Critical Onset of Layering in Sedimenting Suspensions of Nanoparticles A. V. Butenko, 1 P. M. Nanikashvili, 2 D. Zitoun, 2 and E. Sloutskin 1* 1 Physics Department and Institute for Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel 2 Chemistry Department and Institute for Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel (Received 3 September 2013; published 7 May 2014) We quantitatively study the critical onset of layering in suspensions of nanoparticles in a solvent, where an initially homogeneous suspension, subject to an effective gravity a in a centrifuge, spontaneously forms well-defined layers of constant particle density, so that the density changes in a staircaselike manner along the axis of gravity. This phenomenon is well known; yet, it has never been quantitatively studied under reproducible conditions: therefore, its physical mechanism remained controversial and the role of thermal diffusion in this phenomenon was never explored. We demonstrate that the number of layers forming in the sample exhibits a critical scaling as a function of a; a critical dependence on sample height and transverse temperature gradient is established as well. We reproduce our experiments by theoretical calculations, which attribute the layering to a diffusion-limited convective instability, fully elucidating the physical mechanism of layering. DOI: 10.1103/PhysRevLett.112.188301 PACS numbers: 47.57.ef, 47.55.pb, 82.70.Kj Sedimentation of micro- and nano-particles in a solvent under gravity is common in bio- and nano-technology [1], occurring in a wide range of geophysical systems [2] and limiting the shelf life of food products and pharmaceut- icals [3]. Sedimentation is also widely used as an analytical tool for industrial, medical [4], and research applications [5–7]. Under most common experimental conditions, the density of particles in a sedimenting fluid suspension is a continuous function of time and spatial coordinates [8]. However, occasionally, the density of particles develops multiple (roughly) equispaced plateaus, thus adopting a staircaselike appearance along the axis of sedimentation. This phenomenon, called “layering” or “stratification, ” has been known for more than a century [9–11]. Yet, most previous experimental realizations of this effect employed micron-sized particles [10,12,13], for which the layer structure is highly sensitive to tiny temperature gra- dients [10,12,14], prohibiting extraction of quantitative experimental information. Other experiments employed particles with high or unknown polydispersity [6,9], which limited the availability of interpretable experimental data. As a result, the physical mechanism of layering in sedimenting suspensions remained ambiguous [15], with several com- peting theoretical scenarios attributing the layering to either Burger’ s shock formation [16], spinodal decomposition [12], vertical streaming flows [2], spontaneous formation of magic number clusters [6,14,17], long-range hydrodynamic inter- actions [18,19], or convective instability [10,20]. Quantitative experimental information, which would allow the true mechanism of layering to be unequivocally identified, was missing. We follow the full dynamics of layer formation in sedimenting suspensions of several different types of nanoparticles in various organic solvents subjected to an effective gravity in a centrifuge, employing light trans- mission (LT) through the samples. We demonstrate that by using nanoparticles, the layering phenomena are much more robust than in the previous studies [10,20]; this system allows quantitative and reproducible measurements to be collected with our experimental setup. Furthermore, this setup allows the effective gravity a , measured in the units of g ¼ 9.8 m=s 2 , to be varied; we use it to study the critical onset of the layering effect, where pattern formation by layering overcomes the significant thermal diffusion of the nanoparticles. We demonstrate that in this regime, the number of layers N in a sample exhibits a unique power- law scaling as a function of a and the height H of initial suspensions; the dependence on H of the critical effective gravity a c , below which the layers do not form, is explored as well. We reproduce most of our observations by numerical calculations, employing a hydrodynamical model that attrib- utes the layering to a convective instability [10,20]. We suggest that the spontaneous layering in suspensions of nanoparticles may serve as a basis for future analytical techniques for nanoscale colloids, and may have important applications in self-assembly of metamaterials. We prepare Cu@Ag and pure Ag nanoparticles, stabi- lized by either an oleylamine or a dodecanethiol surface monolayer [21], and suspend them in pure hexane or heptane at a low volume fraction c 0 ¼ 10 −4 − 10 −3 ; these particles form promising inks for inkjet printing [21]. The average diameter σ and size distributions PðσÞ of the particles are measured by transmission electron microscopy (TEM). Most samples exhibit a simple Gaussian PðσÞ, peaking between 10 and 20 nm, with a width of ∼4 nm (see Supplemental Material [22]). We load the initially homo- geneous fluid suspension into an analytical tabletop cen- trifuge (Lumifuge), where a is in the range 200 <a< 2500. PRL 112, 188301 (2014) PHYSICAL REVIEW LETTERS week ending 9 MAY 2014 0031-9007=14=112(18)=188301(5) 188301-1 © 2014 American Physical Society