Oil Interface - The Journal of

Article pubs.acs.org/JPCC

Dual Action of Hydrotropes at the Water/Oil Interface Andrei A. Novikov,† Anton P. Semenov,† Viviana Monje-Galvan,‡ Vladimir N. Kuryakov,§ Jeffery B. Klauda,‡ and Mikhail A. Anisimov*,‡,§ †

Gubkin University, Moscow 119991, Russia Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20742, United States § Oil and Gas Research Institute of the Russian Academy of Sciences, Moscow 117333, Russia ‡

S Supporting Information *

ABSTRACT: Hydrotropes are substances containing small amphiphilic molecules, which increase solubility of nonpolar (hydrophobic) substances in water. Hydrotropes may form dynamic clusters (less or about 1 ns lifetime) with water molecules; such clusters can be viewed as “pre-micelles” or as “micellar-like” structural fluctuations. We present the results of experimental and molecular dynamics (MD) simulation studies of interfacial phenomena and liquid−liquid equilibrium in the mixtures of water and cyclohexane with the addition of a typical nonionic hydrotrope, tertiary butanol. The interfacial tension between the aqueous and oil phases was measured by Wilhelmy plate and spinning drop methods with overlapping conditions in excellent agreement between techniques. The correlation length of the concentration fluctuations, which is proportional to the thickness of the interface near the liquid−liquid critical point, was measured by dynamic light scattering. In addition, we studied the interfacial tension and water−oil interfacial profiles by MD simulations of a model representing this ternary system. Both experimental and simulation studies consistently demonstrate a spectacular crossover between two limits in the behavior of the water−oil interfacial properties upon addition of the hydrotrope: at low concentrations the hydrotrope acts as a surfactant, decreasing the interfacial tension by adsorption of hydrotrope molecules on the interface, while at higher concentrations it acts as a cosolvent with the interfacial tension vanishing in accordance with a scaling power-law upon approach to the liquid−liquid critical point. It is found that the relation between the thickness of the interface and the interfacial tension follows a scaling law in the entire range of interfacial tensions, from a “sharp” interface in the absence of the hydrotrope to a “smooth” interface near the critical point. We also demonstrate the generic nature of the dual behavior of hydrotropes by comparing the studied ternary system with systems containing different hydrocarbons and hydrotropes.

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INTRODUCTION Hydrotropes are substances consisting of small amphiphilic molecules. Examples of nonionic hydrotropes are lowmolecular-weight alcohols and amines. Hydrotropes may be completely or significantly water-soluble and can increase solubility of hydrophobic substances (“oil”) in water, serving as a cosolvents.1 Like surfactants, small addition of a hydrotrope reduces the interfacial tension between water and oil.2 Hydrotropes are effectively used as cosurfactants for stabilization of microemulsions.3 However, unlike surfactants, hydrotropes do not form stable micelles in aqueous solutions because the hydrophobic parts of their molecules are too small.4,5 Instead, some nonionic hydrotropes (tertiary butanol (TBA) is one of the most characteristic examples) may form dynamic noncovalent molecular clusters in aqueous solutions. Molecular Dynamics (MD) simulations show that these clusters have a size order of 1 nm and lifetime from dozens to hundreds picoseconds, being stabilized by hydrogen bonds between hydrophilic parts of hydrotrope molecules and water (see ref 6 and a movie in the Supporting Information, showing the simulation of the formation and dissipation of dynamic © 2017 American Chemical Society

micellar-like clusters of TBA in an aqueous solution with 7 mol % TBA). Moreover, hydrotropes may stabilize mesoscopic (100−200 nm) droplets of “oil”, preventing or significantly delaying their coalescence.6−8 In this work, we present the results of experimental and MD simulation studies of interfacial phenomena and liquid−liquid equilibrium in the mixture of water and cyclohexane (CHX), also referred to as “oil”, with the addition of tertiary butanol. TBA is known as a “perfect amphiphile” with hydrophobic (hydrocarbon) and hydrophilic (hydroxyl) parts precisely divided by the water and “oil” interface.9 TBA is completely soluble in both water and CHX at ambient conditions. The physics of water-mediated hydrophobic interactions has been recently reviewed by Ben-Amotz;10 also, Rankin et al.11 suggest that there is essentially no free energy driving force associated with the aggregation of TBA at concentrations up to a mole fraction ∼0.02. However, semidilute aqueous solutions of TBA Received: May 27, 2017 Revised: July 10, 2017 Published: July 12, 2017 16423

DOI: 10.1021/acs.jpcc.7b05156 J. Phys. Chem. C 2017, 121, 16423−16431

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The Journal of Physical Chemistry C

the samples were further equilibrated for at least 16 h for complete stratification of phases. Probes, taken with a pipet from the aqueous and oil phases, were used for the measurements of the refractive index, density, concentration, surface tension between air and each liquid phase, and interfacial tension between two liquid phases. All of the measurements were performed at 20 °C using water circulation baths MPC-E (Huber, Offenburg, Germany) and F25ME (Julabo, Seelbach, Germany). Concentrations of TBA and CHX were determined by gas chromatography with Crystal5000.2 apparatus (SKB Chromatek, Yoshkar-Ola, Russia; automated injection of 1 μL; stainless steel column 2 m × 2 mm with HayeSep D 80/100 mesh was heated from 90 to 210 °C at 10 °C/min; carrier gas was argon from NIIKM, Moscow, Russia of 99.998% purity at 45 mL/min). Measurements of the density, air−liquid surface tension, and liquid−liquid interfacial tension (at values >10−3 N/m) were performed with a force tensiometer K20 (Krüss, Hamburg, Germany) by the Wilhelmy plate method. The results of our measurements of the density and surface tension CHX/air and water/air at 20 °C with the force tensiometer are in good agreement with the literature.15 Interfacial tensions were also measured with a spinning drop tensiometer SVT-20N (DataPhysics, Filderstadt, Germany). The results of the measurements of the interfacial tension of three samples in the range where these two methods overlap (between 1 and 2 × 10−3 N/ m) are in good mutual agreement. Measurements of the Correlation Length. Nine twophase samples with the compositions close to the critical-point were investigated by dynamic light scattering (DLS) using a Photocor Complex spectrometer (Photocor, Moscow, Russia) (see Table S4). The purpose of these measurements was to examine the correlation length of critical fluctuations in the systems with an anomalously low interfacial tension. The measurements were carried out in the aqueous (heavier) phase at 20 °C; the samples for this portion of the study were held at this temperature for more than 10 h before taking the measurements. The light-scattering angle was 90°, with a laser wavelength of 654 nm, a laser power of 25 nW, and a correlation function accumulation time of 100 s. The correlation length of critical fluctuations can be found from the exponential decay of the time-dependent lightscattering intensity correlation function:16

exhibit pronounced thermodynamic anomalies associated with hydrogen-bond-induced water−TBA molecular clustering,6,12 which was also previously suggested in the literature.2 MD simulations6,13,14 of TBA dilute and semidilute aqueous solutions show the formation of small aggregates of TBA with a preference of tail-to-tail configurations to minimize exposure of the hydrophobic portion of the molecule to water (see the simulation movie in the Supporting Information). While the mutual solubility of water and CHX is very low, at high TBA concentrations, the ternary water−CHX−TBA system demonstrates complete mutual solubility of all three components. We focused our attention on water−“oil” interfacial phenomena and phase equilibria in this ternary system. In particular, our goal was to investigate the dual role of the hydrotrope; surfactant-like behavior dominating at small concentrations and cosolvent, near-critical behavior at higher concentrations upon approach to the critical point of liquid− liquid coexistence. Our study consistently demonstrates a spectacular crossover between two universal limits in the behavior of the water−oil interfacial properties upon addition of the hydrotrope: surfactant-like decrease of the interfacial tension at low hydrotropes concentration (Gibbs−von Szyszkowski isotherm, see section 2 in the Supporting Information), caused by adsorption of hydrotrope on the interface, and power-law vanishing of the tension upon approach to the liquid−liquid critical point as followed from the scaling theory. This dual behavior was already suggested in the literature,5 but has not been examined in detail through experiment or simulation. MD simulations were used to expand the study of the ternary system of TBA−water−cyclohexane. These simulations help to interpret the results from experiments by providing details of the components’ interactions at the atomic level. Extensive studies have been made on this ternary system to examine the surfactant-like character of the hydrotrope to shield a hydrocarbon droplet from the water solvent.6,12,14

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EXPERIMENTAL METHODS AND PROCEDURES Measurements of Phase Equilibria. Tertiary butanol (Carl Roth, Karlsruhe, Germany, >99% purity), cyclohexane (Ecos-1, Moscow, Russia, >99.5% purity), and distilled water were used without further purification. The transitions from two-phase liquid−liquid coexistence to a one-phase homogeneous solution in the ternary system was determined by volumetric and gravimetric titration at 20 °C. Because the simulation studies were performed at 25 °C, we checked the temperature dependence of the interfacial tension in the range 20−25 °C and found that for the TBA concentrations below 20 wt %, the changes in the interfacial tension do not exceed experimental uncertainties. Only simulation results with TBA concentrations smaller than 20 wt % were used for the comparison with experimental data. At the gravimetric titration, small titration portions of tertiary butanol (0.1−0.2% of mass) were added to heterogeneous mixtures of water and cyclohexane. The existence of remaining immiscibility was checked after having the sample stirred for 3 min. The titration continued until the disappearance of the meniscus (the signature of complete mutual solubility) was detected. Measurements of Surface and Interfacial Tensions. Heterogeneous, containing two liquid phases, systems were prepared by mixing of the components at room temperature, following by stirring for at least 6 h to ensure phase saturation. Because the phases were emulsified as a result of the stirring,

C(t ) = ⟨I(t )I(t + δt )⟩ = Co e−t / τ

(1)

where I is the intensity, t is time, and τ is the diffusive relaxation time. We obtain the correlation length ξ from the expression for the rate of relaxation: kT 1 = Dq2 = B q2 τ 6πηξ

(2) 4π

θ

where D is the effective diffusion coefficient, q = λ n sin 2 is the light-scattering wavenumber, n is the refractive index, λ is the wavelength of light, θ is the light-scattering angle, and η is the viscosity. Equation 2 is valid for the condition ξq2 ≪ 1, which is always satisfied in our experiments. DLS measurements require a known viscosity value of the medium. The viscosity of the aqueous phase was assumed to be equal to the viscosity of binary TBA solutions in water with the same TBA concentration.17,18 To ensure this assumption was reasonable, the viscosity in the aqueous phase of two samples additionally containing SiO2 nanoparticles of known size (R = 16424


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thickness by fitting a hyperbolic tangent function to the total density profile using Matlab cftool:33

55 nm) was obtained from DLS measurements of the Brownian diffusion of these nanoparticles. In these samples, the light scattering intensity was dominated by the contribution from the nanoparticles. The viscosity was obtained through an equation equivalent to eq 2 in which ξ was replaced by R. The values of viscosity were in good agreement with the estimates used for the correlation-length measurements.

⎛z⎞ Δρ = Δρo tanh⎜ ⎟ ⎝ζ ⎠

where ζ is the characteristic length of the thickness of the interface (thickness = 2ζ), Δρ is the density profile, and Δρo is the difference between the bulk densities of the liquids. All of the profiles were recentered around the interface prior to the fitting.

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COMPUTATIONAL METHODS The systems studied using MD simulations are summarized in Table S5 and have overall compositions corresponding to the experimental studies. Each system has triplicate simulation trajectories to allow for proper average and standard error calculations. Each replica started from a different configuration to ensure they were independent runs and the statistical analysis is unbiased. Initial system setups were built with Packmol software19,20 with a box of water−alcohol mixture on top and bottom of a box containing cyclohexane (see Figure S1; all systems were visualized using VMD,21 and simulation snapshots were generated using this software). A system of the binary mixture water−cyclohexane was also simulated to compare against experimental values. The TIP4P-EW water model22 was used in these systems due to its superior accuracy as compared to the TIP3P model for liquid−liquid equilibrium studies. All systems were initially run for 100 ps to allow a quick thermal equilibration at 25 °C and 1 bar using the NAMD Software Package.23 The NPAT ensemble (constant number of molecules, pressure, temperature, and fixed area) was then used during all production runs to complete trajectories of 75 ns for each system using the CHARMM general force field parameters.24 This setup allows changes in the z-dimension, but x- and y-dimensions were fixed. Systems with high TBA content (S15−S18 in Table S5) were simulated using the NPT ensemble because the use of an area constraint in the NPAT ensemble resulted in negative interfacial tension values. The simulation time-step was 2 fs, and the SHAKE algorithm was used to constrain hydrogen atoms.25 We used Langevin dynamics26,27 to keep the temperature constant, and a Langevin piston coupled to a temperature bath controlled by Langevin dynamics23,28,29 to keep the pressure constant in NAMD. VDW and electrostatics interactions were computed with a LennardJones force-switching function over 8−10 Å.30 Long-range electrostatics were accounted for using the Particle Mesh Ewald method,31 and all runs used periodic boundary conditions. The interfacial tension (γ) was computed from the NAMD pressure output using eq 3: γ = 0.5Lz(Pzz − 0.5(Pxx + Pyy))

(4)

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RESULTS AND DISCUSSION Ternary Phase Diagram. While the obtained liquid−liquid transition boundaries are qualitatively in agreement with earlier reported studies,7 the determination of the component concentrations in the coexisting phases enabled us to accurately locate the liquid−liquid critical point with the composition of 82.61 mol % water (53.36 wt %), 16.22 mol % TBA (43.10 wt %), and 1.17 mol % CHX (3.54 wt %). The tie-lines connecting the equilibrated phases show that TBA initially enriches the aqueous phase (the tie-lines have slope to the right), but then its distribution drastically changes, and near the critical point TBA enriches the oil phase (the tie-lines have slope to the left). The ternary phase diagram at 20 °C and ambient pressure is shown in Figure 1.

Figure 1. Phase diagram of the ternary system water−cyclohexane− tertiary butanol at 20 °C in terms of mass fractions. The red circle indicates the critical point of liquid−liquid coexistence; the rainbow colored lines are the tie-lines (red to violet colors correspond to the change from low to high interfacial tension); the solid blue line shows the phase separation boundary; and the dotted blue line conjugates the midpoints of the tie-lines. Detailed experimental results are summarized in Tables S1−S3.

(3)

where Lz is the size of the simulation box normal to the interface and Pii are the average pressure tensor components at every simulation step in bars. The reported γ values in Table S6 were block-averaged every 1 ns. Hydrotrope concentration in the aqueous phase was determined from the alcohol and water atom number density profiles (see Figure S2), computed using CHARMM32 by dividing the simulation box along the zdirection in equidistant bins and counting the number of molecules of a given species per bin. The symmetric molecule density profiles (MDP; atom density profile (ADP) divided by the corresponding number of atoms per molecule) were used to estimate the interfacial

Interfacial Tension. The interfacial tension between the aqueous and oil phases was measured by Wilhelmy plate and spinning drop methods with excellent agreement between techniques in the overlapping range of concentrations each method can measure. In addition, we studied the interfacial tension with MD simulations of a model that adequately represents this system. The results of the experimental measurements and simulations are presented in Figure 2 and Tables S2, S4−S6. As seen in Figure 2, the simulation results for the interfacial tension of the model system are in good agreement with experiment at low hydrotrope concentrations. However, as 16425


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The Journal of Physical Chemistry C γ = 1 − A ln(1 + Bx) γo

where γo is the interfacial tension of the water−cyclohexane system (no TBA), x is the mole fraction of TBA, and A and B are system-dependent constants. This is approximately the same regime in which the interfacial tension predicted from simulations does not need any adjustment. However, while in water−oil systems with a real surfactant, the interfacial tension almost stops changing at the critical micellar concentration, which is usually very small, in the hydrotrope solution the interfacial tension continues to decrease, ultimately vanishing at the critical point of liquid−liquid separation. Equation 6, being valid only for dilute solutions, obviously cannot describe the observed crossover behavior. Crossover between Sharp and Smooth Interfaces. We suggest the following empirical interpolation between the universal limiting behaviors of the interfacial tension based on the simplest form of Padé approximant:

Figure 2. Interfacial tension measurements and simulation results; the “○” show the simulation results (for S1−S10) with rescaled TBA concentrations using eq 5 (a = 0.07) to adjust them to the TBA solubility in the experimental ternary system.

ψ1ψ2 γ = γo ψ1 + ψ2

TBA concentration increases, the decay of the interfacial tension upon addition of the hydrotrope delays from the real system behavior. The higher is the TBA concentration, the more significantly the simulation data deviate from the experimental ones. This discrepancy arises from a drawback of the model, from a misrepresentation of the TBA−CHX interactions in the force field (see the discussion in section 3 of the Supporting Information). These interactions are not finetuned to reflect TBA solubility in the organic phase. The model systems with high TBA concentration do not reproduce the correct alcohol concentration in the bulk oil phase once the interface is saturated. Moreover, starting with the sample S11 (see Table S6), the thickness of the interface approaches the order of magnitude of the size of the simulation box (3.0 × 3.0 × 10.0 nm). In this region of TBA concentrations (above 7 mol % = 20 wt % of TBA in the aqueous phase), finite-size effect dominates. Therefore, the critical point of liquid−liquid bulk equilibria cannot be determined in the model system, and the asymptotic critical-point behavior cannot be established. This conclusion is supported by the adjustment of the TBA solubility in the simulated model to the TBA solubility in the real ternary system (“○” in Figure 2). In first (linear) approximation, in the diluted TBA concentration range below 2 mol %, the TBA solubility in the model system does not need any adjustment. In fact, the bulk densities of each liquid phase barely change in this range of TBA concentrations. After the interface is saturated by TBA, the bulk solubility of TBA starts to play an increasingly important role, and a correction is needed; the difference in bulk densities of the liquids starts to become noticeable and changes in a linear fashion (refer to Figure S3). This adjustment, performed as a rescaling of the TBA concentration axis: x = x*(1 − ax*)

(6)

where ψ1 =

1 1 + a1x

(7)

≅ 1 − a1x + ... is a function representing

the surfactant-like behavior in the dilute solution limit x → 0. Because 1 − A ln(1 + Bx) = 1 − ABx + ..., ψ1 in linear approximation coincides with the Gibbs−Szyszkowski isotherm given by eq 6 if a1 = AB. We note that in limit x → 0, this function represents the universal result of the Gibbs thermodynamics of adsorption. 34 The other function, ψ2 = a 2

μ

( x x− x ) , c

is also asymptotically universal.35,36 The

limit (xc − x) → 0 represents an asymptotic scaling power law for the interfacial tension vanishing at the critical point (xc = 16.22 mol % = 43.10 wt % of TBA in the aqueous phase). Comparison of this model with other isotherms is discussed in section 2 of the Supporting Information as reference for the reader. The power μ = 3.85 is a universal critical exponent for a specific thermodynamic path to the critical point, along the phase coexistence upon which the concentration of TBA changes in the aqueous phase (left branch of the coexistence in Figure 1). In theory of critical phenomena (scaling theory),16,37 this path corresponds to the change of the “order parameter”, ϕ, which characterizes the difference between the coexisting phases and vanishes at the critical point, where the coexisting phases become identical. In multicomponent fluid systems, the order parameter is a linear combination of concentrations and densities of the coexisting phases.38,39 In the first approximation, the deviations of the density and concentration in each phase from their critical values are proportional to the order parameter.38,39 According to scaling theory, the near-critical interfacial tension γ ∝ ξ2 ∝ ε2ν, where ν = 0.63 is the universal critical exponent of the correlation length, and ε is a “distance” to the critical point along the medium line of the phase coexistence (along the rectilinear diameter in a binary-fluid). In a ternary system, a change in ε at constant temperature and pressure corresponds to the path along the midpoints of tie-lines of the ternary phase diagram37 as shown in Figure 1 by the blue dotted line. However, the path along the liquid−liquid coexistence with changing TBA concentration and the difference of densities of the coexisting phases corresponds to

(5)

where x* is the TBA concentration in the simulated model and a = 0.07, works well for the samples S1−S10. For larger TBA concentration, this simple rescaling is not sufficient. The effect of the hydrotrope on the interfacial tension varies between two extremes. At low concentrations, TBA acts as a typical surfactant with the surface tension and the interfacial tension decreasing in accordance to the Gibbs−von Szyszkowski isotherm34 (see more details in Figures S7 and S8, and the discussion in section 2 of the Supporting Information): 16426


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The Journal of Physical Chemistry C the change of ϕ as ϕ ∝ εβ, where β = 0.326 (the universal critical exponent of the density along the phase coexistence).16,37−39 Consequently, as a function of the density or TBA concentration in the aqueous phase, the interfacial tension varies asymptotically as γ ∝ ξ2 ∝ ϕ2ν/β. Hence, along this path, ψ2 = a 2

μ

( x x− x ) with μ = 2ν/β = 3.85. c

From eq 7, ψ(x→0) = ψ1, while ψ[(xc − x) → 0] = ψ2. The result of the fit of this model with two adjustable system-dependent parameters, a1, a2, and the fixed experimental value xc = 16.22 mol % (TBA in the aqueous phase) to our experimental data is presented in Figure 3. The experimental results clearly show the

Figure 4. Sample MDP fits to estimate the interface thickness for the (A) S1 and (B) S10 systems.

model (see Figure 4B), but in the real (physical) system it partitions into the bulk water and oily regions. The interfacial density profiles for all of the simulated interfaces are well described by the same function of the coordinate z, as given by eq 4. Therefore, if the density difference is normalized by the difference in the bulk densities and the distance z is scaled by 1/2 thickness of the interface, ζ, the density profile becomes universal (Figure 5). Table S7

Figure 3. Crossover behavior of the water−CHX interfacial tension upon addition of the hydrotrope (TBA); fit to eq 7, a1 = 123.84 and a2 = 0.0083 and xc = 16.22 mol % of TBA in the aqueous phase (fixed experimental value).

crossover behavior of the interfacial tension consistent with the dual role of the hydrotrope: at low concentrations, TBA acts as a surfactant-like adsorbate until the water−oil surface is saturated. Upon further addition, the cosolvent ability of TBA to smooth the difference between water and oil becomes more effective, ultimately resulting in the vanishing of the interface. Interestingly, the crossover concentration (about 6 mol % TBA, at which the two limiting behaviors, shown in Figure 3 by the dashed and dotted curves, intercept) corresponds to the TBA concentration at which the molecular clustering of TBA in aqueous solution is most pronounced.6 Furthermore, at the same TBA concentration, we observed a sharp change in the water−oil density difference (Figure S4). One can also note that the air−liquid surface tensions for the coexisting phases tend to converge upon approaching the critical point of demixing (Figure S5). Mesoscopic Thermodynamics of Smooth Interfaces. Universal Interfacial Profile. As shown in Figure 2, the interfacial tension dramatically decreases with the addition of a hydrotrope, while the thickness of the interface increases. The density profiles for two simulated systems, S1 and S10, and the corresponding fits to eq 4 are shown in Figure 4A and B. Each profile has a snapshot from the equilibrated portion of the trajectory that shows the bulk cyclohexane (gray) and water (cyan) phases and TBA molecules (black and red spheres for the carbon and oxygen atoms, respectively). At low TBA concentrations, the interface is sharp; as the TBA concentration increases, the interface saturates and becomes smoother. Excess TBA remains only in the aqueous phase in the simulation

Figure 5. Universal density profile: all simulation data collapse into a single master curve in accordance with eq 4.

summarizes the fitted parameters for systems S1−S10. Figure S3 shows the thickness of the interface and Δρo, the difference in bulk densities of the coexisting liquids as functions of the hydrotrope concentration in the aqueous phase for the simulation systems (S1−S10). As expected, the thickness of the interface increases with decreasing interfacial tension, 16427


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The Journal of Physical Chemistry C diverging when the interface finally vanishes (at the critical point of demixing). The difference in the bulk densities, on the other hand, shows a linear dependence on the hydrotrope concentration (see Figure S3B). The linear trend may be steeper in the real system given the current simulation model does not demonstrate the proper partition of TBA between oil and water, once the interface is saturated at higher hydrotrope concentrations. A detailed discussion on our simulation model and force field and the explanation of why our simulation of the interfacial profiles is still representative of the real systems (up to system S10) can be found in section 3 of the Supporting Information. Scaling Relations between Interfacial Properties. The nature of the observed universality of the density profile originates from a relation between the interfacial tension and the characteristic thickness of the interface, ζ. Scaling theory of a smooth interface35,36 predicts γ∝ζ

1 −d

experimental and computational data shown in Figure 6 support this conclusion. Experimental points were obtained from DLS measurements of the correlation length relatively close to the critical point, where the interface is smooth, with a thickness of the order of a few nanometers. The systems examined through simulations are far away from the critical point, at low to moderate hydrotrope concentration, where the interface is very sharp. Another relation between parameters of the universal profile, which can shed additional light on the dual role of TBA as a surface adsorbate and a cosolvent, is the density difference of the bulk phases. The gradient theory of interfaces35,36 calculates the interfacial tension as γ∝

+∞ ⎛ dρ ⎞2

∫−∞

⎜

⎟

⎝ dz ⎠

dz

(9)

which satisfies the mean field (d = 4) result for smooth interfaces, γ ∝ ζ−3 and (Δρ)2z→±∞ ∝ 1/ξ2, as well as the scaling prediction for a smooth interface at d = 3: γ ∝ 1/ζ2, ζ = ξ, and (Δρ)2z→±∞ ∝ 1/ξ, the latter being valid in the Ornstein− Zernike approximation, which corresponds to the first-order 4D expansion in the renormalization-group theory of critical phenomena.35 Linearization of the integral in eq 9 gives the following estimate of the interfacial tension:

(8)

where d is the space dimensionality. The well-known result of the mean-field van der Waals theory of the near-critical interface,39 γ ∝ ζ−3 ∝ ε3/2, is actually accurate only for an artificial d = 4 space. For a two-dimensional system, the line tension γ ∝ 1/ζ. Consequently, for a three-dimensional space, d = 3, γ ∝ ζ−2. The correlation length of fluctuations of the order parameter, ϕ, diverges at the critical point. In the critical region, scaling theory predicts that the thickness of the smooth near-critical interface is proportional to the correlation length of critical fluctuations of the order parameter and thus diverges at the critical point as the same function of temperature and concentration,16 ζ = ξ, thus resulting in γ ∝ ξ−2. This prediction is in agreement with experiment within the uncertainties of the DLS measurements, as demonstrated in Figure 6. Remarkably, the universality of the interfacial density profile suggests that the interfacial tension is scaled as γ ∝ ζ−2 for any fluid interface, sharp or smooth, even if far away from the critical point the thickness cannot be identified with the correlation length of the order-parameter fluctuations. The

γ∝

(Δρ)2z →±∞ ζ

(10)

Therefore, in the critical region, one expects (Δρ)z→±∞ ∝ (γξ)1/2. However, our simulation data on the water−oil interface show that while both γ and ζ strongly depend on the addition of small amounts of TBA, the difference in the bulk densities, for the sharp interface, does not.

Figure 7. Dependence of the normalized difference between the water and CHX bulk densities on the square root of the product of the normalized interfacial thickness and interfacial tension.

The dependence of (Δρ)z→±∞ on (γζ)1/2 for simulation data is presented in Figure 7, and it can be approximated by an empirical function without any adjustable parameters:

Figure 6. Linear relation between the inverse of the interface thickness (2ζ) and the square root of the reduced interfacial tension (data error bars for both variables are of the size of symbols). Red “×” are the correlation-length measurements (shown in a larger scale in Figure S6).

y = [1 − (1 − ω)2 ] 16428

(11) DOI: 10.1021/acs.jpcc.7b05156 J. Phys. Chem. C 2017, 121, 16423−16431

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Figure 8. Interfacial tension dependence on hydrotrope concentration using (A) different oil phases (toluene, benzene, cyclohexane, and heptane) and (B) a different hydrotrope (isopropanol). The mole fractions for the literature data40,41 were linearly rescaled with respect to our system by eq 5 (atoluene−TBA = 4.25, abenzene−TBA = 0.75, aheptane−TBA = 5.55, atoluene−isoprop = 3.75, abenzene−isoprop = 4.60, aCHX−isoprop = 2.85).

with y = (Δρ)z→±∞/(Δρ)o and ω = (ζγ/ζoγo)1/2. This function satisfies the linear correlation (Δρ)z→±∞ ∝ (γζ)1/2 near the critical point, predicted by the gradient theory. Because in the entire range of TBA concentrations examined in this study the product γζ ≅ constant, the variable (γζ)1/2 ∝ γ = γo(1 − a1x) as x → 0. The experimental measurements suggest a more complex behavior for difference in bulk densities between the liquid phases. Nonetheless, the empirical function that describes the behavior of the real systems does not require an adjustable parameter either: y′ = y[1 + 1/2(1 − ω)2 ]

dual behavior by a crossover function (eq 7) that interpolates two theoretically well-defined limits, and show that the thickness of the interface and the difference between the densities of the bulk phases can be used to reduce the data into a universal density profile. Moreover, it is found that a scaling relation between the thickness of the interface and the interfacial tension is valid in the entire range of interfacial tensions, from a “sharp” interface in the absence of the hydrotrope (with the thickness of the molecular size) to a “smooth” interface near the critical point (with the thickness proportional to the correlation length). We also demonstrate the generic nature of the dual behavior of hydrotropes by comparing the studied ternary system with systems containing different hydrocarbons and hydrotropes. Further studies of the dual behavior of nonalcohol hydrotropes, for example, amines, would be interesting to pursue with both experiments and simulations.

(12)

Comparison with Other Water/Hydrocarbon Systems Containing Hydrotropes. To conclude our study, we compared the behavior of our ternary system with other water−oil mixtures for which data are available in the literature.40−42 TBA exhibits similar behavior regardless of the “oil” in the mixture (Figure 8A). Comparing our results with ternary systems of different hydrophobes as well as a different hydrotrope (isopropanol) shows the same trend. Isopropanol still shows a clear dual action at the water and oil interface, but there is more delay in the reduction of the interfacial tension, that is, the smaller is the alcohol, the slower is the reduction of the interfacial tension. Even smaller alcohols (like methanol41 and ethanol,40 not shown in Figure 8) exhibit this dual behavior in reducing or vanishing the interfacial tension between water and oil phases, as surfactants at low concentrations and as cosolvents at larger concentrations.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b05156. Movie of simulation showing the formation and dissipation of dynamic micellar-like clusters of TBA in water (MOV) Tables with the water−oil interfacial and water−air surface tension measurements and their associated standard errors at different hydrotrope concentrations, system size, and composition for simulations, and fitted parameters of the density profiles; figures included are snapshots of the simulation systems setup, a sample component ADP (profiles for water, CHX, and TBA), and dependence of interface thickness and the water−oil density difference on the hydrotrope concentration (PDF)

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CONCLUSION The presented results of experimental and MD simulation studies on the effects of a typical hydrotrope on water−oil interfacial phenomena unambiguously demonstrate the dual role played by small amphiphilic molecules in aqueous solutions. At diluted concentrations, hydrotropes act as adsorbates, reducing the water−oil interfacial tension in accordance with the Gibbs adsorption theory. In this surfactant-like regime, the hydrotrope is mainly accumulated on the interface, while the bulk densities of the coexisting phases remain almost unchanged. After the interface is saturated, the hydrotrope acts as a cosolvent smoothing the difference between the aqueous and oil phases, ultimately resulting in criticality with vanishing interface. We describe this

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jeffery B. Klauda: 0000-0001-8725-1870 16429


Article

The Journal of Physical Chemistry C Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to V. P. Medvedev, D. S. Kopitsyn, and M. M. Mukhin (Gubkin University) for the help with sample preparation, GC analysis, and spinning-drop measurements, and to Prof. V. A. Vinokurov (Chair, Department of Physical and Colloid Chemistry, Gubkin University) for encouragement and stimulating discussions. The work of A.A.N. and A.P.S. is supported by the Ministry of Education and Science of the Russian Federation (grant 14.Z50.31.0035). V.M.-G. and J.B.K. are supported by the National Science Foundation (U.S.) under grant MCB-1149187.

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ABBREVIATIONS ADP, atom density profile; CHX, cyclohexane; DSL, dynamic light scattering; MDP, molecule density profile; MD, molecular dynamics; NPT, constant number of molecules, pressure, and temperature; NPAT, constant number of molecules, pressure, area, and temperature; TBA, tert-butanol; VMD, visual molecular dynamics

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