Three Dimensional Dynamics and Self-Assembly of Helical Structures

As discussed in detail in Chapter 2, precise three dimensional particle tracking of pNIPAm mi- crospheres in glass microcapillaries is difficult due to imaging artifacts from the highly-curved, index mismatched surfaces involved in the experimental setup. This does not mean that precise three dimensional trajectories are completely inaccessible to a more sophisticated experimental system, however. Recent work has shown that pNIPAm particles synthesized through a semi- batch process are more homogeneously polymerized, and as a result, are much better index- matched to water [148]. Additionally, pNIPAm particles with fluorescent cores would be far easier to distinguish at high densities than the particles we have employed in our investigations.

Assuming the index matching of the aqueous solvent to the capillary can be addressed, more pre- cise three dimensional tracking could then be used to examine new structural order parameters more carefully. Specific interesting analyses would include a careful examination of dislocation structures at boundaries of ordered packings with different pitch or chirality, the radial distribu- tion and dynamics of particles, and vibrational density of states calculations using the methods outlined in Chapter 3.

The stability of helical quasi-1D packings begs a more thorough fundamental investigation of orientational order in confined dimensions. Though we argue that orientational order could be stable in these packings due to the quasi-2D nature of the packings, extensions of the arguments against 1D order [126,162] could be made that disprove such orientational stability. Also, obser- vations of longer helical structures could demonstrate a finite correlation length of orientational order dependent on inter-particle interactions. The stability of orientational order might thus be a result of interactions of the particles with the highly curved cylindrical boundary. Though the improved experimental resolution described above (as well as a larger sample size/field of view) would certainly serve to clarfy such points, a more rigorous theoretical treatment incor- porating the ordering effects of boundaries might provide a more thorough explanation for these effects. Even without a better theoretical explanation, it might be interesting to examine the stability of orientational order in hard sphere simulations. Simulational studies of sphere pack- ings in tubes to date examine translational order without probing orientational order [46]. It would also be interesting to theoretically and experimentally study other quasi-1D systems with orientational order. For example, anisotropic particles (e.g. ellipsoids, cubes, trimers, etc.), or particles with anisotropic interactions (e.g. Janus particles, magnetic dipoles) confined to a

one-dimensional chain might exhibit orientational order beyond a certain pressure, though they might not exhibit long-range translational order. Also, it would be interesting to study experi- mental analogues of simulated systems which always exhibit long-range orientational order, for example, rods/anisotropic particles free to rotate in two dimensions and translate only along a fixed line [50, 70].

Though placing particles in a cylinder is a simple method for creating helical packings, there is evidence that such packings could also be self-assembled from colloids with complex anisotropic interactions. For example, suspensions of so-called Janus particles with dipolar inter- actions have been shown to create chain-like structures with some degree of helical order [56]. Additionally, simulations of spherical particles with competing long-range dipolar and short- range attraction have predicted the self-assembly of helical structures with the exact pitch deter- mined by fine tuning of these interactions [131]. Though this system has not yet been experi- mentally realized, a colloidal analogue could be produced in a relatively straightforward manner using well-characterized techniques. A tunable short-range attraction could be induced by the addition of a size-changing depleting polymer or surfactant, or a binary phase separating solvent (as used in Chapter 3). A tunable long-range dipolar interaction could be produced by applying a uniform magnetic field to superparamagnetic colloids or applying a strong oscillating electric field to index-mismatched particles. Though the engineering of such a system would take time, and both potentials would need to be carefully tuned to have strengths on the order of_≈1𝑘𝐵𝑇,

it is certainly within the realm of possibility. Once these structures were assembled, it would be interesting to see how their phase behavior compared to the confined short-range repulsive thermal system studied in Chapter 2.

6.2.2 Precise Structural Nature and Generality of the Gel-Glass Crossover

The exact structural nature of the low-frequency modes which characterize sparse, gel-like pack- ings is still unclear, despite the finding of a correlation between areas with low local coordination and highly localized vibrational modes presented in Chapter 3. We have found qualitative cor- relation of these modes to local “linear” structures; however, the correlation is not one-to-one (i.e., not all linear structures dominate low-frequency modes, and not all low-frequency modes are localized to linear structures). A more rigorous analysis of the structures surrounding these localized low-frequency modes would better help to define gel-like packings based on their mor- phology alone.

Additionally, the experiments described in Chapter 3 only observe this low-frequency sig- nature of states in a rather specific set of two-dimensional morphologies. Whether or not this signature would be observed in other classes of high-density attractive particles is crucial to de- termining the generality of this gel-glass crossover. It would thus be useful to apply this same analysis to short-range attractive packings at identical area fractions with coarser, sparser or more fractal structures. Additionally, it would be interesting to see whether short-range attrac- tive particles stabilized by long-range repulsion and “patchy” particles with a limited attractive valence (i.e., systems which approach gel states through non-aggregated, “equilibrium” states as proposed in [181]) show similar behavior. It would also be helpful to see if this vibrational crossover can be applied to three-dimensional systems, assuming three-dimensional confocal imaging could be performed at a fast enough speed to capture simultaneous particle displace- ments and thus calculate vibrational modes. Replicating these results in numerical simulations would also serve to verify the generality of this crossover.

A connection must be made between these microscopic vibrational behaviors and bulk rheo- logical properties to give the described analysis more pertinent physical meaning. The localized modes in sparse packings might correspond the fragile regions of the packing in the same way that localized low frequency modes in dense disordered packings correlate to rearrangement- prone regions. The breaking of these “fragile” bonds might correlate to cluster-breaking relax- ations observed in the multi-step yielding of attractive packings [86]. This correlation could be experimentally probed by calculating vibrational modes and then observing consequent shears in colloidal packings using confocal rheolometer setups (such as those used in [6]) or more so- phisticated apparatuses which induce local shear using magnetic fields [73] or optical tweezers.