# Surface dynamics of a silica particle suspension

Agnès Duri, Christian Gutt, Tina Autenrieth, Lorenz-Mathias Stadler, Olaf Leupold, Yuriy Chushkin, Gerhardt Gruebel

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Agnès Duri, Christian Gutt, Tina Autenrieth, Lorenz-Mathias Stadler, Olaf Leupold, et al.. Surface dynamics of a silica particle suspension. [Technical Report] 2007. hal-02818288

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Submitted on 6 Jun 2020

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<figure><img src="image_1.png" /></figure>
Surface dynamics of a silica particle suspension

A. Duri, C. Gutt, T. Autenrieth, L. Stadler, O. Leupold, Y. Chushkin and G. Grübel

HASYLAB at DESY, Notkestrasse 85, 22607 Hamburg, Germany

Confinement effects and the influence of the reduced dimensionality on the glass transition have been the object of recent debates. At the same time, speculations about the existence of a surface glass state arose. In order to address this latter point, we have investigated the surface dynamics of a concentrated suspension (volume fraction≈20%) of silica particles (radius≈17 nm) dispersed in polypropylene-glycol (molecular weight=4000) which serves as a model system for understanding the glass transition at surfaces. More precisely, we focused on the 2D dynamical fluctuations (also called dynamical heterogeneities) and their relevant features in the glassy regime [1, 2].

For this purpose, we performed X-ray Photon Correlation Spectroscopy (XPCS) measurements under grazing incidence at the ID10A Troïka beamline of the European Synchrotron Radiation Facility (ESRF, Grenoble). This technique is based on the illumination of a sample surface by a partially coherent X-ray beam and the time resolved recording of the speckle images by a Charge Coupled Device (CCD) camera.

The fluctuating intensity of each speckle in the images, associated with the displacement of individual scatters in the sample, enabled us to determine the time average dynamics by means of the intensity autocorrelation functions $g_2$ usually calculated in a XPCS experiment. Figure 1 a) shows the correlation function for several scattering vectors $q_\parallel$ parallel to the surface and for a sample temperature of 250 K, thus in the glassy state. We found that for all $q_\parallel$ accessible by the used setup, $g_2(q_\parallel, \tau) - 1$ is well fitted by a compressed exponential that allowed us to deduce the $q_\parallel$ dependence of the relaxation time $\tau_s$ and the compressing exponent $\beta$ represented in Figure 1 b). The $\tau_s \sim q_\parallel^{-\alpha}$ scaling, with $\alpha = 1.09 \pm 0.01$ indicates a ballistic motion of the particles, i.e. a linear growth of the average particle displacement with time. The compressing exponent $\beta$, which is approximately equal to 2 for all $q_\parallel$, can be explained by discrete rearrangements that occur in the sample. Such behaviors have been reported in many other soft glassy systems [3] confirming therefore the existence of a surface glass phase for this system, which would moreover imply the appearance of large fluctuations of the dynamics.

<figure><img src="image_2.png" /><figcaption>Figure 1: a) Intensity autocorrelation function $g_2(q_\parallel, \tau) - 1$ for three different $q_\parallel$ values (from the top to the bottom $q_\parallel = 6.5 \cdot 10^{-3}$, $8 \cdot 10^{-3}$ and $9.4 \cdot 10^{-3} \AA^{-1}$) and for $T = 250$ K. The lines are compressed exponential fits. b) $q_\parallel$ dependence of the relaxation time $\tau_s$ (diamonds, left axis) and the compressing exponent $\beta$ (stars, right axis). The line is a power law fit to $\tau_s$ yielding an exponent equal to -1.09±0.01.</figcaption></figure>
In order to prove this last assumption, we have also investigated the time-resolved dynamics. For that, we have calculated the degree of intensity correlation between pairs of speckle images as a function of both the delay $\tau$ between images and the real time $t$ according to the equation (1).

$$c_I(q_{\parallel}, t, \tau) = \frac{\langle I_p(t) I_p(t + \tau) \rangle_p}{\langle I_p(t) \rangle_p \langle I_p(t + \tau) \rangle_p} - 1 \quad (1)$$

$I_p(t)$ is the scattered intensity at pixel $p$ and time $t$ and $\langle \dots \rangle_p$ is an average over pixels corresponding to a same $q_{\parallel}$ value [4]. Figure 2 a) displays this parameter for several $\tau$ values and for a $q_{\parallel}$ of $6.6 \ 10^{-3} \AA^{-1}$, equivalent to a length scale probed of about 100 nm. The $c_I$'s exhibit temporal fluctuations that have been quantified thanks to their normalized variance, $\sigma_{c_I}^2(\tau)$, by analogy with the dynamical susceptibility $\chi_4$ much studied in theoretical and numerical works on glass formers [5]. As shown in Figure 2 b), $\sigma_{c_I}^2(\tau)$ exhibits a peaked shape which is the signature of dynamical heterogeneities probably arising from the presence of cooperative regions in which the displacements are accomplished by groups of particles.

<figure><img src="image_3.png" /><figcaption>Figure 2: a) Temporal fluctuations of the degree of intensity correlation, $c_I$, for $q_{\parallel} = 6.6 \cdot 10^{-3} \AA^{-1}$ and $T = 250$ K. From the top to the bottom $\tau = 2.8$, 28 and 83 sec. b) Normalized variance $\sigma_{c_I}^2$ as a function of $\tau$ and for the same $q_{\parallel}$ as in a).</figcaption></figure>

In summary, we have demonstrated for the first time that the degree of intensity correlation, $c_I(t, \tau)$, is a powerful tool to underline temporal fluctuations in surface dynamics. Other experiments have been already planed to better understand the physical origins of the dynamical heterogeneities in a confinement geometry.

## References

[1] M. D. Ediger, Annu. Rev. Phys. Chem. 51, 99, (2000).

[2] S. C. Glotzer, J. Non-Cryst. Solids 274, 342, (2000).

[3] L. Cipelletti and L. Ramos, J. Phys.: Condens. Matter 17, R253, (2005).

[4] L. Cipelletti et al., J. Phys.: Condens. Matter 15, S257, (2003).

[5] N. Lacevic et al., J. Chem. Phys. 119, 7372, (2003).