Decoupling of single-particle and collective dynamics in arrested phase-separating glassy mixtures

TL;DR

We address how arrested phase separation interacts with vitrification in a binary mixture of ultrasoft star polymers (soft component) and hard colloids (protein limit). Using coarse-grained molecular dynamics, we analyze structure factors $S_{ij}(q)$, the composition factor $S_{cc}(q)$, van Hove functions $G_s(r,t)$, mean-squared displacement $MSD(t)$, and self/collective ISFs $F_s(q,t)$, $F_c(q,t)$, complemented by local-density analysis and a two-state switching model for population dynamics. We find that adding hard colloids melts the soft glass and drives incipient demixing, while hard tracers display diffusion with a logarithmic relaxation at intermediate scales and pronounced non-Gaussianity due to population splitting; self and collective dynamics decouple at low $q$ because of arrested phase separation. A two-state diffusion framework accounts for Brownian yet non-Gaussian tracer behavior, highlighting how glassiness and demixing co-author multiscale transport. These insights illuminate how structural heterogeneity and composition fluctuations govern dynamics in soft–hard mixtures and offer experimental avenues for validation and control of rheology in such systems.

Abstract

We investigate the structure and dynamics of a hard colloid-star polymer mixture in the range of its arrested phase separation, where an incipient demixing transition is interfering with a nearby vitrification line, focusing on the protein limit (smaller hard component). Soft-hard mixtures present a rich dynamics, influenced by different parameters such as the concentration of the soft and hard components, the softness of the potential, and the size ratio between the two components. Using coarse-grained molecular dynamics simulations, we characterize the single-particle and collective dynamics of the hard colloidal tracers in the soft glassy matrix. The hard tracers show diffusive behavior of the mean squared displacement accompanied by non-exponential relaxation of the intermediate scattering functions at intermediate length scales and non-Gaussian displacement distributions. Moreover, we show that the system exhibits arrested phase separation, leading to population splitting and decoupling between self- and collective dynamics of the hard colloids. Overall, we demonstrate that the interplay between arrested phase separation and glassiness leads to complex, multiscale phenomena that strongly influence the dynamics of the hard additives in the arrested matrix formed by the soft colloids.

Figures (10)

• Figure 1: Schematic phase diagram of a binary star polymer -- colloid mixture for high functionality stars and smaller colloids. The horizontal and vertical axes represent the star polymer- and hard colloid concentrations, respectively. Exact concentration values for which the various transitions occur depend on the softness of the potential and size ratio of the two components. Redrawn with permission from Merola et al.merola2018asymmetric
• Figure 2: Coarse-grained potentials as used in the simulations with $f = 166$ and $\sigma_H = 0.667 \sigma_S$.
• Figure 3: Dynamical quantities of the star polymer species at density $\rho_S\sigma_s = 0.4$, upon addition of hard colloids with densities $\rho_H$ as indicate in the legends. (a) The mean square displacement ${\mathrm {MSD}}_{SS}$ of the stars; (b) the self-ISF computed at $q = 4.99\,\sigma_S^{-1}$; (c) the self-van Hove functions computed at $t=10\tau$ and (d) same as (c) at $t=1000\tau$. The inset in panel (b) shows the values for the diffusion coefficient and the relaxation time as a function of the hard colloid density, rescaled by their reference value set at $\rho_H=0.02 \, \sigma_S^{-3}$. The former are obtained by fitting the MSD in panel (a) while the latter are obtained from the self-ISF curves as $F_s(q,\tau_\mathrm{rel}^S)=1/e$.
• Figure 4: (a) The star-star and (b) the hard sphere-hard sphere structure factors for different values of $\rho_H$, obtained from MD simulations.
• Figure 5: Hard colloid dynamics obtained from MD simulations. (a) The ${\mathrm MSD}_{HH}$ of the hard component for different values of $\rho_H$; the inset shows the values for the diffusion coefficient and the relaxation time as a function of the hard colloid density obtained as in Fig. \ref{['fig:glass-melting']} and rescaled by their reference value set at $\rho_H=0.02 \, \sigma_S^{-3}$. The self ISF for increasing $q$-values at two different concentration: (b) at $\rho_H=0.02 \, \sigma_S^{-3}$ and (c) at $\rho_H=0.08 \, \sigma_S^{-3}$. The dashed black lines indicate a logarithmic fit, valid at $q_{\times}=2.35 \, \sigma_S^{-1}$ for $\rho_H=0.02 \, \sigma_S^{-3}$ and $q_{\times}=2.64 \, \sigma_S^{-1}$ for $\rho_H=0.08 \, \sigma_S^{-3}$.