Morphological Phase Separation Research Articles

Slow coarsening in unstable liquid films under gravity on a disordered substrate.

We study the evolution of unstable liquid films via numerical solutions of the thin-film equation. The film is placed on a coated substrate with disorder. This is modeled by a random spatial variation of the relative value of the Hamaker constants for the substrate and coating. The free energy consists of (a) the van der Waals term for the substrate/coating interactions with the film and (b) a term due to gravity. This free energy admits a Maxwell double-tangent construction with two coexisting phases, i.e., "thin" and "thick" phases. In the absence of disorder, the film dewets by true morphological phase separation (MPS), i.e., the elimination of domain walls between the coexisting phases. The introduction of disorder may result in the trapping of these domain walls, with a drastic slowdown in growth kinetics. We present detailed numerical results in D=2 and D=3 to understand this slow coarsening, where D is the dimensionality of the liquid-film system.

Localization in liquid phase separation: Coarsening and stable structures.

Dynamics of pattern formation in self-organizing systems subjected to spontaneous suppression of diffusion through a recently proposed source-sink-boundary templating technique is presented based on three-dimensional numerical simulations. This template disorder is introduced to divide the system into three different subregions, i.e., a source (outer subregion) at higher potential and a sink (inner subregion) region at a lower potential with the help of a boundary which is at the highest potential. The boundary allows only one-way diffusion from source to sink so diffusion stops completely whenever the sink is filled to its capacity. This technique was shown to be able to spontaneously form stable and complex patterns in the source and the sink parts. While the technique is applicable to any self-organizing or phase-separating system whenever certain conditions are met, a physically realizable system of liquid films supported on chemically heterogeneous substrates which self-organizes through morphological phase separation is chosen to study the dynamics. Free-energy functional of this system shows an asymmetric double-well potential and the Maxwell's double tangent construction on this free energy gives rise to two distinct and finite equilibrium phases. Disorder is introduced in the form of chemical heterogeneity to divide the whole system into different subregions each consisting of two equilibrium phases, thus enabling more finite equilibrium points in the same system. The dynamics uncovers two different pathways for stable localized structures, viz., the defect and the direct pathway. Thinner films are likely to favor the defect pathway whereby the equilibrium pattern forms after coarsening, whereas thicker films will predominantly choose the direct pathway of pattern formation by phase separation. The final localized structure is same irrespective of the chosen pathway. The dynamics also shows that the patterns formed in the inner subregion part can be seen as a result of "localization" and those formed in the outer subregion are due to arrested diffusion under geometric or curvature constraints. Simple measures of localization in terms of free energy and its constituents are also presented. The identification of localization in the above systems opens up the possibility of a systematic approach to create controlled structures at nano- and submicrometer scales with desired shape and size. These structures constitute new building blocks of advanced and tailored materials.

Coarsening and pattern formation during true morphological phase separation in unstable thin films under gravity.

We address in detail the problem of true morphological phase separation (MPS) in three-dimensional or (2+1)-dimensional unstable thin liquid films (>100nm) under the influence of gravity. The free-energy functionals of these films are asymmetric and show two points of common tangency, which facilitates the formation of two equilibrium phases. Three distinct patterns formed by relative preponderance of these phases are clearly identified in "true MPS". Asymmetricity induces two different pathways of pattern formation, viz., defect and direct pathway for true MPS. The pattern formation and phase-ordering dynamics have been studied using statistical measures such as structure factor, correlation function, and growth laws. In the late stage of coarsening, the system reaches into a scaling regime for both pathways, and the characteristic domain size follows the Lifshitz-Slyozov growth law [L(t)∼t^{1/3}]. However, for the defect pathway, there is a crossover of domain growth behavior from L(t)∼t^{1/4}→t^{1/3} in the dynamical scaling regime. We also underline the analogies and differences behind the mechanisms of MPS and true MPS in thin liquid films and generic spinodal phase separation in binary mixtures.

Coarsening Dynamics of True Morphological Phase Separation in Unstable Thin Films.

Unstable thin films can spontaneously phase separate into two equilibrium flat-film morphologies of different thicknesses under the influence of gravity or favorable combinations of apolar and polar excess intermolecular forces. Two distinct pathways and associated dynamics of this morphological phase separation are presented based on numerical simulations of the 2-D thin film equation. The two pathways are (1) the "direct pathway" whereby the thicker phase forms directly and concurrently with the thinner phase and (2) the "defect pathway" whereby the thicker phase forms by the coarsening of defects of intermediate thickness and appears much later than the thinner phase. The defect pathway is favored by films whose initial thickness lies closer to the thickness of the thinner phase. Both pathways show an initial power law decay with exponent -1/4 in time followed by a plateau in the number density of domains/defects. Thereafter, the defect pathway shows another universal power law decay with exponent -1/3 and ends with a logarithmic decay, which is specific to the d = 2 case as there is no interfacial curvature in d = 2. The direct pathway skips the second power law decay and goes directly to the logarithmic decay.

Applications of functional fullerene materials in polymer solar cells

Bulk heterojunction (BHJ) polymer solar cells (PSCs) on the basis of polymer:fullerene blends have delivered numerous impressive results in the last decade and thus have drawn much attention of the scientific and industrial communities. However, BHJ PSCs often suffer from several intrinsic problems, such as the low open-circuit voltage (Voc), energetically-unfavorable and chemically-incompatible interfaces, and morphological phase separation of the polymer:fullerene blend driven by thermal treatment, hindering further advancement. In this review, we summarize the recent progress on applications of fullerene-based materials in the BHJ PSCs. Bis-adduct fullerenes possessing high-lying LUMO energy levels can substitute for mono-substituted fullerenes and higher Voc values can thus be achieved. Incorporation of an n-type fullerene interlayer between inorganic and organic active layers in either inverted or conventional PSCs can help in minimization of charge recombination losses at the interface and improvement of charge transfer from the active layer to the inorganic layer, thus resulting in superior PCEs. The optimal active-layer morphology can be maintained through several approaches, such as in situ polymerization of cross-linkable fullerenes, suppression of large-scale PC61BM aggregation by a polyethylene glycol-functionalized fullerene, supramolecular pentafluorophenyl-fullerene stabilization, and light-induced oligomerization of fullerenes. The morphological phase separation of the active-layer materials can thus be minimized. The research of employing fullerene materials will continue playing a critical role in BHJ PSCs. With further investigation and advancement in this field, it is expected that the ultimate goal of commercialization can be realized.

Developments of highly proton-conductive sulfonated polymers for proton exchange membrane fuel cells

This review paper covers recent publications on the developments of highly proton-conductive sulfonated polymers for proton exchange membrane (PEM) fuel cells. The PEMs presenting proton conductivities exceeding that of Nafion membranes are especially focused on. The proton conductivities of PEMs have been correlated to their ion exchange values and morphological phase-separation. Formation of ionic channels is an effective approach to develop highly proton-conductive PEMs. The approaches could be grouped into (1) developments of microphase-separation with block copolymers, (2) side-chain and grafted sulfonated polymers, and (3) locally and densely sulfonated polymers. Formation of nanocomposites of PEMs with nanofillers has also shown great ability to increase the proton conductivities of the existed PEMs. Besides proton conductivities, the formation of nanocomposites also improves some PEM properties including mechanical strength, dimensional stability, and oxidative stability. The discussed publications have provided promising PEMs for the development of high performance fuel cells.

Amplification of Fluctuations in Unstable Systems with Disorder

We study the early stage kinetics of thermodynamically unstable systems with quenched disorder. We show analytically that the growth of initial fluctuations is amplified by the presence of disorder. This is confirmed by numerical simulations of morphological phase separation in thin liquid films and spinodal decomposition in binary mixtures. We also discuss the experimental implications of our results.

Morphological phase separation in unstable thin films: pattern formation and growth

We present results from a comprehensive numerical study of morphological phase separation (MPS) in unstable thin liquid films on a 2-dimensional substrate. We study the quantitative properties of the evolution morphology via several experimentally relevant markers, e.g., correlation function, structure factor, domain-size and defect-size probability distributions, and growth laws. Our results suggest that the late-stage morphologies exhibit dynamical scaling, and their evolution is self-similar in time. We emphasize the analogies and differences between MPS in films and segregation kinetics in unstable binary mixtures.

Alternative hybrid electrolytes based on a series of bis(trialkoxysilyl)alkanes and 3-(trihydroxysilyl)-1-propane sulfonic acid applied in gas diffusion electrodes of proton exchange membrane fuel cells

This study demonstrates a method for improving the electrolyte distribution in catalyst layers and enhancing the utilization of catalyst existing in primary pores. Bis(trialkoxysilyl)alkanes (BTAS-alkanes) and 3-(trihydroxysilyl)-1-propane sulfonic acid (THS)Pro-SO 3H) precursors have been used to prepare a series of hybrid electrolytes with various organic segment lengths of BTAS-alkanes and ratios of organic moiety and sulfonic acid groups. Investigations of BTAS-alkanes series includes bis(triethoxysilyl)octane (BTES-Oct), bis(trimethoxysilyl)hexane (BTMS-Hex), and bis(triethoxysilyl)ethane (BTES-Eth). Small angle X-ray spectroscopy (SAXS) identifies morphological phase separation in BTES-Oct and BTMS-Hex hybrid electrolytes. The results of mercury porosimetry and BET porosimetry show that the hybrid electrolytes have better capability than Nafion ionomer to penetrate into primary pores of the catalyst layers. Electrochemical measurements including electrode polarization, electrochemical active surface (EAS) and electrochemical impedance spectroscopy (EIS) are discussed. The BTES-Oct or BTMS-Hex hybrid electrolytes with higher ratio of organic moiety and sulfonic acid group have achieved better electrode performance. Oxygen benefit current (OBC) results indicate that higher ratios of BTES-Oct/(THS)Pro-SO 3H provides higher hydrophobicity with better gas transport properties. However, the hybrid electrodes exhibit lower cathode performance than Nafion ®-based electrodes due to excessive electrolyte incorporated in the catalyst layer.

Growth of nanocomposite in eutectic Cu–Ag films

Eutectic composition Cu–Ag alloy thin films were prepared by co-deposition at room temperature onto oxidized Si substrates by thermal evaporation. Morphological development, structure and phase state of the films were investigated by transmission electron microscopy. The films possess fibre morphology 10–30 nm in diameter and strong <111> texture is present. The fibres are nanocrystalline composed of 2–3 nm size zones of Cu and Ag rich solid solution phases and a model for morphological development and phase separation is described. In the early stages of growth phase separation occurs by nucleation in melted islands and a eutectic of randomly oriented crystallites forms. In later stages of growth the phase separation takes place by spinodal decomposition. It results in a strain stabilized unique morphology corresponding to an intermediate stage of phase separation.

A nonlinear stability analysis of pattern formation in thin liquid films

The development of spontaneous stationary equilibrium patterns in thin liquid films is investigated by means of a hexagonal-planform weakly nonlinear stability analysis applied to the appropriate governing evolution equation for this phenomenon. In the long-wavelength limit the mathematical system modeling the liquid film can be reduced to such a single nonlinear partial differential time-evolution equation describing the layer thickness on an unbounded two-dimensional spatial domain and including the effects of gravity, intermolecular forces, and temperature-dependent surface tension. The main result of this analysis is that supercritical equilibrium patterns can occur for an interval of mean layer thickness with subcritical rupture occurring outside that interval. These patterns consist of surface ridges and hexagonal network-like cells or close-packed configurations of nanodroplets separated by relatively flat ultra thin films. In particular those morphological phase separation patterns are generated by the coupling between the long-range attractive and short-range repulsive intermolecular forces with cells being stable for the thicker layers; nanodroplets, for the thinner ones; and ridges, for layers of intermediate thickness. These theoretical predictions are in accord with both relevant experimental evidence involving thin liquid polymer, crystal, and metal films coating a solid substrate and numerical simulations of similar model equations as well as being consistent with dewetting-type rupture occurring for such situations by hole formation in relatively thick layers but by drop formation in thinner ones.

Morphological evolutionduring phase separation and coarsening with strong inhomogeneouselasticity

We studied the morphological evolution during spinodal phaseseparation and subsequent coarsening in systems with a strongdependence of elastic constants on the composition. An efficientnumerical method is developed for solving the two-dimensionalinhomogeneous elastic equilibrium equations by using the conjugategradient method. A simple model binary system with asymmetric miscibility gap is considered. It is shown that theearly stages of spinodal phase separation in a solid solution witha 50-50% composition always result in an interconnectedmorphology, regardless of the degree of elastic inhomogeneity. Forsystems with strong elastic inhomogeneity, particle splitting andcoalescence take place concurrently during coarsening. In the latestages, the morphology has the characteristics that the hard phaseforms precipitates surrounded by the soft phase which formsthe matrix, similar to that predicted previously by others usingfirst-order approximations. An analysis of the coarsening kineticsshows that although the growth exponent decreases with theincrease in the degree of elastic inhomogeneity, there is nofreezing of the coarsening kinetics for all the cases that westudied, in contrast to that predicted previously by others. Theeffect of an externally applied strain on the two-phase morphologyin the elastic regime is also discussed.

Morphological Phase Separation in Thin Liquid Films: II. Equilibrium Contact Angles of Nanodrops Coexisting with Thin Films

When the apolar (LW) and polar (P) components of the spreading pressure ( S LW, S P) are of opposite signs, thin non-equilibrium films can undergo a morphological phase separation (MPS) manifested as a periodic structure of nanodrops in stable coexistence with thinner flat films. The morphology, film pressure, and equilibrium contact angles of the resulting stable microscopic drops are investigated based on the nonlinear dynamics of the growth and saturation of the film-instability. The equilibrium contact angles of microscopic drops are substantially smaller than those of their macroscopic counterparts, which are only attained for relatively large drops. Simulations show that the equilibrium film pressure of the microdrop is largely independent of the drop size, and may be assumed to be the same as for the corresponding large drop in calculations of the contact angle. The reasons microdrop angles are smaller are: that (a) a significant portion of the drop (and not just the contact zone) experiences excess intermolecular interactions, and (b) due to the large curvature of the drop, the capillary pressure is not always negligible compared to the disjoining/conjoining pressure. The contact angles of type II systems ( S LW < 0, S P > 0) are very small compared to those of type IV systems ( S LW > 0, S P < 0) for the same value of the total spreading coefficient, S, because of significant film pressure, II → S, for type II systems. Finally, thick films of type IV systems remain stable (wetting), but thin films evolve into microdrops of finite contact angles, regardless of the sign of the spreading pressure.

Nonlinear Stability, Rupture, and Morphological Phase Separation of Thin Fluid Films on Apolar and Polar Substrates

The total free energy (per unit area) of a thin film on a substrate depends on the film thickness, and the apolar (Lifshitz-van der Waals) and polar (acid-base) spreading coefficients for the system. The free interface of the film becomes unstable and deforms when the second derivative of the free energy (i.e., force per unit volume) is negative. The film stability, kinetics of surface deformation, and the resulting morphology are investigated based on numerical solutions of a nonlinear, dynamic equation for the film thickness. A true rupture of the film always occurs when both the apolar ( S LW) and polar ( S P) components of the spreading pressure, S are negative; i.e., the equilibrium contact angle of the corresponding macroscopic drop is finite. However, the true time of rupture evaluated from the nonlinear formalism may be several orders of magnitude larger or smaller than the results of the linear stability analysis, depending on the mean film thickness, relative magnitudes of the apolar and polar forces, and amplitude and wavelength of initial perturbations. When one of the components of the total force is repulsive (either S LW or S P is positive), the film breakup occurs only if some localized, narrow regions of the film develop sufficient pent-up kinetic energy to penetrate the (positive) force barrier. Failing this, the thin film undergoes a "morphological phase separation," where nanodrops of the fluid attain equilibrium with relatively flat thin films. Some of the interesting observations that emerge are: (a) Films thicker than a certain critical thickness show true breakup, whereas thinner films may merely undergo a morphological phase separation, but a true dewetting of the substrate does not occur; (b) a thin film may be unstable to the extent of rupturing, even when a macroscopic drop of the same system is predicted to be completely wetting from the Young equation; and (c) a thin film may be stable despite a finite contact angle for the corresponding macrodrop. The underlying physics of observations is constructed by selective use of numerical simulations. Comparisons with predictions of the linear theory reveal that the latter fails, both qualitatively and quantitatively, in accounting for the stability and dynamics of thin films.