A lattice model approach to the morphology formation from ternary mixtures during the evaporation of one component

Abstract

Stimulated by experimental evidence in the field of solution-born thin films, we study the morphology formation in a three state lattice system subjected to the evaporation of one component. The practical problem that we address is the understanding of the parameters that govern morphology formation from a ternary mixture upon evaporation, as is the case in the fabrication of thin films from solution for organic photovoltaics. We use, as a tool, a generalized version of the Potts and Blume-Capel models in 2D, with the Monte Carlo Kawasaki-Metropolis algorithm, to simulate the phase behaviour of a ternary mixture upon evaporation of one of its components. The components with spin +1, −1 and 0 in the Blume-Capel dynamics correspond to the electron-acceptor, electron-donor and solvent molecules, respectively, in a ternary mixture used in the preparation of the active layer films in an organic solar cell. Further, we introduce parameters that account for the ccmmms-morph˙preprint.tex -29 agosto 2018 1:15 arXiv:1808.09326v1 [cond-mat.stat-mech] 28 Aug 2018 relative composition of the mixture, temperature, and interaction between the species in the system. We identify the parameter regions that are prone to facilitate the phase separation. Furthermore, we study qualitatively the types of formed configurations. We show that even a relatively simple model, as the present one, can generate key morphological features, similar to those observed in experiments, which proves the method valuable for the study of complex systems. IntroductionMulti-state spin systems on a lattice have been widely studied in the Statistical Mechanics literature, we refer the reader for instance to [33] where efforts have been invested in connecting microscopic dynamics to dynamics at mesoscopic and/or continuum scales. The celebrated Blume-Capel model [3,4,6] is a three-state model which has been originally introduced to study the He 3 -He 4 mixture low temperature properties. More recently, the model has received a lot of interest also in the mathematics literature, since it is a prototype to study the effects of multiple metastable states [12][13][14]24]. The Hamiltonian of the Blume-Capel setting is characterized by a nearest neighbor spin-spin interaction term, a chemical potential contribution, and, finally, a term describing the interaction with an external magnetic field. In the Blume-Capel model the spin can take the values −1, 0, +1 and the three different interface pairs −+, 0−, and 0+ have different energetic costs. More precisely, the two pairs containing a zero have the same cost, whereas the −+ one has a larger cost (four times). Pairs with equal spins −−, ++, and 00 have no energetic cost.A different multi-state model is the Potts model [32,37] -a straightforward generalization of the Ising model in which the spin has q > 2 states and in the Hamiltonian the nearest neighbor interaction and the external field contribution are taken into account. In the standard version of the model, all the pairs of spin interact similarly, but in i...

A Mesoscopic Lattice Model for Morphology Formation in Ternary Mixtures with Evaporation

“…We are using this scenario to explore the effect of various parameters (mixture composition, temperature of the system, volatility, interaction strengths among mixture components) on the formation of morphologies. This type of numerical results show that our mesoscopic model is able to capture the type of results obtained in [4]. Additionally, a few typical mesoscopic features (like dependence of the morphology widths on λ and quicker stabilization of morphologies) can now be pointed out -such features arise at each allowed choice of λ > 1 and set the foundation for what we refer to as near self-similarity in morphology arrangements.…”

“…We refer to such larger scales as mesoscales and we label them by λ. The interest in unveiling mesoscale effects was triggered by our previous simulation results reported in [4,15] and [21], where we noticed the occurrence of different types of morphology shapes. The simple observation that the geometry of the shapes depends on the choice of model parameters (the system's temperature, volatility, interaction parameters, etc.)…”

“…Note that in [4] we explored the parameter space leading to morphologies as obtained with simulations done exclusively at the microscopic scale (i.e., pair-wise interactions involving only the nearest neighbours of randomly selected lattice sites). Further motivation towards performing mesoscale-level simulations in a closely related context is mentioned in [34].…”

Unravelling donor–acceptor film morphology formation for environmentally-friendly OPV ink formulations

“…There is a rich complexity to phase evolution during solvent evaporation. 59,60 To develop tools to predict this phase evolution, and in turn control morphology formation, is the ultimate goal for organic photovoltaic active layers. 61 We here calculated the distance in HSP space (R a ) between both the donor and acceptor material to the primary solvent in order to determine a correlation between HSP and donor-acceptor film morphology.…”

Stability of the stationary solutions of the Allen-Cahn equation with non-constant stiffness

“…Two particular values of the field represent the two homogeneous phases. These models have been widely used in the study of the spinodal decomposition phenomenon [1,2,3], namely, the process in which a system undergoing a second order phase transition is suddenly quenched from the disordered high temperature phase into a Email addresses: butta@mat.uniroma1.it (Paolo Buttà), emilio.cirillo@uniroma1.it (Emilio N.M. Cirillo), giulio.sciarra@ec-nantes.fr (Giulio Sciarra) broken-symmetry low temperature state and the evolving field φ(x, t) encodes the process of separation of the low temperature phases [4].…”