Modeling solvent evaporation during thin film formation in phase separating polymer mixtures

Characterizing Hygroscopic Films of Polyzwitterions in Electric Fields Using Neutron and X-ray Reflectometries: Electrostriction or Mass Loss?

We study responses of thermally annealed ultrathin films deposited on silicon substrates and containing polyzwitterions to applied electric fields by using specular neutron reflectometry (NR). In particular, we applied 7 kV under vacuum at 150 °C on the films containing poly(1-(3-sulfonatopropyl)-2-vinylpyridinium) (P2VPPS) and its blends with either a deuterated ionic liquid (EMIMBF4-d11), potassium bromide (KBr), or deuterated sodium polystyrenesulfonate (NaPSS-d7). The voltage was applied over an air gap, and the in situ neutron reflectivity measurements allowed us to measure changes in the films. In all the cases, we measured decreases in thicknesses of the films, which varied up to ∼8% depending on the added salt. Posteriori X-ray reflectivity (XRR) measurements on the same films at room temperature reveal that these films were highly hygroscopic, which led to the presence of water in these films. Analysis of the NR and the XRR revealed that the decrease in the thickness of the films in the neutron reflectivity experiments on heating resulted from the loss of water and the ionic liquid but not from electrostrictive effects. The in situ NR and posteriori XRR experiments revealed not only the hygroscopic nature of these films but also depth-resolved structural rearrangements due to the applied electric fields in the films containing electrolytes and polyelectrolytes. This work shows that a combination of NR and XRR can be used to distinguish between mass loss and electrostriction in films containing charged polymers such as polyzwitterions.

Morphology of poly-3-hexyl-thiophene blends with styrene-isoprene-styrene block-copolymer elastomers from X-ray and neutron scattering

The nano- and micron scale morphology of poly(3-hexylthiophene) (P3HT) and polystyrene-block-polyisoprene-block-polystyrene (PS-PI-PS) elastomeric blends is investigated through the use of ultra-small and small angle X-ray and neutron scattering (USAXS, SAXS, SANS). It is demonstrated that loading P3HT into elastomer matrices is possible with little distortion of the elastomeric structure up to a loading of ∼5 wt%. Increased loadings of conjugated polymer is found to significantly distort the matrix structure. Changes in processing conditions are also found to affect the blend morphology with especially strong dependence on processing temperature. Processing temperatures above the glass transition temperature (Tg) of polystyrene and the melting temperature (Tm) of the conjugated polymer additive (P3HT) creates significantly more organized mesophase domains. P3HT blends with PS-PI-PS can also be flow-aligned through processing, which results in an anisotropic structure that could be useful for the generation of anisotropic properties (e.g. conductivity). Moreover, the extent of flow alignment is significantly affected by the P3HT loading in the PS-PI-PS matrix. The work adds insight to the morphological understanding of a complex P3HT and PS-PI-PS polymer blend as conjugated polymer is added to the system. We also provide studies isolating the effect of processing changes aiding in the understanding of the structural changes in this elastomeric conjugated polymer blend.

Crystallization of Poly(l-lactic acid) on Water Surfaces via Controlled Solvent Evaporation and Langmuir-Blodgett Films

Solvent evaporation is one of the most fundamental processes in soft matter. Structures formed via solvent evaporation are often complex yet tunable via the competition between solute diffusion and solvent evaporation time scales. This work concerns the polymer evaporative crystallization on the water surface (ECWS). The dynamic and two-dimensional (2D) nature of the water surface offers a unique way to control the crystallization pathway of polymeric materials. Using poly(l-lactic acid) (PLLA) as the model polymer, we demonstrate that both one-dimensional (1D) crystalline filaments and two-dimensional (2D) lamellae are formed via ECWS, in stark contrast to the 2D Langmuir-Blodgett monolayer systems as well as polymer solution crystallization. Results show that this filament-lamella biphasic structure is tunable via chemical structures such as molecular weight and processing conditions such as temperature and evaporation rate.

Controlling the structure of spin-coated multilayer ethylcellulose/hydroxypropylcellulose films for drug release

Porous phase-separated ethylcellulose/hydroxypropylcellulose (EC/HPC) films are used to control drug transport out of pharmaceutical pellets. Water-soluble HPC leaches out and forms a porous structure that controls the drug transport. Industrially, the pellets are coated using a fluidized bed spraying device, and a layered film exhibiting varying porosity and structure after leaching is obtained. A detailed understanding of the formation of the multilayered, phase-separated structure during production is lacking. Here, we have investigated multilayered EC/HPC films produced by sequential spin-coating, which was used to mimic the industrial process. The effects of EC/HPC ratio and spin speed on the multilayer film formation and structure were investigated using advanced microscopy techniques and image analysis. Cahn-Hilliard simulations were performed to analyze the mixing behavior. A gradient with larger structures close to the substrate surface and smaller structures close to the air surface was formed due to coarsening of the layers already coated during successive deposition cycles. The porosity of the multilayer film was found to vary with both EC/HPC ratio and spin speed. Simulation of the mixing behavior and in situ characterization of the structure evolution showed that the origin of the discontinuities and multilayer structure can be explained by the non-mixing of the layers.

Comparative study of convection characteristics for a system with deformable interface based on the Navier-Stokes and Oberbeck-Boussinesq equations

The right choice of the appropriate mathematical model is crucial for evaluating the physical plausibility of modelling results. The issue of the correct application of the classical Boussinesq approximation for studying the heat and mass transfer in fluidic systems with a deformable boundary is a subject of scientific discussions despite the good agreement of numerous theoretical and numerical results obtained within the convection models based on the Oberbeck-Boussinesq equations with the data of physical experiments and observations. A comparative analysis of the results of numerical simulations in the framework of two-sided models based on the Navier-Stokes equations, and their Boussinesq approximation, is performed in the context of a convection problem in a locally heated two-phase system with a deformable interface. It is demonstrated that the application of the standard Boussinesq approximation allows one to give a consistent description of the effect of interface deformations on combined buoyant-thermocapillary driven fluid motions. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.

Quantitative analysis of phase formation and growth in ternary mixtures upon evaporation of one component

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.

Structure formation and coarsening kinetics of phase-separated spin-coated ethylcellulose/hydroxypropylcellulose films

Porous phase-separated ethylcellulose/hydroxypropylcellulose (EC/HPC) films are used to control drug transport from pharmaceutical pellets. The drug transport rate is determined by the structure of the porous films that are formed as water-soluble HPC leaches out. However, a detailed understanding of the evolution of the phase-separated structure in the films is lacking. In this work, we have investigated EC/HPC films produced by spin-coating, mimicking the industrial fluidized bed spraying. The aim was to investigate film structure evolution and coarsening kinetics during solvent evaporation. The structure evolution was characterized using confocal laser scanning microscopy and image analysis. The effect of the EC:HPC ratio (15 to 85 wt% HPC) on the structure evolution was determined. Bicontinuous structures were found for 30 to 40 wt% HPC. The growth of the characteristic length scale followed a power law, L(t) ∼ t⁽ⁿ⁾, with n ∼ 1 for bicontinuous structures, and n ∼ 0.45-0.75 for discontinuous structures. The characteristic length scale after kinetic trapping ranged between 3.0 and 6.0 μm for bicontinuous and between 0.6 and 1.6 μm for discontinuous structures. Two main coarsening mechanisms could be identified: interfacial tension-driven hydrodynamic growth for bicontinuous structures and diffusion-driven coalescence for discontinuous structures. The 2D in-plane interface curvature analysis showed that the mean curvature decreased as a function of time for bicontinuous structures, confirming that interfacial tension is driving the growth. The findings of this work provide a good understanding of the mechanisms responsible for morphology development and open for further tailoring of thin EC/HPC film structures for controlled drug release.

Effects of Local Order Parameter Dependent Transport Coefficient in Diblock Copolymers Under Applied Electric Fields

We present an approach for constructing thermodynamically consistent time-dependent models relevant to thin films of diblock copolymers in applied electric fields. The approach is based on the principles of linear irreversible thermodynamics and in this work, it is applied to study the effects of electric  fields on thin  films of incompressible diblock copolymers. Enforcement of local incompressibility constraint at all times leads to a local order parameter dependent transport coefficient in the model for the diblock copolymers. The dependence of transport coefficient on the local order parameter is used to relate it with diffusion constant of Rouse chains and leads to sensitivity of the model to initial conditions. Also, transient behavior is found to be a affected when compared with an ad hoc model assuming a constant transport coefficient. Numerical results such as electric  field induced alignment of lamellae domains due to the  field are found to be in qualitative agreements with experiments.This approach opens up a systematic way of developing kinetic models for simulating effects of electrolytes added to thin  films containing diblock copolymers in the presence of applied electric  fields.

NMR Profiling of Reaction and Transport in Thin Layers: A Review

Reaction and transport processes in thin layers of between 10 and 1000 µm are important factors in determining their performance, stability and degradation. In this review, we discuss the potential of high-gradient Nuclear Magnetic Resonance (NMR) as a tool to study both reactions and transport in these layers spatially and temporally resolved. As the NMR resolution depends on gradient strength, the high spatial resolution required in submillimeter layers can only be achieved with specially designed high-gradient setups. Three different high-gradient setups exist: STRAFI (STRay FIeld), GARField (Gradient-At-Right-angles-to-Field) and MOUSE (MObile Universal Surface Explorer). The aim of this review is to provide a detailed overview of the three techniques and their ability to visualize reactions and transport processes using physical observable properties such as hydrogen density, diffusion, T1- and T2-relaxation. Finally, different examples from literature will be presented to illustrate the wide variety of applications that can be studied and the corresponding value of the techniques.

Cross-sectional structure evolution of phase-separated spin-coated ethylcellulose/hydroxypropylcellulose films during solvent quenching

Porous phase-separated ethylcellulose/hydroxypropylcellulose (EC/HPC) films are used to control drug transport out of pharmaceutical pellets. The films are applied on the pellets using fluidized bed spraying. The drug transport rate is determined by the structure of the porous films that are formed as the water-soluble HPC leaches out. However, a detailed understanding of the evolution of the phase-separated structure during production is lacking. Here, we have investigated EC/HPC films produced by spin-coating, which mimics the industrial manufacturing process. This work aimed to understand the structure formation and film shrinkage during solvent evaporation. The cross-sectional structure evolution was characterized using confocal laser scanning microscopy (CLSM), profilometry and image analysis. The effect of the EC/HPC ratio on the cross-sectional structure evolution was investigated. During shrinkage of the film, the phase-separated structure undergoes a transition from 3D to nearly 2D structure evolution along the surface. This transition appears when the typical length scale of the phase-separated structure is on the order of the thickness of the film. This was particularly pronounced for the bicontinuous systems. The shrinkage rate was found to be independent of the EC/HPC ratio, while the initial and final film thickness increased with increasing HPC fraction. A new method to estimate part of the binodal curve in the ternary phase diagram for EC/HPC in ethanol has been developed. The findings of this work provide a good understanding of the mechanisms responsible for the morphology development and allow tailoring of thin EC/HPC films structure for controlled drug release.

The EC/HPC/EtOH phase diagram could be estimated from the CLSM monitoring of the cross-sectional in situ phase separation. The findings of this work provide a good understanding of the structure evolution.

Investigation of the Effect of 3D Meniscus Geometry on Fluid Dynamics and Crystallization via In Situ Optical Microscopy-Assisted Mathematical Modeling

Solution-based thin-film solidification is a complex process involving various transport phenomena that are intricately dependent on multiple experimental parameters. The difficulty of analyzing this process experimentally or conducting exact numerical simulation make it challenging to understand, predict, and control the solidification process. In this work, a simple and effective technique to analyze the thin-film solidification process during solution shearing, based on 3D geometrical model of the meniscus, is proposed. The 3D meniscus geometry, which changes depending on the experimental parameters, is attained using high-speed side-view and top-view in situ microscopy. Thereafter, mass and momentum transport mathematical models are applied to obtain numerical solutions of transport phenomena within the meniscus. Utilizing these results, the underlying mechanism of dendritic growth of small molecule organic semiconductor is elucidated, which has previously been unknown. The 3D meniscus modeling is particularly important for this analysis, as dendrite formation is strongly dependent on the meniscus geometry near the contact line and mass transport variation perpendicular to the coating direction. This technique enables the study of complex relationship between experimental parameters and solidification process, which is widely applicable to various materials and coating systems; whereby, better understanding of thin-film growth and device performance optimization is possible.

Phase-Field Simulation of Liquid-Vapor Equilibrium and Evaporation of Fluid Mixtures

In solution processing of thin films, the material layer is deposited from a solution composed of several solutes and solvents. The final morphology and hence the properties of the film often depend on the time needed for the evaporation of the solvents. This is typically the case for organic photoactive or electronic layers. Therefore, it is important to be able to predict the evaporation kinetics of such mixtures. We propose here a new phase-field model for the simulation of evaporating fluid mixtures and simulate their evaporation kinetics. Similar to the Hertz-Knudsen theory, the local liquid-vapor (LV) equilibrium is assumed to be reached at the film surface and evaporation is driven by diffusion away from this gas layer. In the situation where the evaporation is purely driven by the LV equilibrium, the simulations match the behavior expected theoretically from the free energy: for evaporation of pure solvents, the evaporation rate is constant and proportional to the vapor pressure. For mixtures, the evaporation rate is in general strongly time-dependent because of the changing composition of the film. Nevertheless, for highly nonideal mixtures, such as poorly compatible fluids or polymer solutions, the evaporation rate becomes almost constant in the limit of low Biot numbers. The results of the simulation have been successfully compared to experiments on a polystyrene-toluene mixture. The model allows to take into account deformations of the liquid-vapor interface and, therefore, to simulate film roughness or dewetting.

Nonequilibrium Processes in Polymer Membrane Formation: Theory and Experiment

Porous polymer and copolymer membranes are useful for ultrafiltration of functional macromolecules, colloids, and water purification. In particular, block copolymer membranes offer a bottom-up approach to form isoporous membranes. To optimize permeability, selectivity, longevity, and cost, and to rationally design fabrication processes, direct insights into the spatiotemporal structure evolution are necessary. Because of a multitude of nonequilibrium processes in polymer membrane formation, theoretical predictions via continuum models and particle simulations remain a challenge. We compiled experimental observations and theoretical approaches for homo- and block copolymer membranes prepared by nonsolvent-induced phase separation and highlight the interplay of multiple nonequilibrium processes─evaporation, solvent-nonsolvent exchange, diffusion, hydrodynamic flow, viscoelasticity, macro- and microphase separation, and dynamic arrest─that dictates the complex structure of the membrane on different scales.

Understanding interfacial segregation in polymer blend films with random and mixed side chain bottlebrush copolymer additives

Bottlebrush polymers are complex macromolecules with tunable physical properties dependent on the chemistry and architecture of both the side chains and the backbone. Prior work has demonstrated that bottlebrush polymer additives can be used to control the interfacial properties of blends with linear polymers but has not specifically addressed the effects of bottlebrush side chain microstructures. Here, using a combination of experiments and self-consistent field theory (SCFT) simulations, we investigated the effects of side chain microstructures by comparing the segregation of bottlebrush additives having random copolymer side chains with bottlebrush additives having a mixture of two different homopolymer side chain chemistries. Specifically, we synthesized bottlebrush polymers with either poly(styrene-ran-methyl methacrylate) side chains or with a mixture of polystyrene (PS) and poly(methyl methacrylate) (PMMA) side chains. The bottlebrush additives were matched in terms of PS and PMMA compositions, and they were blended with linear PS or PMMA chains that ranged in length from shorter to longer than the bottlebrush side chains. Experiments revealed similar behaviors of the two types of bottlebrushes, with a slight preference for mixed side-chain bottlebrushes at the film surface. SCFT simulations were qualitatively consistent with experimental observations, predicting only slight differences in the segregation of bottlebrush additives driven by side chain microstructures. Specifically, these slight differences were driven by the chemistries of the bottlebrush polymer joints and side chain end-groups, which were entropically repelled and attracted to interfaces, respectively. Using SCFT, we also demonstrated that the interfacial behaviors were dominated by entropic effects with high molecular weight linear polymers, leading to enrichment of bottlebrush near interfaces. Surprisingly, the SCFT simulations showed that the chemistry of the joints connecting the bottlebrush backbones and side chains played a more significant role compared with the side chain end groups in affecting differences in surface excess of bottlebrushes with random and mixed side chains. This work provides new insights into the effects of side chain microstructure on segregation of bottlebrush polymer additives.

Evaporation-Induced Liquid Expansion and Bubble Formation in Binary Mixtures

We observe an anomalous liquid expansion after quenching a binary mixture at coexistence to low pressures in the vapor phase by numerical calculations. This evaporation-induced expansion can be attributed to the pressure imbalance near the liquid-vapor interface, which originates from the interplay between the complex thermodynamics of binary mixtures both in the vapor and liquid phases, as well as their dynamical asymmetries. In addition, careful modulation of the pressure quench in the vapor phase can result in spinodal bubble formation inside liquid phase. The results indicate that the thermodynamics-kinetics interplay could foster our fundamental understanding of the evaporation process and promote its practical applications.

A phase-field model for the evaporation of thin film mixtures

The performance of solution-processed solar cells strongly depends on the geometrical structure and roughness of the photovoltaic layers formed during film drying. During the drying process, the interplay of crystallization and liquid-liquid demixing leads to structure formation on the nano- and microscale and to the final rough film. In order to better understand how the film structure can be improved by process engineering, we aim at theoretically investigating these systems by means of phase-field simulations. We introduce an evaporation model based on the Cahn-Hilliard equation for the evolution of the fluid concentrations coupled to the Allen-Cahn equation for the liquid-vapour phase transformation. We demonstrate its ability to match the experimentally measured drying kinetics and study the impact of the parameters of our model. Furthermore, the evaporation of solvent blends and solvent-vapour annealing are investigated. The dry film roughness emerges naturally from our set of equations, as illustrated through preliminary simulations of spinodal decomposition and film drying on structured substrates.

Anomalous Ostwald Ripening Enables 2D Polymer Crystals via Fast Evaporation

We demonstrate by molecular simulations that the Ostwald ripening of crystalline polymer nuclei within the fast-evaporation-induced 2D skin layer is retarded at suitable temperatures and evaporation rates. Such an anomalous ripening can be attributed to the interplay between the thermodynamically driven diffusion of noncrystalline fragments toward the growing nuclei and the diffusive current away from the free surface caused by the densification in the nonequilibrium skin layer. The growth orientation of the nuclei inside the skin plane can be adjusted during this anomalous ripening process, which is beneficial for fabricating 2D polymer crystals.