Abstract
For ecoSLM -an ultra coarse-grained slip link model -the ability to use a time-step that increases with chain molecular weight is an important source of efficiency in modeling the linear rheology of monodisperse chains. This feature is labeled coarse-graining in this paper. It is compromised for blends of linear chains, where the time-step is set by the short chains, but the length of the simulation run is determined by the long chains. The problem is present for any polydisperse sample, and is particularly acute for binary blends with widely separated molecular weights. To recover temporal coarse-graining, we propose an adaptive time-step algorithm, where the time-step is determined by the shortest unrelaxed chains in the ensemble, which increases as the simulation proceeds. It involves two additional steps: recalibration, which is triggered when any component relaxes completely, and re-equilibration, in which slip links on completely relaxed components are renewed. We obtain reasonable settings for these steps, and validate the the adaptive time-step algorithm by comparing it with the original, constant time-step ecoSLM for binary, ternary, and polydisperse blends. Speedups ranging from 50% to 1500% are obtained when molecular weights of the components are widely separated, without a significant loss of accuracy. Conversely, the adaptive time-step algorithm is not recommended when molecular weights are not well-separated, since it can be slower than the constant time-step method.
Highlights
Despite the popularity of the tube model (TM), the list of its shortcomings keeps getting longer when it is subjected to strong tests [1,2,3], and its assumptions are scrutinized more closely [4,5,6]
To recover temporal coarse-graining, we propose an adaptive time-step algorithm, where the time-step is determined by the shortest unrelaxed chains in the ensemble, which increases as the simulation proceeds
The two main features of the adaptive time-step algorithm (ATSA) are (i) partial recovery of temporal coarse-graining due to larger time-steps upon complete relaxation of a component, and (ii) corrections due to RC and RE steps that account for accelerated dynamics in the presence of constraint release (CR)
Summary
Despite the popularity of the tube model (TM), the list of its shortcomings keeps getting longer when it is subjected to strong tests [1,2,3], and its assumptions are scrutinized more closely [4,5,6] Many of these issues stem from the difficulty in accounting for the process of constraint release (CR), which is a relaxation mechanism by which stress on an internal portion of a test chain is relaxed as a neighboring chain slips away. This is quite conspicuous even in the linear viscoelasticity (LVE) of a bidisperse mixture of long and short chains. SLMs reimagine CR using a simple, yet powerful, insight: when a slip link is destroyed on one of the chains due to reputation or contour length fluctuations, it is simultaneously eliminated on the “partner chain.” This gives them a structural advantage over the TM
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