Sticky monomer interaction potential. Same as in Refs. 14 and 46. Differences in SB formation/breaking rules are noted in the text.
Sticky association in equilibrium; simulation data and test of Eq. (8). All results are for , systems with and . Closed circles are simulation values of from Eq. (4) for polymers and open circles are for dimer-forming systems. The straight lines are exponential fits, to Eq. (8), for .
Cluster size distribution. is the probability that a chain will be part of a disconnected cluster of chains (i.e., the weight fraction of -clusters). All results are for , uniform systems with and . Data for different kinetic rates are shown: (stars), 10 , and 100 . The apparent preponderance of the lower two rates is an artifact of the plotting procedure. The upward slope at large MW is due to the statistics of small numbers. Results are averaged over 100 statistically independent samples.
Sticky bond lifetimes. All results are for 280 000-bead, systems with and . Closed circles are simulation data for polymers, open circles are data for dimer-forming systems, and the straight line is an exponential “fit,” shown only as a guide to the eye.
Arrhenius 2 state model. Refs. 14 and 78 did not introduce an -dependent .
Validation of method. All results are for 280 000-bead, systems with and . Closed circles are simulation data for polymers, open circles are data for dimer-forming systems, and straight lines are exponential fits. Data shown are: (a) , and (b) .
Diffusion as function of , , and . All systems have and . Panel (a): , increasing . Panel (b): ; and , increasing . Panel (c) is a blowup of (b) showing the crossover. Lines from top to bottom for each in panels (b)–(c) are for , 10, 100, and (for ) . The legends for panels (b)–(c) give in units of and in units of .
Scaling of diffusion with various candidate “long” relaxation times. Data shows for (circles), (triangles), and (squares). The last value is chosen so the “bare” diffusion constant can be shown on the same plot. All results are for systems with , , and . is not shown because .
Crossover from DL to KL sticky bond recombination for and . All systems have 70 000 beads, with . The upper data set is for polymers and the lower is for dimer-forming systems. The fastest-kinetic systems use , and all others use . The solid line shows a fit to Eq. (10) with , and . The dashed line shows a fit with set to 1, and .
SB recombination and dynamical heterogeneity. All systems have , , and . Lines from top to bottom are for , 10, and 100. Panel (a): . The black dotted line is for . Panel (b): .
Nonequilibrium capability of method: -jump. Solid (dashed) lines are the predictions of Eq. (17) and upper (lower) circles show simulation data for , (, ) for an , system after turning on sticky bonds. Simulations used .
Linear creep and quiescent diffusion for two systems with the same but different SB recombination. Results are for systems with , , and . Panel (a) stretch under a creep stress . The upper curve is for , and the lower curve is for , . Panel (b): mean squared displacement for the same systems in the quiescent state.
Constant volume tension simulations for systems with different SB kinetics. The stress difference is plotted against . Systems have , , , , and the strain rate is . These runs use for greater accuracy. Data from top to bottom correspond to (no SB breaking/forming allowed during deformation), and . The solid lines are predictions of Eq. (18), with the value of taken from a fit to the data and values of taken from Table I.
Finite-size analysis of the percolation gel transition. Data are at for (circles), (squares), (triangles), and (diamonds) are shown. .
Variation in , , and with , , , and . Times are in units of . Statistical errors are roughly ±2% or less. All systems have and data are averaged over multiple statistically independent states. denotes results. – –indicates calculation is prohibitive or we have insufficient data. Results for in systems are not presented because they are negligibly affected by sticky bonding.
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