Non-Gaussian rotational diffusion in heterogeneous media

The effects of vacancies and their mobility on the dynamic heterogeneity in 1,3-dimethylimidazolium hexafluorophosphate organic ionic plastic crystals

Organic ionic plastic crystals (OIPCs) are the crystals of electrolytes with a long-range translational order. The rotational modes of ions in OIPCs are, however, activated even in solid phases such that the diffusion of dopants such as lithium ions may be facilitated. OIPCs have been, therefore, considered as good candidates for solid electrolytes. Recent experiments and theoretical studies have suggested that both the translational and the rotational diffusion of ions are quite heterogeneous: the diffusion of some ions are quite fast while other ions of the same kind hardly diffuse, either rotationally or translationally. Such dynamic heterogeneity would be a key to the transport mechanism of dopants in solid state electrolytes. In this work, we investigate the effects of defects on the dynamic heterogeneity of OIPCs. We perform atomistic molecular dynamics simulation of 1,3-dimethylimidazolium hexafluorophosphate ([MMIM][PF6]) with a pair of cation and anion vacancies. At low temperature, vacancies undergo hopping motions toward each other and form a charge-neutral cluster. At high temperature, two vacancies act like a loosely bonded molecule and diffuse together via hopping motions. We find that the translational diffusion of ions is correlated strongly with the vacancy diffusion and becomes heterogeneous when the vacancies hop. The rotation of ions also becomes active when the ions are close to vacancies such that the rotational dynamic heterogeneity strengthens.

Heterogeneous Rotational Dynamics of Imidazolium-Based Organic Ionic Plastic Crystals

Organic ionic plastic crystals (OIPCs) are a unique class of materials that undergo orientational and conformational motions while maintaining a long-range ordered lattice structure. OIPCs have attracted attention because the rotational motions were known to accelerate the diffusion of mobile ions such as lithium ions. However, only a small number of combinations of cations and anions lead to OIPCs because the rotational motion may be restricted by both the molecular structure and the crystal class. In this work, we perform molecular dynamics simulations to study the effects of the molecular structure and the crystal class on the rotational motion and the phase transitions. We investigate four imidazolium-based ionic crystals: (1) 1-methyl-3-methylimidazolium hexafluorophosphate ([MMIM][PF₆]), (2) 1-methyl-3-methylimidazolium chloride ([MMIM][Cl]), (3) monoclinic 1-butyl-3-methylimidazolium chloride ([BMIM][Cl]), and (4) orthorhombic [BMIM][Cl] ionic crystals. We construct initial configurations of OIPCs by employing experimental crystalline structures. Then, we increase the temperature gradually and monitor the density and the radial distribution functions. We estimate the rotational van Hove correlation functions and find that molecules in plastic crystal phases undergo rotational hopping motions and OIPCs exhibit rotational dynamic heterogeneity significantly. The structure of anions and cations affect the phase transition of OIPCs. And the crystal class is also critical to the phase transition of OIPCs because the rotational motion of ions depends on the crystal class.

Heterogeneous kinetics of the loop formation of a single polymer chain in crowded and disordered media

The cytoplasmic volume of cells is occupied and crowded by a variety of macromolecules, such as proteins and cytoskeleton structures. Such diverse macromolecules make the cell cytoplasm not only structurally heterogeneous but also dynamically heterogeneous: Some macromolecules may diffuse freely inside cell cytoplasm at certain timescales while others hardly diffuse. Studies on the effects of the dynamic heterogeneity on reaction kinetics have been limited even though the effects of the crowdedness and structural heterogeneity were investigated extensively. In this study, we employ a simple model of mixtures of mobile and immobile matrix particles, tune the degree of dynamic heterogeneity by changing the fraction of immobile matrix particles, and investigate reaction kinetics in such heterogeneous media. We employ the loop formation of a single polymer chain as a model reaction and perform Langevin dynamics simulations. We find that the free-energy barrier of the loop formation is decreased as the systems become more crowded with matrix particles. But the free-energy barrier is not sensitive to the dynamic heterogeneity. As dynamic heterogeneity increases with an increase in the fraction of immobile matrix particles, however, the diffusivity of the system decreases significantly. The decrease in the diffusion (due to the dynamic heterogeneity) and the decrease in the free-energy barrier (due to the crowdedness) lead together to a complicated trend of the loop formation kinetics. As the volume fraction of immobile matrix particles reaches a critical value at the percolation transition, the reaction kinetics becomes significantly heterogeneous and the survival probability distribution of the chain loop formation becomes stretched-exponential. We also illustrate that the heterogeneous reaction rate near the percolation transition relates closely to the structures of local pores in which the polymer is located.

Spatial Dependence of Non-Gaussian Diffusion of Nanoparticles in Free-Standing Thin Polymer Films

The addition of nanoparticles (NPs) to a free-standing polymer film affects the properties of the film such as viscosity and glass transition temperature. Recent experiments, for example, showed that the glass transition temperature of thin polymer films was dependent on how NPs were distributed within the polymer films. However, the spatial arrangement of NPs in free-standing polymer films and its effect on the diffusion of NPs and polymers remain elusive at a molecular level. In this study, we employ generic coarse-grained models for polymers and NPs and perform extensive molecular dynamics simulations to investigate the diffusion of polymers and NPs in free-standing thin polymer films. We find that small NPs are likely to stay at the interfacial region of the polymer film, while large NPs tend to stay at the center of the film. On the other hand, as the interaction between a NP and a monomer becomes more attractive, the NP is more likely to be placed at the film center. The diffusion of monomers slows down slightly as more NPs are added to the film. Interestingly, the NP diffusion is dependent strongly on the spatial arrangement of the NPs: NPs at the interfacial region diffuse faster and undergo more non-Gaussian diffusion than NPs at the film center, which implies that the interfacial region would be more mobile and dynamically heterogeneous than the film center. We also find that the mechanism for non-Gaussian diffusion of NPs at the film center differs from that at the interfacial region and that the NP diffusion would reflect the local viscosity of the polymer films.

Test of the diffusing-diffusivity mechanism using near-wall colloidal dynamics

The mechanism of diffusing diffusivity predicts that, in environments where the diffusivity changes gradually, the displacement distribution becomes non-Gaussian, even though the mean-square displacement grows linearly with time. Here, we report single-particle tracking measurements of the diffusion of colloidal spheres near a planar substrate. Because the local effective diffusivity is known, we have been able to carry out a direct test of this mechanism for diffusion in inhomogeneous media.

Diffusing diffusivity: Rotational diffusion in two and three dimensions

We consider the problem of calculating the probability distribution function (pdf) of angular displacement for rotational diffusion in a crowded, rearranging medium. We use the diffusing diffusivity model and following our previous work on translational diffusion [R. Jain and K. L. Sebastian, J. Phys. Chem. B 120, 3988 (2016)], we show that the problem can be reduced to that of calculating the survival probability of a particle undergoing Brownian motion, in the presence of a sink. We use the approach to calculate the pdf for the rotational motion in two and three dimensions. We also propose new dimensionless, time dependent parameters, αrot,2D and αrot,3D, which can be used to analyze the experimental/simulation data to find the extent of deviation from the normal behavior, i.e., constant diffusivity, and obtain explicit analytical expressions for them, within our model.

Dynamics of highly polydisperse colloidal suspensions as a model system for bacterial cytoplasm

There are various kinds of macromolecules in bacterial cell cytoplasm. The size polydispersity of the macromolecules is so significant that the crystallization and the phase separation could be suppressed, thus stabilizing the liquid state of bacterial cytoplasm. On the other hand, recent experiments suggested that the macromolecules in bacterial cytoplasm should exhibit glassy dynamics, which should be also affected significantly by the size polydispersity of the macromolecules. In this work, we investigate the anomalous and slow dynamics of highly polydisperse colloidal suspensions, of which size distribution is chosen to mimic Escherichia coli cytoplasm. We find from our Langevin dynamics simulations that the diffusion coefficient (D_{tot}) and the displacement distribution functions (P(r,t)) averaged over all colloids of different sizes do not show anomalous and glassy dynamic behaviors until the system volume fraction ϕ is increased up to 0.82. This indicates that the intrinsic polydispersity of bacterial cytoplasm should suppress the glass transition and help maintain the liquid state of the cytoplasm. On the other hand, colloids of each kind show totally different dynamic behaviors depending on their size. The dynamics of colloids of different size becomes non-Gaussian at a different range of ϕ, which suggests that a multistep glass transition should occur. The largest colloids undergo the glass transition at ϕ=0.65, while the glass transition does not occur for smaller colloids in our simulations even at the highest value of ϕ. We also investigate the distribution (P(θ,t)) of the relative angles of displacement for macromolecules and find that macromolecules undergo directionally correlated motions in a sufficiently dense system.