Interactions of Colloidal Particles and Droplets with WaterâOil

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Interactions of colloidal particles and droplets with wateroil interfaces measured by total internal reflection microscopy Laurent Helden, Kilian Dietrich, and Clemens Bechinger Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b03864 • Publication Date (Web): 03 Dec 2016 Downloaded from http://pubs.acs.org on December 12, 2016

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Interactions of colloidal particles and droplets with water-oil interfaces measured by total internal reflection microscopy Laurent Helden a,*, Kilian Dietrich a, Clemens Bechinger a,b a

2. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany

b

Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, 70569 Stuttgart, Germany Total internal reflection microscopy (TIRM) is a well-known technique to measure weak forces

between colloidal particles suspended in a liquid and a solid surface by using evanescent light scattering. In contrast to typical TIRM experiments, which are carried out at liquid-solid interfaces, here we extend this method to liquid-liquid interfaces. Exemplarily, we demonstrate this concept by investigating the interactions of micron-sized polystyrene particles and oil droplets near a flat water-oil interface for different concentrations of added salt and ionic surfactant (SDS). We find, that the interaction is well described by the superposition of van-der-Waals and double layer forces. Interestingly, the interaction potentials are –within the SDS concentration range studied here – rather independent of the surfactant concentration which suggests a delicate counter play of different interactions at the oil-water interface and provides interesting insights into the mechanisms relevant for the stability of emulsions. Keywords: Colloids, emulsions, interfaces, evanescent light scattering

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INTRODUCTION: Total internal reflection microscopy (TIRM) is a reliable tool to measure weak interactions between a flat wall and a solid colloidal probe particle with femtonewton resolution1. During recent years, a variety of colloidal interactions has been measured using TIRM. In addition to double layer forces2, 3 and van-der-Waals interactions4 being omnipresent in colloidal suspensions, also interactions due to optical 5, 6, depletion 7-11 , hydrodynamic 12, 13, steric 14, 15 and critical Casimir forces16, 17 were successfully studied with this method. Common to all previous experiments is that they have been carried out at a flat liquid-solid interface. Here, we present the first TIRM study where colloidal interactions are measured near a flat liquid-liquid interface formed by two immiscible liquids. Compared to solid surfaces, liquid-liquid interfaces are superior regarding their flatness and absence of asperities, the latter known to affect TIRM measurements 18, 19. The surface roughness of liquid-liquid interfaces is essentially determined by thermally excited capillary waves whose amplitude at room temperature and for typical surface tensions is about 0.3 nm and thus comparable to molecular length scales 20. Furthermore, liquid interfaces are free of lateral gradients in their surface charge. When replacing the solid probe particle being typically used in TIRM experiments by a liquid droplet 21, we are able to measure the interaction potential between adjacent liquid-liquid interfaces with exquisite force resolution. This allows us to study systems, resembling unperturbed emulsion where particles undergo Brownian motion on the level of single micron sized particles. Such interactions are important for the stability of emulsions in food, cosmetic and medical industry, however techniques for their direct measurement are rare 22. So far, direct measurements were mainly achieved by atomic force spectroscopy between two oil droplets (or gas bubbles) of about 10 to 100 micron radius attached to a cantilever and a surface 23-25.


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MATERIALS AND METHODS TIRM is a single particle evanescent light-scattering technique which allows to determine the distance 𝑧(𝑡) between a spherical colloidal probe particle and a flat wall from the particle’s scattering intensity. This is achieved by illuminating the particle with an evanescent field, being created by total internal reflection of a laser beam (𝜆 = 473nm) at an interface, the latter usually comprised of a water-glass boundary. The decay length 𝜁 of the evanescent field can be varied by the angle of incidence and thus allows to control the range of particle-wall distances probed with this method. It has been experimentally and theoretically demonstrated, that for p-polarized light and 𝜁 ≲ 200nm26, 27 the scattered intensity decays exponentially with the distance z (1)

𝐼𝑆𝐶 = 𝐼0 𝑒𝑥𝑝{−𝑧/𝜁}.

The maximum scattering intensity 𝐼0 corresponds to the value when the particle’s surface is in direct contact with the interface (z=0). Due to Brownian motion, the probe particle will sample the interaction potential Φ(𝑧) with the interface over a range of typically a few hundred nanometers. From the measured probability distribution 𝑝(𝑧) and employing Boltzmann statistics, one obtains the interaction potential Φ(𝑧) 𝑘𝐵 𝑇

(2)

= −𝑙𝑛(𝑝(𝑧)) + 𝑙𝑛(𝑝0 )

where 𝑙𝑛(𝑝0 ) is an irrelevant offset to the potential. For further details regarding TIRM and its data analysis we refer to the literature 28-30.


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Figure 1. Sketched cross section of the sample cell designed for TIRM at liquid-liquid interfaces. A hydrophilic glass ring is glued to the bottom glass slide forming a trough that is filled with water. The edge of the water interface is pinned to the circumference of the trough. If the upper part of the cell is filled with oil, a laser beam coupled into the oil from the side of the cell can be totally internally reflected at the water-oil interface and an evanescent field decaying into the water phase is generated. The light, a single colloidal particle near the interface scatters from the evanescent field, is detected through a microscope objective. A syringe can be used to deliver salt, surfactants and probe particles to the trough or to adjust the water volume such, that the interface is flat.

Because the scattering intensity strongly depends on the decay length 𝜁 of the evanescent field (Eq.1), a well-defined angle of incidence is required. This can only be achieved at a macroscopically flat interface. To obtain such a flat water-oil interface, we glued a hydrophilic glass ring (diameter 18mm, height 1mm) to a microscope slide, which resulted in a cylindrical trough as shown in Fig.1. After filling this trough with deionized water (from a Millipore


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purification unit) until a slightly convex meniscus is formed, the circumference of the water surface is pinned to the upper edge of the ring. Afterwards the oil is gently layered on top. As oil phase we used a purified mineral oil with density 𝜚𝑜𝑖𝑙 = 0.84 g/cm3 (M5904, purchased from Sigma-Aldrich) containing 36% naphthens (saturated 5- or 6-carbon cyclic paraffins) and 64% other saturated paraffins. It has been chosen because its optical index of refraction (𝑛𝑜𝑖𝑙 = 1.47) is fairly high and thus largely different from water (𝑛𝑤 = 1.33). This leads to a conveniently large critical angle of total internal reflection Θ𝑐 ≅ 64.8°. Because of this combination of indices of refraction and densities for oil and water, the typical TIRM setup has to be inverted, i.e. the evanescent field is created from a laser beam incident from above through the side of the cell and the scattered light is detected from below (Fig.1 and 2). To assure a flat water-oil interface, the water volume inside the trough is slowly adjusted with a syringe temporarily immersed from above (Fig.1). The interface’s flatness is verified by a laser beam, which is incident at the critical angle of total internal reflection in the center of the trough. When this beam is laterally scanned across the entire interface at constant angle of incidence and no laser transmission is observed, this proofs the interface flatness. To add probe particles, salts or surfactants to the water phase, they were injected with a syringe or small pipette from above. To assure that the liquid’s volume is constant and the interface remained flat, the same volume as injected was removed afterwards. As solid probe particles we used polystyrene (PS) spheres of a=5 µm radius (Type 42010A, purchased from Thermo Scientific). The particles are functionalized with sulfonate-surface groups and are therefore negatively charged when suspended in water. Since the density of PS (𝜚𝑃𝑆 = 1.05 g/cm3 ) is larger than that of water, they sediment away from the interface towards the bottom of the sample cell. To compensate for gravitational forces, the particle was pushed towards the


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interface by an optical tweezer created by an additional laser beam (𝜆 = 532nm) incident from below (Fig2). The beam is only slightly focused and thus exerts a constant light pressure onto the probe particle6. In addition, it imposes optical gradient forces parallel to the interface which confine the particle laterally and thus effectively restrict the particles motion to the direction perpendicular to the surface 6.

Figure 2. Sketch of the TIRM setup modified for liquid-liquid interfaces containing sample cell (Fig.1), upper and lower optical tweezers, illumination, photomultiplier and signal acquisition devices.


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Figure 3. (a) Typical scattering intensity 𝐼𝑠𝑐 as a function of time. Large scattering intensities correspond to small distances to the interface (compare Eq. 1). Data are recorded for a=5 µm PS particle dispersed in millipore water. (b) Interaction potential Φ(𝑧) deduced from scattering data shown in (a). Full squares show the potential as evaluated while open squares display the same data after subtraction of gravity and light forces of the optical tweezers. The lines on top of the data are corresponding fits to Φ𝐷𝐿 + Φ𝑒𝑥𝑡 (dashed line) and Φ𝐷𝐿 only (solid line). The inset sketches the probe particle near the oil-water interface.


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Figure 3a displays the typical time-dependent scattering intensity of a PS particle suspended in water close to the oil phase. In order to obtain sufficient statistics, data were taken for 800 s to 2400 s with an acquisition frequency of 1 kHz. Using Eq.(1) and (2) we obtained the particleinterface interaction potential (Fig. 3b, full squares). For distances z ≲ 200nm, we observe a strong repulsion due to the electrostatic interaction between the negatively charged particle and the oil-water interface, the latter known to be also negatively charged due to the presence of OH- ions 31. At larger distances, the potential becomes linear which results from the external gravitational forces 𝐹𝐺 and light forces 𝐹𝐿 acting on the particle. The total potential Φ can be accurately fitted to a superposition of electrostatic double layer repulsion3 Φ𝐷𝐿 and the linear contribution Φ𝑒𝑥𝑡 due to the external forces 𝐹𝐺 and 𝐹𝐿 : Φ = Φ𝐷𝐿 + Φ𝑒𝑥𝑡 = 𝐵𝑒 −𝑧/𝜆𝐷 + (𝐹𝐺 + 𝐹𝐿 )𝑧

(3)

In Φ𝐷𝐿 , the prefactor 𝐵 depends on the surface charge densities of the particle and the interface and 𝜆𝐷 is the Debye screening length. For a symmetric monovalent electrolyte, like NaCl used in our experiments,

𝜀𝜀0 𝑘𝐵 𝑇 1

𝜆𝐷 = √

𝑒2

(4)

2𝑐

with salt concentration 𝑐, electric permittivity of vacuum 𝜀0 , relative permittivity 𝜀, elementary charge 𝑒 and thermal energy 𝑘𝐵 𝑇. Because we are primarily interested in the interactions with the interface, in the remainder of the paper the contribution of external forces Φ𝑒𝑥𝑡 has been subtracted from the data (open squares in Fig. 3b).


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TIRM AT LIQUID-LIQUID INTERFACES Unlike a liquid-solid interface, the position and curvature of a liquid-liquid interface can be affected by an approaching colloidal particle. The energy necessary to deform the interface is given by Δ𝐸 = 𝛾 Δ𝐴, with Δ𝐴 being the increase in interfacial area and 𝛾 =40 - 55 mN/m the interfacial tension of our system (depending on the surfactant concentration). In a simple approach, i.e. by assuming that the interface will be deformed as a spherical cap of hight ℎ and radius 𝑎 = 5µm typical for the probe particle, even a large fluctuation of Δ𝐸 = 10𝑘𝐵 𝑇 will change the interface height only by ℎ = 0.3nm. Such deformations comparable to molecular length scales are clearly negligible. However more refined models, taking the interactions of particle and interface into account can at least for the rare events of closest particle – interface 𝑧

approach (𝜆 < 2) predict larger deformations on the nanometer scale32 . In TIRM experiments, 𝐷

interfacial deformations can in principle alter the relation between scattered light intensity and distance. To show, that Eq.1 remains valid under our conditions and ζ can be treated just as at liquid-solid interfaces, we have performed several TIRM measurements on the same probe particle at different angles of incidence. For these angles, the penetration depth of the evanescent field was calculated to be ζ=154 nm; 210 nm and 306nm from the refractive indices of the liquids. As shown in Fig.4, we obtain (apart from variations in the distance resolution) identical potentials and thereby confirm the applicability of Eq.1 to TIRM measurements at liquid-liquid interfaces. All following measurements are performed at 𝜁 = 154 nm, which fits best to the range of the interactions studied.


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Figure 4. Interaction potentials for the same a=5 µm PS particle in 0.5 mM NaCl solution at the water-oil interface obtained for different penetration depth of the evanescent field 𝜁1 = 306 nm (black squares), 𝜁2 = 210 nm (red circles) and 𝜁3 = 154 nm (green triangles) .

In principle optical forces exerted by the optical tweezers can also lead to mechanical deformations of the interface 33. However for the laser powers ( 1270𝑠) can no longer be interpreted as particle-interface distances. Most likely they are due to changes at the particle-interface contact line. To extract quantitative information about the particle-interface interactions, the experimental data have to be compared with theoretical predictions. We first concentrate on the electrostatic interactions Φ𝐷𝐿 . According to reference

3

and with the approximations discussed therein, the

experimentally accessible prefactor B in Eq. (3) is given by 𝐵 = 1

tanh (2 arsinh (2𝜀𝜀

𝑒 0

𝑘𝐵 𝑇

64𝜋𝜀𝜀0 𝑎 𝑘𝐵 𝑇 𝑒2

𝛾𝑖 𝛾𝑐 with 𝛾𝑖/𝑐 =

𝜆𝐷 𝜎𝑖/𝑐 )). Here i/c correspond to the charge densities of the flat

interface (i) and the colloidal surface (c). Obviously, when the interface and the colloid are comprised of different materials, i and c cannot be independently determined from the fit parameter B. However, for a symmetric conditions, i.e. 𝜎𝑖 = 𝜎𝑐 = 𝜎 an unambiguous relation between 𝜎 and 𝐵 is obtained:


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𝜎=

2𝜀𝜀0 𝑘𝐵 𝑇 𝑒 𝜆𝐷

𝑒2

sinh {2 artanh (√64𝜋𝜀𝜀

0 𝑎 𝑘𝐵 𝑇

𝐵)}.

(5)

As an example, symmetric conditions can be achieved by replacing the solid (PS) probe particle with a liquid droplet of the very same oil as it is used for the water-oil interface. In case of a liquid-solid interface, it has already been demonstrated, that TIRM experiments are possible with liquid probe particles of radius 𝑎 ≲ 3 µm 21, 37, 38. For larger (𝑎 = 5.45 µm) droplets artefacts in the interaction potentials were identified and attributed to deformations of the larger droplet that became possible due to their lower Laplace pressure21. Because for the present system similar artefacts were also observed for droplets having 𝑎 ≳ 4µm, we restrict our analysis to droplets with 𝑎 = 2.5µm. For our experiments, droplets are prepared by shaking a mixture of 10 µl mineral oil and 1 ml Millipore water with 0.15 mM stabilizing surfactant added to the water phase. For the experiments sodium dodecyl sulfate (SDS, > 98.5% purity purchased from Sigma-Aldrich) was used as monovalent ionic surfactant. The dodecylsulfonate anions of SDS will adsorb to the interfaces with their hydrophobic tails pointing into the oil phase and the charged sulfonate head groups oriented towards the water phase. This results in a diluted emulsion of polydisperse (0.2-10µm), negatively charged oil droplets. A small part of this emulsion is added to the water phase in the sample cell. To select oil droplets with a defined size, we have added a dilute amount of PS particles of known radius and then identified oil droplets of identical radius from microscopic images. Because 𝜚𝑜𝑖𝑙 is smaller than 𝜚𝑤𝑎𝑡𝑒𝑟 , the oil droplets are pushed towards the interface by buoyancy forces. To adjust the sampled interfacial distances of the droplets, we have partially compensated this buoyancy with an optical tweezers incident from above (Fig.2).


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Figure 7. Interaction potentials for 𝑎 = 2.5 µm oil droplets in aqueous solution for different concentrations of SDS. The different symbols correspond to cSDS= 0.03 mM (blue squares), 0.06 mM (red circles), 0.12 mM (green triangles) and 0.15 mM (magenta diamonds). The total salt concentration was kept constant at ctot= cSDS + cNaCl = 0.15 mM by adding appropriate amounts of NaCl as simple (non-surfactant) salt. The black line is Φ𝐷𝐿 plotted for 𝐵 = 408 k 𝐵 T and 𝜆𝐷 = 19nm.

To characterize the role of surfactants, we measured interaction potentials of oil droplets at different SDS concentrations 𝑐SDS = 0.03 − 0.15mM, which are all far below the critical micelle ∗ concentration 𝑐𝑆𝐷𝑆 ≈ 8.2mM. Apart from its functionality as surfactant, at such concentrations,

SDS mainly acts as a monovalent salt. To keep the Debye length constant, NaCl was added such that the total salt concentration was kept constant at 𝑐𝑡𝑜𝑡 = 𝑐𝑁𝑎𝐶𝑙 + 𝑐𝑆𝐷𝑆 = 0.15mM. As seen in Fig. 7, the interaction potentials are essentially independent of the surfactant concentration (the remaining variations are not systematic and attributed to small variations of the droplet size). When fitting Φ𝐷𝐿 (Eq.3) with B and 𝜆𝐷 as a free parameter to each curve, we find good agreement with such a functional dependence with 𝐵 = 408 ± 218 k 𝐵 T and 𝜆𝐷 = 19 ± nm (solid line in Fig.7).


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Obviously, the interaction between an oil droplet and a water-oil interface is well described by electrostatic double-layer forces. Inserting the values of 𝐵 and 𝜆𝐷 into Eq. 5, the surface charge C

density of the water-oil interfaces is determined to 𝜎 = (−3.2 ± 1) 10−4 m2. This value agrees well with the surface charge density measured for silicon oil droplets in water at comparable NaCl and SDS concentrations as used in our work obtained by an electrical suspension method 39. The fact, that the surface charge of SDS loaded water-oil interfaces remains constant over a certain SDS concentration range, has been also observed in water-hexadecane systems 40. This – at first glance – astonishing behavior is explained by a delicate counter play of different interactions at the oil-water interface. This involves electrostatic repulsion between the charged surfactant head groups, the attraction of counterions and the interactions between the tail groups of the surfactants 40

.

In contrast to above, where the Debye length was kept constant, Fig.8 shows the interaction potentials of oil droplets in the presence of 𝑐𝑆𝐷𝑆 = 0.15mM SDS but now with a varying salt concentration 𝑐𝑁𝑎𝐶𝑙 = 0 – 20 mM. As expected, electrostatic interactions are increasingly screened at higher 𝑐𝑁𝑎𝐶𝑙 and the particle distance towards the interface decreases. Due to the addition of a surfactant, the droplets remain stable in front of the water-oil interface even at the highest salt concentrations considered here (20mM). With increasing salt concentration, the droplet gets closer to the water-oil interface where an additional short-ranged attraction leads in combination with the repulsive double-layer forces to a potential minimum. As already mentioned above (Fig.6), attractive forces are attributed to van der Waals interactions. For a spherical particle in front of a flat surface such forces are commonly approximated by Hamaker’s hybrid formula 35, 41

. Φ𝑣𝑑𝑊 = −

𝐴𝐻 𝑎 6

𝑎

𝑧

{𝑧 + 2𝑎+𝑧 + 𝑙𝑛 (2𝑎+𝑧)}.

(6)


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Figure 8. Interaction potentials for 𝑎 = 2.5 µm oil droplets in aqueous solution of 0.15 mM SDS (solid squares) and various concentrations of additional NaCl: 0.4 mM (solid circles), 1.0 mM (solid triangles), 2.0 mM (solid diamonds), 6.0 mM (open squares), 10 mM (open circles), 20 mM (open triangles). Double layer forces dominate for the datasets displayed with full symbols, while van der Waals forces play a considerable role for those with open symbols. The lines on top of the data are fits to the data as explained in the main text with fit parameters listed in Table 1.


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Table 1. Fit parameters for Fig. 8 cNaCl cSDS [mMol/l] [mMol/l]

ctot [mMol/l]

calc [nm]

D [nm]

B [kBT]

 [10-4Cm-2]

0.0

0.15

0.15±0.02

24.8±1.8

21.0±1.3

995±50

4.6±0.4

0.4

0.15

0.55±0.03

13.0±0.4

15.5±1.2

252±13

3.1±0.3

1.0

0.15

1.15±0.06

9.0±0.3

9.7±1.5

230±12

4.7±1.0

2.0

0.15

2.15±0.11

6.6±0.2

7.7±1.5

115±6

4.2±1.1

6.0

0.15

6.15±0.31

3.9±0.2

5.5±2

120±6

(6.0±3.6)

10.0

0.15

10.15±0.5

3.0±0.1

4.0±2

85±4

(7.0±7.5)

20.0

0.15

20.15±1.0

2.1±0.1

3.4±2

87±4

(8.2±12)

Errors in ctot and calc are based on preparational uncertainties in handling the small volumes of suspensions. Errors in D are estimated based on reproducibility for different measurements and (for ctot > 6 mM) maximum resolvable steepness of potentials. Errors in B are due to 5% uncertainty in particle radius. Errors given for  result from errors in B and D.

Here, 𝐴𝐻 is the Hamaker constant which depends on the dielectric functions of the involved materials. To determine the value of 𝐴𝐻 from our data, we first fitted Φ𝑡𝑜𝑡 = Φ𝑣𝑑𝑊 + Φ𝐷𝐿 to those potentials where van der Waals forces are most pronounced (6 mM, 10 mM and 20 mM, shown as open symbols in Fig. 8). From such fits we obtained 𝐴𝐻 = 0.16 kBT which is about 4 -8 times smaller than tabulated data for similar alkane-water-alkane systems 24, 35. With 𝐴𝐻 = 0.16 kBT we fitted Φ𝑡𝑜𝑡 to the potentials in Fig.8 with 𝜆𝐷 and 𝐵 as free parameters for each curve. The fits accurately describe all interaction potentials over the entire distance range with the parameters listed in Table 1. Within our experimental errors, the values of 𝜆𝐷 obtained from the single fits agree reasonably well with the predicted Debye length 𝜆𝑐𝑎𝑙𝑐 calculated from 𝑐𝑡𝑜𝑡 using Eq.(4) (cf.


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Tab. 1). From the corresponding values of 𝐵 and 𝜆𝐷 , we also calculate the surface charge using Eq. 5For 𝑐𝑁𝑎𝐶𝑙 ≤ 2mM we obtain a rather constant surface charge density 𝜎 = (−4.2 ± 0.7) ∙ C

10−4 m2 which agrees with the surface charge obtained above for different SDS concentrations (Fig. 7). At higher salt concentrations, our data suggest a systematic increase of In this regime, however, the strongly increasing error in 𝜆𝐷 and thus makes a reliable interpretation of the corresponding values difficult.

CONCLUSIONS & OUTLOOK We have demonstrated, that the TIRM method can be extended to measure particle interaction potentials between a micron-sized probe particle and a water-oil interface with a resolution of about 0.2 𝑘𝐵 𝑇 in energy and 5nm in distance. This also enables the detection of forces on the order of 10 femtonewtons. In addition to solid probe particles, we have also used SDS-stabilized oil droplets which leads to symmetric oil-water-oil interfaces and thus resembles the situation typically encountered in emulsions. Under such conditions, we find, that the interaction is well described by the superposition of van-der-Waals and double layer forces. Interestingly, the interaction potentials are –within the SDS concentration range studied here – rather independent of the surfactant concentration which suggests delicate counter play of different interactions at the oil-water interface. In the future the new variant of the TIRM technique presented here will be helpful to study the role of antagonistic salts at oil-water interfaces and their influence on colloidal interactions. 42-44 ACKNOWLEDGMENTS We thank Martin Oettel for helpful discussions. The support of Daniel Maier and DataPhysics Instruments GmbH with surface tension measurements is gratefully acknowledged.


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AUTHOR INFORMATION Corresponding Author *Laurent Helden, 2. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany. E-Mail: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

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TOC-Graphics


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Fig. 1 85x68mm (300 x 300 DPI)


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Fig. 2 266x355mm (96 x 96 DPI)


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Fig. 3 131x203mm (300 x 300 DPI)


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Fig. 4 Interaction potentials for the 254x203mm (300 x 300 DPI)


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Fig. 5 Spatially resolved diffusion c 288x201mm (300 x 300 DPI)


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Fig. 6 Interaction potentials of a=5 288x201mm (300 x 300 DPI)


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Fig. 7 Interaction potentials for a=2 288x201mm (300 x 300 DPI)


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Fig. 8 Interaction potentials for a=2 288x201mm (300 x 300 DPI)


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