Structure and dynamics of dense colloidal ellipsoids at the nearest-neighbor length scale

Anisotropic particles are known to exhibit a richer and more complex phase behavior in comparison to their spherical counterpart. While the majority of the existing studies address structural properties, the dynamic behavior of anisotropic particles is a relatively lesser explored avenue. Using multispeckle ultra-small-angle x-ray photon correlation spectroscopy (USA-XPCS), we have carried out a systematic investigation of the structural and dynamic properties of colloidal ellipsoids at the nearest-neighbor length scale. The USA-XPCS measurements have allowed us to probe, as a function of the volume fraction, the $q$-dependent effective structure factor, $S_{\text{eff}}\left(q\right)$, along with the effective long time diffusion coefficient, $D_{\text{eff}}\left(q\right)$, for this anisotropic system. Our results indicate a scaling behavior of $D_{\text{eff}}\left(q\right)$ with $1/S_{\text{eff}}\left(q\right)$ from which we have estimated the effective amplitude function $A_{\text{eff}}\left(q\right)$, which can be directly related to the effective hydrodynamic function $H_{\text{eff}}\left(q\right)$. $A_{\text{eff}}\left(q\right)$ shows a similar $q$ dependence to that of $S\left(q\right)$. Our investigation also allows for the precise determination of the volume fraction corresponding to the arrest transition.

Figure 1

(a) A representative TEM image of the core-shell hematite-silica colloidal ellipsoid. (b) Experimental scheme for the multispeckle ultra-small-angle x-ray photon correlation spectroscopy experiment.

Figure 2

(a) 2D scattering pattern and (b) effective structure factor for ${\varphi }_{\text{min}}=0.17$. The black filled circles indicate the $q$ values where the dynamics was measured. (c) Intensity autocorrelation functions for different $q$ values indicated by the black filled circles in (b). The symbols represent the experimental data, while the line corresponds to the fit with the KWW model. (d) Variation of $D_{\text{eff}}$ as a function of $q$; the black filled circles indicate the experimental data, and the blue dashed line is a guide to the eye.

Figure 3

(a) Experimentally measured 2D scattering pattern for ${\varphi }_{\text{max}}=0.42$. Azimuthal sector averages have been taken between two red (yellow) arrows to study the dynamics along the horizontal (vertical) direction. Intensity autocorrelation functions for different $q$ values along (b) the horizontal and (c) the vertical direction, respectively. The symbols represent the experimental data while the line corresponds to the fit with the KWW model. Variation of $D_{\text{eff}}\left(q\right)$ as a function of $q$ along (d) the horizontal and (e) the vertical direction, respectively; the black filled circles indicate the experimental data, and the blue dashed line is a guide to the eye.

Figure 4

(a) Variation of the structure factor $S_{\text{eff}}\left(q\right)$ as a function of $q$. The solid lines represent the experimental data, while the symbols indicate the $q$ values where the dynamics was measured. The inset shows the variation of the $q$ value corresponding to the structure factor peak, $q_m$, as a function of $\varphi$ along with the fit with $q_m\propto {\varphi }^{1/3}$ as a solid red line. (b) Variation of $1/D_{\text{eff}}\left(q\right)$ as a function of $q$. (c) Variation of the amplitude function $A_{\text{eff}}\left(q\right)$ as a function of $q$. (d) Variation of the exponent $\gamma$ as a function of $q$. For (b), (c), and (d), the symbols indicate the experimental data while the solid lines are a guide to the eye. For all of (a), (b), (c), and (d), different colors correspond to different volume fractions $\varphi$.

Figure 5

Variation of $\gamma$ as a function of $\varphi$ for different $q$'s.

Figure 6

(a) Variation of the normalized diffusion coefficient $D_{\text{eff}}\left(q_m\right)/D_0$ with $\varphi$; the symbols represent the experimental data, while the dashed line indicates the fit with modified VFT law. (b),(c) 2D scattering patterns for $\varphi =0.345$ (isotropic arrangement of particles) and $\varphi =0.42$ (formation of a nematic phase), respectively. The inset shows the fitting of the experimental data with VFT law excluding the data corresponding to ${\varphi }_{max}$.