Mode-coupling theory predictions for a limited valency attractive square-well model

TL;DR

This study combines simulations and mode coupling theory to analyze a limited valency square-well model, revealing distinct glass and gel arrest lines and comparing theoretical predictions with numerical results.

Contribution

It introduces mode coupling theory calculations based on simulation data to predict dynamic arrest lines in a limited valency attractive model.

Findings

Theory predicts a repulsive glass line matching simulations.

Attractive glass line appears separate from gel line.

Distinct arrest lines are characterized by temperature and packing fraction.

Abstract

Recently we have studied, using numerical simulations, a limited valency model, i.e. an attractive square well model with a constraint on the maximum number of bonded neighbors. Studying a large region of temperatures $T$ and packing fractions $\phi$, we have estimated the location of the liquid-gas phase separation spinodal and the loci of dynamic arrest, where the system is trapped in a disordered non-ergodic state. Two distinct arrest lines for the system are present in the system: a {\it (repulsive) glass} line at high packing fraction, and a {\it gel} line at low $\phi$ and $T$. The former is essentially vertical ($\phi$-controlled), while the latter is rather horizontal ($T$-controlled) in the $(\phi-T)$ plane. We here complement the molecular dynamics results with mode coupling theory calculations, using the numerical structure factors as input. We find that the theory predicts a repulsive glass line -- in satisfactory agreement with the simulation results -- and an attractive glass line which appears to be unrelated to the gel line.