2.1 Electrostatic Effects in ODMS-MIM^(±) Monolayers

Prior pendant drop tensiometry (PDT) and sum frequency generation spectroscopy (SFG) measurements of monolayer formation showed that the ionic strength-dependent kinetics of self-assembly were comprised of two distinct regimes, namely, an initial one where oligomers first adsorbed and reoriented on relatively fast time scales, followed by conformational sampling and frustrated packing at longer times.^[11] The rates of these events were found to scale with the ionic strength (I → 1 m NaCl) and the species of counterions. This involved a time-dependent, structural transition of the ODMS tails, from being mainly parallel to the interface with low packing density at low ionic strength to extending out more into the oil phase to increase oligomer packing density at the interface with elevated ionic strength. This is consistent with lower monolayer tensions at elevated strength measured with PDT. This is significant since it indicated that the hydrophobic tail backbone configurations in hexadecane were controlled by electrostatic interactions occurring in the aqueous phase, even though the electrolytes were not in direct contact with the tails. These changes also coincided with the disruption of the ordered hydrogen-bonding network of water at the interface with increasing ionic strength, as indicated by SFG spectral changes in the ─OH stretching region of water.^[11]

Additional SFG/MD studies of the monolayer showed that ion pairing and specific ion effects could result in dramatic changes in monolayer assembly, including enhanced ODMS adsorption, morphological changes of the monolayer, and disruption of hydrogen bonding with water at the interface.^[13-16] Importantly, they reduced the electrostatic repulsion of the MIM⁽⁺⁾ headgroups in the aqueous phase, forcing the ODMS tails to extend into the oil phase. At all ionic strengths, “softer”, more polarizable, and surface-active anions (like SCN⁻, compared to Cl⁻) resulted in denser, more ordered brushes, with extended tails and smaller tilt angles normal to the interface, the result of enhanced charge neutralization as a function of changes in the ionic strength.

Because of their strong amphiphilicity, the ODMS-MIM⁽⁺⁾ oligomers were effectively “terminally grafted” at the fluid liquid–liquid interface. This means that the cationic MIM⁽⁺⁾ headgroup grafting points were restricted to diffuse in two dimensions parallel to the interface. Further, since the ODMS tails were covalently bonded to the headgroups, they were effectively grafted at the liquid–liquid interface as well. Our previous PDT and SFG results on monolayers at the oil–aqueous interface indicated that the amphiphilic oligomers had first adsorbed at the interface as dilute “mushrooms”, characterized by the hydrophobic tails adopting coiled conformations with segments adopting a random walk, tracing out non-overlapping hemispheres in the oil phase.^[11] This was followed by increased overlap between neighboring tails at higher surface coverage, forcing them to stretch out from the interface into an extended “brush” configuration.

2.2 Sensitivity of Bilayer Conformation to Charge Regulation

In this subsection, changes in ODMS-MIM⁽⁺⁾ geometry as functions of surface charge density, specifically, oligomer packing density and chain length, will be explored. Our starting point for this analysis is the equilibrium separation distance between the charged methylimidazolium headgroups at the oil–aqueous interface for each droplet before the droplets are brought together to form the droplet interface bilayer, based on our previously reported atomistic molecular dynamics (MD) calculations of the ODMS-MIM⁽⁺⁾ bilayer membrane.^[13]

In Figure 1C, there is a critical thickness, h = h_c = 2L, which corresponds to the point where the hydrophobic tails from the two apposed monolayers begin to sterically interact with each other. For leaflet separation distances above h_c, corresponding to monolayers that are in proximity but are not touching, the interaction forces are weakly attractive, consisting of van der Waals and electrocompression forces that increase with decreasing distance. Below this value, the forces are strongly repulsive due to osmotic stress. These forces are also dependent on the in-plane separation distance between adjacent MIM⁽⁺⁾ headgroups, given by D.

We used the minimum of the radial distribution function of the in-plane MIM⁽⁺⁾-MIM⁽⁺⁾ headgroup pair from atomistic molecular dynamics (MD) simulations we had performed on the monolayer^[13] to determine D₀ (0.90 nm), which we assigned as a minimum distance of closest approach between nearest neighbor imidazolium groups. The corresponding values for the maximum possible grafting and charge densities for the brush phase from the simulations were Γ₀ = 1.57 oligomers nm⁻² and σ₀ = 0.25 C m⁻² respectively.

In Equation (4), σ₁ is the modification of the maximum charge density, given by σ₀, when multiplied by the fraction of dissociated MIM⁽⁺⁾ cations at the liquid–liquid interface, α. The resulting charge density σ₁ is decreased from σ₀ because of the formation of specific MIM⁽⁺⁾-Cl^(-) ion pairs, which neutralized a fraction (1 − α) of the headgroups. In Equation (5), σ₂ is the ionic strength-dependent charge density at the interface. It is what the charge density would have been if there were no ion pair formation, and it was only dependent on the ionic strength of the solution (and pH; however, in this study, we assume a constant pH = 7.4).

Ion pair formation, characterized in terms of the association constant 1/K_d (Equations (1)–(3)), resulted in charge neutralization at the interface, not just an increase in the effective activity coefficients of nearby ions in the solution. This is an example of a charge-regulated system resulting from the adsorption and partial neutralization of Cl^(-) counterions at grafted MIM⁽⁺⁾ surface sites, giving rise to a Langmuir-type adsorption profile as a function of the ionic strength.

For a mixed system consisting of inert (nonbinding, Na⁽⁺⁾) and surface-binding (MIM⁽⁺⁾) cations, Equations (4) and (5) can be solved simultaneously, from which both σ and the surface potential, ψ₀, can be determined numerically from the maximum charge density σ₀ and dissociation constant K_d. This can be accomplished by finding the value of ψ₀ that minimizes the difference σ₁ − σ₂ = 0, with the constraint Δσ ≤ 10⁻⁷ C m⁻² using a nonlinear reduced gradient optimization script,^[21] and by assuming a value for the dissociation constant in Equation (1) from a series of structurally similar alkyl-methylimidazolium chlorides: K_d ≅ 0.2 m.^[22] When this condition is realized, σ₁ = σ₂ = σ.

Figure 3 shows, (A) the membrane surface potential, ψ₀, (B) the effective membrane surface charge density, and (C) the fraction of associated (neutralized) MIM⁽⁺⁾ sites by chloride ions (1 − α), and (D) the corresponding headgroup grafting density at the liquid–liquid interface: Γ₀  =  σ₀(1  −  α)/e , all as functions of the ionic strength in the droplet aqueous solutions (e is the elementary charge, 1.6 × 10⁻¹⁹ C). (E) and (F) show the critical leaflet separation distance (membrane thickness) h_c where the apposed ODMS tails begin to overlap, and the in-plane headgroup separation distance, D. In Figure 3F, the value of D is dependent on ionic strength and K_d and varies from 0.95 to 1.05 nm. The corresponding h_c values, determined from Equation (6), were in the range of 4.4–5 nm and were dependent on ionic strength and K_d as well. These values were consistent with experimental-specific capacitance measurements of ODMS-MIM⁽⁺⁾ bilayers as a function of ionic strength, from 0.1 to 1 m. The specific capacitance was used to experimentally determine bilayer thickness from C_M (µF cm⁻²) = εε₀/h, where εε₀ is the relative electric permittivity and h is membrane thickness (Figure 5B, Table S1, Supporting Information).

Since the ODMS tails were covalently bound to the charged headgroups, the grafting number density of the MIM⁽⁺⁾ cations, Γ, also represents the grafted ODMS density in the hydrophobic tail region. This assumes that the interactions between the tails, governed by steric, osmotic, and dispersive interactions in the oil phase, did not influence the effective charge density of the ionic liquid MIM⁽⁺⁾ cations in the aqueous phase.

The green arrows in Figure 3 indicate the dependence of ion pairing with the value of K_d; lower values of K_d correspond to increased ion pairing, and hence, increased charge neutralization at the interface. K_d controlled the degree of association for MIM⁽⁺⁾-Cl^(-) ion pairs while increasing ionic strength increased the chemical activities of all the ions in the electric double layer (including chloride). The trends from these two contributions are clearly shown in the plots of surface charge, σ, in Figure 4B. Both result in increased molecular packing with time.

The values of the charge density and grafted oligomer number density at the interface with increasing ionic strength were not able to reach their maximum values, Γ₀ and σ₀, values since not all of the positively charged headgroups were completely neutralized by the counterions (determined by 1/K_d), even at the highest applied ionic strength (1 m). Similarly, the in-plane separation distances of the charged headgroups, D (proportional to $$\sqrt {1/\Gamma } $$), did not reach the corresponding minimum value D₀.

2.3 Charge Regulation Affects Bilayer Disjoining Pressure

In this subsection, the total disjoining pressure between the two ODMS-MIM⁽⁺⁾ monolayer leaflets of the two aqueous droplets as a function of separation interval when forming the DIB will be derived. Disjoining pressures are sensitive to the electrochemical variables of charge regulation, parametrized by K_d, and the ionic strength. This is because they affect the oligomer packing density at the interface and the bilayer thickness.

At higher compression (lower h), the osmotic component (π = c × RT) from residual hexadecane concentration in the brush (c) dominates the elastic term. These forces balance at a critical distance h = h_c, which is the distance where the ODMS chains from the two apposing monolayers begin to touch. This value increased somewhat at higher ionic strength and ionic pairing because of chain elongation due to charge neutralization, which led to enhanced excluded volume interactions, stretching the chains. At h  ≥  h_c, P_brush  =  0.

Figure 4B–D shows plots of the total disjoining pressure, Π_tot, as functions of the three parameters associated with charge regulation at the ODMS-MIM⁽⁺⁾ interface in this study: that is, the ionic strength (B), the dissociation constant, K_d, of the MIM⁽⁺⁾-Cl^(-) specific ion pair (C), and the electrocompressive potential (D). Varying K_d or ionic strength changed the repulsive components of the total disjoining pressure (P_brush) but did not affect the attractive components (P_vdW or P_ec). However, varying the applied voltage not only changed the attractive component P_ec, but also P_vdW, because electrocompression thinned the bilayer, which increased the van der Waals interactions according to Equation (9).

Either decreasing K_d or increasing ionic strength increased repulsive component pressures, as shown in Figure 4B,C, but in different ways. In Figure 4B, K_d was kept constant at 0.2 m, while in Figure 4C, the ionic strength remained the same at I = 1 m. The differences at h ≤ h_c between these two panels highlight the dependencies existing between I and K_d. The ionic strength is one of the experimentally accessible independent variables (voltage is the other). It parametrizes K_d via Equations (1)–(3), and the charge density at the interface via Equations (4) and (5). The asterisks in Figure 4B,C indicate changes to the threshold condition h ≤ h_c, corresponding to the onset of the repulsive pressure contribution P_brush to the total disjoining pressure. The threshold condition changes because P_brush is proportional to both the grafting density Γ (nm⁻²) and h⁻² from Equation (8), which in turn depend on the extent of electrostatic shielding of the charges and charge neutralization of the headgroups by chloride ions.

At early times, the ODMS-MIM⁽⁺⁾ monolayers at the oil–water interface of each DIB droplet likely had many heterogeneous, interstitial void spaces in the plane of the membrane (corresponding to the mushroom structures from SFG/MD experiments that formed at early times), resulting in poor electrical resistivity and instability against droplet coalescence, due to an increased probability of nucleation and runaway conductive pore growth in the bilayer. This same behavior has been observed in MD simulations of polymer chains in a theta-solvent versus a good-quality solvent when confined in two dimensions.^[34] The higher repulsive pressures due to charge regulation in Figure 4B,C correspond to denser brushes, with increased molecular packing in the plane, resulting in a stable, highly insulating membrane. The CR model (Equations (1)–(6)) is a combination of Gouy–Chapman electrostatic theory and the Grahame equation of the surface charge density. It presupposes a continuous charged surface or interface without holes or leaks, and so pinholes, voids, or any other defects at earlier times or at lower salt are not treated by the model. This point is somewhat academic since these conditions typically resulted in abrupt DIB droplet coalescence.

2.4 Comparison of CR Model with Experimental Data

The voltage-dependent capacitive currents in Figure 2 chronicle the formation and life cycles of droplet interface bilayers in real time, given by the step-like increases in membrane capacitive currents seen in the middle current/voltage plots in Figure 2A,B. The onset of conductive currents, tended to be closely followed in time by abrupt loss of the bilayer due to droplet coalescence in the DIB. Therefore, they were not considered in this study.

The data in Figure 2 give qualitative information (e.g., rupture potentials, DIB lifetimes) about the formation and stability of ODMS-MIM⁽⁺⁾ bilayers under changes in ionic strength. This data is not quantitative, but we are still able to validate our model quantitatively, from a) experimental measurements of the specific capacitance of the DIBs, which enable membrane thickness determination, and b) estimates of the grafting densities of the charged headgroups, deduced from interfacial tension measurements of pendant droplets (Figure 5D). Both predicted values of the model were very close to their corresponding experimental counterparts (Table 1).

Figure 5A includes bright-field images of the DIB interface at different points in time corresponding to the regions II, III, and IV in the plot of capacitive current. (This current is like those in Figure 2.) This sequence of images enabled the determination of the membrane areas at specific values of the membrane capacitance. This gives the specific capacitance (C_M = C/A), which is related to the bilayer thickness, h, by C_M (µF cm⁻²) = εε₀/h. It is estimated from the slope of membrane capacitance versus bilayer area in Figure 5B. It is also dependent on ionic strength, as seen in Figure 5C, which shows that the specific capacitance increases by ≈15% over the range I = 0.1 to 1 m. These data are also listed in Table S1 (Supporting Information). The value at 1 m (0.39 µF cm⁻²) corresponds to a membrane thickness (5.2 nm) that is very close to that predicted for the critical membrane thickness, h_c at I = 1 m in Figure 3E (4.9 nm).

The ionic strength-dependent tension data in Figure 5D shows that increased ionic strength sharply decreases the interfacial tension of ODMS-MIM⁽⁺⁾ monolayers, suggesting more stable bilayers at high salt (I = 1 m). This is consistent with the large variations observed in ionic strength-dependent rupture potentials and membrane lifetimes, and previous reports correlating surface tension of bilayers with membrane leakiness.^[36]

The two parameters, h_c and Γ_1 m are in fact the most important parameters in the CR model and the disjoining pressure plots in Figure 4. They are also experimentally accessible. Table 1 is a comparison of experimentally determined values for h_c and Γ_1 m from the data in Figure 5 with those predicted from the CR model. The two experimental parameters are close in value to the predictions, corroborating the model.

Table S2 (Supporting Information) contains interfacial energy parameters of ODMS-MIM⁽⁺⁾ bilayers from the monolayer interfacial tension measurements on pendant drops, and contact angle measurements (θ) from bright-field optical images of DIBs (Figure 1A). Bilayer tensions can be estimated from monolayer tensions using γ_b = 2γ_m  ×  cos(θ). From these data, the Young–Dupré relation gives for the specific adhesion energy density of the bilayer, −∆F = 2γ_m [1 − cos(θ)]: 0.27 mJ m⁻² at 0.1 m and 0.19 mJ m⁻² at 1 m ionic strength. These values are close to those experimentally measured for DPhPC DIBs.^[33] The higher adhesion energy at lower salt [NaCl] is likely the result of the interfacial tension almost doubling that at high salt, due to incomplete Debye shielding of the MIM⁽⁺⁾ cations. The fact that the low salt, 0.1 m ionic strength bilayer formation was spontaneous but short-lived is consistent with an initial tension-dependent, higher adhesion energy during nucleation of the bilayer, but also points to the greater importance of the final brush density in forming stable, robust, highly insulating bilayers.