Impurities in crystals generally cause point defects and can even suppress crystallization. This general rule, however, does not apply to colloidal crystals formed by soft microgel particles [Iyer ASJ, Lyon LA (2009) Angew Chem Int Ed 48:4562-4566], as, in this case, the larger particles are able to shrink and join the crystal formed by a majority of smaller particles. Using small-angle X-ray scattering, we find the limit in large-particle concentration for this spontaneous deswelling to persist. We rationalize our data in the context of those counterions that are bound to the microgel particles as a result of the electrostatic attraction exerted by the fixed charges residing on the particle periphery. These bound counterions do not contribute to the suspension osmotic pressure in dilute conditions, as they can be seen as internal degrees of freedom associated with each microgel particle. In contrast, at sufficiently high particle concentrations, the counterion cloud of each particle overlaps with that of its neighbors, allowing these ions to freely explore the space outside the particles. We confirm this scenario by directly measuring the osmotic pressure of the suspension. Because these counterions are then no longer bound, they create an osmotic pressure difference between the inside and outside of the microgels, which, if larger than the microgel bulk modulus, can cause deswelling, explaining why large, soft microgel particles feel the squeeze when suspended with a majority of smaller particles. We perform small-angle neutron scattering measurements to further confirm this remarkable behavior.oint defects in crystalline materials disrupt the crystal structure and often prevent crystallization. This is the case, for instance, when large particles are introduced in a crystal of smaller particles. Bragg illustrated the consequences of this disruption using soap bubbles (1). In metal melts, a size mismatch of 15% between the atoms suppresses crystallization (2), and, in hard spheres, which constitute an important model system for condensed matter, a polydispersity above 12% also prevents crystallization (3). Furthermore, the polydispersity in hard sphere crystals does not exceed 5.7%, due to local segregation of dissimilar particles during crystallization (4, 5).Remarkably, these restrictions do not necessarily apply to suspensions of soft microgels, which are cross-linked polymer particles immersed in a solvent that can exist in either swollen or deswollen states, depending on external conditions like temperature (6) and pH (7). Indeed, microgel suspensions containing a small fraction of larger particles can crystallize without defects by shrinking the larger particles to a size that is identical to that of the smaller and more abundant microgel particles (8). This deswelling was hypothesized to result either from the direct interaction between large and small particles or from the osmotic pressure exerted by the small microgels on the larger ones (2). Here, we show that none of these effects drive this proces...
We study ionic microgel suspensions composed of swollen particles for various single-particle stiffnesses. We measure the osmotic pressure π of these suspensions and show that it is dominated by the contribution of free ions in solution. As this ionic osmotic pressure depends on the volume fraction of the suspension φ, we can determine φ from π, even at volume fractions so high that the microgel particles are compressed. We find that the width of the fluid-solid phase coexistence, measured using φ, is larger than its hard-sphere value for the stiffer microgels that we study and progressively decreases for softer microgels. For sufficiently soft microgels, the suspensions are fluid-like, irrespective of volume fraction. By calculating the dependence on φ of the mean volume of a microgel particle, we show that the behavior of the phase-coexistence width correlates with whether or not the microgel particles are compressed at the volume fractions corresponding to fluid-solid coexistence.
We determine the osmotic pressure of microgel suspensions using membrane osmometry and dialysis, for microgels with different softnesses. Our measurements reveal that the osmotic pressure of solutions of both ionic and neutral microgels is determined by the free ions that leave the microgel periphery to maximize their entropy and not by the translational degrees of freedom of the microgels themselves. Furthermore, up to a given concentration it is energetically favorable for the microgels to maintain a constant volume without appreciable deswelling. The concentration where deswelling starts weakly depends on the crosslinker concentration, which affects the microgel dimension; we explain this by considering the dependence of the osmotic pressure and the microgel bulk modulus on the particle size.
Oxanorbornadiene dicarboxylate (OND) reagents are potent Michael acceptors, the adducts of which undergo fragmentation by retro-Diels–Alder reaction at rates that vary with the substitution pattern on the OND moiety. Rapid conjugate addition between thiol-terminated tetravalent PEG and multivalent ONDs yielded self-supporting hydrogels within 1 min at physiological temperature and pH. Erosion of representative hydrogel formulations occurred with predictable and pH-independent rates on the order of minutes to weeks. These materials could be made non-degradable by epoxidation of the OND linkers without slowing gelation. Hydrogels prepared with OND linkers of equal valence had comparable physical properties, as determined by equilibrium swelling behavior, indicating similar internal network structure. Diffusion and release of entrained cargo varied with both the rate of degradation of PEG-OND hydrogels and the hydrodynamic radius of the entrained species. These results highlight the utility of OND linkers in the preparation of degradable network materials with potential applications in sustained release.
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