Stratification in binary colloidal polymer films: experiment and simulations

Active Stratification of Colloidal Mixtures for Asymmetric Multilayers

Stratified films offer high performance and multifunctionality, yet achieving fully stratified films remains a challenge. The layer-by-layer method, involving the sequential deposition of each layer, has been commonly utilized for stratified film fabrication. However, this approach is time-consuming, labor-intensive, and prone to leaving defects within the film. Alternatively, the self-stratification process exploiting a drying binary colloidal mixture is intensively developed recently, but it relies on strict operating conditions, typically yielding a heterogeneous interlayer. In this study, an active interfacial stratification process for creating completely stratified nanoparticle (NP) films is introduced. The technique leverages NPs with varying interfacial activity at the air-water interface. With the help of depletion pressure, the lateral compression of NP mixtures at the interface induces individual desorption of less interfacial active NPs into the subphase, while more interfacial active NPs remain at the interface. This simple compression leads to nearly perfect stratified NP films with controllability, universality, and scalability. Combined with a solvent annealing process, the active stratification process enables the fabrication of stratified films comprising a polymeric layer atop a NP layer. This work provides insightful implications for designing drug encapsulation and controlled release, as well as manufacturing transparent and flexible electrodes.

Structure Formation in Supraparticles Composed of Spherical and Elongated Particles

We studied the evaporation-induced formation of supraparticles from dispersions of elongated colloidal particles using experiments and computer simulations. Aqueous droplets containing a dispersion of ellipsoidal and spherical polystyrene particles were dried on superamphiphobic surfaces at different humidity values that led to varying evaporation rates. Supraparticles made from only ellipsoidal particles showed short-range lateral ordering at the supraparticle surface and random orientations in the interior regardless of the evaporation rate. Particle-based simulations corroborated the experimental observations in the evaporation-limited regime and showed an increase in the local nematic ordering as the diffusion-limited regime was reached. A thin shell of ellipsoids was observed at the surface when supraparticles were made from binary mixtures of ellipsoids and spheres. Image analysis revealed that the supraparticle porosity increased with an increasing aspect ratio of the ellipsoids.

Inducing stratification of colloidal mixtures with a mixed binary solvent

Molecular dynamics simulations are used to demonstrate that a binary solvent can be used to stratify colloidal mixtures when the suspension is rapidly dried. The solvent consists of two components, one more volatile than the other. When evaporated at high rates, the more volatile component becomes depleted near the evaporation front and develops a negative concentration gradient from the bulk of the mixture to the liquid-vapor interface while the less volatile solvent is enriched in the same region and exhibit a positive concentration gradient. Such gradients can be used to drive a binary mixture of colloidal particles to stratify if one is preferentially attracted to the more volatile solvent and the other to the less volatile solvent. During solvent evaporation, the fraction of colloidal particles preferentially attracted to the less volatile solvent is enhanced at the evaporation front, whereas the colloidal particles having stronger attractions with the more volatile solvent are driven away from the interfacial region. As a result, the colloidal particles show a stratified distribution after drying, even if the two colloids have the same size.

Quantitative imaging methods for heterogeneous multi-component films

The drying of multi-component dispersions is a common phenomenon in a variety of everyday applications, including coatings, inks, processed foods, and cosmetics. As the solvent evaporates, the different components may spontaneously segregate laterally and/or in depth, which can significantly impact the macroscopic properties of the dried film. To obtain a quantitative understanding of these processes, high-resolution analysis of segregation patterns is crucial. Yet, current state-of-the-art methods are limited to transparent, non-deformable labeled colloids, limiting their applicability. In this study, we employ three techniques that do not require customized samples, as their imaging contrast relies on intrinsic variations in the chemical nature of the constituent species: confocal Raman microscopy, cross-sectional Raman microscopy, and a combination of scanning electron microscopy and energy dispersive X-ray analysis (SEM-EDX). For broad accessibility, we offer a thorough guide to our experimental steps and data analysis methods. We benchmark the capabilities on a film that dries homogeneously at room temperature but exhibits distinct segregation features at elevated temperature, notably self-stratification, i.e., autonomous layer formation, due to a colloidal size mismatch. Confocal Raman microscopy offers a direct means to visualize structures in three dimensions without pre-treatment, its accuracy diminishes deeper within the film, making cross-sectional Raman imaging and SEM-EDX better options. The latter is the most elaborate method, yet we show that it can reveal the most subtle and small-scale microseparation of the two components in the lateral direction. This comparative study assists researchers in choosing and applying the most suitable technique to quantify structure formation in dried multi-component films.

Diffusiophoresis-Driven Stratification in Pressure-Sensitive Adhesive Films from Bimodal Waterborne Colloids

The uses of pressure-sensitive adhesives (PSAs) are wide ranging, with applications including labels, tapes, and graphics. To achieve good adhesion, a PSA must exhibit a balance of viscous and elastic properties. Previous research has found that a thin, elastic surface layer on top of a softer, dissipative layer resulted in greater tack adhesion compared with the single layers. Superior properties were achieved through a bilayer obtained via successive depositions, which consume energy and time. To achieve a multilayered structure via a single deposition process, we have stratified mixtures of waterborne colloidal polymer particles with two different sizes: large poly(acrylate) adhesive particles (ca. 660 nm in diameter) and small poly(butyl acrylate) (pBA) particles (ca. 100 nm). We used two types of pBA within the particles: either viscoelastic pBA without an added cross-linker or elastic pBA with a fully cross-linked network. Stratified surface layers of deuterium-labeled pBA particles with thicknesses of at least 1 μm were found via elastic recoil detection and qualitatively verified via the analysis of surface topography. The extent of stratification increased with the evaporation rate; films that were dried slowest exhibited no stratification. This result is consistent with a model of diffusiophoresis. When the elastic, cross-linked pBA particles were stratified at the surface, the tack adhesion properties made a transition from brittle failure to tacky. For pBA without an added cross-linker, all adhesives showed fibrillation during debonding, but the extent of fibrillation increased when the films were stratified. These results demonstrate that the PSA structure can be controlled through the processing conditions to achieve enhanced properties. This research will aid the future development of layered or graded single-deposition PSAs with designed adhesive properties.

Dynamic density functional theory for drying colloidal suspensions: Comparison of hard-sphere free-energy functionals

Dynamic density functional theory (DDFT) is a promising approach for predicting the structural evolution of a drying suspension containing one or more types of colloidal particles. The assumed free-energy functional is a key component of DDFT that dictates the thermodynamics of the model and, in turn, the density flux due to a concentration gradient. In this work, we compare several commonly used free-energy functionals for drying hard-sphere suspensions, including local-density approximations based on the ideal-gas, virial, and Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equations of state as well as a weighted-density approximation based on fundamental measure theory (FMT). To determine the accuracy of each functional, we model one- and two-component hard-sphere suspensions in a drying film with varied initial heights and compositions, and we compare the DDFT-predicted volume fraction profiles to particle-based Brownian dynamics (BD) simulations. FMT accurately predicts the structure of the one-component suspensions even at high concentrations and when significant density gradients develop, but the virial and BMCSL equations of state provide reasonable approximations for smaller concentrations at a reduced computational cost. In the two-component suspensions, FMT and BMCSL are similar to each other but modestly overpredict the extent of stratification by size compared to BD simulations. This work provides helpful guidance for selecting thermodynamic models for soft materials in nonequilibrium processes, such as solvent drying, solvent freezing, and sedimentation.

Modeling Solution Drying by Moving a Liquid-Vapor Interface: Method and Applications

A method of simulating the drying process of a soft matter solution with an implicit solvent model by moving the liquid-vapor interface is applied to various solution films and droplets. For a solution of a polymer and nanoparticles, we observe “polymer-on-top” stratification, similar to that found previously with an explicit solvent model. Furthermore, “polymer-on-top” is found even when the nanoparticle size is smaller than the radius of gyration of the polymer chains. For a suspension droplet of a bidisperse mixture of nanoparticles, we show that core-shell clusters of nanoparticles can be obtained via the “small-on-outside” stratification mechanism at fast evaporation rates. “Large-on-outside” stratification and uniform particle distribution are also observed when the evaporation rate is reduced. Polymeric particles with various morphologies, including Janus spheres, core-shell particles, and patchy particles, are produced from drying droplets of polymer solutions by combining fast evaporation with a controlled interaction between the polymers and the liquid-vapor interface. Our results validate the applicability of the moving interface method to a wide range of drying systems. The limitations of the method are pointed out and cautions are provided to potential practitioners on cases where the method might fail.

Mild stratification in drying films of colloidal mixtures

Size stratification of bidisperse colloidal mixtures during vertical drying was investigated using the implicit solvent Langevin dynamics (LD) simulation and the explicit solvent lattice Boltzmann (LB) method. Simulations were performed for the Péclet number (Pe) over a wide range of 1-1000. In the case of a low size ratio of 2, mild stratification was observed in both simulation methods, in contrast to distinct stratification with thick "small-on-top" or "large-on-top" layers. The LD simulations exhibited a "small-on-top" stratification or mixed state. In contrast, the LB simulations exhibited a "large-on-top" or mixed state, according to the variation in Pe. The results demonstrated that the explicit solvent reduced the collective diffusion under moderate Pe conditions. This suppressed the steep concentration gradient of small particles in the packed region of particles near the air-solvent interface. Thus, distinguishable stratification patterns were obtained for the implicit and explicit solvent models.

Suppression of self-stratification in colloidal mixtures with high Péclet numbers

The non-equilibrium assembly of bimodal colloids during evaporative processes is an attractive means to achieve gradient or stratified layers in thick films. Here, we show that the stratification of small colloids on top of large is prevented when the viscosity of the continuous aqueous phase is too high. We propose a model where a too narrow width of the gradient in concentration of small colloids suppresses the stratification.

Stratification Mechanism in the Bidisperse Colloidal Film Drying Process: Evolution and Decomposition of Normal Stress Correlated with Microstructure

The evolution of the normal stress and microstructure in the drying process of bidisperse colloidal films is studied using the Brownian dynamics simulation. Here, we show that the formation process of small-on-top stratification can be explained by normal stress development. At high Pe_L's, a stratified layer with small particles is formed near the interface. The accumulated particles near the interface induce the localization of normal stress so that the normal stress at the interface increases from the beginning of drying. We analyze this stress development from two points of view, on the global length scale and particle length scale. On the global length scale, the localization of normal stress is quantified by the scaled normal stress difference between the interface and substrate. For all Pe_L's tested in this study, the scaled normal stress difference increases until the accumulation region reaches the substrate. After the maximum, the stress difference remains at the maximum at lower Pe_L's, while it decreases at higher Pe_L's. The microstructural analysis shows that this stress development is explained through the evolution of the particle contact number distribution at the interface and substrate. On the particle length scale, we derive the scaled local force applied to each type of particle by decomposing the local normal stress. At high Pe_L's, the scaled local force for the large particle is large compared to that for the small particle near the interface, indicating that the large particles are strongly pushed away from the interface. Associating the volume fraction profile with the local force field, we suggest that the strong scaled force for the large particle is attributed to the significant increase in the average number of small particles in contact with large ones. This study has significance in probing the drying mechanism of bidisperse colloidal films and the stratification mechanism.

Adaptive Brownian Dynamics

A framework for performant Brownian Dynamics (BD) many-body simulations with adaptive timestepping is presented. Contrary to the Euler-Maruyama scheme in common non-adaptive BD, we employ an embedded Heun-Euler integrator for the propagation of the overdamped coupled Langevin equations of motion. This enables the derivation of a local error estimate and the formulation of criteria for the acceptance or rejection of trial steps and for the control of optimal stepsize. Introducing erroneous bias in the random forces is avoided by rejection sampling with memory due to Rackauckas and Nie, which makes use of the Brownian bridge theorem and guarantees the correct generation of a specified random process even when rejecting trial steps. For test cases of Lennard-Jones fluids in bulk and in confinement, it is shown that adaptive BD solves performance and stability issues of conventional BD, already outperforming the latter even in standard situations. We expect this novel computational approach to BD to be especially helpful in long-time simulations of complex systems, e.g., in non-equilibrium, where concurrent slow and fast processes occur.

Dynamical Density Functional Theory for the Drying and Stratification of Binary Colloidal Dispersions

We develop a dynamical density functional theory based model for the drying of colloidal films on planar surfaces. We consider mixtures of two different sizes of hard-sphere colloids. Depending on the solvent evaporation rate and the initial concentrations of the two species, we observe varying degrees of stratification in the final dried films. Our model predicts the various structures described in the literature previously from experiments and computer simulations, in particular the small-on-top stratified films. Our model also includes the influence of adsorption of particles to the interfaces.

Evaporation-driven self-assembly of binary and ternary colloidal polymer nanocomposites for abrasion resistant applications

We harness the self-assembly of aqueous binary latex/silica particle blends during drying to fabricate films segregated by size in the vertical direction. We report for the first time the experimental drying of ternary colloidal dispersions and demonstrate how a ternary film containing additional small latex particles results in improved surface stability and abrasion resistance compared with a binary film. Through atomic force microscopy (AFM) and energy-dispersive X-ray spectroscopy (EDX), we show that the vertical distribution of filler particles and the surface morphologies of the films can be controlled by altering the evaporation rate and silica volume fraction. We report the formation of various silica superstructures at the film surface, which we attribute to a combination of diffusiophoresis and electrostatic interactions between particles. Brownian dynamics simulations of the final stages of solvent evaporation provide further evidence for this formation mechanism. We show how an additional small latex particle population results in an increased abrasion resistance of the film without altering its morphology or hardness. Our work provides a method to produce water-based coatings with enhanced abrasion resistance as well as valuable insights into the mechanisms behind the formation of colloidal superstructures.

Classification of drying segregation states by a generalized diffusion model

During drying of binary colloidal mixtures, one colloidal particle component can segregate to the top surface. We investigate conditions where the segregation occurs through the analysis of a linearized diffusion model with Fick's law generalized for binary colloidal mixtures. The present model is the simplest representation that includes cross-diffusion between different particle components to describe the segregation. Using the analytical solutions of this model, we classify states in terms of which the particle component segregates for the following variables: the mixture ratio of particle components, diffusion coefficients, and drying rates. The obtained state diagrams suggest how to control the segregation by designing material and operation conditions.

Diffusiophoresis-Driven Stratification of Polymers in Colloidal Films

The molecular composition of polymer blend surfaces defines properties such as adhesion, wetting, gloss, and biocompatibility. The surface composition often differs from the bulk because of thermodynamic effects or modification. Mixtures of colloids and linear polymers in a common solvent are often used to deposit films for use in encapsulants, inks, coatings, and adhesives. However, means to control the nonequilibrium surface composition are lacking for these systems. Here we show how the surface composition and hydrophilicity of a film deposited from a bimodal mixture of linear polymers and colloids in water can be adjusted simply by varying the evaporation rate. Ion beam analysis was used to quantify the extent of stratification of the linear polymers near the surface, and the results are in agreement with a recent diffusiophoretic model. Because our approach to stratification relies solely on diffusiophoresis, it is widely applicable to any system deposited from colloids and nonadsorbing polymers in solution as a means to tailor surface properties.

Stratification of polymer mixtures in drying droplets: Hydrodynamics and diffusion

We study the evaporation-induced stratification of a mixture of short and long polymer chains in a drying droplet using molecular simulations. We systematically investigate the effects of hydrodynamic interactions (HI) on this process by comparing hybrid simulations accounting for HI between polymers through the multiparticle collision dynamics technique with free-draining Langevin dynamics simulations neglecting the same. We find that the dried supraparticle morphologies are homogeneous when HI are included but are stratified in core-shell structures (with the short polymers forming the shell) when HI are neglected. The simulation methodology unambiguously attributes this difference to the treatment of the solvent in the two models. We rationalize the presence (or absence) of stratification by measuring phenomenological multicomponent diffusion coefficients for the polymer mixtures. The diffusion coefficients show the importance of not only solvent backflow but also HI between polymers in controlling the dried supraparticle morphology.

On the effect of particle surface chemistry in film stratification and morphology regulation

Combinations of colloids and binders are often used to formulate functional coatings. In these mixtures, competition between particle migration, polymer chain diffusion, evaporation and sedimentation affects their respective spatial location and therefore can govern the surface features. In addition to this, the surface chemistry of the nanoparticles (NPs) and the resulting interparticle interactions can play a significant role in dictating the morphology and the properties of resultant films. Hence it would be possible to tune the surface and bulk topology of the films by controlling these parameters. A combination of various acrylic binders with two types of silica sols, bare (BSiO2) and modified silica (MSiO2), differing in their ability to gel, were formulated and dried under controlled conditions. Factors influencing the mobility and migration of binder and silica particles were evaluated with respect to particle concentration and drying rate. MSiO2 films showed prominent pores with gradual increase in Si% across the cross-section of the films, whereas, BSiO2 films had no pores and showed a uniform Si content across the cross-section of the films. This difference is explained by the variation in gelation between BSiO2 compared to MSiO2, that hindered the NPs migration and affects the infiltration and stratification process. This study paves a path forward to achieve desired surface and bulk porosity from colloidal silica coatings by effective control of chemistry of particles along with process parameters.

Chemical vs. mechanical microstructure evolution in drying colloid and polymer coatings

Colloidal based films have been widely developed for a wide range of applications including chemical and electrical barrier coatings, photonic materials, biomaterials, and pharmaceutical oral drug delivery. Many previous studies investigate methods to generate uniformity or desired stratification of the final components with a desired microstructure. Few studies have been able to investigate this microstructure in-situ during drying. This experimental study directly tracks fluorescent colloids that are either stable in suspension or have attractive interactions during the drying process using high speed laser scanning confocal microscopy to obtain details of microstructural evolution during drying. The colloidal microstructure in stable suspensions evolves continuously during drying. Microstructures in these systems have a signature Voronoi polyhedra distribution that is defined by lognormal curve having a constant standard deviation that only depends on its chemical composition. Those formulations having strongly attractive constituents have microstructure that is heterogeneous and non-monotonic due to the mechanics associated with internal convection and capillary forces. Toward the end of drying, the influence of the mode of microstructure rearrangements remains evident.

Drying-induced back flow of colloidal suspensions confined in thin unidirectional drying cells

A clear back flow was observed in the thin unidirectional drying cell of a colloidal suspension. Flow around the colloidal-particle packing front was more complex than expected, even though a colloidal suspension was confined in a narrow space with a submillimeter-scale or shorter gap height. We propose that an increase in particle concentration around the packing front induces downward flow, which is the origin for back flow inside the cell. A mathematical model, which considered both a drying induced horizontal flow and a circulation flow caused by a concentration gradient of particles, showed a reasonable agreement with experimental data for the width of the back-flow region. The concentration gradient of particles was not negligible and it generated a rather complicated flow even in a thin drying liquid film.

Positive and negative birefringence in packed films of binary spherical colloidal particles

We have investigated the birefringence in packed films of binary spherical colloidal particles. Particulate films were obtained by drying a mixed suspension of colloidal particles with two different diameters. We observed positive and negative birefringence depending on the diameters and volume ratios of the large and small particles. When the diameters of the large and small particles were similar, the films showed positive birefringence. However, negative birefringence or weakening of positive birefringence was observed in films with a large diameter ratio and an optimal volume fraction of large particles. The large particles were embedded in packed small particles in the negative and weakened positive birefringent films. We propose a packing structure in which a single shell layer of small particles formed around a large particle. Using this model, we estimated the required volume ratio of large particles, and it was in good agreement with the optimal volume fraction. The relation between the packing structure of the binary colloidal particles and the birefringence is discussed.

We have investigated the birefringence in packed films of binary spherical colloidal particles.

Experimental and theoretical evidence for molecular forces driving surface segregation in photonic colloidal assemblies

Surface segregation in binary colloidal mixtures offers a simple way to control both surface and bulk properties without affecting their bulk composition. Here, we combine experiments and coarse-grained molecular dynamics (CG-MD) simulations to delineate the effects of particle chemistry and size on surface segregation in photonic colloidal assemblies from binary mixtures of melanin and silica particles of size ratio (D large /D small) ranging from 1.0 to ~2.2. We find that melanin and/or smaller particles segregate at the surface of micrometer-sized colloidal assemblies (supraballs) prepared by an emulsion process. Conversely, no such surface segregation occurs in films prepared by evaporative assembly. CG-MD simulations explain the experimental observations by showing that particles with the larger contact angle (melanin) are enriched at the supraball surface regardless of the relative strength of particle-interface interactions, a result with implications for the broad understanding and design of colloidal particle assemblies.

Control of Stratification in Drying Particle Suspensions via Temperature Gradients

A potential strategy for controlling stratification in a drying suspension of bidisperse particles is studied using molecular dynamics simulations. When the suspension is maintained at a constant temperature during fast drying, it can exhibit "small-on-top" stratification with an accumulation (depletion) of smaller (larger) particles in the top region of the drying film, consistent with the prediction of current theories based on diffusiophoresis. However, when only the region near the substrate is thermalized at a constant temperature, a negative temperature gradient develops in the suspension because of evaporative cooling at the liquid-vapor interface. Since the associated thermophoresis is stronger for larger nanoparticles, a higher fraction of larger nanoparticles migrate to the top of the drying film at fast evaporation rates. As a result, stratification is converted to "large-on-top". Very strong small-on-top stratification can be produced with a positive thermal gradient in the drying suspension. Here, we explore a way to produce a positive thermal gradient by thermalizing the vapor at a temperature higher than that of the solvent. Possible experimental approaches to realize various thermal gradients in a suspension undergoing solvent evaporation and thus to produce different stratification states in the drying film are suggested.

Sandwich layering in binary nanoparticle films and effect of size ratio on stratification behavior

HYPOTHESIS

Stratification or self-segregation of multicomponent particle mixtures during drying is an important phenomenon to understand for the development of single-step deposition processes for complex coatings. We hypothesize that varying the ratio of particle Peclet numbers will lead to different types of stratification behavior.

EXPERIMENTS

Binary colloidal films of polystyrene and silica were prepared by evaporative film formation, and stratification of nanoparticles of different size ratio (7.7-1.2) was studied using microbeam small-angle X-ray scattering (SAXS).

FINDINGS

SAXS spectra showed noticeable variations at different film depths, consistent with stratification. These results are quantified to obtain vertical composition profiles. We observe "sandwich"-type layered structures at different nanoparticle size ratios, which to our knowledge have not been previously observed experimentally or predicted by theory. For example, for films of larger particle size ratios (7.7-4.8), large particles are enriched at the film top and bottom, leading to a large-small-large or "LSL" behavior; while within films of smaller particle size ratio (2.2-1.2), small particles are enriched at the top and bottom of the film (small-large-small or "SLS" structures). The enrichment of particles at the top persists over several hundred particle layers and is not just a single monolayer pinned to the upper surface.

A critical and quantitative review of the stratification of particles during the drying of colloidal films

For a wide range of applications, films are deposited from colloidal particles suspended in a volatile liquid. There is burgeoning interest in stratifying colloidal particles into separate layers within the final dry film to impart properties at the surface different to the interior. Here, we outline the mechanisms by which colloidal mixtures can stratify during the drying process. The problem is considered here as a three-way competition between evaporation of the continuous liquid, sedimentation of particles, and their Brownian diffusion. In particle mixtures, the sedimentation of larger or denser particles offers one means of stratification. When the rate of evaporation is fast relative to diffusion, binary mixtures of large and small particles can stratify with small particles on the top, according to physical models and computer simulations. We compare experimental results found in the scientific literature to the predictions of several recent models in a quantitative way. Although there is not perfect agreement between them, some general trends emerge in the experiments, simulations and models. The stratification of small particles on the top of a film is favoured when the colloidal suspension is dilute but when both the concentration of the small particles and the solvent evaporation rate are sufficiently high. A higher particle size ratio also favours stratification by size. This review points to ways that microstructures can be designed and controlled in colloidal materials to achieve desired properties.

Stratification in Drying Films Containing Bidisperse Mixtures of Nanoparticles

Large scale molecular dynamics simulations for bidisperse nanoparticle suspensions with an explicit solvent are used to investigate the effects of evaporation rates and volume fractions on the nanoparticle distribution during drying. Our results show that "small-on-top" stratification can occur when Pe _sϕ _s ≳ c with c ∼ 1, where Pe _s is the Péclet number and ϕ _s is the volume fraction of the smaller particles. This threshold of Pe _sϕ _s for "small-on-top" is larger by a factor of ∼α² than the prediction of the model treating solvent as an implicit viscous background, where α is the size ratio between the large and small particles. Our simulations further show that when the evaporation rate of the solvent is reduced, the "small-on-top" stratification can be enhanced, which is not predicted by existing theories. This unexpected behavior is explained with thermophoresis associated with a positive gradient of solvent density caused by evaporative cooling at the liquid/vapor interface. For ultrafast evaporation the gradient is large and drives the nanoparticles toward the liquid/vapor interface. This phoretic effect is stronger for larger nanoparticles, and consequently the "small-on-top" stratification becomes more distinct when the evaporation rate is slower (but not too slow such that a uniform distribution of nanoparticles in the drying film is produced), as thermophoresis that favors larger particles on the top is mitigated. A similar effect can lead to "large-on-top" stratification for Pe _sϕ _s above the threshold when Pe _s is large but ϕ _s is small. Our results reveal the importance of including the solvent explicitly when modeling evaporation-induced particle separation and organization and point to the important role of density gradients brought about by ultrafast evaporation.

Particulate Coatings via Evaporation-Induced Self-Assembly of Polydisperse Colloidal Lignin on Solid Interfaces

Polydisperse smooth and spherical biocolloidal particles were suspended in aqueous media and allowed to consolidate via evaporation-induced self-assembly. The stratification of the particles at the solid-air interface was markedly influenced, but not monotonically, by the drying rate. Cross-sectional imaging via electron microscopy indicated a structured coating morphology that was distinctive from that obtained by using particles with a mono- or bimodal distribution. Segregation patterns were found to derive from the interplay of particle diffusion, interparticle forces, and settling dynamics. Supporting our experimental findings, computer simulations showed an optimal drying rate for achieving maximum segregation. Overall, stratified coatings comprising nano- and microparticles derived from lignin are expected to open opportunities for multifunctional structures that can be designed and predicted on the basis of experimental Péclet numbers and computational order.

Diffusiophoresis in nonadsorbing polymer solutions: The Asakura-Oosawa model and stratification in drying films

A colloidal particle placed in an inhomogeneous solution of smaller nonadsorbing polymers will move towards regions of lower polymer concentration in order to reduce the free energy of the interface between the surface of the particle and the solution. This phenomenon is known as diffusiophoresis. Treating the polymer as penetrable hard spheres, as in the Asakura-Oosawa model, a simple analytic expression for the diffusiophoretic drift velocity can be obtained. In the context of drying films we show that diffusiophoresis by this mechanism can lead to stratification under easily accessible experimental conditions. By stratification we mean spontaneous formation of a layer of polymer on top of a layer of the colloid. Transposed to the case of binary colloidal mixtures, this offers an explanation for the stratification observed recently in these systems [A. Fortini et al., Phys. Rev. Lett. 116, 118301 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.118301]. Our results emphasize the importance of treating solvent dynamics explicitly in these problems and caution against the neglect of hydrodynamic interactions or the use of implicit solvent models in which the absence of solvent backflow results in an unbalanced osmotic force that gives rise to large but unphysical effects.