Mechanism of Time-Dependent Adsorption for Dilauroyl

Article Cite This: Langmuir XXXX, XXX, XXX−XXX

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Mechanism of Time-Dependent Adsorption for Dilauroyl Phosphatidylcholine onto a Clean Air−Water Interface from a Dispersion of Vesicles Jennifer A. Staton† and Stephanie R. Dungan*,†,‡ †

Department of Chemical Engineering and ‡Department of Food Science and Technology, University of California, Davis, Davis, California 95616, United States

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S Supporting Information *

ABSTRACT: This study focused on mechanisms of adsorption for dilauroyl phosphatidylcholine (DLPC) from a dispersion of large, unilamellar vesicles (LUVs) onto a clean air−water interface. The adsorption kinetics were tracked using dynamic surface tension measurements for 0.01−10 mM concentrations of DLPC, contained within monodisperse LUVs with mean diameters between 100 and 300 nm. Any lipid in excess of the solubility limit, determined to be 1.1(±0.7) × 10−5 mM (1.1 × 10−8 M), was assumed to be in vesicle form. The adsorption rate was found to increase with increasing lipid concentration and decreasing vesicle diameter, indicating a clear mechanistic role for the vesicles. An induction regime was observed, during which lipid adsorption occurred without significantly changing the surface tension. Pressure−area isotherm data suggested that the surface concentration at the end of this induction period was ∼50% of the concentration at saturation, with the latter estimated as 4.2(±0.7) × 10−6 mol/m2. Convection was also introduced into these experiments to probe the importance of bulk transport mechanisms to the overall kinetics. Theoretical expressions for possible contributing mechanisms and pathways, via molecular and/or vesicle transport, were developed and used to predict associated transport time scales for different scenarios. These theoretical time scales were compared to experimentally measured characteristic times for a variety of DLPC concentrations, vesicle diameters, and convection rates. For DLPC concentrations ≥0.25 mM, our results were consistent with the monolayer formation arising from a molecular transport mechanism that is enhanced by vesicle-to-monomer exchange beneath the interface. At lower concentrations, experimental rates of adsorption increased with increasing convection, and a strong effect of lipid concentration was also observed. For DLPC ≤0.25 mM, transport controlled by direct interfacial vesicle adsorption reasonably captured the observed effect of lipid concentration; however, neither monomer nor vesicle pathway mechanisms captured the influence of convection. Understanding the adsorption kinetics for such nearly insoluble surfactant systems is important in several areas, including food emulsification, foam or microbubble formulation, spray drying techniques, and therapeutics.

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INTRODUCTION The adsorption kinetics of nearly insoluble surfactants to an air−water interface are of interest in a variety of practical applications, including the stabilization of foams and microbubbles, particle formulation in spray drying, and the design of therapeutic lung surfactants.1−7 Commercial lecithin, a complex mixture of long-chain phospholipids, is a commonly used hydrophobic surfactant in the food, cosmetic, and pharmaceutical industries.2,3,6,7 When mixed with excess water, these long-chain phospholipids absorb water to form lamellar liquid crystal structures. Extrusion of the mixture allows for the formation of dispersed, kinetically stable unilamellar vesicles.8 Such vesicle dispersions are used in many practical situations to deliver lipid to a surface or interface, thus lowering its energy and modifying other interfacial characteristics. Despite such widespread utilization, © XXXX American Chemical Society

the mechanistic basis for phospholipid adsorption behavior from a vesicle dispersion remains unclear. In contrast, adsorption mechanisms for soluble surfactants are well-studied, and involve pure molecular mass transfer for concentrations below the critical micelle concentration and micelle-mediated mass transfer at higher concentrations.9−17 Within the micelle-mediated pathway, micelles dissociate beneath the interface to provide a reservoir of monomers.14,16,17 It has also been suggested that micelles may directly adsorb to the interface and rearrange to form the monolayer at sufficiently high concentrations.14,15 Received: February 21, 2018 Revised: July 19, 2018

A

DOI: 10.1021/acs.langmuir.8b00595 Langmuir XXXX, XXX, XXX−XXX

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removal of lipid from the glass wall. The 1 mL dispersion was then extruded through 100, 200, or 400 nm polycarbonate membranes with an Avanti Mini-Extruder (Alabaster, AL), with 17 passes through the membrane. This method creates unilamellar vesicles in the fluid state and ensures unwanted particulates formed on the “starting” side of the membrane do not end up in the final sample.27 Negligible loss of lipid is expected during the extrusion process.28 Finally, 0.8 mL of the extruded dispersion was diluted with 4.2 mL of water to create a 5 mL dispersion with a final concentration of 0.01, 0.05, 0.1, 0.25, 0.75, 1, 5, or 10 mM DLPC. Size Determination. Vesicle diameters were determined from diffusion coefficients, as measured from dynamic light scattering using a Malvern laser diffraction instrument (model: ZS90, Worcestershire, U.K.) at a scattering angle of 90°. From the 5 mL of extruded dispersion, 0.1 mL was removed and diluted with water to create a 1 mL dispersion free of dust particles. The only exceptions to this procedure was when performing the analysis of the 0.01 or 0.05 mM DLPC dispersion; in this case, 1 mL of the full concentration was needed to ensure an adequate scattering signal for the measurements. All measurements yielded intensity-weighted size distributions with a single peak of narrow width. The method of cumulants was used to determine the Z-average diameter and polydispersity index (PDI), with the latter 99%) was purchased as 10 or 25 mg/mL solutions in chloroform from Avanti Polar Lipids, Inc. (Alabaster, AL) and used without further purification. The water used for sample preparation was “molecular-grade biology” water from Sigma (St. Louis, MO) with a resistivity >18 MΩ. This water, which was processed through 0.1 μm filters by the manufacturer, was used to ensure the absence of dust particles for dynamic light scattering measurements. Vesicle Preparation. For each prepared vesicle dispersion, an appropriate aliquot of DLPC (Tm = −2 °C)26 was removed from the stock chloroform solution and dispensed in a glass conical vial. The solution was gently dried with nitrogen and placed under mild vacuum for a minimum of 4 h to ensure complete evaporation of the chloroform. The resulting lipid cake was then hydrated with water to create 1 mL of dispersion. The hydrated lipid cake was sonicated for 10 min in a Fisher FS20 (Pittsburgh, PA) bath sonicator to facilitate B


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Figure 1. (a) Surface pressure as a function of trough surface area for spread DLPC on water at 22 °C. The different open symbols each represent an independent experiment, with monolayers spread using 40 μL of chloroform with 1 mg/mL DLPC. In (b), open symbols are plotted versus their apparent molecular area, assuming complete DLPC insolubility; filled symbols are corrections to these molecular areas after factoring in maximum partitioning of molecules to the subphase. accurate surface pressure measurements.29 DLPC stock solutions in chloroform were diluted with chloroform to concentrations of 1 mg/ mL. Thirty-five to fifty microliters of this solution was then spread onto a clean water subphase with a microsyringe and left untouched for 10 min to allow for solvent evaporation. The monolayer was then compressed by the Teflon barrier at a constant rate of 5 cm2/min (∼1 Å2/(molecule min)) to obtain the isotherm. This was the slowest rate of compression allowed by the instrument and was used to allow sufficient time for equilibration with the subphase. The isotherms performed at 10 cm2/min (data not shown) did not deviate from those performed at a compression rate of 5 cm2/min. The water subphase temperature was controlled by a thermostatted water bath to 22 °C, and all experiments were repeated in triplicate with an accuracy of 0.1 mN/m.

reproducibility at different initial loadings and for two different slow compression rates. These observations support the idea that the isotherms represent equilibrium properties for the monolayer and the subphase. DLPC added initially to the surface ns will partition into the aqueous subphase at equilibrium, as represented with the mass balance, ns = ΓA + CmV.31,32 Here, Γ is the surface excess concentration, Cm is the dissolved monomer concentration, and V is the aqueous volume (Supporting Information). To account for any such partitioning effects, the total number of lipid molecules ns added to the trough was varied at constant surface pressure values (Figure S1). At high surface pressures that approach the collapse pressure, the extent of partitioning of the lipid into the subphase should become limited by its aqueous solubility. Regression of ns versus A at surface pressures between 35 and 45.8 mN/m (Figure S1) yielded a value for the intercept CmV, which was used to provide an ∞ estimate for the aqueous solubility C∞ m . A value for Cm of −5 −8 1.1(±0.7) × 10 mM (1.1 × 10 M) was obtained, in reasonable agreement with results in buffer using a different approach by Buboltz and Feigenson.33 The slope of fits to ns versus A yielded values for the surface excess concentration Γ, which reaches saturation when the collapse pressure is achieved. At the collapse pressure, our data yielded a value of Γ∞ = 4.2(±0.2) × 10−6 mol/m2 for this maximum surface concentration. Actual molecular areas at specific surface pressures were calculated assuming maximum partitioning of lipid to the subphase (i.e., Cm = C∞ m ), with these results shown as filled symbols in Figure 1b. The open symbols in Figure 1b are the uncorrected experimental isotherm results, assuming a perfectly insoluble monolayer. From Figure 1b, it is apparent that accounting for the finite solubility in the subphase is important. Dynamic Tension Measurements. The surface tension relaxation over time due to the adsorption of DLPC onto a clean air−water interface was measured with the drop-profile tensiometer in the rising bubble configuration. A clear timedependent decrease in surface tension was observed for all experiments, which occurred gradually from that of pure water at 72.3 ± 0.4 mN/m to an equilibrium tension of 23.9 ± 0.5 mN/m. These values were obtained by averaging initial and long-time data for all experiments reported in this study. The equilibrium tension is in good agreement with previously reported results,21 as well as with our pressure−area isotherm results in Figure 1. The comparison between surface tension and surface pressure is made evident by recognizing that the latter is the difference between the pure solvent surface tension

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RESULTS AND DISCUSSION The objective of this research was to identify key contributing transport mechanisms in the process of DLPC surface adsorption from a dispersion of vesicles. These mechanisms comprise possible roles for convective−diffusion of lipid as dissolved molecules or within vesicles, interfacial barriers as the lipid reaches the surface, and exchange of lipid between vesicles and dissolved monomer. The significance of these steps and pathways was assessed by experiments in which we measured the DLPC equilibrium solubility and surface excess concentration, and the evolution of surface tension over time due to adsorption. In the latter experiments, the influence of stirring rates and vesicle concentration and diameter was evaluated. Results are compared to predictions from fundamental mass transfer theory to help us identify the key mechanisms driving the adsorption rates for DLPC. Langmuir Trough Isotherms. Surface pressure−area isotherms for DLPC were obtained using a Langmuir trough, and the results are plotted against the total trough surface area A in Figure 1a. These isotherms are in reasonable agreement with those from Mangiarotti et al.30 The surface pressure was observed to be nearly zero at large surface areas, indicating that the lipid was in a surface gaseous phase. The pressure started to rise as the total area fell below ∼320 cm2, as the lipid transitioned into a two-dimensional liquid expanded phase. As the area was decreased further, the pressure rose steeply to an average collapse pressure of 45.8 ± 0.8 mN/m. The isotherms did not exhibit reversibility once compressed beyond this collapse pressure due to the irreversible loss of material from the surface. This subsequently led to instabilities in the surface pressures beyond the collapse pressure (i.e., below trough areas of ∼170 cm2). Below the collapse pressure, surface pressures were stable and the isotherms exhibited reversibility, with C


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and 3, it is evident that as the lipid concentration was increased, the surface tension decreased to reach equilibrium at a significantly faster rate. The unstirred samples at the lowest concentration, 0.01 mM, did not equilibrate within 14 h, the length of time a stable bubble could be maintained in the device. Thus, the induction time for this condition was longer than the experimental window. Dependence on Convection. In Figure 3, dynamic surface tension data from unstirred systems (0 rpm) are compared with stirred experiments to probe effects of convection on the adsorption dynamics. As the rate of convection increased, the time required for equilibration decreased for dispersions of 0.01−0.1 mM (Figure 3a). At these low concentrations, convection appeared to decrease primarily the induction time. At 0.1 mM, the induction time was reduced from 180 to 70 min as convection was increased from 0 to 170 rpm. A clear decrease in the induction regime was also observed at 0.01 mM (Figure 3a) and 0.05 mM (data not shown). In contrast, no effect of convection on the adsorption dynamics was observed at higher concentrations (≥0.25 mM), for stirring rates up to 330 rpm (Figure 3b). Stirring did not influence the dynamics for 5 or 10 mM concentrations, using stirring rates up to 170 rpm (data not shown). The dynamics at 170 rpm were therefore identical to those shown in Figure 2 in the absence of stirring. Dependence on Vesicle Diameter. The induction time was significantly influenced by the vesicle diameter dv (Figure 4) at

and the measured surface tension. Thus, an average collapse pressure of 45.8 ± 0.8 mN/m, from a mean starting surface tension of 70.7 ± 0.3 mN/m, resulted in an equilibrium tension of approximately 24.9 mN/m. These results were obtained from the analysis of isotherms of four different spreading concentrations, each repeated in triplicate. The consistency between long-time dynamic tension measurements and the collapse surface pressure data provides further evidence that the isotherms probed were at equilibrium. In Figure 2 it is evident that, initially, the surface remains at the water tension value for a certain length of time before

Figure 2. Surface tension as a function of time at 22 °C for DLPC concentrations of 0.1 mM (○), 0.25 mM (+), 0.75 mM (△), 1 mM (×), 5 mM (◇), and 10 mM (◁). Vesicle diameter was 130 nm. Dotted lines show the characteristic time that corresponds to a surface tension of 65 mN/m.

beginning to decrease. This initial “induction” period has also been observed in dynamic tension experiments with soluble surfactants.12,34 For phospholipid, it seems likely that, during the induction period, the surface concentration of adsorbed DLPC is too low to alter the tension. This low concentration would correspond to an apparent surface gas regime observed at high trough areas in Figure 1. We analyzed the isotherm data for ns versus A at a constant surface pressure of 1 mN/m, where the surface pressure begins to rise (and surface tension begins to fall) with increased surface concentration (Supporting Information). Regression results yielded an estimate for the surface concentration of 2.2(±0.1) × 10−6 mol/m2, which corresponds to ∼50% of the saturated surface concentration. At later times, the surface tension decay entered a steeply falling regime, with almost constant decay rate over time. Dependence on Concentration. Figure 3 shows the results for the surface tension evolution at various bulk phospholipid concentrations and levels of convection. Examining Figures 2

Figure 4. Surface tension as a function of time and vesicle diameter for 1 mM DLPC. Vesicle diameters of 130 nm (□, △), 181 nm (○, ×), and 285 nm (+, ◇) obtained for stirring rates of 0 (□, ○, +) or 170 rpm (△, ×, ◇).

a concentration of 1 mM. The induction time more than doubled as the diameter was increased from 130 to 285 nm, indicating slower initial kinetics from dispersions with larger

Figure 3. Dynamic surface tensions of DLPC dispersions as a function of bulk phospholipid concentration and convection rate at 22.1 ± 0.4 °C. (a) Concentrations of 0.01 mM (○, +) and 0.1 mM (△, ×, □) obtained by stirring at 0 (○, △), 60 (×), or 170 rpm (+, □); (b) concentrations of 0.25 mM (○, ▽, +), 0.75 mM (◇, □, ▷), and 1 mM (×, ◁, △), obtained by stirring at 0 (○, ◇, ×), 170 (▽, □, ◁), or 330 rpm (+, ▷, △). D


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analysis of adsorption kinetics for water-soluble surfactants from micelles.14,16,17 From each flux expression, we can determine the characteristic lipid adsorption time that is associated with transport controlled by that step or steps. Mechanisms and their delivery kinetics can then be assessed against measured τe values under different experimental conditions. Steps with predicted times that are much less or much greater in magnitude than the measured τe value cannot be the rate-determining mechanism under those conditions. Monomer concentration, vesicle concentration, rates of stirring, and vesicle diameter each influence some of these mechanisms but not others, and these dependencies can also be tested against our experimental observations. The flux expressions we present below are primarily obtained from well-known, limiting solutions to the onedimensional conservation equation (i.e., the time-dependent diffusion equation) for a species j in the absence of convection

vesicles. Convection had no observable effect on the adsorption dynamics for any of the three vesicle sizes at this concentration, when stirring rates of 170 rpm were compared with the unstirred system. Measured Characteristic Adsorption Times. A characteristic time for adsorption τe may be empirically identified from the dynamic surface tension results presented above. Using a simple approach, τe was defined as that required to reach a surface tension of 65 mN/m, which corresponds to a decrease in tension of 15% of the total change from initial to final. This characteristic time, shown with dotted lines in Figure 2, corresponds to the early phase of the adsorption process and is mainly influenced by the duration of the induction period. It is clear from Figures 3 to 4 that τe varied inversely with vesicle concentration, depended on convection rate only at low vesicle concentrations, and increased directly with vesicle diameter. These observations and the quantified values of τe can be compared to results from mass transfer theory, developed in the section below, to assess the role of transport steps and pathways in the lipid adsorption process. Theory. As shown in Figure 5, there are two available pathways for the lipid to move to the interface and form a

∂Cj ∂t

= Dj

∂ 2Cj ∂z 2

+r

(1)

Here, Cj is the concentration of lipid in monomer (Cm) or in vesicle (Cv) form, Dj is the monomer or vesicle diffusivity, z is the distance from the air−water (planar) surface, and t is time. r is a “reaction” term representing a rate of formation of j in the bulk volume; in our case, this term captures the release of lipid monomer from vesicles. Equation 1 must be solved together with boundary conditions that (1) relate Cj to known bulk monomer/vesicle concentrations far from the surface and (2) set conditions for either the flux or the subphase concentration at z = 0. The latter condition also allows us to treat interfacial adsorption barriers, if present. Development of eq 1 and methods for its solution can be found in most textbooks on transport phenomena, such as Deen (1998).35 Application of this equation to describe diffusion across a convective boundary, and thus to determine lipid flux in stirred samples, is described in the Convective Contributions section. Bulk Transport by Diffusion. We start with pure monomer or vesicle diffusion, when contributions from convection or from transfer of DLPC from vesicle to solution (i.e., reactionmediated transport) are negligible (r ≈ 0). Diffusive transport out of the bulk dispersion of either monomer or vesicle, driven by lipid surface adsorption that depletes the adjacent subphase, creates a gradient in Cm or Cv, over a region that grows as time progresses. Eventually, this region of concentration variation adjacent to the surface either (1) reaches a steady state when its extent becomes comparable to the radius a of the bubble35 or (2) disappears when enough lipid is delivered to fully saturate the interface. In the latter case, we define thicknesses hm and hv that correspond to the depth of solution that must be depleted of lipid monomer or vesicles, respectively, to achieve a surface concentration Γ∞

Figure 5. Alternative transport pathways for the delivery of lipid to the air−water (bubble) interface: (a) reaction-enhanced molecular transport and (b) direct vesicle adsorption. Shown are monomer (m) or vesicle (v) diffusion coefficients Dm or Dv, interfacial adsorption rate constants ki,m or ki,v, and on or off reaction rate constants for the vesicle-to-monomer reaction or k+.

monolayer: (1) molecular transport of dissolved phospholipid and (2) lipid delivery by vesicles directly to the interface. Both pathways comprise bulk transport and interfacial adsorption steps. In addition, a reaction mechanism in which lipid molecules transfer from vesicles to the dissolved monomer form can couple the two pathways (Figure 5). The overall kinetics for lipid adsorption are determined by the fastest pathway, whereas within that pathway, the slowest step controls the rate at which the pathway proceeds. Identification of the key controlling pathway and step thus yields the ratedetermining mechanism for adsorption. To help identify these controlling pathways and steps, in the sections below, we identify appropriate mass-transfer flux expressions at the surface, corresponding to the various mechanisms for lipid transport in the bulk or interface. A similar approach has been used previously to good effect in the

hm =

Γ∞ Γ∞ ∞ ; hv = Cm Cv∞

(2)

If hm ≪ a and hv ≪ a, pure diffusion (i.e., in the absence of stirring) of monomer or vesicle occurs over a region of characteristic thickness hm or hv. In this case, treating the bubble surface as planar is justified. To assess transport rates associated with pure diffusion, interfacial adsorption rates must be treated as relatively fast, and therefore the local concentrations Cm or Cv are set to zero at z = 0. Boundary E


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adsorption were effectively decoupled: adsorbing lipid monomers had to diffuse to the surface from the initial pool of existing monomers, without withdrawing lipid from the vesicles. However, vesicles have the potential to significantly speed up transport of lipid through the monomer pathway, by delivering lipid molecules into the solution throughout the bulk and moving the region of concentration variation much closer to the surface. In other words, this vesicle-to-monomer transfer, if sufficiently rapid, effectively keeps the monomer concentration close to its equilibrium value outside a thin region of thickness δr adjacent to the surface. To predict the magnitude of δr, an expression for the “reaction rate” r is needed. The rate of release of monomer from a vesicle has been described as being proportional to a reaction off-rate constant, k+(units of s−1), multiplied by the number of lipid molecules per unit volume in the outer leaflet of the vesicles.36 The latter factor is given by the product φCv, where φ is the fraction of lipid in the outer leaflet, relative to the total lipid in the vesicle. The reverse reactionthe rate at which monomer enters a vesicleis proportional to the product of an on-rate constant k− (in m/s), the concentration of free monomer Cm, and the total external vesicle surface area per unit volume of solution. This external surface area is given by sφCv, where s is the area per mole of phospholipid. This rate expression requires that the “flip-flop” of lipid inside the vesicles proceeds very slowly.36,37 The net rate of monomer production from vesicles is therefore

and initial conditions for this transport mechanism are then written as ∞ Cj = 0 at z = 0; Cj = C ∞ j for z → ∞ ; Cj = C j for t = 0

(3)

C∞ j

is the known bulk concentration of lipid in monomer or vesicle form (j = m or v, respectively). Solving eq 1 with r = 0, subject to eq 3, yields the well-known solution 35 2 Cj = C ∞ From this j erf(z /(2 Dj t )), for times t ≪ hj /Dj. result, the early-stage fluxes - j of lipid to the interface at z = 0, by pure diffusion of the monomer or vesicle, are -m ≡ Dm

∂Cm ∂z

and - v ≡ Dv z=0

∂Cv ∂z

z=0

(4)

Using the solution for Cj, one finds -m = DmCm∞

1 1 and - v = Dv Cv∞ πDmt πDv t

(5)

for the two diffusion pathways. During these early-stage dynamics, interactions between adsorbed molecules are treated as negligible. When the monomer solubility C∞ j in eq 2 is sufficiently low, hm ≫ a. In this case, diffusion persists long enough (for a time of order a2/Dm) that the monomer concentration can reach a steady-state profile over a region of thickness a. Then, the monomer flux corresponds to the well-known result for the steady-state transport to a sphere35 C∞ -m = Dm m a

r=

D C∞ DmCm∞ ; -v = v v δc,m δc,v

(8)

Because at equilibrium the monomer solubility eq 8 simplifies to

(6)

ij Cm yzz r = ka +Cv jjj1 − ∞ z j Cm zz{ k

The flux expressions in eqs 5 and 6 are used below to determine a characteristic time for adsorption when lipid transport is controlled by pure diffusion. Convective Contributions. Convection can speed up diffusive transfer rates through the bulk by reducing the extent of the concentration variation region adjacent to the surface, from hm or hv, to a convective boundary layer of thickness δc,m or δc,v (depending on the pathway). Convection is effective at speeding up bulk transport if δc,m ≤ min[a, hm] or δc,v ≤ min[a, hv]. The magnitude of δc,m and δc,v may be determined from knowledge of the characteristic linear fluid velocity U (due to stirring in our experiments), continuous phase viscosity μ, fluid density ρ, and Dm or Dv. (see the Supporting Information.) With significant convection, diffusion at steady state takes place across the convective boundary layer region of thickness δc,m or δc,v. A “stagnant film model”35 allows us to solve eq 1 (with ∂Cj/∂t = 0 and r = 0) in the region 0 ≤ z ≤ δc,j for j = m 35 or v, with Cj = 0 at z = 0 and Cj = C∞ The j at z = δc,j. 35 convective−diffusive flux to the surface then becomes -m =

dCm = φCv[k+ − sk _Cm] dt

C∞ m

= k+/sk−,

(9)

where we have defined an effective rate constant ka+ = k+φ, with φ depending on the radius of the vesicle and the leaflet thickness. Equation 9 may be substituted into eq 1 to include the effect of vesicle-to-monomer transfer on transport of dissolved lipid to the interface35 ij Cm yzz ∂Cm ∂ 2C = Dm 2m + ka +Cv∞jjj1 − ∞ z j Cm zz{ ∂t ∂z k

(10)

The bubble surface is again treated here as flat, and diffusion occurs at steady state across the film of thickness δc,m (as in stagnant film theory), with Cm = 0 at z = 0 as in eq 3. It is assumed in eq 10 that the vesicle concentration is constant at C∞ v throughout the dispersion due to the high concentration of lipid in the vesicles. The governing eq 10 can then be rewritten, using a dimensionless concentration Ĉ m ≡ (C∞ m − Cm)/C∞ and ẑ ≡ z/δ . This yields at steady state m c,m ̂ ij δc,m yz d2Cm z Ĉ = jjj 2 j δ zzz m dz ̂ r k {

(7)

2

Note that the flux -m of monomer due to pure diffusion (eqs 5 or 6) or convective−diffusion (eq 7) depends only on the monomer concentration C∞ m , which is fixed at the solubility limit, and is independent of the total amount of added lipid in our experiments. Reaction-Enhanced Monomer Diffusion (Vesicle-toMonomer Transfer). In the sections above, we assumed that r ≈ 0, so that the monomer and vesicle pathways to lipid

(11)

with δr ≡

DmCm∞ ka +Cv∞

(12)

Boundary conditions are F


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Langmuir ̂ = 1 at z ̂ = 0; Cm ̂ = 0 at z ̂ = 1 Cm

when δc,v is small due to rapid stirringbulk transport becomes relatively fast and interfacial adsorption controls the rate. It is interesting to note in eq 17 that vesicle concentration C∞ v does not affect the relative importance of bulk transport compared to the interfacial kinetic step, because both these mechanisms depend linearly on vesicle concentration, and thus 38 changes in C∞ v affect both steps comparably. Predicted Characteristic Adsorption Time. The flux expressions associated with different types of transport mechanisms within the monomer and vesicle pathways can be used to determine the order of magnitude estimates of the times τ for adsorption according to each mechanism. A mass balance at the bubble surface indicates that dΓ/dt = -m + - v . From this equation, the characteristic time required to modify the interfacial concentration Γ significantly, relative to its ultimate equilibrium value Γ∞, may be identified. If -m ≫ - v (or vice versa), then the monomer (or vesicle) pathway is ratecontrolling. With the magnitude of dΓ/dt given by Γ∞/τ, scaling analysis would indicate that

(13)

After solving eq 11 with eq 13, the flux at the bubble surface is found to be38 -m =

ij δc,m yz DmCm∞ z cothjjj j δ zzz δr k r {

(14)

When the release of monomer from the vesicles is fast enough,

δc,m δr

δc,m

( ) ≈ 1 and the reaction reduces the

≫ 1, coth

δr

film thickness for diffusion to δr: -m = DmCm∞/δr . In this limit, stirring no longer affects the bulk transport kinetics, because the vesicle-to-monomer reaction is more effective than convection at delivering a saturated monomer solution near the interface. Because higher vesicle concentrations speed up this monomer release rate and reduce δr (eq 12), the flux in eq 14 will switch from a stir-speed dependent, convective− diffusive mechanism at low C∞ v , to a convection-independent mechanism at high C∞ . v Interfacial Adsorption Barriers. Having established flux expressions for bulk monomer or vesicle transport, in the limits of pure diffusion, convective−diffusion, or reaction-enhanced transport, we now turn our attention to the contribution of interfacial adsorption barriers. If the latter barriers are substantial, vesicle or monomer delivery could be controlled by the rate of transfer at z = 0 from the subphase to the interface. This interfacial adsorption step is generally treated as first order in the subphase concentration of monomer or vesicle18,23,24,39,40 -m = k i,mCm at z = 0; - v = k i,vCv at z = 0

τm ∼

(18)

where τm and τv values are characteristic times for the monomer or vesicle pathway, respectively. By comparing the magnitude of τm or τv against experimentally measured adsorption times τe, we can test the plausibility of different controlling mechanisms within the monomer and vesicle pathways for various lipid concentrations, stirring rates, and vesicle diameters. Comparison of Mechanistic Predictions and Experiment. Assessing Bulk Transport Contributions. For the lowest vesicle concentrations (0.01−0.1 mM in Figure 3a), convection increased the experimental rate of adsorption significantly, indicating that bulk transport mechanisms contributed significantly to the adsorption kinetics. As C∞ v was increased to values ≥0.25 mM and adsorption became faster, however, convection no longer influenced the overall dynamics (Figure 3b). This result signifies a shift at higher lipid concentrations to a mechanism that is distinct from pure convective−diffusive processes. In light of these observations, it is important to assess contributions to adsorption kinetics predicted based on pure diffusion (τD,j, using eqs 5 or 6 and 18) or diffusion across the convective boundary layer (τc,j, using eqs 7 and 18), for j = m or v. In predictions for pure monomer diffusion, diffusion coefficients at 295 K for monomer (Dm) from the Wilke− Chang formula41 were used, with a DLPC molar volume of 0.55 m3/kmol,42 a water association factor of 2.6, and an aqueous dynamic viscosity μ of 9.54 × 10−4 kg/(m s). The vesicle diffusion coefficient Dv was determined from the Stokes−Einstein equation for a spherical particle, using measured average vesicle diameters. In the absence of convection or reaction, diffusion takes place across a region either of hj = Γ∞/C∞ j (see Table 2 for values) or of the bubble radius a, whichever is smaller. For stirred systems, the characteristic length scale for diffusion is effectively shortened to δc,m for monomer transport or δc,v for the vesicle, as determined from a standard boundary layer analysis (Supporting Information). This analysis yielded the expression35,43,44 δc,j/2a = 1.506Re−1/2Sc−1/3, where Re = 2aρU/μ and Scj = μ/ρDj are the Reynolds and Schmidt

(15)

This equation defines interfacial rate constants ki,m or ki,v for monomer or vesicle. Equation 15 is most appropriate for early times in our experiment, when adsorbed surface concentrations of lipid (Γ) are low. As the packing increases at the interface, further barriers to adsorption that are dependent on Γ must be considered. When the interfacial transfer step controls the adsorption of vesicles or monomers, stirring speeds and other characteristics of bulk transport do not affect the adsorption rates. It is possible to combine the sequential contributions of bulk transport and interfacial adsorption steps into a single flux expression. For the vesicle, this is done by again solving for the steady-state flux across a stagnant film (eq 1 with ∂Cj/∂t = 0 and r = 0), with the concentration at the outer boundary matching the bulk value (Cv = C∞ v at z = δc,v). At z = 0, however, the diffusive flux is now equated to that due to interfacial transfer rates given in eq 15 Dv

dC v = k i,vCv at z = 0 dz

(16)

Solving eq 1 with this new boundary condition, the lipid flux via vesicles to the surface becomes -v =

Cv∞ δ c,v Dv

1 +

1 k i,v

i Dv Cv∞ jjjj 1 jj = j δc,v jj 1 + Dv k i,vδc,v k

yz zz zz zz zz {

Γ∞ Γ for -m ≫ - v ; and τv ∼ ∞ for - v ≫ -m -m -v

(17)

Equation 17 describes the vesicle adsorption via sequential bulk transport and interfacial adsorption steps and encompasses the possibility of either of these two mechanisms controlling the overall rate. If Dv/(ki,vδc,v) ≫ 1for example, G


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Table 1. Pertinent Transport Parameters Used to Determine Characteristic Time Scales for Adsorption of a DLPC Monomer or Vesicle with Diameter dv, at 170 rpm and 295 Ka vesicle description

monomer

dv = 130 nm

dv = 181 nm

dv = 285 nm

diffusion coefficient Dm or Dv (m2/s) Schmidt number Sc = μ/ρDj boundary layer thickness δc,m or δc,v (m)

3.5 × 10−10 2.7 × 103 1.4 × 10−5

3.5 × 10−12 2.7 × 105 3.0 × 10−6

2.5 × 10−12 3.8 × 105 2.6 × 10−6

1.6 × 10−12 6.0 × 105 2.3 × 10−6

Bubble radius a = 600 μm.

a

Table 2. Predicted Characteristic Lengths and Times for Transport without Convection, via Monomer (m) or Vesicle (v) Pathway, Compared to Measured Times τe at 295 K in Unstirred Systems with Vesicle Diameters of 130 nm

ki,v = 0.0034 μm/s from fit to yield τv = τe at 0.75mM DLPC. bka+ = 0.0022 s−1 from fit to yield τr,m= τe at 0.75mM DLPC.

a

numbers, respectively. The linear velocity U in the former was estimated as 0.07 m/s, based on an 8 mm stir bar rotating at 170 rpm. Based on this value of U, Re = 90 and ReSc ≫ 1 (Table 1). Resulting values for the convective boundary layer thickness are δc,m =14 μm and δc,v = 3 μm for monomer and vesicle, respectively. With all parameters determined for these bulk transport mechanisms, diffusion lengths and adsorption times for bulk transport control were characterized for pure diffusive (Table 2) or convective−diffusive mechanisms (Table 3). Results were calculated as a function of lipid concentration C∞ v , using −5 mM, and a bubble Γ∞ = 4.2 × 10−6 mol/m2, C∞ m = 1.1 × 10 radius a = 600 μm. Equation 6 was used to determine τD,m because a ≪ hm, whereas τD,v was calculated using eq 5 and hv for the vesicle diffusion length. Comparing τD,m and τD,v to the measured induction times τe in Table 2, it is clear that pure diffusion of monomer, without a contributing vesicle-to-monomer reaction, is several orders of magnitude too slow to act as a plausible controlling mechanism for lipid delivery to the interface. Pure vesicle diffusion as a rate-limiting mechanism, in contrast, is 1−2 orders of magnitude too rapid to explain the observed experimental kinetics, except perhaps at the lowest lipid concentration of 0.01 mM. Similar conclusions pertain when stirring is introduced into the system (Table 3). Convective−diffusion of monomers across a 14 μm boundary layer occurs too slowly to account for the observed induction time, except at the lowest lipid

Table 3. Predicted Characteristic Times for Transport with Convection, via the Monomer (m) or Vesicle (v) Pathway, Compared to Measured Times τe at 295 K in Stirred Systems (Re = 90) with Vesicle Diameters of 130 nm

δc,m = 14 μm. bδc,v = 3 μm. cki,v = 0.0034 μm/s as in Table 2. dka+ = 0.0022 s−1 as in Table 2. eBecause hv < δc,v at these concentrations, transport occurs across the distance hv within the boundary layer, and the bulk transport time reverts to τD,v.

a

H


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Langmuir

Figure 6. (a) Comparison of measured (τe, □, ○) and predicted (τv, curves) adsorption times for unstirred (□, ---△---, ---◇---) or stirred (○,  ×, +) systems. Predictions reflect control by vesicle pathway, with ki,v = 0.0034 μm/s (---△---, ×) or ki,v = 0.0101 μm/s (---◇---,  +). (b) Data and predictions in low DLPC concentration region (≤0.3 mM). Arrows show conditions for ki,v fits.

concentration, whereas vesicle transport with δc,v = 3 μm is again too fast compared to τe. Although contributions from bulk transport mechanisms are required to explain the observed dependence on stirring at low lipid concentrations, these contributions appear to exist within a hybrid mechanism: one that either speeds up monomer diffusion or slows rates of vesicle transport. Mechanisms contributing to τD,m or τc,m depend only on monomer concentration, which in our experiments remained constant at the lipid aqueous solubility limit. Thus, diffusive transport of monomer alone is not only predicted to be too slow to account for observed adsorption rates, but also does not capture the strong dependence on C∞ v . Instead, the controlling mechanism must involve vesicle particles, either through the vesicle pathway or by contributions of a vesicle-tomonomer reaction. These two possibilities are considered in the sections below. Their plausibility is assessed by examining whether characteristic times predicted from mass transfer theory for each pathway approximate the measured induction times τe, and, in particular, are consistent with the experimental dependence of τe on convection and lipid concentration C∞ v . Assessment of Vesicle Pathway. The vesicle pathway (Figure 5b), comprising sequential bulk transport and interfacial steps, is next considered as a potential controlling process. In the absence of independent information, the interfacial rate constant ki,v was determined by equating the adsorption time τv predicted for the vesicle pathway to the experimentally measured τe value at a single concentration of 0.75 mM DLPC in unstirred samples. τv was obtained (eq 18) by dividing Γ∞ by a vesicle pathway flux expression analogous to eq 17, but with the interfacial step occurring in series with pure vesicle diffusion τv =

hv2 h + v = τD,v + τi,v without convection Dv k i,v

(τv ≈ τi,v), consistent with a slow transfer step from the subphase to the interface, with significant energy barriers to vesicle penetration and negligible contribution of bulk transport to the kinetics. In Figure 6, the dependence of τe and the vesicle pathway prediction τv on lipid concentration are shown. When compared with τe for the unstirred experiments, τv from eq 19 displayed a similar steep decline with increased C∞ v , when lipid concentrations were low ([DLPC] ≤ 0.25 mM, Figure 6b). However, τv significantly underpredicted the experimental values at higher lipid concentrations ([DLPC] > 1 mM, Figure 6a). The value for ki,v obtained from the unstirred experiments was next applied to the stirred results, with the recognition that ki,v should not change with convection. For the stirred systems, τv was determined from eqs 17 and 18, based on convective− diffusive vesicle transport in series with an interfacial barrier step τv =

hv δc,v Dv

+

hv = τc,v + τi,v with convection k i,v

(20)

Above 0.75 mM, both measured and predicted adsorption times were unaffected by stirring (Figure 6a, Tables 2 and 3). However, at lower lipid concentrations (≤0.1 mM), τe was substantially shorter with convection than without, and this difference was not captured by predictions from eq 20 (Figure 6b). Values in Table 3 show that if ki,v = 0.0034 μm/s, convective−diffusion of vesicles through the bulk is very rapid compared to interfacial barrier rates at all concentrations (τc,v ≪ τi,v). The result is complete interfacial control within the vesicle pathway, which prevents bulk transport mechanisms from playing any role and precludes any sensitivity to the presence or absence of convection. The vesicle pathway prediction can perhaps be made more responsive to convection by increasing ki,v and reducing the interfacial barrier. A value of ki,v = 0.0101 μm/s was determined by equating τv to τe at 0.1 mM for the stirred experiments. This higher ki,v value, and hence lower interfacial barrier, was then used for all other concentrations. This change introduced a small dependence on convection rate at the lowest concentration of 0.01 mM (Figure 6b), but the effect was not nearly strong enough to capture the influence of stirring on the kinetics at and below 0.1 mM. Results in Figure 6a also show that the underprediction of τe at high C∞ v is more severe with the higher ki,v value. Assessment of Reaction-Mediated Monomer Pathway. Within the monomer pathway, pure diffusive (τD,m) or

(19)

Γ∞/C∞ v

Here, we have used the definition = hv and defined the time τi,v ≡ hv/ki,v for transfer against a barrier at the interface. Setting τv from eq 19 equal to τe at C∞ v = 0.75 mM yielded ki,v =0.0034 μm/s. This value was then used to calculate τv for all other lipid concentrations in the absence of convection (Table 2 and Figure 6). Except at [DLPC] = 0.01 mM, the contributions of bulk transport mechanisms within the vesicle pathway (Table 2) are at least an order of magnitude faster than the measured adsorption rates; i.e., τD,v ≪ τe. Thus, the vesicle pathway model as applied to our system will only be as slow as our experimental rates if the pathway is controlled at the interface I


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Langmuir

Figure 7. (a) Comparison of measured (τe, □, ○) and predicted (τr,m, black curves) adsorption times for unstirred (□, ---△---) or stirred (○,  ×) systems. Predictions reflect control by reaction-mediated monomer pathway, with ka+ = 0.0022 s−1. Control by vesicle pathway is shown in gray for comparison, with ki,v = 0.0034 μm/s (---) or ki,v = 0.0101 μm/s (). (b) Data and predictions in low DLPC concentration region (≤0.3 mM). Arrow shows condition for ka+ fit.

For the latter regime, rates predicted by the reaction-enhanced monomer mechanism matched the experimental data well (Figure 7), with effects of stirring eliminated for δr ≪ δc,m at these higher concentrations. At a high DLPC concentration of 1 mM, dynamic surface tension curves in Figure 4 show the relationship between vesicle diameter and adsorption dynamics. (Note that the total number of vesicles in the dispersion decreased as vesicle diameter was increased, for a constant total lipid concentration of 1 mM.) A decrease in adsorption rate with increased diameter was observed. At this high lipid concentration, no effect of convection was discerned, even for the samples with larger vesicles and slower dynamics. As this behavior was observed for all vesicle diameters, it is plausible that the reaction-mediated molecular pathway remained the dominant mechanism for adsorption, even as characteristic adsorption times increased with increasing vesicle diameter. In eqs 12 and 14, the only parameter likely to be significantly influenced by vesicle diameter is ka+, the vesicle-to-monomer reaction rate constant. An estimation of the effect of vesicle diameter dv on this rate constant was achieved by first setting the characteristic time τe = τr,m, using values in Table 4, and determining the film

convective−diffusive (τc,m) transport times are too slow to account for the observed adsorption, and on their own, these mechanisms lack the required dependence on lipid concentration (Tables 2 and 3). However, when coupled to a reaction-mediated mechanism, lipid monomer released from vesicles accelerates diffusion rates along the monomer pathway, to an extent that increases with increasing vesicle concentration. As a result, the modified adsorption time τr,m depends on the film thickness δr created by this vesicle-tomonomer reaction contribution and its rate constant ka+ (eq 12). We estimated ka+ by requiring that τr,m = τe at a lipid concentration of 0.75 mM, where τr,m is the reaction-enhanced time scale obtained from eqs 14 and 18 τr,m =

ij δc,m yz hmδr z tanhjjj j δ zzz Dm k r {

(21)

The resulting value, ka+ = 0.0022 s−1, then sets δr and τr,m for all conditions studied45,46 (Tables 2 and 3). Predicted values for τr,m are compared in Figure 7 to experimental τe values, in the presence and absence of stirring. The dependence of τr,m on C∞ v is weaker than that of τv for the vesicle pathway, and as a result, τr,m captured well the experimental results for C∞ v ≥0.25 mM (Figure 7a). On the other hand, this reaction-mediated mechanism underpredicted the increase in τe with decreasing lipid concentration at lower values (Figure 7b). As C∞ v is decreased, the thickness δr of the reactioncontrolled zone will eventually become larger than δc,m, allowing convection to become the controlling factor facilitating the delivery of monomer to the interface (eq 21). This switch to a convective−diffusive mechanism would cause adsorption to depend on stirring rates at sufficiently low concentrations, as explained in the theory treating ReactionEnhanced Monomer Diffusion (Vesicle-to-Monomer Transfer). As shown in Figure 7b, this effect of convection on adsorption times can in fact be discerned with τr,m for C∞ v < 0.1. However, the predicted difference for results with and without convection is small in comparison with the experimental observations, indicating that, for C∞ v < 0.1 mM, the value ka+ = 0.0022 s−1 did not allow δr to increase sufficiently to set up a strong dependence on convection. High-Concentration Region and Vesicle Diameter Effects. Our experiments indicate two concentration regimes for the adsorption kinetics: a low-concentration regime (≤0.25 mM) with a steep dependence on C∞ v and faster adsorption rates in the presence of convection; and a high-concentration region, unaffected by convection, with a weaker dependence on C∞ v .

Table 4. Estimated Reaction Film Thickness δr, Rate Constant ka+, and Predicted Characteristic Times for Transport without Convection via the Monomer (m) or Vesicle (v) Pathway, with Comparison to Measured Times τe at 295 K for various vesicle diameters dv characteristic transport time (min) unstirred (Re = 0)

reaction length scale (μm)

reaction rate constant (ms−1)

vesicle diameter dv (nm)

measured τe

predicted τD,m

predicted τD,v

predicted δr

predicted ka+

130 181 285

17 22 39

11 × 103

0.1 0.1 0.2

0.9 1.3 2.2

4.5 2.5 0.8

thickness δr from eq 18. The rate constant ka+ was then estimated from eq 12. Values for δr and ka+ for 181 and 285 nm diameter vesicles from this analysis are given in Table 4. It is interesting to compare these results to estimates made using a relationship, provided by Israelachvili,47 between molecular lifetimes in a bilayer and the lipid aqueous solubility. Based on this relationship, the effective off-rate constant for DLPC in a J


Article

Langmuir bilayer is ∼1 ms−1, which is comparable to the results we obtain. In comparing monomer release from dimyristoyl phosphatidylcholine (DMPC) 100 nm vesicles or 8 nm nanodiscs, Nakano et al.48 showed that the transfer rate increased 20-fold for this order of magnitude decrease in diameter. The change was attributed to a more constrained packing and hydrophobic edge effects in the nanodisc. Similarly, as vesicle diameter increased in our system, DLPC monomer packing may become less constrained and entropically more favorable as a result of decreased curvature. Such contributions could give rise to slower reaction rates. As the vesicle diameter was increased by ∼2.2-fold, the magnitude for ka+ predicted in Table 4 decreased more than 5-foldan effect quantitatively similar to the results for DMPC by Nakano et al.48 As discussed in the above section, the vesicle pathway seems less likely to be the mechanism for adsorption at a high concentration of 1 mM DLPC (Figure 6). However, it is worth noting that an increase in vesicle diameter would also be expected to decrease the rate of vesicle penetration into the interface, and thus to lower ki,v and increase τi,v. Low-Concentration Region. At concentrations below 0.25 mM, adsorption times were observed to decrease more rapidly with increasing C∞ v than that predicted by the reactionmediated monomer pathway (Figure 7b). This observed behavior was reasonably consistent with eqs 19 and 20 for a vesicle pathway mechanism in which the time τv scales as 1/ C∞ v . This is not to imply that there is a simple switch from a vesicle pathway alone at low C∞ v to a reaction-mediated monomer mechanism at high C∞ . Because these pathways exist v as parallel mechanisms, it is the faster (shorter adsorption time) mechanism that controls the rate at any set of conditions. Figure 7 shows that, based on the adsorption times of each pathway, the reaction-enhanced monomer mechanism (black curves) would in fact be predicted to win out at low C∞ v and the vesicle pathway (gray curves) at high C∞ v the opposite of what is needed to match the experimental results. On the other hand, the influence of convection on experimental adsorption rates at low C∞ v was captured neither by monomer or vesicle mechanisms, as indicated above. One possible explanation for the results at low [DLPC] is that, as C∞ v decreased, the reaction-mediated pathway was slowed due to vesicle transport limitations that increased the dependence of τr,m on C∞ v and on bulk transport rates. If vesicle transport is insufficiently fast, gradients in Cv develop near the interface: these reduce local rates of vesicle-to-monomer production and the overall adsorption rate through the monomer pathway. Table 2 values for τD,v demonstrate that the vesicle diffusive flux slows substantially at low lipid concentrations, and with convection introducing a very thin boundary layer region for vesicle transport (δc,v ≪ δr), convection may be able to play a significant role in influencing τr,m. Assessment of such a coupled pathway mechanism requires further exploration in future research.

from which to assess the contributions of various transport mechanisms to the experimentally measured adsorption times. Our results suggest that the formation of a monolayer may occur through one of two plausible pathways: (1) reactionmediated molecular transport of dissolved phospholipid or (2) lipid delivery by vesicles directly to the interface. The former involves a homogeneous vesicle-to-monomer reaction that has the potential to accelerate the bulk transport of the dissolved lipid molecules. The latter involves bulk transport of vesicles, followed by a step to overcome an interfacial barrier to adsorption. For DLPC concentrations of 0.25−10 mM, rates predicted by the reaction-mediated molecular pathway matched experimental observations well, whereas the vesicle pathway showed too strong a dependence on concentration. At concentrations below 0.25 mM, effects of convection were present but poorly captured using predictions for either pathway, raising the possibility of a mechanism in which vesicle transport and reaction-mediated monomer transport are coupled. Identifying an appropriate adsorption mechanism for hydrophobic surfactants has implications for a wide array of applications such as the stabilization of foams and emulsions, particle formulation in spray drying, and the design of therapeutic lung surfactants. Understanding the delivery mechanism provides information on the effect of external variables, such as convection or temperature, which can be controlled for the system of interest. The theoretical approach outlined in this article is transferable and should be useful in identifying contributing mechanisms for a variety of dispersed surfactant systems.

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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.langmuir.8b00595.

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Determination of the aqueous solubility, convective boundary layer scaling analysis, and derivation of the reaction-mediated monomer flux (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jennifer A. Staton: 0000-0002-8604-4930 Stephanie R. Dungan: 0000-0001-8420-987X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Agriculture and Food Research Initiative Competitive Grant No. 2014-67017-21831 and by Hatch project 1010420, from the USDA National Institute of Food and Agriculture. We thank Dr Tonya Kuhl for the use of her Langmuir trough.

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SUMMARY AND CONCLUSIONS Time-dependent adsorption of DLPC onto a clean air−water interface was probed using dynamic surface tension measurements to identify possible rate-controlling transport mechanisms. Experimentally, the time scale for adsorption varied inversely with vesicle concentration, depended on convection rate only at low vesicle concentrations, and increased directly with vesicle diameter. We developed a theoretical framework

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ABBREVIATIONS DLPC, dilauroyl phosphatidylcholine; LUV, large unilamellar vesicle; PDI, polydispersity index; DMPC, dimyristoyl phosphatidylcholine K


Article

Langmuir

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Adsorption of Phospholipids and Lower their Surface Tension at the Air/Water Interface. ChemPhysChem 2011, 12, 2646−2652. (23) Pinazo, A.; Wen, X. Y.; Liao, Y. C.; Prosser, A. J.; Franses, E. I. Comparison of DLPC and DPPC in Controlling the Dynamic Adsorption and Surface Tension of their Aqueous Dispersions. Langmuir 2002, 18, 8888−8896. (24) Vassilieff, C. S.; Panaiotov, I.; Manev, E. D.; Proust, J. E.; Ivanova, T. Kinetics of Liposome Disintegration from Foam Film Studies: Effect of the Lipid Bilayer Phase State. Biophys. Chem. 1996, 58, 97−107. (25) Davies, R. J.; Genghini, M.; Walters, D. V.; Morley, C. J. The Behaviour of Lung Surfactant in Electrolyte Solutions. Biochim. Biophys. Acta 1986, 878, 135−145. (26) Lewis, B. A.; Engelman, D. M. Lipid Bilayer Thickness Varies Linearly with Acyl Chain Length in Fluid Phosphatidylcholine Vesicles. J. Mol. Biol. 1983, 166, 211−217. (27) Hope, M. J.; Bally, M. B.; Webb, G.; Cullis, P. R. Production of Large Unilamellar Vesicles by a Rapid Extrusion Procedure Characterization of Size Distribution, Trapped Volume and Ability to Maintain a Membrane-Potential. Biochim. Biophys. Acta 1985, 812, 55−65. (28) Berger, N.; Sachse, A.; Bender, J.; Schubert, R.; Brandl, M. Filter Extrusion of Liposomes Using Different Devices: Comparison of Liposome Size, Encapsulation Efficiency, and Process Characteristics. Int. J. Pharm. 2001, 223, 55−68. (29) Gaines, G. On the Use of Filter Paper Wilhelmy Plates with Insoluble Monolayers. J. Colloid Interface Sci. 1977, 62, 191−192. (30) Mangiarotti, A.; Caruso, B.; Wilke, N. Phase Coexistence in Films Composed of DLPC and DPPC: A Comparison between Different Model Membrane Systems. Biochim. Biophys. Acta 2014, 1838, 1823−1831. (31) Maget-Dana, R. The Monolayer Technique: A Potent Tool for Studying the Interfacial Properties of Antimicrobial and MembraneLytic Peptides and their Interactions with Lipid Membranes. Biochim. Biophys. Acta 1999, 1462, 109−140. (32) Schwarz, G.; Taylor, S. E. Thermodynamic Analysis of the Surface-Activity Exhibited by a Largely Hydrophobic Peptide. Langmuir 1995, 11, 4341−4346. (33) Buboltz, J. T.; Feigenson, G. W. Phospholipid Solubility Determined by Equilibrium Distribution between Surface and Bulk Phases. Langmuir 2005, 21, 6296−6301. (34) Subramanyam, R.; Maldarelli, C. Fluorescence Evidence that a Phase Transition Causes the Induction Time in the Reduction in Dynamic Tension During Surfactant Adsorption to a Clean Air/Water Interface and a Kinetic-Diffusive Transport Model for the PhaseInduced Induction. J. Colloid Interface Sci. 2002, 253, 377−392. (35) Deen, W. Analysis of Transport Phenomena; Oxford University Press: New York, 1998; pp 44−47, 54−56, 58−59, 93, 93, 412−413, 424−426. (36) Thilo, L. Kinetics of Phospholipid Exchange Between Bilayer Membranes. Biochim. Biophys. Acta 1977, 469, 326−334. (37) Nichols, J. W.; Pagano, R. E. Kinetics of Soluble Lipid Monomer Diffusion Between Vesicles. Biochemistry 1981, 20, 2783− 2789. (38) Cussler, E. L. Diffusion: Mass Transfer in Fluid Systems, 2nd ed.; Cambridge University Press: New York, 2009; pp 377−378, 392−394. (39) Mitev, D. J.; Ivanova, Tz; Vassilieff, C. S. Kinetics of Lipid Layer Formation at Interfaces. Colloids Surf., B 2002, 24, 185−192. (40) Schindler, H. Exchange and Interactions between Lipid Layers at the Surface of a Liposome Solution. Biochim. Biophys. Acta 1979, 555, 316−336. (41) Wilke, C.; Chang, P. Correlation of Diffusion Coefficients in Dilute Solutions. AIChE J. 1955, 1, 264−270. (42) Small, D. M. The Physical Chemistry of Lipids: From Alkanes to Phospholipids; Plenum Press: New York, 1986; pp 479−480. (43) Peaudecerf, F. J.; Landel, J. R.; Goldstein, R. E.; Luzzatto-Fegiz, P. Traces of Surfactants Can Severely Limit the Drag Reduction of

REFERENCES

(1) Beneventi, D.; Carre, B.; Gandini, A. Role of Surfactant Structure on Surface and Foaming Properties. Colloids Surf., A 2001, 189, 65− 73. (2) Millqvist-Fureby, A.; Smith, P. In-Situ Lecithination of Dairy Powders in Spray-Drying for Confectionery Applications. Food Hydrocolloids 2007, 21, 920−927. (3) Kabalnov, A.; Tarara, T.; Arlauskas, R.; Weers, J. Phospholipids as Emulsion Stabilizers. J. Colloid Interface Sci. 1996, 184, 227−235. (4) Walters, R. W.; Jenq, R. R.; Hall, S. B. Distinct Steps in the Adsorption of Pulmonary Surfactant to an Air-Liquid Interface. Biophys. J. 2000, 78, 257−266. (5) Goerke, J. Pulmonary Surfactant: Functions and Molecular Composition. Biochim. Biophys. Acta 1998, 1408, 79−89. (6) Borden, M. A.; Longo, M. L. Dissolution Behavior of Lipid Monolayer-Coated, Air-Filled Microbubbles: Effect of Lipid Hydrophobic Chain Length. Langmuir 2002, 18, 9225−9233. (7) Kralova, I.; Sjöblom, J. Surfactants Used in Food Industry: A Review. J. Dispersion Sci. Technol. 2009, 30, 1363−1383. (8) Lasic, D. D. The Mechanism of Vesicle Formation. Biochem. J. 1988, 256, 1−11. (9) Hua, X. Y.; Rosen, M. J. Dynamic Surface Tension of Aqueous Surfactant Solutions. J. Colloid Interface Sci. 1988, 124, 652−659. (10) Chang, C. H.; Franses, E. I. Adsorption Dynamics of Surfactants at the Air/Water InterfaceA Critical Review of Mathematical Models, Data, and Mechanisms. Colloids Surf., A 1995, 100, 1−45. (11) Eastoe, J.; Dalton, J. S. Dynamic Surface Tension and Adsorption Mechanisms of Surfactants at the Air-Water Interface. Adv. Colloid Interface Sci. 2000, 85, 103−144. (12) Datwani, S. S.; Stebe, K. J. The Dynamic Adsorption of Charged Amphiphiles: The Evolution of the Surface Concentration, Surface Potential, and Surface Tension. J. Colloid Interface Sci. 1999, 219, 282−297. (13) Moorkanikkara, S. N.; Blankschtein, D. Short-Time Behavior of Mixed Diffusion-Barrier Controlled Adsorption. J. Colloid Interface Sci. 2006, 296, 442−457. (14) Song, Q.; Couzis, A.; Somasundaran, P.; Maldarelli, C. A Transport Model for the Adsorption of Surfactant from Micelle Solutions onto a Clean Air/Water Interface in the Limit of Rapid Aggregate Disassembly Relative to Diffusion and Supporting Dynamic Tension Experiments. Colloids Surf., A 2006, 282, 162−182. (15) Kabalnov, A. Ostwald Ripening and Related Phenomena. J. Dispersion Sci. Technol. 2001, 22, 1−12. (16) Kabalnov, A.; Weers, J. Kinetics of Mass Transfer in Micellar Systems: Surfactant Adsorption, Solubilization Kinetics and Ripening. Langmuir 1996, 12, 3442−3448. (17) Zhmud, B.; Tiberg, F.; Kizling, J. Dynamic Surface Tension in Concentrated Solutions of CnEm Surfactants: A Comparison between the Theory and Experiment. Langmuir 2000, 16, 2557−2567. (18) Denizot, B. A.; Tchoreloff, P. C.; Proust, J. E.; Puisieux, F.; Lindenbaum, A.; Dehan, M. Adsorption of Phosphatidylcholine Liposomes at the Air-Water-Interface. J. Colloid Interface Sci. 1991, 143, 120−126. (19) Heyn, S. P.; Egger, M.; Gaub, H. E. Lipid and Lipid Protein Monolayers Spread from a Vesicle SuspensionA Microfluorescence Film Balance Study. J. Phys. Chem. 1990, 94, 5073−5078. (20) Lawrie, G. A.; Schneider, P. B.; Battersby, B. J.; Barnes, G. T.; Cammenga, H. K. Spreading Properties of Dimyristoyl Phosphatidylcholine at the Air/Water Interface. Chem. Phys. Lipids 1996, 79, 1− 8. (21) Lee, S.; Kim, D. H.; Needham, D. Equilibrium and Dynamic Interfacial Tension Measurements at Microscopic Interfaces Using a Micropipet Technique. 2. Dynamics of Phospholipid Monolayer Formation and Equilibrium Tensions at the Water-Air Interface. Langmuir 2001, 17, 5544−5550. (22) Nguyen, P. N.; Thuan, T. T. D.; Waton, G.; Vandamme, T.; Krafft, M. P. A Nonpolar, Nonamphiphilic Molecule Can Accelerate L


Article

Langmuir Superhydrophobic Surfaces. Proc. Nat. Acad. Sci. U.S.A. 2017, 114, 7254−7259. (44) Geankoplis, C. J. Transport Processes and Separation Process Principles, 4th ed.; Pearson Education: Upper Saddle River, 2003; p 480. (45) Nichols, J. W.; Pagano, R. E. Use of Resonance Energy Transfer to Study the Kinetics of Amphiphile Transfer Between Vesicles. Biochemistry 1982, 21, 1720−1726. (46) Bayerl, T. M.; Schmidt, C. F.; Sackmann, E. Kinetics of Symmetric and Asymmetric Phospholipid Transfer between Small Sonicated Vesicles Studied by High-Sensitivity Differential Scanning Calorimetry, NMR, Electron Microscopy, and Dynamic Light Scattering. Biochemistry 1988, 27, 6078−6085. (47) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed.; Academic Press: San Diego, 1991; pp 375−377. (48) Nakano, M.; Fukuda, M.; Kudo, T.; Miyazaki, M.; Wada, Y.; Matsuzaki, N.; Endo, H.; Handa, T. Static and Dynamic Properties of Phospholipid Bilayer Nanodiscs. J. Am. Chem. Soc. 2009, 131, 8308− 8312.

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Mechanism of Time-Dependent Adsorption for Dilauroyl

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