would be very helpful. Complementary, more theoretical modeling is necessary in
order to fully understand the mechanisms and kinetic pathways. Here computer
simulations are particularly useful. A summary of existing works on this topic will
be covered in the next section.
5.1.4 Computer Simulations
The central questions occupying theoreticians and experimentalists are the mechanism and kinetic pathways of self-assembly. To answer these questions, computer
simulations are particularly useful because the coordinates of each molecule can be
traced individually and pathways can be observed directly. The challenge for
computer simulations is to access the relatively long time scales needed to observe
micellization kinetics, which can only be done using coarse-grained models, relatively few particles, and/or by excessively long computation times.
An early simulation work was presented by Mattice and coworkers [184] in
which A-B diblock copolymers consisting of 5–45 monomers for each block were
studied. The simulations were performed in cubic simulation cells with 44
3 –88
3
lattice sites. The total concentration of the polymers were found to be in the range of
0.5–6%. Results obtained after starting from typically a few hundred chains
revealed a rapid initial step that essentially consumed all single unimers, followed
by a very slow coarsening process that was not fully equilibrated within the
simulation time. In the work, no direct detailed analysis or evaluation of the kinetic
pathway was performed. Nevertheless it was observed that upon increasing the
interaction strength between the hydrophobic block and the solvent or increasing
the insoluble block length, smaller trapped metastable micelles were detected.
These micelles were found to essentially “freeze” the self-assembly process, at
least on the time scale of the simulations.
Using full atomistic force field-based molecular dynamics simulations, Marrink
et al. [185] simulated the micellization process of 54 dodecylphosphocholine (DPC)
surfactant molecules in water on short time scales from some picoseconds to some
tenths of nanoseconds. The results showed that the process is diffusion limited but
that the surfactant aggregation still occurred on time scales much faster than expected
from theoretical calculations. It was speculated that long-range interactions could
enhance the aggregation rate. However, upon varying the interaction potential, it was
concluded that this did not influence the results. Instead, water-mediated long-range
hydrophobic interactions were suggested as a possible alternative explanation for the
observed behavior. Interestingly, the simulation runs revealed that the micelles
aggregate into larger cylindrical micelles at higher DPC concentration, whereas
smaller spherical micelles are formed at lower concentrations. The difference was
attributed to finite size effects and a small number of particles.
In a work by Chen et al. [186], Brownian dynamics was used to simulate the
formation of micelles constituted of PS-PEO in water, with the particular aim of
investigating the processes involved in “flash nanoprecipitation”. The effective
(coarse-grained) potential was carefully mapped to experimentally determined
Kinetics of Block Copolymer Micelles Studied by Small-Angle Scattering Methods
147
order to fully understand the mechanisms and kinetic pathways. Here computer
simulations are particularly useful. A summary of existing works on this topic will
be covered in the next section.
5.1.4 Computer Simulations
The central questions occupying theoreticians and experimentalists are the mechanism and kinetic pathways of self-assembly. To answer these questions, computer
simulations are particularly useful because the coordinates of each molecule can be
traced individually and pathways can be observed directly. The challenge for
computer simulations is to access the relatively long time scales needed to observe
micellization kinetics, which can only be done using coarse-grained models, relatively few particles, and/or by excessively long computation times.
An early simulation work was presented by Mattice and coworkers [184] in
which A-B diblock copolymers consisting of 5–45 monomers for each block were
studied. The simulations were performed in cubic simulation cells with 44
3 –88
3
lattice sites. The total concentration of the polymers were found to be in the range of
0.5–6%. Results obtained after starting from typically a few hundred chains
revealed a rapid initial step that essentially consumed all single unimers, followed
by a very slow coarsening process that was not fully equilibrated within the
simulation time. In the work, no direct detailed analysis or evaluation of the kinetic
pathway was performed. Nevertheless it was observed that upon increasing the
interaction strength between the hydrophobic block and the solvent or increasing
the insoluble block length, smaller trapped metastable micelles were detected.
These micelles were found to essentially “freeze” the self-assembly process, at
least on the time scale of the simulations.
Using full atomistic force field-based molecular dynamics simulations, Marrink
et al. [185] simulated the micellization process of 54 dodecylphosphocholine (DPC)
surfactant molecules in water on short time scales from some picoseconds to some
tenths of nanoseconds. The results showed that the process is diffusion limited but
that the surfactant aggregation still occurred on time scales much faster than expected
from theoretical calculations. It was speculated that long-range interactions could
enhance the aggregation rate. However, upon varying the interaction potential, it was
concluded that this did not influence the results. Instead, water-mediated long-range
hydrophobic interactions were suggested as a possible alternative explanation for the
observed behavior. Interestingly, the simulation runs revealed that the micelles
aggregate into larger cylindrical micelles at higher DPC concentration, whereas
smaller spherical micelles are formed at lower concentrations. The difference was
attributed to finite size effects and a small number of particles.
In a work by Chen et al. [186], Brownian dynamics was used to simulate the
formation of micelles constituted of PS-PEO in water, with the particular aim of
investigating the processes involved in “flash nanoprecipitation”. The effective
(coarse-grained) potential was carefully mapped to experimentally determined
Kinetics of Block Copolymer Micelles Studied by Small-Angle Scattering Methods
147