# Hydrodynamic interactions in colloidal suspensions: From highly charged to electrostatically screened particles

Tina Autenrieth, Fabian Westermeie, Aymeric Robert, Christian Gutt, Olaf Leupold, Agnès Duri, Gerhardt Gruebel

► To cite this version:

Tina Autenrieth, Fabian Westermeie, Aymeric Robert, Christian Gutt, Olaf Leupold, et al.. Hydrodynamic interactions in colloidal suspensions: From highly charged to electrostatically screened particles. [Technical Report] 2007. hal-02818290

HAL Id: hal-02818290

https://hal.inrae.fr/hal-02818290

Submitted on 6 Jun 2020

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution - ShareAlike 4.0 International License
Hydrodynamic interactions in colloidal suspensions:
From highly charged to electrostatically screened particles

Tina Autenrieth, Fabian Westermeier, Aymeric Robert', Christian Gutt, Olaf Leupold, Agnès Duri
and Gerhard Grübel

Hasylab, DESY, Notkestr. 85, 22607 Hamburg, Germany
'SLAC, Stanford University, 2575 Sand Hill Rd, Menlo Park CA-94025, USA

We synthesized different charge stabilized colloidal suspensions to investigate the dynamic
behaviour of liquid like ordered systems as a function of the direct particle interactions. The tailor-
made particles, consisting of silica (SiO₂) or fluorinated poly-methacrylates, are stabilized by
charged surface groups and can be considered as “macroions”. They interact via a long range,
screened Coulomb potential that can be theoretically described by the RMSA model [1]. In detail,
we want to investigate the dynamics within the transition from highly charged, highly interacting
particles into highly screened particle interactions. The interaction strength can be influenced not
only by the volume fraction but also by electrolyte, screening the electrostatic interactions.
Furthermore, indirect hydrodynamic interactions (HI), mediated by the solvent medium and
expressed by the hydrodynamic function H(Q), play an important role for particle mobility. For
uncharged (hard sphere) systems, indirect HI are acting as a friction force and reduce the mobility
of the particles (e.g. H(Q)<1) on all length scales. Here, the experimental data can be described by
the δγ-expansion, a theoretical approach developed by Beenakker and Mazur [2]. Charge stabilized
systems behave differently. For highly charged colloidal suspensions, under extremely dilute
conditions, it has been theoretically predicted by the pairwise additive (PA) approximation [3] and
experimentally observed [4] that the hydrodynamic interactions can speed up the dynamics of the
particles (e.g. H(Q~Qmax)>1) on length scales corresponding to the mean interparticle distance.
However, this behaviour changes with increasing concentration. The hydrodynamic interaction in
more concentrated charge-stabilized colloidal suspensions seems to behave more hard sphere like
(e.g. H(Q)<1) as shown by recent experiments using X-ray photon correlation spectroscopy
(XPCS) [5]. The hydrodynamic function in the latter case can be described neither by the PA
approximation nor by the δγ-expansion.

We started a detailed investigation of the short-time dynamics of charged SiO₂ suspensions as a function of the direct particle interactions to elucidate the transition from H(Q_max)>1 to H(Q_max)<1. Highly diluted to moderately concentrated nanoparticle suspensions have been probed by light scattering experiments using cross-correlation technique (3DDLS) to prevent multiple scattering effects. As this technique is limited by the accessible Q-range, small angle X-ray scattering (SAXS) and XPCS (at ID10, ESRF) have been used for more concentrated systems.

The results are of outmost importance for the formation of a theoretical framework urgently needed
to describe highly charged and concentrated colloidal systems. Starting with static scattering
experiments, the analysis of the structure factor S(Q) of the colloidal suspensions yields a detailed
description of the direct Coulomb interactions (volume fraction, effective number of charges per
particle, free electrolyte concentration) in the systems. Subsequently, we used photon correlation
spectroscopy to probe the dynamics of the systems. The Q-dependent diffusion coefficient D(Q)
can be obtained by fitting the intermediate scattering function (f(Q,τ)=exp[-Γ(Q)τ] with
Γ(Q)=D(Q)Q²) in the short-time limit. D(Q) =limt→0(Q,t). D(Q) is related to the static structure
factor by D(Q)=D₀H(Q)/S(Q), where D₀ is the free-particle diffusion coefficient. D₀/D(Q)
expresses the dynamic structure factor, also shown in figure 1a and 2a. Thus, the combination of
static and dynamic scattering techniques offers a unique possibility to extract solely experimentally
the hydrodynamic functions (fig 1b and 2b).

In fig 1b) a speeding-up (H(Q<sub>max</sub>)>1) of the hydrodynamics is only valid for the dilute case (φ=0.017) corresponding to the theoretical predictions of the PA. For higher concentrated particle suspensions (φ=0.054), the dynamic behaviour shows a slowing down of the dynamics which is not supported by any model. In addition, screening of the particles' surface charges affects the hydrodynamics in the suspensions too. Figure 1g) shows an increase of the hydrodynamics of a suspensions with 200μml/l added salt in comparison to the case without added salt. To which
extend a complete screening leads to hard sphere behaviour is of high interest for the investigation
of the hydrodynamic interactions in charge-stabilized colloidal systems.

<figure><img src="image_2.png" /><figcaption>Figure 1a) Static S(Q) and dynamic structure factors D₀/D(Q) of suspensions with increasing volume fractions φ (0.017, 0.054, 0.153) and 1b) the extracted hydrodynamic functions H(Q).</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2a) Static and dynamic structure factors of a suspension without and with added electrolyte ($c_{\text{salt}} = 2 \times 10^{-4} \text{mol/l}$) and 2b) the extracted hydrodynamic functions.</figcaption></figure>

References

[1] J.K. Percus and G.J. Yevick, Phys. Rev. 110 (1), 1 (1958)

[2] C.W.J. Beenakker and P. Mazur, Physica A 120, 388 (1983)

[3] G. Nägele, Phys. Rep. 272 (5/6), 215 (1996)

[4] W. Härtl et al., J. Chem. Phys. 110 (14), 7070 (1999)

[5] D.O. Riese et al., Phys. Rev. Lett. 85 (25), 5460 (2000)