Letter pubs.acs.org/Langmuir
Pressure Reentrant Assembly: Direct Simulation of Volumes of Micellization Bin Meng and Henry S. Ashbaugh* Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, Louisiana 70118, United States ABSTRACT: Surfactants exhibit maxima in their critical micelle concentrations upon application of hydrostatic pressure, which is attributable to changes in their volumes of micellization from positive to negative values with increasing pressure. We present a direct molecular simulation analysis of the volumes of micellization of an anionic, cationic, and nonionic surfactant in aqueous solution at pressures up to 2500 bar. Excellent agreement with experiment is observed. A Kirkwood−Buff theory analysis based on proximal solvent distributions permits the breakdown of the volumes of micellization into constituent surfactant headgroup and tailgroup contributions. Although the micellization volume crossover is analogous to the transfer of an alkane from water to its pure liquid, significant differences are observed, including lower compressibilities of micelle volumes compared to that of the alkane liquid, negative partial compressibilites for anionic sulfated surfactant monomers, and large nonionic ethoxy headgroup contributions to the micellization volume.
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INTRODUCTION Pressure presents an orthogonal variable to temperature with which to tune phase separation and self-assembly in aqueous solution. Despite being thermodynamic peers, the comparative scarcity of experimental data exploring pressure compared to temperature reflects the difficulty of controlling pressure over a broad enough range to provoke appreciable state changes. Perhaps the earliest pressure-dependent assembly studies examined pressure-induced protein denaturation.1−4 Thermodynamically, protein unfolding with increasing pressure is associated with negative volumes of denaturation, although theoretical considerations indicate the potential for denaturation under tension because of sign changes in the volume of denaturation with decreasing pressure.5,6 Similar to proteins, starting from ambient conditions surfactant critical micelle concentrations (cmc’s) increase with increasing pressure as a result of negative volumes of disassembly (positive volumes of micellization) (Figure 1).7−10 A difference compared to proteins, however, is that surfactant cmc’s pass through a maximum at ∼1000 bar with increasing pressure, allowing micelles to form more readily, which is so-called pressurereentrant micellization. When an analogy is drawn between micelle formation and phase separation, comparable pressurereentrant behavior has been observed for thermoresponsive polymers such as poly(N-isopropylacrylamide) in aqueous solution.11 A conclusion drawn from the analysis of the coil− globule transition of thermoresponsive polymers using a model originally developed to examine protein folding is that the synthetic polymers exhibit an inverted free energy in the temperature−pressure plane compared to that of proteins.12 Technologically, pressure-dependent micelle assembly can impact surfactant efficacy in applications such as the dispersant remediation of deep-sea oils spills where the pressure dramatically varies from the sea floor to the water surface.13 © 2013 American Chemical Society
Figure 1. Simulation snapshots of nonionic micelles and monomers of C10E5 in water with increasing pressure. Experimentally, micelles are favored at low pressure. With increasing pressure to ∼1000 bar, Le Chatlier’s principle shifts the assembly equilibrium toward monomeric surfactants as a result of positive volumes of assembly. With further increases in pressure to 2500 bar, the volume of assembly changes sign and the equilibrium shifts back in favor of micellization. In these images, carbon is cyan, hydrogen is white, and oxygen is red. The surfactant ethoxy headgroup is identified with the oxygen-rich half of the surfactant, whereas the tailgroup has no oxygen units. The solvating water molecules have been deleted from these images for clarity.
The connection between a maximum in the cmc and the volume of micellization can be established through the free energy. If we assume an effectively infinite aggregation number, then the micellization free energy from the phase separation model of surfactant aggregation is ΔG̅ mic = RT(1 + β)ln cmc, where β is the fraction of charged surfactants neutralized by bound counterions and RT is the product of the gas constant and temperature.7,10 The response to changes in pressure subsequently is Received: July 22, 2013 Revised: August 9, 2013 Published: August 9, 2013 14743
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Figure 2. Partial molar volumes and volumes of micellization for surfactants and alkanes directly evaluated from molecular simulations at 300 K as a function of pressure. Panels a−d report partial molar volumes of monomers in aqueous solution and in the micellized (or pure alkane) state. The symbol legend in a indicates the results for the monomeric (mono) and micellized (mic) simulations for a−d. Results for SDeS, DeTAB, C10E5, and nonane are reported in a−d, respectively. Panels e−h compare volumes of association, determined as the difference between partial molar volumes in the micellized (or pure alkane) and monomeric states (eq 1), evaluated from simulation and experiment. The symbol legend in e indicates the results from simulation (sim) and experiment (expt) for e−h. Results for SDeS, DeTAB, C10E5, and nonane are reported in e−h, respectively. Panels e and f compare available experimental results for SDeS and DeTAB reported by Tanaka et al.,7 we were unable to locate results for C10E5 and nonane. In the case of C10E5 (g), we compare simulation with the experiments of Lesseman et al.8 for the shorter pentaethylene glycol monooctyl ether, C18E5. Simulation error bars indicate one standard deviation.
∂ΔG̅mic ∂P
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= ΔVmic ̅
Isothermal−isobaric (NPT) molecular dynamics simulations20 were performed using GROMACS 4.21 The temperature and pressure were maintained using a Nosé-Hoover thermostat20 and a ParrinelloRahman barostat,22 respectively. Pressures of 1, 500, 1000, 1500, 2000, and 2500 bar were simulated at 300 K. Water was modeled using the TIP4P-EW potential,23 whereas surfactants and n-nonane were modeled using the generalized Amber force field.24 The simulated surfactants were anionic sodium decylsulfate (SDeS, formula C 10 H 21 SO 4 − Na + ), cationic decyltrimethylammonium bromide (DeTAB, formula C10H21N(CH3)3+Br−), and nonionic pentaethylene glycol monodecyl ether (C10E5, formula C10H21(OCH2CH2)5OH). Tail lengths were set to 10 carbon units, and micelle aggregation numbers were fixed at 40, the experimental aggregation numbers of SDeS and DeTAB,25 to facilitate comparison between surfactants. Simulations of hydrated monomers included approximately 1000 waters, whereas 5000 to 10000 waters were included in the micelle simulations, which was sufficient for a minimum of a 24 Å separation between periodic micelle surface images. Simulations of 500 waters and 100 nonanes were conducted to characterize the pure solvents. Nonbonded Lennard-Jones interactions were truncated beyond 10 Å, while particle mesh Ewald summation was used to evaluate long-range electrostatic interactions.20,21 Bonds involving hydrogen were constrained using the LINCS algorithm.21 A 2 fs time step was used to integrate the equations of motion. After equilibration for at least 10 ns, thermodynamic averages were evaluated over 40 ns. Partial molar volumes were evaluated two different ways. In the direct method, the surfactant partial molar volume V̅ i (i = monomeric or micellized surfactant) is approximated by the finite difference
T
= Vmic ̅ − Vmono ̅ = RT (1 + β)
∂ ln cmc ∂P
T
COMPUTATIONAL METHODS
(1)
where the volume of micellization, ΔV̅ mic, is the difference between the surfactant partial molar volumes in the micellar (mic) and monomeric (mono) states, whereas a constant counterion binding fraction has been assumed. It follows that reentrant micellization results from ΔV̅ mic changing from positive to negative with increasing pressure, with the cmc extremum at ΔV̅ mic = 0. Although a number of simulation studies have examined the effects of pressure on hydrophobic interactions and protein denaturation14−18 to gain molecular insight into the counterintuitive “unfolding upon squeezing”, we found only a single simulation study of the pressure response of surfactant assembly.19 This simulation demonstrated that micellar cores are more compressible than proteins. Here we report volumes of micellization for anionic, cationic, and nonionic surfactants directly evaluated from molecular simulations that agree with experimentally reported values. Our simulations capture the differential compressibilites of the monomeric and assembled surfactants, and we trace pressure-reentrant micellization to hydrophilic headgroup and hydrophobic tailgroup contributions via Kirkwood−Buff theory analysis.
Vi̅ ≈ 14744
⟨V ⟩Nw + nagg − ⟨V ⟩Nw nagg
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Figure 3. Division of surfactant micellization volumes between headgroup and tailgroup contributions as evaluated from Kirkwood-Buff theory (eq 4) at 300 K as a function of pressure. The symbol legend to the right indicates the Kirkwood-Buff results for the total, headgroup, and tailgroup contributions to the volume as well as the volumes determined directly from simulation (Figure 2e−g). Results for SDeS, DeTAB, and C10E5 are reported in a−c, respectively. Error bars indicate one standard deviation. where the brackets indicate NPT averages evaluated with Nw pure waters or a solution of Nw waters and nagg surfactants. For surfactant monomers, nagg = 1, and for micelles, nagg = 40, the aggregation number assuming all of the surfactants are micellized. We observed negligible monomer disaggregation during our micelle simulations confirming this assumption. Alternatively, we evaluated surfactant partial molar volumes from Kirkwood-Buff (KB) theory starting from the expression26
∫V [1 − gi(r)] dr
Vi̅ = RTκ +
subdomains for the micellized surfactants, except that each integration subdomain is divided by the aggregation number to evaluate the volume of an individual surfactant.
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RESULTS AND DISCUSSION Simulation results for the surfactant partial molar volumes at infinite dilution in water and in the micellar state as a function of pressure are reported in Figure 2a−c. At ambient pressure, the partial molar volumes of the micellized surfactants are greater than those of their monomers (i.e., assembly expands the solution). With increasing pressure, the micellized surfactant volumes generally decrease, and the monomer solution volume behaviors are more diverse. For example, whereas the volume of monomeric C10E5 weakly decreases with pressure, the volume of SDeS increases with increasing pressure, displaying a negative partial compressibility (i.e., −∂V̅ mono/∂P|T < 0). Whereas the expansion of a hydrated solute with increasing pressure is curious, negative partial compressibilities have been reported for sodium alkylsulfate monomers in aqueous solution7 and are attributable to electrostriction effects. 28 The DeTAB monomer volume, however, is independent of pressure within the simulation error, whereas experiments indicate a slightly positive compressibility.7,28 We attribute the weaker pressure dependence of the partial molar volume of the cationic surfactant to the presence of nonpolar methyl groups enshrouding the quaternary ammonium head of DeTAB compared to the electronegative oxygens surrounding the sulfur head of SDeS, resulting in less favorable hydration of DeTAB. Despite differences in detail for the monomer volume pressure dependencies, the volumes of the micellized surfactants ultimately cross those of the hydrated monomers at pressures ranging from 1500 to 2000 bar as a consequence of the larger micelle compressibilities. Taking the surfactant partial molar volume difference between the micellar and monomeric states (eq 1), the volumes of micellization change sign from positive to negative with increasing pressure (Figure 2e−g) and cross the x axis at the point where the partial molar volumes cross. Experimental results for the volumes of micellization are directly compared with simulation in Figure 2e−g as well. Although we were unable to find experimental data for C10E5, we compare our simulations with reported micellization volumes for C8E5 whose alkyl tail group is only two carbon units shorter than the simulated surfactant.8 Generally good agreement is observed between the simulated and experimental volumes of micellization. The largest discrepancy with experiment is observed for SDeS (Figure 2e), where the simulation volumes are shifted
(3)
where κ is the pure solvent isothermal compressibilitiy, gi(r) is the solvent/solute pair correlation function, and the integration domain V is the total system volume. Although the integral in eq 3 is typically performed by assuming that the pair correlation function is isotropic, this is not required. When the 3D distribution of water is interrogated about molecular solutes in water, the KB expression can be broken down into surfactant headgroup and tailgroup contributions by dividing the integration domain into two nonoverlapping subdomains determined by the regions of space closest (proximal) to a heavy atom , or tailgroup, Vtail on either the headgroup, Vhead i i , alone, averaged over surfactant configurations.27 Although the tailgroup heavy atoms consist of alkyl carbons for the surfactants studied here, the headgroup heavy atoms include not only the heavy atoms bonded to the tailgroup but the surfactant counterion as well in the case of ionic surfactants. For ionic surfactants, a second RTκ should be included in the partial molar volume calculation to account for the counterion’s ideal contribution. Assuming the micelle can be treated as a composite entity at infinite dilution and that the pure solvent and mixture compressibilities cancel, we can express the micellization volume as head tail ΔVmic ̅ = ΔV̅mic + ΔV̅mic
∫V
≈{
head mic
∫V
+{
[1 − gmic(r)] dr −
tail mic
∫V
[1 − gmic(r)] dr −
head mono
∫V
[1 − gmono(r)] dr}head
tail mono
[1 − gmono(r)] dr}tail (4)
where the first and second integral groupings on the right-hand side of the equation represent the headgroup and tailgroup contributions, respectively. Although the evaluation of the integrals in eq 4 following the proximity criteria is discussed in detail in ref 27, we briefly summarize the approach used here. For the monomeric surfactant, each water oxygen from individual simulation snapshots is sorted on the basis of whether it is closest to either a headgroup or tailgroup heavy atom to evaluate the proximal correlation functions in each subdomain, whereas the integration subdomains are evaluated by following a Monte Carlo procedure by randomly inserting points within simulation snapshots and determining whether they are closest to a headgroup or tailgroup heavy atom. A similar procedure is followed to evaluate the correlation functions and integration 14745
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upward from experiment by ∼5 mL/mol, resulting in the predicted maximum in the cmc being shifted approximately 500 bar higher. Nevertheless, the experimental and simulated volumes of micellization are nearly parallel over the simulated pressure range, indicating that the simulations accurately capture assembly compressibilities. Assuming that the aggregation of surfactant tailgroups to form a micelle is analogous to the transfer of an alkane chain from water to an organic liquid, we have evaluated the volumes of nonane in water and in pure nonane (Figure 2d). As for surfactants, at ambient pressure, nonane has a larger partial molar volume in the liquid phase than in water. Moreover, pure liquid nonane is significantly more compressible than the alkane in water, resulting in the transfer volume changing signs at 2000 bar (Figure 2h). Although qualitatively similar to the volumes observed from pressure-reentrant micellization, important differences lie between these two processes. For example, whereas the molar volume of pure liquid nonane decreases by ∼22 mL/mol over the pressure range studied (Figure 2d), neither of the ionic surfactant micelles exhibit as significant a volume decrease (Figure 2a,b). Specifically, the volumes of SDeS and DeTAB drop by 7 and 10 mL/mol, respectively, over the simulated pressure range. The ionic micelle partial compressibilities are significantly less than that of pure nonane. The volume change for the micellized nonionic surfactants, however, is comparable to that of pure nonane, although less on a monomer volume percent basis. These observations suggest ionic headgroup/headgroup repulsion on the micelle surface resists compression. The surfactant headgroup and tailgroup micellization volumes evaluated using KB theory (eq 4) are presented in Figure 3. Although statistically more uncertain, the total micellization volumes evaluated from eq 4 are in quantitative agreement with those determined by the direct simulation volume differences. For the ionic surfactants (Figure 3a,b), the headgroup contributions to the volume of micellization nearly cancel over the simulated pressure range, indicating the ionic headgroups are similarly hydrated in the monomeric and assembled states. The tailgroups resultantly dominate the ionic surfactant micellization volumes, and the crossover from positive to negative values of the micellization volume approximately coincides with the tailgroup contribution. As a difference from the ionic surfactants, the ether headgroup of C10E5 makes a significant contribution to its micellization volume. In particular, the nonionic surfactant headgroup volume is positive and comparable to the total micellization volume at ambient pressure and subsequently decreases with increasing pressure to near zero at 2500 bar, consistent with small-angle neutron-scattering experiments indicating ethoxy headgroup dehydration with pressurization.29 The C10E5 tailgroup contribution is shifted downward relative to those of the ionic surfactants, crossing zero at pressures in the range of 500 to 1000 bar. Adding the nonionic headgroup and tailgroup association volumes results in a crossover in the total volume at pressures near 1500 bar. The larger contribution of the C10E5 headgroup to the micellization volume crossover suggests significant changes in the headgroup structure with increasing pressure. A visual inspection of nonionic micelle simulation snapshots at 1 and 2500 bar (Figure 1) reveals that the ethoxy headgroups appear to extend further out into solution at low pressure than at elevated pressure. The headgroup and tailgroup heavy-atom density distributions relative to micelle centers of mass (Figure
4) for the ionic and nonionic surfactants compare qualitatively, with similarly sized hydrophobic cores and headgroup corona
Figure 4. Surfactant headgroup and tailgroup heavy-atom density distributions as a function of distance from the micelle center of mass. Results for SDeS, DeTAB, and C10E5 reported in a−c, respectively. The symbol legend indicates the headgroup and tailgroup densities at 1 and 2500 bar.
placements. The micelle cores of each surfactant slightly contract and densify with increasing the pressure whereas the maximum in the headgroup densities simultaneously shrinks to smaller radii, consistent with micelle compression. The most significant apparent differences in the headgroup density distributions occur for C10E5, with the headgroup peak density increasing by ∼12% over the simulated pressure range (Figure 4c). If the KB integral, eq 3, had been recast following the micelle center-of-mass distribution rather than the proximity criteria used in eq 4, it would not be possible to parse the assembly volume into individual group contributions. As a result, the correlation between the relative peak density increase in the nonionic surfactant (Figure 4c) to the greater pressure response of the nonionic headgroup micellization volume (Figure 3c) compared to the ionic surfactants is only qualitative.
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CONCLUSIONS We have demonstrated that molecular simulations accurately capture reentrant micellization for a range of surfactants with varying headgroup functionalities as encapsulated by the positive-to-negative sign change in the volumes of micellization with increasing pressure. Although this crossover results in large part from the greater compressibility of the aggregated surfactants compared to that of monomers, analogies between alkane transfer from water to the alkane liquid capture only part of the picture, and surfactant headgroup chemistry plays a role in determining the assembly’s response to pressure perturbations. Notably, micelle compressibilites were shown to be muted relative to that of the liquid alkane; the partial molar 14746
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(13) Thibodeaux, L. J.; Valsaraj, K. T.; John, V. T.; Papadopoulos, K. D.; Pratt, L. R.; Pesika, N. S. Marine oil fate: knowledge gaps, basic research, and development needs; a perspective based on the Deepwater Horizon Spill. Environ. Eng. Sci. 2011, 28, 87. (14) Payne, V. A.; Matubayasi, N.; Murphy, L. R.; Levy, R. M. Monte Carlo study of the effect of pressure on hydrophobic association. J. Phys. Chem. B 1997, 101, 2054. (15) Paschek, D.; Nonn, S.; Geiger, A. Low-temperature and highpressure induced swelling of a hydrophobic polymer-chain in aqueous solution. Phys. Chem. Chem. Phys. 2005, 7, 2780. (16) Sarupria, S.; Ghosh, T.; García, A. E.; Garde, S. Studying pressure denaturation of a protein by molecular dynamics simulations. Proteins: Struct., Funct., Bioinf. 2010, 78, 1641. (17) Okumura, H. Temperature and pressure denaturation of chignolin: folding and unfolding simulation by multibaric-multithermal molecular dynamics method. Proteins: Struct., Funct., Bioinf. 2012, 80, 2397. (18) Grigera, J. R.; McCarthy, A. N. The behavior of the hydrophobic effect under pressure and protein denaturation. Biophys. J. 2010, 98, 1626. (19) Pereira, B.; Jain, S.; Sarupria, S.; Yang, L.; Garde, S. Pressure dependence of the compressibility of a micelle and a protein: insights from cavity formation analysis. Mol. Phys. 2007, 105, 189. (20) Frenkel, D.; Smit, B. Understanding Molecular Simulation: From Algorithms to Applications, 2nd ed.; Academic Press: San Diego, 2001. (21) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation. J. Chem. Theor. Comput. 2008, 4, 435. (22) Parrinello, M.; Rahman, A. Polymorphic transitions in single crystals: a new molecular dynamics method. J. Appl. Phys. 1981, 52, 7182. (23) Horn, H. W.; Swope, W. C.; Pitera, J. W.; Madura, J. D.; Dick, T. J.; Hura, G. L.; Head-Gordon, T. Development of an improved four-site water model for biomolecular simulations: TIP4P-Ew. J. Chem. Phys. 2004, 120, 9665. (24) Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and testing of a general Amber force field. J. Comput. Chem. 2004, 25, 1157. (25) Tamoto, Y.; Segawa, H.; Shirota, H. Solvation dynamics in aquoeus anionic and cationic micelle solutions: sodium alkyl sulfate and alkyltrimethylammonium bromide. Langmuir 2005, 21, 3757. (26) Kirkwood, J. G.; Buff, F. P. The statistical mechanical theory of solutions. 1. J. Chem. Phys. 1951, 19, 774. (27) Sangwai, A. V.; Ashbaugh, H. S. Aqueous partial molar volumes from simulation, and individual group contributions. Ind. Eng. Chem. Res. 2008, 47, 5169. (28) Mathieson, J. G.; Conway, B. E. Partial molal compressibilities of salts in aqueous solution ans assignment of ionic contributions. J. Soln. Chem. 1974, 3, 455. (29) Lesemann, M.; Nathan, H.; DiNola, T. P.; Kirby, C. F.; McHugh, M. A.; van Zanten, J. H.; Paulaitis, M. E. Self-assembly at high pressures: SANS study of the effect of pressure on microstructure of C8E5 micelles in water. Ind. Eng. Chem. Res. 2003, 42, 6425. (30) Roche, J.; Caro, J. A.; Norberto, D. R.; Barthe, P.; Rouestand, C.; Schlessman, J. L.; García, A. E.; Garcia-Moreno, B.; Royer, C. A. Cavities determine the pressure unfolding of proteins. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 6945.
volumes of the monomeric alkyl sulfate surfactant were observed to increase with increasing pressure (i.e., a negative partial compressibility) with respect to the difference in hydrated alkanes, and dehydration of the nonionic surfactant ethoxy headgroup was shown to play a significant role in the volume of micellization. Although micelle heavy-atom centerof-mass density distributions are consistent with micelle compression with increasing pressure, these distributions lack sufficient detail to apportion assembly volumes to the constituent surfactant groups. Partitioning the water distribution about micelles and monomers based on the solvent’s proximity to the headgroups and tailgroups, however, allows the various contributions to the volume of micellization to be evaluated via a group-based KB analysis. The framework developed herein is extendable to examining volumes of assembly for a wider range of systems and may find its greatest utility applied to volumes of denaturation by locating internalized protein cavities30 via KB analysis.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We gratefully acknowledge financial support from the Gulf of Mexico Research Initiative and computational support from the Louisiana Optical Network Initiative.
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REFERENCES
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