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Phase behavior of microgel suspensions using
Neutron Scattering and Hydrostatic Pressure.

Juan Jose Lietor-Santos¹, Urs Gasser² ³, Alberto Fernandez-Nieves¹

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 crosslinked-polymeric networks immersed in a solvent, whose size can change using external stimuli. Microgels are gels in the colloidal domain.

Fig.1. Sketch of the behavior of a microgel particle. Its size can be controlled using external variables such as Temperature, pH or salt concentration.

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=np V1p, with np the number density of particles and V1p 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 pH-sensitive group, acrylic acid. As the acrylic groups get ionized by increasing the pH, the crystalline region narrows down and, eventually, disappears.

Fig.2. A) Classical phase diagram for hard spheres. In the absence of interaction, the volume fraction is the only parameter relevant in the phase transition. B) Experimental phase behavior of a NIPAM-Acc system. As the Acc ionizes, the crystalline region shrinks and disappears for high enough pH.
Taken from Meng et al, J.Phys. Chem, B, 113, 4590, 2009.

Colloidal phase behavior and phase transitions.
The aim of this project is to study the phase behavior, including the glassy phase, of a system of microgel particles. By changing the particle size we would be able to change the volume fraction of the system and thus, transitions can be induced within the same experimental sample in a very elegant manner.

Our experimental system is a NIPAM microgel copolymerized with acrylic acid (2%). Thus, the system is both sensitive to temperature and pH changes in the sample. The phase behavior of the system as a function of the generalized volume fraction &xi=npV c ~ 0 with V c ~ 0 the volume of one particle in the dilute state, is shown in Fig. 3. At low &xi, the system shows an isotropic, liquid phase. When &xi is increased, the system forms a crystalline phase characterized by Bragg reflections. At higher concentrations, the Bragg reflections disappear and we observe a glassy phase (the color shift from green to blue is a signature of the decrease in the nearest neighbor distance, as expected since the particle concentration increases).

Fig.3. Phase behavior of the NIPAM-Acc. The system shows liquid,
crystalline and glassy phases similar to hard spheres.

Hydrostatic pressure as a tuning variable for particle size.
We use a novel approach based on tuning the particle size using hydrostatic pressure, P. As P increases, the interaction between the polymer and the solvent becomes increasingly unfavorable and the particle deswells, as is shown in Fig.4. Its role is similar to that of Temperature with the advantage that hydrostatic pressure changes transmit homogeneously throughout the sample and are achieved faster.

Fig.4. Dependence of the particle size with hydrostatic pressure. The pressure changes the miscibility of the polymer on the solvent and, as it increases, the particle deswells.

Neutron Scattering as a tool for elucidating structural and dynamical properties of the system.
The characteristic size of the microgel particles (~100 nm) makes Small Angle Neutron Scattering (SANS) a suitable technique to study and characterize the different phases observed in the system. In any scattering experiment, the collected intensity has an angular dependence which can be expressed as:

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.

We first measure the form factor in dilute conditions, where S(q) = 1, and that allow us to obtain an independent measurement of the form factor of the particles. This is shown in Fig.5

Fig.5. Particle form factor as a function of hydrostatic pressure. The solid lines represent the expected form factors for hard spheres at a = 145nm (corresponding to particle size at P =0) and a = 90 nm (corresponding to particle size at P=350nm)

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 core-shell model in which the core is represented as a hard sphere of radius R and for the shell, a Gaussian function of characteristic size &sigmasurf 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).

Fig.6. (a) Scattered intensity and (b) structure factor vs q at different hydrostatic pressures for volume fraction » 0.68

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).

An alternative possibility is an increased polydispersity of the sample with volume fraction, for sufficiently high volume fractions. In the case of polydisperse hard-sphere systems, the structure factor exhibits a nearest neighbor peak which is smaller than the plateau at higher q [Scheffold], similar of what we observe experimentally.

Some useful references:

Contact Information:
Juan Jose Lietor-Santos
Office: Boggs Building, Room B-54
Email address: jjlietors [at] gatech.edu
Phone: 404-385-3681

Soft Condensed Matter Laboratory, School of Physics, Georgia Institute of Technology
770 State Street NW, Atlanta, GA, 30332-0430, USA
Phone: 404-385-3667 Fax: 404-894-9958
alberto.fernandez [at] physics.gatech.edu