Complex Aggregation Patterns in Drying Nanocolloidal Suspensions

Sep 30, 2010 - Complex Aggregation Patterns in Drying Nanocolloidal Suspensions: Size Matters When It Comes to the Thermomechanical Stability of ...
0 downloads 0 Views 2MB Size
Download PDF
pubs.acs.org/Langmuir © 2010 American Chemical Society

Complex Aggregation Patterns in Drying Nanocolloidal Suspensions: Size Matters When It Comes to the Thermomechanical Stability of Nanoparticle-Based Structures Samer Darwich, Karine Mougin, and Hamidou Haidara* Institut de Science des Mat eriaux de Mulhouse (IS2M), LRC 7228-CNRS/UHA 15, rue Jean Starcky B.P. 2488, 68057 Mulhouse, Cedex, France Received August 14, 2010. Revised Manuscript Received September 13, 2010 We report the results of a model study on the interrelation among the occurrence of complex aggregation patterns in drying nanofluids, the size of the constitutive nanoparticles (NPs), and the drying temperature, which is a critical issue in the genesis of complex drying patterns that was never systematically reported before. We show that one can achieve fine control over the occurrence and topological features of these drying-mediated complex structures through the combination of the particle size, the drying temperature, and the substrate surface energy. Most importantly, we show that a transition in the occurrence of the patterns appears with the temperature and the particle size, which accounts for the size dependence of the thermomechanical stability of the aggregates in the nanoscale range. Using simple phenomenological and scaling considerations, we showed that the thermomechanical stability of the aggregates was underpinned by physical quantities that scale with the size of the NPs (R) either as R-2 or R-3. These insights into the size-dependent dissipation mechanisms in nanoclusters should help in designing NPs-based structures with tailored thermomechanical and environmental stability and hence with an optimized morphological stability that guarantees their long-term functional properties.

Introduction The spontaneous formation of complex aggregation morphologies (dendrites, treelike fractals, and concentric rings) is ubiquitous to the drying of nanocolloidal solutions (drops and wetting films1-8). Despite the importance of these structures in studying, for instance, the morphology-dependent catalytic or optical (SERS) properties of such aggregates,1,9,10 the number of works dedicated to these structures remains singularly low compared to that of coffee-ringlike deposits11-20 or “pure” diffusion-controlled aggregation at surfaces.21-24 Although recent interest in coffee-ring-like patterns *Corresponding author. E-mail: [email protected]. (1) Chen, W.; Bovin, J.-O.; Wang, S.; Joly, A. G.; Wang, Y.; Sherwood, P. M. A. J. Nanosci. Nanotechnol. 2005, 5, 1309–1322. (2) Jang, J.; Oh, J. H. Langmuir 2004, 20, 8419–8422. (3) Zhang, L.; Maheshwari, S.; Chang, H.-C.; Zhu, Y. Langmuir 2008, 24, 3911– 3917. (4) Fang, J.; Soto, C. M.; Lin, T.; Johnson, J. E.; Ratna, B. Langmuir 2002, 18, 308–310. (5) Tang, J.; Ge, G.; Brus, L. E. J. Phys. Chem. B 2002, 06, 5653–5658. (6) Mougin, K.; Haidara, H. Langmuir 2002, 18, 9566–9569. (7) Haidara, H.; Mougin, K. In Dekker Encyclopedia of Nanoscience and Nanotechnology, 2nd ed.; Contescu, C. I., Putyera, K., Eds.; CRC Press/Taylor & Francis Group: Boca Raton, FL, 2009; pp 882-892. (8) Liu, X.-Y.; Wang, M.; Li, D.-W.; Strom, C. S.; Bennema, P.; Ming, N.-B. J. Cryst. Growth 2000, 208, 687–695. (9) Lim, B.; Jiang, M.; Yu, T.; Camargo, P. H. C.; Xia, Y. Nano Res. 2010, 3, 69–80. (10) Khatri, O. P.; Murase, K.; Sugimura, H. Langmuir 2008, 24, 3787–3793. (11) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827–829. (12) Parisse, F.; Allain, C. Langmuir 1997, 13, 3598–3602. (13) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Phys. Rev. E 2000, 62, 756–765. (14) Fischer, B. J. Langmuir 2002, 18, 60–67. (15) Soltman, D.; Subramanian, V. Langmuir 2002, 18, 9566–9569. (16) Park, J.; Moon, J. Langmuir 2006, 22, 3506–3513. (17) Hu, H.; Larson, R. G. J. Phys. Chem. B 2006, 110, 7090–7094. (18) Marty, G.; Tsapis, N. Eur. Phys. J. E 2008, 27, 213–219. (19) Zhang, Y.; Yang, S.; Chen, L.; Evans, J. R. G. Langmuir 2008, 24, 3752– 3758. (20) Shen, X.; Ho, C.-M.; Wong, T.-S. J. Phys. Chem. B 2010, 114, 5269–5274.

16928 DOI: 10.1021/la103244c

has led to a significant understanding of the conditions that govern the formation of these rather regular patterns, the genesis of the complex morphologies issued from the evaporation of nanofluid drops (films) still remain in many respects an open issue.1-8,25-28 From a theoretical viewpoint, the work of Rabani et al.,26 who used an “extended” coarse-grained model to calculate and predict the emergence and topological features of dryingmediated nanoparticle aggregates, probably represents one of the most complete approaches in this domain. Interestingly, by using a Hamiltonian involving mainly adjacent particle/particle, particle/ solvent, and solvent/solvent interactions,26 some of the basic experimental drying patterns (discrete clusters and wormlike and polygonal networks) were closely captured by this model, depending on the evaporation regime (homogeneous vs heterogeneous). Although dynamic aspects such as solvent fluctuations induced by evaporation are included in this model, there are recurrent phenomena that have been shown experimentally to critically determine the topology of the occurring patterns, which are absent in this model. These include the particle/substrate interaction controlling the balance of nanoparticle sticking versus sliding and, most importantly, hydrodynamic-induced shear stress at the interface. Depending on whether the contact line (CL) retires or on whether the residual drop (film) confining the (21) Tang, J.; Li, Z.; Xia, Q.; Williams, R. S. Langmuir 2009, 25, 7222–7225. (22) Thiel, P. A.; Shen, M.; Liu, D.-J.; Evans, J. W. J. Phys. Chem. C 2009, 113, 5047–5067. (23) Mokari, T.; Sztrum, C. G.; Salant, A.; Rabani, E.; Banin, U. Nat. Mater. 2005, 4, 855–863. (24) Lu, W.; Kim, D. Nano Lett. 2004, 4, 313–316. (25) Bigerelle, M.; Haidara, H.; Gorp, A. V. Mater. Sci. Eng., C 2006, 26, 1111– 1116. (26) Rabani, E.; Reichman, D. R.; Geissler, P. L.; Brus, L. E. Nature 2003, 426, 271–274. (27) Xiong, H.; Li, H.; Chen, W.; Xu, J.; Wu, L. J. Colloid Interface Sci. 2010, 344, 37–43. (28) Hsu, C.-L.; Chu, S.-M.; Wood, K.; Yang, Y.-R. Phys. Status Solidi A 2007, 204, 1856–1862.

Published on Web 09/30/2010

Langmuir 2010, 26(22), 16928–16933

Darwich et al.

Article

Table 1. Characteristics of Au Nanocolloidal Suspensions with Different Particle Sizes concentration in weight %

concentration in volume fraction

0.00508 0.00515 0.00493 0.00508

2.582  10-4 2.589  10-4 2.562  10-4 2.582  10-4

number of particles average in 20 μL diameter (nm) 2.3  1011 6.3  1011 2.9  1012 3.6  1014

35 25 15 3

concentrated particles ruptures, these two parameters determine the ultimate topologies of the networks through the late stage hydrodynamic events and related shear restructuration of the nanoparticle assemblies at the interface.6,7,29 Indeed, experiments show that several of these drying-mediated complex patterns clearly exhibit fingerprints of the local flow and hydrodynamic shear experienced during their formation (axisymmetric vs anisotropic aggregates),6,7 underscoring the crucial role of these interface parameters. Finally, if hydrodynamics plays such a crucial role in the viscous shear at the substrate interface, then determining the ultimate morphology of the aggregate in the late stage of the drying and thus knowing the state of the nanocolloids within the residual film (more or less connected spherically shaped or wormlike clusters) become equally important. The pre-existence of such “more or less open” aggregates in the concentrated residual thin drop/film, before any restructuring shear stress is applied, is well supported both by experiments6,7 and model simulation,26-30 although the latter contains no explicit interaction potential or shear field between the substrate and the aggregates (particles). It thus appears, both from a theoretical and experimental viewpoint, that deeper insight into this drying-mediated pattern formation is still required for a reliable description of the genesis of the complex aggregation structures arising from the “spontaneous” assembly of nanoparticles in drying nanofluids. This report is a step forward for this issue, focusing on the interrelation among the size of the nanoparticles, the drying temperature, and the substrate-controlled drying dynamics, which we show hereafter to determine the occurrence of the complex (dendrite) aggregation patterns through size-dependent effects.

Figure 1. Final drying patterns of nanocolloid suspensions of varying size on SiO2 at different drying temperatures. For (15 nm, T > 45 °C) and (25 and 35 nm, T > 20 °C), only featureless particle deposits are formed in the final drying spot; the occurrence of the structures is zero under these conditions.

An ensemble of three model homogeneous surfaces has been used: a clean, bare silicon substrate bearing its native oxide layer (SiO2) and two Si-supported self-assembled monolayers (SAM) of organosilane molecules. The cleaning of the bare SiO2 substrates simply consisted of sonication for a few minutes in cyclohexane, followed by drying under a flow of nitrogen before use. The organosilane compounds composing the SAMs were amineterminated 6-aminopropyltrimethoxysilane, referred to as NH2, and methyl-terminated hexadecyltrichlorosilane, referred to as CH3. These SAMs were prepared on silicon wafers that had been cleaned and activated in a piranha solution (3:7 v/v 30% H2O2/ H2SO4), thoroughly rinsed in Milli-Q water, and then dried under nitrogen. These silanol-enriched substrates were then immersed for at least 6 h in millimolar (10-3 M) solutions of 6-aminopropyltrimethoxysilane (in ethanol) and hexadecyltrichlorosilane (in cyclohexane) to make the corresponding compact NH2- and CH3-terminated monolayers. Citrate-stabilized suspensions of spherical gold nanoparticles of 3, 15, 25, and 35 nm diameter were prepared and characterized as shown in Table 1 before use. The 15, 25, and 35 nm nanocolloids were synthesized following the standard method of Frens31

using tetrachloroauric(III) acid hydrate (HAuCl4) and trisodium citrate (Na3-citrate). Starting aqueous solutions of HAuCl4 (0.01% by weight = solution 1) and Na3-citrate (1% by weight = solution 2) were first prepared using Milli-Q water. Then, 50 mL of solution 1 was heated to 70 °C, and a defined amount of the reducing Na3-citrate (solution 2) was added under stirring to adjust the size of the growing NPs (Table 1). The solution was maintained for a few minutes under stirring at constant temperature until the color attesting to the produced NP size was stabilized. The small 3 nm nanocolloids were prepared from the following aqueous solutions: HAuCl4 (1 wt % = solution 1), Na3citrate (1 wt % = solution 2), and NaBH4 (0.075 wt %) in Na3citrate (1 wt % solution = solution 3). For the synthesis, 1 mL of solution 1 was first added to 100 mL of water. After 1 min, 1 mL of solution 2 was added with stirring, and after 1 more min, this was followed by the addition of 1 mL of solution 3. The mixture was stirred for 5 min at room temperature. During this process, HAuCl4 is dispersed by water, reduced by NaBH4, and stabilized by citrate. The synthesized nanocolloidal solutions were then cooled to room temperature and stored at 4 °C before use (Supporting Information; representative TEM images of synthesized NPs). The experiments, properly speaking, consisted of depositing a 20 μL drop of the suspension on the substrate in a thermally equilibrated chamber (T°) and following its drying and resulting structure formation under a video microscope (Olympus optical microscope coupled to a COHU CCD camera operating at 25 images/s). The drying kinetics was captured through the variation of the contact angle and diameter of the drop using the Kr€ uss G2 contact angle analyzer. For all experiments, the starting relative humidity in the chamber was that of the ambient environment (33 ( 2%). For each substrate, the drying and structure formation were investigated for all four sizes of Au nanocolloids particles and for drying temperatures (evaporation rate) of 20 (∼ambient), 45, 75, and 100 °C. All of the drying structures were captured right after the residual drop had dried.

(29) Becker, V.; Briesen, H. A. J. Colloid Interface Sci. 2010, 346, 32–36. (30) Khan, S. J.; Pierce, F.; Sorensen, C. M.; Chakrabarti, A. Langmuir 2009, 25, 13861–13868. (31) Frens, G. Nat. Phys. Sci. 1973, 241, 20–22.

The 2D diagram of Figure 1 represents the occurrence of complex aggregation patterns in the final drying spot of the nanofluid

Experimental Section

Langmuir 2010, 26(22), 16928–16933

Results

DOI: 10.1021/la103244c

16929

Article

Darwich et al.

Figure 4. Typical dendrite structures (4-fold with secondary branches) observed on CH3-terminated surfaces for the conditions where these complex aggregation patterns appear on the nonwetted substrate: the smallest NP size (3 nm) and drying temperatures of 20-ambient, 45, and 75 °C. For any other combination of the NP size and drying temperature, no structure-dendrites or any other fractal-is formed on this substrate after the drying of the nanofluid. Figure 2. Drying kinetics of 3 nm nanoparticle suspension drops on SiO2 at 20 °C, which is typical of most complex-aggregateforming systems: (9) contact angle and (O) contact diameter.

Figure 3. Dense arborescent patterns arising from the drying of 25 nm particles on NH2-terminated surfaces at the four drying temperatures (20, 45, 75, and 100 °C).

drops on the SiO2 substrate over the whole range of investigated nanoparticle size (d) and drying temperature (T). Figure 2 represents the typical evaporation kinetics given by the time variation of the contact angle and the contact diameter of the drop under conditions where the complex structures are formed on the substrate. The kinetics is shown here in Figure 1 for a drying temperature of 20 °C and the smallest particle size (3 nm), a case where large, well-defined thick dendrite aggregates occur in this system. Figures 3 and 4 show, respectively, the corresponding occurrences and morphologies of the drying-mediated aggregation patterns observed for the hydrophilic NH2-terminated and hydrophobic CH3-terminated substrates. In all cases, the structures and patterns shown are those generally taken halfway between the center and the border of the final drying spot. These Figures contain all of the essential and relevant features of this drying and pattern-formation process, the most striking of which is the modulation of the occurrence and morphological features of the aggregates (dendrites) by the temperature (T ), the size of the nanocolloid particle, and the wetting properties (nature) of the substrate. The influence of temperature and particle size on the aggregate morphology is well illustrated by the first-column (3 nm particles) images of Figure 1 where the size and the 16930 DOI: 10.1021/la103244c

complexity of the aggregation structures gradually decrease (degenerated dendrites) when the drying temperature and the size of the nanoparticles (NPs) increase. This influence of the temperature and particle size on the occurrence of the aggregates and their morphology is confirmed and particularly exalted in Figures 3 and 4 involving amine (NH2)- and methyl (CH3)terminated surfaces. Indeed, the only aggregation structures that appear on the almost “non-pattern-forming” hydrophobic substrate (Figure 4) are observed exclusively for the smallest particle size (3 nm) and only up to 75 °C, thus illustrating an ideal case of a size-exalted effect. However, the aggregation structures at NH2 surfaces are more illustrative of the thermal effect, which can be seen in the striking increase in the elongation of the patterns with the temperature in Figure 3. In addition, these results involving NH2 surfaces show that the nature of the substrate (wetting properties) can completely cancel out the influence of the nanoparticle size and temperature on the occurrence (not the morphology) of the complex aggregates. Indeed, it is worth noting that the series of aggregation patterns that are shown here (Figure 3) for the 25 nm particles at the four studied temperatures is representative of our results on that fully structure forming substrate NH2terminated surface. Otherwise stated, the patterns of arborescent dendrites systemically occur on this substrate, regardless of the NP size and drying temperature, within the limit of the studied particle sizes (3-35 nm) and temperatures (20-100 °C). This results in particular accounts of the impact of the drying dynamics and hydrodynamics events on structure formation and the way that these are controlled by the nature and wetting property of the substrate (Discussion section). This influence of the wetting properties and related hydrodynamic events that determine to a large extent the occurrence of the structures are illustrated in Figure 5a,b. These two plots compare the typical drying kinetics on SiO2 and NH2 for an identical particle size (25 nm) and drying temperature (75 °C). As a result, only the substrates that modulate the drying dynamics are different. Under those conditions where the role of the substrate is purposely amplified and made crucial, dendritic structures occur systematically on NH2 but are totally absent on SiO2.

Discussion In view of the above results (Figures 1, 3, and 4, in particular), it appears that the occurrence of the complex dendrite structures in drying nanofluids is governed by the coupling between the particle size on the one hand and the wetting properties of the substrate on the other hand, with both being temperature-sensitive parameters. Although the particle size clearly dominates and controls the formation of the structures at the partially wetted SiO2 and Langmuir 2010, 26(22), 16928–16933

Darwich et al.

Figure 5. Drying kinetics for 25 nm nanoparticle suspension drops at 75 °C on (a) SiO2 and (b) NH2-terminated substrates: (9) contact angle and (O) contact diameter. Note that under these conditions the complex aggregation structures appear on the NH2-terminanted surface and not on SiO2.

nonwetted CH3 surfaces, the occurrence of these structures at the wetted NH2 surface for all studied particle sizes rather points to a process that is dominated by the substrate and related wetting properties. Because the growth of dendrite structures from drying suspensions is essentially a colloidal crystallization process, one may expect these crystallization mechanisms a priori to account for the observed drying-mediated structure formation in general and in particular to account for its dependence on the particle size on SiO2 and CH3 surfaces. Assuming such a colloidal crystallization mechanism to predominate and drive the structure formation, regardless of the nature of the substrate, the size of the particle, or the drying temperature, one should expect high evaporation rates (high T°) to promote the crystallization of the smallest (ionlike) nanoparticles versus larger ones. Indeed, at high evaporation rates, the timescale allowed for particles to encounter each other and to aggregate into crystal-like structures is much shorter and therefore promotes the crystallization of the smallest particles of higher mobility. The corollary to this colloidal crystallization mechanism is that structure formation should no longer depend on the nature of the substrate but only on the particle size for a given drying temperature. However, this is obviously not the case, as our results show. Instead, the growth of the dendrite structures depends not only on the drying temperature and particle size but also in a more crucial way on the nature of the substrate for an identical particle size and drying temperature. Indeed, as compared to CH3 surfaces, the occurrence of the highly ramified dendrite patterns on NH2 over the entire range of drying temperature (20-100 °C) and for all particle sizes (3 to 35 nm) shows at least that neither the size of the particles nor the temperature prevails in the formation of the structures in this case. Langmuir 2010, 26(22), 16928–16933

Article

In the following text, we show from simple physical considerations that these structure formations are consistently accounted for by the coupling between the wetting properties of the substrates on the one hand and, most importantly, the size-dependent cohesion of the particle aggregates in the drying drop on the other hand. Wetting Properties of the Substrate and Related Hydrodynamic Events. The following discussion aims to show in what the occurrence of structures on NH2 substrates, which covers the entire range of particle sizes and drying temperatures is primarily determined by wetting properties, unlike SiO2, and CH3-terminated substrates in particular. The first answer lies in the surface chemistry that determines the strength of the particle/surface interactions at the interface. For NH2-coated substrates, these interactions involve both hydrogen and electrostatic bonds between the citrate (COO-)-stabilized nanoparticles and the surface amine or ammonium NH3þ (after protonation).6,7 These NH2/ particle bonds ensure a stronger attachment and stability of the aggregates at the interface versus convective flow and contact line motion during drying, unlike CH3- and solvent-cleaned SiO2 surfaces that mainly attach particles through van der Waals forces. In addition, the drying nanofluids on NH2 surfaces, which have low receding CA (θr ≈ 0) and hysteresis ( 0 for attractive forces), R is the radius of the monodisperse nanospheres, and δe is the equilibrium separation between two nanospheres in the potential minimum. Because the surrounding medium of the core particles issued from the dried nanofluid is identical for each particle size, the Hamaker constant of the particle/medium/particle interaction is to a good approximation identical for all clusters. Now let n be the average number of nearest interacting nanospheres in a randomly packed cluster, which represents a more realistic picture for drying aggregates. The ced of the system is defined by the ratio between the molar amount of the interaction energy and the molar volume Vm of the interacting units (molecules in general and nanospheres here).33,34 For the above pairwise vdW attraction potential (UvdW), this gives, to first order, a cohesive energy density (ced) of ∼(-NAnHR/12δeVm), where NA is Avogadro’s number for the interacting nanosphere units. Observing that Vm = NAvnanosph, with vnanosph= (4πR3/3), we arrive at an expression of the cohesive energy density that scales with the size of the nanosphere as ced ≈ -(nH/δeR2). Assuming n and δe (in particular) to be independent of the size of the sphere,36 we find that the size dependence of the ced finally scales as ced ≈ -H/R2. Interestingly, but not really surprisingly, we can recognize in that last expression an adhesion energy (in J/m2) that when reported for the “thickness” of the equilibrium separation between nanospheres (δe) gives rise to a conjoining adhesive pressure of Padh ≈ -H/δeR2, which is nothing but the ced. The same phenomenological reasoning provides a third physical quantity that is tightly bonded to the previous two (ced, Padh) and that similarly accounts for the observed size-dependent stability of the NP-based aggregates. This is the frictional resisting force that may occur between nanospheres under thermal agitation. This frictional force Ffrict or more specifically its strength per unit volume of cluster F*frict = (Ffrict/V) is related to a first approximation to the internal area density (area/volume= A/V) as Ffrict ≈ τA/V, where τ is the internal shear stress. Observing that τ is locally related to the adhesive pressure by τ ≈ μfrictPadh ≈ μfrict(-H/δeR2), where μfrict is the internal static friction coefficient and that (A/V) ≈ (1/R), we arrive at a density of frictional resisting force that now varies with the size of the nanopshere as F*frict ≈ (1/R3). This last scaling relation more specifically accounts for the stability of smaller particle aggregates against the hydrodynamic shear restructuration induced by the confined and eventually retracting residual drop in the final stage of drying. Finally, what results is that the cohesion of NP-based structures (clusters, aggregates, and nanostructures) is strongly dependent on and thus crucially determined by the size of the constituent NPs, regardless of whether these structures form spontaneously (self-assembly) or under applied external fields. (35) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1991; pp 176-179 and 246-249. (36) That assumption amounts to neglect here, within the range of particle sizes studied (from 3 to 35 nm), of the curvature dependence of the thickness of the “citrates and hydration” layer adsorbed on the nanoparticles.

Langmuir 2010, 26(22), 16928–16933

Darwich et al.

Article

In addition, this size effect in the nanoscale range happens to follow a simple rule that can be stated here as follows: the smaller the nanoparticles, the higher the cohesion and hence the greater the thermomechanical stability of the nanostructures. It is worth noting that such size effects (amplification) resulting from the surface-to-volume ratio are well-known for MEM and NEM devices, where they determine the reliability of the mobile parts that experience relatively high adhesion and frictional forces. More closely related to our results and to that general issue of size and confinement effects is the recent work of Keten et al.,37 which reveals that confined β-sheet silk nanocrystals achieve higher stiffness, strength, and mechanical toughness than do larger nanocrystals. The present report represents, to our knowledge, one the most complete approaches and descriptions of these size and confinement effects in NP-based structures. Indeed, this work provides both new and original experimental evidence for these size effects (thermomechanical stability) while providing a simple phenomenological basis and description that account for the observed behaviors and properties. Though not dealing directly or truly with the fabrication of a specific functional nanostructure or device, the present work nonetheless sheds light on the mechanisms by which size effects control the general physical properties of NP-based structures, particularly their long-term mechanical, thermal, and environmental stability. In this respect, it provides key parameters for describing reliable nanostructures, with physical properties that can be adjusted for specific applications. A possible illustration of this would be size-adjusted structures that lose their percolating morphology and hence their related conduction above a certain temperature as a result of a weakening of the cohesion (thermomechanically instability threshold). And even more immediately, these findings could contribute significantly to the enhanced cohesion and thermomechanical stability of inkjet-printed nanocolloid conductive patterns, which are currently being developed.

Conclusions We reported a model study on the interrelation between the occurrence of complex aggregation patterns in drying nanofluids, (37) Keten, S.; Xu, Z.; Ihle, B; Buehler, M. J. Nat. Mater. 2010, 9, 359–367.

Langmuir 2010, 26(22), 16928–16933

the size of the constitutive nanoparticles (from 3 to 35 nm), and the drying temperature (from 20 to 100 °C). Besides the substrate wetting properties that we firmly established here, our results show that the emergence of the large-scale, well-defined aggregation patterns was dictated by the size of the nanoparticle for a given temperature within the explored range. More precisely, the thermal stability and hence the occurrence of the complex patterns were enhanced for smaller particles. Though this may appear a priori counterintuitive owing to the higher thermal mobility of smaller particles, we showed that these results actually account for the size dependence of the cohesion of nanoparticlebased structures. Clearly stated, this size effect expresses the fact that assemblies of smaller nanoparticles have much higher cohesion than those made of larger ones. Using a rather simple phenomenological picture of a nanoparticle assembly located in the minimum of a potential that is dominated by vdW forces, we showed that the thermomechanical stability of the aggregate was closely underpinned by physical quantities that scale with the size R of the NPs either as R-2 or R-3. Beyond the demonstrated sizedependent thermomechanical stability of the complex patterns arising from drying nanofluids, this work provides new insights into size-dependent dissipation/damping mechanisms in NP-based structures in general. These gained insights should help in designing nanoparticle-based structures with tailored and optimized thermomechanical and environmental stability and hence with a morphological stability that guarantees their long-term functional properties. Supporting Information Available: Movie sequences, videoSi and videoNH2, representative of the drying kinetics shown in Figure 5. VideoSi describes the drying kinetics on the Si substrate, characterized by strong and abrupt pinningdepinning instabilities that are typical of cases where no structures occur on the substrate. VideoNH2 describes the regular and quite smooth kinetics typical of the drying on structure-forming NH2-terminated substrates. TEM images of some of the spherical nanoparticles (NPs) used in our studies (3 and 25 nm spherical NPs). This material is available free of charge via the Internet at http://pubs.acs.org.

DOI: 10.1021/la103244c

16933