Crystal-to-Crystal Transition of Ultrasoft Colloids under Shear

Ultrasoft colloids typically do not spontaneously crystallize, but rather vitrify, at high concentrations. Combining in situ rheo–small-angle-neutron-scattering experiments and numerical simulations we show that shear facilitates crystallization of colloidal star polymers in the vicinity of their glass transition. With increasing shear rate well beyond rheological yielding, a transition is found from an initial bcc-dominated structure to an fcc-dominated one. This crystal-to-crystal transition is not accompanied by intermediate melting but occurs via a sudden reorganization of the crystal structure. Our results provide a new avenue to tailor colloidal crystallization and the crystal-to-crystal transition at the molecular level by coupling softness and shear.

Figure 1

(a) Theoretical state diagram of star polymers [9, 14] in the $(f,\eta )$ plane. State points investigated in this work are marked with symbols. (b) Schematic illustration of the rheo-SANS experiments and measured diffraction patterns in the radial and tangential plane. See text for details.

Figure 2

Degree of ordering (DOO) versus time calculated for experiments (a) and simulations (b). In (a) the shear parameters are $\omega =10\mathrm{rad}/\mathrm{s}$ and ${\gamma }_0=11.5\%$ (squares), $\omega =5\mathrm{rad}/\mathrm{s}$ and ${\gamma }_0=15\%$ (circles), and $\omega =10\mathrm{rad}/\mathrm{s}$ and ${\gamma }_0=15\%$ (triangles). Lines are guides to the eye to highlight the onset of crystallization. (c) Nucleation time $t_X$ as a function of Pe for simulations at different packing fractions (filled symbols) and for experiments (scaled by an arbitrary factor) at $\eta =0.167$ [open symbols as in panel (a)].

Figure 3

(a) SANS diffraction patterns in the radial direction and strain amplitude sweep depicting the measured $G^{\prime }$ (storage modulus) $G^{\prime \prime }$ (loss modulus) for stars at $\eta =0.167$. The flipping between the two crystals was observed for $\omega =5\mathrm{rad}/\mathrm{s}$ in a range of strain amplitude (0.1%–300%), amounting to a range in Péclet numbers ($0–8\times {10}^{-2}$). Vertical arrows indicate the strain values at which the images were extracted. (b)–(d) Numerical results for simulations at $\eta =0.167$ and $\mathrm{Pe}=2\times {10}^{-3}$. Radial diffraction patterns after the first step (b1) and after the second step (b2). System snapshots in the tangential view after the first step (c1) and after the second step (c2). Here, the size of the particles is reduced to help visualization. Density profiles measured for bcc (d1) and fcc or hcp (d2) particles in the vorticity direction (upper panels) and gradient direction (lower panels). Continuous lines are drawn to indicate the behavior of the density profiles in the absence (flat line) or in the presence (periodic curve) of layers of particles.