Dynamics and rheology of a supercooled polymer melt in shear flow

Fingerprinting Brownian Motions of Polymers under Flow

We present a quantitative approach to the self-dynamics of polymers under steady flow by employing a set of complementary reference frames and extending the spherical harmonic expansion technique to dynamic density correlations. Application of this method to nonequilibrium molecular dynamics simulations of polymer melts reveals a number of universal features. For both unentangled and entangled melts, the center-of-mass motions in the flow frame are described by superdiffusive, anisotropic Gaussian distributions, whereas the isotropic component of monomer self-dynamics in the center-of-mass frame is strongly suppressed. Spatial correlation analysis shows that the heterogeneity of monomer self-dynamics increases significantly under flow.

Decoding polymer self-dynamics using a two-step approach

The self-correlation function and corresponding self-intermediate scattering function in Fourier space are important quantities for describing the molecular motions of liquids. This work draws attention to a largely overlooked issue concerning the analysis of these space-time density-density correlation functions of polymers. We show that the interpretation of non-Gaussian behavior of polymers is generally complicated by intrachain averaging of distinct self-dynamics of different segments. By the very nature of the mathematics involved, the averaging process not only conceals critical dynamical information, but also contributes to the observed non-Gaussian dynamics. To fully expose this issue and provide a thorough benchmark of polymer self-dynamics, we perform analyses of coarse-grained molecular dynamics simulations of linear and ring polymer melts as well as several theoretical models using a "two-step" approach, where interchain and intrachain averagings of segmental self-dynamics are separated. While past investigations primarily focused on the average behavior, our results indicate that a more nuanced approach to polymer self-dynamics is clearly required.

Shear-Thinning in Oligomer Melts-Molecular Origins and Applications

We investigate the molecular origin of shear-thinning in melts of flexible, semiflexible and rigid oligomers with coarse-grained simulations of a sheared melt. Entanglements, alignment, stretching and tumbling modes or suppression of the latter all contribute to understanding how macroscopic flow properties emerge from the molecular level. In particular, we identify the rise and decline of entanglements with increasing chain stiffness as the major cause for the non-monotonic behaviour of the viscosity in equilibrium and at low shear rates, even for rather small oligomeric systems. At higher shear rates, chains align and disentangle, contributing to shear-thinning. By performing simulations of single chains in shear flow, we identify which of these phenomena are of collective nature and arise through interchain interactions and which are already present in dilute systems. Building upon these microscopic simulations, we identify by means of the Irving-Kirkwood formula the corresponding macroscopic stress tensor for a non-Newtonian polymer fluid. Shear-thinning effects in oligomer melts are also demonstrated by macroscopic simulations of channel flows. The latter have been obtained by the discontinuous Galerkin method approximating macroscopic polymer flows. Our study confirms the influence of microscopic details in the molecular structure of short polymers such as chain flexibility on macroscopic polymer flows.

Synchronized Molecular-Dynamics Simulation of the Thermal Lubrication of an Entangled Polymeric Liquid

The thermal lubrication of an entangled polymeric liquid in wall-driven shear flows between parallel plates is investigated by using a multiscale hybrid method, coupling molecular dynamics and hydrodynamics (i.e., the synchronized molecular dynamics method). The temperature of the polymeric liquid rapidly increases due to viscous heating once the drive force exceeds a certain threshold value, and the rheological properties drastically change at around the critical drive force. In the weak viscous-heating regime, the conformation of polymer chains is dominated by the flow field so that the polymers are more elongated as the drive force increases. However, in the large viscous-heating regime, the conformation dynamics is dominated by the thermal agitation of polymer chains so that the conformation of polymers recovers more uniform and random structures as the drive force increases, even though the local shear flows are further enhanced. Remarkably, this counter-intuitive transitional behavior gives an interesting re-entrant transition in the stress–optical relation, where the linear stress–optical relation approximately holds even though each of the macroscopic quantities behaves nonlinearly. Furthermore, the shear thickening behavior is also observed in the large viscous-heating regime—this was not observed in a series of previous studies on an unentangled polymer fluid. This qualitative difference of the thermo-rheological property between the entangled and unentangled polymer fluids gives completely different velocity profiles in the thermal lubrication system.

Solid crystal suspensions containing griseofulvin--preparation and bioavailability testing

The improvement of the bioavailability of poorly soluble drugs has been an important issue in pharmaceutical research for many years. Despite the suggestion of several other technologies in the past, drug particle size reduction is still an appropriate strategy to guarantee high bioavailability of various drugs. A few years ago, the Solid Crystal Suspension (SCS) technology was suggested, in which crystalline drug particles are ground and dispersed in a highly soluble crystalline carrier by a hot melt extrusion process. The current study demonstrates the scale-up of the SCS technology to standard, lab-scale extrusion equipment--a change from previous investigations, which used small batch sizes. A twin-screw extruder was modified to account for the rapid crystallization of the carrier. The screw speed and the barrel temperature were identified as critical process parameters and were varied systematically in several experimental designs. Finally, parameters were identified that produced extrudates with rapid dissolution rates. After extrusion, the extrudates were milled to granules and then tableted. These tablets were investigated with respect to their bioavailability in beagle dogs. It was found that drug particle size reduction in the hot melt extrusion led to 3.5-fold higher bioavailability in these dogs than occurred with the physical mixture of the used substances. The solid crystal suspension formulation had a slightly higher bioavailability than the marked product. In conclusion, the SCS technology was successfully scaled up to lab-scale equipment, and the concept was confirmed by a bioavailability study.

Non-equilibrium relaxation and tumbling times of polymers in semidilute solution

The end-over-end tumbling dynamics of individual polymers in dilute and semidilute solutions is studied under shear flow by large-scale mesoscale hydrodynamic simulations. End-to-end vector relaxation times are determined along the flow, gradient, and vorticity directions. Along the flow and gradient directions, the correlation functions decay exponentially with sinusoidal modulations at short times. In dilute solution, the decay times of the various directions are very similar. However, in semidilute solutions, the relaxation behaviors are rather different along the various directions, with the longest relaxation time in the vorticity direction and the shortest time in the flow direction. The various relaxation times exhibit a power-law shear-rate dependence with the exponent  - 2/3 at high shear rates. Quantitatively, the relaxation times are equal to the tumbling times extracted from cross-correlation functions of fluctuations of radius-of-gyration components along the flow and gradient direction.

Simulated glass-forming polymer melts: glass transition temperature and elastic constants of the glassy state

By means of molecular-dynamics simulation we study a flexible and a semiflexible bead-spring model for a polymer melt on cooling through the glass transition. Results for the glass transition temperature T(g) and for the elastic properties of the glassy state are presented. We find that T(g) increases with chain length N and is for all N larger for the semiflexible model. The N dependence of T(g) is compared to experimental results from the literature. Furthermore, we characterize the polymer glass below T(g) via its elastic properties, i.e., via the Lamé coefficients λ and μ. The Lamé coefficients are determined from the fluctuation formalism which allows to split λ and μ into affine (Born term) and nonaffine (fluctuation term) contributions. We find that the fluctuation term represents a substantial correction to the Born term. Since the Born terms for λ and μ are identical, the fluctuation terms are responsible for the different temperature dependence of the Lamé coefficients. While λ decreases linearly on approaching T(g) from below, the shear modulus μ displays a much stronger decrease near T(g). From the present simulation data it is not possible to decide whether μ takes a finite value at T(g), as would be expected from mode-coupling theory, or vanishes continuously, as suggested by recent work from replica theory.

Dynamic rheology of a supercooled polymer melt in nonuniform oscillating flows between rapidly oscillating plates

The dynamic rheology of a polymer melt composed of short chains with ten beads between rapidly oscillating plates is investigated for various oscillation frequencies by using the hybrid simulation of the molecular dynamics and computational fluid dynamics. In the quiescent state, the melt is in a supercooled state, and the stress relaxation function G(t) exhibits a stretched exponential relaxation on the time scale of the α relaxation time τ(α) (the structural relaxation of beads) and then follows the Rouse relaxation function characterized by the Rouse relaxation time τ(R) (the conformational relaxation of polymer chains). In the rapidly oscillating plates, nonuniform boundary layer flows are generated over the plate due to inertia of the fluid, and the local rheological properties of the melt are spatially varied according to the local flow fields. The local strain and local strain rate of the melt monotonically decrease with the distance from the plate at each oscillation frequency of the plate, but their dependencies on the oscillation frequency at a fixed distance from the plate vary with the distance. Far from the plate, the local strain decreases as the oscillation frequency increases such that the dynamic rheology deviates from the linear moduli at the low oscillation frequencies rather than high oscillation frequencies. On the contrary, near the plate, the local strain rate increases with the oscillation frequency such that the shear thinning is enhanced at high oscillation frequencies. In close vicinity to the plate, the dynamic viscosity is mostly independent of the oscillation frequency, and the shear thinning behavior becomes similar to that observed in steady shear flows. We show the diagram of the loss tangent of the melt for different oscillation frequencies and local strain rates. It is seen that the melt generates three different rheological regimes, i.e., the viscous fluid regime, liquidlike viscoelastic regime, and solidlike viscoelastic regime, according to the oscillation frequency and local strain rate. Nonlinear rheological properties are also investigated by the spectrum analysis and the Lissajous-Bowditch curve. It is found that the fractional amplitude of the higher harmonics to the linear harmonics is suppressed within the boundary layer due to the nonslip boundary on the oscillating plate. We also find that the melt exhibits intercycle shear thinning between different positions but exhibits intracycle shear thickening at a fixed position in the vicinity of the plate.

Multiscale modeling and simulation for polymer melt flows between parallel plates

The flow behaviors of polymer melt composed of short chains with ten beads between parallel plates are simulated by using a hybrid method of molecular dynamics and computational fluid dynamics. Three problems are solved: creep motion under a constant shear stress and its recovery motion after removing the stress, pressure-driven flows, and the flows in rapidly oscillating plates. In the creep/recovery problem, the delayed elastic deformation in the creep motion and evident elastic behavior in the recovery motion are demonstrated. The velocity profiles of the melt in pressure-driven flows are quite different from those of Newtonian fluid due to shear thinning. Velocity gradients of the melt become steeper near the plates and flatter at the middle between the plates as the pressure gradient increases and the temperature decreases. In the rapidly oscillating plates, the viscous boundary layer of the melt is much thinner than that of Newtonian fluid due to the shear thinning of the melt. Three different rheological regimes, i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid in a region for omegatauR < approximately 1 , and the crossover between the liquidlike and solidlike regime takes place around omegataualpha approximately equal 1 (where omega is the angular frequency of the plate and tauR and taualpha are Rouse and alpha relaxation time, respectively).

Molecular-dynamics simulation study of the glass transition in amorphous polymers with controlled chain stiffness

We report computation results obtained from extensive coarse-grained molecular-dynamics simulations of amorphous ensembles of polymer chains at constant density. In our polymer model, we use bending and torsion potentials acting along the polymer backbone to control the chain stiffness. The static and dynamic properties of the polymer bulk have been analyzed over a large temperature interval in search for the onset of the glass transition. The glass transition temperatures Tg, for different types of chain stiffness, have been determined from the dependence of the self-diffusion coefficient D on the temperature T as the limiting value where the diffusion vanishes. Increasing the chain stiffness induces an increase of the glass transition temperature. The Tg values estimated from diffusion are confirmed by analyzing the relaxation times of the autocorrelation functions for the torsion angle and for the end-to-end vector. The dependence of the diffusion coefficient D on the chain length N is strongly affected by temperature for chains with bending and torsion stiffness. For systems with relatively short chains (N<or=50), the exponent nu from D proportional to N(-nu) increases from the value nu approximately 1 expected in the Rouse regime to nu approximately 2 as the temperature is lowered towards Tg.

Length-scale-dependent relaxation in colloidal gels

We use molecular dynamics computer simulations to investigate the relaxation dynamics of a simple model for a colloidal gel at a low volume fraction. We find that due to the presence of the open spanning network this dynamics shows at low temperature a nontrivial dependence on the wave vector which is very different from the one observed in dense glass-forming liquids. At high wave vectors the relaxation is due to the fast cooperative motion of the branches of the gel network, whereas at low wave vectors the overall rearrangements of the heterogeneous structure produce the relaxation process.

Aging after shear rejuvenation in a soft glassy colloidal suspension: evidence for two different regimes

The aging dynamics after shear rejuvenation in a glassy clay suspension have been investigated through dynamic light scattering (DLS). Two different aging regimes are observed: one is attained if the sample is rejuvenated before its gelation and one after the rejuvenation of the gelled sample. In the first regime, the application of shear fully rejuvenates the sample, as the system dynamics soon after shear cessation follow the same aging evolution characteristic of standard aging. In the second regime, aging proceeds very fast after shear rejuvenation, and classical DLS cannot be used. An original protocol to measure an ensemble-averaged intensity-correlation function is proposed and its consistency with classical DLS is verified. The fast aging dynamics of rejuvenated gelled samples exhibit a power-law dependence of the slow relaxation time on the waiting time.

Aging under shear: structural relaxation of a non-Newtonian fluid

The influence of an applied shear field on the dynamics of an aging colloidal suspension has been investigated by the dynamic light-scattering determination of the density autocorrelation function. Though a stationary state is never observed, the slow dynamics crosses between two different nonequilibrium regimes as soon as the structural relaxation time tau(s) approaches the inverse shear rate gamma (-1) . In the shear-dominated regime (at high gamma values) the structural relaxation time is found to be strongly sensitive to the shear rate ( tau(s) approximately gamma (-alpha) , with alpha approximately 1 ) while aging proceeds at a very slow rate. The effect of the shear on the detailed shape of the density autocorrelation function is quantitatively described, assuming that the structural relaxation process arises from the heterogeneous superposition of many relaxing units, each one independently coupled to shear with a parallel composition rule for time scales: 1/tau-->1/tau+A gamma .

Entanglements in quiescent and sheared polymer melts

We visualize entanglements in polymer melts using molecular dynamics simulation. A bead at an entanglement interacts persistently for long times with the nonbonded beads (those excluding the adjacent ones in the same chain). The interaction energy of each bead with the nonbonded beads is averaged over a time interval tau much longer than microscopic times but shorter than the onset time of tube constraints tau e. Entanglements can then be detected as hot spots consisting of several beads with relatively large values of the time-averaged interaction energy. We next apply a shear flow with rate much faster than the disengagement motion of entangled chains. With increasing strain the chains take zigzag shapes and one-half of the hot spots become bent. The chains are first stretched as a network but, as the bends approach the chain ends, disentanglements subsequently occur, leading to stress overshoot observed experimentally.

Supercooled liquids under shear: theory and simulation

We analyze the behavior of supercooled fluids under shear both theoretically and numerically. Theoretically, we generalize the mode-coupling theory of supercooled fluids to systems under stationary shear flow. Our starting point is the set of generalized fluctuating hydrodynamic equations with a convection term. A nonlinear integrodifferential equation for the intermediate scattering function is constructed. This theory is applied to a two-dimensional colloidal suspension. The shear rate dependence of the intermediate scattering function and the shear viscosity is analyzed. We have also performed extensive numerical simulations of a two-dimensional binary liquid with soft-core interactions near, but above, the glass transition temperature. Both theoretical and numerical results show the following. (i) A drastic reduction of the structural relaxation time and the shear viscosity due to shear. Both the structural relaxation time and the viscosity decrease as gamma(-nu) with an exponent nu< or =1, where gamma; is the shear rate. (ii) Almost isotropic dynamics regardless of the strength of the anisotropic shear flow.

Plastic flow in two-dimensional solids

A time-dependent Ginzburg-Landau model of plastic deformation in two-dimensional solids is presented. The fundamental dynamic variables are the displacement field u and the lattice velocity v=delta(u)/delta(t). Damping is assumed to arise from the shear viscosity in the momentum equation. The elastic energy density is a periodic function of the shear and tetragonal strains, which enables the formation of slips at large strains. In this work we neglect defects such as vacancies, interstitials, or grain boundaries. The simplest slip consists of two edge dislocations with opposite Burgers vectors. The formation energy of a slip is minimized if its orientation is parallel or perpendicular to the flow in simple shear deformation and if it makes angles of +/-pi/4 with respect to the stretched direction in uniaxial stretching. High-density dislocations produced in plastic flow do not disappear even if the flow is stopped. Thus large applied strains give rise to structurally disordered states, which are metastable due to the Peierls potential. We divide the elastic energy into an elastic part due to affine deformation and a defect part. The latter represents degree of disorder and is nearly constant in plastic flow under cyclic straining.

Molecular hydrodynamic theory of supercooled liquids and colloidal suspensions under shear

We extend the conventional mode-coupling theory of supercooled liquids to systems under stationary shear flow. Starting from generalized fluctuating hydrodynamics, a nonlinear equation for the intermediate scattering function is constructed. We evaluate the solution numerically for a model of a two-dimensional colloidal suspension and find that the structural relaxation time decreases as gamma;(-nu) with an exponent nu</=1, where gamma; is the shear rate. The results are in qualitative agreement with recent molecular dynamics simulations. We discuss the physical implications of the results.