Simulation of Solvent Evaporation from a Diblock Copolymer Film: Orientation of the Cylindrical Mesophase

Abstract

Using particle-based Monte Carlo simulations and continuum modeling, we study the self-assembly of asymmetric diblock copolymers in the course of solvent evaporation. We examine the effects of evaporation rate and solvent selectivity on the structure formation, especially the alignment of the cylindrical domains of the minority block. The comparison of the two simulation techniques facilitates identifying general trends upon parameter variation, while their inherent differences help us to understand the role of single-chain dynamics, fluctuations, and additional model details. In both cases, the simulation models feature a liquid and a gas phase with an explicit surface, across which solvent evaporates. We propose a "layer evolution model" that links processing parameters to the final morphology via the time dependence of layers, in which characteristic microphases, for example, spherical or cylindrical, can form. The evolution of these layers varies with the processing conditions and determines the morphology. This allows us to discuss the interplay of various experimentally accessible parameters, which we support by respective simulations. Our results single out two main factors to ensure the formation of minority-block cylinders, perpendicular to the film surface: (i) Fast evaporation rates induce a steep gradient in the polymer-density profile; that is, the polymer density immediately beneath the gas− liquid surface rapidly exceeds the critical value for cylinder formation. This confines cylinder formation into a layer that is thinner than the actual cylinder diameter, forcing a perpendicular alignment. (ii) A certain selectivity of the gas phase for the matrix-forming, majority block is necessary to disrupt an otherwise entropically favored surface layer of the minority block that would lead to parallel cylinder alignment.

Simulation of Membrane Fabrication via Solvent Evaporation and Nonsolvent-Induced Phase Separation

“…In our soft, coarse-grained model, there are no significant liquid-like packing effects of segments, and we account for the plasticizing effect of the solvents by a mobility modifier, 0 ≤ m i ({ϕ̂( c )}) ≤ 1. , It allows us to control the local dynamics of a segment of type i as a function of the local environment, without altering the thermodynamic equilibrium properties. To this end, we modify the original acceptance probability, p acc 0 ( r → r ′), of a proposed segment displacement from position r in cell c to r ′ in c ′ to p acc ( r → r ′ ) = p acc 0 ( r → r ′ ) m i ( false{ ϕ̂ ( c ) false} ) m i false( { ϕ̂ ′ false( c ′ false) } where {ϕ̂( c )} and {ϕ̂′( c ′)} denote the densities before and after the MC trial move, respectively.…”

“…This modified acceptance probability does not alter the detailed balance. We simulate the system in the semi-grand-canonical ensemble; that is, the total number of segments is constant, but solvent molecules, S or C, are converted into gas, G, in the case of EISA [23][24][25]27,34 or nonsolvent, N, in the case of NIPS at a distance above the film surface. This distance is set to d EISA = 2R e for solvent evaporation and d NIPS = 1.3R e for nonsolvent− solvent exchange, respectively.…”

“…Many aspects of the ordering can be rationalized by the time evolution of layers, in which (1) spherical micelles or (2) cylindrical domains can be formed. 25 NIPS modeling approaches for homopolymer membranes have been reviewed in ref 12. Recently, Grzetic et al studied the NIPS of copolymer films using dynamic self-consistent field theory (SCFT).…”

Modeling Microstructure Formation in Block Copolymer Membranes Using Dynamical Self-Consistent Field Theory

“…To account for the evaporation step, we construct a postevaporation initial condition for the partially ordered film using equilibrium self-consistent field theory (SCFT), which we then feed into dynamical self-consistent field theory (DSCFT) to simulate the membrane’s structural evolution during nonsolvent immersion. Although in recent decades there have been numerous theoretical/numerical studies of both homopolymer membrane formation via NIPS − as well as solvent evaporation of block copolymer films, − this is to our knowledge the first attempt to construct a theoretical framework that can be used to systematically investigate how the structure of block copolymer membranes, formed during nonsolvent-induced phase separation, depends on thermodynamic and kinetic parameters. Figure (right panel) shows an example of an initialized film–bath interface in 2D for an AB diblock copolymer (P) plus solvent (S) and nonsolvent (N) system, containing an ordered interfacial surface layer of thickness h , as well as the 1D SCFT density profile that is used to construct it.…”

“…For example, exploring the role of the solvent–nonsolvent exchange rate and the consideration of additional cosolvent species will be important in future work to more realistically describe experimental SNIPS protocols. The thickness and composition of the ordered surface layer could also be treated as proxy variables for the solvent evaporation time, in lieu of a more sophisticated, explicit theoretical treatment − of the evaporation step. The incorporation of thermal fluctuations and hydrodynamic effects ,, will also be important for future improvements to our model and workflow, which will enhance its ability to screen candidate polymer chemistries and architectures and solvent and nonsolvent selections and help achieve process optimization in SNIPS.…”