| 1. |
- Cirillo, Emilio N.M., et al.
(author)
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A lattice model approach to the morphology formation from ternary mixtures during the evaporation of one component
- 2019
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In: The European Physical Journal Special Topics. - : Springer. - 1951-6355 .- 1951-6401. ; 228:1, s. 55-68
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Journal article (peer-reviewed)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. Furthermore, we introduce parameters that account for the 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.
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| 2. |
- Kronberg, Vi C. E., et al.
(author)
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Numerical explorations of solvent borne adhesives : A lattice-based approach to morphology formation
- 2023
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In: Modelling and Simulation in Materials Science and Engineering. - : Institute of Physics (IOP). - 0965-0393 .- 1361-651X. ; 31:7
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Journal article (peer-reviewed)abstract
- The internal structure of adhesive tapes determines the effective mechanicalproperties. This holds true especially for blended systems, here consisting ofacrylate and rubber phases. In this note, we propose a lattice-based modelto study numerically the formation of internal morphologies within a fourcomponent mixture (of discrete particles) where the solvent components evaporate. Mimicking numerically the interaction between rubber, acrylate, andtwo different types of solvents, relevant for the technology of adhesive tapes,we aim to obtain realistic distributions of rubber ball-shaped morphologies—they play a key role in the overall functionality of those special adhesives.Our model incorporates the evaporation of both solvents and allows for tuningthe strength of two essentially different solvent–solute interactions and of thetemperature of the system.
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| 3. |
- Lyons, Rainey, et al.
(author)
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A Continuum Model for Morphology Formation from Interacting Ternary Mixtures : Simulation Study of the Formation and Growth of Patterns
- 2023
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In: Physica D. - : Elsevier. - 0167-2789 .- 1872-8022. ; 453
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Journal article (peer-reviewed)abstract
- Our interest lies in exploring the ability of a coupled nonlocal system of two quasilinear parabolic partial differential equations to produce phase separation patterns. The obtained patterns are referred here as morphologies. Our target system is derived in the literature as the rigorous hydrodynamic limit of a suitably scaled interacting particle system of Blume–Capel–type driven by Kawasaki dynamics. The system describes in a rather implicit way the interaction within a ternary mixture that is the macroscopic counterpart of a mix of two populations of interacting solutes in the presence of a background solvent. Our discussion is based on the qualitative behavior of numerical simulations of finite volume approximations of smooth solutions to our system and their quantitative postprocessing in terms of two indicators (correlation and structure factor calculations). Our results show many similar qualitative features (e.g. general shape and approximate coarsening rates) which have been observed in previous works on the stochastic Blume–Capel dynamics with three interacting species. The properties of the obtained morphologies (shape, connectivity, and so on) can play a key role in, e.g., the design of the active layer for efficient organic solar cells.
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| 4. |
- Muntean, Stela Andrea, et al.
(author)
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Quantitative analysis of phase formation and growth in ternary mixtures upon evaporation of one component
- 2022
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In: Physical review. E. - : American Physical Society. - 2470-0045 .- 2470-0053. ; 106:2
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Journal article (peer-reviewed)abstract
- We perform a quantitative analysis of Monte Carlo simulation results of phase separation in ternary blends upon evaporation of one component. Specifically, we calculate the average domain size and plot it as a function of simulation time to compute the exponent of the obtained power law. We compare and discuss results obtained by two different methods, for three different models: two-dimensional (2D) binary-state model (Ising model), 2D ternary-state model with and without evaporation. For the ternary-state models, we study additionally the dependence of the domain growth on concentration, temperature and initial composition. We reproduce the expected 1/3 exponent for the Ising model, while for the ternary-state model without evaporation and for the one with evaporation we obtain lower values of the exponent. It turns out that phase separation patterns that can form in this type of systems are complex. The obtained quantitative results give valuable insights towards devising computable theoretical estimations of size effects on morphologies as they occur in the context of organic solar cells.
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| 5. |
- Setta, Mario, et al.
(author)
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A mesoscopic lattice model for morphology formation in ternary mixtures with evaporation
- 2023
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In: Communications in nonlinear science & numerical simulation. - : Elsevier. - 1007-5704 .- 1878-7274. ; 119
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Journal article (peer-reviewed)abstract
- We develop a mesoscopic lattice model to study the morphology formation in inter-acting ternary mixtures with the evaporation of one component. As concrete potentialapplication of our model, we wish to capture morphologies as they are typically arisingduring the fabrication of organic solar cells. In this context, we consider an evaporatingsolvent into which two other components are dissolved, as a model for a 2-componentcoating solution that is drying on a substrate. We propose a 3-spins dynamics to describethe evolution of the three interacting species. As main tool, we use a Monte CarloMetropolis-based algorithm, with the possibility of varying the system’s temperature,mixture composition, interaction strengths, and evaporation kinetics. The main novelty isthe structure of the mesoscopic model – a bi-dimensional lattice with periodic boundaryconditions, divided into square cells to encode a mesoscopic range interaction amongthe units. We investigate the effect of the model parameters on the structure of theresulting morphologies. Finally, we compare the results obtained with the mesoscopicmodel with corresponding ones based on an analogous lattice model with a short rangeinteraction among the units, i.e. when the mesoscopic length scale coincides with themicroscopic length scale of the lattice.
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| 6. |
- Ackelh, A.S., et al.
(author)
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Preface to "modeling with measures"
- 2015
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In: Mathematical Biosciences and Engineering. - : American Institute of Mathematical Sciences (AIMS). - 1547-1063 .- 1551-0018. ; 12:2
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Journal article (peer-reviewed)
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| 7. |
- Ackleh, Azmy S., et al.
(author)
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Mathematical modeling with measures
- 2019
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In: Nieuw Archief voor Wiskunde. - Leiden : Koninklijk Wiskundig Genootschap. - 0028-9825. ; 20:September, s. 218-220
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Journal article (peer-reviewed)
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| 8. |
- Ackleh, Azmy S., et al.
(author)
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Special issue: Mathematical modeling with measures
- 2020
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In: Mathematical Biosciences and Engineering. - : American Institute of Mathematical Sciences. - 1547-1063 .- 1551-0018. ; :3, s. 2451-2452
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Journal article (peer-reviewed)
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| 9. |
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| 10. |
- Aiki, Toyohiko, et al.
(author)
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A free boundary problem describing migration into rubbers : Quest of the large time behavior
- 2022
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In: Zeitschrift für angewandte Mathematik und Mechanik. - : John Wiley & Sons. - 0044-2267 .- 1521-4001. ; 102:7
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Journal article (peer-reviewed)abstract
- In many industrial applications, rubber-based materials are routinely used in conjunction with various penetrants or diluents in gaseous or liquid form. It is of interest to estimate theoretically the penetration depth as well as the amount of diffusants stored inside the material. In this framework, we prove the global solvability and explore the large time-behavior of solutions to a one-phase free boundary problem with nonlinear kinetic condition that is able to describe the migration of diffusants into rubber. The key idea in the proof of the large time behavior is to benefit from a contradiction argument, since it is difficult to obtain uniform estimates for the growth rate of the free boundary due to the use of a Robin boundary condition posed at the fixed boundary.
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