Large Amplitude Oscillatory Shear Study of a Colloidal Gel at the Critical State

We investigate the nonlinear viscoelastic behavior of a colloidal dispersion at the critical gel state using large amplitude oscillatory shear (LAOS) rheology. The colloidal gel at the critical point is subjected to oscillatory shear flow with increasing strain amplitude at different frequencies. We observe that the first harmonic of the elastic and viscous moduli exhibits a monotonic decrease as the material undergoes a linear to nonlinear transition. We analyze the stress waveform across this transition and obtain the nonlinear moduli and viscosity as a function of frequency and strain amplitude. The analysis of the nonlinear moduli and viscosities suggests intracycle strain stiffening and intracycle shear thinning in the colloidal dispersion. Based on the insights obtained from the nonlinear analysis, we propose a potential scenario of the microstructural changes occurring in the nonlinear region. We also develop an integral model using the time-strain separable K-BKZ constitutive equation with a power-law relaxation modulus and damping function obtained from experiments. At low strain amplitudes, this model compares well with experimental data at all frequencies. However, a stronger damping function, which can be efficiently inferred using a spectral method, is required to obtain quantitative fits across the entire range of strain amplitudes and the explored frequencies.Comment: 34 pages, 10 figure

Molecular simulation of tracer and self-diffusion in entangled polymers

The dependence of tracer diffusivity ($D_\infty \sim N^{-x_\infty}$), where probe chains move in an environment of infinitely long matrix chains, and self-diffusion coefficient ($D_s \sim N^{-x_s}$), where probe and matrix chains are identical, on the molecular weight of the probe chain $N$ are investigated using three different molecular simulation methods, viz. molecular dynamics, the bond-fluctuation model (BFM) and the slip-spring (SS) model. Experiments indicate $x_s \approx 2.4 \pm 0.2$ over a wide intermediate molecular weight range, and $x_{\infty} \approx 2.0 \pm 0.1$, although the lower molecular weight limit for observing pure reptation in short probes is unclear. These results are partly inconsistent with some tube theories, and older, somewhat underpowered, molecular simulations. Estimating $x_{\infty}$ using brute-force BFM simulations is difficult because it involves large simulation boxes and long trajectories. To overcome this obstacle, an efficient method to estimate $D_\infty$ in which ends of matrix chains are immobilized, is presented and validated. BFM simulations carried out on systems with different probe and matrix chain lengths reveal that $x_s = 2.43 \pm 0.07$, and $x_\infty = 2.24 \pm 0.03$. Over a wider range of molecular weights, probe diffusivities obtained from the more coarse-grained SS model, calibrated with bead-spring molecular dynamics, reveal $x_s > x_\infty$, and $x_\infty > 2$ for weakly and intermediately entangled chains. Tracer diffusivities obtained by artificially switching off constraint release in the SS simulations essentially overlap with probe diffusivities, strongly suggesting that constraint release is primarily responsible for the difference between $x_s$ and $x_\infty$. Nevertheless, both BFM and SS simulations indicate that below a certain chain length threshold, contributions of contour length fluctuations to $D_s$ and $D_\infty$ are important, and result in deviations from pure reptation scaling

Advances in modeling of polymer melt rheology

No abstract.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/55922/1/11064_ftp.pd

A hierarchical algorithm for predicting the linear viscoelastic properties of polymer melts with long-chain branching

The “hierarchical model” proposed earlier [Larson in Macromolecules 34:4556–4571, 2001] is herein modified by inclusion of early time fluctuations and other refinements drawn from the theories of Milner and McLeish for more quantitative prediction. The hierarchical model predictions are then compared with experimental linear viscoelastic data of well-defined long chain branched 1,4-polybutadienes and 1,4-polyisoprenes using a single set of parameter values for each polymer, which are obtained from experimental data for monodisperse linear and star polymers. For a wide range of monodisperse branched polymer melts, the predictions of the hierarchical model for monodisperse melts are very similar to those of the Milner–McLeish theories, and agree well with experimental data for many, but not all, of the branched polymer samples. Since the modified hierarchical model accounts for arbitrary polydispersity in molecular weight and branching distributions, which is not accounted for in the Milner–McLeish theories, the hierarchical algorithm is a promising one for predicting the relaxation of general mixtures of branched polymers.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47217/1/397_2004_Article_415.pd

Linear viscoelasticity of branched polymer melts.

Standard analytical techniques like chromatography and spectrometry are not sensitive enough to resolve architectural details in branched polymer melts such as metallocene-catalyzed polyethylene to industrially acceptable levels. This has led to the belief that linear rheology, which is highly responsive to subtle differences in branching structure, can be employed as an analytical technique. A major difficulty hindering the application of rheology as an analytical tool has been the inability of the current analytical theory for branched polymers, which is based on the idea of dynamic dilution, to describe the physics of branch point motion. We examine shortcomings of this theory, including the problem of branch point motion, using three case studies. We use a simulation model called the dual slip link model in which entanglements between chains are modeled as slip links that couple the dynamics of pairs of chains. First, in the late-time relaxation of symmetric stars we investigate the breakdown of the molecular picture implied by the dynamic dilution theory, by monitoring the dielectric and stress relaxation functions. We present a terminal relaxation model using the slip link model that offers a better description of the late-time dynamics. Next, we address the failure of the analytical theory to predict the anomalously slow viscoelastic response of asymmetric stars. We need to distinguish between the first-passage time and complete retraction time of the asymmetric arm in order to correctly set the timescale for the diffusion of the branch point. Although the slip link model fails for long arms, where it over-predicts the relaxation time, it points out that the timescale which sets the frequency of the branch point motion should be larger than the first-passage time of an arm. Finally, we study the effects of polydispersity on stars and H-polymers and find that the viscoelasticity of star polymers is insensitive to moderate amounts of poly-dispersity. However, H-polymers are extremely sensitive, especially to polydispersity in the arms. We submit that the relaxation of H-polymers is greatly accelerated if any one of the four arms is short. We suggest the experimental synthesis of asymmetric H-polymers in order to test this hypothesis.Ph.D.Applied SciencesCondensed matter physicsPlasticsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/124314/2/3137942.pd

What Happens When Threading is Suppressed in Blends of Ring and Linear Polymers?

Self-diffusivity of a large tracer ring polymer, D r , immersed in a matrix of linear polymers with N l monomers each shows unusual length dependence. D r initially increases, and then decreases with increasing N l . To understand the relationship between the nonmonotonic variation in D r and threading by matrix chains, we perform equilibrium Monte Carlo simulations of ring-linear blends in which the uncrossability of ring and linear polymer contours is switched on (non-crossing), or artificially turned off (crossing). The D r ≈ 6 . 2 × 10 − 7 N l 2 / 3 obtained from the crossing simulations, provides an upper bound for the D r obtained for the regular, non-crossing simulations. The center-of-mass mean-squared displacement ( g 3 ( t ) ) curves for the crossing simulations are consistent with the Rouse model; we find g 3 ( t ) = 6 D r t . Analysis of the polymer structure indicates that the smaller matrix chains are able to infiltrate the space occupied by the ring probe more effectively, which is dynamically manifested as a larger frictional drag per ring monomer

Unentangled Vitrimer Melts: Interplay between Chain Relaxation and Cross-link Exchange Controls Linear Rheology

Using this theoretical approach, we explore the influence of molecular structure and temperature on vitrimer linear viscoelasticity. We observe that vitrimers with uniform and random cross-link distributions exhibit larger viscosities and relaxation times than gradient and blocky types. Polydimethylsiloxane vitrimer (which has a flexible backbone) shows an Arrhenius temperature dependence for viscosity, while polystyrene vitrimers (which has rigid backbones) are only Arrhenius at high temperatures. During stress relaxation, the short time dynamics represent monomer friction, while the long time dynamics encompass a combination of network strand relaxation and cross-link exchange. Because of the different temperature dependences of the processes, time-temperature superposition fails. We also show that the effective rheological activation energy can be estimated a priori using only the cross-link exchange activation energy and the backbone Williams-Landel-Ferry parameters.(Submitted to Macromolecules)</div