Surface forces between colloidal particles at high hydrostatic pressure

D. W. Pilat, B. Pouligny, A. Best, T. A. Nick, R. Berger, and H.-J. Butt

Phys. Rev. E 93, 022608 – Published 25 February 2016

Abstract

It was recently suggested that the electrostatic double-layer force between colloidal particles might weaken at high hydrostatic pressure encountered, for example, in deep seas or during oil recovery. We have addressed this issue by means of a specially designed optical trapping setup that allowed us to explore the interaction of a micrometer-sized glass bead and a solid glass wall in water at hydrostatic pressures of up to 1 kbar. The setup allowed us to measure the distance between bead and wall with a subnanometer resolution. We have determined the Debye lengths in water for salt concentrations of 0.1 and 1 mM. We found that in the pressure range from 1 bar to 1 kbar the maximum variation of the Debye lengths was <1 nm for both salt concentrations. Furthermore, the magnitude of the zeta potentials of the glass surfaces in water showed no dependency on pressure.

Received 31 July 2015
Revised 25 January 2016

DOI:https://doi.org/10.1103/PhysRevE.93.022608

Physics Subject Headings (PhySH)

Electrostatic double layer forces Pressure effects

Colloids

Polymers & Soft Matter

Authors & Affiliations

D. W. Pilat¹, B. Pouligny², A. Best¹, T. A. Nick¹, R. Berger^1,*, and H.-J. Butt¹

¹Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
²Centre de Recherche Paul-Pascal, 115 Avenue Schweitzer, 33600 Pessac, France

^*berger@mpip-mainz.mpg.de

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Issue

Vol. 93, Iss. 2 — February 2016

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Images

Figure 1
(a) Surface-force measurement inside a high-pressure cell: The high-pressure cell allowed light to be transmitted through two sapphire windows (window thickness $= 2.2 mm$ ). The cell was filled with water that could be pressurized by a piston screw pump (not shown). A sealed rectangular glass capillary filled with the sample solution and the glass beads was placed inside the cell. A single glass bead was pushed against the upper wall of the glass capillary by a moderately focused trapping beam (green). The distance D was determined by measuring the interference between the reflection of a second laser beam (red) off the surface of the bead and the wall. (b) Optical trapping and interferometry setup for measurements inside a high-pressure cell: The components were mounted on a vertical optical breadboard. Thick green line: beam path of the trapping laser. Thin red line: Beam path of interference laser. Yellow: Light path of optical microscope. The drawing of the high-pressure cell (HP Cell) is based on the high-pressure cell described by Hartmann et al. [25] and a technical drawing provided by Andreas Zumbach (RECORD Maschinenbau GmbH, Königsee, Germany). APD: Avalanche photodiode.
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Figure 2
Scanning electron microscopy images of the beads used here, shown at two different magnifications. Beads were supplied as a dry powder. For scanning electron microscopy imaging a small amount of the dry powder was poured onto a Si wafer coated with 20 nm of Pt. A 3-nm-thick layer of Pt was then sputtered onto the sample. (b) Closeup of (a).
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Figure 3
Example of a bead pushed against the wall by the trapping beam with $P_{Laser} = 124 mW$ . Black line and left axis: Intensity of the reflected interference signal $I_{APD}$ between bead and wall versus time. Empty blue squares, blue line, and right axis: Trajectory of the bead. D is the absolute distance of the bead and the upper inner wall of the glass capillary [Eq. (4)]. At times >1.13 s the bead showed thermal motion around the distance $D_{eq}$ where $F_{bead} = - F_{DL} (D_{eq})$ . In this case, we measured $D_{eq} = 176.4 \pm 0.9 nm$ and $F_{bead} = 19.6 \pm 0.3 pN$ . The error of the absolute force value was 22% and arose mainly from the error in determining the bead radii $Δ R = 0.5 μ m$ due to the resolution of the microscope. The red line is a fit on the interval [0.2 µm, 3 µm] with Eq. (5). We notice an envelope of the cosine signal in the measured intensity signal that is not accounted for by Eq. (4). This envelope is due to a lensing effect of the bead.
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Figure 4
Surface force versus distance at ambient pressure for NaCl concentrations of 0.1 and 1 mM in water: $p H = 4 – 4.5, T = 21 \pm 1^{\circ} C$ . By increasing $P_{Laser}$ with every single measurement, we increased $F_{bead}$ in equidistant steps of approximately 1.6 pN from 4.7 to 37.6 pN for 0.1 mM and in steps of approximately 3.7 pN from 7.5 to 82.2 pN for 1 mM. Solid lines represent fits with Eq. (1). At 0.1 mM the obtained fit values were $λ_{D} = 24.0 \pm 0.3 nm$ and $F_{0} = 31 \pm 3 nN$ and at 1 mM $λ_{D} = 8.8 \pm 0.2 nm$ and $F_{0} = 69 \pm 9 nN$ . The uncertainties of force values were 22% at 0.1 mM and 25% at 1 mM and arose mainly from the error in determining the bead radii due to the resolution of the optical microscope $(Δ R = 0.5 μ m)$ .
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Figure 5
Force measurement at pressures of 1 bar, 0.5 kbar, and 1 kbar for a concentration of (a) 0.1 mM and (b) 1 mM NaCl in water: All measurements at the same salt concentration were performed using the same sample liquid and the same bead $(T = 21 \pm 1^{\circ} C)$ . The experimental procedure was to measure in succession at pressures of 1 bar, 0.5 kbar, 1 kbar, 1 bar, 1 kbar, and finally at 1 bar. Results are plotted without error bars for better readability. Errors of single data points were accounted for by the fitting algorithm. The black and red lines are exemplary fits by Eq. (1) of the first force curve recorded at 1 bar and 1 kbar, respectively.
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