Structure Formation in Soft Matter Solutions Induced by SolventEvaporation

Jiajia Zhou 1,3,†, Xingkun Man 2,3,†, Ying Jiang 1,3,†, and Masao Doi 3,4,∗

1 Key Laboratory of Bio-inspired Smart Interfacial Science and Technology ofMinistry of Education, School of Chemistry, Beihang University, Beijing

100191, China2 School of Physics and Nuclear Energy Engineering, Beihang University,

Beijing 100191, China3 Center of Soft Matter Physics and Its Applications, Beihang University,

Beijing 100191, China4 Beijing Advanced Innovation Center for Biomedical Engineering, Beihang

University, Beijing 100191, China

∗ corresponding author: masao.doi@buaa.edu.cn† equal contribution

AbstractSolvent evaporation in soft matter solutions (solutions of colloidal par-

ticles, polymers and their mixtures) is an important process in materialmaking and in printing and coating industries. The solvent evaporationprocess determines the structure of the materials, and strongly affectstheir performance. Solvent evaporation involves many physico-chemicalprocesses: flow, diffusion, crystallization, gelation, glass transition, etc.,and is quite complex. In this article, we report recent progresses in thisimportant process, with a special focus on theoretical and simulation stud-ies.

1 Introduction

Solvent evaporation is a phenomenon we see in our daily life. One can observethis phenomenon when watching the drying paint [1] or the ring-like deposit ofcoffee stain. [2, 3] It is a process widely used in many industries: chemical, ma-terial, food, and pharmaceutical industries. It is also important in technologicalfrontiers, such as large-scale manufacture of device by printing and coating, anddevelopment of advanced materials.

Solvent evaporation is generally considered to be a process of diffusion, thetransport of nonvolatile solvents driven by chemical potential gradient createdby the evaporation. However, the process is intrinsically non-equilibrium, andthe simplicity in the practical procedure sometimes disguises the complexity ofthe underlying mechanisms. The drying phenomenon actually involves manyphysico-chemical processes such as flow, diffusion, phase separation, crystalliza-tion, gelation, glass transition, etc., and the interplay between different processesdetermines the final structure of the dried materials.

In this Research News, we report recent advances of self-assembled struc-tures induced by uniform evaporation, examples including drying in a thin-film

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geometry or evaporating a spherical droplet on a superhydrophobic surface. [4]In this situation, the structure formation takes place in the direction of the evap-oration. This excludes the case where lateral flow is induced by non-uniformdrying. The lateral flow is important in explaining the coffee-ring effect, whereexcellent reviews exist in literature. [5, 6] After introducing the general pro-cedure in experiments, we explain the physical mechanisms responsible for thestructure formation in solvent evaporation. We then discuss recent advancesbased on single- and binary-component solutions, with a special emphasis onthe theoretical approaches.

2 Drying of single-component solutions

A general experiment starts with spin-coating a thin film solution on a substrate,then the sample is left to dry. In the first step, it is important that the spin-castfilm is uniform. [7, 8] In the second step, the evaporation flux, i.e., the massremoved from the liquid phase to the vapor phase in unit time from unit surfacearea, needs to be controlled precisely. Even for the pure solvent evaporation,the process is complex and involves the diffusion of solvent molecules in boththe liquid and vapor phases, and external flow in the vapor phase to preventsaturation. The evaporation flux can be computed using the Hertz-Knudsenequation which is based on the thermodynamics variables, [9, 10, 11] or solvingthe diffusion equation in the vapor phase using suitable boundary conditions.[12, 13, 14]

The solvent evaporation drives the free surface to recede towards the sub-strate, resulting in an accumulation of the solutes at the surface. Two competingprocesses determine the spatial distribution of the solutes. One is the Brown-ian motion, which is characterized by the diffusion constant D of the solutes.The other is the evaporation, characterized by the rate vev at which the freesurface recedes. Two time scales are related to these two process: the diffusiontime τD = `2/D, where ` is a characteristic length, and the evaporation timeτev = `/vev. To quantify the relative importance between the diffusion and theevaporation, one can define a dimensionless number called film formation Pecletnumber [15]

Pe =τDτev

=vev`

D.

If Pe < 1, the diffusion takes place quickly; the concentration gradient createdby evaporation is quickly flattened by diffusion, leading to a uniform concentra-tion profile. If Pe > 1, the evaporation dominates; the concentration gradientincreases with time, and the solutes accumulate at the solution/air interface.These two different scenarios are shown schematically in Figure 1A. The timeevolution of the film structures are shown for the evaporating colloidal dispersion[16] (Figure 1B) and polymer solution [17] (Figure 1C), respectively.

The final structure of the dried material depend on the evaporation rate. Thegeneral consensus is when the evaporate is slow, the solutes have ample timeto adjust and self-organize, resulting in a more ordered structure. Otherwise,

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disordered structure forms. This provides an external means to control thefinal structure through the evaporation rate, which can be modified during theexperiment.

Industrial applications prefer fast evaporation because of the short produc-tion time. However, there are several new phenomena emerge at high evapora-tion rate. Fast evaporation increases the solute concentration at the surface, andthe viscosity of this part increases. When the concentration exceeds a certaincritical value, the viscosity diverges, and the solutions at the surface becomesgel-like, which is called skin. [15, 17, 18] For applications, skin is usually consid-ered to be avoided since it causes various unfavorable effects on the dried mate-rial, such as surface roughening [15], buckling and dimpling [7, 19, 20, 21, 22],cavity formation [17, 23, 24, 25] On the other hand, skins are utilized in somesituations. For example, in spray drying, small droplets ejected from a nozzlequickly dry up and create a hollow or buckled particles due to skin formation,which is helpful in food industries. [26]

Skin formation is a process that material changes from viscoelastic fluid toviscoelastic solid. There are many fundamental questions unanswered, such aswhen the skin formation starts, how skin grows in time, and how it affects thedrying dynamics. Therefore, it is a challenge for both experimentalists andtheorists. Measuring the change of rheological properties on a scale less than1 µm is difficult in experiments. Constructing a continuum mechanical theoryfor materials which transform from fluid to solid is a challenge for theorists.Okuzono et al. [27] developed a simple theory to discuss the growth of theskin layer. They assumed that skin appears when solute concentration exceedscertain critical concentration and discussed the condition for the formation ofskin layers and the growth dynamics of skin layer. A more detailed calculationwas conducted based on a Lagrangian scheme. [28]

As the evaporation proceeds, the skin layer is compressed, and the elasticenergy of deformation increases. This causes various mechanical instabilities inthe solution. A typical mechanical instability is buckling. The former has beenanalyzed by Bornside et al. [7] and de Gennes [19], and discussed intensivelyin the literature [29]. Another type of instability is cavitation. In this case, theelastic energy is release by the appearance of gas bubbles inside the solution(Figure 1C). Meng et al. developed a theory to model the cavitation process inthe drying droplet. [24, 25] This theory showed that the shear modulus of theskin layer is essential for cavitation.

For colloidal dispersion, when the concentration increases further near thefree surface, colloidal particles can form crystal. The quality of the crystalformation is found to be better at slow evaporation rate, while defects and grainboundaries start to appear at high evaporation rate. [30]. Novel method hasbeen implemented to identify the crystalline structures during the evaporation.[31]

The evaporation can also take place on a curved surface, as the solutiontakes a cylindrical or spherical geometry. Su et al. have developed a methodto produce nanowires composed of polymers or nanoparticles. [32, 33] Liquidbridges are formed in between micropillars. The cylindrical filament are subse-

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quently dried and uniform structures emerge (Figure 2A). In the case of polymersolution, the initial polymer concentration is a vital controlling parameter; ei-ther too small or too large concentration causes the nanowires to break. Amore controlled experiment was performed in extensional rheometer by Crestet al. [34] In this case, the competition between elasticity, evaporation, andcapillarity needs to be carefully tuned (Figure 2B). A solution droplet keeps aspherical shape on a superhydrophobic surface. When the spherical solution isdried [35, 36], supraballs of different ordering and mechanical properties can beproduced (Figure 2C).

3 Drying of two-component solutions

The one-component solution discussed in previous section is an ideal case. Inpractical applications, the solutions contain particles of different sizes or ofdifferent properties, surfactants, polymers, etc. Each component contributesdifferent functionality to the material. To realize specific functionality, the ar-rangement of various species in the dried film has to be controlled precisely. Onedesired case is the uniform distribution, as in nanocomposite, the nanoparticlesneed to be dispersed uniformly in the polymer matrix to enhance the mechan-ical property. [37] Another case is the layered structure, which is traditionallyproduced by layer-by-layer assembly. Evaporation can create multilayer coatingduring a single drying step, therefore it is highly desirable from industrial pointof view. [15]

Consider a colloidal solution consisting of two kinds of particles, big andsmall (see Fig. 3A). In the solution, they mix each other uniformly. As solventevaporates, the concentration at the surface becomes larger than in the bulk, andconcentration gradient is created. This effect eventually creates a compositiongradient in the dried film. Here we have two Peclet numbers, Pe1 for smallcolloids and Pe2 for big colloids. For hard spheres, the Peclet numbers arerelated by the size ratio, Pe1/Pe2 = R1/R2. When Pe2 > 1 and Pe1 < 1, bigparticles are expected to remain at the surface and small particles can quicklydiffuse away, giving the big-on-top stratification. Indeed, Trueman et al. [38, 39]reported that the big-on-top stratification is observed in many colloidal systems.However, they also reported that when the size ratio becomes large (roughlylarger than 3), the inverted structure, small-on-top stratification is observed.They conjectured that this is due to the interaction between particles. [38]On the other hand, Fortini et al. [40] conducted a computer simulation andreported that the small-on-top structure appears for hard sphere systems whenboth Peclet numbers are large (Pe1 > 1, Pe2 > 1) and the size ratio is large(larger than 7). Howard et al. [41] performed a through examination of theparameter space on a similar system.

Zhou et al. recently proposed a simple explanation for the small-on-topstructure. [42] They assumed a hard sphere model, and accounted for theparticle-interaction by the virial expansion for the free energy. Based on thestandard diffusion model, [43] they derived time evolution equations for parti-

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cle concentrations, and showed that the small-on-top structure indeed appearsfor mixed suspensions with large size ratio. The key point is that the effect ofinteraction on the particles is not symmetric: the force exerted on big particlesby small particles is much pronounced than the force exerted on small particlesby big particles. Hence, if the concentration gradient is created at the surface,big particles feel larger forces than small particles and are pushed away from thesurface. A state diagram was constructed to indicate which type of stratificationis created when evaporation rate and particle concentration are varied (Figure3B). Their results are in quantitative agreement with the results of simulationand experiments [39, 40].

These studies have highlighted the importance of particle interaction. An-other interesting system is the mixture of polymers and nanoparticles, in whichtheir interaction can be varied via the pH. At low evaporation rate, Kim etal. [44] reported weak particle-polymer attraction produce dense aggregatesof bare particles in the dried film, while strong particle-polymer attraction re-sults in more homogeneous distribution (Figure 4A). At high evaporation rate,Cheng et al. [45] performed large-scale molecular dynamics simulations. Theirresults indicates that stratified structure can be produced by evaporation: poorparticle-polymer affinity leads to polymer-on-top structure, while good particle-polymer affinity results in the opposite particle-on-top structure (Figure 4B).At fast evaporation, the skin layer is present and may be the reason for strati-fication.

Interaction between particles of the same type can also be modified by col-loidal surface property. Martın-Fabiani et al. [46] synthesized nanoparticleswith a hairy shell composed of hydrophilic PMAA chains. By increasing thepH, the polymer chains change from a collapse state to extended state, effec-tively increase the particle size. When these hairy nanoparticles are mixed withlarge particles, the dried structure can be switched from homogeneous to layeredby adjusting the pH value (Figure 4C). On the theoretical side, Atmuri et al. de-veloped a diffusive model which explicitly took into account the self-interactionbetween particles of the same type, but the cross-interaction is absent. [47]

4 Outlook

Understanding the solvent evaporation process, especially how to control thestructural change taking place during the evaporation is an important subjectin many applications. There are two advantages for solution-based method incomparison to methods without solvents: (1) The solutes are kinetically mo-bile in the solution, therefore the dynamics is fast and fabrication time can bereduced. (2) The final structure can be controlled by external means such asevaporation rate and solution pH value. If the layered structure is preferred, itis possible to create multi-layered coatings in one simple fabrication step. Herewe have highlighted recent development in structure control through the evap-oration rate and the solute interactions, with a special emphasis on the synergybetween theory, simulation, and experiment. By combining different research

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approaches, we can have a better understanding of the governing principles ofstructure formation during evaporation and aid the development of advancedmaterials.

5 Acknowledgments

This work was supported by the National Natural Science Foundation of China(NSFC) through the Grant No. 21434001, 21404003, 21504004, 21574006, and21622401, and the joint NSFC-ISF Research Program, jointly funded by theNSFC and the Israel Science Foundation (ISF) under grant No. 51561145002(855/15). M. D. acknowledges the financial support of the Chinese CentralGovernment in the Thousand Talents Program.

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Figure 1: A. The film structure after evaporation is determined by the evapora-tion rate. B. Cryo-SEM images showing a consolidation front in a evaporatingfilm composed of polystyrene particles in water. Reproduced with permission.[16] Copyright 2005 Elsevier. C. Top views of a evaporating PVAc/aceton so-lution. Bubbles can be seen in the last picture. Reproduced with permission.[17] Copyright 2012 Springer.

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Figure 2: A. Evaporation of a colloidal solution filament in between two mi-cropillars. Reproduced with permission. [33] Copyright 2013 Wiley. B. Evap-oration of a polymer solution filament in extensional rheometer. Comparisonbetween the experiment and numerical simulation are shown. Reproduced withpermission. [34] Copyright 2009 MIT. C. Evaporation of a spherical droplet.Supraballs of different ordering are produced under different pH values. Repro-duced with permission. [36] Copyright 2017 ACS.

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Figure 3: A. Evaporation in a colloidal solution composed of big and smallparticles. B. State diagram of final structure based on the initial concentrationof small particles and the Peclet number. Three structures are predicted: small-on-top, big-on-top, and homogeneous structure. Reproduced with permission.[42] Copyright 2017 APS. C. Experimental observations of small-on-top andbig-on-top structures. Reproduced with permission. [39] Copyright 2012 ACS.

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Figure 4: A. Structure change by tuning the pH value, which changes the inter-action between polymers and nanoparticles. Reproduced with permission. [44]Copyright 2016 ACS. B. Structure change by tuning the attraction betweenpolymers and nanoparticles. Reproduced with permission. [45] Copyright 2016ACS. C. Structure change by tuning the self-interaction of small particles. Re-produced with permission. [46] Copyright 2016 ACS.

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