Snapshots of a typical expanded coil (E = 0) and corresponding collapsed crystallite (E = −4N) for two types of polymers, where upper panel is a linear polymer (N a = 2 and L a = 240), and the lower panel is a 12-arm star polymer (N a = 12 and L a = 60). Images are rendered by visual molecular dynamics (see Ref. 67).
The schematic diagram of the hybrid movement algorithm including four types of simple movements, i.e., BFM movement, pivot movement, crankshaft movement, and center imaging movement.
The entropy function ln g(E) (left panels) and the corresponding average entropy function ln g(E)/N (right panels) as a function of the specific energy E/N. The apparent intersection regions in the left panels are magnified in the inset chart. The arrows in the right panels label the shifting directions of the maximum entropy point with the increasing of the arm length L a . (a) Linear polymers; (b) 6-arm star polymers; and (c) 12-arm star polymers.
The ln g(E) of the intersection regions in the ln g(E) ∼ E/N curves as a function of N a 3, which is fitted as a straight line.
Dependence of the specific heat per monomer C V (T)/N on the canonical temperature T (unit in k B ). (a) Linear polymers; (b) 6-arm star polymers; and (c) 12-arm star polymers.
Freezing transition temperature as a function of N −1/3, where all polymer samples show a common linear relation towards the direction of an infinite chain. The linear relation has been extrapolated to N→∞ to obtain the limit freezing temperature at about T freezing = 2.13.
The shape factor ρ as a function of the specific energy. The valley region in each panel is labeled with an arrow. (a) Linear polymers; (b) 6-arm star polymers; and (c) 12-arm star polymers.
Comparison of the inverse temperature with the corresponding shape factor as a function of the specific energy, where the three polymer samples are from the three sets of polymer chains mentioned above. The valley positions in both panels are labeled with three vertical lines showing that they have the identical energy states.
The derivative of the shape factor ρ as a function of the canonical temperature (unit in k B ). (a) Linear polymers; (b) 6-arm star polymers; and (c) 12-arm star polymers.
The LC and CG transition temperatures as a function of N −1/2 for the linear polymers and the 6-arm star polymers, respectively. The two transitions are fitted according to the scaling equation shown in the chart. The symbols are derived from Fig. 9. See the main text for a discussion.
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