A comparison of implicit- and explicit-solvent simulations of self-assembly in block copolymer and solute systems

Abstract

We have developed explicit- and implicit-solvent models for the flash nanoprecipitation process, which involves rapid coprecipitation of block copolymers and solutes by changing solvent quality. The explicit-solvent model uses the dissipative particle dynamics (DPD) method and the implicit-solvent model uses the Brownian dynamics (BD) method. Each of the two models was parameterized to match key properties of the diblock copolymer (specifically, critical micelle concentration, diffusion coefficient, polystyrene melt density, and polyethylene glycol radius of gyration) and the hydrophobic solute (aqueous solubility, diffusion coefficient, and solid density). The models were simulated in the limit of instantaneous mixing of solvent with antisolvent. Despite the significant differences in the potentials employed in the implicit- and explicit-solvent models, the polymer-stabilized nanoparticles formed in both sets of simulations are similar in size and structure; however, the dynamic evolution of the two simulations is quite different. Nanoparticles in the BD simulations have diffusion coefficients that follow Rouse behavior (D ∝ M(-1)), whereas those in the DPD simulations have diffusion coefficients that are close to the values predicted by the Stokes-Einstein relation (D ∝ R(-1)). As the nanoparticles become larger, the discrepancy between diffusion coefficients grows. As a consequence, BD simulations produce increasingly slower aggregation dynamics with respect to real time and result in an unphysical evolution of the nanoparticle size distribution. Surface area per polymer of the stable explicit-solvent nanoparticles agrees well with experimental values, whereas the implicit-solvent nanoparticles are stable when the surface area per particle is roughly two to four times larger. We conclude that implicit-solvent models may produce questionable results when simulating nonequilibrium processes in which hydrodynamics play a critical role.

Controlling crystal self-assembly using a real-time feedback scheme

“…Both these choices 31,32 act to reduce the diffusion of large clusters of particles. This favours the Ostwald ripening mechanism for assembly, compared with the process by which diffusing clusters collide and fuse.…”

“…Our model therefore neglects hydrodynamic effects arising from the solvent, and may underestimate the rates of diffusion for large clusters of colloidal particles. 31 However, Langevin dynamics do capture the essential physical processes at work in self-assembly: 3,10,11,16,20 reversible bonding, nucleation of ordered phases, the possibility for kinetic trapping, and Ostwald ripening. We therefore use this method for computational convenience and for ease of comparison with other studies.…”

Molecular dynamics simulation: a tool for exploration and discovery using simple models

“…While both are capable of serving as heat baths to absorb the bond formation energy, as well as curtailing the ballistic nature of the particle motion to ensure conditions closer to thermal equilibrium, only the explicit approach allows particles that have assembled into structures to offer mutual shielding against disruptive solvent effects, aids cluster breakup without subassemblies needing to collide directly, and incorporates the dynamical correlations of the fluid medium. The choice of solvent representation is also capable of affecting the outcome of self-assembly simulations [101]. The size ratio of the particles relative to the solvent atoms is much smaller than in reality, in order to enhance particle mobility and compress the time scales over which assembly occurs; the corresponding mass ratio (here 15) is also reduced.…”

Molecular dynamics simulation of trimer self-assembly under shear

“…Accordingly, the model simulated here lacks explicit solvent and ignores some solvent mediated phenomena, such as hydrodynamic effects and buffeting due to random forces. Although hydrodynamics can influence dynamical properties in non-equilibrium self-assembly processes [41], implicit solvent simulations allow for the simulation of larger system sizes [42] and have been shown to possess similar self-assembled structural properties as explicit solvent simulations [41]. …”