Colloidal crystals and water: Perspectives on liquid–solid nanoscale phenomena in wet particulate media

Colloidal Crystals and Water: Perspectives on Liquid-Solid Nanoscale Phenomena in Wet Particulate Media Francisco Gallego-Gómez,a* Víctor Morales-Flórez,b,c Miguel Morales,a Alvaro Blancoa and Cefe Lópeza a Instituto de Ciencia de Materiales de Madrid (CSIC), c/ Sor Juana Inés de la Cruz 3, 28049 Madrid, Spain. b Departamento de Física de la Materia Condensada, Universidad de Sevilla, Av. Reina Mercedes, 41012 Seville, Spain. c ICMS (CSIC-US) Av. Américo Vespucio 49, 41092 Seville, Spain. Keywords: colloidal crystal; particulate media; wet granular materials; interfacial water; micromechanical properties. Abstract Solid colloidal ensembles inherently contain water adsorbed from the ambient moisture. This water, confined in the porous network formed by the building submicron spheres, greatly affects the ensemble properties. Inversely, one can benefit from such influence on collective features to explore the water behavior in such nanoconfinements. Recently, novel approaches have been developed to investigate in-depth where and how water is placed in the nanometric pores of self-assembled colloidal crystals. Here we summarize these advances, along with new ones, that are linked to general interfacial water phenomena like adsorption, capillary forces and flow. Waterdependent structural properties of the colloidal crystal give clues to the interplay between nanoconfined water and solid fine particles that determines the behavior of ensembles. We elaborate on how the knowledge gained on water in colloidal crystals provides new opportunities for multidisciplinary study of interfacial and nanoconfined liquids and their essential role in the physics of utmost important systems such as particulate media. 1. Introduction The behavior of a liquid interacting with a solid surface [ 1 ,] is a fundamental subject for a vast number of phenomena. Topics such as adsorption and condensation [ 2 , 3 ], wetting and capillarity [ 4 , 5 ], or liquid-mediated forces [ 6 − 78 ] rely on the physics of liquid-solid interfaces at the smallest scales and are critical for many natural processes in e.g. geology [ 9 ], biology [ 10 , 11 ] or meteorology [ 12 ]. Nowadays, such phenomena become ever more important in scientific and technological fields, the more, the smaller the relevant scales at play. Nanofluidics [ 13 , 14 ], microseparation [ 15 , 16 ], super liquidrepellency and superwettability [ 17 , 18 ], confined liquids [ 19 , 20 ] and nanotribology [ 21 , 22 ] are only some related issues of significance in current nanomaterials science. However, despite its importance, the behavior of interfacial liquids is still far from being well understood, especially in confined environments. In turn, the properties of a solid system are often determined by the presence of a liquid. This circumstance is especially true in systems composed of discrete particles, not only due to the high surface-to-volume ratio but also because the presence of a liquid dramatically affects the interparticle action −to a large extent through capillary forces. No matter the particles size, the influence of a liquid (above all, water [ 23 ]) in such particulate systems essentially relies on interfacial features at the nanoscale, which govern the behavior at the particle level. For instance, familiar examples are sand, which becomes ‘workable’ when is wetted by liquid films 5-nm thick or less on the grains [ 24 ], and flour in everyone’s kitchen, which is sticky on rainy days through adsorption of a few water layers [ 25 ]. Set plasters are formed by gypsum crystallites linked by physisorbed water films ~ 1 to 10- nm thick (from dry to saturation conditions) [ 26 ]; similarly, clay swelling is typically due to moisture uptake of one to three water layers in the clay interlayer [ 27 ]. Friction and wear in soils, along with aging effects, depend on the presence of molecularly thin water films at the nanocontacts between mineral particles [ 28 ]. Particulate (or divided) systems generally refer to disperse phase systems containing particles disseminated in a continuous phase, and may extent, in the broadest sense, from protein solutions and bacterial cultures to interstellar systems [ 29 ]. In this article, we restrictively consider ternary solid-liquid-gas systems composed of a dense assembly of solid particles distributed in a gaseous environment that is partially filled by a liquid phase. These are referred to as (partially) wet or unsaturated particulate media, in which the liquid creates pendular (surrounded by gas phase) bridges between the particles exerting capillary interactions. By extension, one can include into this type capillary suspensions [ 30 , 31 ], which are dense particles-liquid-liquid systems governed by capillary forces. Unsaturated particulate media include solid colloidal aggregates [ 32 ], powders [ 33 , 34 ] and granular materials [ 35 −, 36 , 37 ]. Such systems are ubiquitous in nature (from soot to feathers to rocks and soils) as well as in technological and industrial materials, in intermediate or final form (coatings, desiccants, cements, pharmaceuticals, foodstuffs, modern ceramics, thermal and radiation shields, metallurgy...). Although the continuous phase in these media is formed, in principle, only by a gas (air, mostly), it virtually always involves some amount of liquid, frequently due to the mere adsorption of water from the moist surrounding. For example, the important influence of humidity in the mechanical behavior of powders and granular media exposed to habitual atmospheric conditions [e.g.−, 38 , 39 , 40 , 41 ] shows that water must be almost universally considered. Thus knowing its interaction with particles is essential for e.g. materials science, biomedicine, civil engineering, mining, catalysis, oil recovery, agriculture and transport in soils, or even to prevent erosion and natural hazards like landslides and avalanches. Hence, the vast majority of divided media are wet particulate materials with huge practical interest. Nevertheless, most work has focused on dry particulate systems (solid-gas) [37, 42 , 43 ] and, more recently, colloidal and granular suspensions (solid-liquid) [ 44 , 45 ] because of the much simpler binary-phase scenario −even so, they are still poorly understood. The additional fluid phase in the unsaturated case strongly complicates the picture and justifies that, apart from the phenomenology, the physics of wet particulate systems have been little studied and remains largely unknown [35, 46 ]. One reason is that, although liquid-particles behavior relies on nanoscale phenomena, most research has been limited to relatively large scales, from millimeter down to micrometer (as in wet granular media [24,35,36,39, 47 ]).Thus, new experimental and theoretical approaches are needed to facilitate access to smaller scales, which is especially challenging for bulk features in such opaque systems. Another reason is that the treatment of particulate media is fundamentally complex because they are composed of unequal particles with irregular arrangement. In the presence of a liquid, knowing the distribution and interplay of the different phases becomes an extremely difficult task, principally at the nanoscale. In order to overcome these difficulties, one can consider a kind of both ‘tractable’ and ‘small’ divided systems such as solid colloidal crystals (CCs), which commonly designates threedimensionally ordered arrangements of self-assembled submicron, monodisperse spheres surrounded by air [ 48 ]. Thereby, in spite of the small particle scale, Brownian motion is suppressed by the compactness of the structure. Since the position, size and shape of the spheres are known, CCs constitute an attractive approach for the study of general features of particulate media. Our laboratory has lately dedicated much work to investigate the interfacial water in CCs, which is taken up from the surrounding moisture in significant and controllable amounts. In particular, studies focused on silica CCs, being silica-water a most essential system in nature and technology. Among versatility and availability, CCs possess two prominent advantages: 1) they have a welldefined particles arrangement, as already mentioned; 2) as periodic dielectric structures, they exhibit photonic bandgaps (Figure 1) that, as it turns out, can be employed as a signal to probe water. Based on these characteristics, innovative methods have recently been developed to study how water is nanoconfined in the opal interstices [ 49 ]. In this article we summarize these latest techniques and describe former and new findings that not only teach about detailed nanometric features of water in opals but also open interesting perspectives on general, interdisciplinary liquid-solid physics. More specifically, we discuss possible links between CCs, as well-defined wet particulate materials, and general ternary particlesliquid-gas systems which are relevant in many different fields. Important aspects found in CCs, especially those dependent on water content, like mechanical properties, are pointed out as useful analogies to e.g. wet granular materials to be exploited in the future. 2. Water in Colloidal Crystals CCs (also referred to as artificial opals) are in their own right a relevant material class for numerous applications in photonics and energy [ 50 , 51 ], detection [ 52 , 53 ] or as atomic/molecular models [ 54 ]. For such uses it is important to know how the unavoidable presence of liquid (e.g. from condensation of a surrounding gas atmosphere) affects their performance, although historically this issue has barely received attention. Other applications of CCs as membranes [ 55 ], nanostructured platforms [ 56 , 57 ] and templates [ 58 , 59 ] depend on flow and diffusion processes of liquids in nanoconfinements such as the opal interstices. Any advance in the comprehension of these features is also beneficial for fields such as colloidal assembly or capillary/evaporation-assisted lithography [ 60 , 61 ]. We will show that CCs inherently contain a nonnegligible amount of water picked up from the ambient, especially if the constitutive spheres are hydrophilic, as it occurs in typical cases like silica opals. Water is demonstrated to significantly affect the photonic properties of the ensemble, a fact that renders the CC a suitable labon-a-chip to study the behavior of the confined liquid. This method, which provides an indirect means to know the water morphology within the CC, is complemented by quasi-direct visualization of the water structures. Special attention is given to discern, under different conditions, how water is distributed, whether located between the particles as capillary bridges (necks or menisci) or on the spheres surface as a wetting film. The distribution of the liquid phase between the solid particles is decisive for the behavior of CCs as well as any divided system, as it determines aspects such as the intergrain capillary attraction or the flow of liquid across the medium. Presently there is no satisfactory manner to predict or measure such distribution. 2.1. Water Adsorption in Silica CCs Submicron silica spheres (in particular, amorphous silica prepared by Stöber synthesis [ 62 ]) are extensively used for easy fabrication of high-quality face-centered- cubic (fcc) artificial opals [ 63 ]. Silica exhibits high hy- Figure 1 Typical reflectance spectrum of a CC (silica spheres with 335 nm diameter) showing a photonic bandgap (Bragg peak). Inset: sketch of the CC and the simple recording scheme. drophilicity due to the presence of a large number of −OH groups (silanols) at its surface [ 64 ]. In a humid ambient, water molecules in vapor phase tend to adsorb on the silanol groups through hydrogen bonds, building a monolayer or, potentially, a multilayer of successively adsorbed water molecules, until a wetting film is formed on the silica surface. This type of water, loosely bound to the silica surface by physical bonding, is referred to as physisorbed water. Its content depends not only on the density of surface silanols but also on the ambient conditions, temperature (T) and relative humidity (RH), so this water readily begins to desorb (desorption or dewetting) by e.g. increasing the temperature or decreasing the ambient pressure. This amount of water in an untreated (asgrown) silica CC can be directly measured by thermogravimetry (TGA) from weight loss upon heating [ 65 ]. It is found that a very significant percentage of water, as large as ~ 7 wt.%, is physisorbed at room temperature (RT ≈ 25 ºC) and RH ≈ 40 %, which is easy to remove by gentle heating, until complete elimination at ~ 120 ºC (Figure 2a). Further heating leads to silanol condensation (at  150 ºC) and, consequently, loss of water affinity of the surface [65]. Such thermal annealing is a simple means to adjust the surface hydrophilicity of silica, which we employ to study the influence of the surface type. The RH dependence of water uptake gives further insight into its provenience. Therefore, we performed water adsorption isotherms in the silica CC, confirming the large amount of water present (Figure 2b). The water content at RH ≈ 40 % approaches 7 wt.%, in accordance with TGA. The form of the isotherm is signature of initial adsorption of a monolayer of water molecules at low RH, followed by a remarkable multilayer formation [2]. The convex shape at RH < 10 % (isotherm type II) denotes the presence of narrow micropores (< 1 nm) in the spheres. Such pores are expected in Stöber particles [ 66 ] while larger micropores (1-2 nm) are discarded by nitrogen adsorption measurements [65]. Thus, further water adsorption (up to 90% RH) appears to be due to multilayer formation on the outer surface of the spheres, constituting the largest water contribution. Above 90% RH additional water uptake is visible, due to capillary condensation of water vapor in the porous CC structure, that is, in the gaps between spheres. For sake of comparison, similarly large amount of physisorbed water and analogous temperature behavior have been reported in comparable silica spheres assemblies [63,66− 68 ]. Water isotherms in cellulose and pharmaceutical powders also show a water content of ~ 6−10 wt.% at moderate humidities, largely due to multilayers [ 69 ]. Clay minerals show multilayer adsorption above 15% RH and contents of 5−10 wt.% at 40% RH [ 70 , 71 ], and setup of capillary condensation at 80% RH [71]. Capillary condensation is settled by the radius rk of the liquid meniscus to be formed (Kelvin radius) given by rk = −  Vm/RgTln(RH/100), where  is the liquid-gas surface tension, Vm is the molar volume of the liquid and Rg is the molar gas constant. In the CC interstices, which are in the range of tens of nm, capillary water condensation sets in only at high humidities, when rk is comparable to the pores dimensions (rk ≈ 5 nm at 90% RH). Capillary condensation at lower humidities would denote the existence of mesostructure. This is the case, for instance, of assemblies of mesoporous silica spheres with diameter in the 100-nm range, in which stepwise capillary condensation first occurs at 40−60% RH in the spheres pores of 2−6 nm, and later at ~ 90% RH in the gaps between spheres [52, 72 ]. Such step at intermediate RH is absent in the CC. Thus, silica CCs are macroporous structures naturally containing a considerable amount of water, mainly originated by multilayer adsorption in the voids formed between the spheres. It is worth noting that, before any measurement, samples were heated at ~ 120 ºC (for complete dehydration while keeping the silica surface unchanged) and cooled down to RT. Hence, spurious contributions like excess water in suspension [28,64] or remnants from opal fabrication [ 73 ] can be safely neglected. That is, we deal with water that truly comes from surrounding moisture and is an intrinsic part of the CC, along with the spheres and the interstices between them. In hydrophilic CCs like silica ones, the presence of water is very significant (7 wt.% water fills about half the volume of the voids of an ideal fcc opal), so it must surely be considered in order to faithfully characterize the opal. The distribution and behavior of this water in a CC was unknown until recently. Two original approaches were used to investigate the water morphology in such nanoconfinments, as described in the next Subsections. 2.2. PBG Method: The CC as Lab-on-a-Chip A prominent use of CCs is as 3D photonic crystals. Indeed, the well-ordered spheres arrangement composes a periodic dielectric material, in which light cannot be transmitted in certain energy ranges, referred to as stopbands or photonic bandgaps (PBGs). The lowest-energy PBG, or Bragg peak, is associated to the diffraction produced by the (111) family of crystallographic planes (Figure 1). The Bragg peak properties, described by the Figure 2 (a) TGA analysis of an as-grown silica CC (335-nm spheres). Adapted from Ref. 65 with permission. (b) Water adsorption isotherm on an as-grown silica CC (260-nm spheres). Adapted from Ref. 49 with permission. position (  Bragg) and width, are determined by the CC parameters. On the one hand, the dimensions and packing of the spheres define the lattice parameter a (the side of the fcc unit cell) and the filling fraction of the spheres f. On the other hand, the materials building the opal give the respective refractive indices, that is, the spheres (ns) and the media filling the voids (nv). An intuitive but only approximated description of the Bragg peak position is given by the Bragg’s law, which can be expressed (at normal incidence) as:   22 )1( 34/ = vsBragg nfnfaλ . (1) Although not described by the Bragg’s law, the peak width depends on the dielectric contrast ns/nv and the lattice parameter, so that the width broadens for higher contrast and a. Experimentally, the width is taken as the full-width at half-maximum of the Bragg peak. For an ideal fcc structure, f = 0.74 and a = √2 D (D being the spheres diameter). Conventionally, voids have been considered to be filled just by air (nv = 1). However, the non-negligible fraction of water in the CC must directly affect its photonic properties. This fact is illustrated by two simple, qualitative experiments: 1) some gas (dry air or nitrogen) is blown against the silica opal; 2) the atmospheric pressure surrounding the CC is reduced. In both cases, the optical spectrum is simultaneously measured. Figure 3 demonstrates that  Bragg (and the width −not shown), significantly decreases in both tests, and it occurs in a reversible and fast manner. Such behavior has a trivial explanation if one considers the large amount of physisorbed water in the CC, which is susceptible to easily change upon variation of the ambient conditions. Concretely, in both experiments the water content decreases, and so it does the average refractive index in the opal voids, leading to blueshift of the Bragg peak (as simply deduced from Eq. (1)). The fast recovery of the shift demonstrates a rapid water re-adsorption by the CC. Such important role of adsorbed water, however, has been generally ignored and only exceptionally (and rather qualitatively) considered [63]. To establish a quantitative correspondence between Bragg peak and water is, however, more complicated because the PBG properties do not only depend on the amount of water. Indeed, its precise spatial distribution in the CC interstices is not included explicitly in the oversimplistic Bragg’s law and only averaged in nv and f values but decisively affects both peak position and width. The latter, which is often disregarded in opals characterization, is a pivotal experimental parameter to discern the water distribution, as discussed below. By adequately correlating the Bragg peak properties with a complete description of the CC (solid, liquid and gas phases), one can infer the morphology of the adsorbed water just by simple reflectance measurements. This is the approach we developed recently [ 74 , 75 ], in which the PBG is taken as a sensitive probe signal. Thus, the CC becomes a lab-on-a-chip, whose optical response provides access to structural information of any material within the pores network. We refer to this technique as the PBG method. The procedure consists in correlating the measured Bragg peak with the exact water distribution by using a simple model (Figure 4, left). Hereby, it is distinguished between (1) water placed in the voids, which is assumed to build up a homogeneous wetting film with uniform thickness d around the spheres surface, and (2) water placed between nearest−neighbor spheres forming a pendular neck defined by size R (azimuthal radius) and thickness η (see figure). This bridge is assumed as axially-symmetric (gravity force negligibly affects capillary water in sub-millimeter pores [ 76 ]). Although such a liquid neck is known to generally approach a toroidal profile (circular approximation for capillary bridges [7, 77 ]), the interface with air is here assumed to be flat for simplicity. The curvature of this interface (the meridional radius of the meniscus, r), which is relevant for the resulting capillary force (see Section 3.3.1), can be straightforwardly obtained geometrically by imposing the circular approach. The model considers η ≥ 0, so some separation is allowed to exist between the spheres; that is, a nonclose-packed fcc structure is permitted for the CC. This is an important assumption in our model, as discussed later. Given the importance of capillary force, Figure 4 Left: Sketch of the modeled distribution pattern of the water in the CC assumed for the PBG method. A wetting film of thickness d on the spheres and a capillary neck between each two neighboring spheres, described by R and  , are distinguished. The meniscus radius r can be obtained geometrically. Right: Limit cases for the ratio ρ, for which water is uniformly distributed on the spheres as a wetting film (ρ = 0, top) or entirely accumulates in the necks (ρ = 1, bottom). Figure 3 Bragg peak position (  Bragg) of different silica CCs during changing ambient conditions. (a) Dry air is blown against the sample (identical results were obtained using nitrogen). (b) Decrease of atmospheric pressure (low vacuum). The external action was set on and off at t=4 and 11 s, respectively. Note that the different time response are rather due to the dissimilar onset/offset times of the external action.  Bragg was calculated from in situ fast-recorded (intervals of 2 ms) spectra. Reprinted from Ref. 49 with permission. another relevant aspect is how much water accumulates in the necks. This fact is conveniently apprehended by a further parameter ρ, dependent of the other ones, which is defined as the ratio of the water bridge volume to the total water volume. Thus, ρ  → 0 when the water entirely forms a wetting film (no bridges), and ρ  → 1 when it builds only bridges between the spheres without wetting film (Figure 4, right). The PBG method is applied to an experimental series in which controlled desorption of the physisorbed of CC is induced by gentle heating until complete dewetting, while measuring in situ the changes in the Bragg peak [74,75]. For each T, a number of triads of parameters {d, R,  } is compatible with the corresponding amount of water (known from TGA), so any triad describes a possible distribution pattern. Using a simulation software that calculates the exact solutions for the PBGs, the Bragg peak properties are obtained for each possible case. We performed accurate calculations based on the plane-wave expansion method, which allowed for the computation of heterogeneous periodic structures having a nonuniform distribution [74]. Finally, an iterative process finds the three variables {d, R,  } that fit best the measured PBG, and thus the water pattern in the CC is obtained along the experiment. Note that precise knowledge of the spheres diameter D is critical for the calculations (affecting the lattice parameter), but even electron microscopy yields a typical error of several nanometers, apart from the inevitable (although small) size dispersion. Measuring at the completely dewetted CC (T ~ 120 ºC) enables to accurately establish D (at least, an ‘effective diameter’), as long as a strictly close-packed fcc structure is assumed when dehydrated. Water desorption has a straightforward effect (typically, in about 1 s) on the Bragg peak properties (Figure 5), which basically resembles the progression of the amount of water measured by TGA (Figure 2a), confirming their close correlation. As long as the CC was heated below 150 ºC, the changes provoked in the PBG were fully reversible upon cooling the CC down and desorption and re-adsorption curves perfectly matched without hysteresis [74]. Such reversibility is a fundamental support that temperature only causes water desorption without any further structural changes in the opal, and it additionally confirms that we exclusively deal with water adsorbed from the ambient. By contrast, heating above 150 °C induced partial dehydroxylation of the silica surface [65] and prevented complete water re-adsorption, so the PBG did not fully recovered its original form and position at RT, showing a clear hysteresis loop. The desorption data (up to 150 ºC in Figure 5) allow to obtain the parameters {d, R,  } in the hydrophilic (as- Figure 5 Evolution of the Bragg peak properties of an as-grown CC (335- nm silica spheres),  Bragg (a) and width (b) upon three heating/cooling cycles (solid/empty symbols with same shape each). Between RT and 150 °C (black squares and red solid circles), changes are reversible without hysteresis. After heating above 150 ºC (red circles and green triangles), partial irreversibility and pronounced hysteresis is observed. This behavior is schematized in the inset: below 150 ºC, black line; above 150 ºC, red and green lines. Reprinted from Ref. 74 with permission. Figure 6 Top: Evolution of the parameters of the modeled water distribution (depicted in the inset) upon water desorption in as-grown (black symbols) and annealed (colored symbols) CCs of 335-nm silica spheres. Solid lines follow the values obtained at RT (open symbols). Bottom: Graphical representation of the water distribution (azimuthal view of an internal (111) plane) using the model parameters obtained for the asgrown silica CC at RT. Water in the central sphere is not depicted to remark the wetting film. Adapted from Ref. 75 with permission. grown) silica CC between RT and complete dewetting. These are shown in Figure 6 (black symbols) as function of the water content (decreasing values to the right side of the figure, as it is the change direction in the experiment). At RT, the physisorbed water considerably concentrates between the spheres, building big necks (η = 12 nm and R = 64 nm; these values lead to r ~ 20 nm by assuming contact angle  = 0º). The large η means that the spheres are substantially separated, forming a nonclose fcc packing. Note that this result is direct consequence of the pronounced narrowing of the PBG width upon desorption, until 6% reduction (Figure 5b). As the dielectric contrast increases (nv decreases down to 1), the expected width broadening must be counterweighed by a marked reduction of the lattice parameter upon dewetting, which makes necessary a nonclose configuration at RT [74]. In spite of the accumulation in the necks (ρ = 0.6), water also builds relatively thick wetting film (d = 4.5 nm), which is consistent with the massive multilayer adsorption measured in Figure 2b. The modeled water distribution resulting from these parameters is graphically represented in Figure 6 (bottom). Upon water desorption, two marked regimes are observed in Figure 6. First, down to ~ 2−3 wt.% water (T ~ 60−70 °C), both d and  quickly diminish until vanishing, while R keeps constant. At this point, all the remaining water is placed in the necks (ρ = 1), actually building an annulus around the contact points of the already touching spheres (close-packed fcc, η = 0). Second, below ~ 2 wt.% water (T  70º C), further dehydration leads to abrupt decrease of R, since the annuli are the last reservoir of water. On the one hand, this behavior shows that water on the spheres surface (more exposed without an adjacent sphere) desorbs more easily than the water between the spheres. This is in accordance with the general behavior in porous systems, in which higher temperatures are needed to dewet narrower pores, where the equilibrium vapor pressure is lower [1]. On the other hand, it seems that R remains constant until d vanishes, which suggests that water would flow from the wetting film, as long as it persists, compensating the volume loss of the neck. The influence of the surface in the water pattern is studied by employing the PBG method on progressively hydrophobic (annealed at increasing temperatures) silica CCs (Figure 6, colored symbols) [75]. The gradual loss of hydrophilicity logically leads to less amount of water at RT. The {d, R,  } values deduced at the experiment start (empty symbols of each data set) show a welldefined trend (solid lines) toward 0 in a perfect hydrophobic CC. Note that the spheres tend to adopt a closepacked fcc arrangement in hydrophobic CCs (  → 0). Simultaneously,  tends to 0, which indicates that the more hydrophobic the opal, the more uniform is the water distribution (the lower is the fraction of water forming bridges). Regarding the evolution of the parameters upon dewetting, two general conclusions can be drawn. First, each data set evolved nearly parallel to each other, indicating that, independently of the type of surface, water desorption proceeds almost identically as described above for the as-grown CCs. Second, none of the resulting water patterns coincides with one another, even at same water contents. In other words, the water always distributes differently on surfaces with different hydrophilicities, so the water pattern is unique for each type of surface. This finding eventually denotes that the surface energy affects the mechanisms determining the water distribution, which are discussed in Section 3.2. These results show that a great deal of information on the behavior of nanoconfined water can be obtained by a simple optical procedure. The distribution of water in wetting films or necks between submicron particles and the influence of the surface hydrophilicity, which are most important subjects in nanoscale materials science, can be relatively easily studied and demonstrates the potential of the PBG method. Kinetics of water adsorption and bridge formation can also be studied in this way. 2.3 One-Pulse CVD: Imaging of Water Morphologies Despite the described capabilities, the PBG method is an extrapolative technique which, in addition, takes account for the average behavior of the whole CC structure, so the verification of the deduced results by an independent means is desirable. Besides, the modeled distribution is expected to depart from the actual water morphology in some aspects like the homogeneity of the wetting film. An obvious goal would be to directly image the water in the particulate medium, which is actually a very difficult task, pursued in different systems since decades. For instance, in granular materials the gasliquid phase has not been resolved below the micrometer range, even with exigent techniques like X-ray microtomography [ 78 , 79 ]. The use of optical microscopy requires the immersion in index-matching fluids [ 80 , 81 ], thus departing strongly from the original water-air configuration. Sophisticated techniques like environmental or in situ liquid-phase electron microscopies [ 82 ] allow direct submicron analysis but currently limited by factors such as restricted operating conditions or possible system distortion by the high applied voltage. Scanning electron microscopy (SEM), as a customary facility in laboratories, would be ideal for inspection at the nanoscale but the required vacuum removes the water. However, a quasi-direct visualization of the water morphology would success if the water pattern is ‘fixed’ under ambient conditions previous to SEM inspection. We recently developed this approach in silica CCs by transforming the water into silica with a modified chemical vapor deposition (CVD) [ 83 ]. Standard CVD typically applies alternating pulses of SiCl4 and water vapors for sequential silica growth and further wetting, respectively. In contrast, since we aimed to ‘catch’ only the native water in the CC avoiding any additional contribution, we used one single SiCl4 cycle and no water pulses, so the reaction occurs only where moisture was previously adsorbed. Hence, this one-pulse CVD, performed at chosen ambient conditions, replicates the original water pattern into silica and allows submicrometric analysis by conventional SEM. Several tests, including simulations and experiments with variable pulse lengths, supported the reliability of the experiment [83]. It is worth noting that akin ‘fixing’ strategies have also been used in wet particulate systems [31,80, 84 ]. Thereby, a liquid polymer with low melting point serves as the wetting phase, which is solidified by lowering the temperature to allow electron microscopy imaging of the original morphologies. An obvious shortcoming of such approach is that it is only applicable with certain fluid phases, so the study conditions radically departs from the initial system. Concretely, if the polymer substitutes adsorbed water, essential original features can be missed. The silica-transformed water structures in the CC resulting from the one-pulse CVD are indeed visible at SEM (Figure 7a). The patterns immediately confirm a main conclusion deduced by the PBG method: water predominantly accumulates between the spheres forming necks (Figure 7b), bearing a close resemblance to the graphical representation of the parameters in Figure 6 (bottom). The pendular state (non-connected capillary bridges) of the CC is also confirmed. This is significant because it indirectly supports two further results of the PBG method, namely the relatively thick wetting film and the nonclose spheres packing, although SEM images does not allow accurate estimate of d and  . Indeed, a large water amount such as 7 wt.% would otherwise lead to coalescent necks (funicular state) unless, first, a relevant portion resides on the spheres surface (  clearly less than 1) and, second, there exists some separation between spheres increasing the void volume. (In an ideal 335-nm spheres fcc packing, and without wetting film, the funicular state would occur up ~ 2 wt.% liquid). On larger spheres, a ‘skin’ coming from the transformed wetting film is observable (Figure 7c), which straightforwardly demonstrates that water can adsorb in stable nanometer-thick multilayers under standard conditions. We also apply this technique using different ambient conditions or spheres surfaces. Figures 8a−c show some examples, in which the opals contain much less water (due to desorption or larger hydrophobicity). The images confirm another relevant feature predicted by the PBG method: the bridge size barely decreases upon significant reduction of the water content from about 7 wt.% (Figure 7b) to 3 and 1.5 wt.% (Figures 8a and 8b, respectively). Clear decrease of the neck size (Figure 8c) is only ob- Figure 7 (a) SEM image of as-grown silica CCs subjected to one-pulse CVD at 25 ºC and 40% RH, in which the necks connected to the cleaved spheres are observable. (b) Azimuthal view of CC spheres. Missing necks denote arrangement imperfections. (c) Zoomed-in CC spheres, on which the wetting film is recognizable. Spheres diameter is 335 nm in (a) and (b), and 900 nm in (c). Adapted from Ref. 49 with permission. Figure 8 SEM images of different 335-nm spheres CCs subjected to onepulse CVD at 40% RH. (a) As-grown silica CC, at 55 ºC. (b) 560 ºC annealed silica CC and (c) polystyrene (PS) CC, at 25 ºC. (d) Quantitative comparison, for different CCs and conditions as function of the amount of water, between the water neck radii R predicted by the PBG method (open symbols) and the (silica-transformed) values measured by SEM (solid symbols). The latter were calculated taking into account a reduction of ~ 25 % in volume due to transformation of water into silica [83]. Adapted from Ref. 49 with permission. served at very low water contents, like in CCs made of highly hydrophobic polystyrene spheres (< 0.3 wt.% water at RT [83]). Even so, the neck size is still considerably large, which ratifies that water, when scarce, tends to wholly reside in the bridges between particles. In this case, d and  , although not measurable by SEM, must be vanishing small to allow such large R, as deduced in Figure 6. Together with the qualitative agreement, the predictions of the PBG method were also quantitatively endorsed, since a fair agreement with SEM values is obtained for the different situations (Figure 8d). The steep R decrease predicted in Figure 6b for water contents below ~ 2 wt.% (marked by the dashed line) makes this region much more sensitive (indeed, the accordance with SEM is worse) and, therefore, interesting for forthcoming studies. Beside the strong support to the PBG method, visualizing the (silica-transformed) water structures also allowed the study of other aspects that cannot be concluded from the photonic properties of the CC. An interesting feature concerns the topography of the wetting film. While a quite uniform film is found on as-grown spheres under standard conditions (Figure 7), the scarce water remaining on them at higher T (55 ºC) or on annealed spheres rather builds nanodroplets (Figures 8a, b) [83]. This is a crucial aspect that tells us about the wetting and dewetting properties of a surface under different conditions and the arrangement of the adsorbed water molecules [ 85 ]. SEM images also allowed straightforward investigation of the effect of CC disorder in the water pattern, in particular, in the bridge size [83]. It was found that R diminished in the regions of imperfect spheres packing (a lower quality of the opal is easily stated by an inferior Bragg reflectance). In fact, R = 61 ± 11 nm, measured in less-ordered regions of an as-grown CC (reflectance below 50%), contrasted to R = 67 ± 5 nm in high-quality areas (reflectance above 75%). An increase of missing necks with disorder was also observed, although no quantification was made. Obviously, disorder of the fcc packing leads to larger average distance between spheres and less-regular packing, explaining the formation of less bridges, with smaller R value and higher dispersion. These features illustrate the influence of the particles packing in the bridge formation, which is a key aspect in particulate systems (see Section 3.3), for which this method easily provides quantitative information, even dealing with submicron water menisci. As a last application example, the technique makes the silica-transformed capillary bridge readily accessible for direct analysis with nanometer resolution. The examination of small menisci has been so far elusive, although the precise knowledge their size and shape are critical (the more, the smaller the bridge) for calculation of the induced capillary forces (see Section 3.3.1). Furthermore, the bridge profile concerns the underlying Young- Laplace theory [ 86 ], whose validity may be questionable at small scales [ 87 , 88 ]. Figures 9a,b illustrates a fairly accurate description of the nanomeniscus formed between two silica spheres (in this case, they are not part of a CC). By taking the resulting D, R and d, we calculate r = 65 nm according to the abovementioned circular approximation, which surpasses about two-fold the observed curvature radius. This fact should attract attention to the possible deviation of the neck shape from a toroid at such scales [ 89 , 90 ]. Another features are deduced from the images. A thick adsorbed wetting film around the spheres is discerned and its thickness is straightforwardly estimated. Such a thick water film is consistent with the visible skin in Figure 7c and the values of several nm predicted for d by the PBG method (Figure 6a). The large neck size leads to merging in the presence of a further neighboring sphere (Figure 9c). Interestingly, water does not flood the interstice between the spheres (which contradicts observations and predictions elsewhere [47,78,79, 91 ]), which is a relevant aspect because menisci need of the gaseous phase to exert a capillary force between the spheres [33,36]. 3. Colloidal Crystals and Liquid in Wet Particulate Systems: Perspectives As seen, unprecedented quantitative information about the nanoconfinement of water in CCs has recently been gained from innovative optical and imaging means. The influence of factors like desorption or surface type has also been obtained. These data, when contrasted with macroscopic theories or measurements in planar systems, give insight into fundamental liquid-solid nanoscale topics and, further, singularities of not only opals but particulate systems in general. As an additional point of interest, since no water was added to the CCs, the results are particularly interesting regarding adsorption and capillary condensation in divided media. In this Section we first discuss CC features like the massive multilayer adsorption and nonclose packing as they give clues to the interactions at particle surfaces connected by water. Second, the accumulation (or not) of water in bridges in the CCs is a notable aspect to look into. Indeed, the bridge formation is determined not only Figure 9 Geometrical analysis of nanomenisci formed between ~ 900-nm silica spheres. (a) Between two spheres; (b) Zoom-in of image a; (c) Between three spheres. Water was transformed into silica by one-pulse CVD at normal conditions prior to SEM imaging. Adapted from Ref. 49 with permission. by the energies at play in the system but also by the flowability of water at the nanoscale, the latter being intimately linked to the debated water structure and mobility in nm-thick films. And third, we examine the influence of water on the properties of the particles ensemble, whereby the most obviously aspect affected is its mechanical behavior. We analyze the cohesion of the CC and correlate with the individual water bridges and the forces exerted on the submicron spheres. We also inspect the rheology of CCs and identify analogies to granular materials. Along the Section, we point out nanoscale features found in the CC that are relevant in general particulate media and concern open questions to be addressed. 3.1. Surface Forces Forces acting very close to a solid surface are responsible for the condensation of an adjoining vapor and critically affect the interfacial liquid [6], whose behavior may greatly differ from that in bulk. In turn, these forces are altered by the liquid. This interplay eventually determines two decisive characteristics: 1) the amount of adsorbed liquid; 2) the equilibrium distance between particles, which also defines the packing density. (In a particulate medium, the formation of capillary bridges and the subsequent interparticle adhesion result from these features −see following Sections). In CCs, these two characteristics actually lead to controversy: on the one hand, the massive water adsorption surpasses by far the expected value, and, on the other hand, the apparent noncontact between spheres denotes significant repulsive forces that need to be explained. These discrepancies reveal clues to the underlying surface forces in the CC, which are also present in every wet particulate system. 3.1.1. Wetting Film Thickness The equilibrium thickness d of a film adsorbed on a surface is given by the disjoining pressure  , which expresses the net repulsion between the solid-liquid and the liquid-vapor interfaces [86]. By considering only van der Waals forces, d3  = −AH/6  , where AH is the Hamaker constant across the liquid film and  = −(RgT/Vm) ln(RH/100). This predicts water film adsorption on a planar hydrophilic surface in air (AH ~ −10−20 J) of less than a monolayer for humidities below 80%. Nonetheless, water adsorption higher than expected has often been reported [6, 92 ], including multilayer adsorption at ~ 50% RH of about 3 layers (d ~ 1 nm) [ 93 , 94 ] or even more (d ~ 1.5−2.5 nm) [ 95 − 97 ]. Such adsorption excess has been attempted to explain by adding terms to  [6,92,93] although they cannot not fully explain the observations and their precise physical origin remains elusive. These contributions are principally electrostatic (double-layer forces due to surface ionization) or structural (hydration forces caused by ordering of the first water layers), while the presence of surface contaminants [92, 98 ] must also be considered. In particular, the initial wetting of the silica can lead to surface ionization (and to subsequent electrical double layer) due to the silanol groups, which can also favor structuring of the adsorbed water layers [94]. Water film thickness drastically decreases on dehydroxylated silicas (Section 2.2 and literature [92,93]). Contrary to the case of flat, open surfaces, the thickness of wetting films in divided systems is affected by factors such as the interfacial tension on the convex particles surface and the capillary pressure in the gaps at contacts [ 99 ], which additionally limit the wetting film thickness. In soil and plant science, for example, these different contributions are more usually accounted for by means of the matric potential  , currently being an active research topic. Here we use it to estimate the maximum wetting film thickness predicted in a silica CC. In an ensemble of spherical grains of size D the impact of the interfacial curvature is included [ 100 ] to obtain d3  = −A/6    −  /D, where  is the surface tension. By considering only van der Waals forces,  = −  and A = AH. At 40−50 % RH,   ≈−108 Pa and d is practically identical to the value in planar systems, while hydration and electric double-layer would increase both  (less negative) and d. However, from capillary scaling there exists an upper limit for the matric potential at which the bridges coalesce given by  = − 9  /D [100], and sets a maximum d that depends on the spheres size D. The large neck size measured above indicates that the CC is not far from this point. For 335-nm spheres, this limit is about −106 Pa, which yields d ~ 1 nm by taking A = −10−20 J. Or and Tuller [ 101 ] find an “effective”A about six-fold the Hamaker constant, which would yield a maximum thickness close to 1.5 nm. In conclusion, adsorption of nm-thick wetting films in a system like the silica CC is theoretically feasible but the still superior thickness observed (d ~ 4 nm, that is, about 12 water layers) needs to be explained yet. A rigorous evaluation of the CC system using the concept of matric potential could be a convenient approach. Note that even thicker films were found on 900-nm spheres, which agrees with the trend of higher (less negative) limit to  and, hence, larger d for larger D. While the assessment of multilayer adsorption at moderate humidities is still debated in planar systems, the situation becomes even more complex in convoluted surfaces [3, 102 , 103 ] like those in particulate media. Water film thickness may increase on corrugated surfaces in a manner not attributable to capillary condensation at the asperities. While roughness is known to affect the wettability of surfaces [5], it is less clear how it influences adsorption. In different systems, water adsorption appears to positively correlate with the material rugosity. For instance, adsorbed films on rough calcite were significantly thicker (2- to 40-fold) than those on smooth calcite [96,97]. Similarly, the thickness of brine films on silica increased over 100 times with surface roughness [ 104 ]. Multilayer adsorption is observed on rather hydrophobic self-assembled monolayers, from d ~ 2 nm at low humidity up to 4 nm at 65% RH [ 105 , 106 ]. Steps in mica terraces lead to nucleation of water deposits of height of 7 nm at 65% RH [ 107 ]. In the gap between a force microscope tip and a substrate, water condensation often surpasses the theoretical predictions, building e.g. structures of 15 nm height at 58% RH [4, 108 , 109 ]. Results in soil science show that the adsorbed water films are significantly thicker in highly structured soils [ 110 ]. Indirectly, the abovementioned influence of moisture in than in its absence (T  120 ºC). We also found this trend in other works on water-controlled adsorption [135,144, 177 ], which suggests high sensitivity of the resulting force to slightly dissimilar water necks along a single experimental series. The CC strength clearly reduced from ‘wet’ to ‘dry’ state about a factor of two. Similar factors are reported in numerous pull-off force experiments between relatively smooth surfaces [136−138,144, 178 ]. This suggests that this remarkable ‘dry adhesion’ is due to van der Waals attraction, which increases when water desorption proceeds, because spheres surfaces approach close contact and the Hamaker constant is about ten times larger in air. Hence, the friction between sliding spheres is probably less significant. It must also be considered that vanishing amounts of strongly bonded water could persist at T  120 ºC and lead to non-negligible capillary adhesion [136, 179 ]. In any case, the non-collapse of cohesion supports that basically all neighboring spheres are in close contact after dewetting, which is allowed by the well-ordered opal arrangement (H and E are measured at low penetration depths, so distortion of the bulk fcc packing is negligible). Thus, the number of necks (and, later, of dry contacts) can be considered approximately constant (equal to 12) along the whole experiment. It also indicates that spheres roughness, which would radically preclude meniscus formation at low water contents and reduce the dry contact surface [ 180 ], is not determining in the CC features. Both aspects, not fulfilled in powders or granular matter, are crucial to simplify quantitative analysis in studies performed on CCs. The strength difference between wet and dry states evidences that the existence of capillary bridges clearly increases the opal cohesion. Within the wet range, H and E seem to diminish with decreasing water content before complete desorption but the trend is not sufficiently conclusive. Nevertheless, it can be assessed that the CC cohesion varies less pronouncedly than the amount of water. Correlation of the macroscopic cohesion of an ensemble with the interparticle forces has not satisfactorily been resolved to-date. The classical Rumpf model [33] simply describes the tensile strength  of a disordered granular assembly as proportional to the interparticle bond strength F exerted by an individual bridge, assuming equal bridges and particles size D and known coordination number. These assumptions are generally unrealistic in particulate systems but true in a CC. For instance, by considering yielding along the (111) plane of an ideal fcc packing, the CC hardness is given by H = 3  = 18F/D2 [162]. Often, F is assumed to be mainly due to capillary force, as in assemblies with relatively large particles bound by low-viscous bridges [33]. However, the ensemble strength can be importantly augmented by dissipative contributions like interparticle friction and viscous forces [33,118]. Indeed, F ~ 900 nN is obtained for the CC from the experimental H ~ 150 MPa, which largely surpasses the value of Fcap ~ 60 nN for a single capillary bridge (see Eq. (2) below). This discrepancy is quantitatively less because, on the one hand, the expression of H, which is deduced from the tensile strength, may significantly overpredict F in a compressive experiment like nanoindentation [118], and also neglects the force chains [34], surely important in the CC. On the other hand, if the actual meniscus radius r were smaller than expected, as we already observed in 900-nm spheres (Figure 9), the calculated Fcap would increase (Eq. (2)). In any case, this estimate shows that the ‘shear resistance’ of each sphere contact against deformation of the CC in the wet range is largely due by friction and viscous forces, probably dominating over capillary interaction. In this sense, F would approach the dynamic liquid bridge force, which is the sum of capillary and viscous forces [156,157]. To evaluate how these mechanisms correlate with the characteristics of the bridge, whose viscosity is unknown, thickness-dependent and probably much higher than that of bulk water, is a challenging issue to be tackled in the future. In spite of not knowing the weight of capillary forces in silica CCs cohesion, the precise information of the water necks we gathered gives an opportunity to evaluate the progress of Fcap exerted by an individual bridge upon desorption (Figure 17c), and juxtapose with the micromechanical strength. It eventually concerns how behaves Fcap between micro/nanometric surfaces, where D is too small to justify the standard approximation. A compact expression for a pendular bridge is given by [49,124] Fcap =   R(1+R/r), (2) Figure 17 (a, b) Dependence of hardness H and modulus E of a silica CC with the water content, measured by temperature-controlled nanoindentation at hmax = 600 nm and rate 50 μN/s. (c) Left axis (open symbols): capillary force Fcap individually exerted by the water meniscus between two CC spheres, considering either constant or temperaturedependent surface tension  (squares and triangles, respectively); right axis (solid circles): meniscus radius r as calculated from the bridge parameters (Figure 6) obtained from the PBG method. Data in (a, b) are taken from Ref. 161 and represented against water content as calculated from T in the original experiment and using TGA from Figure 2a. which explicitly shows the dependence with the bridge size (through R) and curvature (through R and r. (Note that Eq. (2) slightly varies depending on which point of the bridge is considered to evaluate Fcap [33]). Empirical demonstration of these dependences is actually lacking in the literature because of the inaccessibility of the necks characteristics at small scales. Most studies, both experimental and theoretical, actually investigate Fcap as function of the relative humidity, where the bridge volume is unknown and must be assumed from theoretical adsorption and capillary condensation. Moreover, these standard approaches appear to fail in predicting the bridge morphology in a particulate system such as the CC, as discussed in Sections 3.1 and 3.2. Here, in contrast, Fcap between any two opal spheres is directly calculated from Eq. (2) and the known {d, R,  } parameters (Figure 6). Unfortunately, since the meniscus radius r is not provided by the PBG method, the calculation is limited by the necessity of imposing a bridge profile, in our case, a toroidal interface (the abovementioned circular approximation). The resulting r (solid symbols in Figure 17c) decreases for smaller bridges, and consequently Fcap shows, by taking  = 0.072 N/m, a general increase upon desorption until it drops to zero by no water at all (open squares). However,  significantly decreases with temperature [179], which is important for heating experiments. By taking this fact into account, an overall but slight (about 10%) decrease of Fcap is obtained in the wet range, except at vanishing water contents when Fcap diverges (open triangles in Figure 17c). Note that same trends are also obtained using more sophisticated expressions for Fcap [7, 181 ]. Most literature on experimental adhesion between small, individual surfaces shows decreasing Fcap with decreasing water volume, at least below a certain amount (in humidity experiments, below 30–60% RH) [108,136,138,144,177,178, 182 ]. Disparate and systemspecific behaviors have also been reported, sometimes explained by micro/nanoscopic features like surface roughness precluding meniscus formation at very low amounts of water [138,180, 183 ], influence of the wetting film [181, 184 ] or behavior of the confined water layers [88]. The counterintuitive increase of Fcap with shrinking bridge in Figure 17c (for constant  ) must be attributed to the circular approximation, according to which the decrease of r dominates over that of R2 upon volume reduction (see Eq. (2)). The toroidal assumption also leads to a divergent Fcap for vanishing water contents, which should have been noticeable in CC cohesion; however, clearly lower values were measured below 0.5 wt.% (Figures 17a,b). As mentioned earlier, the capillary bridge contour probably deviates from a toroid at submicron scales. More importantly, the formulation employed derives from a continuum description of the liquid bridge, which must gradually fail under certain volume. In fact, calculations of the exact profile of nanomenisci lead to decreasing Fcap for decreasing bridge volume [88−90, 185 ]. The analysis here performed exemplifies how the simplified features of opals allow progresses in understanding cohesion in particulate media, but it remains a complex task. Dissipative interparticle forces may importantly contribute to the strength of an ensemble, due to friction and, probably to a larger extent, viscous forces generated by the nm-thin capillary bridges between particles. Dissipation caused by rupture of bridges must also be considered. Quantitative description of capillary forces needs to be further improved, for which the meniscus curvature is a critical parameter. Direct access to bridge characteristics would be greatly helpful but difficult, especially at small scales, for which the one-pulse CVD, applicable to any system, emerges as a useful empirical tool for meticulous SEM examination. Finally, though system-specific, one should not forget water-assisted phenomena like softening, dissolution or corrosion that affect granulates cohesion through e.g. plastic deformation of grain asperities (larger contact area), crystallization of solid bridges or chemical change of the surface [28,167]. Some of these processes may contribute to aging in humid granular materials [39, 186 ]. 3.3.2. Rheology and Rate Dependence Flow in powders, granular materials or suspensions is typically investigated by shear experiments [37,170]: the medium is sheared between two rough walls moving at a relative shear rate and the shear stress developed tangentially to the motion (i.e. the resistance to yielding) is measured. In contrast, information about rheology of CCs has been accessed so far only through nanoindentation [161], whereby the micromechanical performance is tested for varying rates of compressive loading. Regardless the experimental approach, the essential aspect of how the material response depends on the velocity of deformation is obtained, and, thus, the frictional or viscous behavior of the system is determined. In any case, contrary to dry granular media and suspensions, rheology and rate-dependent deformation in wet particulate systems [30,31,40,116,156,157, 187 , 188 ] have been little investigated, so the CC offers a good opportunity to gain insight into them. P–h curves (Figure 15a) readily demonstrate that the CC is more resilient to yielding (steeper loading curves) upon growing load rates and, correspondingly, H and E increases with the rate (Figure 15b). Such rate-dependent performance evidences a marked viscoplastic response [161] and is comparable to the behavior usually observed in dense suspensions [159,160] or capillary suspensions [31], in which the shear stress increases with the shear rate. Typically in nanoindentation experiments, the viscous character of a medium is revealed by the occurrence of creep displacement h (Figure 15a) [169]. Creep is consequence of the retarded reaction of the material, which remains flowing in response to the deformation energy stored in the structure during the loading; hence, the creep depends on how fast the stress has been induced. In a viscous medium, h is larger and evolves faster with increasing load rate. Measurements on opals [161] demonstrate, at ambient conditions, both large and remarkably rate-dependent h (black solid symbols in Figure 18a), and the creep dynamics clearly speeds up with the load rate (lines in Figure 18b). These facts straightforwardly endorse the viscous nature of yielding in wet CCs. Moreover, temperature-controlled nanoindentation allowed to follow the creep behavior as function of the water content [161]. Indeed, h and its rate dependence, manifestly decrease in heated, that is, drier CCs (Figure 18a). The remnant creep observed at T ≥ 120 ºC (or 0 wt.% water) can be compared to the viscoplasticity exhibited by dense dry granular media at rates high enough [37]. Such behavior demonstrates the key role of water in the CC viscosity, though it remains to question how it causes the rate-dependent response. In granular materials, rate dependence may occur because of slow formation of capillary bridges, due to slow condensation with characteristic times of several minutes [39,40,111], or viscous transport of the liquid across the pores network [80, 189 ] through ~ 100-nm-thick wetting films on micron-sized grains. However, in the experimental time scale, bridge evolution in the CC would not explain the viscous behavior. On the one hand, water adsorption in silica CCs is fast, with characteristic times of less than ~ 1 s (Section 2.2) or even milliseconds [ 190 ]. On the other hand, the high viscosity of water in the nanometer-thick wetting films would preclude significant macroscopical flow across the opal. In any case, slow bridge development causes the formation of less and smaller bridges (lower Fcap) during particles flow and leads to lower resistance deformation at increasing rates, a trend which is the opposite to that found in the CC (Figures 15a,b). As expressed above, although dense particulate media are in general viscoplastic, dry materials show a rather frictional-dominated behavior while dense suspensions exhibit viscous-dominated response because of the viscosity of the interstitial liquid and the lubricated contacts between grains [158,159]. Interestingly, rheology of both systems can be described with a common framework by properly substituting the inertial time scale by a viscous time scale including the viscosity of the fluid phase [160]. Unsaturated wet granular media represent a different scenario, where the more or less viscous liquid forms capillary bridges. Like any thin fluid film between moving particles, the bridge generates a viscous force, which is repulsive when the particles approach or attractive when they separate, and whose magnitude increases with both liquid viscosity and interparticle velocity [124]. Moreover, the capillary force exerted by the bridge may increase the interparticle friction or decrease it, if the liquid viscosity or the deformation rate is high enough to prevent solid-solid contact [153,156,158]. Hence, there exists a complex interrelation between forces, which can be treated by means of the capillary number Ca =  D/  cos  (  is the liquid viscosity and  is the rate) as the ratio of viscous to capillary forces [33]. Thus, the viscous response is more pronounced in the system when Ca>1. Such systems typically show increasing stress (resistance to deformation) at increasing rate, which leads to higher viscous force. Additionally, the energy dissipation due to rupture and formation of bridges between moving particles increases with both liquid viscosity and separation velocity [157], also leading to higher yield stress at faster deformation rates. Only a few studies have investigated these mechanisms causing rate dependence in unsaturated granular media containing rather large amounts of highly viscous liquids [33,156,157,187]. We propose the rate-dependent behavior of CCs to be caused by the viscous response generated by the nm-thin moisture-originated capillary bridges. As shown, an increase of both the mechanical cohesion and the viscoplastic response upon faster strain rates is observed the wet silica CC. Indeed, the expected high viscosity of confined water would justify that the thin (12 nm, and less under stress) water nanomenisci exhibit such a viscous response (but remaining fluid) to render the CC viscous flow behavior. From the analysis in the previous Section, the opal strength suggests that nanomenisci exert a viscous force larger than the capillary force, leading to Ca > 1. This behavior could be linked to the ratedependent and viscous liquid-like mechanical performance of more confined water [142]. In the CC, the system viscosity reduced, from wet to dry, progressively with the amount of water. This becomes evident by representing the h data [161] as function of the decreasing water content (Figure 19a, solid symbols), which suggests that the viscous response of the CC correlates with the volume of bridges. Undoubtedly, the exact physical process inducing viscoplasticity must be further investigated. In order to assess the role of the nature of the particles contacts, an interesting and simple approach is investigating the rheology of CCs subjected to one-pulse CVD [161]. Thereby, the spheres are rigidly bonded by silica necks, easily providing a ‘nongranular’ replica for direct comparison with the original opal. The creep behavior (Figure 19) demonstrates non-viscous system response as it exhibited vanishing rate-dependence and small, slow h (close to that of the opal at the lowest rate). Such drastically different performance compared to that of regular CCs even after dewetting shows the fundamental role of the particulate character in the system rheology. Besides, this distinction increases linearly with the degree of hydration, as the liquid bonds, contrary to rigid bridges between spheres, generate rate-dependent forces in the material. The water adsorbed on the CVD-silica of the nongranu- Figure 18 (a) Dependence of the creep displacement Δh with the load rate measured by temperature-controlled nanoindentation (dwell time of 60 s) at load rate 50 μN/s on bare (solid symbols) and a CVD-infiltrated (empty symbols) silica CCs. Lines are linear fits. (b) Normalized transient creep h(t) measured at 25 ºC in bare silica CCs with increasing rates, and in the ´nongranular’ CC (at 50 μN/s –no rate-dependence was observed). Adapted from Ref. 161 with permission. lar CC (approximately in the same amount as in the regular opal) caused no rate dependence, since it does not affect the cohesion of the crosslinked (nonparticulate) ensemble. Consistently, no significant variation was measured upon removing this water by heating (Figure 19a, empty symbols). Transition from granular to nongranular behavior has also been investigated by progressively solid-bonding the CC spheres by sintering or atomic layer deposition [162]. To conclude this Subsection, a relevant aspect related to rheology in particulate materials such as energy dissipation upon (plastic) deformation must be mentioned. This is an important aspect in many practical issues, from impact absorption to digging [ 191 , 192 ], and it is ultimately related to the effective viscosity of the system in response to stress. In wet particulate media, capillary bridges play a central role since they not only generate friction and viscous forces but also their rupture and reformation during strain is a hysteretic, dissipative process [154,157]. In CCs, energy dissipation has been studied by means of the plastic work WP obtained from nanoindentation, which measures the irreversible distortion of the spheres packing (Figure 15a) [161]. Figure 19b demonstrates a clear rate dependence (WP increases one order of magnitude by rising the strain rate in two decades), which evidences the viscous nature of dissipation due to the CC nanomenisci. For sake of comparison, WP measured in the opal is comparable to the highly absorbing polymer foams and periodic epoxy nanoframes [161]. Such performance is consistent with the mostcompact packing of the CC leading to highest number of liquid necks and with the marked viscoplastic behavior exhibited by them. Along with the fact that CCs themselves may be efficient impact-absorbing materials, their controllable parameters (water content, hydrophilicity, order) can help study the role of liquid bridges in dissipative particulate media. In particular, rate-dependent system viscosity is an active research subject in colloidal and granular science [132], related e.g. to shear thickening (viscosity increase with shear rate), which is desirable for damping or protective materials [ 193 ] but unfavorable for many industrial processes. The opposite behavior (shear thinning) leads, for example, to devastating phenomena like landslides. Micromechanics of colloidal ensembles is still practically unknown and much progress is to be done in the next future. Desirably, such advances will help understand dense granular flows in unsaturated powders and granular materials. For example, the contribution to granular rheology of highly viscous nanomenisci due to water adsorption, ignored so far, should be explored. The fact that moisture affects the mechanical response of granular materials suggests that such influence is not negligible. Powerful numerical tools for investigation of force networks and granular flows like the discrete element method have a great difficulty in assuming a distribution of the liquid, in particular, the liquid fraction forming bridges and their shape [46,172, 194 ]. Since these factors are achievable in silica CCs, accurate simulations can be compared to opal mechanical performance, and, in turn, it may help refine the modeling of such aspects. More generally, a better connection between macroscopic experiments used for granular-like systems and microscopic techniques like nanoindentation is needed. The fact that CCs exhibit ‘granular’ features points to parallelisms between the different systems irrespective the distinct scales and peculiarities. Certainly, some CC characteristics drastically differ from those of general particulate media, like the high compactness or the crystal-like structure. But even these diverging aspects can be useful if considered as extreme cases of interest, like the fcc packing related to the behavior of jammed systems. The versatile disorder degree of CCs, which is controllable from ideal fcc compacts to perfectly random assemblies (photonic glasses) [114], is an attractive advantage to study the role of parameters like coordination number or packing density, which are hardly tractable in general particulates. To what extent such parallelisms can be established must still be elucidated. Finally, we must allude to an important case that has been not covered, namely, when the amount of wetting liquid progressively increases in the CC up to fully immersion of the spheres. The opal, then, passes from pendular to funicular state (capillary bridges begin to coalesce) until reaching capillary and slurry states, in which the gas phase is displaced by the liquid, turning into a two-phase system. The ensemble cohesion saturates at a certain point of the funicular state and drops in the binary state as the capillary action vanishes [30,31,33,36]. The exact evolution of cohesive and rheological properties of the CC throughout these regimes is of interest as it connects, on the one hand, to dense suspensions. These are an outstanding class of materials in industry and technology, ranging from paints or fresh concrete to many food products, and consequently a great effort has been made in recent years to know better their rheology. A related material, close to immersed CCs, are matrix-embedded nanocolloidal films, which are relevant for electronic and optical applications and whose micromechanical properties begin to be investigated [ 195 ]. On the other hand, Figure 19 (a) Dependence of the creep displacement Δh with the water content measured by temperature-controlled nanoindentation (load rate of 50 μN/s and dwell time of 60 s) on bare and CVD-infiltrated (nongranular) silica CCs (solid and empty symbols, respectively). Lines are linear fits. (b) Plastic work WP measured by nanoindentation on a bare silica CC at 25 ºC and load rates of 5, 50, and 500 μN/s (black, green and orange symbols, respectively). Data in (a) are taken from Ref. 161 and represented against water content as calculated from T in the original experiment and using TGA from Figure 2a. (b) is adapted from Ref. 161 with permission. both loss of stability and drastic rheological changes may be qualitatively understood in liquid-filled granular media and soils [ 196 ] but many quantitative aspects are still not accessible [36], in spite of being of obvious interest in civil engineering or geology. Such lack of precise understanding is tragically proved by the to-date unpredictability of catastrophic phenomena like landslides [ 197 ]. The study of less-cohesive states in CCs can be an useful approach to investigate the mechanical behavior of saturated particulate media. 4. Conclusions The understanding of the behavior of water in small environments represents an outmost complex but stimulating task in materials science and technology. In spite of the great interest for numerous aspects in both scientific and industrial fields, our knowledge of many related topics is still poor, especially those affecting particulate systems. Undoubtedly, a major difficulty is the deficit of experimental approaches to investigate liquid-solid phenomena in micro/nanometric disperse media. In view of recent advances, we have described how colloidal crystals constitute a simple, advantageous lab-on-a-chip to gain new insight into water interactions within submicron spheres assemblies. Their unique structural characteristics allow the development of original techniques that configure an incipient research area to address fundamental aspects of nanoconfined water. We have described aspects of CCs that are relevant in diverse, apparently disconnected areas at different scales, and emphasized open questions concerning all these fields that must be further explored by upcoming studies. Latest results open interesting perspectives on general wet particulate media like granular materials, which render CCs a kind of ‘nano-sand’ with promising utilities. 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