On Modelling Surface Directed Spinodal Decomposition

Long-Range Surface-Directed Polymerization-Induced Phase Separation: A Computational Study

The presence of a surface preferably attracting one component of a polymer mixture by the long-range van der Waals surface potential while the mixture undergoes phase separation by spinodal decomposition is called long-range surface-directed spinodal decomposition (SDSD). The morphology achieved under SDSD is an enrichment layer(s) close to the wall surface and a droplet-type structure in the bulk. In the current study of the long-range surface-directed polymerization-induced phase separation, the surface-directed spinodal decomposition of a monomer-solvent mixture undergoing self-condensation polymerization was theoretically simulated. The nonlinear Cahn-Hilliard and Flory-Huggins free energy theories were applied to investigate the phase separation phenomenon. The long-range surface potential led to the formation of a wetting layer on the surface. The thickness of the wetting layer was found proportional to time t*1/5 and surface potential parameter h 1 1/5. A larger diffusion coefficient led to the formation of smaller droplets in the bulk and a thinner depletion layer, while it did not affect the thickness of the enrichment layer close to the wall. A temperature gradient imposed in the same direction of long-range surface potential led to the formation of a stripe morphology near the wall, while imposing it in the opposite direction of surface potential led to the formation of large particles at the high-temperature side, the opposite side of the interacting wall.

Optimization and Validation of Efficient Models for Predicting Polythiophene Self-Assembly

We develop an optimized force-field for poly(3-hexylthiophene) (P3HT) and demonstrate its utility for predicting thermodynamic self-assembly. In particular, we consider short oligomer chains, model electrostatics and solvent implicitly, and coarsely model solvent evaporation. We quantify the performance of our model to determine what the optimal system sizes are for exploring self-assembly at combinations of state variables. We perform molecular dynamics simulations to predict the self-assembly of P3HT at ∼350 combinations of temperature and solvent quality. Our structural calculations predict that the highest degrees of order are obtained with good solvents just below the melting temperature. We find our model produces the most accurate structural predictions to date, as measured by agreement with grazing incident X-ray scattering experiments.

Simulating charge transport in organic semiconductors and devices: a review

Charge transport simulation can be a valuable tool to better understand, optimise and design organic transistors (OTFTs), photovoltaics (OPVs), and light-emitting diodes (OLEDs). This review presents an overview of common charge transport and device models; namely drift-diffusion, master equation, mesoscale kinetic Monte Carlo and quantum chemical Monte Carlo, and a discussion of the relative merits of each. This is followed by a review of the application of these models as applied to charge transport in organic semiconductors and devices, highlighting in particular the insights made possible by modelling. The review concludes with an outlook for charge transport modelling in organic electronics.

Phase behavior of diblock copolymer/star-shaped polymer thin film mixtures

We investigated the phase behavior of thin film, thickness h≈ 100 nm, mixtures of a polystyrene-b-poly(2-vinylpyridine) (PS-b-P2VP) diblock copolymer with star-shaped polystyrene (SPS) molecules of varying functionalities f, where 4 ≤f≤ 64, and molecular weights per arm Marm. The miscibility of the system and the surface composition varied appreciably with Marm and f. For large values of Marm, regardless of f, the miscibility of the system was qualitatively similar to that of linear chain PS/PS-b-P2VP mixtures - the copolymer chains aggregate to form micelles, each composed of an inner P2VP core and PS corona, which preferentially segregate to the free surface. On the other hand, for large f and small Marm, SPS molecules preferentially resided at the free surface. Moreover, blends containing SPS molecules with the highest values of f and lowest values of Marm were phase separated. These observations are rationalized in terms of competing entropic interactions and the dependence of the surface tension of the star-shaped molecules on Marm and f.

Pattern formation in polymer blend thin films: surface roughening couples to phase separation

We introduce a model for thin films of multicomponent fluids that includes lateral and vertical phase separation, preferential component attraction at both surfaces, and surface roughening. We apply our model to thin films of binary polymer blends, and use simulations of different surface-blend interaction regimes to investigate pattern formation. We demonstrate that surface roughening couples to phase separation. For films undergoing lateral phase separation via a transient wetting layer, this results in distinct stages of roughening as the film evolves between different phase equilibria.

Lateral phase separation in polymer-blend thin films: surface bifurcation

We use simulations of a binary polymer blend confined between selectively attracting walls to identify and explain the mechanism of lateral phase separation via a transient wetting layer. We first show that equilibrium phases in the film are described by one-dimensional phase equilibria in the vertical (depth) dimension, and demonstrate that effective boundary conditions imposed by the film walls pin the film profile at the walls. We then show that, prior to lateral phase separation, distortion of the interface in a transient wetting layer is coupled to lateral phase separation at the walls. Using Hamiltonian phase portraits, we explain a "surface bifurcation mechanism" whereby the volume fraction at the walls evolves and controls the dynamics of the phase separation. We suggest how solvent evaporation may assist our mechanism.

Breakup of a transient wetting layer in polymer blend thin films: unification with 1D phase equilibria

We show that lateral phase separation in polymer blend thin films can proceed via the formation of a transient wetting layer which breaks up to give a laterally segregated film. We show that the growth of lateral inhomogeneities at the walls in turn causes the distortion of the interface in the transient wetting layer. By addressing the 1D phase equilibria of a polymer blend thin film confined between selectively attracting walls, we show that the breakup of a transient wetting layer is due to wall-blend interactions; there are multiple values of the volume fraction at the walls which solve equilibrium boundary conditions. This mechanism of lateral phase separation should be general.

Kinetics of phase separation in thin films: lattice versus continuum models for solid binary mixtures

A description of phase separation kinetics for solid binary (A,B) mixtures in thin film geometry based on the Kawasaki spin-exchange kinetic Ising model is presented in a discrete lattice molecular field formulation. It is shown that the model describes the interplay of wetting layer formation and lateral phase separation, which leads to a characteristic domain size l(t) in the directions parallel to the confining walls that grows according to the Lifshitz-Slyozov t;{13} law with time t after the quench. Near the critical point of the model, the description is shown to be equivalent to the standard treatments based on Ginzburg-Landau models. Unlike the latter, the present treatment is reliable also at temperatures far below criticality, where the correlation length in the bulk is only of the order of a lattice spacing, and steep concentration variations may occur near the walls, invalidating the gradient square approximation. A further merit is that the relation to the interaction parameters in the bulk and at the walls is always transparent, and the correct free energy at low temperatures is consistent with the time evolution by construction.

Wetting-layer formation mechanisms of surface-directed phase separation under different quench depths with off-critical compositions in polymer binary mixture

Focusing on the off-critical condition, the quench depth dependence of surface-directed phase separation in the polymer binary mixture is numerically investigated by combination of the Cahn-Hilliard-Cook theory and the Flory-Huggins-de Gennes theory. Two distinct situations, i.e., for the wetting, the minority component is preferred by the surface and the majority component is preferred by the surface, are discussed in detail. The simulated results show that the formation mechanism of the wetting layer is affected by both the quench depth and the off-critical extent. Moreover, a diagram, illustrating the formation mechanisms of the wetting layer with various quench depths and compositions, is obtained on the basis of the simulated results. It is found that, when the minority component is preferred by the surface, the growth of the wetting layer can exhibit pure diffusion limited growth law, logarithmic growth law, and Lifshitz-Slyozov growth law. However, when the majority component is preferred by the surface, the wetting layer always grows logarithmically, regardless of the quench depth and the off-critical extent. It is interesting that the surface-induced nucleation can be observed in this case. The simulated results demonstrate that the surface-induced nucleation only occurs below a certain value of the quench depth, and a detailed range about it is calculated and indicated. Furthermore, the formation mechanisms of the wetting layer are theoretically analyzed in depth by the chemical potential gradient.

Numerical treatment of the dynamics of a conserved order parameter in the presence of walls

We discuss how the diffusive dynamics of a conserved order parameter should be numerically treated when impenetrable wall surfaces are present and interact with the degrees of freedom characterized by the order parameter. We derive the discretization scheme for the dynamics, paying particular attention to the conservation of the order parameter in the strict numerical sense. The discretized chemical potential, or the functional derivative of the free energy, contains a surface contribution inversely proportional to the grid spacing Delta z, which was proposed heuristically in a recent paper of Henderson and Clarke [Macromol. Theory Simul. 14, 435 (2005)]. Although apparently that surface contribution diverges in the continuum limit Delta z --> 0, we can show, by an analytic argument and numerical calculations, that this divergence does not yield any anomalies, and that our discretization scheme is well defined in this limit. We also discuss the correspondence of our treatment to the model proposed by Puri and Binder [Phys. Rev. A 46, R4487 (1992)] extensively used for the present problem.