The growth step during the radical-like polymerization algorithm. A radical (white) is randomly assigned one of its first monomers neighbors (blue ones, numbered from 1 to 4) to create a new covalent bond and increase the local chain length .
Mean chain length size evolution during polymerization stage vs the number of growth step, and for the two polydisperse and unrelaxed simulated monodisperse systems. Also plotted is the standard deviation represented by vertical bars centered on symbols. Inset: size distribution for the same systems at the end of the generation procedure.
Generation stage: evolution of the mean radius of gyration normalized by the average bond length and averaged over all chains. Generation exhibits two distinct stages: (i) a pure growth stage characterized by a growth kinetics; (ii) a saturation stage where gyration radii reach a plateau value. A value of has been used for polydisperse and monodisperse methods (see Table II).
Equilibration stage (e.g., after polymerization): evolution of the mean gyration radius as a function of the number of MD steps necessary to reach a total number MD steps. Fast push off (FPO) and monodisperse methods converge to the same value.
Growth and equilibration stages: evolution of the mean radius of gyration as a function of the mean chain size during growth (curves) and equilibration (vertical arrows) stages. Data from Kremer and Grest (Ref. 6) and Gao (Ref. 2) are also represented. They predict a dependence. After the removal of the remaining monomers and MD equilibration steps, all generation techniques are in very good agreement with Kremer and Gao’s results.
Evolution of the mean radius of gyration as a function of time (in MD steps) during growth and equilibration stages: generation of chains of length at and . Two different values of (the number of MD steps between each growth step) are compared. A larger value of slows down the growth kinetics, but leads to better equilibrated systems once growth is completed. For , no equilibration stage is required to reach the mean radius of gyration obtained with the FPO method.
Mean square internal distance (MSID) of generated melts measured after long MD runs ( MD steps). The target function of Auhl et al. (Ref. 5) is compared to the following systems: unrelaxed, polydisperse, monodisperse and FPO. Error bars are calculated using standard error function on statistical samples. All methods lead to well equilibrated melts.
MSID of monodisperse melts [(a): , (b): ]. The effect of the number of MD steps between each growth step is studied. A larger value of leads to better equilibrated systems: MSID fits nicely with FPO and the target function of Auhl et al. (Ref. 5).
Evolution of the number of monomers in straight primitive path segments along simulation times for monodisperse systems, namely, monodisperse and FPO. PPA has been performed during both the generation stage and the equilibration stage separated by the vertical dashed line. Units of time are in units, i.e., . The horizontal line gives value for from Sukumaran et al. (Ref. 19).
Ratio for polydisperse systems unrelaxed and polydisperse against simulation time. Dashed (middashed) vertical line separates generation to equilibration stages for the unrelaxed (polydisperse) method. Also shown is the same ratio from Sukumaran et al. (Ref. 19) for chains length as an indicative value.
Lamellar spacing of diblock copolymer after MD steps at and . Scaling law expected in the strong segregation limit (Refs. 27–32) is clearly observed.
Snapshots of diblock and triblock copolymers generated using the radical-like copolymerization method for chains of length under periodic boundary conditions. Chains are unfolded according to the position of the first bead of the chain. Two macromolecules are highlighted and the simulation box is shown in black. diblock: and . triblock: , and .
Relevant parameters used in the radical-like polymerization algorithm.
Parameters used to simulate the different radical-like polymerization processes discussed in text, during the generation stage.
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