Non-central forces in microgel colloidal crystals*

Microgels are stimuli-sensitive colloids formed by cross-linked polymer networks and are a good model system for soft colloids. Poly(N-isopropylacrylamide) microgel copolymerized with acrylic acid (AAc) synthesized with APS or KPS initiators features a counterion cloud bound electrostatically to the charge groups at the particle surface. In concentrated suspensions, the percolation of the cloud causes a sharp increase of the osmotic pressure of the suspension that can overcome the bulk modulus of the microgels and, as a consequence, triggers their isotropic deswelling. It has been shown that for colloidal crystals of hard colloids, non-central forces dominate the interparticle interactions due to the presence of free counterions. Consequently, models that rely on the addition of pair-wise potentials, such as the DLVO model, can no longer sufficiently describe the system. Given the presence of free counterions in suspension, the microgel-microgel interaction is found to be non-central and analogous to the case of slightly charged hard colloids. In our experiment, at ζ~1.5 and ζ~1.3, the crystalline state of the pNIPAM-AAc microgels with a fluorescent core is studied at pH < 4 and pH = 7, corresponding to ACC being uncharged and charged, respectively. By measuring the normal modes using confocal microscopy with particle tracking, we extract the dynamic matrix of the crystal and the force constants of 1st neighbors and 2nd neighbors, as well as the elasticity constants of the crystal. The results turn out contradicting to the Cauchy relation, which indicates the non-central nature of the interaction force. In addition, we notice that F⁽²⁾_xx ~ -1/2 F⁽¹⁾_xx, indicating that the displacement of the 1st neighbor attracts the 2nd neighbor, contrary to the central force prediction. Our results show that the counterions of microgels with surface charge control both their swelling and their interaction at high concentrations. These findings must be considered for models of the swelling and phase behavior of soft colloids.