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Temperature-Induced Gelation in Dilute Nanofluids Vijutha Sunny, T. Muthukumaran, and John Philip* SMARTS, NDE Division, Metallurgy & Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam-603102, India ABSTRACT: We report a temperature-induced gelation in dilute nanofluids containing surfactant capped iron oxide and alumina particles of average diameter ∼10 nm. We observe a dramatic enhancement in the elastic modulus, viscous modulus, and viscosity, by 36 orders of magnitude for a volume fraction (ϕ) less than 0.035, above a critical shear rate (γ_ c) and temperature (Tc). The Tc follows a weak power law scaling with ϕ as Tc ∼ ϕβ, where the scaling exponent β is found to be 0.24. The observed gel-like transition at elevated temperature is attributed to strong van der Waals attractions on the kT energy scale due to poor solvent conditions, which is reminiscent of the phase behavior reported in polymer-coated colloids.
1. INTRODUCTION Colloidal self-assembly is an elegant and simple approach to produce optical, electronic, and biosensing devices.1,2 Colloidal suspensions of nanoparticles (NPs), popularly known as nanofluids (NFs), are fascinating materials owing to their interesting properties and flow behavior.38 Nanofluids containing electrically or magnetically polarizable particles come under the category of smart materials and have several fascinating technological applications, besides being a model system for fundamental studies.912 These soft matter systems exhibit interesting phase behavior under different conditions.1326 The aggregation mechanisms of nanoparticles in base fluids27 and polymer melts26,28,29 have been another topic that have captured the attention of scientific community recently. The sol to gel transition is mostly seen in polymeric materials or polymers incorporated with particles. Gelling materials exhibit critical behavior that is manifested by the divergence of several physical properties, including the zero shear viscosity, equilibrium modulus, and long relaxation time.30 At the solgel transition point, a samplespanning critical network cluster is formed first. The actual gel point appears to be determined by the formation of a particle cluster near the wall. Multifold increase in viscosity can be either due to the formation of clusters leading to an increase in the effective volume fraction (ϕ) of disperse phase due to occlusion of liquid within the clusters or due to shape of clusters (e.g., elongated nonspherical structures). In general, structural transition studies are observed in dispersion of high ϕ, with relatively large particle size, where the surface area effects are not so predominant. For example, Trappe et al. elegantly demonstrated the composite jamming phase diagram for attractive colloidal particles where the ratio of thermal energy (kBT) to the strength of the attractive interparticle interaction (U) is less than unity.24,31 They used relatively high ϕ of submicrometer-sized particle of carbon black, polymethyl methacrylate, and polystyrene to demonstrate that the fluid-to-solid transition undergoes markedly similar gelation behavior with increasing concentration and decreasing r 2011 American Chemical Society
thermalization or stress. However, the present study deals with nanoparticles of very small size ( ∞, 0 < r < 2ða þ δÞ > > < d , 2ða þ δÞ < r < d Eas ðrÞ ¼ ln > 12τðd 2ða þ δÞÞ > > : 0, r > d ð1Þ where a is the bare particle radius, δ is the coating thickness, r is the center to center distance between two particles, and τ is the attraction parameter. The adhesion parameter τ for a potential E(r) has been obtained from the virial coefficient as 8ða þ δÞ3 Z ∞ EðrÞ 2 2π τ¼ r exp 1 dr þ kT 8ða þ δÞ3 0 3
ð2Þ
An increase in stickiness, τ1, indicates an increased attraction. Calculations of the strength of attraction show that the observed
gel transitions in silica dispersions correspond to the percolation threshold, and the strength of attraction τ1 roughly decreases linearly with temperature.40 The collapse of adsorbed layers in poor solvent conditions can produce very strong van der Waals attractions on the kT energy scale that can lead to fluidgel transitions.38 The light-scattering studies in silica dispersions40 show that at ϕ < 0.01, the entropic effects can prevent formation of a network at finite τ1. In dilute dispersions, the gelation transition may follow the spinodal decomposition curve, and τ1 can diverge as ϕ f 0. The mobility for relative motion decreases linearly with separation and vanishes at contact for adhesive colloidal particles surrounded by a solvent. For particles with grafted organic layers, the mobility of particles interacting within the attractive well can be substantially reduced by the interpenetration of organic layers.41 The long-range entropic forces between two colloidal spheres in fluid show that the potential is monotonically attractive at low concentrations and oscillatory at higher concentrations.42 Fully atomistic molecular dynamics simulations for two approaching coated nanoparticles show that the solvent-mediated and lubrication forces are purely repulsive.43 The dynamic shear-thickening behavior observed in colloidal suspensions consisting of 1730 wt % of fumed silica 12364
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Figure 7. (a) Temperature-dependent viscosity of Fe8 (ϕ = 0.035) with the base fluid at different γ_ = 0.0001, 0.1, and 5 s1 and for the base fluid at γ_ = 1 s1 (b) Viscosity versus temperature plots of Al10 (ϕ = 0.03) at different γ_ = 0.05, 0.1, 5, and 10 s1.
Figure 8. Shear rate dependence of Tc for different nanofluids of Fe8, Fe15, and Al10.
nanoparticles in polypropylene glycol is attributed to the formation of large hydrodynamic clusters, which is unambiguously confirmed by small-angle light scattering measurements.20 The calculated values of interparticle spacing for Fe8 with ϕ = 0.035, 0.017, 0.008, and 0.001 are 13.01, 18.81, 26.47, and 60.94 nm, respectively. The lowering of Tc with increasing volume fraction may be due to the increased hydrodynamic interactions that favor the structural transition. Studies in a model system consist of uniform, spherical silica particles with grafted octadecyl chains on their surfaces suspended in decalin or tetradecane show that the strength of interparticle attraction increases with decreasing temperature due to octadecyl chain/solvent interactions, which leads to a reversible space filling gels and the gel temperature dependent on the volume fraction of the suspension.44 In the above system, at elevated temperatures, there is no attraction between the particles.45,46 The observed transition in our system is therefore attributed to the synergistic effect of the shear force, the attractive force due to the collapse of adsorbed organic layers on the particles due to diminishing solvent conditions at higher temperature, and the increased stickiness of the particles. Figure 6 shows the schematic of the temperatureactivated phase transitions in the nanofluids (a) sterically stabilized nanoparticles in base fluids at room temperatures and (b) gelation induced at elevated temperature due to the collapse of adsorbed layers (poor solvent condition).
Figure 9. Elastic modulus, G0 , and viscous modulus, G00 , verses temperature plots of (a) Fe8 (ϕ = 0.035) measured at an angular frequency of 10 s1 and (b) a mixture of Al2O3 nanoparticles (Al10) and Al2O3 nanorods (in 1:1 ratio) measured at an angular frequency of 1 rad/s (strain of 1%).
Figure 7a shows the temperature-dependent viscosity plots of Fe8 with ϕ = 0.035 at γ_ = 0.0001, 0.1, and 5 s1 along with that of the base fluid at a shear rate of 1 s1. Figure 7b depicts the variation of viscosity with temperature of Al10 (ϕ= 0.030) at γ_ = 0.05, 0.1, 0.5, and 10 s1. In the low-temperature regime, the _ viscosity remains nearly constant irrespective of the applied γ, where as Tc shifts toward higher temperature as γ_ increases. Figure 8 shows the variation of Tc with γ_ of Fe8, Fe15, and Al10, _ Since the where Tc is found to have a very weak dependence on γ. power law fit was rather poor, it is not shown in Figure 8. Unlike jamming transition observed at high volume fractions, our results show gelation transitions at very low volume fractions. Figure 9a shows the variation of elastic modulus, G0 , and viscous modulus, G00 , as a function of temperature in Fe3O4 nanostructures. Below the critical temperature Tc, both the moduli were temperature-independent with a plateau (∼1 Pa), above 12365
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Langmuir which the G0 and G00 increases sharply by about 5 orders of magnitude in Fe8 (ϕ = 0.035), at an angular frequency of 10 s1 . Indeed, the elastic modulus scales directly with the number density of clusters and the cohesive energy density in many disordered systems. The sudden increase in the elastic modulus confirms the structural transition to an elastic medium where the particles lose mobility due to adhesive contacts with neighbors. The dominant elastic response (G0 > G00 ) observed above Tc indicates the stiffening through compaction and interpenetration of the stabilizing organic layers on the particles. Figure 9b shows the temperature-dependent moduli measured at an angular frequency of 1 s1 and 1% strain for a mixture of Al2O3 nanoparticles and nanorods in 1:1 ratio dispersed in PAO. Both G0 and G00 increases sharply by about 2 orders of magnitude above Tc. Further, the observed transition can also be understood from the concept of fragility that has a parallel in the temperature dependence of purely thermodynamic properties, such as entropy.47,48 The fragility originates from a proportionality of the height of the high-energy barriers between inherent states to the infinitefrequency shear modulus G.49 The logarithmic slope of the relaxation time of the flow process is a measure of the fragility of a glass former and the strength of an asymmetric relaxation increases with increasing temperature because of the increase in the thermal population of the upper level. The fragility depends crucially on the barrier density of primitive relaxations. Recent studies show that the fragility concept can be directly adapted to suspensions of deformable colloidal particles, where particle concentration controls glass formation and the origin of the variation in fragility depends on the elastic properties of the particles; i.e., hard particles lead to fragile behavior.50 This observation is an experimental realization of the prediction of structural transition with temperature in colloids and is reminiscent of the transition observed in thermal systems in the vicinity of point J, where the system is isostatic and on the brink of mechanical failure.51 Interestingly, a power law scaling between packing fraction and temperature is also observed in the above study (Δϕv µ Tx, where x is 0.4 and 0.5 for harmonic repulsions and Hertzian repulsions).
4. CONCLUSIONS In summary, the observed dramatic enhancement in viscosity, elastic modulus (G0 ), and viscous modulus (G00 ) resembles the gel-like transitions. Room temperature flow curves of Fe8 and _ which Al10 NFs show strong shear thinning behavior at low γ, indicates the large change in the microstructures of particles under weak flow that depends on the balance of Brownian, interparticle, and hydrodynamic forces in equilibrium. At high shear rates, the system exhibits a Newtonian plateau and the flow curves are best described by the HerschelBulkley equation, where the yield stress obtained from the fit data was about 9.7 mPa. Below the critical temperature Tc, both the moduli were temperature-independent with a plateau (∼1 Pa), above which the G0 and G00 increases sharply by about 5 and 4 orders of magnitude, respectively, in Fe8 (ϕ = 0.035) nanofluid. The Tc follows a weak power law scaling with ϕ. The observed structural arrest at elevated temperature is attributed to the net attractive force induced by poor solvent conditions. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
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’ ACKNOWLEDGMENT J.P. thanks Prof. J. Buongiorno (MIT) for the Al10 sample and Prof. Srinivasa Raghavan for performing the temperature- and time-dependent rheological studies of some of our samples. The authors thank Mr. S. C. Chetal, Director, IGCAR, and Dr.T. Jayakumar, Director, Metallurgy and Materials Group, for fruitful discussions. ’ REFERENCES (1) Grzelczak, M.; Vermant, J.; Furst, E. M.; Liz-Marzan, L. M. ACS Nano 2010, 4, 3591. (2) Madivala, B.; Fransaer, J.; Vermant, J. Langmuir 2009, 25, 2718. (3) Eberle, A. P. R.; Wagner, N. J.; Castaneda-Priego, R. Phys. Rev. Lett. 2011, 106, 105704. (4) Chen, H.; Ding, Y.; Tan, C. New J Phys. 2007, 9, 367. (5) Rosenzweig, R. E. Ferrohydrodynamics; Cambridge University Press: Cambridge, 1985. (6) Morris, J. F. Rheol. Acta 2009, 48, 909. (7) Lemke, T.; Bagusat, F.; Kohnke, K.; Husemann, K.; M€ogel, H.-J. Colloid Surf. A 1999, 150, 283. (8) Veld, P. J. i. t.; Petersen, M. K.; Grest, G. S. Phys. Rev. E 2009, 79, 021401. (9) Leunissen, M. E.; Vutukuri, H. R.; Blaaderen, A. v. Adv. Mater. 2009, 29, 1. (10) Philip, J.; Shima, P. D.; Raj, B. Appl. Phys. Lett. 2008, 92, 043108. (11) Jordanovic, J.; Klapp, S. H. L. Phys. Rev. Lett. 2008, 101, 038302. (12) Philip, J.; Gnanaprakash, G.; Jaykumar, T.; Kalyanasundaram, P.; Raj, B. Phys. Rev. Lett. 2002, 89, 268301. (13) Romeo, G.; Fernandez-Nieves, A.; Wyss, H. M.; Acierno, D.; Weitz, D. A. Adv. Mater. 2010, 22, 3441. (14) Lu, P. J.; Zaccarelli, E.; Ciulla, F.; Schofield, A. B.; Sciortino, F.; Weitz, D. A. Nature 2008, 453, 499. (15) Osuji, C. O.; Kim, C.; Weitz, D. A. Phys. Rev. E 2008, 77, 060402(R). (16) Wagner, N. J.; Brady, J. F. Phys. Today 2009, 62, 27. (17) Brown, E.; Forman, N. A.; Orellana, C. S.; Zhang, H.; Maynor, B. W.; Betts, D. E.; DeSimone, J. M.; Jaeger, H. M. Nat. Mater. 2010, 9, 220. (18) Cates, M. E.; Wittmer, P.; Bouchaud, J.-P.; Claudin, P. Phys. Rev. Lett. 1998, 81, 1841. (19) Guery, J.; Bertrand, E.; Rouzeau, C.; Levitz, P.; Weitz, D. A.; Bibette, J. Phys. Rev. Lett. 2006, 96, 198301. (20) Chellamuthu, M.; Arndt, E. M.; Rothstein, J. P. Soft Matter 2009, 5, 2117. (21) Bhardwaj, A.; Richter, D.; Chellamuthu, M.; Rothstein, J. P. Rheol. Acta 2007, 46, 861. (22) Raghavan, S. R.; Khan, S. A. J. Colloid Interface Sci. 1997, 185, 57. (23) Kirkland-York, S.; Gallow, K.; Ray, J.; Loo, Y.-l.; McCormick, C. Soft Matter 2009, 5, 2179. (24) Trappe, V.; Prasad, V.; Cipelletti, L.; Segre, P. N.; Weitz, D. A. Nature 2001, 411, 772. (25) Trappe, V.; Weitz, D. A. Phys. Rev. Lett. 2000, 85, 449. (26) Filippone, G.; Romeo, G.; Acierno, D. Langmuir 2010, 26, 2714. (27) Shima, P. D.; Philip, J.; Raj, B. Appl. Phys. Lett. 2010, 97, 153113. (28) Romeo, G.; Filippone, G.; Fernandez-Nieves, A.; Russo, P.; Acierno, D. Rheol. Acta 2008, 47, 989. (29) Liu, J.; Gao, Y.; Cao, D.; Zhang, L.; Guo, Z. Langmuir 2011, 27, 7926. (30) Winter, H. H.; Chambon, F. J. Rheol. 1986, 30 (2), 367. (31) Trappe, V.; Weitz, D. A. Phys. Rev. Lett. 2000, 85, 449. (32) Philip, J.; Shima, P. D.; Raj, B. Nanotechnology 2008, 19, 305706. 12366
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(33) Gnanaprakash, G.; Philip, J.; Jayakumar, T.; Raj, B. J. Phys. Chem. B 2007, 111, 7978. (34) Bingham, E. C. Fluidity and Plasticity; McGraw-Hill Book Co., Inc.: New York, 1922. (35) Bertrand, E.; Bibette, J.; Schmitt, V. Phys. Rev. E 2002, 66, 060401(R). (36) Goyon, J.; Colin, A.; Overlez, G.; Ajari, A.; Bocquet, L. Nature 2008, 454, 84. (37) Kiefer, J. E.; Parsegian, V. A.; Weiss, G. H. J. Colloid Interface Sci. 1975, 51, 543. (38) Hwang, K.; Wu, H.-J.; Bevan, M. A. Langmuir 2004, 20, 11393. (39) Baxter, R. J. J. Chem. Phys. 1968, 49, 2770. (40) Chen, M.; Russel, W. B. J. Colloid Interface Sci. 1991, 141, 564. (41) Grant, M. C.; Russel, W. B. Phys. Rev. E 1993, 47, 2606. (42) Crocker, J. C.; Matteo, J. A.; Dinsmore, A. D.; Yodh, A. G. Phys. Rev. Lett. 1999, 82, 4352. (43) Lane, J. M. D.; Ismail, A. E.; Chandross, M.; Lorenz, C. D.; Grest, G. S. Phys. Rev. E 2009, 79, 050501(R). (44) Rueb, C. J.; Zukoski, C. F. J. Rheol. 1997, 41, 197. (45) Vrij, A.; Jansen, J. W.; Dhont, J. K. G.; Pathmamanoharan, C.; Kops-Werkhoven, M. M.; Fijnaut, H. M. Faraday Discuss. Chem. Soc. 1983, 76, 19. (46) de Kruif, C. G.; Rouw, P. W.; Briels, W. J.; Duits, M. H. G.; Vrij, A.; May, R. P. Langmuir 1989, 5, 422. (47) Ito, K.; Moynihan, C. T.; Angell, C. A. Nature 1999, 398, 492. (48) Martinez, L.-M.; Angell, C. A. Nature 2001, 410, 663. (49) Buchenau, U. Phys. Rev. B 2009, 80, 172201. (50) Mattsson, J.; Wyss, H. M.; Fernandez-Nieves, A.; Miyazaki, K.; Hu, Z.; Reichman, D. R.; Weitz, D. A. Nature 2009, 462, 83. (51) Zhang, Z.; Xu, N.; Chen, D. T. N.; Yunker, P.; Alsayed, A. M.; Aptowicz, K. B.; Habdas, P.; Liu, A. J.; Nagel, S. R.; Yodh, A. G. Nature 2009, 459, 230.
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