Iteración 2

The content of this thesis is organized as follows. We first discuss our investigation of parti- cle behavior in evaporating drops and the coffee-ring effect (Chapter 2). This work was pub- lished [186]. We demonstrate that particle shape strongly affects the deposition of particles during evaporation. Next, we investigate the role of particle shape in evaporating drops in con- fined geometries, and show how to extract the bending rigidity of the membranes formed by particles adsorbed on the air-water interface (Chapter 3). This work is published [185]. We then shift to experiments investigating the behavior of glasses and related transitions. We first discuss experiments that use optical heating to quench a liquid to a glass; this scheme permits the detailed study of aging in glasses (Chapter 4). This work is published [181]. Then, we report

the mechanisms by which crystals transform into glasses as the amount of quenched disorder increases (Chapter 5). This work is published [182]. In Chapter 6 we investigate the effect of particle shape on the vibrational modes in glasses composed of ellipsoidal particles. This work is published [183]. Next, we investigate the effect of particle number and network connectivity on the vibrational modes in disordered clusters, allowing is to identify when small clusters start to behave like bulk glasses (Chapter 7). This work is published in [184]. Finally, in Chapter 8 we summarize the work presented in this dissertation, and suggest future directions for the investigation of nonequilibrium colloids.

Chapter 2

Coffee Ring Effect Undone by Shape

Dependent Capillary Interactions

2.1

Introduction

When a drop of liquid dries on a solid surface, its solute is deposited in ring-like fashion. This phenomenon, known as the coffee ring effect [37, 40, 76], is familiar to anyone who has dried a drop of coffee. During the drying process, drop edges become pinned, and capillary flow outward from drop center brings suspended particles to the edge as evaporation proceeds. After evapo- ration, suspended particles are left highly concentrated along the original drop edge. The coffee ring effect is manifest in systems with diverse constituents ranging from large colloids [36–38] to nanoparticles [15] to individual molecules [89]. In fact, notwithstanding the many practical applications for uniform coatings in printing [128], biology [46,47], and complex assembly [39], the ubiquitous nature of the effect has proven difficult to avoid [15, 77, 83, 124, 126, 171]. Here

we experimentally show that suspended particleshapematters for coatings and can be used to eliminate the coffee ring effect. Ellipsoidal particles deposit uniformly during evaporation. The anisotropic particles significantly deform interfaces, producing strong interparticle capillary in- teractions [16, 19, 105, 106, 111, 112, 127]. Thus, after the ellipsoids are carried to the air-water interface by the same outward flow that causes the coffee ring effect for spheres, strong long- ranged interfacial attractions towards other ellipsoids lead to the formation of loosely-packed quasi-static or arrested structures on the air-water interface [54, 105, 106, 111]. These structures prevent the suspended particles from reaching the drop edge and ensure uniform deposition. In- terestingly, under appropriate conditions, suspensions of spheres mixed with a small number of ellipsoids also produce uniform deposition.

A drop of evaporating water is a complex, difficult-to-control, non-equilibrium system. Along with capillary flow, the evaporating drop features a spherical-cap-shaped air-water in- terface and Marangoni flows induced by small temperature differences between the top of the drop and the contact line [38]. Attempts to reverse or ameliorate the coffee ring effect have thus far focused on manipulating capillary flows [15, 77, 83, 124, 126, 171]. In this contribution we

show that uniform coatings during drying can be obtained simply by changing particleshape.

The uniform deposition of ellipsoids after evaporation (Fig. 2.1 a) is readily apparent, and it stands in stark contrast to the uneven “coffee ring” deposition of spheres (Fig. 2.1 b) in the same solvent, with the same chemical composition, and experiencing the same capillary flows (Fig. 2.1 c).

A landmark paper by Deegan,et al., captured all of the qualitative theoretical features of the

0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.05 0.10 0.15 0.20 = 1.0 = 1.05 = 1.1 = 1.2 = 1.5 = 2.5 = 3.5 / N [ m ] r / R - 2 1 2 3 4 0 20 40 60 80 M a x / M i d e d = 1.0 = 3.5 a b c Air W ater Substrate 0.5 mm 0.5 mm

Figure 2.1: a. Image of the final distribution of ellipsoids after evaporation. b. Image of the final distribution of spheres after evaporation. c. Schematic diagram of the evaporation process depicting capillary flow induced by pinned edges. If the contact line were free to recede, the drop profile would be preserved during evaporation (dashed line). However, the contact line remains pinned, and the contact angle decreases during evaporation (solid line). Thus, a capillary flow is induced, flowing from the center of the drop to its edges; this flow replenishes fluid at the contact

line. d. Droplet-normalized particle number density,ρ/N, plotted as function of radial distance

from center of drop for ellipsoids with various major-minor axis aspect ratios. e. The maximum

local density,ρM ax, normalized by the density in the middle of the drop,ρM id, is plotted for all

recede, i.e., the drop diameter cannot decrease Fig. 2.2. As the edge of the drop is thinner than the middle of the drop, fluid must flow from the middle of the drop to the edge of the drop to replenish the water that has evaporated away. In other words, the water lost due to evaporation,

quantified by the evaporative flux, J, must be canceled by water gained via a flow of fluid,

with flow velocityv. In a square shaped area with lengthland height h,J l2 must be equal to

vlh. To first order,J ∝ v (Fig. 2). By solving the diffusion equation, it can be shown that J

diverges as the edge is approached asJ ∝(R−r)λ, whereλ= (π−2θc)/(2π−2θc). Thus,

v ∝ (R−r)λ. Additionally, since the drop height, h, decreases approximately linearly over

time, ash ∝(tf −t). However, the outward flow must cancel the evaporative flux at all times,

sov∝(tf −t). Thus, simply be pinning the edges of a drop, a complex radially outward flow

is induced.

Figure 2.2: Schematic diagram of the evaporation process depicting capillary flow induced by pinned edges. If the contact line were free to recede, the drop profile would be preserved during evaporation (dashed line). However, the contact line remains pinned, and the contact angle decreases during evaporation (solid line). Thus, a capillary flow is induced, flowing from the center of the drop to its edges; this flow replenishes fluid at the contact line.