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Effects of the evaporation rate on the segregation in drying bimodal colloidal suspensions
Applied Physics Letters
Abstract
When suspensions containing colloidal particles of two different sizes are coated on substrates to form films by evaporating the host fluids, the smaller particles can segregate to the top surface of the films. We investigate the effects of the evaporation rate on the segregation by use of Langevin dynamics simulations. The evaporation rate is scaled by the Brownian diffusion rate of the particles, yielding a dimensionless number which we define as the particle drying Péclet number. We show that there is a Péclet number at which the segregation is the most enhanced. Our result indicates the need for the regulation of the evaporation rate to control the segregation.
... Toward this end, numerical simulation is an effective method to visualize the microstructures and to evaluate their structural color. The structure formation in drying colloidal suspensions coated on substrates has been investigated by numerical simulations solving the motion of colloidal particles, 8,[11][12][13][18][19][20][21][22][23][24] such as Langevin dynamics and molecular dynamics. The relationship between the microstructures and structural color has also recently been investigated by the finite-difference time-domain (FDTD) simulations of electromagnetic field analysis for the microstructures formed by molecular dynamics, 16,17 where they have focused only on the structure formation of repulsive particles driven by condensation during drying, without considering the roles of attractive colloidal interactions and capillary interactions as in many previous studies. ...
... The relationship between the microstructures and structural color has also recently been investigated by the finite-difference time-domain (FDTD) simulations of electromagnetic field analysis for the microstructures formed by molecular dynamics, 16,17 where they have focused only on the structure formation of repulsive particles driven by condensation during drying, without considering the roles of attractive colloidal interactions and capillary interactions as in many previous studies. [11][12][13][21][22][23] In this Letter, we first perform Langevin dynamics simulations including these interactions and then perform FDTD simulations calculating the reflectance spectra of the obtained microstructures to discuss how the material and operational parameters to be set to improve the intensity of structural color originating from the Bragg diffraction. As material parameters, we focus on the surface tension of the solvent and the Hamaker constant depending on the material combination of particles and solvent. ...
... We describe the Brownian motion of the particles by the Langevin equations and solve them numerically. The velocity v i and the position r i of the i-th particle evolve with time according to the following equation: 8,[18][19][20]23,24 ...
Colloidal assembly formed by drying of suspensions is expected to be applied to optical materials using their structural color resulting from the microstructure. We combine two numerical simulation techniques to investigate how the fabrication conditions of the self-assembled colloidal films affect their structural color. We first perform Langevin dynamics simulations to form colloidal films with various microstructures depending on the several fabrication parameters and then perform the finite-difference time-domain simulations of electromagnetic field analysis to calculate the structural color intensity of the obtained microstructures. To improve the structural color intensity, we show that the surface tension of the solvent should be sufficiently large so that capillary interactions exceed the interparticle adhesion by van der Waals force and furthermore that under this condition the smaller drying rate is favorable. This study suggests a guideline to design the fabrication process of colloidal films generating structural color.
... The drying characteristics of respiratory droplets plays an important role in determining the fate and transmissibility of respiratory viruses including the COVID-19 virus responsible for the ongoing pandemic [17,18]. Because of its practical importance and rich nonequilibrium physics [4,19], many efforts have been devoted to elucidate the fundamental processes and mechanisms of drying for soft matter solutions [3,20], including molecular dynamics simulations [15,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. ...
... Recently, implicit solvent models have been applied to study the evaporation process of particle suspensions and polymer solutions and reveal many interesting phenomena induced by drying [26][27][28][29][30][33][34][35]38]. Fortini et al. used Langevin dynamics simulations based on an implicit solvent model to study the drying of a bidisperse colloidal suspension film and demonstrated the counterintuitive "small-on-top" stratification in which the smaller particles are predominately distributed on top of the larger particles after drying [26,27]. ...
... Fortini et al. used Langevin dynamics simulations based on an implicit solvent model to study the drying of a bidisperse colloidal suspension film and demonstrated the counterintuitive "small-on-top" stratification in which the smaller particles are predominately distributed on top of the larger particles after drying [26,27]. Tatsumi et al. used a similar model to investigate the role of evaporation rates on stratification [35]. Howard et al. and Statt et al. employed this approach to simulate the drying of colloidal suspensions [30], colloidal mixtures [28], polymer-colloid mixtures [29], polymer-polymer mixtures [29,34], and polydisperse polymer mixtures [33], and observed stratifying phenomena as well. ...
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.
... Neglects environmental characteristics such as temperature and dielectric constant, limited in considering force fields such as friction and collision forces Langevin dynamics None [13,[30][31][32][33][34][35][36] [ 13,30,32] Particle dynamics evolution with time, realistic molecular systems Oversimplified hydrodynamic interactions between solvent and particles Brownian dynamics [37] [ 38] [ 38] Particle dynamics evolution with time, realistic molecular systems Neglects inertial effects, oversimplified hydrodynamic interactions between solvent and particles Stokesian dynamics None [39] [ 39] Particle dynamics evolution with time, realistic molecular systems, full consideration of force fields ...
... Evaporation rate: Fortini et al. [36] did not investigate how evaporation rate affects stratification in the regime where Péclet numbers for both small and large particles are much larger than 1. Inverted stratification has been studied using both molecular dynamics [27] and Langevin dynamics models [33,35] that considered the effects of different evaporation rates on stratification. ...
... In addition, larger size ratios resulted in thicker stratified layers. Tatsumi et al. [35] and Cusola et al. [33] obtained similar results using Langevin dynamics simulations. Tatsumi et al. [35] explained that the inverted stratification was caused by larger particles being pushed away from the evaporating interface by local accumulation of smaller particles. ...
Dispersion drying is an essential step in an enormous number of research and industry fields, including self-assembly, membrane fabrication, printing, battery electrode fabrication, painting, and large-scale solar cell fabrication. The drying process of a dispersion directly influences the structure and properties of the resulting dried film. Thus, it is important to investigate the underlying physics of dispersion drying and the effects of different drying parameters. This article reviews modeling studies of coating drying processes, along with corresponding experimental observations. We have divided drying processes into two conceptual stages. In the first drying stage, liquid evaporation, particle sedimentation and Brownian motion compete and affect the particle distribution during drying and thus in the final film structure. We have included a comprehensive discussion of the influences of drying parameters, such as evaporation rate, particle sizes and temperature, on the above competition and the resulting film structure. A drying regime map describing where different drying phenomena dominate was formulated based on the literature. We also extended our discussion to the practical applications of battery slurry drying an essential step in conventional battery electrode manufacturing. In the second drying stage, the physics of porous drying and crack formation are reviewed. This review aims to provide a comprehensive understanding of dispersion drying mechanisms and to provide guidance in the design of film products with favorable structures and properties for targeted practical applications.
... Mixtures of two or more types of nanoparticles can lead to additional control over the surface composition and separation between particles, potentially tuning the absorption and contrast. It is thus critical to understand how and why binary nanoparticles assemble at surfaces/interfaces. Stratification of binary mixtures of varying particle sizes during evaporative film formation has been studied via both experiments and simulations (25)(26)(27)(28)(29)(30)(31)(32); these studies have comprehensively mapped the set of particle size ratios, evaporation rates, and mixture compositions to either encourage or suppress surface stratification in films composed of particles with the same surface chemistry. However, to the best of our knowledge, no such complementary work exists for particle mixtures of varying chemistry or for the emulsion assembly process. ...
... This demonstrates that, in the mixtures studied herein, smaller SPs do not segregate at the film surfaces, in contrast to those in the binary SP supraballs. We note that previous work from the literature suggests that increasing the large/small size ratio or modifying the evaporation rate can produce stratification in films (31,32), but given the moderate small/large size ratios (1.36 to 2.15) and slow evaporation rates in this study, the lack of film stratification is unsurprising. ...
... We used implicit-solvent CG-MD simulations to study the assembled supraball and film structures over experimentally relevant micrometer length scales, which would not be possible using explicitsolvent MD simulation models that have been used to understand particle assembly at liquid/liquid (41)(42)(43)(44) and liquid/vapor interfaces (45)(46)(47) at much smaller length scales. Such implicit-solvent approaches have been widely applied to study stratification in the evaporative film assembly process (25,26,31,32), which we adapt to mimic the emulsion assembly. Here, we chose particle-particle and particle-interface interaction potentials to mimic the impact of the solvent and fluidfluid interfaces on the particle assembly. ...
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 ( Dlarge/Dsmall ) 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.
... The stratifying phenomena in drying suspensions of polydisperse particles have recently attracted great interest since the clear demonstration of the counterintuitive "small-on-top" stratification by Fortini et al., 1 where smaller particles are found to be enriched at the evaporating surface and distributed on top of larger particles after very fast drying. Since then, a burgeoning number of papers have appeared on the physical mechanisms underlying stratification [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and possible approaches of its control. 2,19 The current physical picture for understanding stratification is based on the competition between the accumulation of particles at a receding liquid-vapor interface during evaporation and their diffusion away from the interface. ...
... 18 Molecular modeling has played an important role in the process of discovering and revealing the fundamental physics of stratification. 1,2,[5][6][7]11,13,15 Fortini et al. conducted Langevin dynamics simulations to unequivocally establish the occurrence of "small-on-top" stratification during fast drying in bidisperse particle suspensions. 1,2,7 Howard et al. adopted a similar method and combined it with a dynamical density functional theory to show that "small-on-top" stratification is enhanced when the particle size ratio α is increased. ...
... 5,6 Tatsumi et al. performed Langevin dynamics simulations for α = 1.5, 2, and 4 with particle-particle interactions described by the Hertzian theory of a nonadhesive elastic contact and showed that segregation is most enhanced at an intermediate value of Pe l . 11 In all these studies, the solvent was treated as a continuous, viscous, and isothermal background with hydrodynamic flow ignored, which is consistent with the assumption usually made in phenomenological theories of stratification. 1,3 However, the recent analyses of Sear and Warren showed that the solvent backflow around a migrating particle may be important and theories neglecting it may substantially overestimate stratification. ...
Large scale molecular dynamics simulations are used to study drying suspensions of a binary mixture of large and small particles in explicit and implicit solvents. The solvent is first modeled explicitly and then mapped to a uniform viscous medium by matching the diffusion coefficients and the pair correlation functions of the particles. "Small-on-top" stratification of the particles, with an enrichment of the smaller ones at the receding liquid-vapor interface during drying, is observed in both models under the same drying conditions. With the implicit solvent model, we are able to model much thicker films and study the effect of the initial film thickness on the final distribution of particles in the dry film. Our results show that the degree of stratification is controlled by the Péclet number defined using the initial film thickness as the characteristic length scale. When the Péclet numbers of large and small particles are much larger than 1, the degree of "small-on-top" stratification is first enhanced and then weakens as the Péclet numbers are increased.
... The one-sided limit approximation is used extensively in the literature on drying colloidal blends. 6,27,40 One could extend our model by incorporating more of the physics of evaporation, for example, by treating the effects of diffusion in the vapor 42 or by using the Hertz−Knudsen relation 43 to relate the evaporation rate to the environmental conditions. Thus, we assume that the distance between the two interfaces depends on time as follows: ...
... This observation is in line with the work of Tatsumi et al., who reported the existence of optimal Pećlet numbers above and below which the size segregation is not as efficient. 40 Note also that Figure 3d shows that the number of big particles right at the interfaces increases as time progresses. This buildup is due to the fact that the total density is increasing over time, and so the depletion interaction between the big particles and the interface also over time increases in strength. ...
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.
... To quantify the formation of a dense colloidal lm, one could turn to particle dynamics simulations that account for the nite size of particles. Some recent work has been done in this direction [74][75][76][77][78][79] but, to the authors' knowledge, the electrophoretic component of diffusiophoresis has been ignored. It will be of interest to conduct particle dynamics simulations that include complete diffusiophoresis and compare with present results for the development of a reduced-order model. ...
Recent experiments (K. Inoue and S. Inasawa, RSC Adv., 2020, 10, 15763-15768) and simulations (J.-B. Salmon and F. Doumenc, Phys. Rev. Fluids, 2020, 5, 024201) demonstrated the significant impact of gravity on unidirectional drying of a colloidal suspension. However, under gravity, the role of colloid transport induced by an electrolyte concentration gradient, a mechanism known as diffusiophoresis, is unexplored to date. In this work, we employ direct numerical simulations and develop a macrotransport theory to analyze the advective-diffusive transport of an electrolyte-colloid suspension in a unidirectional drying cell under the influence of gravity and diffusiophoresis. We report three key findings. First, drying a suspension of solute-attracted diffusiophoretic colloids causes the strongest phase separation and generates the thinnest colloidal layer compared to non-diffusiophoretic or solute-repelled colloids. Second, when colloids are strongly solute-repelled, diffusiophoresis prevents the formation of colloid concentration gradient and hence gravity has a negligible effect on colloidal layer formation. Third, our macrotransport theory predicts new scalings for the growth of the colloidal layer. The scalings match with direct numerical simulations and indicate that the colloidal layer produced by solute-repelled diffusiophoretic colloids could be an order of magnitude thicker compared to non-diffusiophoretic or solute-attracted colloids. Our results enable tailoring the separation of colloid-electrolyte suspensions by tuning the interactions between the solvent, electrolyte, and colloids under Earth's or microgravity, which is central to ground-based and in-space applications.
... The particles can outrun the descending interface to yield a more homogeneous distribution of particles during drying. If two differently sized particles are mixed together into a single dispersion (i.e., large (L) and small (S) particles) and have Pe L > Pe S > 1, the stratification of small particles on the top surface was discovered in both experimental and computational work, [20][21][22][23][24][25][26][27]33 as is illustrated in Figure 1b. ...
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.
... Interestingly, the Langevin dynamics simulation conducted by Tatsumi et al. further showed that, at a given particle size ratio, the evaporation rate does not affect this stratification monotonically. 49 There exists an optimal Péclet number at which the "small-on-top" stratification is mostly enhanced. Apparently, this behavior cannot be explained based only on the difference in the particle Péclet numbers because it would predict a "large-on-top" structure. ...
The diffusion of colloids, nanoparticles, and small molecules near the gas–liquid interface presents interesting multiphase transport phenomena and unique opportunities for understanding interactions near the surface and interface. Stratification happens when different species preside over the interfaces in the final dried coating structure. Understanding the principles of stratification can lead to emerging technologies for materials’ fabrication and has the potential to unlock innovative industrial solutions, such as smart coatings and drug formulations for controlled release. However, stratification can be perplexing and unpredictable. It may involve a complicated interplay between particles and interfaces. The surface chemistry and solution conditions are critical in determining the race of particles near the interface. Current theory and simulation cannot fully explain the observations in some experiments, especially the newly developed stratification of nano-surfactants. Here, we summarize the efforts in the experimental work, theory, and simulation of stratification, with an emphasis on bridging the knowledge gap between our understanding of surface adsorption and bulk diffusion. We will also propose new mechanisms of stratification based on recent observations of nano-surfactant stratification. More importantly, the discussions here will lay the groundwork for future studies beyond stratification and nano-surfactants. The results will lead to the fundamental understanding of nanoparticle interactions and transport near interfaces, which can profoundly impact many other research fields, including nanocomposites, self-assembly, colloidal stability, and nanomedicine.
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.
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.
The non-equilibrium assembly of bimodal colloids during evaporative processes is an increasingly attractive means to achieve gradient or stratified layers in thick films. Here, we show that the stratification of...
This study focuses on determining fabrication conditions to create high-performance roll-to-roll-coated (R2R-coated) gas-diffusion electrodes (GDEs) for proton-exchange-membrane fuel cells (PEMFCs). Here, we examine how process conditions influence the distribution of ionomer in the electrode, which is shown to be critical for high performance. Using a combination of Kelvin probe, X-ray photoelectron spectroscopy, and nano-scale X-ray computed tomography we show that formation of an ionomer-rich surface is promoted by using a higher drying rate. We show that R2R-coated GDEs have higher surface ionomer concentration than spray-coated GDEs, which enables these R2R-coated GDEs to not need an additional ionomer overlayer, as is typically the case for spray-coated GDEs. This will reduce the number of processing steps and lower material costs in a manufacturing setting. This work shows that with the appropriate selection of materials, ink formulation, and processing conditions, direct-coated GDEs are a viable pathway for fuel cell manufacturing.
Colloidal suspensions are coated on substrates and upon drying produce various functional materials. The non-equilibrium structure formation of colloidal particles is induced during coating and drying’ affecting operational efficiency and material performance. To understand the relation between operation conditions and structure formation, we have developed a simulator of colloidal suspensions, SNAP. We discuss the non-equilibrium structure formation through the results calculated by SNAP.
Depositing inks on a planar substrate by printing is a facile way to fabricate conductive traces and other complicated functional devices. However, irrespective of the printing methods used, the thickness of the inks has an upper limit due to their fluidic property and subsequent wetting on the substrates. Herein, we present a method for creating high-aspect ratio conductive traces by combining hot-embossing and gravure doctoring techniques. Binary-sized colloidal pastes containing Ag nanoparticles and micrometer-sized spherical Ag powder additives were filled using a doctor blade in the grooves of polycarbonate (PC) films inscribed via hot-embossing to create buried traces. Under optimal mixing conditions in which the minimum resistivity was achieved, voids between the microparticles provided a pathway for the volatile solvents to smoothly escape from the filled ink and minimized thickness reduction during the thermal sintering process. A fabricated trace buried in the PC film with an aspect ratio of around 3:1 and a linewidth of 55 μm showed extremely low resistance of less than 10 Ω/m. A flexible transparent heater was developed using the reported binary colloidal paste.
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.
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.
Wrinkles formed during the drying of polymer films by hot-air flow but not when drying by infrared irradiation, even though drying rates were comparable. The top surface was hotter than the bottom during hot-air drying. Conversely, the temperatures of the top and bottom surfaces were very similar when drying by infrared irradiation. We also examined uniform heating with faster and slower drying rates using drying with combined infrared irradiation and air flow (hot or room temperature). Wrinkles formed in both cases. This demonstrated the negative effect of air flow. Features and mechanism of each drying method are discussed.
In drying liquid films of polymer–colloid mixtures, stratification in which polymers are placed on top of larger colloids is studied. It is often presumed that the formation of segregated polymer–colloid layers is solely due to the proportion in size at fast evaporation as in binary colloid mixtures. By comparing experiments with a theoretical model, we found that the transition in viscosity near the drying interface was another important parameter for controlling the formation of stratified layers in polymer–colloid mixtures. At high evaporation rates, increased polymer concentrations near the surface lead to a phase transition from a semidilute to concentrated regime, in which colloidal particles are kinetically arrested. Stratification only occurs if the formation of a stratified layer precedes the evolution to the concentrated regime near the drying interfaces. Otherwise, the colloids will be trapped by the polymers in the concentrated regime before forming a segregated layer. Also, no stratification is observed if the initial polymer concentration is too low to form a sufficiently high polymer concentration gradient within a short period of time. Our findings are relevant for developing solution-cast polymer composites for painting, antifouling and antireflective coatings.
Achieving control over the distribution of biocides across the thickness of polymer nanocomposite films is one of the largest challenges to develop efficient antibacterial surfaces. In such applications, it is key to maximize the biocide presence at the film top surface to ensure contact with bacteria. Here, we make use of evaporation driven colloidal self-assembly to control the vertical distribution of biocides in polymer composite films cast from colloidal blends of polymer and zinc oxide (ZnO) nanoparticles. We present a thorough study which shows that the evaporation rate and ZnO volume fraction have a strong impact on the final film architecture and on its wetting and antibacterial properties. For high enough ZnO volume fraction, the ZnO nanoparticles assemble in superstructures on top of the film, which are higher the slower the evaporation rate used, and maximum ZnO surface coverage achieved through slow film drying. At high ZnO volume fraction (ϕ=0.29), the zone of inhibition diameter against E. Coli increases as evaporation rate decreases, with the nanocomposite films having the strongest antibacterial activity when formed at slow evaporation rate. We propose a model for the formation of these colloidal superstructures based on the segregation of large (polymer) and small (ZnO) particles during drying, followed by the assembly of small particles around packed large particles due to differences in the surface charge of the two populations. Our work provides valuable guidelines for the design and assembly of not only antibacterial colloidal films, but of a wider range of functional colloidal polymer films including abrasion resistant, self-cleaning and others.
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 using 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. Towards 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. 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.
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.
The distribution of hydrophilic species, such as surfactants, in latex films is of critical importance for the performance of adhesives, coatings and inks, among others. However, the evolution of this distribution during the film formation process and in the resulting dried films remains insufficiently elucidated. Here, we present in situ (wet) and ex situ (dry) SANS experiments that follow the film formation of two types of latex particles, which differ in their stabilizer: either a covalently bonded poly(methacrylic acid) (PMAA) segment or a physically adsorbed surfactant (sodium dodecyl sulfate, SDS). By fitting the experimental SANS data and combining with gravimetry experiments, we have ascertained the hydrophilic species distribution within the drying film and followed its evolution by correlating the size and shape of stabilizer clusters with the drying time. The evolution of the SDS distribution over drying time is being driven by a reduction in the interfacial free energy. However, the PMAA-based stabilizer macromolecules are restricted by their covalent bonding to core polymer chains and hence form high surface-area disc-like phases at the common boundary between particles and PMAA micelles. Contrary to an idealized view of film formation, the PMAA does not remain in the walls of a continuous honeycomb structure. The results presented here shed new light on the nanoscale distribution of hydrophilic species in drying and ageing latex films. We provide valuable insights into the influence of the stabilizer mobility on the final structure of latex 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 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.
When films are deposited from mixtures of colloidal particles of two different sizes, a diverse range of functional structures can result. One structure of particular interest is a stratified film in which the top surface layer has a composition different than in the interior. Here, we explore the conditions under which a stratified layer of small particles develops spontaneously in a colloidal film that is cast from a binary mixture of small and large polymer particles that are suspended in water. A recent model, which considers the cross-interaction between the large and small particles (Zhou et al., Phys. Rev. Lett., 2017, 118, 108002), predicts that stratification will develop from dilute binary mixtures when the particle size ratio (α), initial volume fraction of small particles (ϕS), and Péclet number are high. In experiments and Langevin dynamics simulations, we systematically vary α and ϕS in both dilute and concentrated suspensions. We find that stratified films develop when ϕS is increased, which is in agreement with the model. In dilute suspensions, there is reasonable agreement between the experiments and the Zhou et al.
Model:
In concentrated suspensions, stratification occurs in experiments only for the higher size ratio α = 7. Simulations using a high Péclet number, additionally find stratification with α = 2, when ϕS is high enough. Our results provide a quantitative understanding of the conditions under which stratified colloidal films assemble. Our research has relevance for the design of coatings with targeted optical and mechanical properties at their surface.
When a rigid colloidal particle is placed in a solution which is not uniform in the concentration of some solute that interacts with the particle, the particle will be propelled in the direction of higher or lower concentration of the solute. The resulting locomotion is called diffusiophoresis. Experimental observations and theoretical predictions of the migration velocity of hydrosoIs are reviewed. Present commercial applications include the formation of rubber gloves and the deposition of paint films onto a steel surface. New applications to the analysis of colloidal mixtures and solid-liquid separation are suggested.
Lagrangian-type numerical simulation was carried out on plug flow of cohesionless, spherical particles conveyed in a horizontal pipe. The motion of individual particles contacting each other was calculated using the equations of motion and a modified Cundall model. Forces between particles were expressed by using the Hertzian contact theory. The Ergun Equation was applied to give the fluid force acting on particles in a moving or stationary bed.The flow patterns obtained in the present work appear to be realistic. The wave-like motion of the flow boundary reported previously by several other researchers was observed clearly in the simulation. Also, good agreement was obtained for the relation between the height of the stationary deposited layer and the plug flow velocity. Due to the limitations of computation time, only the case of large particles (ie. d > 10 mm) could be considered here.
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.
By means of Brownian Dynamics simulations, we investigate the drying process of three component and polydisperse colloidal suspensions. We have previously reported [Phys. Rev. Lett. 116 p.118301 (2016)] 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 the smaller particles on top of a layer of the larger particles. Here, we find that stratification by size is very general, and also occurs in ternary and polydisperse mixtures. We name the segregation mechanism colloidal diffusiophoresis. In particular, we show that by changing the composition of a ternary mixture, you can achieve different stratification morphologies, and so tune the film properties. In polydisperse spheres, colloidal diffusiophoresis leads to an enrichment in the large particles at the bottom part of the film, while the top part is enriched in the smaller particles. This segregation means that in the final film, the particle size distribution depends on height. Thus 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 good agreement.
Stratification in binary colloidal mixtures was investigated using implicit-solvent molecular dynamics simulations. For large particle size ratios and film P?clet numbers greater than unity, smaller colloids migrated to the top of the film, while big colloids were pushed to the bottom, creating an "inverted" stratification. This peculiar behavior was observed in recent simulations and experiments conducted by Fortini et al. (Phys. Rev. Lett. 2016, 116, 118301). To rationalize this behavior, particle size ratios and drying rates spanning qualitatively different P?clet number regimes were systematically studied, and the dynamics of the inverted stratification were quantified in detail. The stratified layer of small colloids was found to grow faster and to larger thicknesses for larger size ratios. Interestingly, inverted stratification was observed even at moderate drying rates where the film P?clet numbers were comparable to unity, but the thickness of the stratified layer decreased. A model based on dynamical density functional theory is proposed to explain the observed phenomena.
When a liquid film of colloidal solution consisting of particles of different sizes is dried on a substrate, the colloids often stratify, where smaller colloids are laid upon larger colloids. This phenomenon is counter intuitive because larger colloids which have smaller diffusion constant are expected to remain near the surface during the drying process, leaving the layer of larger colloids on top of smaller colloids. Here we show that the phenomenon is caused by the interaction between the colloids, and can be explained by the diffusion model which accounts for the interaction between the colloids. By studying the evolution equation both numerically and analytically, we derive the condition at which the stratified structures are obtained.
In simulations and experiments, we study the drying of films containing mixtures of large and small colloidal particles in water. During drying, the mixture stratifies into a layer of the larger particles at the bottom with a layer of the smaller particles on top. We developed a model to show that a gradient in osmotic pressure, which develops dynamically during drying, is responsible for the segregation mechanism behind stratification.
A three-dimensional structure formation simulator of colloidal nanoparticles during drying is developed. Motion of the nanoparticles is modeled by Langevin equation, in which forces exerted on each nanoparticle consist of contact force, capillary force, Brownian force, van der Waals force, electrostatic force and fluid drag force. Drying of the colloid is expressed by a decrease of the 'thickness of a colloid film. The present simulator is applied to a drying process of the colloid film on a flat substrate, so that a multilayer structure of nanoparticles is formed. The structure formation is visualized with time, and the vertical and the planar structure of nanoparticles are evaluated temporally and quantitatively. The result indicates a mechanism of multilayer structure formation of colloidal nanoparticles during drying.
A simulation model of concentrated colloidal rod-like nanoparticles is developed. As the governing equation of motion of a nanoparticle, the Langevine equation with external force is used. The external force includes capillary force, contact force, electrostatic force, van der Waals force, and elastic force which occurs inside an elastic rod. Numerical simulations are performed for the system of concentrated colloidal rod-like nanoparticles, which experiences solvent evaporation with a constant rate. Consequently, some structures of self-organized rod-like nanoparticles are obtained for the specified aspect ratios. The time evolution of the system is quantitatively analyzed by using the orientational order parameter and the non-dimensional boundary area. Moreover the two quantities are found to resolve the structures obtained in the simulation.
Key microstructural properties of particulate coatings such as porosity and particle order are established during drying. Therefore, understanding the evolution of particulate distributions during drying is useful for designing coating properties. Here, a 1D model is proposed for the particle distribution through the coating thickness at different drying times and conditions, including Brownian diffusion, sedimentation, and evaporation. Effects of particle concentration on diffusion and sedimentation rates are included. Results are condensed onto a drying regime map which predicts the presence of particle surface accumulation or sediment based on two dimensionless numbers: the Peclet number and the sedimentation number. Cryogenic scanning electron microscopy (cryoSEM) is used to image the transient particulate distributions during the drying of a model system comprised of monodisperse silica particles in water. Particle size and evaporation rates are altered to access various domains of the drying map. There is good agreement between cryoSEM observations and model predictions. © 2010 American Institute of Chemical Engineers AIChE J, 2010
The mechanism by which the particles in a drying film come into close packing during solvent evaporation has an important role to play in the final film morphology. During drying the particles can develop non-uniform concentrations across the vertical height of the film, depending on their diffusion rate. By applying the principles of classical diffusion mechanics to a hard sphere system, a theory for this novel method of stratification during drying of a two component film has been derived. The model is dependent on the particle Peclet numbers and when one is above unity and the other below, maximum stratification is observed.
In films cast from a colloidal dispersion comprising two particle sizes, we experimentally examine the distribution of particles normal to the substrate. The particle concentrations at various positions in the film are determined through atomic force microscopy and NMR profiling. The results are compared to a previously derived diffusional model. Evidence for diffusional driven stratification is found, but the importance of other flows is also highlighted. The conditions that enhance particle stratification are found to be a colloidally stable dispersion, low initial volume fractions, a low concentration of the stratifying particle, and for the Peclet numbers of the two components to straddle unity.
Ceramic nanoparticle/monodisperse latex coatings with a nanoparticle-rich surface and a latex-rich body were created by depositing aqueous dispersions of monodisperse latex, approximately 550 nm in diameter, and nanosized ceramic particles onto substrates and drying. On the top surface of the dried coating, the latex particles are closely packed with nanoparticles uniformly occupying the interstitial spaces, and along the cross section, nanoparticles fill the spaces between the latex particles in the near surface region; a compacted latex structure, nearly devoid of nanoparticles, lies beneath. Cryogenic scanning electron microscopy images of partially dried coatings at successive drying stages reveal two important steps in forming this structure: top-down consolidation of latex particles and accumulation of nanoparticles in interstitial spaces among latex particles near the surface. A systematic study of the effect of processing conditions, including nanoparticle concentration, nanoparticle size, latex glass transition temperature, and drying conditions, on the final microstructure was carried out. The unique microstructure described above forms when the monodisperse latex is large enough to create pore channels for the transport of nanosized particles and the drying conditions favor "top-down" as opposed to "edge-in" drying.