









Soft Particles Crossing the Glass Transition
John S. Hyatt and Alberto FernandezNieves
I am one of our group's resident light scattering and rheology specialists, and I use both tools to study colloidal microgels both in dilute and denselypacked solutions.
I work with a system of microgel particles whose structure can be controlled by ambient temperature and pH to achieve volume (and therefore density) changes by a factor of over 100 (see Fig. 1). They are synthesized from Nisopropylacrylamide (which becomes hydrophobic at high temperatures) and acrylic acid (which ionizes at high pH) and crosslinked with poly(ethyleneglycol), a hydrophilic polymer.
These particles are unusual in that they undergo several dramatic changes in their internal structure at different conditions. Fig. 2 shows the form factors (Fouriertransformed radial density functions, obtained via light scattering) of the particles at different conditions. The form factors at low pH are welldescribed by the polydisperse coreshell model[1] with additional terms accounting for the heterogeneous distribution of polymer inside the particle[2], $$P(q)=\int\textrm{d}R_{core}f\left(R_{core}\right)\left[3\exp\left(\frac{q\sigma_{surf}}{2}\right)\frac{\sin\left(qR_{core}\right)qR_{core}\cos\left(qR_{core}\right)}{\left(qR_{core}\right)^3}\right]^2+\frac{I_{1}}{\left[1+\left(q\xi_{het}\right)^2\right]^2}+I_0,\,\,\,\,\,\,\,\,\,\,(\textrm{Eq.}1)$$ and at high pH by the star polymer model[3], $$P(q)=A_1\int\textrm{d}R_{g}f\left(R_{g}\right)\exp\left[\frac{1}{3}\left(qR_g\right)^2\right]+\frac{A_2}{\mu q\xi_{blob}}\frac{\sin\left[\mu\arctan\left(q\xi_{blob}\right)\right]}{\left[1+\left(q\xi_{blob}\right)\right]^{\mu/2}}.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\textrm{Eq.}2)$$ The integrals include particle polydispersity following a distribution f, in this case a Gaussian. In Eq. 1, the relevant parameters are the radius of the core, the thickness of the surrounding fuzzy shell, the length scale of the heterogeneities, and the intensity amplitudes of the heterogeneous term and constant background. In Eq. 2, the relevant parameters are the radius of gyration, the blob size of the polymer branches inside the particle, μ, a factor related to the internal fractal dimension of the polymer, and the relative amplitudes of the two terms.
We are currently trying to understand the way in which the softness and internal structure of the particles influences their behavior in highlypacked states, where they display a liquidglass transition at concentrations far above spacefilling; in other words suspensions of these particles remain liquid even when they are so tightlypacked that they must compress to fit into the available space. Fig. 3 shows relaxation times vs. ζ, the generalized volume fraction, obtained from a combination of light scattering and rheology measurements.
The glass transition is visible as a dramatic increase in the relaxation time. Surprisingly, although the particles are overpacked when the transition occurs, it is quite abrupt, in contrast to earlier work our group has done that found a much more gradual approach to the glass transition for soft particles[4]. Our work with this system is aimed at better understanding the mechanisms link particle softness (a somewhat nebulous term that includes particle interpenetration, compression, and deformation) to the onset of a liquidsolid phase change as the particle concentration is increased. For more information about our lab's work with denselypacked microgel suspensions, visit my colleague Miguel's page here.

Soft Condensed Matter Laboratory, School of Physics, Georgia Institute of Technology
770 State Street NW, Atlanta, GA, 303320430, USA
Phone: 4043853667 Fax: 4048949958
alberto.fernandez [at] physics.gatech.edu