Alberto Fernandez-Nieves, Georgia Institute of Technology
Colloidal suspensions are widely used to study fundamental problems in condensed matter physics since they behave in many aspects like model atomic systems, exhibiting liquid, crystal and glassy phases. For hard interparticle interactions, these phase changes are achieved by tuning the particle volume fraction, f, which is the only independent thermodynamic variable in this case. For more general interparticle interactions, these phase changes can also be achieved by changing either the range or the strength of the interaction. Interestingly, the intrinsic softness of microgel particles, which are colloidal-size, crosslinked polymer networks, can also have important effects over the suspension phase behavior; for instance, Senff and Richtering found that crystallization and melting occurred at higher volume fractions and exhibited a narrower phase coexistence region compared to hard sphere suspensions. Furthermore, particle softness can also affect kinetic arrest and hence the liquid-to-glass transition; Mattson et.al. recently found that while hard microgel suspensions behave like fragile molecular glass formers, suspensions comprised of soft microgels exhibited a behavior reminiscent of strong molecular glass formers.
While there is evidence that particle softness affects the phase and non-equilibrium behavior of the suspension, the physical scenario behind such influence remains largely unknown. This, in part, results from the lack of an adequate way to think about particle softness. Indeed, one could think about softness in terms of the interparticle potential, which would exhibit a soft repulsion for center-to-center distances below the particle diameter. Alternatively, one could think about softness in terms of a relevant elastic modulus of the particle or even in terms of internal degrees of freedom, since these contribute to the thermodynamics of the suspension. We have performed work to unravel this puzzle and to elucidate the way particle softness affects the suspension behavior.
We have employed three classes of microgel particles. The first one consists of vinylpyridine, a weak base that ionizes at low pH, and divinylbenzene (DVB), a crosslinker. This particle was used to understand the influence of particle stiffness, which we tuned by using different amounts of DVB, over the suspension phase and non-equilibrium behavior. We always worked at a constant pH of 3, where the particles are fully swollen. For stiff microgels, the suspension exhibits liquid, crystal and glassy phases. This is reminiscent of hard sphere behavior. However, for our microgels, we find that the width of the liquid-crystal phase coexistence region increases as the DVB concentration decreases. We believe this results from the influence of the microgel internal degrees of freedom that can contribute to the entropy of the system and hence to the particle concentration jump involved when the liquid phase transform into the crystal phase. For softer microgels, we observe that the suspension does not crystallize. Instead, there is a glass transition at certain particle concentration. But even more remarkably, for even softer microgels, the suspension remains liquid irrespective of the concentration. Overall, these results emphasize the rich phenomenology that can be brought about when the particles are deformable and compressible as opposed to being rigid and non-interacting.
The second class of microgel particles consists of poly-(N-isopropylacrylamide), pNIPAM, a thermosensitive polymer, acrylic acid, a weak acid, and the crosslinker methylene-bis-acrylamide (BIS); these particles change size in response to temperature and pH changes. The suspension size distribution has a width of 12% of the mean. With this system we focused on the crystal phase and did extensive Small Angle Neutron Scattering to determine the suspension structure factor. We then compared the experimental results with the expected structure factor of well known crystal structures and found that the agreement was best for suspension polydispersities that were less than that measured in dilute conditions. These results suggest that the suspension phase behavior can rely on polydispersity changes. For hard spheres, crystallization is driven by the increase in entropy that results from the gain in free volume per particle. For soft, deformable objects, this entropy gain competes with the entropic penalty associated to changing the preferred equilibrium size of some microgels to reduce the suspension polydispersity. For sufficiently soft particles, this entropy penalty might be smaller than the entropy gained by crystallizing and as a result these suspensions will change their polydispersity to allow the system to crystallize. We have recently synthesized large batches of microgel suspensions with different average sizes to make suspensions with home-made size distributions. This will allow us to test this hypothesis and understand the apparent polydispersity change in the crystal phase with respect to the dilute situation.
The third type of microgel particles also consists of pNIPAM, but it is crosslinked with poly(ethylene glycol diacrylate), PEG, which is a hydrophilic polymer. Particles based on pNIPAM appreciably deswell at a lower critical solution temperature (LCST) of approximately 305 K; it is the change in solubility around this temperature which is responsible for this behavior. A major problem is that pNIPAM microgels aggregate and eventually gel at temperatures above the LCST; the change in solubility responsible for particle deswelling also induces the required interparticle attraction for the suspension to become colloidally unstable. This hinders exploring the influence of swelling alone over the suspension phase behavior, as changes in temperature change the interparticle interactions from repulsive at low temperature to attractive at high temperatures. By using PEG as cross-linker, the repulsion is maintained beyond the LCST. It is the hydrophilicity of this polymer which, at high temperature, segregates towards the periphery of the particles to assure the desired repulsion. Our aim is to use these particles to explore how the swelling degree and hence the stiffness of pNIPAM microgels affects glass formation. At this point (i) we have performed a detailed light and neutron scattering characterization of the particles to understand how the microgel morphology changes with temperature, and (ii) we have exploited the colloidal stability of the suspension to measure how the bulk modulus of the particles changes through the swelling transition. Consistent with what was found for pNIPAM macrogels, the bulk modulus of our microgels drops at the LCST.