Exploring the validity of time-concentration superposition in glassy colloids: Experiments and simulations

Abstract

Superposition approaches have generally been proposed to create a dynamic rheological map to access colloidal glassy dynamics beyond experimental time windows. However, the validity of the superposition approaches in colloids near the glass transition is questionable owing to the well-known emergence of a β-relaxation process there. Here, we employ a time-concentration superposition (TCS) approach, analogous to time-temperature superposition (TTS) and TCS approaches in molecular systems, utilizing a combination of macroscopic rheological experiments and microscopic Brownian dynamics (BD) simulations, where concentration jumps are performed by a sudden growth of particle size (soft PS-PNIPAM particles in experiment and nearly hard spheres in simulation) at a fixed number of particles. We have examined whether a characteristic master curve can be obtained through horizontal and vertical shifting of the dynamic data, finding that TCS does not hold for either the experimental or simulation systems. We identify the origin of this breakdown as not only the emergence of a strong β-relaxation process but also its overlap with the α-relaxation in both the experimental soft-sphere and the simulated near hard-sphere colloids near to the glass transition concentration. Further understanding of the lack of validity of TCS results from analysis of both experimental and simulation data in the framework of the Baumgaertel-Schausberger-Winter (BSW) relaxation spectrum which provide a means to determine the concentration dependences of both the α-and the β-relaxations, which seem to follow TCS themselves.

“Dense diffusion” in colloidal glasses: short-ranged long-time self-diffusion as a mechanistic model for relaxation dynamics

“…We carried out experiments to compare with simulations, and here we describe the materials and methods. The colloidal samples are polystyrene-poly(N-isopropylacrylamide) (PS-PNIPAM) core-shell particles, with 18% polydispersity determined by dynamic light scattering 108 . The detailed synthesis process is discussed in our previous work 108 .…”

“…The colloidal samples are polystyrene-poly(N-isopropylacrylamide) (PS-PNIPAM) core-shell particles, with 18% polydispersity determined by dynamic light scattering 108 . The detailed synthesis process is discussed in our previous work 108 . We focus on a narrow temperature range between 27 • C and 30 • C, such that the size of PS-PNIPAM particles measured by dynamic light scattering depends linearly on the temperature and can be described by a linear fit d H (T ) = 194.65 − 2.15T , where d H is the hydrodynamic particle diameter in nanometers and T is temperature in • C, although the accuracy of locating the no-slip surface on microgel particles is the subject of ongoing study.…”

“…The descriptor "effective" is meant to convey that the volume fraction in our experiments is calculated based on the hydrodynamic diameter of particles in dilute suspensions obtained via dynamic light scattering and does not account for particle deformation at high particle concentrations. The measured volume fraction of the collapsed state further introduces uncertainty to the true volume fraction of the particles 105,108,[135][136][137] . As a result, we report "effective" volume fraction as a relative volume fraction comparing to a reference state (the collapsed state).…”

“…Because the microgel particles are thermo-responsive, cooling causes particle size to increase, triggering a volume fraction upjump (quench), analogous to the process modeled in our simulations. To make consistent temporal comparison to our simulations, we normalized experimental timescales with the diffusive time of PS-PNIPAM particles, which was calculated as a 2 /D = 6πηa 3 /kT ≈ 0.01s 108 . All volume fraction jumps took place over a time interval of 100 s, which corresponds to ∼ 10, 000a 2 /D.…”

“…In the present work, we combine large-scale dynamic simulations with experiments to carry out constant-volume, constantnumber-density particle-size jumps from a colloidal liquid state to varying depths near and beyond the putative glass transition. Experimental realization of a similar protocol to trigger the glass transition was recently implemented with thermo-responsive microgel particles [103][104][105][106][107] ; the first in silico modeling of a size-jump volume-fraction quench was implemented recently in our study of time-concentration superposition 108 . Here we expand that model to interrogate detailed particle-scale dynamics.…”