Drying of thin colloidal films

Segregation in Drying Binary Colloidal Droplets

When a colloidal suspension droplet evaporates from a solid surface, it leaves a characteristic deposit in the contact region. These deposits are common and important for many applications in printing, coating, or washing. By the use of superamphiphobic surfaces as a substrate, the contact area can be reduced so that evaporation is almost radially symmetric. While drying, the droplets maintain a nearly perfect spherical shape. Here, we exploit this phenomenon to fabricate supraparticles from bidisperse colloidal aqueous suspensions. The supraparticles have a core-shell morphology. The outer region is predominantly occupied by small colloids, forming a close-packed crystalline structure. Toward the center, the number of large colloids increases and they are packed amorphously. The extent of this stratification decreases with decreasing the evaporation rate. Complementary simulations indicate that evaporation leads to a local increase in density, which, in turn, exerts stronger inward forces on the larger colloids. A comparison between experiments and simulations suggest that hydrodynamic interactions between the suspended colloids reduce the extent of stratification. Our findings are relevant for the fabrication of supraparticles for applications in the fields of chromatography, catalysis, drug delivery, photonics, and a better understanding of spray-drying.

Flow of condensed particles around a packing front visualized by drying colloidal suspensions on a tilted substrate

A gravity effect was demonstrated for 10 nm particles drying in colloidal suspensions. The particles were well-dispersed and did not sediment. However, when a suspension was dried on a tilted directional cell, a clear downward flow of particles was observed around the packing front, which was the boundary between the packed particles layer and the suspension. Three particle sizes (10-110 nm) were examined, with the most pronounced effect being on the 10 nm particles. The primary origin of the downflow was attributed to condensation of particles near the packing front and the subsequent increase in the overall density of the condensed layer. Because of the flow, the packing front was not parallel to the drying interface and tilted cracks formed in the packed layer. A mathematical model was proposed that considered conservation of the suspended particles in the condensed layer. Three competing factors of particle transport (advection, particle consumption by packing, and particle transport by the downward flow) were used to explain the experimental results. Overall, the results suggested that simple substrate tilting would be useful to evaluate whether suspended particles are easily packed or not during drying.

Drying-induced stresses before solidification in colloidal dispersions: in situ measurements

We first report an original setup that enables continuous measurements of stresses induced by the drying of confined drops of complex fluids. This setup is mainly based on a precision scale working with an electromagnetic force compensation technique that provides accurate measurements of forces, while allowing simultaneously controlled evaporation rates, in situ microscopic observations, and thus quantitative estimates of normal stresses. We then performed an extensive study of the drying of a charged colloidal dispersion using this setup. Stress measurements clearly show the emergence of large tensile stresses during drying, well-before the solidification stage evidenced by the invasion of the porous colloidal material by air. Combined measurements of solid deformation and concentration profiles (particle tracking, Raman micro-spectroscopy) help us to demonstrate that these stresses are due to the formation of a solid at a low volume fraction, which further undergoes drying-induced shear deformations up to the colloid close-packing, as also supported by large deformation poroelastic modeling. Above all, our results highlight the importance of repulsive colloidal interactions in the build-up of mechanical stresses during drying.

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.

Capillary Stress and Structural Relaxation in Moist Granular Materials

A numerical and theoretical framework to address the poromechanical effect of capillary stress in complex mesoporous materials is proposed and exemplified for water sorption in cement. We first predict the capillary condensation/evaporation isotherm using lattice-gas simulations in a realistic nanogranular cement model. A phase-field model to calculate moisture-induced capillary stress is then introduced and applied to cement at different water contents. We show that capillary stress is an effective mechanism for eigenstress relaxation in granular heterogeneous porous media, which contributes to the durability of cement.

Influence of Bénard-Marangoni instability on the morphology of drying colloidal films

The drying of colloidal suspensions is a very complex process leading to a sol-gel transition induced by solvent evaporation. The resulting film can even crack and delaminate. In this study, we investigate the drying process of a colloidal suspension with a highly volatile solvent and we show for initially millimeter-thick layers that the resulting pattern of delaminated plates considerably differs from what is usually observed for aqueous colloidal suspensions. Visualization using an IR camera reveals that hexagonal convection cells can develop during the drying of suspensions with a highly volatile solvent and may persist until the film consolidation. This leads to the formation of non-homogeneous films presenting surface corrugations. Thus, we highlight the importance of the hydrodynamics during the first phase of strong solvent evaporation and its consequences for the following drying steps. A criterion predicting whether or not Bénard-Marangoni instability effectively occurs will be discussed. Finally, we report a non-classical delamination mode generating fragments with convex surfaces, whereas buckle-driven delamination usually results in concave shapes.

Structuration of the Surface Layer during Drying of Colloidal Dispersions

During evaporative drying of a colloidal dispersion, the structural behavior at the air-dispersion interface is of particular relevance to the understanding of the consolidation mechanism and the final structural and mechanical properties of the porous media. The drying interface constitutes the region of initial drying stress that, when accumulated over a critical thickness, leads to crack formation. This work presents an experimental study of top-down drying of colloidal silica dispersions with three different sizes (radius 5, 8, and 13 nm). Using specular neutron reflectivity, we focus on the structural evolution at the free drying front of the dispersion with a macroscopic drying surface and demonstrate the existence of a thick concentrated surface layer induced by heterogeneous evaporation. The reflectivity profile contains a strong structure peak due to scattering from particles in the interfacial region, from which the interparticle distance is deduced. A notable advantage of these measurements is the direct extraction of the corresponding dispersion concentration from the critical total reflection edge, providing a straightforward access to a structure-concentration relation during the drying process. The bulk reservoir of this experimental configuration renders it possible to verify the evaporation-diffusion balance to construct the surface layer and also to check reversibility of particle ordering. We follow the structural evolution of this surface layer from a sol to a soft wet-gel that is the precursor of a fragile skin and the onset of significant particle aggregation that precedes formation of the wet-crust. Separate complementary measurements on the structural evolution in the bulk dispersion are also carried out by small-angle neutron scattering, where the particle concentration is also extracted directly from the experimental curves. The two sets of data reveal similar structural evolution with concentration at the interface and in the bulk and an increase in the degree of ordering with the particle size.

Probing the Colloidal Particle Dynamics in Drying Sessile Droplets

Particle deposition and assembly in the vicinity of contact lines of evaporative sessile droplets have been intensively investigated during the past decade. Yet little is known about particle arrangement in the contact-line region initiated by the self-assembled particles at the air-liquid interface and how the particle pinning behaves differently compared with that when particles are transported from the bulk of the sessile droplet to the three-phase contact line. We utilized the dual-droplet inkjet printing process to elucidate the versatility in particle deposition and assembly generated near the contact-line region and demonstrated the influence of such printing technique on particle pinning at the contact line after solvent evaporation. Wetting droplets containing sulfate-functionalized polystyrene (sulfate-PS) nanoparticles were jetted over the supporting droplets with carboxyl-PS nanoparticles, where the interplay between the solvent evaporation and particle transport dictates the final morphology of particle deposition. Depending on the particle size and concentration used in the supporting droplet, different morphologies of particle depositions near the periphery of the supporting droplet have been obtained such as stratified rings, blended rings, and rings of particles mainly from the air-liquid interface. Three characteristic times are considered in this study, namely, total time for solvent evaporation ( t_evp), time required for the colloidal particles in the supporting droplet to reach the contact line and form the first layers of deposition ( t_ps), and time needed for the particles at the interface to reach the contact line ( t_pw). The ratios of characteristic times ( t_ps/ t_evp) and ( t_ps/ t_pw) determine the final particle assembly near the contact-line region. The ability to control such particle deposition and assembly could have a direct implication on developing facile, cost-effective technologies essential for patterning heterogeneous structured coatings and devices.

Universal scaling of polygonal desiccation crack patterns

Polygonal desiccation crack patterns are commonly observed in natural systems. Despite their quotidian nature, it is unclear whether similar crack patterns which span orders of magnitude in length scales share the same underlying physics. In thin films, the characteristic length of polygonal cracks is known to monotonically increase with the film thickness; however, existing theories that consider the mechanical, thermodynamic, hydrodynamic, and statistical properties of cracking often lead to contradictory predictions. Here we experimentally investigate polygonal cracks in drying suspensions of micron-sized particles by varying film thickness, boundary adhesion, packing fraction, and solvent. Although polygonal cracks were observed in most systems above a critical film thickness, in cornstarch-water mixtures, multiscale crack patterns were observed due to two distinct desiccation mechanisms. Large-scale, primary polygons initially form due to capillary-induced film shrinkage, whereas small-scale, secondary polygons appear later due to the deswelling of the hygroscopic particles. In addition, we find that the characteristic area of the polygonal cracks, A_{p}, obeys a universal power law, A_{p}=αh^{4/3}, where h is the film thickness. By quantitatively linking α with the material properties during crack formation, we provide a robust framework for understanding multiscale polygonal crack patterns from microscopic to geologic scales.

Formation of desiccation crack patterns in electric fields: a review

Desiccation crack formation is an important and interesting part of the broad area of fracture mechanics. Generation of cracks due to drying depends on ambient conditions, which may include externally applied fields. In this review, we discuss the effect of both direct and alternating electrical fields on desiccation crack formation. After a brief introduction to materials which crack on drying, e.g. colloids, clay and ceramics we discuss how they respond to an electric field. Following that, we present an account of experiments and modelling studies performed on granular pastes or clays drying while exposed to an electric field. Specific patterns formed under different geometries, strengths and frequencies of the electric field are described and explained. The review includes work on cracks formed in clay droplets, where a memory effect has been observed and analysed using a generalized calculus formalism.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Rapid Pulsed Light Sintering of Silver Nanowires on Woven Polyester for personal thermal management with enhanced performance, durability and cost-effectiveness

Fabric-based personal heating patches have small geometric profiles and can be attached to selected areas of garments for personal thermal management to enable significant energy savings in built environments. Scalable fabrication of such patches with high thermal performance at low applied voltage, high durability and low materials cost is critical to the widespread implementation of these energy savings. This work investigates a scalable Intense Pulsed Light (IPL) sintering process for fabricating silver nanowire on woven polyester heating patches. Just 300 microseconds of IPL sintering results in 30% lesser electrical resistance, 70% higher thermal performance, greater durability (under bending up to 2 mm radius of curvature, washing, humidity and high temperature), with only 50% the added nanowire mass compared to state-of-the-art. Computational modeling combining electromagnetic and thermal simulations is performed to uncover the nanoscale temperature gradients during IPL sintering, and the underlying reason for greater durability of the nanowire-fabric after sintering. This large-area, high speed, and ambient-condition IPL sintering process represents an attractive strategy for scalably fabricating personal heating fabric-patches with greater thermal performance, higher durability and reduced costs.

Field-Assisted Contact Line Motion in Thin Films

The balance of intermolecular and surface forces plays a critical role in the transport phenomena near the contact line region of an extended meniscus in several technologically important processes. Externally applied fields can alter the equilibrium and stability of the meniscus with concomitant effects on its shape and spreading characteristics and may even lead to an oscillation. This feature article provides a detailed account of the present and past efforts in exploring the behavior of curved thin liquid films subjected to mild thermal perturbations, heat input, and electrical and magnetic fields for pure as well as colloidal suspensions, including the effects of particle charge and polarity. The shape-dependent intermolecular force field has been evaluated in situ by a nonobtrusive optical technique utilizing the interference phenomena and subsequent image processing. The critical role of disjoining pressure is identified along with the determination of the Hamaker constant. The spatial and temporal variations of the capillary forces are evaluated for the advancing and receding menisci. The Maxwell-stress-induced enhanced spreading during electrowetting, at relatively low voltages, and that due to the application of a magnetic field are discussed with respect to their distinctly different characteristics and application potentials. The use of the augmented Young-Laplace equation elicited additional insights into the fundamental physics for flow in ultrathin liquid films.

Drying colloidal systems: Laboratory models for a wide range of applications

The drying of complex fluids provides a powerful insight into phenomena that take place on time and length scales not normally accessible. An important feature of complex fluids, colloidal dispersions and polymer solutions is their high sensitivity to weak external actions. Thus, the drying of complex fluids involves a large number of physical and chemical processes. The scope of this review is the capacity to tune such systems to reproduce and explore specific properties in a physics laboratory. A wide variety of systems are presented, ranging from functional coatings, food science, cosmetology, medical diagnostics and forensics to geophysics and art.

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.

Beyond Fullerenes: Indacenodithiophene-Based Organic Charge-Transport Layer toward Upscaling of Low-Cost Perovskite Solar Cells

Phenyl-C₆₁-butyric acid methyl ester (PCBM) is universally used as the electron-transport layer (ETL) in the low-cost inverted planar structure of perovskite solar cells (PeSCs). PCBM brings tremendous challenges in upscaling of PeSCs using industry-relevant methods due to its aggregation behavior, which undermines the power conversion efficiency and stability. Herein, we highlight these, seldom reported, challenges with PCBM. Furthermore, we investigate the potential of nonfullerene indacenodithiophene (IDT)-based molecules by employing a commercially available variant, 3,9-bis(2-methylene-(3-(1,1-dicyanomethylene)-indanone))-5,5,11,11-tetrakis(4-hexylphenyl)-dithieno[2,3- d:2',3'- d']- s-indaceno[1,2- b:5,6- b'] dithiophene (ITIC), as a PCBM replacement in ambient-processed PeSCs. Films fabrication by laboratory-based spin-coating and industry-relevant slot-die coating methods are compared. Although similar power-conversion efficiencies are achieved with both types of ETL in a simple device structure fabricated by spin-coating, the nanofibriller morphology of ITIC compared to the aggregated morphology of PCBM films enables improved mechanical integrity and stability of ITIC devices. Upon slot-die coating, the aggregation of PCBM is exacerbated, leading to significantly lower power-conversion efficiency of devices than spin-coated PCBM as well as slot-die-coated ITIC devices. Our results clearly indicate that IDT-based molecules have great potential as an ETL in PeSCs, offering superior properties and upscaling compatibility than PCBM. Thus, we present a short summary of recently emerged nonfullerene IDT-based molecules from the field of organic solar cells and discuss their scope in PeSCs as electron or hole-transport layer.

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.

In Situ and Real-Time Studies, via Synchrotron X-ray Scattering, of the Orientational Order of Cellulose Nanocrystals during Solution Shearing

In this manuscript, we report on the ordering of the cellulose nanocrystals (CNCs) as they experience shear forces during the casting process. To achieve these measurements, in situ and in real time, we used synchrotron-based grazing incidence wide-angle X-ray scattering (GIWAX). We believe that the GIWAX technique, although not commonly used to probe these types of phenomena, can open new avenues to gain deeper insights into film formation processes and surface-driven phenomena. In particular, we investigated the influence of solution concentration, shear-cast velocity, and drying temperature on the ordering of cellulose nanocrystals (CNCs) using GIWAXS. The films were prepared from aqueous suspensions of cellulose nanocrystals at two concentration values (7 and 9 wt %). As the films were cast, the X-ray beam was focused on a fixed position and GIWAXS patterns were recorded at regular time intervals. Structural characterization of the dry films was carried out via polarized optical microscopy and scanning electron microscopy. In addition, a rheological study of the CNC suspensions was performed. Our results show that the morphology of the CNC films was significantly influenced by shear velocity, concentration of the precursor suspension, and evaporation temperature. In contrast, we observed that the orientation parameter of the films was not significantly affected. The scattering intensity of the peak (200) was analyzed as a function of time, following a sigmoidal profile, hence indicating short- and long-range interactions within the anisotropic domains as they reached their final orientation state. A model capable of describing the resulting film morphologies is also proposed. The results and analysis presented in this manuscript provide new insights into the controlled alignment of cellulose nanocrystals under shear. This controlled alignment has significant implications in the development of advanced coatings and films currently used in a myriad of applications, such as catalysis, optics, electronics, and biomedicine.

Vertical drying of a suspension of sticks: Monte Carlo simulation for continuous two-dimensional problem

The vertical drying of a two-dimensional colloidal film containing zero-thickness sticks (lines) was studied by means of kinetic Monte Carlo (MC) simulations. The continuous two-dimensional problem for both the positions and orientations was considered. The initial state before drying was produced using a model of random sequential adsorption with isotropic orientations of the sticks. During the evaporation, an upper interface falls with a linear velocity in the vertical direction, and the sticks undergo translational and rotational Brownian motions. The MC simulations were run at different initial number concentrations (the numbers of sticks per unit area), p_{i}, and solvent evaporation rates, u. For completely dried films, the spatial distributions of the sticks, the order parameters, and the electrical conductivities of the films in both the horizontal, x, and vertical, y, directions were examined. Significant evaporation-driven self-assembly and stratification of the sticks in the vertical direction was observed. The extent of stratification increased with increasing values of u. The anisotropy of the electrical conductivity of the film can be finely regulated by changes in the values of p_{i} and u.

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

Preparation of thin films by dissolving polymers in a common solvent followed by evaporation of the solvent has become a routine processing procedure. However, modeling of thin film formation in an evaporating solvent has been challenging due to a need to simulate processes at multiple length and time scales. In this work, we present a methodology based on the principles of linear non-equilibrium thermodynamics, which allows systematic study of various effects such as the changes in the solvent properties due to phase transformation from liquid to vapor and polymer thermodynamics resulting from such solvent transformations. The methodology allows for the derivation of evaporative flux and boundary conditions near each surface for simulations of systems close to the equilibrium. We apply it to study thin film microstructural evolution in phase segregating polymer blends dissolved in a common volatile solvent and deposited on a planar substrate. Effects of the evaporation rates, interactions of the polymers with the underlying substrate and concentration dependent mobilities on the kinetics of thin film formation are studied.

Shear Rheology Control of Wrinkles and Patterns in Graphene Oxide Films

Drying graphene oxide (GO) films are subject to extensive wrinkling, which largely affects their final properties. Wrinkles were shown to be suitable in biotechnological applications; however, they negatively affect the electronic properties of the films. Here, we report on wrinkle tuning and patterning of GO films under stress-controlled conditions during drying. GO flakes assemble at an air-solvent interface; the assembly forms a skin at the surface and may bend due to volume shrinkage while drying. We applied a modification of evaporative lithography to spatially define the evaporative stress field. Wrinkle alignment is achieved over cm² areas. The wavelength (i.e., wrinkle spacing) is controlled in the μm range by the film thickness and GO concentration. Furthermore, we propose the use of nanoparticles to control capillary forces to suppress wrinkling. An example of a controlled pattern is given to elucidate the potential of the technique. The results are discussed in terms of classical elasticity theory. Wrinkling is the result of bending of the wet solid skin layer assembled on a highly elastic GO dispersion. Wavelength selection is the result of energy minimization between the bending of the skin and the elastic deformation of the GO supporting dispersion. The results strongly suggest the possibility to tune wrinkles and patterns by simple physicochemical routes.

Triggering molecular assembly at the mesoscale for advanced Raman detection of proteins in liquid

An advanced optofluidic system for protein detection based on Raman signal amplification via dewetting and molecular gathering within temporary mesoscale assemblies is presented. The evaporation of a microliter volume of protein solution deposited in a circular microwell precisely follows an outward-receding geometry. Herein the combination of liquid withdrawal with intermolecular interactions induces the formation of self-assembled molecular domains at the solid-liquid interface. Through proper control of the evaporation rate, amplitude of the assemblies and time for spectral collection at the liquid edge are extensively raised, resulting in a local enhancement and refinement of the Raman response, respectively. Further signal amplification is obtained by taking advantage of the intense local electromagnetic fields generated upon adding a plasmonic coating to the microwell. Major advantages of this optofluidic method lie in the obtainment of high-quality, high-sensitivity Raman spectra with detection limit down to sub-micromolar values. Peculiarly, the assembled proteins in the liquid edge region maintain their native-like state without displaying spectral changes usually occurring when dried drop deposits are considered.

A quantitative study of enhanced drying flux from a narrow liquid–air interface of colloidal suspensions during directional drying

Drying flux changes by the drying interfacial area of a colloidal suspension that affects the formation kinetics of particulate films.

Dynamical Density Functional Theory for the Evaporation of Droplets of Nanoparticle Suspension

We develop a lattice gas model for the drying of droplets of a nanoparticle suspension on a planar surface, using dynamical density functional theory (DDFT) to describe the time evolution of the solvent and nanoparticle density profiles. The DDFT assumes a diffusive dynamics but does not include the advective hydrodynamics of the solvent, so the model is relevant to highly viscous or near to equilibrium systems. Nonetheless, we see an equivalent of the coffee-ring stain effect, but in the present model it occurs for thermodynamic rather the fluid-mechanical reasons. The model incorporates the effect of phase separation and vertical density variations within the droplet and the consequence of these on the nanoparticle deposition pattern on the surface. We show how to include the effect of slip or no-slip at the surface and how this is related to the receding contact angle. We also determine how the equilibrium contact angle depends on the microscopic interaction parameters.

Horizontal drying fronts in films of colloidal dispersions: influence of hydrostatic pressure and collective diffusion

The origin and time evolution of heterogeneities in drying colloidal films is still a matter of debate. In this work, we studied the behaviour of horizontal drying fronts in a 1D configuration. The effects of hydrostatic pressure and collective diffusion of charged particles, neglected so far, were introduced. We made use of the new simulation tool based on cellular automata we recently presented (Langmuir 2015 & 2017). To check the simulation results, measurements of film profiles in the wet state and drying front velocities were performed with silica colloids. It was shown that taking hydrostatic pressure into account much improves agreement between theory and experiment. On the other hand, the simulation showed that collective diffusion slows down the drying fronts, even more when the Debye length is increased. This latter effect remains to be checked experimentally. This work opens the way to further improvements of theory and simulation, notably 2D and 3D simulations.

Role of Vapor Mass Transfer in Flow Coating of Colloidal Dispersions in the Evaporative Regime

In flow-coating processes at low substrate velocity, solvent evaporation occurs during the film withdrawal and the coating process directly yields a dry deposit. In this regime, often referred to as the evaporative regime, several works performed on blade-coating-like configurations have reported a deposit thickness h_d proportional to the inverse of the substrate velocity V. Such a scaling can be easily derived from simple mass conservation laws, assuming that evaporation occurs on a constant distance, referred to as the evaporation length, noted L_ev in the present paper and of the order of the meniscus size. However, the case of colloidal dispersions deserves further attention. Indeed, the coating flow leads to a wet film of densely packed colloids before the formation of the dry deposit. This specific feature is related to the porous nature of the dry deposit, which can thus remain wet when capillary forces are strong enough to prevent the receding of the solvent through the pores of the film (the so-called pore-emptying). The length of this wet film may possibly be much larger than the meniscus size, therefore modifying the solvent evaporation rate, as well as the scaling h_d ∼ 1/V. This result was suggested recently by different groups using basic modeling and assuming for simplicity a uniform evaporation rate over the wet film. In this article, we go a step further and investigate the effect of multidimensional vapor mass transfer in the gas phase on L_ev and h_d in the specific case of colloidal dispersions. Using simplified models, we first provide analytical expressions in asymptotic cases corresponding to 1D or 2D diffusive vapor transport. These theoretical investigations then led us to show that L_ev is independent of the evaporation rate amplitude, and roughly independent of its spatial distribution. Conversely, h_d strongly depends on the characteristics of vapor mass transfer in the gas phase, and different scaling laws are obtained for the 1D or the 2D case. These theoretical findings are finally tested by comparison with experimental results supporting our theoretical simplified approach.

Structure Formation in Soft-Matter Solutions Induced by Solvent Evaporation

Solvent evaporation in soft-matter solutions (solutions of colloidal particles, polymers, and their mixtures) is an important process in material making and in the printing and coating industries. The solvent-evaporation process determines the structure of materials and strongly affects their performance. Solvent evaporation involves many physicochemical processes: flow, diffusion, crystallization, gelation, glass transition, etc. and is quite complex. Here, recent progress in this important process is reported, with a special focus on theoretical and simulation studies.

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.

Microstructures and mechanics in the colloidal film drying process

We use Brownian Dynamics (BD) simulations and continuum models to study the microstructures and mechanics in the colloidal film drying process. Colloidal suspensions are compressed between a planar moving interface and a stationary substrate. In the BD simulations, we develop a new Energy Minimization Potential-Free (EMPF) algorithm to enforce the hard-sphere potential in confined systems and to accurately measure the stress profile. The interface moves either at a constant velocity U_w or via a constant imposed normal stress Σ_e. Comparing the interface motions to the particle Brownian motion defines the Péclet numbers Pe_U = U_wa/d₀ and Pe_Σ = Σ_ea³/k_BT, respectively, where d₀ = k_BT/ζ with k_BT the thermal energy scale, ζ the single-particle resistance, and a the particle radius. With a constant interface velocity, thermodynamics drives the suspension behavior when Pe_U ≪ 1, and homogeneous crystallization appears when the gap spacing between the two boundaries pushes the volume fraction above the equilibrium phase boundary. In contrast, when Pe_U ≫ 1, local epitaxial crystal growth appears adjacent to the moving interface even for large gap sizes. Interestingly, the most amorphous film microstructures are found at moderate Pe_U. The film stress profile develops sharp transitions and becomes step-like with growing Péclet number. With a constant imposed stress, the interface stops moving as the suspension pressure increases and the microstructural and mechanical behaviors are similar to the constant velocity case. Comparison with the simulations shows that the model accurately captures the stress on the moving interface, and quantitatively resolves the local stress and volume fraction distributions for low to moderate Péclet numbers. This work demonstrates the critical role of interface motion on the film microstructures and stresses.

Stratification in Drying Polymer-Polymer and Colloid-Polymer Mixtures

Drying polymer-polymer and colloid-polymer mixtures were studied using Langevin dynamics computer simulations. Polymer-polymer mixtures vertically stratified into layers, with the shorter polymers enriched near the drying interface and the longer polymers pushed down toward the substrate. Colloid-polymer mixtures stratified into a polymer-on-top structure when the polymer radius of gyration was comparable to or smaller than the colloid diameter, and a colloid-on-top structure otherwise. We also developed a theoretical model for the drying mixtures based on dynamical density functional theory, which gave excellent quantitative agreement with the simulations for the polymer-polymer mixtures and qualitatively predicted the observed polymer-on-top or colloid-on-top structures for the colloid-polymer mixtures.

Effect of including a gas layer on the gel formation process during the drying of a polymer solution

In this paper, we study the influence of the upper gas layer on the drying and gelation of a polymer solution. The gel is formed due to the evaporation of the binary solution into (inert) air. A one-dimensional model is proposed, where the evaporation flux is more realistically described than in previous studies. The approach is based on general thermodynamic principles. A composition-dependent diffusion coefficient is used in the liquid phase and the local equilibrium hypothesis is introduced at the interface to describe the evaporation process. The results show that the high thickness of the gas layer reduces evaporation, thus leading to longer drying times. Our model is also compared with more phenomenological descriptions of evaporation, for which the mass flux through the interface is described by the introduction of a Peclet number. A global agreement is found for appropriate values of the Peclet numbers and our model can thus be considered as a tool allowing to link the value of the empirical Peclet number to the physics of the gas phase. Finally, in contrast with other models, our approach emphasizes the possibility of very fast gelation at the interface, which could prevent all Marangoni convection during the drying process.

Kinetics in directional drying of water that contains deformable non-volatile oil droplets

Herein, we report assessments of the kinetics in directional drying of water that contains non-volatile oil droplets, based on direct observations using a confocal microscope. The water was found to evaporate at a constant rate during the initial stage of drying, after which the evaporation rate decreased. The dispersed oil droplets were compressed and distorted as the surrounding water was lost. Further evaporation of water resulted in coalescence of the oil droplets, with the eventual formation of an oil layer at the drying interface. However, it was apparent that the drying rate decreased even before the formation of this oil layer. We propose that the restricted transport of water via the narrow paths between the distorted oil droplets was responsible for the decreased drying rate. A mathematical model based on foam drainage theory is proposed and describes the experimental data very well. This work also determined that the critical disjoining pressure for the oil droplets is affected by the drying rate, such that higher pressure values are associated with slow drying conditions. The drying kinetics and stability of the dispersed oil droplets are discussed.

Tailoring crack morphology in coffee-ring deposits via substrate heating

The drying of a sessile drop consisting of colloidal particles and the formation of particulate deposits with spatially periodic cracks were ubiquitous. The drying induced stress, which is generated during the evaporation of a colloidal drop, is released by the formation of cracks. We find that the morphology of cracks formed in particulate films dried at substrate temperature, T_sub = 25 °C is markedly different from that of cracks formed at T_sub > 45 °C. The cracks are disordered in the former case, but ordered and periodic in the latter. The disorderedness of cracks observed at T_sub = 25 °C is mainly due to the formation of a coffee-ring like particle deposit that exhibits a larger height gradient. The ultimate deposit pattern after complete drying is observed to be different for colloidal dispersion drops evaporated at different substrate temperatures. This is attributed to temperature-dependent solvent flow mechanisms and capillary-driven flow, which occur inside the colloidal drop during the course of drying. In addition, for the coffee-ring-like particulate deposit obtained at T_sub ≤ 45 °C, the ratio between the width of the deposit w and the radius of the ring R scales with the volume fraction of the colloids φ, w/R ∼ φ^0.5, in the range of volume fractions studied in this work. The deposited patterns obtained at temperature T_sub > 45 °C are largely dominated by the capture of particles by the receding liquid-vapor interface. This is due to the faster rate of decrease of the liquid-vapor interface position with an increase in substrate temperature.

Bio-inspired intelligent evaporation modulation in a thermo-sensitive nanogel colloid solution for self-thermoregulation

Intelligent evaporation and temperature modulation plays an important role in self-regulation of living organisms and many industrial applications. Here we demonstrate that a poly(N-isopropylacrylamide) (PNIPAM) nanogel colloid solution can spontaneously and intelligently modulate its evaporation rate with temperature variation, which has a larger evaporation rate than distilled water at a temperature higher than its lower critical solution temperature (LCST) and a smaller evaporation rate at a temperature lower than its LCST. It performs just like human skin. Theoretical analysis based on the thermodynamic derivation reveals that the evaporation rate transition around the LCST may originate from the saturated vapor pressure transition caused by the status transformation of the PNIPAM additives. An intelligent thermoregulation system based on the PNIPAM colloid solution is also demonstrated, illustrating its potential for intelligent temperature control and acting as an artificial skin.

Free-standing monolayer films of ordered colloidal particles

We report a novel method for the fabrication of large area, free standing monolayer films of close-packed colloidal particles. The method involves creating a free-standing, wet film of colloidal dispersion containing mono-dispersed hard particles (such as polystyrene or silica) mixed with smaller and softer polymer particles. During drying, hard particles present in the free standing film arrange in a hexagonal close-packed structure in a monolayer while the softer particles fill the interstices, and deform and coalesce to produce a continuous matrix around the hard particles. The deformation of the soft particles dissipates the stress generated during drying thereby preventing rupture of the monolayer film. The method is facile and very general, applicable to a large variety of colloidal particles. The monolayer films exhibit strong iridescence indicating potential application in photonic devices.

Modeling Evaporation and Particle Assembly in Colloidal Droplets

Evaporation-induced assembly of nanoparticles in a drying droplet is of great importance in many engineering applications, including printing, coating, and thin film processing. The investigation of particle dynamics in evaporating droplets can provide fundamental hydrodynamic insight for revealing the processing-structure relationship in the particle self-organization induced by solvent evaporation. We develop a free-energy-based multiphase lattice Boltzmann method coupled with Brownian dynamics to simulate evaporating colloidal droplets on solid substrates with specified wetting properties. The influence of interface-bound nanoparticles on the surface tension and evaporation of a flat liquid-vapor interface is first quantified. The results indicate that the particles at the interface reduce surface tension and enhance evaporation flux. For evaporating particle-covered droplets on substrates with different wetting properties, we characterize the increase of evaporate rate via measuring droplet volume. We find that droplet evaporation is determined by the number density and circumferential distribution of interfacial particles. We further correlate particle dynamics and assembly to the evaporation-induced convection in the bulk and on the surface of droplet. Finally, we observe distinct final deposits from evaporating colloidal droplets with bulk-dispersed and interface-bound particles. In addition, the deposit pattern is also influenced by the equilibrium contact angle of droplet.

Superlattice growth and rearrangement during evaporation-induced nanoparticle self-assembly

Understanding the assembly of nanoparticles into superlattices with well-defined morphology and structure is technologically important but challenging as it requires novel combinations of in-situ methods with suitable spatial and temporal resolution. In this study, we have followed evaporation-induced assembly during drop casting of superparamagnetic, oleate-capped γ-Fe₂O₃ nanospheres dispersed in toluene in real time with Grazing Incidence Small Angle X-ray Scattering (GISAXS) in combination with droplet height measurements and direct observation of the dispersion. The scattering data was evaluated with a novel method that yielded time-dependent information of the relative ratio of ordered (coherent) and disordered particles (incoherent scattering intensities), superlattice tilt angles, lattice constants, and lattice constant distributions. We find that the onset of superlattice growth in the drying drop is associated with the movement of a drying front across the surface of the droplet. We couple the rapid formation of large, highly ordered superlattices to the capillary-induced fluid flow. Further evaporation of interstitital solvent results in a slow contraction of the superlattice. The distribution of lattice parameters and tilt angles was significantly larger for superlattices prepared by fast evaporation compared to slow evaporation of the solvent.

Formation of Tough Films by Evaporation of Water from Dispersions of Elastomer Microspheres Crosslinked with Rotaxane Supramolecules

Compared to rigid microspheres that consist, for example, of polystyrene or silica, soft and deformable elastomer microspheres can be used to generate colorless transparent films upon evaporating the solvent from microsphere-containing dispersions. To obtain tough films, a post-polymerization reaction to crosslink the microspheres is usually necessary, which requires extra additives during the drying process. This restriction renders this film-formation technology complex and rather unsuitable for applications in which impurities are undesirable. In the present study, it is demonstrated that tough elastomer microspheres that are crosslinked with rotaxanes can form tough bulk films upon evaporation of water from microsphere dispersions, so that post-polymerization reactions are not required. The results of this study should thus lead to new applications including coatings for biomaterials that need complete removal of all impurities from the materials prior to use.

Evaporation of Drops Containing Silica Nanoparticles of Varying Hydrophobicities: Exploiting Particle-Particle Interactions for Additive-Free Tunable Deposit Morphology

We describe the systematic and quantitative investigation of a large number of patterns that emerge after the evaporation of aqueous drops containing fumed silica nanoparticles (NPs) of varying wettabilities for an extended particle concentration range. We show that for a chosen system, the dry pattern morphology is mainly determined by particle-particle interactions (Coulomb repulsion and hydrophobic attraction) in the bulk. These depend on both particle hydrophobicity and particle concentration within the drop. For high and intermediate particle concentrations, interparticle hydrophobic attraction is the dominant factor defining the deposit morphology. With increasing particle hydrophobicity, patterns ranging from rings to domes are observed, arising from the time needed for the drop to gel compared with the total evaporation time. On the contrary, drops of dilute suspensions maintain a finite viscosity during most of the drop lifetime, resulting in dry patterns that are predominantly rings for all particle hydrophobicities. In all investigated systems, the NP concentration corresponded to a large excess of NPs in the bulk compared with the maximal amount that could be adsorbed at available interfaces, making particle-interface interactions such as adsorption of hydrophobic NPs at the air-water interface a negligible contribution over bulk particle-particle interactions. This work emphasizes the advantage of particle surface chemistry in tuning both particle-particle interactions and particle deposition onto solid substrates in a robust manner, without the need for any additive such as a surfactant.

Stratification and Size Segregation of Ternary and Polydisperse Colloidal Suspensions during Drying

We investigate the drying process of three-component and polydisperse colloidal suspensions using Brownian dynamics simulations. We have previously reported (Phys. Rev. Lett. 2016, 116, 118301) on the drying of binary mixtures. For binary mixtures, we found that a gradient of colloidal osmotic pressure develops during drying and that this leads to the final film being stratified with a layer of smaller particles on top of a layer of larger particles. Here, we find that stratification by size is very general and also occurs in ternary and polydisperse mixtures. We name the segregation effect colloidal diffusiophoresis. In particular, we show that by changing the composition of a ternary mixture, different stratification morphologies can be achieved and hence the film properties can be tuned. In polydisperse spheres, colloidal diffusiophoresis leads to enrichment in the large particles at the bottom part of the film, whereas the top part is enriched with smaller particles. This segregation means that in the final film, the particle size distribution depends on height. Thus, the properties of the film will then depend on height. We propose a model that predicts a power-law dependence of the phoretic velocity on particle size. Results from the model and simulation show a good agreement.