Diffusiophoresis in Ionic Surfactant Gradients - Langmuir (ACS

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Diffusiophoresis in Ionic Surfactant Gradients Rodrigo Nery-Azevedo, Anirudha Banerjee, and Todd M. Squires Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b01094 • Publication Date (Web): 30 Aug 2017 Downloaded from http://pubs.acs.org on September 4, 2017

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Diffusiophoresis in Ionic Surfactant Gradients Rodrigo Nery-Azevedo, Anirudha Banerjee, and Todd M. Squires∗ Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080 E-mail: [email protected]

Abstract Surfactants play a ubiquitous role in many areas of science and technology, and gradients often form – either spontaneously or intentionally – in a variety of non-equilibrium situations and processes. We visualize and measure the diffusiophoretic migration of latex colloids in response to gradients of cationic and anionic surfactants, both below and above the critical micelle concentration (CMC). Below the CMC, colloidal migration can be described using classic theories for diffusiophoresis under electrolyte gradients, although subtleties and distinctions do appear. Cationic surfactants adsorb onto anionic colloids, changing the surface charge and thus reversing the direction of diffusiophoretic migration. Above the CMC, diffusiophoretic mobilties decrease by orders of magnitude. We argue this to occur because charged monomers (rather than micelles) dominate colloidal diffusiophoresis. Because monomer concentrations remain essentially constant above the CMC, surfactant gradients imposed above the CMC result in very small monomer gradients – and therefore, very weak diffusiophoresis. Our findings suggest conceptual strategies to understand diffusiophoresis in the presence of surfactants, as well as strategies to predict and design systems that harness them. ∗ To

whom correspondence should be addressed

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Introduction The amphiphilic properties of soluble surfactants allow them to be employed as detergents, surface tension modifiers and suspension stabilizers. 1 Uses for surfactants range from the highly specialized to the mundane, in large scale industrial processes like reservoir flooding in secondary oil recovery, 1 in formulated and multiphase mixtures including foams and emulsions, 2 and in common consumer products like shampoos and lotions. 3 This ubiquity makes understanding interactions between soluble surfactant solutions and their environment especially important in non-equilibrium systems. Whether intentionally or unintentionally, concentration gradients arise in different systems and in different contexts, including evaporating films, near permeable membranes and reacting interfaces, and during mixing. 4 When suspended particles are present in these gradients, they migrate via a phenomenon known as diffusiophoresis. Diffusiophoretic migration of particles was first reported by Derjaguin in 1947 5 in the context of latex deposition and film formation, and has since been observed and described in many other systems, ranging from dissolving steel interfaces, 6 micropumps driven by dissolving salt crystals, 7 active particles, 8,9 reverse osmosis membranes, 10 driving motion into dead-end pores, 11,12 and soluto-inertial interactions. 13 Although ubiquitous, diffusiophoresis has remained difficult to observe directly, in large part because of the challenges in reliably establishing steady concentration gradients that are strong enough to drive appreciable migration, while avoiding buoyancy-driven convective flows. Microfluidic devices have allowed diffusiophoresis to be examined in a direct, detailed way, first by co-flowing solutions of different concentrations 14 and later by imposing gradients using agarose gel devices to control concentration profiles. 15 Building on these efforts, we developed microfluidic devices with integrated microdialysis membranes, which allowed concentration gradients to be designed and imposed, and the diffusiophoretic migration of colloids to be systematically measured. 16 The present work refines and expands this technique, and applies it to study diffusiophoresis in surfactant gradients. Beyond to the broad importance of surfactants, we are additionally motivated by our recent 2 ACS Paragon Plus Environment

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work on soluto-inertial interactions, in which soluto-inertial ‘beacons’ were designed to slowly emit a solute flux, which in turn drives diffusiophoretic migration among colloids in the surrounding suspension. 13 The specific material system we employed to demonstrate SI interactions involved hydrogel beacons that associate with – and slowly release – ionic surfactants, which ultimately mediate the SI interactions with the surrounding suspension. To more broadly design and engineer such systems, it would be very useful to understand diffusiophoresis under surfactant gradients, both quantitatively and conceptually. Ionic surfactants consist of a charged, amphiphilic molecule and a counterion. It would thus seem reasonable to try to describe particle diffusiophoresis in gradients of ionic surfactants using the classic expression for the particle diffusiophoresis in electrolyte gradients, 5,6,17

ε kB T UDP = η ze

4kB T zeζ ζβ + ln cosh ze 4kB T

∇ lnC,

(1)

where ε is the permittivity of the fluid, kB is Boltzmann’s constant, T the temperature, η the fluid viscosity, z is the ion valence, e is the elementary charge and ζ is the zeta potential of the particle. This expression reflects the combined action of two effects. Ions with different mobilities diffuse in an ambipolar fashion, spontaneously establishing an electric field in response to electrolyte gradients 18 E=

kB T β ∇ lnC, ze

(2)

where C is the electrolyte concentration. This spontaneous field drives electroosmotic flow within the electrical double layer around a charged particle, which drives the particle diffusiophoretically. The parameter β , defined by

β=

D+ − D− , D+ + D−

(3)

depends on the diffusivities of the cations and anions, D+ and D− respectively, and ranges between −1 ≤ β ≤ 1. This spontaneous electric field points up or down the concentration gradient, depending on which ion has the larger diffusivity. A slow anion (e.g. Cl− ) paired with a fast cation (e.g. H+ ) gives rise to a positive β and an electric field which points up the gradient. The opposite is 3 ACS Paragon Plus Environment

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true for a fast anion paired with a slow cation (e.g. NaOH). The larger the difference between ion mobilities, the closer |β | gets to one, and the stronger the electro-diffusiophoretic contribution. The second mechanism contributing to diffusiophoresis arises when the concentration gradient establishes an osmotic pressure gradient along the electrical double layer itself. The resulting chemiphoretic migration is also proportional to ∇ lnC, but is always directed up ionic strength gradients, regardless of particle surface charge or the ions involved. Strictly speaking, Eq. 1 holds only for electric double-layers that are infinitesimally thin compared with the particle radius, yet with electrolyte concentrations that remain low enough to be accurately described by the Poisson-Nernst-Planck equations (implying point-like ions that obey the mean-field approximation). It is not clear that either of these two approximations hold for ionic surfactants. Extensions for large-ζ , finite EDL that account for double-layer polarization and concentration polarization in the bulk electrolyte during diffusiophoresis 19,20 will be discussed in light of our measurements, as will steric effects within the EDL due to finite-sized ions. 21,22 Ionic surfactants differ from simple electrolytes in a number of important ways. First, the large size of the surfactant ion relative to its co-ion renders β large, strengthening the diffusioelectrophoretic contribution. Second, surfactant molecules often physically adsorb onto interfaces, 3 and may therefore change surface properties such as surface charge, acting effectively like potential-determining ions in the colloidal context. Without advance knowledge of how such adsorption affects the colloidal surface, it is difficult to predict particle diffusiophoresis in advance – after all, diffusiophoresis has been observed to reverse direction under certain salts. 7 A final complication is that many surfactants spontaneously form aggregates called micelles above a critical micelle concentration (CMC). Here we perform systematic measurements of the diffusiophoretic migration of particles in gradients of two ionic surfactants, one anionic and the other cationic. We find that sub-CMC diffusiophoresis can be understood in terms of the classical theory for electrolytes, but find significant differences above CMC. In particular, the magnitude of DP migration drops dramatically under gradients above CMC.


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to maintain constant concentrations on either side. Once the sample channel flow is stopped, 2000 images are recorded, each with 0.1 s exposure time, with a CCD fluorescent camera (Andor iXon) to capture the positions of the colloids. For each set of solutions, experiments were repeated at least 8 times to improve statistical sampling of the measurements. To improve image quality for data analysis, a time-averaged image is subtracted from each individual image, thus removing immobile features and highlighting moving particles for velocimetry. Moreover, we do not consider the first 110 s worth of images to ensure that the surfactant profile has reached a diffusive steady state in the frames that are analyzed. This time significantly exceeds that required for SDS to diffuse across the channel, approximately τD ≈ w2ch /(4DSDS ) ≈ 10 s, for SDS. The images are then analyzed using a Microparticle Image Velocimetry (µ PIV ) algorithm 25 to produce a time-averaged velocity map of the channel. Since the migration of particles along the gradient form a depleted area on one side of the channel, measured values located within this depleted zone are excluded from our analysis. The remaining data is averaged over the y-direction of the channel, since the concentration gradient is established in the x-direction.

Results and Discussion Below CMC For sub-CMC surfactant concentrations, PS beads move down gradients of both SDS and DTAB for all experimental conditions tested. Quantitative interpretation of the results requires the full concentration profile within the sample channel, C(x), which is not known a priori but will be discussed below. Before doing so, we highlight basic trends for diffusiophoretic mobilities that emerge under extremely simplifying approximations. Completely ignoring any interactions between the surfactant and the hydrogel membranes – which would introduce an as-yet unknown mass transfer resistance for surfactants traversing the membrane – gives a crude estimate for the local gradient, |∇C| ≈

∆Ctot , wch


(4)

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and where Ds is the (ambipolar) diffusivity of the surfactant/counter-ion pair, 18

Ds =

2D+ D− , D+ + D−

(8)

which reflects the fact that the anion and cation must diffuse as a pair to preserve electroneutrality. Ds = 810 µ m2 /s for SDS, and 930 µ m2 /s for DTAB. Under these assumptions, the total mass transfer resistance between the reservoir channels is given by

Rtot = 2Rg + Rch ,

(9)

which leads to a steady-state surfactant concentration with a simple linear profile across within the sample channel, C(x) =

Chigh Rtot − (Rg + Rch x/wch )∆Ctot . Rtot

(10)

Inserting C(x) from (10) into (6) gives a prediction for the DP migration profile throughout within the sample channel, U(x) =

DDP x+

Rg wch Rch

−

DsChigh Rtot ∆Ctot DDP

.

(11)

Thus far, however, the gel resistance Rg remains unknown. The impact of Rg on DDP can be eliminated by taking the reciprocal of (11), giving Rg Ds DsChigh Rtot x 1 = + − . U(x) DDP DDP ∆Ctot DDP

(12)

Plotting measured velocity profiles UDP (x) in this manner, then, enables DDP to be determined −1 from the slope of measured UDP profiles, whereas unknown quantities relating to the gel resistance

influence only the y−intercept of this line. This approach should hold so long as the gradient is indeed linear, DDP is constant within the sample channel, and the diffusive steady state is attained. Figure 4(a) shows U −1 versus position across the sample channel for diffusiophoresis of PS colloids under sub-CMC gradients of SDS. Data shows straight lines, as expected from (12), whose


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negative slopes indicate DDP to be negative, consistent with the down-gradient DP migration. The slope of each line is extracted from a linear regression, and plotted against sample channel concentration, Cmid , in Figure 4(b). Measured mobilities range from -66 µ m2 /s to -3 µ m2 /s and decrease in magnitude with increasing concentration for weak gradients (∆C = 2mM). Stronger imposed gradients introduce significant scatter, as discussed below. -

Raw measurements

-

Corrected for polarization

- - - -

-

( )

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( )

Raw measurements

Corrected for polarization

( )

Figure 5: Zeta potential measurements for PS beads in SDS (a) and DTAB (b). Negatively charged PS show slightly more negative zeta potentials at higher SDS concentrations. In DTAB, PS beads show positive potentials likely due to surfactant adsorption on the surface. Figure 5 shows ‘raw’ ζ -potentials, as reported by the Malvern ZetaSizer Nano – which uses Henry’s equation 26 to account for finite electric double-layers. Henry’s formula does not account for electric double-layer polarization, which becomes significant at higher ζ potentials. 27,28 Figure 5 thus also shows ‘corrected’ ζ potentials, determined from measured mobilities using the approximate analytical theories of Pawar et al. 20 to account for double-layer polarization. This theory accurately captures the full theories of Prieve & Roman on diffusiophoresis, 19 and of O’Brien & White, 27 Dukhin and others 28 on electrophoresis for these double-layer thicknesses (65 < κ R < 170). Likewise, we later compute DP mobilities using both Eq. (1), as well as the theory of Pawar et al. 20 Additionally, electrophoretic and diffusiophoretic mobility measurements can be interpreted using the same theory in this fashion. Diffusion coefficients for each ion in the SDS electrolyte, DNa+ = 1334 µ m2 /s and DSD− = 11 ACS Paragon Plus Environment

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580 µ m2 /s, to give βSDS = 0.40. 29 A positive β implies Es points up SDS gradients, so that electrodiffusiophoresis drives negatively-charged colloids down SDS gradients, in the direction opposite to chemiphoresis. The zeta potentials ζ of PS beads measured at the relevant SDS concentrations were negative (Fig. 5(a)), indicating that EDP would indeed proceed down-gradient. Whether PS colloids move up or down SDS gradients, then, depends on whether CP is stronger than EDP, or vice versa. Given β and ζ measured for PS beads in SDS, Eq. 1 suggests DDP is negative – consistent with measurements – and decreases as ζ becomes increasingly negative. Values for DDP computed from (1) and theories that account for double-layer polarization 19,20 are shown against measured values in Figure 4(b), with reasonable agreement: while the order of magnitude, sign, and trends are correct, theories overpredict measurements by a factor of approximately 2. Having characterized the migration of PS beads in an anionic surfactant (SDS), we now turn our attention to its near cationic analog, DTAB. The bromide anion in DTAB is much faster than the DTA+ cation, with DBr− = 2080 µ m2 /s and DDTA+ = 602 µ m2 /s, yielding βDTAB = −0.55. 30 The negative β suggests that the electric field now points down-gradient, and might be expected to drive EDP in the same direction as CP, both directed up DTAB gradients. However, U −1 profiles measured in sub-CMC DTAB gradients all show negative slopes, indicating DP migration proceeds down DTAB gradients, just like for SDS. Zeta potential measurements (Fig. 5b) reveal that DTAB reverses the sign of the surface charge of the PS colloids, with ζ values all positive in the DTAB concentrations studied. This is not surprising, as DTAB and other alkyl-trimethyl-ammonium bromides are commonly used to modify negatively-charged surfaces and reverse the direction of electroosmotic flows. 31,32 Their positively charged surfactant molecules adsorb to negatively-charged surfaces, forming a monolayer onto which subsequent adsorption forms a bilayer or hemimicelle on the surface, changing its charge. 33 Measured values of DDP for PS particles in DTAB gradients are compared with those computed from (1) and from higher-ζ theories 19,20 based on measured

ζ -potentials (Fig. 6). Diffusiophoretic mobilities are about an order of magnitude higher in DTAB than in SDS, consistent with theoretical predictions. Again, however, theories overpredict mobilities two- to three-fold, as they did for SDS.


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ments spanning the CMC, for several reasons. In steady-state, any imposed gradients must be divergence-free; consequently, discontinuous changes in concentration gradients are expected in systems that bracket the CMC, because surfactant diffusivities can change by orders of magnitude across the CMC. 18 This introduces additional uncertainties regarding the location of the CMC within the device, and the strength of the gradients on either side. In practice, moreover, the CMC would often occur close to (or even within) the hydrogel membranes, where measurements were challenging or impossible. This effect also prevented measurements closer to the CMC: the closer Cmid becomes to CCMC , the smaller a ∆C can be imposed without crossing the CMC. We could only get so close to CMC before the applied driving forces became too weak to reliably measure DP migration. Although more challenging to interpret, transient systems may hold more promise to make measurements spanning the CMC. We argue that the dramatic drop in diffusiophoretic migration above the CMC can be understood in terms of the changes in the surfactant solution itself. For PS particles in both SDS and DTAB, the small ion (Na+ and Br− , respectively) represents the counter-ion, and therefore plays the most significant role in driving diffusiophoresis. The strength of the diffusio-osmotic flow within the double-layer, which drives the diffusiophoretic motion of the particle, thus depends on the chemical potential gradient (or, equivalently, the flux) of these small ions in solution. Above the CMC, less free energy is required to form additional micelles than to dissolve the corresponding number of monomers – as reflected by a chemical potential that grows much more slowly with concentration: ∂ µ /∂ C for SDS drops by 3 orders of magnitude at the CMC. 34 Above the CMC, adding further surfactant primarily forms additional micelles, leaving the monomer concentration relatively constant. Concentration gradients above the CMC, then, appear predominantly as gradients in the micelle concentration, rather than in monomer concentration. Likewise, each micelle is screened by its own double-layer, implying that micellar concentration gradients effectively ‘tie up’ the corresponding counter-ion gradients (whether Na+ or Br− ). Since chemical potential gradients represent forces on dispersed solutes, which therefore drive diffusio-osmosis and diffusiophoresis, the dramatic drop in ∇µ for a given ∇C (when compared


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with its sub-CMC analog) should naturally give rise to much weaker diffusiophoretic migration, as we measure. The electro-diffusiophoretic component of the migration should also change, but is complicated by the presence of three components - free surfactants, free counterions and micelles - which are all coupled electrostatically. A more detailed investigation into how micellar systems interact with colloids is required to more accurately predict how diffusiophoretic mobilities change above the CMC. If the simplest electrolyte theory (e.g. Eq. 1) held, one would expect mobility reversal in SDS gradients for ζ below approximately −90 mV (Fig. 8), which is consistent with electrokinetic measurements of ζ above CMC. Still, however, the data lacks the precision to reach such conclusions confidently, and a more sophisticated, multicomponent theory would be required for its interpretation.

Eq. (3)

Eq. (3)

80 mM

80 mM

16 mM

16 mM

8 mM 4 mM

8 mM 2 mM

4 mM 2 mM

Figure 8: Theoretical predictions of diffusiophoretic mobilities vs. ζ for in gradients of (a) SDS and (b) DTAB. The curves show the theory of Pawar et. al. (1993) for values of R/λD ranging from 50 to ∞, which reduces to Eq. 1.

Discussion and Conclusions To summarize, we measured the diffusiophoretic mobilities of polystyrene particles in gradients of two canonical ionic surfactants, both above and below the critical micellar solution. The standard, classic theory of DP migration under electrolyte gradients, based on (1), captures the magnitude, 16 ACS Paragon Plus Environment

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direction, and scaling of diffusiophoretic mobilities under both SDS and DTAB gradients, although the theory overpredicts measured values two- to three-fold (Figs. 4 and 6). Notably, this discrepancy was not observed for measurements of diffusiophoretic mobilities under NaCl, made in very similar devices. In that case, measured diffusiophoretic mobilities agreed with predictions based on (1) to within experimental uncertainties. We do not know why surfactant gradients give rise to the two-to-threefold discrepancy seen here, whereas ionic gradients do not, but will now raise and discuss several possible mechanisms. One candidate is electric double-layer polarization, which generally becomes significant for particle with radii that do not significantly exceed the screening length, and with ζ -potentials that are moderate to high. This mechanism arises due to an excess surface transport of the counter-ion within the electric double-layer, and is better-known in electrophoresis, where it is captured by the Dukhin number, Du ∼

exp(e|ζ |/kB T ) , κa

(13)

where κ = λD−1 is the Debye screening length, and a is the particle radius. When Du becomes appreciable, the excess ionic flux associated with the surface becomes strong enough to perturb the electrolyte concentration in the surrounding (bulk) electrolyte. This effect – generally called concentration polarization, or double-layer polarization – gives rise to a well-known mobility maximum in electrophoresis. 27,28 Double-layer polarization can have an stronger effect in diffusiophoresis – e.g. even reversing the direction of diffusiophoresis. 19 In the sub-CMC experiments described here, ζ˜ ∼ 2 − 3, and κ R ranges from about 70 to 170. These have been studied numerically by Prieve & Roman, 19 followed by analytical approximations 20,36 that are accurate over the range of κ R relevant to our sub-CMC measurements. Theoretical curves for these various doublelayer thicknesses, based on the theory of Pawar et al., 20 are shown in Fig. 8 for SDS and DTAB, and compared with experiments in Figs. 4 and 6. To our surprise, polarization increases the magnitude of the DP mobility in the conditions of our experiments, and thus increases the discrepancy between experiment and theory, while preserving the order-of-magnitude agreement and general qualitative trends. 17 ACS Paragon Plus Environment

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A second possibility involves diffusio-osmotic flows (DOF) that may be driven along the top and bottom surfaces of the channels, which would in principle drive a uniform fluid velocity field directed from one membrane to the other. In particular, we generally expect the ζ -potential of these surfaces to have the same sign as the colloids, in which case this DOF would be driven in a direction opposite to the particles’ DP migration. Because fluid generally can not flow through the hydrogel membranes, 24 conservation of mass would suggest an equal and opposite (pressuredriven) back-flow. In that case, DOF would have no effect on the spatially-averaged DP migration velocities measured in our experiments. Because the hydrogel membranes in our experiments are not infinite in length, however, some fraction of this backflow may be driven back on either side of the membranes, so that there may be some influence of DOF on our measurements. We tried to control for this by restricting measurements to the central portion of the HMM chamber, but can not rule out the influence of DOF on our experiments. Finally, these quantitative discrepancies may of course reflect errors introduced by the experimental system that we have not accounted for in our analysis. For example, the mass transport resistance of the hydrogel membranes may have a nonlinear dependence on surfactant concentration, which our analysis does not contain. Additionally, the interpretation of electrophoretic mobilities in terms of zeta-potentials – measurements that are routinely performed in commercial instruments – are not unambiguous, and require a theoretical model. Moreover, polydispersity in the colloidal suspension may give rise to a range of DP mobilities, whereas our experiments only track those particles that remain within the experimental window, potentially biasing the measured sample towards the slower end of the distribution. Finally, surfactants may exhibit longer, or more non-trivial, mass transport timescales than we have estimated or expected. We attempted to control for potentially long transients within the HMMs by starting experiments for each set of conditions with 10-15 minutes of continuously flowing solutions in the channels, and then performing 8-10 identical experiments within the same device, under the same conditions. That is, after each experiment was completes, the sample channel was flushed with fresh suspension fluid, after which the center channel flow was stopped and a new experiment started. We would expect that any


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particularly long transients, putatively associated with the hydrogel membranes, would relax over the time scales of these multiple experiments; by contrast, successive experiments were consistent with each other, showing no evidence of drift from experiment to experiment. Broadly speaking, however, the present work reveals that diffusiophoresis in relatively dilute solutions of ionic surfactants can be understood and predicted reasonably well using the wellknown theories for diffusiophoresis in electrolyte gradients, to within a factor of two or three. Whether the theory or the experiments/analysis are responsible for these discrepancies will require further research. Additional subtleties that arise in surfactant gradients include surfactant adsorption to the colloids, which can modify the surface charge density. ζ -potentials must therefore be determined in the appropriate surfactant solutions in order to predict DDP in such systems. DP migration slows dramatically in surfactant solutions above the CMC, which we argue occurs because surfactant monomer concentrations remain relatively constant once the CMC is exceeded. While further work - both experimental and theoretical - will be required to understand and predict DP in concentrated surfactant solutions, the present work establishes that DP in more dilute gradients of ionic surfactants can be understood in terms of classic theories for DP in electrolytes, which we hope will enable the design, prediction, and engineering of systems that exploit surfactant gradients to manipulate suspensions.

Acknowledgement The authors gratefully acknowledge support from the NSF under Grant No. CBET-1438779 and the American Chemical Society Petroleum Research Foundation (Grant 54141-ND5). The content of the information does not necessarily reflect the position or the policy of the U.S. Government, and no official endorsement should be inferred. A portion of this work was performed in the Microfluidics Laboratory within the California NanoSystems Institute, supported by the University of California, Santa Barbara and the University of California, Office of the President, and in the Materials Research Laboratory Central Facilities, which are supported by the NSF MRSEC Program under Grant No. DMR 1121053, a member of the NSF-funded Materials Research Facilities 19 ACS Paragon Plus Environment

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References (1) Kronberg, B.; Holmberg, K.; Lindman, B. Types of Surfactants, their Synthesis, and Applications. Surface Chemistry of Surfactants and Polymers 2014, 1–47. (2) Lang, P. R. Lecture Notes in Physics 917: Soft Matter at Aqueous Interfaces; Springer International: New York, NY, 2016. (3) Rosen, M. J.; Kunjappu, J. T. Surfactants and Interfacial Phenomena; John Wiley and Sons: Hoboken, NJ, 2012; pp 1–38. (4) Velegol, D.; Garg, A.; Guha, R.; Kar, A.; Kumar, M. Origins of concentration gradients for diffusiophoresis. Soft Matter 2016, 12, 4686–4703. (5) Derjaguin, B. V.; Sidorenkov, G.; Zubashchenko, E.; Kiseleva, E. Kinetic Phenomena in the Boundary Layers of Liquids 1. The Capillary Osmosis. Kolloid. Zh. 1947, 9, 335–347. (6) Prieve, D. C. Migration of a colloidal particle in a gradient of electrolyte concentration. Advances in Colloid and Interface Science 1982, 16, 321–335. (7) McDermott, J. J.; Kar, A.; Daher, M.; Klara, S.; Wang, G.; Sen, A.; Velegol, D. Selfgenerated diffusioosmotic flows from calcium carbonate micropumps. Langmuir 2012, 28, 15491–15497. (8) Moran, J. L.; Posner, J. D. Phoretic Self-Propulsion. Annual Review of Fluid Mechanics 2017, 49, 511–540. (9) Golestanian, R.; Liverpool, T.; Ajdari, A. Propulsion of a molecular machine by asymmetric distribution of reaction products. Phys. Rev. Lett. 2005, 94. (10) Kar, A.; Guha, R.; Dani, N.; Velegol, D.; Kumar, M. Particle deposition on microporous membranes can be enhanced or reduced by salt gradients. Langmuir 2014, 30, 793–799. 20 ACS Paragon Plus Environment

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