Transient formation of bcc crystals in suspensions of poly($N$-isopropylacrylamide)-based microgels

Transient formation of bcc crystals in suspensions of poly( $N$ -isopropylacrylamide)-based microgels

U. Gasser, J.-J. Lietor-Santos, A. Scotti, O. Bunk, A. Menzel, and A. Fernandez-Nieves

Phys. Rev. E 88, 052308 – Published 13 November 2013

Abstract

We present a small-angle x-ray scattering study of crystals formed by temperature-sensitive, swollen microgel particles consisting of poly( $N$ -isopropylacrylamide) copolymerized with acrylic acid and 5 mol % of a cross-linker. As for hard spheres, the random hexagonal close-packed structure is predominant during crystal growth and slowly transforms toward the face-centered-cubic structure. However, a transient phase of body-centered-cubic crystal is observed in an intermediate range of effective volume fractions. We estimate that the studied suspensions are close to a transition from face-centered-cubic to body-centered-cubic structure that can be understood by the tendency of the system to maximize the excluded volume and minimize the contact area between the particles.

Received 1 July 2013

DOI:https://doi.org/10.1103/PhysRevE.88.052308

Authors & Affiliations

U. Gasser^*

Laboratory for Neutron Scattering, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland

J.-J. Lietor-Santos

School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA

A. Scotti

Laboratory for Neutron Scattering, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland

O. Bunk and A. Menzel

Swiss Light Source, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland

A. Fernandez-Nieves

School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA

^*urs.gasser@psi.ch

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Vol. 88, Iss. 5 — November 2013

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Images

Figure 1
Hydrodynamic radius of pNIPAM-AAc particles at $p H = 4.5$ , determined by dynamic light scattering, vs temperature.Reuse & Permissions
Figure 2
Phase behavior of pNIPAM-AAc microgel particles at $p H = 4.5$ as determined by visual inspection. The opal-like appearance of the crystal samples is due to Bragg peaks observed with visible light.Reuse & Permissions
Figure 3
(a) SAXS measurement of the particle form factor taken with a sample at $c_{p} \approx 0.01 wt . %$ ( $ζ \approx 0.0024$ ). The red line shows the fit obtained with the form-factor model of Stieger and Richtering; see text for details. (b) (Symbols) Structure factor of a fluid sample at $c_{p} \approx 1.90 wt . %$ ( $ζ = 0.46$ ) compared with (red line) the Percus-Yevick structure factor.Reuse & Permissions
Figure 4
(a,b) Detector images taken at (a) $ζ = 0.61$ with Bragg rings and (b) $ζ = 0.59$ with a hexagonal pattern of Bragg peaks. (c) The three stacking positions $A$ , $B$ , and $C$ for hexagonal particle planes for close-packed crystals. See text for details. (d) Sketch of the scattering intensity in $q$ space obtained from a rhcp lattice. The reciprocal-lattice points of the hexagonal plane are highlighted by dots, and Bragg rods are shown by fading vertical bars. (e,f) Azimuthally averaged structure factor of rhcp crystals formed in young samples with (e) $a_{rhcp} = (289 \pm 2) nm$ , $α = 0.60 \pm 0.05$ , $ζ = 0.61$ prepared $\approx 2 h$ before the measurement and (f) $a_{rhcp} = (302 \pm 2) nm$ , $α = 0.50 \pm 0.05$ , $ζ = 0.51$ after melting with a temporary increase of temperature to $41^{\circ} C$ . The red curves represent the rhcp fits. The vertical lines show the Bragg peak positions of a single hexagonal plane.Reuse & Permissions
Figure 5
Azimuthally averaged structure factors $S (q)$ of crystal with predominant fcc stacking. (a) $a_{rhcp} = (299 \pm 2) nm$ , $ζ = 0.52$ , $α = 0.70 \pm 0.05$ , and (b) $a_{rhcp} = (280 \pm 2) nm$ , $ζ = 0.61$ , $α = 0.72 \pm 0.05$ . Both samples were prepared 26 days before the measurement. The red lines represent the rhcp fit. The vertical lines show the Bragg peak positions of a single hexagonal plane.Reuse & Permissions
Figure 6
(a) Measured structure factor at $ζ = 0.57$ showing peaks corresponding to rhcp and bcc crystals. The red curve shows the structure factor expected for a superposition of rhcp (45%), with $a_{rhcp} = (289 \pm 2) nm$ , $α = 0.5 \pm 0.05$ , and bcc (55%) crystal, with $a_{bcc} = (326 \pm 2) nm$ . The magenta vertical lines show the Bragg peak positions of a single hexagonal plane, while the green lines show bcc Bragg peak positions. (b) Detector image of the measurement shown in (a) with a logarithmic color scale. The original detector image is shown on the left, and the same image with the bcc-like Bragg peaks highlighted in red is shown on the right. The position of the bcc peaks is calculated with an incident beam direction $k_{i} = (1, 1, 0)$ in the bcc reciprocal lattice.Reuse & Permissions

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