Scaling the glassy dynamics of active particles: Tunable fragility and reentrance

TL;DR

This work investigates how activity, parameterized by self-propulsion amplitude $f_0$ and persistence time $\tau_p$, modifies glassy dynamics in dense soft repulsive particles by mapping a full 3D phase diagram in $(f_0,\tau_p,\phi)$. Using AOUP dynamics at $T=0$, it analyzes self-intermediate scattering functions $F_s(k,t)$ and mean-squared displacement to extract relaxation times $\tau_\alpha$, and demonstrates a non-monotonic $\tau_\alpha(\tau_p)$ due to a crossover between glassy and jamming relaxation mechanisms. A dynamic scaling framework, extending equilibrium soft-sphere scaling to active matter via an effective temperature $T_{\text{eff}}=f_0^2/(1+G\tau_p)$, reveals a tunable glass fragility that transitions from sub- to super-Arrhenius with density and persistence time, and shows data collapse across branches with a $\tau_p$-dependent hard-sphere line $\phi_0(\tau_p)$. The results provide a unified picture linking active matter to equilibrium glass theory and offer insights into tissue-like materials where confluent dynamics and activity compete, with implications for understanding biological processes and designing active materials.

Abstract

Understanding the influence of activity on dense amorphous assemblies is crucial for biological processes such as wound healing, embryogenesis, or cancer progression. Here, we study the effect of self-propulsion forces of amplitude $f_0$ and persistence time $τ_p$ in dense assemblies of soft repulsive particles by simulating a model particle system that interpolates between particulate active matter and biological tissues. We identify the fluid and glass phases of the three-dimensional phase diagram obtained by varying $f_0$, $τ_p$, and the packing fraction $φ$. The morphology of the phase diagram directly accounts for a non-monotonic evolution of the relaxation time with $τ_p$, which is a direct consequence of the crossover in the dominant relaxation mechanism, from glassy to jamming. A second major consequence is the evolution of the glassy dynamics from sub-Arrhenius to super-Arrhenius. We show that this tunable glass fragility extends to active systems analogous observations reported for passive particles. This analogy allows us to apply a dynamic scaling analysis proposed for the passive case, in order to account for our results for active systems. Finally, we discuss similarities and differences between our results and recent findings in the context of computational models of biological tissues.

Figures (5)

• Figure 1: Characterization of the active glassy dynamics. (a) The two-step decay of $F_s(k,t)$ becomes faster with increasing $f_0$ at constant $\phi=0.65$ and $\tau_p=10^{-2}$. (b) The corresponding MSD has sub-diffusive to diffusive crossover at intermediate times, and particle motion is faster with increasing $f_0$. (c) The liquid-glass $(f_0,\phi)$ phase diagram for $\tau_p=10^{-2}$. Squares represent the simulated state points with the corresponding $\tau_\alpha$ color-coded, and dashed lines representing iso-$\tau_\alpha$ contours. Stars are the $\phi_c$ values obtained using Eq. (\ref{['eq:VFT']}), while the solid line connecting them is a fit to Eq. (\ref{['f0eq']}).
• Figure 2: Constructing the three-dimensional phase diagram. (a) The liquid-glass critical lines (symbols) determined via Eq. (\ref{['eq:VFT']}) for different values of $\tau_p$. These lines are themselves fitted to a power law form, Eq. (\ref{['f0eq']}), shown as lines. Vertical dashed line indicates the limit $\phi_d(\tau_p \to \infty)$. (b) The three-dimensional liquid-glass phase diagram can then be reconstructed from the fitted analytical expressions, with the glass phase occurring for large $\phi$ and low $f_0$, with a non-trivial evolution with $\tau_p$. Two iso-$f_0^2$ lines are shown; the one corresponding to $f_0^2=3.5\times 10^{-2}$ is non-monotonic.
• Figure 3: Re-entrant glassy dynamics. (a) Non-monotonic behaviour of $\tau_\alpha$ as a function of $\tau_p$ at various $f_0^2$ and $\phi=0.65$. The lines combine Eqs. (\ref{['eq:VFT']}, \ref{['f0eq']}) (see SM Table S1). (b, c, d) The dependence of $\phi_c(f_0^2,\tau_p)$ on $\tau_p$ for a small, an intermediate and a large value of $f_0^2$, showing a change from a monotonically increasing to a monotonically decreasing trend, with non-monotonic variation for the intermediate $f_0^2$. Lines represent the analytical description in Eq. (\ref{['critsurf']}). (e) Time decay of $F_s(k,t)$ for $\phi=0.65$ and $f_0^2=0.045$ and various $\tau_p$. The intermediate time plateau at small $\tau_p$, i.e. in the glassy regime, disappears at large $\tau_p$ in the jamming regime.
• Figure 4: Evolution of the glass fragility shown using Angell plots. Each panel represents data obtained at a given packing fraction, $\phi$ with (a) $\phi = 0.625$, (b) $\phi= 0.650$, (c) $\phi= 0.693$, and (d) $\phi= 0.800$, and each panel contains data for a range of $\tau_p$ values. The glass fragility decreases systematically with increasing $\tau_p$, and increases systematically with increasing $\phi$. The behavior of $\tau_\alpha$ crosses over from sub-Arrhenius at low $\phi$ and/or large $\tau_p$ to super-Arrhenius for large $\phi$ and/or small $\tau_p$.
• Figure 5: Dynamic scaling analysis collapses the glassy dynamics of active particles. (a) Angell plot using the rescaled relaxation time $\tau_\alpha \sqrt{T_\text{eff}}$ as a function of $1/T_\text{eff}$. Different symbols are for different $\phi$, different colors are for different $\tau_p$. (b) Global data collapse along the two branches describing the $\phi<\phi_0$ sub-Arrhenius and $\phi > \phi_0$ super-Arrhenius family of curves, as described in Eq. (\ref{['eq:BW']}). (c) The exponents $\delta$ and $\mu$ depart weakly from their equilibrium value as $\tau_p$ increases. (d) The critical hard sphere density $\phi_0(\tau_p)$ changes smoothly with $\tau_p$.