Iteración 1

Most experiments described in this dissertation utilize relatively standard techniques in new ways. However, some of the experiments required development of new techniques, or extension of old ones to new situations. To study aging glasses, we developed a technique that uses optical heating to rapidly quench microgel suspensions from the liquid phase to the glass phase. In our phonon studies, we extended a technique that calculates a system’s vibrational modes from

1 2 3 4 5 1x10 5 2x10 5 3x10 5 M e d NN c

Figure 1.10: a. Purely repulsive hard spheres form a fluid phase at low packing fractions. b. Conversely, particles with short-range attraction can form solid phases at low packing fractions,

such as macroscopic gels and locally dense clusters. c. Median vibrational frequency (ωM ed

plotted versus average number of nearest neighbors (N N) for clusters of many different sizes

particle displacements to include a rotational degree of freedom that is required for investigation of glasses composed of anisotropic particles. Finally, we developed a method to extract elastic properties of quasi-2D membranes from images of buckled membranes by extension of similar techniques previously employed for spherical membranes.

1.4.1 Rapid Quenching of Microgel Particle Liquids

In order to study aging, it is desirable to observe a glass starting from just after its formation. As noted in Section 1.2.1, previous methods of rejuvenating glass prevented observation for tens or hundreds of seconds after the glass is formed. In order to observe aging at the earliest times, we developed a method to rapidly quench from liquid to glass through a new experimental twist utilizing optical heating. A small amount of red dye, is released into the suspension. This dye absorbs light from a mercury lamp focused through the microscope objective. The sample field

of view lies at the center of the illumination region. There, the temperature is increased by∼4

degrees in∼0.1 seconds via light absorption and molecular relaxation processes. The NIPA par-

ticle radii are thus abruptly decreased by∼0.1µm, and the local area fraction (ϕA) is decreased

by ∼10%. While the lamp is on, the particles are in the liquid state. The Brownian time of

micron sized particles is∼1 second, and the lamp is only on for∼6 seconds, so thermophoretic

effects are avoided. However, everything else (e.g., the rest of the sample, the microscope, etc.) is held at the original low temperature; thus when the mercury lamp is turned off, the excess heat rapidly dissipates, and particles swell to their original size in less than 0.1 seconds. The

rapid change from small-ϕA(liquid) to large-ϕAcreates a glass. Aging begins (tw = 0 seconds)

once the sample returns to thermal equilibrium and particles have completely returned to their original size. Thus, this technique enables us to begin watching a glass age immediately after it

is formed. Increase Temperature 25 30 35 40 45 0.2 0.3 0.4 0.5 0.6 R H [ m ] T [C] b a

Figure 1.11: a. PNIPAM particles are depicted in cartoon form. When temperature is increased,

PNIPAM particles decrease their diameters. b. Hydrodynamic radius, RH of PNIPAM particles

as a function of T.

1.4.2 Measurement of Phonon Modes for Anisotropic Particles

As introduced in Section 1.2.3, we measured the vibrational properties of ellipsoidal glasses. Previously, we were among the first researchers to apply displacement correlation matrix meth- ods to translational degrees of freedom [23, 57, 58, 90]. Those methods work well for suspen- sions of spheres. However, for anisotropic particles, rotations are important and must be taken into account. We extracted vibrational properties of ellipsoidal glasses by measuring rotational and translational displacement correlations. To do so, we extended the procedure for spheres

( [24]) to incorporate a rotational degree of freedom. Following [18], we expect undamped hard particles that repel entropically near but below the jamming transition to give rise to solidlike vibrational behavior on time scales long compared to the collision time but short compared to the time between particle rearrangement events [57, 58]. Thus, the stiffness matrix arising from entropic repulsions is directly related to the dynamical matrix characterizing vibrations. By per- forming this analysis, we found that the vibrational properties of glasses are highly dependent on particle shape.

1.4.3 Theory of Buckled Quasi-2D Membranes

By analyzing the shape of a buckled spherical membrane, information can be extracted about the membrane’s elastic properties [99]. However, far less work has been done on disc-shaped mem- branes, as introduced in in Section 1.1. To understand the elastic properties of the membrane that forms when a drop is evaporated in confinement (i.e., the elastic properties of the CMMs), we extended analytical descriptions of elastic membranes to our quasi-2D geometry wherein ob- servations about bending and buckling geometry are unambiguous. Following [99], we describe the stretching and bending energy associated with membrane buckling events. The deformation energy is located within the deflected rim. Membranes buckle in such a way as to minimize their energy, so we then minimize the total buckling energy with respect to the rim size. As a result of

minimizing the total bending and stretching energy,κ/E=d4/(3r2), whereκis the membrane

bending rigidity,E is the Young’s modulus,dis the rim width, andris the drop radius. Thus,

Figure 1.12: Cartoon representation of a buckling event. The dotted line represents the initial membrane configuration (before the buckling event).