Depletion forces in the presence of electrostatic double layer repulsion.

We report direct measurements of the repulsive force-distance profiles between submicronic colloidal droplets stabilized by an ionic surfactant in the presence of the same surfactant micelles. We establish that the repulsive force profile may be described by a sum of two contributions. One is repulsive and arises from the presence of the droplets’ double layers. The other originates in the depletion of charged micelles and is attractive. We conclude that the electrostatic repulsion between the micelles and the droplets enhances the depletion force. This effect is simply accounted for by considering an effective larger droplet diameter. We present the empirical relation between this extra thickness and the Debye length. PACS numbers: 82.70. Dd, 68.15. +e Two colloidal particles may attract each other when surrounded by smaller ones. This attraction is an inherent consequence of the size asymmetry and is known as the depletion force [1‐3]. Indeed, when the bigger particles approach, the smaller ones are expelled from the interspace, and their contribution to the osmotic pressure locally vanishes. This exclusion leads to an uncompensated pressure from which arises the attractive interaction. The depletion force develops at a separation equal to the effective size of the small component and monotonically increases up to the surface contact. The intensity is related to both the small component osmotic pressure and its size, which also governs the extension of the excluded range [4‐7]. This attractive depletion force may coexist with other types of interactions and particularly the repulsive double layer one, which is mainly responsible for the stability of aqueous dispersions [8]. Such repulsion arises from the confinement of counterions which are thermally dissociated from surface charges within the diffuse double layer [9]. As an example, charged colloids mixed with neutral polymer coils would exhibit these two forces at the same time. Moreover, electrostatic repulsion between small particles and colloids may also superimpose; a mixture of identically charged colloidal particles and micelles or polyelectrolyte coils are one example. In that case the net interaction between colloids is certainly a combination of both the double layer repulsion and some depletion mechanisms. When acting together, the behavior of these two forces is still obscure. In previous experiments using the surface force apparatus [7,10], one of the two involved forces was always largely predominant with respect to the other, which precludes a reliable observation of their interplay. In this Letter we report direct measurements of the repulsive force distance profile between submicronic colloidal droplets stabilized by ionic surfactant in the presence of the same surfactant micelles. Our system is made of a mixture of colloidal oil-inwater emulsion droplets (with a diameter of 0.2 mm) and surfactant micelles (with a diameter of about 5 nm). We use a cationic surfactant (CTAB: cetyltrimethylammonium bromide), which forms micelles above its critical micellar concentration (CMC › 9 3 10 24 M), and which adsorbs on the colloidal droplets. This ionic surfactant ensures that both species repel each other and that (big) droplets and (small) micelles also repel one another. The force profile between droplets is directly measured using the recently developed chaining technique [11]. A magnetic oil (ferrofluid) octane in which small grains (10 nm) of Fe2O 3 are dispersed is used to create monodisperse emulsion droplets stabilized wiht CTAB. By imposing a magnetic field, polarized droplet chains align along the field and diffract the light, allowing their spacing to be measured precisely. Since a given field corresponds to an applied known attractive force between droplets [12], we deduce the opposing repulsive force at various separations. This force profile is measured from the onset of chaining up to the saturation of the ferrofluid magnetization which correspond to ratios FyR, where F is the force and R the droplet radius, that range from 10 26 to 10 24 Nym.