pNIPAm microspheres

The colloidal particles used in these experiments are aqueous microgels of poly-N-isopropylacrylamide (pNIPAm). These particles are composed of a sparse crosslinked pNIPAm network; in fact, a given particle’s mass is only taken up by approximately 3% polymer. As a result, the particles have soft sphere interactions, deforming under pressure or crowding. This softness makes pNI- PAm particles quite useful for creating and then controlling dense packings in tight confinement. In geometries where more commonly used hard-sphere colloidal particles (i.e. polystyrene, poly- methylmethacrylate) will easily jam, pNIPAm particles will deform, flow and re-arrange. Addi- tionally, the composition of pNIPAm gives them an index of refraction closely matched to that of water, making them useful for three dimensional imaging applications.

The primary experimental benefit of pNIPAm microspheres compared to other commonly used colloids is their thermo-responsive diameter. The polymer pNIPAm undergoes a tempera- ture induced phase transition in water from being largely hydrophilic to largely hydrophobic at a lower critical solution temperature (LCST) of32₋34∘ _{C. When crosslinked into a microgel} sphere, this results in a swollen, larger-diameter sphere at temperatures below the LCST, and

a collapsed, small-diameter sphere at temperatures above the LCST. Approaching the LCST, the aqueous solvent quality gradually decreases. This effect causes a gradual and predictable deswelling of the particles, leading to a near-linear change in diameter with temperature. This predictable and reversible change in particle diameter has led to these particles becoming widely used in experimental studies of volume-fraction mediated phase behavior [178].

Figure 2.5: Bright field microscopy images of a dense aqueous suspension of pNIPAm micro- gel particles at 25 ∘C (left) and 28 ∘C (right). Particles deswell with increasing temperature (as depicted in the illustration insets), decreasing packing fraction, melting the packing from a crystalline packing (left) to an isotropic disordered fluid (right). Scale bar =10𝜇m.

2.3.1.1 pNIPAm Synthesis and Fluorescent Functionalization

The pNIPAm particles used were synthesized using a surfactant-mediated emulsion polymer- ization method, which has been well characterized elsewhere [100, 127, 140, 178]. In order to image these particles using fluorescence confocal microscopy, they are functionalized with a fluorophore. Specifically, an additional copolymer, 2-aminoethylmethacrylate hydrochloride (AEMA), is added to the pNIPAm microgels during the synthesis process. This provides the microgels with additional free amine groups, i.e., more than if they were made using NIPAm monomer alone. After synthesis, the particles are swollen in a suspension of a rhodamine-based

fluorescent dye, 5-(6)-carboxytetramethylrhodamine, succinimidyl ester (TAMRA), which cova- lently bonds to the free amine groups in the microgels. The particles are then thoroughly washed and re-suspended in an aqueous solution.

2.3.1.2 pNIPAm Particle Diameter Characterization

Though dynamic light scattering is a prolific and useful technique for characterizing the size of colloidal particles, and it certainly captures the linear changes in particle diameter with tempera- ture expected for pNIPAm particles, light scattering does not yield a particularly useful diameter value for characterizing dense colloidal packings. Dynamic light scattering extracts a hydro- dynamic diameter 𝑑ℎ for particles, derived from the particle diffusion coefficient, 𝐷, which is

measured by laser intensity fluctuations scattered through a dilute suspension of particles and defined via the Stokes-Einstein relation:

𝑑ℎ=

𝑘𝐵𝑇

3𝜋𝜂𝐷. (2.5)

Here,𝜂 is the fluid viscosity. The resulting hydrodynamic diameter𝑑ℎ is typically only 80%-

90% of the inter-particle separation observed in close-packed, dynamically arrested packings of pNIPAm spheres. There are multiple reasons for this difference, including the porous nature of the pNIPAm particles, as well as the difficulties in defining a discrete “diameter” for a particle with a soft inter-particle potential.

We derive a more useful “value” of particle diameter from direct microscopic observations of inter-particle interactions. Dilute suspensions of the same pNIPAm particles used in the helical packing experiments were placed between glass coverslips such that the gap between coverslips

Figure 2.6: Two-dimensional spatial correlation functions for the two sizes of pNIPAm micro- spheres (a, smaller, b, larger) used in helical packings experiments at different temperatures in a dilute suspension in a quasi-2D cell. Horizontal line indicates𝑔(𝑟) = 1/𝑒, an effective definition of sphere diameter. Shoulders in𝑔(𝑟)curves in (a) occur due to the presence of one or two stuck particles in the field-of-view.

was slightly larger than the diameter of the pNIPAm particles, creating a quasi-2d monolayer. Videos of these particles diffusing in two dimensions were taken using a 100_×oil-immersion objective (N.A. = 1.4) at five temperatures from 24 to 28∘C. Particle centers were tracked using standard particle tracking routines [26]. The two dimensional pair correlation function𝑔(𝑟) of the particle locations was then calculated from the particle tracks. At each temperature, the approximate diameter of the particles taken to be the first value𝑟 where𝑔(𝑟) = 1/𝑒, since, in the first approximation,𝑔(𝑟) =𝑒−𝑈(𝑟)/𝑘𝐵𝑇_{, and the effective diameter of particles is often taken} as the value of𝑟for which𝑈(𝑟) =𝑘𝐵𝑇.

We take a linear fit of these data points to find a functional relationship between effec- tive particle diameter and temperature (shown in Fig. 2.7), since previous studies have ob- served a linear relationship between diameter and temperature for pNIPAm particles in this temperature range [1, 51, 52, 174, 187]. For the larger species used in this experiment, we find the relationship 𝑑𝑒𝑓 𝑓 = 2.52𝜇m−0.037(𝜇m/∘𝐶)×𝑇, and for the smaller species, we find

𝑑𝑒𝑓 𝑓 = 2.41𝜇m−0.054(𝜇m/∘𝐶)×𝑇.

Figure 2.7: Approximate diameters for the smaller (blue_∙) and larger (red▲) pNIPAm particles used in helical packing experiments at different temperatures, with linear fits.