









Phase behavior of microgel suspensions using
Neutron Scattering and Hydrostatic Pressure.
Juan Jose LietorSantos¹, Urs
Gasser² ³, Alberto FernandezNieves¹
1 School of Physics, Georgia Institute of Technology, Atlanta, Georgia, 30332.
2 Laboratory for Neutron Scattering, ETH, Zurich and Paul Scherrer Institute, 5232, Villingen, PSI, Switzerland.
3 Adolphe Merkle Institut, University of Fribourg, P.O.Box 209, 1723 Marly 1, Switzerland
Gels are crosslinkedpolymeric networks immersed in a solvent, whose size can change using
external stimuli. Microgels are gels in the colloidal domain.
From a fundamental point of view, they have been treated as colloidal hard
spheres and when concentrated, they exhibit a liquid, crystal and glassy phases depending
solely on the volume fraction of the particles, Φ=n_{p} V_{1p},
with n_{p} the number density of particles
and V_{1p} the volume of a single particle, as is sketched in Fig.2A. However, there are
several experimental evidences which suggest that, in certain conditions, microgel suspensions
can display a considerably richer and more fascinating behavior, as is shown in Fig.2B for a
typical thermosensitive polymer NIPAM microgel copolymerized with a pHsensitive group, acrylic
acid. As the acrylic groups get ionized by increasing the pH, the crystalline region narrows down
and, eventually, disappears.
Colloidal phase behavior and phase transitions.
Hydrostatic pressure as a tuning variable for particle size.
Neutron Scattering as a tool for elucidating structural and dynamical
properties of the system. I(q) ~ P(q) S(q)
where q is the scattering vector defined as the difference between
the incident and the scattered wave vector and thus depends
on the scattering angle, P(q) is called the form factor and accounts
for particle properties (geometry, size…) and S(q) is called the structure
factor and accounts for the structural properties of the system.
The form factor displaces to smaller q’s as the particle size increases (hydrostatic pressure decreasing) as expected from Fig.4. The form factor can be described using a polydisperse coreshell model in which the core is represented as a hard sphere of radius R and for the shell, a Gaussian function of characteristic size &sigma_{surf} is used. In addition, the internal structure of the particles is taken into account using a Lorentzian term of characteristic length &sigmaf [see Stiger et al]:
Thus, by measuring I(q) (Fig.6a) we can calculate the structure factor of the system dividing by P(q). This is presented in Fig.6(b).
These structure factors are considerably different from those of a monodisperse
system of hard spheres at similar volume fractions. A possible reason for this difference
[Stieger et al] is the inadequacy of the form factor used to obtain the structure
factor from the scattered intensity, since at high volume fractions
the particles would deform and interpenetrate. However, this procedure seems
to yield reasonable results when comparing experiment and theoretical expectation
for crystal samples, in which the volume fraction is slightly smaller (see Fig.3).
Some useful references:
Contact Information: Juan Jose LietorSantos Office: Boggs Building, Room B54 Email address: jjlietors [at] gatech.edu Phone: 4043853681 
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