Parisi, Daniele; Costanzo, Salvatore; Jeong, Youncheol; Ahn, Junyoung; Chang, Taihyun; Vlassopoulos, Dimitris; Halverson, Jonathan D.; Kremer, Kurt; Ge, Ting; Rubinstein, Michael; Grest, Gary S.; Srinin, Watee; Grosberg, Alexander Y.
Steady-state shear viscosity (γ˙) of unconcatenated ring polymer melts as a function of the shear rate γ˙ is studied by a combination of experiments, simulations, and theory. Experiments using polystyrenes with Z ≈ 5 and Z ≈ 11 entanglements indicate weaker shear thinning for rings compared to linear polymers exhibiting power law scaling of shear viscosity ∼γ˙-0.56 ± 0.02, independent of chain length, for Weissenberg numbers up to about 102. Nonequilibrium molecular dynamics simulations using the bead-spring model reveal a similar behavior with ∼γ˙-0.57 ± 0.08 for 4 ≤ Z ≤ 57. Viscosity decreases with chain length for high γ˙. In our experiments, we see the onset of this regime, and in simulations, which we extended to Wi ∼104, the nonuniversality is fully developed. In addition to a naive scaling theory yielding for the universal regime ∼γ˙-0.57, we developed a novel shear slit model explaining many details of observed conformations and dynamics as well as the chain length-dependent behavior of viscosity at large γ˙. The signature feature of the model is the presence of two distinct length scales: the size of tension blobs and much larger thickness of a shear slit in which rings are self-consistently confined in the velocity gradient direction and which is dictated by the size of a chain section with relaxation time 1/γ˙. These two length scales control the two normal stress differences. In this model, the chain length-dependent onset of nonuniversal behavior is set by tension blobs becoming as small as about one Kuhn segment. This model explains the approximate applicability of the Cox-Merz rule for ring polymers.
A small number of associating groups incorporated onto a polymer backbone have dramatic effects on the mobility and viscoelastic response of the macromolecules in melts. These associating groups assemble, driving the formation of clusters, whose lifetime affects the properties of the polymers. Here, we probe the effects of the interaction strength on the structure and dynamics of two topologies, linear and star polymer melts, and further investigate blends of associative and non-associating polymers using molecular dynamics simulations. Polymer chains of approximately one entanglement length are described by a bead-spring model, and the associating groups are incorporated in the form of interacting beads with an interaction strength between them that is varied from 1 to 20 kBT. We find that, for all melts and blends, interaction of a few kBT between the associating groups drives cluster formation, where the size of the clusters increases with increasing interaction strength. These clusters act as physical crosslinkers, which slow the chain mobility. Blends of chains with and without associating groups macroscopically phase separate for interaction strength between the associating groups of a few kBT and above. For weakly interacting associating groups, the static structure function S(q) is well fit by functional form predicted by the random phase approximation where a clear deviation occurs as phase segregation takes place, providing a quantitative assessment of phase segregation.
Here, we describe recent efforts to improve our predictive modeling of rate-dependent behavior at, or near, a phase transition using molecular dynamics simulations. Cadmium sulfide (CdS) is a well-studied material that undergoes a solid-solid phase transition from wurtzite to rock salt structures between 3 and 9 GPa. Atomistic simulations are used to investigate the dominant transition mechanisms as a function of orientation, size and rate. We found that the final rock salt orientations were determined relative to the initial wurtzite orientation, and that these orientations were different for the two orientations and two pressure regimes studied. The CdS solid-solid phase transition is studied, for both a bulk single crystal and for polymer-encapsulated spherical nanoparticles of various sizes.
Peters, Brandon L.; Salerno, K.M.; Ge, Ting; Perahia, Dvora; Grest, Gary S.
Polymer synthesis routes result in macromolecules with molecular weight dispersity M that depends on the polymerization mechanism. The lowest dispersity polymers are those made by anionic and atom-transfer radical polymerization, which exhibit narrow distributions M = Mw/Mn ∼1.02-1.04. Even for small dispersity, the chain length can vary by a factor of two from the average. The impact of chain length dispersity on the viscoelastic response remains an open question. Here, the effects of dispersity on stress relaxation and shear viscosity of entangled polyethylene melts are studied using molecular dynamics simulations. Melts with chain length dispersity, which follow a Schulz-Zimm (SZ) distribution with M = 1.0-1.16, are studied for times up to 800 μs, longer than the terminal time. These systems are compared to those with binary and ternary distributions. The stress relaxation functions are extracted from the Green-Kubo relation and from stress relaxation following a uniaxial extension. At short and intermediate time scales, both the mean squared displacement and the stress relaxation function G(t) are independent of M. At longer times, the terminal relaxation time decreases with increasing M. In this time range, the faster motion of the shorter chains results in constraint release for the longer chains.
Adding small amounts of ring polymers to a matrix of their linear counterparts is known to increase the zero-shear-rate viscosity because of linear-ring threading. Uniaxial extensional rheology measurements show that, unlike its pure linear and ring constituents, the blend exhibits an overshoot in the stress growth coefficient. By combining these measurements with ex-situ small-angle neutron scattering and nonequilibrium molecular dynamics simulations, this overshoot is shown here to be driven by a transient threading–unthreading transition of rings embedded within the linear entanglement network. Prior to unthreading, embedded rings deform affinely with the linear entanglement network and produce a measurably stronger elongation of the linear chains in the blend compared to the pure linear melt. Thus, rings uniquely alter the mechanisms of transient elongation in linear polymers.
Intuition tells us that a rolling or spinning sphere will eventually stop due to the presence of friction and other dissipative interactions. The resistance to rolling and spinning or twisting torque that stops a sphere also changes the microstructure of a granular packing of frictional spheres by increasing the number of constraints on the degrees of freedom of motion. We perform discrete element modeling simulations to construct sphere packings implementing a range of frictional constraints under a pressure-controlled protocol. Mechanically stable packings are achievable at volume fractions and average coordination numbers as low as 0.53 and 2.5, respectively, when the particles experience high resistance to sliding, rolling, and twisting. Only when the particle model includes rolling and twisting friction were experimental volume fractions reproduced.
Polymer-tethered nanoparticles (NPs) are commonly added to a polymer matrix to improve the material properties. Critical to the fabrication and processing of such composites is the mobility of the tethered NPs. Here, we study the motion of tethered NPs in unentangled polymer melts using molecular dynamics simulations, which offer a precise control of the grafted chain length Ng and the number z of grafted chains per particle. As Ng increases, there is a crossover from particle-dominated to tethered-chain-dominated terminal diffusion of NPs with the same z. The mean squared displacement of loosely tethered NPs in the case of tethered-chain-dominated terminal diffusion exhibits two subdiffusive regimes at intermediate time scales for small z. The first one at shorter time scales arises from the dynamical coupling of the particle and matrix chains, while the one at longer time scales is due to the participation of the particle in the dynamics of the tethered chains. The friction of loosely grafted chains in unentangled melts scales linearly with the total number of monomers in the chains, as the friction of individual monomers is additive in the absence of hydrodynamic coupling. As more chains are grafted to a particle, hydrodynamic interactions between grafted chains emerge. As a result, there is a nondraining layer of hydrodynamically coupled chain segments surrounding the bare particle. Outside the nondraining layer is a free-draining layer of grafted chain segments with no hydrodynamic coupling. The boundary of the two layers is the stick surface where the shear stress due to the relative melt flow is balanced by the friction between the grafted and melt chains in the interpenetration layer. The stick surface is located further away from the bare surface of the particle with higher grafting density.
Molecular dynamics simulations confirm recent extensional flow experiments showing ring polymer melts exhibit strong extension-rate thickening of the viscosity at Weissenberg numbers Wi « 1. Thickening coincides with the extreme elongation of a minority population of rings that grows with Wi. The large susceptibility of some rings to extend is due to a flow-driven formation of topological links that connect multiple rings into supramolecular chains. Links form spontaneously with a longer delay at lower Wi and are pulled tight and stabilized by the flow. Once linked, these composite objects experience larger drag forces than individual rings, driving their strong elongation. The fraction of linked rings depends non-monotonically on Wi, increasing to a maximum when Wi 1 before rapidly decreasing when the strain rate approaches 1/Te.
The Center for Integrated Nanotechnologies (CINT) is a Department of Energy/Office of Science Nanoscale Science Research Center (NSRC), operating as a national user facility devoted to establishing the scientific principles that govern nanoscale integration. Nanoscale integration is defined as assembling diverse nanoscale materials across length scales to design and achieve new properties and functionality. The CINT Theory and Simulation of Nanoscale Phenomena thrust is the component of CINT dedicated to developing and applying theory to enable nanoscale integration. Our focus is on understanding and simulating the unique behavior of integrated materials and systems with nanoscale structure. This mission is achieved through collaborations with CINT Users, between thrust scientists, and with CINT scientists from other thrusts. Our research is focused on three science directions that together form the basis for integration at the nanoscale, namely (i) Hierarchical structure and dynamics in soft matter, (ii) Excitation and Transport in Nanostructured Systems, and (iii) Emergent phenomena at surfaces and interfaces. A broad spectrum of techniques is developed and applied including continuum fluid theory, atomistic and coarse-grained molecular dynamics simulations, static and dynamic electronic structure calculations, multiscale modeling, low-energy effective Hamiltonian methods, and perturbative and exact quantum many-body approaches. These tools are applied to physical systems of interest to CINT Users, the other CINT thrusts, and the general scientific community with the goals of understanding and controlling the interactions between nanoscale building blocks to assemble specific integrated structures, controlling energy transfer and other interactions over multiple length scales, and designing and exploiting the interactions within assembled structures to achieve new materials functionality.
Using random walk analyses we explore diffusive transport on networks obtained from contacts between isotropically compressed, monodisperse, frictionless sphere packings generated over a range of pressures in the vicinity of the jamming transition p→0. For conductive particles in an insulating medium, conduction is determined by the particle contact network with nodes representing particle centers and edges contacts between particles. The transition rate is not homogeneous, but is distributed inhomogeneously due to the randomness of packing and concomitant disorder of the contact network, e.g., the distribution of the coordination number. A narrow escape time scale is used to write a Markov process for random walks on the particle contact network. This stochastic process is analyzed in terms of spectral density of the random, sparse, Euclidean and real, symmetric, positive, semidefinite transition rate matrix. Results show network structures derived from jammed particles have properties similar to ordered, euclidean lattices but also some unique properties that distinguish them from other structures that are in some sense more homogeneous. In particular, the distribution of eigenvalues of the transition rate matrix follow a power law with spectral dimension 3. However, quantitative details of the statistics of the eigenvectors show subtle differences with homogeneous lattices and allow us to distinguish between topological and geometric sources of disorder in the network.