We show that the slowing-down of diffusion-limited reaction rates in dense liquids can be explained in terms of an effective two-body Smoluchowski framework where many-body correlations are accounted for by means of a nonequilibrium mean-force field. This framework explains recent observations from numerical simulations.

The growth of amyloid fibrils requires a disordered or partially unfolded protein to bind to the fibril and adapt the same conformation and alignment established by the fibril template. Since the H-bonds stabilizing the fibril are interchangeable, it is inevitable that H-bonds form between incorrect pairs of amino acids which are either incorporated into the fibril as defects or must be broken before the correct alignment can be found. This process is modeled by mapping the formation and breakage of H-bonds to a one-dimensional random walk. The resulting microscopic model of fibril growth is governed by two timescales: the diffusion time of the monomeric proteins, and the time required for incorrectly bound proteins to unbind from the fibril. The theory predicts that the Arrhenius behavior observed in experiments is due to off-pathway states rather than an on-pathway transition state. The predicted growth rates are in qualitative agreement with experiments on insulin fibril growth rates as a function of protein concentration, denaturant concentration, and temperature. These results suggest a templating mechanism where steric clashes due to a single mis-aligned molecule prevent the binding of additional molecules.

We have developed the lattice model for describing polypeptide chains in the presence of crowders. The influence of crowding confinement on the fibrillation kinetics of polypeptide chains is studied using this model. We observed the non-trivial behavior of the fibril formation time τfib that it decreases with the concentration of crowders if crowder sizes are large enough, but the growth is observed for crowders of small sizes. This allows us to explain the recent experimental observation on the dual effect of crowding particles on fibril growth of proteins that for a fixed crowder concentration the fibrillation kinetics is fastest at intermediate values of total surface of crowders. It becomes slow at either small or large coverages of cosolutes. It is shown that due to competition between the energetics and entropic effects, the dependence of τfib on the size of confined space is described by a parabolic function.

The velocity relaxation of an impulsively forced spherical particle in a fluid confined by two parallel plane walls is studied using a direct numerical simulation approach. During the relaxation process, the momentum of the particle is transmitted in the ambient fluid by viscous diffusion and sound wave propagation, and the fluid flow accompanied by each mechanism has a different character and affects the particle motion differently. Because of the bounding walls, viscous diffusion is hampered, and the accompanying shear flow is gradually diminished. However, the sound wave is repeatedly reflected and spreads diffusely. As a result, the particle motion is governed by the sound wave and backtracks differently in a bulk fluid. The time when the backtracking of the particle occurs changes non-monotonically with respect to the compressibility factor ɛ = ν∕ac and is minimized at the characteristic compressibility factor. This factor depends on the wall spacing, and the dependence is different at small and large wall spacing regions based on the different mechanisms causing the backtracking.

Investigation of segregation of polymer coils in open channel was extended relative to previous studies from flexible chains to semiflexible chains. Our results are based on simulation of confinement free energy of a chain in channel and on direct simulation of coil segregation process. For confinement free energy, we confirm the predicted opposite trend with increasing chain stiffness for the weak and for strong confinement regimes. Results of two different approaches are consistent, in agreement with theoretical analysis and indicate a stronger segregation tendency of flexible chains in channel relative to semiflexible chains both in its extent and dynamics.

The dynamical properties of dipolar Janus particles are studied through simulation using our previously-developed detailed pointwise (PW) model and an isotropically coarse-grained (CG) model [M. C. Hagy and R. Hernandez, J. Chem. Phys. 137, 044505 (2012)]. The CG model is found to have accelerated dynamics relative to the PW model over a range of conditions for which both models have near identical static equilibrium properties. Physically, this suggests dipolar Janus particles have slower transport properties (such as diffusion) in comparison to isotropically attractive particles. Time rescaling and damping with Langevin friction are explored to map the dynamics of the CG model to that of the PW model. Both methods map the diffusion constant successfully and improve the velocity autocorrelation function and the mean squared displacement of the CG model. Neither method improves the distribution of reversible bond durations f(tb) observed in the CG model, which is found to lack the longer duration reversible bonds observed in the PW model. We attribute these differences in f(tb) to changes in the energetics of multiple rearrangement mechanisms. This suggests a need for new methods that map the coarse-grained dynamics of such systems to the true time scale.

The linear and nonlinear rheological measurements were utilized to study the mechanical response of concentrated mixtures of colloidal particles with opposite charges. The particle volume fraction (Φ) spans the region from low volume fraction (Φ = 0.18) gel to high volume fraction (Φ = 0.53) glass. In the linear viscoelastic region, the storage moduli G' exhibits deferent Φ dependence at low and high Φ's. It follows a power law relationship as G' ∼ Φ(6.2±0.2) for Φ < 0.46, and follows an exponential relationship as G' ∼ exp[(13.8 ± 0.6)Φ] for Φ ≥ 0.46. The difference can be taken as a distinction between a colloidal gel and an attractive glass (or dense gel) for the present system. The loss moduli G" is almost frequency independent within the whole experimental frequency range (10(-1)-10(2) rad∕s) for colloidal gel, and G" exhibits a weak minimum for attractive glass. In the nonlinear large amplitude rheological measurement, samples with Φ < 0.46 show one-step yielding, and samples with Φ ≥ 0.46 exhibit two-step yielding which is in agreement with numerous experiments in attractive glassy systems. The first yielding is due to the breaking of short range interactions which bond the interconnected clusters or local clusters, while the second yielding is attributed to the breaking of long range interaction, normally the caging forming or glass forming interactions. The qualitative distinction between attractive glass and gel in terms of their yielding behavior is consistent with the linear rheological results. The particle-particle interactions were modulated by salt concentration. It was found that, when the attraction interaction is enhanced, both yielding points in attractive glass shift to higher strain amplitude and the gap between the two yielding points become more separated.

Equilibrium and non-equilibrium molecular dynamics were performed to determine the relationship between the static structure factor, the molecular conformation, and the rheological properties of chain molecules. A spring-monomer model with Finitely Extensible Nonlinear Elastic and Lennard-Jones force field potentials was used to describe chain molecules. The equations of motion were solved for shear flow with SLLOD equations of motion integrated with Verlet's algorithm. A multiple time scale algorithm extended to non-equilibrium situations was used as the integration method. Concentric circular patterns in the structure factor were obtained, indicating an isotropic Newtonian behavior. Under simple shear flow, some peaks in the structure factor were emerged corresponding to an anisotropic pattern as chains aligned along the flow direction. Pure chain molecules and chain molecules in solution displayed shear-thinning regions. Power-law and Carreau-Yasuda models were used to adjust the generated data. Results are in qualitative agreement with rheological and light scattering experiments.