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Langmuir 2006, 22, 8826-8830
Microscopic and Thermodynamic Properties of the HFA134a-Water Interface: Atomistic Computer Simulations and Tensiometry under Pressure Robson P. S. Peguin, Parthiban Selvam, and Sandro R. P. da Rocha* Department of Chemical Engineering and Materials Science, Wayne State UniVersity, 5050 Anthony Wayne Dr., Detroit, Michigan 48202 ReceiVed March 27, 2006. In Final Form: June 21, 2006 A combined computational and experimental approach is used to determine the interfacial thermodynamic and structural properties of the liquid 1,1,1,2-tetrafluoroethane (HFA134a)-vapor and liquid HFA134a-water (HFA134a|W) interfaces at 298 K and saturation pressure. Molecular dynamics (MD) computer simulations reveal a stable interface between HFA134a and water. The “10-90” interfacial thickness is comparable with those typically reported for organic-water systems. The interfacial tension of the HFA134a|W interface obtained from the pressure tensor analysis of the MD trajectory is in good agreement with the experimental value determined using in situ high-pressure tensiometry. These results indicate that the potential models utilized are capable of describing the intermolecular interactions between these two fluids. The tension of the HFA134a|W interface is significantly lower than those typically observed for conventional oil-water interfaces and similar to that of the compressed CO2-water interface, observed at moderate CO2 pressures. The MD and tensiometric results are also compared and contrasted with the HFA134a|W and chlorofluorocarbon-water tension values estimated from a parametric relationship. This represents the first report of the interfacial and microscopic properties of the (propellant) hydrofluoroalkanes (HFA)|W interface. The results presented here are of relevance in the design of surfactants capable of forming and stabilizing water-in-HFA microemulsions. Reverse aqueous microemulsions in HFA-based pressurized metered-dose inhalers are candidate formulations for the systemic delivery of biomolecules to and through the lungs.
Introduction The most common device for inhalation therapy is the pressurized metered-dose inhaler (pMDI). pMDIs account for approximately 65% of the total prescribed aerosols1 and generate worldwide sales in excess of $2 billion per year.2 pMDI-based formulations are, therefore, potential candidates for the systemic delivery of pharmaceutically relevant peptides, proteins, and DNA.3 However, polar moleculessincluding watershave very low solubility in hydrofluoroalkanes (HFAs), which are the ozonefriendly alternatives4 to chlorofluorocarbons (CFCs) and the propellants of choice for use in pMDIs.5 Although the operation of pMDIs with HFAs is similar to that of CFCs, previous formulations are not compatible due to the significantly different physicochemical properties between these two classes of fluids.6 For example, none of the FDA-approved surfactants commonly used in CFC formulations are soluble in HFAs.7 Aqueous reverse aggregates have been suggested as a carrier for biomolecules in pMDIs.8 However, difficulties in studying the fundamental interfacial properties of volatile propellant mixtures has hindered the development of novel, reversemicroemulsion-based pMDI formulations.9 For example, up to * Corresponding author. Phone: 313-577-4669. Fax: 313-577-3810. E-mail:
[email protected]. (1) One of the reviewers suggested that a more updated number for the pMDI participation in the market is ∼65%, compared to the 80% reported in the following reference: Courrier, H. M.; Butz, N.; et al. Crit. ReV. Ther. Drug Carrier Syst. 2002, 19, 425-498. (2) Solvay. HFA Propellants for Medical Use; Solkane 227 pharma and Solkane 134a pharma; Solvay Fluor und Derivate GmbH: Hannover, Germany, 2003; p 43. (3) Keller, M. Int. J. Pharm. 1999, 186, 81-90. (4) UNEP. Montreal Protocol on Substances That Deplete the Ozone Layer; U. N. E. Programme. UNON: Nairobi, Kenya, 2000; p 52. (5) Ashayer, R.; Luckham, P. F.; et al. Eur. J. Pharm. Sci. 2004, 21, 533-543. (6) Blondino, F. E.; Byron, P. R. Drug DeV. Ind. Pharm. 1998, 24, 935-945. (7) Byron, P. R.; Patton, J. S. J. Aerosol Med. 1994, 7, 49-75. (8) Hickey, A. J. In Inhalation AerosolssPhysical and Biological Basis for Therapy; Lenfant, C., Ed.; Marcel Dekker: New York, 1996; pp 417-436.
now, there has been no report on the most fundamental property of the bare or surfactant-modified HFA|water (HFA|W) interface, its interfacial tension (γ). Lack of such fundamental knowledge is preventing us from extending the applicability of pMDIs for the delivery of biomolecules to treat medically important diseases, including cancer, cystic fibrosis, and diabetes.1 Surface tension is a basic thermodynamic property relating to a vapor-liquid interface. There have been several reports of the surface tension of pure 1,1,1,2-tetrafluoroethane (HFA134a)10-13 and its mixtures with other refrigerant gases (R32, R125, R143a, and R152a),13 using different experimental techniques, including the differential capillary rise11-13 and surface light scattering10 methods. However, there are no experimental or computer simulation reports, as of yet, that describe the HFA|W interface and its microscopic and thermodynamic properties. The ability of computer simulations to relate molecular interactions to macroscopic bulk thermodynamic phenomena has been recently applied to hydrofluoroalkanes14-19 and their mixtures.20-23 In (9) Blondino, F. E. Ph.D. Thesis, Virginia Commonwealth University, Richmond, VA, 1995. (10) Froba, A. P.; Will, S.; et al. Int. J. Thermophys. 2000, 21, 1225-1253. (11) Higashi, Y.; Shibata, T.; et al. J. Chem. Eng. Data 1997, 42, 438-440. (12) Chae, H. B.; Schmidt, J. W.; et al. J. Chem. Eng. Data 1990, 35, 6-8. (13) Heide, R. Int. J. Refrig. 1997, 20, 496-503. (14) Lisal, M.; Budinsky, R.; et al. Int. J. Thermophys. 1999, 20, 163-174. (15) Stoll, J.; Vrabec, J.; et al. J. Chem. Phys. 2003, 119, 11396-11407. (16) Fermeglia, M.; Pricl, S. Fluid Phase Equilib. 1999, 166, 21-37. (17) Chen, K. H.; Walker, G. A.; et al. Theochem 1999, 490, 87-107. (18) Fermeglia, M.; Ferrone, M.; et al. Fluid Phase Equilib. 2003, 210, 105116. (19) Lisal, M.; Vacek, V. Fluid Phase Equilib. 1997, 127, 83-101. (20) Budinsky, R.; Vacek, V.; et al. Fluid Phase Equilib. 2004, 222-223, 213-220. (21) Galindo, A.; Gil-Villegas, A.; et al. J. Phys. Chem. B 1998, 102, 76327639. (22) Milocco, O.; Fermeglia, M.; et al. Fluid Phase Equilib. 2002, 199, 1521. (23) Gao, G. T.; Wang, W.; et al. Fluid Phase Equilib. 1999, 158-160, 6978.
10.1021/la0608157 CCC: $33.50 © 2006 American Chemical Society Published on Web 09/19/2006
Properties of the HFA134a-Water Interface
Langmuir, Vol. 22, No. 21, 2006 8827 Table 1. Lennard-Jones (LJ) Parameters and Partial Charges for HFA134a
Figure 1. (a) SPC/e water model and (b) geometry for HFA134a (MMFF94, SPARTAN’02).31
this respect, an essential point in the molecular simulation is the availability of an accurate potential model. Several authors have reported simulation studies and force field development16,17,22 for HFAs and their mixtures in an attempt to reproduce experimental PVT data, but the ability of such models in predicting the interfacial properties of HFAs has not been tested yet. In this study, we focus on the evaluation of the equilibrium microscopic and interfacial properties of the liquid HFA134a|air and liquid HFA134a-water (HFA134a|W) interfaces. To a large extent, the properties of the binary interface, including free energy density, aqueous hydrogen-bonding network, and orientation of the interfacial water molecules, dictate the interfacial activity of the adsorbed amphiphiles.24 Consequently, to design surfactants for the HFA134a|W interface, the properties of the bare interface need to be investigated first. We combine atomistic molecular dynamics (MD) computer simulations and high-pressure tensiometry to investigate the properties of the interface.
Materials and Methods Computational Model and Simulation Methodology. Molecular Models and Potentials. Water was represented by the SPC/e model.25 When accounting for the long-range electrostatic interaction with the Ewald summation technique, the SPC/e model has been shown to quantitatively describe the effect of temperature on the surface tension of pure water.26 The Lennard-Jones (LJ) parameters are σOwOw ) 3.166 Å and OwOw/kB ) 78.208 K, while the charges are qOw ) -0.8476 |e| and qHw ) +0.4238 |e|, as indicated in Figure 1a. The potential for HFA134a used in this work is similar to that reported in the literature.19 σij and ij are those from the AMBER force field.27 The fractional charges are based on the work of Yamamoto et al.28 and Davis et al.,28,29 with the C point charge being adjusted so that both CF3 and CH2F are neutral groups.19 The parameters for HFA134a are given in Table 1. Except for HW, all atoms were represented by a 6-12 LJ segment and a simple point charge, as given in eq 1:
Uij )
∑ij
{ [( ) ( ) ] σij
4ij
rij
12
-
σij rij
6
+
1 qiqj 4πo rij
}
(1)
where Uij is the potential between atoms i and j, qi and qj are the charges centered on the individual atoms, and rij is the distance between the sites i and j. σij and ij are the size and energy parameters for the LJ potential, respectively. For Hw, σij and ij are zero. Both HFA134a and water are treated as rigid bodies; (24) da Rocha, S. R. P.; Johnston, K. P.; et al. J. Phys. Chem. B 2002, 106, 13250-13261. (25) Berendsen, H. J. C.; Grigera, J. R.; et al. J. Phys. Chem. 1987, 91, 62696271. (26) Alejandre, J.; Tildesley, D. J.; et al. J. Chem. Phys. 1995, 102, 45744583. (27) Gough, C. A.; DeBolt, S. E.; et al. J. Comput. Chem. 1992, 13, 963-970. (28) Yamamoto, R.; Kitao, O.; et al. Fluid Phase Equilib. 1995, 104, 349361. (29) Davis, D. W.; Banna, M. S.; et al. J. Chem. Phys. 1974, 60, 237-245.
atom
/kB (K)
σ (Å)
q (|e|)
atom
/kB (K)
σ (Å)
q (|e|)
C1 C2
55.05 55.05
3.82 3.82
+0.90 +0.24
F H
30.70 7.55
3.50 2.58
-0.30 +0.03
i.e., there are no intramolecular degrees of freedom. This is a typical assumption made for small molecules, where the intramolecular degree of freedom represents a small contribution to the overall energy of the system.24,30 The geometry of HFA134a was minimized using SPARTAN’02,31 under the MMFF94 approximation and is shown in Figure 1b. The parameters for unlike interactions were computed using standard LorentzBerthelot combining rules given in eq 2:
1 ij ) (iijj)1/2 σij ) (σii + σjj) 2
(2)
The HFA134a potential model was tested by running a state point in the isobaric-isothermal (constant number of particles, pressure, and temperaturesNPT) ensemble and by comparing the resulting density with the experimental value obtained from REFPROP.32 Simulations were performed with a cubic box of 21 952 Å3 containing 156 molecules of the hydrofluoroalkane. Equilibration and production runs of 500 ps each were performed. The observed density, at 298 K and 20 bar, was 1.02 g‚mL-1. Under the same conditions, the experimental value of the density is 1.21 g‚mL-1. Previous works indicate that while polarizabilities might strongly affect dynamical interfacial properties and the overall dipole moment of the interfacial region,33 structural interfacial properties are not expected to be strongly influenced by polarization effects.34,35 It is also interesting to note that, in two independent investigations, while the tension reported for the CCl4|air and CCl4|W interfaces with polarizable potential models compares poorly with the experiments,33 excellent agreement was observed with nonpolarizable models.36 Moreover, there are no polarizable force fields available for HFA134a. Since the focus of this investigation is on the structural and thermodynamic aspects of the interface, less-computer-intensive, nonpolarizable models have been selected for water and HFA134a. Simulation Details. The HFA134a|air interface was modeled by placing 140 molecules in the center of a rectangular box (28 × 28 × 100 Å), giving rise to two interfaces. The initial configuration was equilibrated in the NPT ensemble, at 298 K and 1.5 MPa, for at least 1000 ps. The production runs were also carried out for at least 1000 ps in the microcanonical (constant number of particles, volume, and energysNVE) ensemble. The HFA134a|W interface was constructed by combining two cubic boxes of 21 952 Å3, one containing 156 pure HFA134a molecules and the other 735 pure water molecules. In this case, the system had two HFA134a|W interfaces. The other alternative would have been to create a system with the air|HFA134a|W|air interfaces.37 However, when using such an approach, the surface tension of HFA134a and water must be known at each condition. (30) Dang, L. X. J. Chem. Phys. 1999, 110, 10113-10122. (31) Spartan’02 Linux/UnixsTutorial and User’s Guide, version 119a; Wavefunction Inc.: Irvine, CA, 2001. (32) Lemmon, E. W.; McLinden, M. O.; et al. REFPROPsReference Fluid Thermodynamic and Transport Properties, version 7.0; NIST, 2002. (33) Chang, T.-M.; Dang, L. X. J. Chem. Phys. 1996, 104, 6772-6783. (34) Wallqvist, A. Chem. Phys. Lett. 1990, 165, 437-442. (35) Motakabbir, K. A.; Berkowitz, M. L. Chem. Phys. Lett. 1991, 176, 6166. (36) Senapati, S.; Berkowitz, M. L. Phys. ReV. Lett. 2001, 87, 176101/176101176101/176104. (37) Dominguez, H.; Berkowitz, M. L. J. Phys. Chem. B 2000, 104, 53025308.
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Previous results show that, at least for the chosen simulation box size, no interfacial correlations are expected.38 The initial Lz dimension of the HFA134a|W simulation box was chosen in order to represent the correct bulk density of water (0.998 g‚mL-1) and HFA134a (1.212 g‚mL-1), at 298 K and 15 bar.32 Periodic boundary conditions were applied in all directions. Equilibration of the HFA134a|W interface was performed in the NPT ensemble, at 298 K and 1.5 MPa, for 1000 ps. The statistics were stored for 500 ps, in the NVE ensemble. Atomistic MD simulations of the HFA134a|air and HFA134a|W interfaces were carried out in parallel, using DL_POLY version 2.13.39 Equilibration was monitored through the configurational energy (van der Waals plus Coulombic energies) in both systems. This procedure is similar to previous works on both fluid|air and fluid|fluid interfaces.37,40 Standard deviations of the ensemble averages were computed by breaking the production runs into blocks of 25 ps. The Ewald sum was used for the long-range electrostatic potential. The cutoff for van der Waals interactions and the real part of the Ewald sum was 12 Å. It has been shown that, for parallelepipeds, a minimum number of reciprocal lattice vectors are required to accurately describe the long-range electrostatic interactions.26 In this work, the minimum number of reciprocal lattice vectors was set by using an Ewald precision of 10-6. A time step of 1 fs was adopted. Bond lengths were constrained using the SHAKE algorithm. The NPT ensemble was coupled to a heat bath, through Nose´Hoover thermostat, and to a Hoover barostat with constants of 1.0 and 5.0 ps, respectively. Both surface (σHFA134a) and interfacial (γHFA134a|W) tensions were calculated with the pressure tensor equation:41
tension )
(
)
Pxx + Pyy 1 Pzz Lz 2 2
(3)
where PRR (R ) x, y, or z) is the RR element of the pressure tensor and Lz is the linear dimension of the simulation box in the z direction. The factor of 1/2 in the equation arises from the two liquid|liquid (or air) interfaces in the system. The CCl4|W interface was used to validate the methodology applied to study the HFA134a|W interface. The interfacial tension value of 41.6 ( 9 mN/m calculated in this work is in perfect agreement with the previously reported (also MD) value of 41.6 ( 11 mN/m.37 Experimental Section Materials. HFA134a (>99.99%) was a gift from Solvay fluor und Derivate GmbH & Co. 2H,3H-perfluoropentane (HPFP, 99.9%) was purchased from SynQuest Labs, Inc. HFA134a and HPFP were further purified using basic alumina, using a procedure similar to that in the literature.42 Deionized water (NANOpure DIamond UV ultrapure water system, Barnstead International), 17.6 MΩ‚cm-1, and with a surface tension of 72.9 mN/m at 298 K was used in all experiments. Interfacial and Surface Tension Measurements. The surface (σHFA134a) and interfacial (γHFA134a|W) tensions at HFA134a|air and HFA134a|water interfaces, respectively, were experimentally determined in situ using a high-pressure tensiometer. The apparatus (38) da Rocha, S. R. P.; Johnston, K. P.; et al. J. Phys. Chem. B 2001, 105, 12092-12104. (39) Forester, T. R.; Smith, W. DL-POLY Package of Molecular Simulations, version 2.13; CCLRC, Daresbury Laboratory: Daresbury, Warrington, England, 2001. (40) Rivera, J. L.; McCabe, C.; et al. Phys. ReV. E: Stat., Nonlinear, Soft Matter Phys. 2003, 67, 011603/011601-011603/011610. (41) Croxton, C. A. Statistical Mechanics of the Liquid Surface; John Wiley & Sons: New South Wales, Australia, 1980; p 345. (42) Rogueda, P. G. A. Drug DeV. Ind. Pharm. 2003, 29, 39-49.
Figure 2. Schematic diagram of the high-pressure tensiometer. is schematically represented in Figure 2. The setup consisted of a high-pressure cell equipped with two side windows that allowed for the extraction of the droplet profile and a front window for visualization of the system under pressure. Temperature was monitored directly inside the pressure cell, close to the droplet. Temperature control was attained with heating-tape wrapped around the cell and a temperature controller (Cole Parmer, EW-89000-10) to (0.4 K. The presence of an HFA134a liquid-vapor meniscus guarantees that the experiments are run at saturation conditions. However, pressure was also monitored in the front part of the pressure cell with a pressure transducer (Sensotec FP2000) to (0.7 bar. For the measurement of the γHFA|W, the system was initially filled with purified HFA134a. After equilibration of the saturated HFA134a with water, hanging drops of water were formed at the tip of a stainless steel capillary tube using a six-port injection valve (Valco Instruments). The interfacial tension was determined using the Laplace equation: ∆P ) γ
(
)
1 2γ 1 + ) + ∆Fgz R1 R2 Ro
(4)
where ∆P is the pressure difference across the interface, R0 is the radius of curvature at the apex of the drop, and z is the vertical distance from the apex.43,44 The whole droplet profile is fit to the equation above, allowing for an accurate determination of the tension (KSV CAM-200). After the injection of each drop, several pictures were taken over time. It was assumed that equilibrium was attained after the variation in γ became less than the maximum expected experimental error ((0.05 mN/m).45 The reported values represent an average of at least three measurements. Even though there is an appreciable solubility of H2O in HFA134a of ∼1200 ppm (wt) at 298 K,2 the variation in density at the conditions investigated in this work is estimated to be less than 0.02 g‚mL-1 (Phase Equilibria v 2.9.9.a)46 using the Peng-Robinson equation of state. The solubility of HFA134a in H2O is very small, about 193 ppm at 298 K.2 Its effect on the density of the aqueous-rich phase is, therefore, neglected. The densities of pure HFA134a and water,32 therefore, were used to calculate the interfacial tension. For the σHFA134a, pendant drops of purified liquid HFA134a were formed inside of the pressure cell saturated with its vapor. The remaining procedure was similar to that used to measure the γHFA134a|W.
Results and Discussions Surface Tension. The average σHFA134a obtained from the MD simulations at 301 K was 9.1 ( 3.4 mN/m. The determined tension is comparable with the experimental value of 8.1 ( 0.3 mN/m, at 298 K and saturation conditions. Both MD and experimental σHFA134a agree with the previously reported value (43) Adamson, A. W. G.; A. P. Physical Chemistry of Surfaces, 6th ed.; Wiley: New York, 1997. (44) da Rocha, S. R. P.; Harrison, K. L.; et al. Langmuir 1999, 15, 419-428. (45) Da Rocha, S. R. P. J.; Keith, P. Langmuir 2000, 16, 3690-3695. (46) Brunner, G.; Petkov, S.; et al. Phase Equilibria for Windows, version 2.9.9.a; TUHH: Hamburg, Germany, 2002.
Properties of the HFA134a-Water Interface
Langmuir, Vol. 22, No. 21, 2006 8829
of 7.7 mN/m obtained with the capillary height12 13 11 and surface light scattering10 techniques. We have also determined the σ value for HPFP, a model fluid for HFA’s.5,42 At 298 K and ambient pressure, σHPFP is 13.5 ( 0.1 mN/m. This value is in agreement with the reported value of 13.3 mN/m, under the same conditions.42 It is worth noticing that the tension for HPFP is significantly higher than that of HFA134a. Interfacial Tension. The γHFA134a|W at 298 K and saturation pressure was also determined. The pressure tensor analysis of the MD trajectories reveals a tension of 30.8 ( 10.7 mN/m. The experimental equilibrium value obtained by in situ high-pressure tensiometry at the same temperature and saturation conditions is 33.5 ( 0.3 mN/m. The observed γHFA134a|W value is lower than that of conventional alkanes (∼50 mN/m).47 The lower tension compared to alkanes can be attributed to the increased polarity of HFA134a, which arises due to the presence of both H and F in asymmetric positions in the molecule. The HFA134a|W interfacial tension is higher than for the CO2|W interface at moderate pressures, where CO2 density is liquidlike, ∼30 mN/ m.48 This is somewhat unexpected, given that HFA134a is significantly more polar than CO2 (has zero dipole).38 One possible explanation is that HFA134a molecules interact better with each other (compared with CO2 molecules) and would thus be less likely than CO2 to be favorably oriented (maximize enthalpic interactions) at the interface. Such an interplay between interfacial CO2-CO2 and water-CO2 interactions has been shown to contribute to the low tension of the CO2|W interface.38 The γ for HPFP against water was also determined at 298 K. Our value of 36.0 ( 0.1 mN/m at 298 K and ambient pressure compares well with the literature value of 35.5 mN/m,42 under the same conditions. Given the higher interfacial tension of HPFP and the significantly different structural formula compared to HFA134a, which leads to differences in polarity and dielectric behavior,42 we anticipate that candidate surfactants will behave somewhat differently at the HPFP|W and HFA134a|W interfaces. Thus, care should be exercised when using HPFP as model propellant. Preference should be given to running experiments with HFA134a in situ. Perfluorohexane has an interfacial tension of 56.4 mN/m.47 Similarly to the analysis between HFA134a and the corresponding alkanes, the lower tension of HPFP relative to perfluorohexane can be attributed to the presence of the asymmetrical F and H in the molecule. Interfacial tension values for (propellant) HFA|W or CFC|W have not been previously reported in the literature. However, it is instructive to compare and contrast the properties of the HFA|W with that of the CFC|W interface given that the FDA-approved hydrogenated surfactants have been shown to form reverse aqueous aggregates in CFCs, but not in HFAs.49-51 It has been shown that the work of adhesion between water and several immiscible organic liquids obeys a linear solvation free energy relationship, which can be summarized in a simple two-parameter equation:52
WOW ) 61.5 + 10.6 log Lw + 2.13NC
(5)
γO|W ) σW + σO - WO|W
(6)
where WO|W is the work of adhesion between the organic phase (47) Handa, T.; Mukerjee, P. J. Phys. Chem. 1981, 85, 3916-3920. (48) Hebach, A.; Oberhof, A.; et al. J. Chem. Eng. Data. 2002, 47, 15401546. (49) Evans, R. M.; Farr, S. J.; et al. Pharm. Res. 1991, 8, 629-635. (50) Evans, R. M.; Attwood, D.; et al. J. Aerosol Sci. 1989, 20, 1309-1312. (51) Evans, R. M.; Attwood, D.; et al. J. Pharm. Pharmacol. 1990, 42, 601605. (52) Freitas, A. A.; Quina, F. H.; et al. J. Phys. Chem. B 1997, 101, 74887493.
and water, σO and σW are the surface tensions of the pure organic liquid and water, respectively, γO|W is the interfacial tension, Lw is the dimensionless Ostwald coefficient for solubility of the gaseous organic compound in water, and NC is correction parameter for the chain length. Using the described correlation, with the experimental value of σHFA134a, NC ) 0 and Lw obtained from Henry’s law constant database,53 and σW ) 71.99 mN/m,32 the estimated γHFA134a|W at 298 K is 22.1 mN/m. The deviation between the estimated and the experimental γHFA134a|W is inside of the residual deviation observed for other organic liquids.52,53 The same correlation was used to obtain γ for CFCs traditionally used in medical sprays, including CFC-11 (CCl3F), CFC-12 (CCl2F2), and CFC-114 (C2Cl2F4).2 Surface tensions of 17.7, 8.6, and 10.9 mN/m, for CFC-11, CFC-12, and CFC-114, respectively, have been reported at 298 K.32 The γ estimated with the above relationships for these CFCs are 34.7, 31.9, and 39.3 mN/m. Even though the correlation described does not seem to predict the interfacial tension quantitatively, the trend of the estimated interfacial tension values shows that γHFA134a|W is smaller than those estimated for CFCs, especially for CFC-114, which shows a similar structural formula to the hydrofluoroalkane in question. The higher dipole moment of HFA134a of 2.06 D2 is expected to play an important role in decreasing the interfacial tension of the propellant against water. CFC-11, -12, and -114 present dipole moments of 0.45, 0.51, and 0.66 D,2 respectively, and thus the larger γ values. Aggregate formation is favored at lower tension values.24 The lower tension of the bare HFA|W interface (compared to CFC|W) suggests that even lower surfactant coverages can be sufficient to form such aggregates in HFAs. However, no hydrogenated amphiphile has been shown to form such reverse aggregates in HFAs, indicating a mismatch between surfactant tail-group and the properties of the hydrofluorinated propellants.9 Understanding such interactions is key to the design of amphiphiles for the HFA|W interface. Previous surfactants used to stabilize suspended drugs in CFC formulations are not soluble in HFAs.54 Also, recent studies have shown limited success in forming and stabilizing water-in-HFA134a microemulsions, even with fluorinated amphiphiles.55-57 Since the behavior of the amphiphiles at the HFA134a|W interface depends, to a large extent, on the interfacial properties of the bare interface, it is paramount to determine the thermodynamic and microstructural characteristics of the HFA propellant-water system. Microscopic Properties of the HFA134a|W Interface. Figure 3 is a snapshot from an equilibrium MD configuration (close-up of the interface) of the HFA134a|W interface. A stable interface is indicative of the appropriateness of the chosen potential models for HFA134a and water. Protrusions of water into HFA134a and vice-versa can be qualitatively observed. The roughness of the overall interface can be attributed to thermal capillary waves.33,58,59 The equilibrium density profiles for the HFA134a and water interface are shown in Figure 4 as a function of the z coordinate, which is normal to the interface. The center of mass density profiles was obtained from the average over 500 ps in the NVE ensemble. As evident in the figure, there is a stable interface, and (53) Sander, R. Compilation of Henry’s Law Constants for Inorganic and Organic Species of Potential Importance in EnVironmental Chemistry; http:// www.mpch-mainz.mpg.de/∼sander/res/henry.html, 1999; Vol. 3, p 107. (54) Williams, R. O., III; Liu, J. Eur. J. Pharm. Sci. 1999, 7, 137-144. (55) Patel, N.; Marlow, M.; et al. J. Colloid Interface Sci. 2003, 258, 345353. (56) Steytler, D. C.; Thorpe, M.; et al. Langmuir 2003, 19, 8715-8720. (57) Patel, N.; Marlow, M.; et al. J. Colloid Interface Sci. 2003, 258, 354362. (58) Linse, P. J. Chem. Phys. 1987, 86, 4177-4187. (59) Benjamin, L. J. Chem. Phys. 1992, 97, 1432-1445.
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Figure 3. Snapshot of an equilibrium configuration of the HFA134a|water interface at 298 K.
is determined as the distance along the interface over which the density changes from a value of 10% to 90% of the water bulk density.40 The interfacial width of an organic-water system is known to be significantly affected by the polarity of the organic phase.62 The HFA134a|W interface shows a “10-90” thickness of 5.2 Å. This value is close to that of the n-alkane|W systems (γ ) ∼50 mN/m), 5.0 Å,40 and the value determined in this work for CCl4|W (γ ) 41.6 ( 9 mN/m), 4.9 Å. Indeed, as the polarity increases from alkanes and CCl4 to HFA143a, an increase in interfacial width is observed. This increase correlates with a decrease in tension, as dictated by capillary wave theory.41 Systems with low γ are, therefore, expected to protrude more into each other’s phase, as can be qualitatively observed in Figure 3. One would expect that any parameter that represents well such protrusions should be able to capture this correlation with tension. Despite following the correct trend, the “10-90” thickness is a slowly varying parameter with tension, at least within the range of tension investigated. It should be noted that the thickness definition applied in the above-mentioned studies (and this investigation as well) uses a space-fixed definition for the interface position. This induces an artificial smoothing of the density profile, which limits the discrimination between the different systems on the basis of such measurement as the “1090” thickness. To obtain a more revealing time average picture of the interfacial density profile, a dynamic local interface definition can be utilized.38,63
Conclusions
Figure 4. The z-dependent density profile for the HFA134a|W interface, at 298 K. The circles represent the hyperbolic tangent fit to the water profile, as described in the text.
the bulk HFA134a and water are well-separated, which indicates that the potential models are capable of describing the intermolecular interactions. The density profile of water is smooth and fast-decaying, while that of HFA134a exhibits some oscillations. The oscillations may be due to the smaller number of hydrofluoroalkane molecules used in the simulation as compared to that of water, and/or due the relatively short simulation time.36 Similar oscillations were previously reported in CCl4|W studies.33,36 The density profile of the interfacial region is typical of organic|W (O|W) systems, showing a sharp but smooth transition from one liquid phase to the other.33,59 The water density profile can be fitted into a hyperbolic tangent functional form:
[
( )]
z - zwo 1 o Fw ) Fw 1 + tanh 2 w
(7)
where Fwo is the water bulk density, zwo is the position of the Gibb’s dividing surface, and w is an estimate of the interfacial width. The average HFA134a and water densities correspond to 1.123 and 1.045 g‚mL-1, respectively. The experimental bulk density of water at 298 K and saturation conditions is 1.000 g‚mL-1.32 The experimental density for HFA134a, under the same conditions, is 1.202 g‚mL-1.32 Its average density can be affected by the oscillations showed previously in the profile due to the small number of molecules and/or the limitations of the potential model. The so-called “10-90” thickness,60 t, of a hyperbolic tangent is mathematically related to w by t ) 2.197w.61 The thickness
The thermodynamic and structural properties of the HFA134a|air and HFA134a|W interfaces were investigated using atomistic molecular dynamics computer simulations and in situ high-pressure tensiometry. This work is the first report of the interfacial tension and microstructural properties of the HFA134a|W interface. The γHFA134a|W of 30.8 mN/m is observed to be lower than that for alkanes. The lower tension is attributed to the increased polarity of HFA134a. The interfacial tension results for HPFP suggest that care should be exercised when using this hydrofluoroalkane as a model propellant system for HFA propellants. Agreement between the calculated and the experimental surface and interfacial tension values suggests that the chosen potential models are capable of reasonably describing the HFA134a and water molecular interactions. As indicated by the z-density profile, a stable HFA134a|W interface can be attained using the chosen potential models. The HFA134a|W interface shows a “10-90” thickness of 5.2 Å, larger than the less polar alkanes and CCl4, in agreement with capillary wave theory. Accurate description of the interfacial properties of the bare interface will help guide the design of surfactants capable of forming and stabilizing reverse aqueous aggregates in HFA propellants. Such pMDI-based formulations are candidate systems for the systemic delivery of biomolecules to and through the lungs. Acknowledgment. We thank WSU for start-up funds and a Ph.D. assistantship for R.P. P.S. acknowledges a Thomas C. Rumble Fellowship. We also thank Solvay fluor und Derivate GmbH & Co., Hannover, Germany, for the HFA134a samples and GRID/WSU for computer time. LA0608157 (60) Sides, S. W.; Grest, G. S.; et al. Phys. ReV. E: Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 1999, 60, 6708-6713. (61) Chapela, G. A.; Saville, G.; et al. J. Chem. Soc., Faraday Trans. 2 1977, 73, 1133-1144. (62) Benjamin, I. Annu. ReV. Phys. Chem. 1997, 48, 407-451. (63) Fernandes, P. A.; Cordeiro, M. N. D. S.; et al. J. Phys. Chem. B 1999, 103, 8930-8939.
