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

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 $\varphi$, 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 $\varphi$ and $T$. The former is essentially vertical ($\varphi$-controlled), while the latter is rather horizontal ($T$-controlled) in the $(\varphi -T)$ 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.