modified by introducing a bending potential to make the chains stiffer. For each value of $N$, the ring polymers were found to have a higher diffusivity than their linear counterparts. While the ring polymers are found to be roughly spherical in shape, they display complex dynamic correlations as revealed by a primitive path analysis.   

Microscopic definition of entanglement

We propose to define polymer entanglements as long-lived contacts between the mean paths. The mean path is defined as a path connecting average positions of every monomer over characteristic time of entanglement $\tau_e$. We performed molecular dynamics simulations on variety of bead-spring models in equilibrium and under shear and investigated properties of entanglements defined in such way. A new algorithm for identification of entanglements allows tracing evolution of individual entanglements and quantifying such mechanisms as constraint release and convective constraint release.   

Polymer Architecture Effects on the Viscoelastic Bulk Modulus

The hypothesis that the bulk and shear responses arise from the same molecular mechanisms at short times but that the long-time chain mechanisms are unavailable to the bulk response is consistent with the results of our first work on polystyrene as well as with previous work by Plazek on an epoxy. Here we examine the effects of polymer architecture on the viscoelastic bulk modulus and its relationship to the shear response. A custom-built pressurizable dilatometer is used to study linear and star polystyrenes, as well as polycyanurates of differing crosslink density. The pressure-volume-temperature behavior (PVT) of the materials in the glassy and rubbery regimes is well characterized. In addition, at temperatures in the vicinity of the pressure-dependent glass transition temperature, the pressure relaxation response is measured, and this data is transformed to yield the time-dependent bulk modulus. Relaxation and retardation spectra derived from the bulk relaxation modulus measurements are compared to those from shear stress relaxation experiments.   

Localization and elasticity in entangled polymer liquids as a mesoscopic glass transition

The reptation-tube model is widely viewed as the correct zeroth order model for entangled linear polymer dynamics under quiescent conditions. Its key ansatz is the existence of a mesoscopic dynamical length scale that prohibits transverse chain motion beyond a tube diameter of order 3-10 nm. However, the theory is phenomenological and lacks a microscopic foundation, and many fundamental questions remain unanswered. These include: (i) where does the confining tube field come from and can it be derived from statistical mechanics? (ii) what is the microscopic origin of the magnitude, and power law scaling with concentration and packing length, of the plateau shear modulus? (iii) is the tube diameter time-dependent? (iv) does the confinement field contribute to elasticity ? (v) do entanglement constraints have a finite strength? Building on our new force-level theories for the dynamical crossover and activated barrier hopping in glassy colloidal suspensions and polymer melts, a first principles self-consistent theory has been developed for entangled polymers. Its basic physical elements, and initial results that address the questions posed above, will be presented. The key idea is that beyond a critical degree of polymerization, the chain connectivity and excluded volume induced intermolecular correlation hole drives temporary localization on an intermediate length scale resulting in a mesoscopic ``ideal kinetic glass transition.'' Large scale isotropic motion is effectively quenched due to the emergence of chain length dependent entropic barriers. However, the barrier height is not infinite, resulting in softening of harmonic localization at large displacements, temporal increase of the confining length scale, and a finite strength of entanglement constraints which can be destroyed by applied stress.   

Coupling Effects in Molecular Dynamics Simulation of Polymer melts

The motion in concentrated polymer systems is described by the Rouse or reptation models, which both assume that the relaxation of each polymer is essentially independent of the other polymers. However, various experiments have shown that there is certain cooperativity in the orientational relaxation which is called coupling effects. In our simulation, we calculate orientation self- and cross-correlation functions to quantify this coupling effect for original monomer and for coarse-grained blob. We use bead-spring to investigate this effect in binary blend of unentangled and weakly entangled chains in wide range of density and chain stiffness. We found that the coupling effects are very significant: the orientational corss-correlation functions of one chain with other chains are almost the same as the auto-correlation function at late time, whereas at early time it is 5 times smaller. A universal time-dependent coupling parameter for monodisperse and bidisperse melts was introduced, and is consistent to the results in the experiments and other simulations. Based on this universal coupling parameter, we can obtain orientation self- and cross-correlation functions in binary blends by using relaxation functions in monodisperse melt of each component. This coupling parameter is also introduced for different level of coarse-graining.   

Interplay of cooperativity and entanglements in polymer melt dynamics: insights from theory and simulations

Dynamical heterogeneities in polymer melts generate cooperative ?motion, which results in subdiffusive center-of-mass mean-square ?displacement at times shorter than the longest Rouse relaxation time. ?This behavior is described by our Generalized Langevin Equation ?for cooperative dynamics, which is found to be in agreement with data ?from simulations and from Neuron Spin Echo experiments. We present a ?study of the interplay between cooperative dynamics and polymer ?confinement due to the presence of entanglements. Semiflexibility, ?which is specific to the chemical structure of the polymer, and ?intermolecular interactions, which generate dynamical cooperativity ?and entanglements and are functions of the degree of polymerization, ?are explicitly included in the theory.   

Predicting non-linear rheology of randomly branched entangled polymer melts

We recently published a computational algorithm [C. Das et al Journal of Rheology 50, 207-235 (2006)] for predicting the linear rheology of arbitrarily branched polymer melts, which was successfully used for well defined architectures (stars, combs, Cayley trees etc.) and well-characterised industrial resins. We now discuss an extension to the non-linear regime, via a mapping onto a multi-mode ``pom-pom" ensemble. There is, in principle, sufficient information in the algorithm to do this without additional free parameters. However, the procedure is not exact and one must consider the most important physics to represent. In particular, we highlight the need to distinguish between stress relaxation via constraint release and via tube escape. We also discuss the topological ``priority" variable (which limits the stress in extension) and the considerations needed when assigning this to each polymer strand (which polymer segments should one count as relaxed?) In doing this, and as a result of tube advection, we find we need to introduce a new variable (``altitude") related to the topological distance of a strand from the molecule centre.   

Entanglement in miscible blends

The entanglement length $L_{\mathrm{e}}$ of polymer chains (corresponding to the entanglement molecular weight $M_{\mathrm{e}}$) is not an intrinsic material parameter but changes with the interaction with surrounding chains. For miscible blends of \textit{cis}-polyisoprene (PI) and poly(\textit{tert}-butyl styrene) (PtBS), changes of $L_{\mathrm{e}}$ on blending was examined. It turned out that the Le averaged over the number fractions of the Kuhn segments of the components (PI and PtBS) satisfactorily describes the viscoelastic behavior of pseudo-monodisperse blends in which the terminal relaxation time is the same for PI and PtBS.   

Comparing tube models for predicting the linear rheology of branched polymer melts

The hierarchical [1,2] and bob (or branch-on-branch) [3] models are tube-based computational models developed for predicting the linear rheology of general mixtures of polydisperse branched polymers. These two models are based on a similar tube-theory framework, but differ in their numerical implementation and details of relaxation mechanisms. We present a detailed overview of the similarities and differences of these models, and examine the effects of these differences on the predictions of the linear viscoelastic properties of a set of representative branched polymer samples, in order to give a general picture of the performance of these models. Our analysis confirms that the hierarchical and bob models quantitatively predict the linear rheology of a wide range of branched polymer melts, but also indicate that there is still no unique solution to cover all types of branched polymers without case-by-case adjustment of parameters such as the dilution exponent $\alpha$ and the factor $p^2$ which defines the hopping distance of a branch point relative to the tube diameter. An updated version of the hierarchical model, which shows improved computational efficiency and refined relaxation mechanisms, is introduced and used in these analyses. [1] R. G. Larson, Macromolecules 34, 4556 (2001). [2] S. J. Park {\it et al.}, Rheol. Acta 44, 319 (2005). [3] C. Das {\it et al.}, J. Rheol. 50, 207 (2006).   

Foundational issues in nonlinear rheology of entangled polymeric liquids

Nonlinear dynamic and mechanic responses of entangled polymeric liquids to external deformations determine processing behavior of a hundred billion pounds of thermoplastic and rubber materials that are produced every year. The emerging phenomenology and theoretical concepts suggest that we need to go beyond the conventional description of polymer rheology involving high external deformations. The new understanding emphasizes the need to monitor the deformation field without predicating that homogeneous deformation would prevail in these highly viscoelastic materials. Entangled polymeric liquids are transient soft solids with finite cohesion and necessarily have to transform from a solid-like network state to a state of flow. Apparently, this yielding often results in inhomogeneous flow. About two dozen movies of particle-tracking velocimetric observation and publications can be found at our website: http://www3.uakron.edu/rheology/