Dissipative Particle Dynamics Approaches to Modeling …
81
phase diagrams were developed for BCPs with pH-sensitive coronal blocks through
free energy expressions for spherical, cylindrical, or lamellar micelles, according to
their respective packing geometries [63].
Several theoretical studies have been devoted to the properties of polymer
networks or gels formed from amphiphilic polyelectrolyte triblock copolymers [81–
86]. The addition of salt screens the electrostatic interactions between the polyelectrolytes and induces deswelling or collapse of the polymer network [50–53, 81, 82,
84–87]. However, theoretical analysis of the micellization of polyelectrolyte triblock
or multiblock copolymers is challenging. Currently, no power law dependencies for
the parameters of these systems have been determined.
Overall, current theories can be used to predict various characteristic properties of
a micellar system assembled from di/triblock copolymers. These properties include
the aggregation number, the radius of gyration of the micelle and the core, and the
thickness of the corona. These properties depend upon the molecular characteristics
of the block copolymers and the solvent, such as the pH or the ionic strength of
polyelectrolyte block copolymer systems. However, improved property characterization and detailed prediction is necessary for increased potential of BCP systems.
For example, DNA-amphiphilic polymers with hydrophobic spacers can form nanotapes, a morphology currently not predicted by theories [88, 89]. This knowledge
gap can be overcome by the advancements of mesoscale particle based modeling
techniques.
3 DPD Simulations
Simulating the BCPs self-assembling behavior requires mesoscopic spatial resolution
to capture the morphology of polymer aggregates, and mesoscopic or even macroscopic temporal resolution for capturing the processes and mechanisms underlying
the equilibration of the system. Polymer scaling laws suggest that simulating typical
behavior of BCPs will require hundreds to thousands of chains in a very large simulation box so that most of chains do not interact with themselves through the periodic
boundaries [90]. It also requires capturing the dynamics over extended temporal
scales, namely hundreds of nanoseconds to even microseconds, for the chains to
relax sufficiently. This is particularly important in the study of the self-assembly
behavior of BCPs in solution where many solvent molecules are present.
While this chapter primarily focuses on using DPD to address the need for characterizing BCP micellization, there are other approaches capable of predicting the selfassembling behavior of various BCPs. Coarse-grained molecular dynamics (MD)
combines the MD technique with low-resolution representation of the molecular
components along with the use of suitable force fields to model the desired system.
Detailed reviews outline the benefits, limitations and various studies using coarsegrained MD simulations [91, 92]. For example, block copolymer self-assembled
morphologies can be predicted using particle based coarse-grained approaches
utilizing Brownian or Langevin dynamics in combination with a Lennard–Jones
81
phase diagrams were developed for BCPs with pH-sensitive coronal blocks through
free energy expressions for spherical, cylindrical, or lamellar micelles, according to
their respective packing geometries [63].
Several theoretical studies have been devoted to the properties of polymer
networks or gels formed from amphiphilic polyelectrolyte triblock copolymers [81–
86]. The addition of salt screens the electrostatic interactions between the polyelectrolytes and induces deswelling or collapse of the polymer network [50–53, 81, 82,
84–87]. However, theoretical analysis of the micellization of polyelectrolyte triblock
or multiblock copolymers is challenging. Currently, no power law dependencies for
the parameters of these systems have been determined.
Overall, current theories can be used to predict various characteristic properties of
a micellar system assembled from di/triblock copolymers. These properties include
the aggregation number, the radius of gyration of the micelle and the core, and the
thickness of the corona. These properties depend upon the molecular characteristics
of the block copolymers and the solvent, such as the pH or the ionic strength of
polyelectrolyte block copolymer systems. However, improved property characterization and detailed prediction is necessary for increased potential of BCP systems.
For example, DNA-amphiphilic polymers with hydrophobic spacers can form nanotapes, a morphology currently not predicted by theories [88, 89]. This knowledge
gap can be overcome by the advancements of mesoscale particle based modeling
techniques.
3 DPD Simulations
Simulating the BCPs self-assembling behavior requires mesoscopic spatial resolution
to capture the morphology of polymer aggregates, and mesoscopic or even macroscopic temporal resolution for capturing the processes and mechanisms underlying
the equilibration of the system. Polymer scaling laws suggest that simulating typical
behavior of BCPs will require hundreds to thousands of chains in a very large simulation box so that most of chains do not interact with themselves through the periodic
boundaries [90]. It also requires capturing the dynamics over extended temporal
scales, namely hundreds of nanoseconds to even microseconds, for the chains to
relax sufficiently. This is particularly important in the study of the self-assembly
behavior of BCPs in solution where many solvent molecules are present.
While this chapter primarily focuses on using DPD to address the need for characterizing BCP micellization, there are other approaches capable of predicting the selfassembling behavior of various BCPs. Coarse-grained molecular dynamics (MD)
combines the MD technique with low-resolution representation of the molecular
components along with the use of suitable force fields to model the desired system.
Detailed reviews outline the benefits, limitations and various studies using coarsegrained MD simulations [91, 92]. For example, block copolymer self-assembled
morphologies can be predicted using particle based coarse-grained approaches
utilizing Brownian or Langevin dynamics in combination with a Lennard–Jones