A direct comparison of crystallization transitions and glassy dynamics in polymers and colloids

Using computer simulations, we compare the freezing transitions in systems composed of $N$ spherical particles with and without covalent-bonding constraints. Linear polymer chains with $N-1$ permanent covalent bonds are compared to ``colloidal'' systems with the same nonbonded interactions but no covalent bonds. In the ``sticky hard sphere'' limit, where covalent bonds act as holonomic constraints, the melting temperatures $T_{\rm melt}$ for both polymers and colloids (with the same $N$) are inversely proportional to the number of unconstrained degrees of freedom. We also examine the effect of the thermal quench rate $|\dot{T}|$ on collapse. At $|\dot{T}|$ below a lower ``critical'' value, which decreases rapidly with increasing $N$, polymers and colloids form similar ground states. This critical value is lower for polymers than colloids and has different $N$-dependence. In both cases, the dynamics of the systems slow down near $T_{\rm melt}$ as the system approaches isostaticity. For high $|\dot{T}|$, glassy dynamics produces disordered final states. At intermediate $|\dot{T}|$, we find complex nonmonotonic behavior in $T$, which we relate to the very different rearrangement kinetics of polymeric and colloidal clusters.