How the interplay of molecular and colloidal scales controls drying of microgel dispersions

Significance

Microgel aqueous dispersions are shown to display drying behavior in between that of a colloidal dispersion and a polymer solution. Like a colloidal dispersion, drying proceeds through the propagation of a drying front separating a dense film from the dispersion’s bulk. However, microgels are able to deform, interpenetrate, and deswell, which allows them to compact further than hard-sphere close packing, similarly to polymers. A steep and complex water gradient thus exists throughout the film, along which both water activity and water transport strongly decrease toward the air/liquid interface. The weak influence of the air relative humidity on the drying process illustrates the interplay between water activity and water transport, which stems from water deprivation in mesostructures at the air/liquid interface.

Abstract

Bringing an aqueous dispersion or solution into open air leads to water evaporation. The resulting drying process initiates the buildup of spatial heterogeneities, as nonvolatile solutes and colloids concentrate. Such composition gradients associate with mesostructure gradients, which, in turn, impact flows within these multicomponent systems. In this work, we investigate the drying of microgel dispersions in respect to two reference systems, a colloidal dispersion and a polymer solution, which, respectively, involve colloidal and molecular length scales. We evidence an intermediate behavior in which a film forms at the air/liquid interface and is clearly separated from bulk by a sharp drying front. However, complex composition and mesostructure gradients develop throughout the drying film, as evidenced by Raman and small-angle X-ray scattering mapping. We show that this results from the soft colloidal structure of microgel, which allows them to interpenetrate, deform, and deswell. As a result, water activity and water transport are drastically decreased in the vicinity of the air/liquid interface. This notably leads to diffusional drying kinetics that are nearly independent on the air relative humidity. The interplay between water fraction, water activity, and mesostructure on water transport is generic and, thus, shown to be pivotal in order to master evaporation in drying complex fluids.

Drying is a ubiquitous process consisting of solvent evaporation from a multicomponent system. It occurs through matter transport driven by the solvent chemical potential difference between liquid and gas phases or otherwise expressed solvent activity in the liquid. Thermodynamics is thus central in drying problems. Two main categories of systems can be distinguished: solutions, which are one-phase equilibrium molecular mixtures, and dispersions, which are two-phase nonequilibrium systems. This thermodynamic and length-scale difference is unsurprisingly crucial in understanding their respective drying behavior.

The literature devoted to drying solutions identified that, as solvent fractions may reach exceedingly low values, locally or globally, during drying, a collapse of both solvent activity and transport could occur. This notably leads to a kinetics change from an initial constant-rate regime to a falling-rate one when drying polymer solutions (1–3). Water evaporation from solutions of amphiphilic molecules in contact with an infinite reservoir, which model mammals’ biomembranes with air, is nearly insensitive to the air relative humidity (RH), which results from the simultaneous collapse of water activity and effective diffusion in the vicinity of the air/liquid interface (4–6).

In contrast, the field of drying dispersions, emblematically represented by coffee-stain patterns (7), has, rather, been focused on hydrodynamics, substrates, and colloidal interactions in model systems (8–16) or technological problems such as spray-drying and paints (17, 18). Thermodynamics have been considered through including colloidal interactions, expressed as osmotic pressures, in a generalized Stokes–Einstein approach (19, 20), to model colloidal transport. For most colloidal dispersions, the corresponding osmotic pressures are well below 1 MPa, even at the highest reachable concentrations (21, 22). This roughly corresponds to decreasing RH at most from 100 to 99%. Only very small nanoparticles, typically smaller than 20 nm, may yield much larger osmotic pressures at packing due to the interfacial cost of nanomenisci (23), which closely relates to crack formation (24). Overall, these contributions are expected to be negligible for most particles in comparison with the osmotic pressure changes related to RH variations. This means that solvent activity is expected to remain close to that of pure solvent over the whole accessible concentration range, as colloids’ concentration is limited by their close packing.

In practice, these two limiting cases may be simultaneously at play when drying complex fluids. For instance, particles may be deformable, swollen by solvent, surface-grafted by polymers, or coexist with polymers or amphiphiles in the same continuous phase. Therefore, the respective influence of each length scale on the overall drying behavior needs to be systematically assessed. To this purpose, we have chosen cross-linked poly (N-isopropylacrylamide) (PNIPAM) microgels as intermediate systems due to their well-known colloid/polymer duality (25–27). Indeed, microgels are colloidal particles of a polymer in good solvent, which is prevented from dissolving by a sufficient cross-linking degree (26, 27). Below their volume phase-transition temperature (VPTT), such microgels are highly water-swollen, but still behave like hard spheres up to a fluid–crystal transition taking place at an effective volume fraction around 0.56 (28). Their softness comes into play at higher concentrations due to their ability to interpenetrate, deform, and deswell (29–31). The extent of deswelling and deformation for a given mesostructure is determined by water activity within microgels (22, 32, 33), which significantly varies with water concentration (34, 35). The interplay between mesostructure and intermolecular interactions notably determines the value of water permeability of microgel filter cakes in the context of filtration processes (22, 32, 33). Drying microgel dispersions, which allows them to reach high microgel concentrations, should thus provide an efficient means to probe this generic interplay between water transport, water activity, and microgel mesostructure.

A large diversity of drying geometries exist, and we focus in this article on unidirectional drying in millifluidic channels, which considerably simplifies the hydrodynamic conditions and experimental monitoring (11). Notable experimental and theoretical contributions devoted to the drying of colloidal dispersions have been published by Dufresne et al. (8, 36), Wallenstein and Russel (37), Inasawa and Yamaguchi (38), Sarkar and Tirumkudulu (39), and Lidon and Salmon (23). Two different drying regimes were identified: For large colloids and/or early times, the drying front grows with a constant velocity and, thus, linearly with time (advective regime). For smaller colloids and or/longer times, the drying front, rather, grows linearly with the square root of time and, thus, at decreasing velocity (diffusive regime). This second regime has been explained by the small recessing of the air/liquid interface in the sample (36, 37) and the water activity change due to the Kelvin effect (23). In a previous study dedicated to evaporation from aqueous solutions of amphiphilic molecules, we also designed a special unidirectional drying setup (4–6). The main innovation of the design was to connect the millifluidic channel to an infinite reservoir, which allows us to probe drying dynamics up to months. This semi-infinite geometry sets constant boundary conditions, which greatly facilitate the modeling of water evaporation (5). We evidenced that drying proceeded in a diffusive regime, but with the buildup of concentration gradients and a near-independence on the air RH, which is very different from the diffusive regime observed for small colloidal particles.

In this article, we systematically investigate the interplay of colloidal and molecular scales when drying PNIPAM microgel dispersions. We start by examining a first limiting case, “hard ” colloidal dispersions, by using two reference systems, a dispersion of hydrophobic polystyrene (PS) particles and a PNIPAM microgel dispersion in bad-solvent conditions. We then investigate the impact of good-solvent conditions on the drying of PNIPAM microgel dispersions. We thus first characterize both composition and structure gradients developing in the drying film and then monitor drying kinetics and assess the role of the air RH. A second limiting case is then introduced, a linear PNIPAM polymer solution in good-solvent conditions. The phenomenological proximity between drying PNIPAM polymer solutions and microgel dispersions then motivates a thermodynamic sorption study to monitor water/PNIPAM intermolecular interactions by measuring water activity as a function of water fraction. This signature of complex fluids leads to a qualitative interpretation of both drying kinetics and RH impact.

Results and Discussion

Unidirectional Drying: Characterizing Composition and Structure Gradients

Drying is investigated with a millifluidic setup con- sisting of a capillary with one end placed in an airflow of controlled RH and attached on the other end to an infinite reservoir containing the aqueous dispersion, as schematized in Fig. 1 (4). Water evaporation at the air/liquid interface triggers unidirectional advection from the reservoir toward the air/liquid interface. Additionally, the water chemical potential difference between the air and the reservoir leads to diffusion. A typical experiment proceeds as follows: The aqueous dispersion or solution is placed in the reservoir of the drying cell, from which it flows by capillarity to its tip. There, it experiences an airflow of controlled RH, which triggers evaporation. As water evaporates, we observe the formation of a film in the vicinity of the air/liquid interface, which continuously grows over time. This corresponds to the buildup of a water gradient from the interface toward the reservoir. The drying film is observed through optical microscopy to localize drying fronts and any visible structuration. Time series of optical observations are typically converted to distance/time profiles by spatial averaging perpendicularly to the flow/capillary’s axis, since drying is unidirectional and along the flow/capillary axis. Then, Raman confocal microscopy is used to quantitatively characterize the composition gradient developing in the capillary. Raman spectroscopy probes the rovibrational molecular modes, and each type of chemical bonds thus yields distinct spectra signatures. This technique is extremely efficient to probe aqueous systems, as water is a rather poor Raman scatterer. In each voxel (X/Y/Z = 0.5/0.5/2.8 µm), we obtain a Raman scattering spectrum. Since water and organic materials display very different spectral signatures (SI Appendix, Fig. S1), a calibration curve allows us to quantify their respective amounts. Finally, gradients in mesostructure are probed through high-resolution Small-Angle X-Ray Scattering (SAXS).

Fig. 1.

Schematic view of the millifluidic setup, which consists of a rectangular capillary connected on one end to a reservoir containing the microgel dispersion and exposed on its other end to an air flux of controlled RH.

Drying Colloidal Dispersions: PS Particles and PNIPAM Microgels in Bad-Solvent Conditions

We first present the behavior of a reference system for the drying of colloidal dispersions, a dispersion of hydrophobic PS particles. PS particles have an overall hydrodynamic radius of 116 nm, as determined by dynamic light scattering (DLS). They are stabilized by a thin layer of an anionic surfactant (sodium dodecyl sulfate [SDS]), as evidenced from their form-factor analysis (SI Appendix, Fig. S2). The dispersion is sufficiently uniform/monodisperse to crystallize upon increasing colloids concentration (40) with a size-polydispersity in the order of 5%, assuming a Gaussian distribution as determined from SAXS (SI Appendix, Fig. S2) and transmission electron microscopy (TEM) (SI Appendix, Fig. S3A) analysis. Since PS is hydrophobic and below its glass transition at room temperature, these particles can be considered as nondeformable and noninterpenetrable, as confirmed by the scanning electron microscopy (SEM) of the dried dispersion (SI Appendix, Fig. S3 B and C).

Fig. 2A displays a transmission optical microscopy image and an associated composition gradient obtained by Raman microscopy. A rather homogeneous film with purple tones in transmission is forming from the air/liquid interface toward the bulk, with a clear drying front separation. This simple composition gradient can be separated in three parts: 1) a film with a constant volume fraction in PS of 0.74 obtained by Raman, which corresponds visually to the purple area. A SAXS investigation of this film reveals that it is homogeneous and corresponds to a slightly distorted hexagonal close packing (SI Appendix, Fig. S4). 2) The drying front, where there is an abrupt decrease of the PS volume fraction and that corresponds visually to a thin green area; and 3) the bulk, which corresponds to the constant initial PS volume fraction and is transparent. Fig. 2B displays the distance/time profile obtained from optical microscopy time series (Movie S1). The drying front propagates linearly with time. Also, the purple crystallites display horizontal trajectories in this representation, which means they do not compact. Only the green crystallites, which correspond to the onset of colloidal crystallization, compact in the vicinity of the drying front to yield the purple final crystallite at close packing. This is consistent with center-to-center distances obtained through SAXS experiments, which show that the purple region corresponds to hexagonal close packing (SI Appendix, Fig. S4). All RHs lead to the same qualitative behavior, but differ in drying speed (SI Appendix, Fig. S5). The drying front velocity, which is the slope of distance/time profiles, is displayed as blue dots in Fig. 2C. It decreases linearly with increasing RH. Interestingly, we determined in a different experiment pure water evaporation velocity in the capillary setup by monitoring the displacement of an air/meniscus. In a purely advective colloidal deposition process, the drying front should grow as the product of solvent velocity multiplied by the colloids volume fraction ratio between close packing (0.74) and the dispersion (0.0095). The result is displayed in Fig. 2C as green dots and closely matches the experimental growth front.

Fig. 2.

(A) Water volume fraction obtained from Raman microscopy at RH = 90%, with the microscopy image overlaid. Close packing at a PS volume fraction of 0.74 is achieved within the film. (B) Microscopy profile of a PS dispersion (hydrodynamic radius R${}_H=115$ nm) at RH = 0.7%. A linear relationship between the film thickness and time is observed at all RH. (C) Slope of the thickness vs. time profile as a function of RH (blue dots), compared to direct measurement of the advective velocity rescaled by the bulk/close packing volume fraction ratio (green dots). (D) Microscopy profile obtained for a PNIPAM microgel dispersion heated to 40 ${}^{°}$C (R${}_H=118$ nm), displaying also a linear distance/time relationship for the drying front.

Overall, the PS dispersion follows a well-described advective regime, with a drying front propagating by advection and linearly with RH. This is expected from the literature, as the particle size (116 nm) is much higher than the typical size threshold from a diffusive to advective regime (around 20 nm) (23), although a deviation is progressively observed at larger times (¿100 min), indicating a progressive transition toward a diffusional regime.

Since we have a clear reference for colloidal drying, we first investigated the behavior of PNIPAM microgels above their VPTT. At T = 40 ${}^{°}$C, PNIPAM is collapsed due to bad-solvent conditions, and the microgel size is very similar to the size of PS particles, as found by DLS (SI Appendix, Fig. S6), SAXS (SI Appendix, Fig. S7), and SEM (SI Appendix, Fig. S8), which enables a direct comparison. Fig. 2D displays the optical monitoring of PNIPAM microgel drying at T = 40 ${}^{°}$C. We observe a linear growth of the drying front with time, which means that microgels in their collapsed state dry like usual colloidal dispersions. This observation is consistent with the collapsed structure of microgels above their VPTT, which display low deformability and interpenetration like a hard PS latex. This consistency suggests that we should now investigate the situation in which microgels are highly water-swollen, deformable, and interpenetrable, which is achieved at temperatures lower than their VPTT. We will thus first look on the consequences of good-solvent conditions on both composition and structure gradients and then on drying kinetics and environmental dependence.

Unidirectional Drying of Microgel Dispersions in Good-Solvent Conditions: Complex Composition and Structure Gradients

We first describe the gradients’ profiles when evaporating a microgel dispersion in the capillary setup, after exposing it many hours at ambient humidity (RH = 50%). A microscopy image with crossed polarizers is given in Fig. 3A. From right to left, which corresponds to moving from the bulk toward the air/liquid interface, we first observe a sharp drying front separating colorful domains from the bulk. Moving further toward the air/liquid interface, colors disappear to yield a uniform transparent area, which cracks in the immediate vicinity of the air/liquid interface. Such cracking has been described in microgel films submitted to deformation leading to self-healing upon rehydration (41) and in drying polymer solutions (42).

Fig. 3.

(A) As water evaporates, microgel particles pack at the air/liquid interface and form a film, displayed in the polarized microscopy image. The colors stem from typical light diffraction by a colloidal crystal. Microgel particles have a heterogeneous structure that can be described as a denser core (radius at half-width R_hw = 180 nm) surrounded by a looser network (2 σ = 110 nm of fuzziness; orange shaded area) yielding a hydrodynamic radius R${}_{H({20}^{°}C)}$ = 224 nm. In collapsed conditions at 40 ${}^{°}$C, the hydrodynamic radius R${}_{H({20}^{°}C)}$ = 128 nm, close to R${}_{hw}-\sigma$, but a bit larger than what is measured in vacuum with SEM R_SEM = 110 nm. Raman confocal microscopy yields the water gradient through the film. Close to the air/liquid interface, water is scarce, and the gradient is linear. Moving further away beyond this water-poor and cracked area, water fractions steadily increase with a more complex profile up to the drying front. From there, there is no significant water gradient, which corresponds to bulk conditions. (B) Typical SAXS spectra measured at different positions within the film. Close to the air/liquid interface, the scattering intensity (a.u., arbitrary unit) follows a power law with an exponent of 2, which is consistent with a dense and branched polymer network in a good solvent (43). Moving away from the cracked water-poor area, we observe a structure factor, with two-dimensional patterns showing a sixfold symmetry, consistent with a slightly distorted hexagonal close-packed structure that is progressively swelling until the end of the film, where it dissolves into a disordered microgel dispersion. (C) Center-to-center distances extracted from SAXS measurements assuming a hexagonal close-packed structure (RH = 50%). Interestingly, this structural gradient has a similar shape to the composition gradient displayed in B. Confocal optical microscopy images are also presented for two positions (red squares) and also evidence a hexagonal close-packed structure. The center-to-center distance extracted at the drying front also matches the data obtained from SAXS, highlighting the consistency of the analysis. (D) Scheme of the local microgel structure within the film deduced from the observations.

Fig. 3A shows a typical result of a Raman experiment and analysis, yielding the water mass fraction within the film. From right to left, the water fraction is first constant outside of the film and then abruptly falls at the drying front. A complex profile is observed in the film that can be separated in two parts, one intermediate and one in the immediate vicinity of the air/liquid interface. Similar observations were done by using fluorescence microscopy with labeled microgels (SI Appendix, Fig. S9).

This complex composition gradient suggests that microgels pack and deswell continuously from the drying front to the air/liquid interface. We thus probed the associated structural gradient using SAXS. Fig. 3B displays typical scattering curves within the film. In most of the film, the structure is a slightly distorted hexagonal packing, which gives well-defined structure peaks (SI Appendix, Fig. S10). This structure is also confirmed via fluorescence confocal microscopy at the single microgel level, as shown in the insets of Fig. 3C, SI Appendix, Fig. S11 and Movie S2. The colorful domains thus correspond to colloidal crystallites. In the immediate vicinity of the air/liquid interface, where we observe cracks, the spectrum drastically changes and, rather, yields a power-law dependence with an exponent close to 2. Such a behavior is typical for concentrated ramified polymer solutions in a good solvent.

The structure peak positions allow us to extract a center-to-center distance between adjacent microgels (Fig. 3C) which enables a quantitative comparison with the microgel characteristic distances. The microgels used in this study can be described as fuzzy spheres consisting of a core with a higher cross-linking degree than the outer shell, which originates from the faster consumption of the cross-linker during the precipitation polymerization (44, 45). Different length scales may be measured with different techniques to characterize the microgels. The overall hydrodynamic radius, R_H, is determined at low concentration by DLS in the swollen and collapsed state from the swelling curve (SI Appendix, Fig. S6). The polymer distribution and fuzziness extent is obtained from the analysis of the form factor determined by SAXS (SI Appendix, Fig. S7). This yields a half-width radius R_hw and a fuzziness factor σ, leading to an outer radius $R_{hw}+\sigma$ similar to the hydrodynamic radius R_H. Finally, the dehydrated radius can be estimated from SEM, R_SEM, as discussed in SI Appendix, Fig. S8.

At the drying front, we observe a center-to-center distance matching their hydrodynamic diameter: Microgels are thus touching, consistently with close packing, but retaining their bulk structure. However, the center-to-center distance continuously decreases within the film, which means that microgels interpenetrate, deform, and deswell at high volume fractions (29, 30, 32, 46). In the driest area lying in the immediate vicinity of the air/liquid interface, we no longer observe a colloidal crystalline structure in SAXS, and we thus cannot extract center-to-center distances. Yet, it is remarkable that center-to-center distances fall below distances measured by SEM, which indicates that microgels are completely collapsed. They thus lose their colloidal identity and merge into a continuous polymeric network. Following these observations, Fig. 3D schematically describes how microgels are organized within the film, as deduced from the simultaneous determination of both composition and structuration gradients.

While microgels behave like other colloidal particles in forming a film clearly separated from the bulk of the dispersion by a drying front, the complex composition and structure gradients forming within this film set them apart. For the PS particle dispersion, the composition gradient is constant within the film and corresponds to close packing, with a step-wise change at the drying front to reach a constant value in the bulk. For the microgel dispersion, we rather observe a complex and steep water gradient within the film itself. The intermicrogel distance continuously decreases within the film from the drying front to the air/liquid interface. This enables us to reach much larger compacities than hard-sphere close packing. This marked difference between the two systems stems from their structural difference: Contrarily to PNIPAM microgels below their VPTT, PS particles are hydrophobic and therefore not water-swollen, which sets constant their volume and prevents them from deforming and interpenetrating.

We will now describe how these complex gradients’ profiles, stemming from the inner structure of microgels, lead to changes in drying kinetics and impact of the air RH.

Drying Kinetics of Microgel Dispersions in Good-Solvent Conditions and Influence of the RH

In Fig. 3, both composition and structure gradients are presented at a given time and RH, as the overall features are always the same. Yet, since drying is a dynamic process, its control and understanding must also include a description of kinetics and influence of its driving force, RH.

Performing optical microscopy observations over time, for several humidity and temperature conditions, yields a large number of images. Two typical time-series acquired with polarized microcopy for low and high humidity are provided in Movies S3 and S4. Since drying is unidirectional and along the flow/capillary axis, we display these large datasets to distance/time profiles by spatial averaging perpendicularly to the flow/capillary’s axis over a few pixels. The resulting optical microscopy profiles are displayed in Fig. 4A for two different humidities and temperature conditions. On these profiles, the drying-front growth is visible as the curve separating the film, a colored area, from the bulk, a dark area. At T = 23 ${}^{°}$C, the colorful curves stemming from the drying front and vanishing when approaching the air/liquid interface correspond to crystallite trajectories and, thus, demonstrate their compaction. Fig. 4B displays the corresponding drying fronts as a function of the square root of time. We observe that for an initial period, the drying front propagates linearly with the square root of time and independently of RH. This is observed over the whole humidity range, as displayed in Fig. 4C. This observation is striking and unexpected in a water-evaporation process. At some stage, a nonmonotonous deviation is observed at RH 0.7%, which corresponds to cracking. Looking at the colorful curves corresponding to crystallite compaction, we observe that this compaction is enhanced prior to cracking. Cracking is thus preceded by a sudden compaction of the drying film and followed by a continued growth. Interestingly, this additional phenomenon leads to another striking observation: At longer times, decreasing the air humidity reduces the growth of the drying front.

Fig. 4.

(A) Microscopy profiles obtained by slicing each image of the time series along the z direction (capillary axis) at two RHs (RH = 0.7 and 90%, T= 23 ${}^{°}$C). (B) Film boundary extracted from profiles (A) and plotted as the square root of time for the two humidities, displaying a linear distance/square root of time relationship. A deviation is observed in the RH 0.7% case due to cracking within the portion of the film located close to the air/liquid interface. (C) Slope of the distance vs. square root of time profiles for several RH (x = z/t${}^{1/2}$) at t = 3 h, evidencing the near-independence on RH influence prior to cracking. (D) Water gradient profiles obtained from Raman microscopy at the two RHs and as a function of time. These profiles are rescaled by using the mixed length/time variable x. For each humidity, water gradients were measured every hour from 1 to 16 h, with higher times corresponding to darker curve shades.

We also perform a Raman confocal microscopy characterization and obtain the composition gradient within the film. Fig. 3D displays such gradients for both humidities at T = 23 ${}^{°}$C, using a rescaling by the space/time variable x = z/t${}^{1/2}$ suggested by Fig. 4B, with t the time and z the distance. Curves are acquired every hour for 20 h, with increasingly darker color meaning increasing time. We observe that this rescaling is excellent for RH = 90% and good for RH = 0.7%, with deviations occurring at longer times due to cracking. All profiles are similar to what is presented in Fig. 4. It is interesting to note the similarity between profiles at both humidities with differences only visible in the immediate vicinity of the air/liquid interface. Notably, water fraction reaches lower values at lower humidities, which is consistent with part of the film reaching drier conditions, thus enabling its cracking.

As a side experiment, we probe the possible impact of salinity on the drying process by adding sodium chloride, KCl, at a 0.1 M concentration to the microgel dispersion (SI Appendix, Fig. S12). We do not observe any significant differences in our experiments, in which full drying never occurs, which likely indicates that salt is not concentrating significantly in the drying film. This situation is distinct from full drying, for instance, in sessile droplets, in which salt crystallization eventually occurs and is observed at the very end of the drying process. We also observe that films could redissolve if left in water for a sufficient time.

Overall, we observe a diffusional growth of the drying film for microgel dispersions below their VPTT. Since microgels are colloidal particles, such a behavior could seem reminiscent, at first glance, of the diffusional regime described in the colloidal drying literature (8). However, this idea can be quickly dispelled by major differences between microgels and PS particles: 1) Microgels below their VPTT are twice as large, which should promote the advective regime; 2) the RH independence for microgels, in contrast with the linear dependence for PS particles; 3) the presence of a substantial water gradient throughout the solid region, in contrast to what was observed by Dufresne et al. (8) and here with PS particles; and 4) the constant compaction of microgels within the drying film.

We are thus facing an altogether different drying regime for microgel dispersions than what has been described in the literature devoted to the drying of hard colloidal dispersions. This motivates us to investigate another reference system that rather relates to the “soft” polymeric characteristics of microgels, such as compaction, swelling, and interpenetration: a PNIPAM polymer solution.

Drying of an Aqueous PNIPAM Polymer Solution

We now report some drying experiments on a second reference case, a polymer solution (linear PNIPAM, molecular weight = 85,000 g/mol) at 1 wt%. In this case, optical microscopy is ill-adapted and only allows us to distinguish a thin layer forming in the immediate vicinity of the air/liquid interface in the RH = 0.7% case, due to cracking. Raman microscopy is much more informative and yields the variation of the water mass fraction over time. Profiles obtained at both RH = 0.7 and 90% collapse into a single master curve when plotted as a function of the distance/time mixed variable x = z/t${}^{1/2}$, as displayed in Fig. 5. Note that curves were cut at higher x values for improving readability at low water fractions, but do reach asymptotically the bulk concentration value of 1 wt%. At RH = 0.7%, a small cracked region is observed, which corresponds to water fractions lower than 0.25 to 0.3, similar to PNIPAM microgels.

Fig. 5.

Water gradients determined by using Raman microscopy of linear PNIPAM (85,000 g/mol) in water solutions rescaled by the length/time variable x for several hours. For each humidity, water gradients were measured every hour from 1 to 19 h, with higher times corresponding to darker curve shades. The x scale was cut at an arbitrary value of 4 in order to highlight gradients in the vicinity of the air/liquid interface, but measurements show that the water fraction reaches asymptotically the bulk value of 0.01 (1 wt%) toward large x values. For the RH = 0.7% case, a small cracked area is detected at the air/liquid interface, as shown in the pictures inlaid above the profiles.

Compared to the PNIPAM microgel dispersion, drying a PNIPAM polymer solution does not yield a sharply defined drying front, but, rather, a continuous gradient extending asymptotically toward the reservoir. This difference highlights the particle vs. macromolecule (or dispersion vs. solution) difference between the two systems. Yet, they both otherwise display striking similarities. Notably, composition gradients both collapse to a single master curve when plotted as a function of x, which evidences a diffusional scaling law. Overall, both gradients display rather similar shapes, but still differ, which is reminiscent of their remaining structural differences in the concentrated state. Cracking is also observed in both cases, but its extent is much larger in the microgel case, which, again, shows that some structural differences remain visible, even at very low water contents.

Both systems also display the striking observation that RH plays only a limited role in the drying dynamics, which is unexpected in an evaporation-induced phenomenon, but which we previously evidenced in solutions of amphiphiles (4). Molecularly, both systems are built from the same hydrophilic monomer and are in good-solvent conditions, contrasting with, for instance, PS dispersions. Since water evaporation results from a difference of water activity between air and liquid, this suggests that we should probe the impact of PNIPAM/water interactions on water activity through thermodynamic measurements in order to explain the common drying signatures of microgels and polymers.

Water Activity in Drying Microgel Dispersions: Nonideal Thermodynamics

To probe water/PNIPAM molecular interactions, we determine the water sorption isotherm using a sorption microbalance. Experimentally, this consists of setting RH, and thus water activity, and then measuring water fraction at equilibrium through a gravimetric analysis. We then obtain the relationship between water activity and water fraction or, equivalently, in a binary mixture between PNIPAM${}_{(\mu \mathit{gel})}$ activity and PNIPAM${}_{(\mu \mathit{gel})}$ fraction. The results are displayed as blue dots in Fig. 6 and closely resemble published data for linear PNIPAM in water (47), which is coherent with the probing of monomer/water interactions that should be similar between the two systems. We observe that water activity largely deviates from water fraction, which means that we, unsurprisingly, study a highly nonideal system. For comparison, we display as a black line the expected (water activity = water fraction) relationship for ideal binary mixtures, which assumes the absence of intermolecular interactions. Instead, the activity/fraction relationship for microgels can rather be described with two main regimes, which is similar to many complex fluids such as solutions of amphiphiles (4). At high RH, water activity weakly varies with water fraction, while at lower RH (RH $\le$ 93%), we observe the reverse, as water fraction weakly varies with water activity.

Fig. 6.

Thermodynamic characterization of PNIPAM microgel drying. Dark blue dots and light blue diamonds correspond to experimental sorption isotherm measurements of, respectively, PNIPAM microgels and PNIPAM polymer. The water activity ($a_w=RH/100$)/water fraction relationship strongly deviates from the expected behavior of an ideal binary mixture (black line), which stems from water/PNIPAM molecular interactions. Two regimes are observed: small water fraction variation with low RH and strong water fraction variation with high RH. Both systems yield superimposed curves, which evidences their similarity at high solute/particle concentration as in drying films. In contrast, the purple line corresponds to what is observed with a standard colloidal dispersion such as the PS dispersion, for which water activity remains close to unity up to maximum compacity.

This two-regime profile can be qualitatively explained from water/PNIPAM interactions. At low PNIPAM concentrations, water molecules mostly interact with other water molecules, and water activity remains close to unity. Decreasing water fraction does not significantly decrease water activity, as water molecules remain in large excess compared to PNIPAM. As microgels close pack, the proportion of free water molecules decreases as PNIPAM pendant chains first interpenetrate, leading to a moderate change of average water activity with water concentration. Note that since microgels are highly water-swollen objects, close packing occurs at rather low water fraction. Combining SAXS and Raman characterizations displayed in Fig. 3, hexagonal close packing is achieved for a water mass fraction of around 0.93. In excess water conditions, a microgel particle thus contains around 91.3% water in volume, which illustrates that it is highly water-swollen. Further compaction above close packing thus leads to a water shortage, and water activity collapses. This water-activity collapse quantifies microgel deswelling upon forced compaction. Interestingly, the onset of cracking, which occurs at water fractions below 0.3, according to our Raman measurements displayed in Fig. 3, coincides with the change of interaction regime observed in Fig. 6. Overall, this nonideal behavior of aqueous microgel dispersions thus results from two properties of PNIPAM microgels that relate to interactions and mesostructure: 1) their molecular interactions with water that would favor full mixing without the cross-linking (good-solvent conditions); and 2) their ability to densely pack through interpenetration, deformation, and deswelling, which brings water in shortage.

Interestingly, the whole activity/fraction relationship is explored upon drying microgel dispersions. Indeed, bulk conditions correspond to water fraction higher than 0.93 (close packing). One end of the capillary thus corresponds to the regime in which water activity weakly varies with water fraction. On the contrary, the other end exposed to air sets a value for water fraction that lies in the regime in which water fraction weakly varies with water activity. To demonstrate this, we measure using Raman microscopy the water fraction at the air/liquid interface for a large RH range, which is displayed at orange dots. These dots follow the sorption isotherm, which demonstrates that a local equilibrium is achieved at the air/liquid interface. This experiment also shows that, indeed, the air/liquid interface sets conditions associated with the regime in which water fraction weakly varies with water activity. As water evaporates, microgels assemble into a film that is thus placed in between two boundaries that each correspond to a different water activity vs. water fraction regime.

Overall, the most crucial observation is that the activity/fraction relationship of microgel aqueous dispersions thus closely resembles that of other molecular mixtures, but largely deviates from what is observed for usual colloidal dispersions. Indeed, in colloidal dispersions, water activity remains close to unity throughout the whole system, as only a small fraction of water molecules interact with colloids, even at the maximal packing that can then be achieved of 26% water.

While the proximity between microgels and other colloidal particles is evident from a structural standpoint in dilute solutions, water activity highlights, in contrast, the proximity between microgels and polymer solutions in concentrated mixtures. Combined together, these two indicators locate the drying behavior of microgel dispersions at the cross-point between colloidal and molecular scales.

We will now discuss qualitatively how both diffusional scaling law and the moderate role of RH result from the polymeric behavior, or predominance of molecular scales, of microgels in the drying film.

Diffusional Scaling Law and RH Influence

Drying kinetics relate to the propagation over time and space of composition gradients from the air/liquid interface toward the bulk. Yet, we have observed, for both PNIPAM polymer solutions and PNIPAM microgel dispersions, that a single master curve was obtained when performing a change of variable distance over square root of time, which evidences a diffusional scaling law. We previously demonstrated that this scaling law was general to the unidirectional advection/diffusion transport of complex fluids (5), providing that they could be described as molecular mixtures. Quantitatively, mutual coefficients can be extracted and shown to decrease by several orders of magnitude in the vicinity of the air/liquid interface, consistent with other reports, for instance, for polymer solutions (48, 49). Together with the nonlinear variation of water activity, this decrease of mutual coefficient with decreasing water fraction is at the basis of a peculiar, but typical, signature of complex fluids drying: the weak influence of the air RH.

For linear PNIPAM, this influence is limited to the vicinity of the air/liquid interface: There, lowering RH lowers water fraction. Otherwise, composition gradients are similar and propagate at the same velocity. For microgels, a larger difference is observed when the film has grown sufficiently, since cracking occurs. However, looking only at the drying front leads to the very counterintuitive observation that the drying front propagates faster at RH = 90% than at RH = 0.7%. In reality, the water-mass loss obtained by integrating composition gradients variations over time is slightly higher at RH = 0.7% than at RH = 90%. Overall, RH has a very weak influence on drying kinetics. This strongly contrasts with the behavior of standard colloidal dispersions such as PS, in which the advective flow varies linearly with RH.

We already observed this effect in water–amphiphiles mixtures (4) and predicted its generality in complex fluids (5). Qualitatively, the two important factors are the following:

• •An extended composition range in which composition weakly varies with activity. Over most of the RH range, ${\varphi }_{\mathit{water}}$ weakly increases with a_water and, thus, RH. As a result, RH changes are dampened at the air/liquid interface. In the transport equation, this corresponds to dampening the boundary condition change at the air/liquid interface.
• •Hindered diffusion in the vicinity of the air/liquid interface. Mutual diffusion coefficients reach much smaller values in the drying film than in bulk. The resulting effect is to compress the composition gradient in the vicinity of the air/liquid interface, which further dampens the changes due to the boundary condition change.

Importantly, the overall weak dependence on RH of water evaporation in complex fluids stems from restricting the impact of RH to the vicinity of the air/liquid interface. There, it notably manifests through the extent of cracking. Indeed, cracking occurs in the regime in which water activity strongly varies with concentration, and its extent is directly determined by the boundary condition at the air/liquid interface, which is set by RH. While cracking remains limited, even after hours in our infinite-reservoir setup, it will become prominent at the end of a drying process when using a finite reservoir, such as in drying drops.

Interestingly, cracking is much more prominent when drying microgel dispersions than polymer solutions. From the previous discussion on the similar water activity in both systems, such a difference can only stem from their structural difference: colloid vs. macromolecule. This influence of the colloidal nature of microgels is, at first glance, surprising since we demonstrated that molecular scales dominate in the water-poor region of the drying film. Yet, it is worth recalling that the colloidal structure of a microgel holds through chemical cross-linking, at the molecular scale, of polymeric chains that would otherwise dissolve. Thus, the colloidal nature of microgels manifests in the driest part of the drying film through its molecular basis. This exemplifies again how the behavior of drying microgels is located at the cross-point of colloidal and molecular scale and why its description requires a multiscale approach for all its characteristics.

Conclusion and Perspectives

We have shown through this work that microgel dispersions, like other colloidal dispersions, display a well-defined drying front propagating from the air/liquid interface toward bulk. However, their drying dynamics and structuration otherwise proceeds very similarly with their polymeric counterparts. A diffusional scaling is observed, with only a weak overall dependence on RH. This behavior contrasts with previously described colloidal drying regimes and is explained by the ability of microgels to pack above close packing thanks to interpenetration, deformation, and deswelling. In the vicinity of the air/liquid interface, microgels are packed into a dense polymeric network, in which water activity strongly varies with water concentration, and mutual diffusion coefficients collapse. These characteristics restrict the impact of the air RH to the vicinity of the air/liquid interface, where it controls the extent of cracking, while leaving unaffected the rest of the composition gradient. This leads to the original feature that water evaporation proceeds nearly independently of its driving force, the air RH.

Such a drying behavior is reminiscent of what we previously observed in aqueous amphiphilic mixtures (4) and which we predicted to apply in complex fluids, when molecular scales dominate (5). Despite the colloidal nature of microgels, their drying behavior is indeed dominated by molecular scales due to their ability to interpenetrate, deform, and deswell. Interestingly, our methodology allows us to uncouple the different contributions, as both composition and structuration gradients can be obtained via, respectively, Raman and SAXS microscopy, and the composition/activity relationship can be obtained by sorption measurements. This notably allows us to obtain swelling curves as a function of both water fraction and water activity, which will reflect microgel structure such as fuzziness and cross-linking.

Our methodology is more generally well-suited to study the impact of polymeric stabilizers on more rigid particles and the presence of polymers, small molecules, or other particles in complex composite dispersions. A quantitative modeling of the drying process is also within reach for future work, thanks to the variety of experimentally determined quantities relating to local structure or thermodynamics. To conclude, this work lays the foundation for a qualitative and quantitative multiscale description of drying processes in complex solutions and dispersions.

SI Appendix

SI Appendix provides additional characterizations of synthesized particles and supporting drying experiments.

Materials and Methods

Materials

Styrene (BASF) was destabilized by passing it through an Al₂O₃ column prior to synthesis. SDS (Sigma-Aldrich), N-isopropylacrylamide (NIPAM), N,N’-methylene bis acrylamide (BIS) (Sigma-Aldrich), and methacryloxyethyl thiocarbamoyl rhodamine B were used as received without any further purification.

Particles’ Synthesis

PS latex synthesis

SDS (0.447 g) and MilliQ water (176.5 g) were weighted, added to a 500-mL three-neck round-bottom flask, and mixed at 300 rpm with a magnetic stirrer. The mixture was degassed with vacuum and flushed with nitrogen five times. A total of 48.3 g of styrene was added, and the emulsion was degassed and flushed with nitrogen three times. The emulsion was heated at 60 ${}^{°}$C for 1 h under nitrogen and then at 80 ${}^{°}$C for 45 min. Thereafter, 10 mL of a solution of potassium persulfate (KPS) (0.195 g in 20 mL of MilliQ water) was added drop-wise over 10 min. The reaction mixture was then stirred overnight at 80 ${}^{°}$C at 300 rpm. The next morning, the reaction was cooled down to 25 ${}^{°}$C and filtered through glass wool to remove traces of coagulum. Purification was performed by dialysis of the obtained latex dispersion against pure MilliQ water for 3 wk (Medicell; 12,000 to 14,000 Da). The stock dispersion was then diluted to 1 wt% for the experiments.

Microgel synthesis

The microgel particles were synthesized by precipitation polymerization following the procedure described in a former study (50). A total of 10 g of NIPAM monomer and 0.68 g of BIS (5 mol% with respect to NIPAM) cross-linker were dispersed into 420 mL of MilliQ water under constant stirring. Two batches were synthesized: one containing a cross-linkable rhodamine dye added to the reacting mixture (10.0 mg in 10 mL of water) (labeled microgels LMs), and another one used for the Raman confocal microscopy experiments, which is unlabeled (UMs). Nitrogen was flushed through the dispersion for 30 min prior to polymerization to remove the oxygen from the mixture. The reaction was initiated at 80 ${}^{°}$C by dropwise addition of a KPS solution (10 mg in 10 mL). The polymerization was then carried on under constant stirring and nitrogen flow for 4 h. Afterward, the dispersion was cooled down to room temperature and filtered through glass wool. The final dispersion was cleansed by dialysis for 2 wk. The stock dispersion was then diluted to 1 wt% either with MilliQ water or by adjusting the ionic strength to 0.1 M using a concentrated KCl solution.

Fluorescently labeled or not microgels

We synthesized both fluorescently labeled und unlabeled PNIPAM microgels in this study. They were characterized by an array of methods described in SI Appendix, such as DLS (SI Appendix, Fig. S6), SAXS (SI Appendix, Fig. S7), and SEM (SI Appendix, Fig. S8). Both have similar swelling and structural properties, and control microscopy experiments did not evidence any significant quantitative differences between the two types in respect to their drying behavior. SI Appendix, Table S1 summarizes what microgels were used for each experiment.

Cell Design

The drying cell was made of a rectangular borosilicate capillary with a cross-section of 0.1 × 1 mm² and a length of a few centimeters. One end of the capillary was connected to a small capped plastic cylinder, which served as a reservoir. The reservoir’s cap was pinched with a small hole, in which we inserted a tubing to hinder water evaporation from it, but ensure pressure equilibration. Both capillary and reservoir were glued on a microscope glass cover slide using an ultraviolet photocurable epoxy glue. The other end, which was cleanly cut, was opened to air. Typically, 200 µL of the sample solution/dispersion was placed into the reservoir and then flew to the free tip, at which point it was exposed to an airflow of controlled humidity, and the drying process started. The second element of this setup was made of a larger rectangular borosilicate capillary with a cross section of 1 × 10 mm². One end was connected to an airflow of controlled humidity (see below). The other end was placed exactly in front of the smaller capillary that contained the sample. For the SAXS experiments, the reservoir was slightly modified, as the X-ray beam was horizontal contrarily to the microscopy setups, whose observation path were vertical (90${}^{°}$ tilt).

Air of Controlled RH

The airflow of controlled RH was generated by using a humidity generator from HumiSys (InstruQuest Inc.) used together with a humidity/temperature probe. The desired RH was achieved through the mixing of dry and water-saturated air that was performed automatically.

DLS

DLS (LS Instruments) experiments were performed in pseudo cross-polarization. on a dilute PS particle dispersion (0.01 wt%) at 20 ${}^{°}$C at angles ranging from 45${}^{°}$ to 135${}^{°}$ with 15${}^{°}$ steps. The diffusion coefficient D was determined from a first cumulant analysis, and the linear extrapolation of the decay rate Dq² against q², q being the scattering vector. The hydrodynamic radius was derived from the Stokes–Einstein relationship. Labeled and unlabeled microgels were characterized on an ALV light scattering at angles ranging from 30 to 50${}^{°}$ with 5${}^{°}$ step. The hydrodynamic radius was determined following the same data analysis as for the PS latex with increasing and decreasing temperature from 20 to 40 ${}^{°}$C with 1 ${}^{°}$C increments.

SAXS

SAXS experiments were performed at the Paul Scherer Institute (PSI) at the cSAXS beamline and at the European Synchrotron Research Facility (ESRF) on the ID02 beamline. Measurements were performed on labeled 1 wt% dispersions contained in 1-mm quartz capillary at 20 ${}^{°}$C. The temperature regulation was ensured by a thermostated cell connected to a thermostat. The form-factor measurements were analyzed following standard procedure after transmission normalization and solvent subtraction. Experiments were performed on a flat capillary connected to a reservoir described in Fig. 1. Samples were dried at ambient temperature and then taped to the thermostated cell, the temperature of which was set at 23 ${}^{°}$C. After 10-min equilibration, scans along the capillary were performed to characterize the density profile.

TEM

The TEM imaging of the PS particles was performed on a TEM-CM100 (Philips) with an acceleration voltage of 80 kV. Samples for conventional TEM were prepared by dropcasting a 1 wt% dispersion on a 300 mesh carbon-coated copper grid placed on paper filter at room temperature. The statistical micrograph analysis was done by using ImageJ.

SEM

SEM micrographs of dried PS and PNIPAM salt-free dispersions were captured on a JSM 6700F NT microscope (JEOL) with an acceleration voltage of 10 kV. The 1 wt% dispersions were dried at ambient temperature and sputtered with gold.

Laser-Scanning Confocal Microscopy

An SP5 inverted Leica microscope equipped with a resonant scanner was employed. The temperature was set at 23 ${}^{°}$C by a thermostated enclosure with an accuracy of 0.1 ${}^{°}$. The analysis of the fluorescence profile was carried out by using a low-magnification 10× objective, whereas higher magnifications were achieved by using a 100× oil objective. Labeled microgels were excited by a 543-nm HeNe laser, and the fluorescence recorded was typically from 580 to 700 nm. Experiments at low magnification were performed by using the typical drying cell, whereas experiments at high magnification were done on a thinner cell consisting of 1-mm-wide channel connected to a reservoir. The channel consisted of two superposed thin coverslips separated by an 80-µm-thick double-tape film.

Cross-Polarized Bright-Field Microscopy

We used a Zeiss Axioplan microscope or a WITec Alpha 300s confocal Raman microscope, with the sample placed in between two crossed polarizers. Following the experiments, either a 20× or 40× objective were used. The drying cell was placed on a thermostated metal block connected to a thermostat. The control humidity was achieved by using a humidity generator HumiSys from InstruQuest, used together with a humidity/temperature probe. The desired RH was achieved through the mixing of dry and water-saturated air. The air was blown on the open end of the capillary. We observed all systems, including UM and LM microgels (which yielded similar results).

Raman Confocal Microscopy

Raman experiments were performed on a WITec Alpha 300R confocal Raman microscope with a 532-nm laser wavelength (Power 54 mW). Each spectrum was the average of 20 measurements of 14.5 ms (detector in electron-multiplying–charge-coupled device mode). On a given line, spectra were acquired every micrometer, with a ×50 long-distance objective (ZEISS EPI “Achromat ELWD”; numerical aperture: 0.55; working distance: 8.7 mm), which gives a lateral resolution of around 500 nm and a depth resolution of around 2.8 m. We verified the absence of sample damaging over time due to laser exposure. Composition gradients were obtained from the resulting spectra series by using a two-component fitting procedure, based on the spectra of pure water and pure PNIPAM. This procedure was checked against binary PNIPAM/water mixtures of known composition to obtain a calibration curve. In practice, the correction was only relevant at very low PNIPAM content, close to bulk. Otherwise, the two-component analysis readily yielded PNIPAM and water volume fractions.

Sorption Balance

Water-activity variation with water fraction (sorption isotherm) was obtained by using a DVS Advantage sorption balance (Surface Measurement Systems Ltd.). This technique requires a small amount of the dried sample (4 to 6 mg), which is placed in a glass cup and exposed to a stream of N₂ with a programmed RH. The sample was first dried in dry N₂ for 4 h and then exposed to an RH ramp from 0 to 94% for 46 h. The sorption was continuously determined by weighing the sample with a microbalance.

Data Availability

All study data are included in the article and/or supporting information.