Dips and rims in dried colloidal films

Drying Liquid Coatings with an Evaporation Mask: Theory and Experiments

We report a study of the spatially varying thickness of dried films of polymer solutions resulting from a nonuniform evaporation flux. The controlled heterogeneity of the evaporation flux is imposed by placing a solid mask above the evaporating film spread on a solid substrate. At the end of drying, a depression has formed under the mask, together with overthicknesses extending from the edge of the mask and over distances that may be larger than its size. By considering the flows induced in a vertically homogeneous film, we obtain analytical solutions for the thickness profiles during drying using a linear approximation in the limits of either gravity or capillarity-driven flows. We demonstrate that gravity can play a role in the deformations of the films, even if their initial thicknesses are 1 order of magnitude smaller than the capillary length. In addition, we examine two possible reference states for the linear approximation, i.e., far from the mask in the film of decreasing thickness and increasing viscosity, or under the mask where no evaporation occurs. We further compare these results with experimental ones obtained by drying thin films of polymer solutions under a mask. Both the extent and amplitude of the thickness heterogeneities of the dry film are quantitatively predicted by the linear analysis for a reference state under the mask. Our results therefore provide new insight on the patterns resulting from evaporation masks and can be generalized to minimize thickness heterogeneities in any situation in which the evaporation flux is nonuniform.

Applying droplets and films in evaporative lithography

This review covers experimental results of evaporative lithography and analyzes existing mathematical models of this method. Evaporating droplets and films are used in different fields, such as cooling of heated surfaces of electronic devices, diagnostics in health care, creation of transparent conductive coatings on flexible substrates, and surface patterning. A method called evaporative lithography emerged after the connection between the coffee ring effect taking place in drying colloidal droplets and naturally occurring inhomogeneous vapor flux densities from liquid-vapor interfaces was established. Essential control of the colloidal particle deposit patterns is achieved in this method by producing ambient conditions that induce a nonuniform evaporation profile from the colloidal liquid surface. Evaporative lithography is part of a wider field known as "evaporative-induced self-assembly" (EISA). EISA involves methods based on contact line processes, methods employing particle interaction effects, and evaporative lithography. As a rule, evaporative lithography is a flexible and single-stage process with such advantages as simplicity, low price, and the possibility of application to almost any substrate without pretreatment. Since there is no mechanical impact on the template in evaporative lithography, the template integrity is preserved in the process. The method is also useful for creating materials with localized functions, such as slipperiness and self-healing. For these reasons, evaporative lithography attracts increasing attention and has a number of noticeable achievements at present. We also analyze limitations of the approach and ways of its further development.

Substrate-Assisted Visualization of Surfactant Micelles via Transmission Electron Microscopy

The visualization of the micellar morphological evolution for surfactant has drawn much attention due to its self-assemble ability to fold into various structures. However, the direct observation of the soft materials with low atomic number has been hampered because of the poor scattering contrast and complex staining process by the traditional transmission electron microscopy (TEM) techniques. Herein, we reported a novel strategy to the visualization of surfactant micelles with the assistance of layered double hydroxides (LDHs) via TEM. Owing to the uniformly distributed metal ions and positive charges in the LDHs, the surfactant at the micelle-water interface reacted with LDHs to form a stabilized architecture through electrostatic and hydrogen-bond interactions. The morphologies of the surfactant can be clearly observed through the surfactant-LDHs architectures, exhibiting high contrast by TEM techniques. Significantly, the micellar evolutions involving the spherical, rodlike, and wormlike shapes were successfully distinguished. Our results may provide great possibilities and inspirations for the visualization for morphology of soft matters.

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.

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.

Modeling of mass transfer in a film of solution evaporating under the mask with holes

In this work, a model is developed for investigating the redistribution of colloidal particles in the film of an aqueous solution evaporating on a solid horizontal substrate under a mask with holes. Considering the characteristic horizontal film size as large and taking into account the symmetry in the arrangement of the holes in the mask the problem is solved for one film cell under a mask with a hole in its center. It is believed that vapour passes into the atmosphere only through the hole in the mask, the vapor flux density is calculated on the basis of the equation of steady-state diffusion of vapor in the atmosphere. The height-averaged velocity and volume fraction of colloidal particles are calculated using the conservation of mass, taking into account diffusion and deposition of particles onto the substrate. The calculation is performed using FlexPDE. We study the effect of the ratio of hole radius to hole spacing, the distance between the film and the mask, the diffusion, the deposition, the initial volume fraction of particles on the redistribution of particles in solution and on the substrate at the initial stage of film drying. These studies have shown that the behavior of the redistribution of particles in the solution and on the substrate depends primarily on the distance between the film and the mask, on the ratio of hole radius to hole spacing, on the diffusion coefficient of the particles. These parameters determine whether the particles will accumulate under the holes in the mask or will be distributed uniformly. The results agree with the experimental data.

Modeling Flow Coating of Colloidal Dispersions in the Evaporative Regime: Prediction of Deposit Thickness

We investigate flow coating processes, i.e., the formation of dry coatings starting from dilute complex fluids confined between a static blade and a moving substrate. In particular, we focus on the evaporative regime encountered at low substrate velocity, at which the coating flow is driven mainly by solvent evaporation in the liquid meniscus. In this regime, general arguments based on mass conservation show that the thickness of the dry film decreases as the substrate velocity increases, unlike the behavior in the well-known Landau-Levich regime. This work focuses on colloidal dispersions, which deserve special attention. Indeed, flow coating is expected to draw first a solvent-saturated film of densely packed colloids, which further dries fully when air invades the pores of the solid film. We first develop a model based on the transport equations for binary mixtures, which can describe this phenomenon continuously, using appropriate boundary conditions and a criterion to take into account pore-emptying in the colloidal film. Extensive numerical simulations of the model then demonstrate two regimes for the deposit thickness as a function of the process parameters (substrate velocity, evaporation rate, bulk concentration, and particle size). We finally derive an analytical model based on simplified transport equations that can reproduce the output of our numerical simulations very well. This model can predict analytically the two observed asymptotic regimes and therefore unifies the models recently reported in the literature.

On Localized Vapor Pressure Gradients Governing Condensation and Frost Phenomena

Interdroplet vapor pressure gradients are the driving mechanism for several phase-change phenomena such as condensation dry zones, interdroplet ice bridging, dry zones around ice, and frost halos. Despite the fundamental nature of the underlying pressure gradients, the majority of studies on these emerging phenomena have been primarily empirical. Using classical nucleation theory and Becker-Döring embryo formation kinetics, here we calculate the pressure field for all possible modes of condensation and desublimation in order to gain fundamental insight into how pressure gradients govern the behavior of dry zones, condensation frosting, and frost halos. Our findings reveal that in a variety of phase-change systems the thermodynamically favorable mode of nucleation can switch between condensation and desublimation depending upon the temperature and wettability of the surface. The calculated pressure field is used to model the length of a dry zone around liquid or ice droplets over a broad parameter space. The long-standing question of whether the vapor pressure at the interface of growing frost is saturated or supersaturated is resolved by considering the kinetics of interdroplet ice bridging. Finally, on the basis of theoretical calculations, we propose that there exists a new mode of frost halo that is yet to be experimentally observed; a bimodal phase map is developed, demonstrating its dependence on the temperature and wettability of the underlying substrate. We hope that the model and predictions contained herein will assist future efforts to exploit localized vapor pressure gradients for the design of spatially controlled or antifrosting phase-change systems.

Formation of Shear Bands in Drying Colloidal Dispersions

In directionally dried colloidal dispersions regular bands can appear behind the drying front, inclined at ±45° to the drying line. Although these features have been noted to share visual similarities with shear bands in metal, no physical mechanism for their formation has ever been suggested, until very recently. Here, through microscopy of silica and polystyrene dispersions, dried in Hele-Shaw cells, we demonstrate that the bands are indeed associated with local shear strains. We further show how the bands form, that they scale with the thickness of the drying layer, and that they are eliminated by the addition of salt to the drying dispersions. Finally, we reveal the origins of these bands in the compressive forces associated with drying, and show how they affect the optical properties (birefringence) of colloidal films and coatings.

Surface patterns in drying films of silica colloidal dispersions

We report an experimental study on the drying of silica colloidal dispersions. Here we focus on surface instability occurring in a drying paste phase before crack formation which affects the final film quality. Observations at macroscopic and microscopic scales reveal the occurrence of instability, and the morphology of the film surface. Furthermore, we show that the addition of adsorbing polymers on silica particles can be used to suppress the instability under particular conditions of molecular weight and concentration. We relate this suppression to the increase of the paste elastic modulus.

Droplet pattern and condensation gradient around a humidity sink

We describe the evolution of a water drop saturated with NaCl and the growth of pure water droplets in a breath figure pattern (BF) condensing around it. This salty drop acts as a humidity sink, inhibiting the BF inside a ring at a distance r=δ from the sink center and slowing down BF growth outside the ring. The initial salty drop is taken either from a salt-saturated solution (type I experiment) or by placing an NaCl crystal on the substrate (type II experiment). The results are similar, provided that the initial time for type II evolution is taken at the end of the crystal dissolution. The evolution of the salty drop radius R is deduced from the establishment of a three-dimensional hyperbolic concentration profile around the salty drop. This profile scales with r/δ. Accounting for the salt concentration decrease with salty drop growth, R is seen to grow as t5. In the region r>δ, water droplets nucleate and grow. The rate of evolution of the water droplets at constant r/δ can be used to determine the local water pressure. The corresponding data reasonably agree with a hyperbolic water vapor profile around the salty drop. These results can be applied to the growth of BF patterns to determine whether hyperbolic or linear water vapor profiles apply.

Drying of thin colloidal films

When thin films of colloidal fluids are dried, a range of transitions are observed and the final film profile is found to depend on the processes that occur during the drying step. This article describes the drying process, initially concentrating on the various transitions. Particles are seen to initially consolidate at the edge of a drying droplet, the so-called coffee-ring effect. Flow is seen to be from the centre of the drop towards the edge and a front of close-packed particles passes horizontally across the film. Just behind the particle front the now solid film often displays cracks and finally the film is observed to de-wet. These various transitions are explained, with particular reference to the capillary pressure which forms in the solidified region of the film. The reasons for cracking in thin films is explored as well as various methods to minimize its effect. Methods to obtain stratified coatings through a single application are considered for a one-dimensional drying problem and this is then extended to two-dimensional films. Different evaporative models are described, including the physical reason for enhanced evaporation at the edge of droplets. The various scenarios when evaporation is found to be uniform across a drying film are then explained. Finally different experimental techniques for examining the drying step are mentioned and the article ends with suggested areas that warrant further study.

Patterned surfaces in the drying of films composed of water, polymer, and alcohol

A study of the complex drying dynamics of polymeric mixtures with optical microscopy and gravimetric measurement is presented. Droplet formation is observed, followed by a collapse that leads to the residual craters in the dried film. The process is followed in situ under well-defined temperature and hygrometric conditions to determine the origin and nature of these droplets and craters. The drying process is usually completed within 1 h. The observations are explained using a simple diffusion model based on experimental results collected from mass and optical measurements as well as Raman confocal microspectrometry. Although the specific polymeric mixtures used here are of interest to the cosmetic industry, the general conclusions reached can apply to other polymeric aqueous solutions with applications to commercial and artistic painting.

Drying dip-coated colloidal films

We present the results from a small-angle X-ray scattering (SAXS) study of lateral drying in thin films. The films, initially 10 μm thick, are cast by dip-coating a mica sheet in an aqueous silica dispersion (particle radius 8 nm, volume fraction ϕ(s) = 0.14). During evaporation, a drying front sweeps across the film. An X-ray beam is focused on a selected spot of the film, and SAXS patterns are recorded at regular time intervals. As the film evaporates, SAXS spectra measure the ordering of particles, their volume fraction, the film thickness, and the water content, and a video camera images the solid regions of the film, recognized through their scattering of light. We find that the colloidal dispersion is first concentrated to ϕ(s) = 0.3, where the silica particles begin to jam under the effect of their repulsive interactions. Then the particles aggregate until they form a cohesive wet solid at ϕ(s) = 0.68 ± 0.02. Further evaporation from the wet solid leads to evacuation of water from pores of the film but leaves a residual water fraction ϕ(w) = 0.16. The whole drying process is completed within 3 min. An important finding is that, in any spot (away from boundaries), the number of particles is conserved throughout this drying process, leading to the formation of a homogeneous deposit. This implies that no flow of particles occurs in our films during drying, a behavior distinct to that encountered in the iconic coffee-stain drying. It is argued that this type of evolution is associated with the formation of a transition region that propagates ahead of the drying front. In this region the gradient of osmotic pressure balances the drag force exerted on the particles by capillary flow toward the liquid-solid front.