quantities of the system in order to obtain as realistic simulations as possible. In that
way, the authors were able to reproduce the structural and thermodynamic properties
of the system. Still, instead of changing the interaction parameters associated with the
abrupt change in solvent composition experienced by the diblock copolymer under
the experimental conditions, micellization was induced by quenching the temperature. Thus, the quenching time, corresponding to the mixing time in experiments, is
controlled by the cooling rate. The results showed that the block copolymers
aggregated into micelles with similar sizes and dimensions as observed experimentally. However, the time scale (a few milliseconds) was found to be considerably
faster than that experimentally determined, which ranged from 20 to 60 ms. Also,
although previous experiments showed that the micellar size decreases with increasing mixing time until the break (20–60 ms), the simulations showed the opposite
trend; the micellar size increases with mixing time until a breakpoint that occurs at
lower times than in experiments. This discrepancy was attributed to the different time
scales probed in simulations (t 5 ms) and that in the experiments the system was
allowed to grow further through fusion/fission, although the mechanisms were not
analyzed in detail in this work.
The mechanism and pathways of self-assembly were investigated in great detail
in a work by Li and Dormidontova [162], who analyzed a system consisting of
oligomeric block copolymers, A 2 -B 3 and A 4 -B x (the numbers indicate the numbers
of beads, x ¼ 4, 6, or 8) using dissipative particle dynamics. This simulation
technique combines molecular dynamics and Brownian dynamics-type simulations,
giving the advantage of accessing relatively large temporal and spatial time scales.
The growth curve associated with the weight and number average molecular
weights of the aggregates (M w and M n respectively), was found to be significantly
different. Here M n was found to stabilize to an equilibrium size more rapidly than
M w , indicating that the number of micelles assumes a constant value earlier but the
micelles are increasingly polydisperse in size with time. By tagging different
micelles as a function of time, it was found that the aggregation numbers exhibited
discrete jumps with amplitudes much larger than 1, indicating fusion events during
the course of the reaction. It was also found that unimer exchange was primarily
important in the first part of the micellization process (nucleation event); at later
stages processes involving fusion/fission of micelles were more dominating. The
latter was manifested in a bimodal character of the distribution function of M w
where two peaks were clearly visible at intermediate stages during the micellization
process. Increasing oligomer concentrations were found to speed up the whole
micellization process, which was attributed to increased probabilities of micellar
collision and fragmentation. The distribution function in terms of the aggregation
number is plotted as a function of time in Fig. 39.
In order to understand the interactions controlling the mechanisms behind selfassembly, the interaction energy between the hydrophobic core chains and the
solvents as well as the corona chain length were also varied. The results show that
the effect of incrementing the hydrophobic energy is threefold: First, the initial
nucleation-like event appears to be essentially unaffected; second, the time window
of micellization expands, i.e., the time for completion increases; and third, the
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R. Lund et al.
way, the authors were able to reproduce the structural and thermodynamic properties
of the system. Still, instead of changing the interaction parameters associated with the
abrupt change in solvent composition experienced by the diblock copolymer under
the experimental conditions, micellization was induced by quenching the temperature. Thus, the quenching time, corresponding to the mixing time in experiments, is
controlled by the cooling rate. The results showed that the block copolymers
aggregated into micelles with similar sizes and dimensions as observed experimentally. However, the time scale (a few milliseconds) was found to be considerably
faster than that experimentally determined, which ranged from 20 to 60 ms. Also,
although previous experiments showed that the micellar size decreases with increasing mixing time until the break (20–60 ms), the simulations showed the opposite
trend; the micellar size increases with mixing time until a breakpoint that occurs at
lower times than in experiments. This discrepancy was attributed to the different time
scales probed in simulations (t 5 ms) and that in the experiments the system was
allowed to grow further through fusion/fission, although the mechanisms were not
analyzed in detail in this work.
The mechanism and pathways of self-assembly were investigated in great detail
in a work by Li and Dormidontova [162], who analyzed a system consisting of
oligomeric block copolymers, A 2 -B 3 and A 4 -B x (the numbers indicate the numbers
of beads, x ¼ 4, 6, or 8) using dissipative particle dynamics. This simulation
technique combines molecular dynamics and Brownian dynamics-type simulations,
giving the advantage of accessing relatively large temporal and spatial time scales.
The growth curve associated with the weight and number average molecular
weights of the aggregates (M w and M n respectively), was found to be significantly
different. Here M n was found to stabilize to an equilibrium size more rapidly than
M w , indicating that the number of micelles assumes a constant value earlier but the
micelles are increasingly polydisperse in size with time. By tagging different
micelles as a function of time, it was found that the aggregation numbers exhibited
discrete jumps with amplitudes much larger than 1, indicating fusion events during
the course of the reaction. It was also found that unimer exchange was primarily
important in the first part of the micellization process (nucleation event); at later
stages processes involving fusion/fission of micelles were more dominating. The
latter was manifested in a bimodal character of the distribution function of M w
where two peaks were clearly visible at intermediate stages during the micellization
process. Increasing oligomer concentrations were found to speed up the whole
micellization process, which was attributed to increased probabilities of micellar
collision and fragmentation. The distribution function in terms of the aggregation
number is plotted as a function of time in Fig. 39.
In order to understand the interactions controlling the mechanisms behind selfassembly, the interaction energy between the hydrophobic core chains and the
solvents as well as the corona chain length were also varied. The results show that
the effect of incrementing the hydrophobic energy is threefold: First, the initial
nucleation-like event appears to be essentially unaffected; second, the time window
of micellization expands, i.e., the time for completion increases; and third, the
148
R. Lund et al.