Langmuir 2007, 23, 1815-1823
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On the Dissolution of Vapors and Gases N. Wu¨stneck,*,†,‡ R. Wu¨stneck,† U. Pison,† and H. Mo¨hwald‡ Anaesthesiologie, Charite´ Campus Virchow-Klinikum, Humboldt-UniVersita¨t Berlin, AugustenburgerPlatz 1, 13344 Berlin, Germany, and Max-Planck-Institut fu¨r Kolloid- und Grenzfla¨chenforschung, 14424 Potsdam, Germany ReceiVed August 3, 2006. In Final Form: NoVember 3, 2006 The captive bubble technique in combination with axisymmetric drop shape analysis (ADSA-CB) and with micro gas chromatography is used to study the dynamics of dissolution of different gases and vapors in water in situ. The technique yields the changes in the interfacial tension and bubble volume and surface. As examples, the dissolution of methanol and hexane vapors, inhaled anesthetic vapors, and gases, that is, diethyl ether, chloroform, isoflurane, enflurane, sevoflurane, desflurane, N2O, and xenon, and as nonimmobilizers perfluoropentane and 1,1,2-trichloro1,2,2-trifluoro-ethane (R113) were investigated. The examination of interfacial tension-time and bubble volumetime functions permits us to distinguish between water-soluble and -insoluble substances, gases, and vapors. Vapors and gases generally differ in terms of the strength of their intermolecular interactions. The main difference between dissolution processes of gases and vapors is that, during the entire process of gas dissolution, no surface tension change occurs. In contrast, during vapor dissolution the surface tension drops immediately and decreases continuously until it reaches the equilibrium surface tension of water at the end of dissolution. The results of this study show that it is possible to discriminate anesthetic vapors from anesthetic gases and nonimmobilizers by comparing their dissolution dynamics. The nonimmobilizers have extremely low or no solubility in water and change the surface tension only negligibly. By use of newly defined molecular dissolution/diffusion coefficients, a simple model for the determination of partition coefficients is developed.
Introduction Dissolution processes are ubiquitous. The dissolution of vapors and gases is one of the most important processes in various fields of biology and the chemical industry, stimulating intensive ongoing research activities in this area. In particular, the solubility of drugs influences their absorption, transport, and release and is a key determinant of their delivery in the body.1 Dissolution is usually a dynamic process that is connected with a mass transfer across a phase boundary. The classical approach to studying dissolution is to bring two phases into contact and to follow the mass transfer. This may be very timeconsuming as in most cases the equilibrium does not appear rapidly. Therefore, different methods have been developed to accelerate the process of dissolution and to strive only for the maximum amount of dissolved substances at equilibrium, neglecting the kinetics of the process. Intensive mixing of two phases, however, may lead to oversaturated systems, especially when a large amount of mechanical energy is applied to force the dissolution. Instead of equilibrium, the system may be forced into different steady states, which is not desirable. The subject of our investigation is the kinetics of the dissolution process. It is a matter of common knowledge that the dissolution of one phase in another one is connected with the interfacial tension change at the interface between the two phases. However, it is not known in detail how this surface tension change takes place, and few experimental data are available. Up to now it has not been possible to predict the entire process of dissolution, although there are many results concerning the solubility of hydrophobic organic substances and drugs in water, including mathematical concepts to determine the solubility parameters.2,3 * Corresponding author. E-mail:
[email protected]. † Humboldt-Universita ¨ t Berlin. ‡ Max-Planck Institut fu ¨ r Kolloid- und Grenzfla¨chenforschung. (1) Abraham, M. H.; Le, J. J. Pharm. Sci. 1999, 88, 868. (2) Yaffe, D.; Cohen, Y.; Espinosa, G.; Arenas, A.; Giralt, F. J. Chem. Inf. Comput. Sci. 2001, 41, 1177.
The shortcomings of several theoretical predictions of solubility of hydrophobic substances in water result from the use of the only moderately large available pool of data gained by modern experimental methods. To achieve better models for such predictions, using experimental data acquired with modern methods can be very useful. In the present study a new method will be introduced to investigate dissolution processes of gases and vapors in liquids, which is based on the captive-bubble surfactometer. This device has been developed only in the past 15 years.4-6 Originally it was used to investigate adsorption processes of pulmonary surfactants by measuring the interfacial tension. A step forward was the adaptation of axisymmetric drop shape analysis to the bubble problem, yielding the ADSA-CB technique, which describes the bubble profile comprehensively.7 Meanwhile, the field of application of this device has been greatly extended. It was found to be applicable to study monolayers, using the method as a kind of micro-film balance,8,9 not only to characterize the interfacial tension but also to study interfacial rheological properties.10,11 The effect of pulmonary surfactant on mass transfer of oxygen (one-component system) by use of the captive bubble technique was studied by Zuo et al.12 In the present study we will (3) Chen, X. Q.; Cho, S. J.; Li, Y.; Venkatesh, S. J. Pharm. Sci. 2002, 91, 1838. (4) Schu¨rch, S.; Bachofen, H.; Goerke, J.; Possmayer, F. J. Appl. Phys. 1989, 67, 2389. (5) Schoel, W. M.; Schu¨rch, S.; Goerke, J. Biochim. Biophys. Acta 1994, 1200, 281. (6) Schu¨rch, S. Clin. Perinatol. 1993, 20, 669. (7) Prokop, R. M.; Jyoti, A.; Cox, P.; Frndova, H.; Policova, Z.; Neumann, A. W. Colloids Surf., B 1999, 13, 117-126. (8) Wu¨stneck, R.; Wu¨stneck, N.; Vollhardt, D.; Miller, R.; Pison, U. Mater. Sci. Eng., C 1999, 8-9, 57. (9) Wu¨stneck, N.; Wu¨stneck, R.; Perez-Gil, J.; Pison, U. Biophys. J. 2003, 84, 1940. (10) Wu¨stneck, N.; Wu¨stneck, R.; Fainerman, V. B.; Pison, U.; Miller, R. Colloids Surf., A 2000, 164, 267. (11) Wu¨stneck, N.; Wu¨stneck, R.; Fainerman, V. B.; Miller, R.; Pison, U. Colloids Surf., B 2001, 21, 191. (12) Zuo, Y. Y.; Li, D. Q.; Acosta, E.; Cox, P. N.; Neumann, A. W. Langmuir 2005, 21, 5446.
10.1021/la0622931 CCC: $37.00 © 2007 American Chemical Society Published on Web 12/15/2006
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use the captive-bubble technique in combination with ADSACB and micro gas chromatography to investigate the dynamics of dissolution of different gas/vapor mixtures in water in situ. The following definition of vapors and gases is used in this study: A vapor exists in the gaseous and in the liquid state under the experimental conditions, whereas a gas exists only in the gaseous state under the same conditions. The proximity of the experimental conditions to the critical pressure and temperature is crucial for this definition. The action of inhaled anesthetic vapors and gases is one of the enigmas of medicine and as yet there is no generally accepted theory to explain the reversible action of anesthetic agents on the central nervous system. This is not surprising, taking into account that the inhaled anesthetic agents belong to different classes of substances, such as halogenated hydrocarbons (chloroform, halothane), halogenated ethers (isoflurane, sevoflurane etc.), and simple gases (N2O, xenon). It is unlikely that these different anesthetic substances act at the molecular level through a specific common mechanism. A generally accepted and widely discussed model is the Meyer-Overton correlation, which suggests that the potency of anesthetics correlates with their oil solubility.13-15 There are, however, a number of critical exceptions to the Meyer-Overton rule. For instance, the so-called nonimmobilizers are volatile compounds that are highly lipophilic but they are not potent anesthetics. Therefore, there is so far no simple model to correlate solubility and interfacial data with the anesthetic impact. Another aspect, which was already mentioned by Meyer and Overton, is the interaction between the anesthetics and water molecules. This aspect is usually unjustifiably neglected, although due to the further development of direct molecular force measuring techniques,16 thermodynamic theories of hydrophobic hydration were developed and new models in basic research17-21 made steady progress in recent years, thus clarifying the dissolution process of nonpolar molecules in water. The molecular dynamic simulations describing the interaction of anesthetics with water demonstrate that water solubility, and especially the interaction at the interface, correlate very well with their anesthetic potencies.22,23 Short and to the point is the statement by Dill et al.:24 “The limitations in our understanding of water are largely responsible for the limitations in our ability to predict protein structures or to design drugs”. As a representative selection, we chose several examples of inhaled anesthetics to investigate the dissolution process: diethyl ether and chloroform as old-fashioned anesthetic vapors; isoflurane, enflurane, sevoflurane, and desflurane as modern clinical anesthetic vapors; N2O and xenon as gases; and perfluoropentane and 1,1,2-trichloro-1,2,2-trifluoroethane (R113) as nonimmobilizers. (13) Overton, E. Vierteljahresschr. Naturforsch. Ges. Zu¨rich 1899, 44, 88. (14) Overton, E. Studien u¨ber die Narkose. Zugleich ein Beitrag zur allgemeinen Pharmakologie; Gustav Fischer: Jena, 1901. (15) Meyer, H. H. Arch. Exp. Pathol. Pharmakol. (Naunyn-Schmiedebergs) 1899, 42, 109. (16) Meyer, E. E.; Lin, Q.; Hassenkam, T.; Oroudjev, E.; Israelachvili, J. N. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 6839. (17) Fisicaro, E.; Compari, C.; Braibanti, A. Phys. Chem. Chem. Phys. 2004, 6, 4156. (18) Graziano, G. Biophys. Chem. 2004, 110, 249. (19) Plyasunov, A. V.; Shock, E. L. Geochim. Cosmochim. Acta 2000, 64, 439. (20) Plyasunov, A. V.; O’Connel, J. P.; Wood, R. H. Geochim. Cosmochim. Acta 2000, 64, 495. (21) Graziano, G.; Lee, B. J. Phys. Chem. B 2005, 109, 8103. (22) Chipot, C.; Wilson, M. A.; Pohorille, A. J. Phys. Chem. B 1997, 101, 782. (23) Pratt, L. R.; Pohorille, A. Chem. ReV. 2002, 102, 2671. (24) Dill, K. A.; Truskett, T. M.; Vlachy, V.; Hribar-Lee, B. Annu. ReV. Biophys. Biomol. Struct. 2005, 34, 173.
Wu¨stneck et al. Table 1. Investigated Compounds: Their Physical Properties and Sources
compd
molecular mass (Da)
boiling vapor pressure point at 22 °C (°C) (mmHg)
diethyl ether chloroform halothane enflurane isoflurane sevoflurane desflurane R113 (C2Cl3F3)
74.1 119.4 197.4 184.5 184.5 200.1 168 187.4
Liquids 34 62 50 56.5 48.5 58.5 22.8 47.6
perfluoropentane hexane methanol
288 86.18 32.04
29 69 65
N2O O2 xenon
44 32 131.3
Gases -89 -183 -108.1
470 172 266 189 262 172 660 307 580 133 108
source Merck-100921 J.T. Baker-9257-22 Fluka-16730 Abbott Lab. Rhodia Organ. Ltd. Abbott Lab. Baxter GmbH Sigma-Aldrich91433 Fluka-09973 Fluka-52765 Merck LiChrosolv Air Liquide Air Liquide Air Liquide
There are four objectives of this study. The first is to introduce a new, powerful method to investigate the dissolution process. The second is to show the kinetics of dissolution process of vapors and gases in situ and to find out the differences between the dissolution of vapors and the dissolution of gases. The third objective is to state a simple model for the acquisition of partition coefficients by use of newly defined molecular dissolution/ diffusion coefficients. Finally, the last objective is to explain the lack of anesthetic action of nonimmobilizers. Materials and Methods Materials. The compounds investigated, their physical properties, and sources are listed in Table 1. Water was purified by use of a Milli-Q Plus water system (Millipore, Eschborn, Germany) and had a surface tension of 72.5 ( 0.2 mN/m at 22 °C determined by ADSACB. All glass vessels and the measuring cell used for this study were cleaned in KOH-saturated 2-propanol. Vapor Mixtures. The vapors of liquids used were prepared by mixing their headspace vapors with air in gastight Hamilton syringes with a sample lock valve (100 µL, no. 1710SL, Hamilton Bonaduz AG) at 22 °C. The concentration of all mixtures was 22.7 vol %, which is equal to the vapor pressure of sevoflurane at 22 °C. This high concentration was chosen to measure the kinetics of the dissolution process for all samples investigated at the same concentration. A rapid dosage of the samples into the measuring cell guarantees unchanged composition. The vapor concentrations were checked by gas chromatographic analysis (GC) of each mixture in a separate experiment. GC was performed with a two-channel highspeed M200 micro gas chromatograph (Serie G2890A, Agilent Deutschland) with a thermal conductivity detector. One channel analyzed all gases and halogenated compounds with a fused silica capillary column (10 m × 0.15 mm, 2 µm film thickness, OV-1), and a second channel separated oxygen and nitrogen on a PLOT column (10 m molecular sieves 5 Å). After bubble formation, the gas inside a CB chamber was saturated with water vapor. The relative humidity was measured by GC. For some experiments a gas sample (50 µL) was taken from the bubble by use of a microsyringe to determine the gas or vapor content after dissolution and analyzed by GC. Sample acquisition from the bubble was possible only when the volume of the bubble after dissolution was large enough and requires some experience. Captive-Bubble Surfactometer. Interfacial tension was measured by use of a modified captive bubble chamber as described in detail earlier.8,9 This is a closed stainless steel chamber with a volume of 2.5 mL with different ports and two windows. One window is used to illuminate the bubble and the other to take images of the bubble profile with a charge-coupled device (CCD) camera connected to a computer. Different ports are used to create the bubble and to take
On the Dissolution of Vapors and Gases gas samples from the bubble. The temperature in the chamber is controlled by electric heating and water cooling. The temperatures given are values ( 0.1 °C. A motorized pump is connected with the chamber to fill it with liquid and to clean the chamber. Kinetic Experiments and Observation of the Dissolution Process. The dissolution experiments were carried out in the captivebubble chamber. A gas- or vapor-containing bubble of constant volume was injected into the water-filled chamber by use of a sample lock microsyringe. The time between bubble dosage and bubble resting before image acquisition was less than 2 s. Bubble images were recorded each second during the dissolution and were usually followed for 900-4200 s. Each experiment was repeated at least three times. During the experiments any additional air dissolution was excluded so that exclusively the dissolution of the gases or vapors was characterized, because this is particularly relevant for anaesthetics. Therefore, air-saturated water was used. For vapor experiments, water deaeration would cause a superposition of vapor and air dissolution, which was not desired. Two different kinds of experiments were performed. The first (experiment I) was carried out at constant pressure (P ) constant); the captive-bubble chamber was connected to the atmospheric pressure. The second (experiment II) was performed at changed pressure (P * constant); the chamber was closed to atmospheric pressure. Phenomenology of Dissolution and a Simplified Model for a Dissolving Bubble. The microscopic theory of dissolution and diffusion has been a matter of intensive investigations. We will examine the dissolution process of gas bubbles from the molecular point of view. During bubble formation an interface between gas and liquid is rapidly created. Immediately after bubble formation first gas molecules are adsorbed at the interface because in the gas phase the diffusion velocity of molecules is approximately 10,000 times higher than in the liquids. There are two possible ways for adsorbed molecules to leave the interface. Either they desorb from the interface back into the gas phase or they diffuse from the interface into the liquid bulk, if the interaction with water is high enough to dissolve the solute. In current theories of dissolution, the process has been subdivided into cavity formation within the liquid and insertion of the solute into this cavity. Molecular dynamics studies22,25-27 have calculated the free energy profiles characterizing the transfer of anesthetic solutes across the liquid-vapor interface. In these studies solubility is interpreted only under conditions of thermodynamic equilibrium. The anesthetic action is not an equilibrium process; it may be at best a stationary process. The recent molecular dynamics studies of interaction of anesthetics with water do not treat the adsorption of the anesthetic solute as a separate step or take into consideration the kinetics of the dissolution22 because of the lack of reliable experimental data. After adsorption, the first step of the process (cavity formation) is facilitated and the work to create the cavity is partially done. After adsorption, the free energy of 72.5 mN/m will change to a lower value depending on the kind of adsorbed molecules. Both the “mechanical” work against the surface tension and a part of the “chemical” work of mass transfer from the gas phase into the interface have been already performed. The second step of the process (insertion of the solute into the cavity) is determined by the interaction between the solute and the liquid phase. Dissolution occurs if the interaction between the solute and water is high enough to compensate the work of dissolution. After adsorption of the solute molecules at the interface, the chemical potential has been increased and the excess of chemical potential has to change to reach the local equilibrium. Diffusion starts, but only if the interaction with water is high enough to dissolve the solute. Otherwise the molecules stay adsorbed in the interfacial layer. (25) Garde, S.; Garcia, A. E.; Pratt, L. R.; Hummer, G. Biophys. Chem. 1999, 78, 21. (26) Pohorille, A.; Wilson, M. A.; New, M. H.; Chipot, C. Toxicol. Lett. 1998, 100-101, 421. (27) Katz, Y. J. Theor. Biol. 2003, 225, 341.
Langmuir, Vol. 23, No. 4, 2007 1817 The molecules move very rapidly from the bubble to the interface. In the case of dissolution the bubble volume decreases, and the bubble-liquid interface moves with time. This movement of the interface depends on the rate of mass transfer. The time of this motion is characteristic for each kind of solute and determines the diffusion kinetics as well as the interaction of solute molecules with the solvent. All other possible stresses (possible local temperature change, convection during dissolution, etc.) are neglected in our simplified model for the dissolution process of bubbles that contain mixtures of vapors and gases at constant temperature and pressure. Two theories are utilized to describe the dissolution process of anesthetic solutes in a liquid: the common flux theory and the Epstein-Plesset theory28 for the solution of bubbles in a liquid. The first theory describes several transport processes, that is, heat, electromagnetic, or mass transfer, by use of Fick’s laws. The flux is defined as the amount of a given quantity that flows through a unit area per unit of time. Analogous to the diffusion flux, the dissolution flux JA is defined by Fick’s first law as JA ) -Ddiss dC/dx
(1)
The concentration gradient dC/dx is a vector that causes a directed mass flow from the gas phase to the liquid. The new coefficient Ddiss for the complete dissolution process as molecular dissolution/diffusion coefficient is introduced to distinguish it from the common diffusion coefficient. Ddiss is the coefficient for the entire process, describing diffusion as well as dissolution processes. It has the same unit as the common diffusion coefficient, that is, square centimeters per second. According to the diffusion coefficient definition and by analogy with the Einstein equation,29,30 we obtain for the dissolution/diffusion coefficient Ddiss ) l2/2t
(2)
with l being the path of the interface movement during the dissolution process and t the time of dissolution of all gas-phase molecules in the liquid at unity concentration gradient. At first the radius of the sphere with the starting bubble volume is calculated. Using the difference between the bubble area at the beginning and the end of the dissolution process, we calculated the radius of the sphere at the end of dissolution. Our assumption is that the difference of the radii determines the path l of the interface movement with sufficient approximation. The time is determined graphically. Using ADSACB for the estimation of mass transfer coefficient, Zuo et al.12 suggested a correction of gas transfer area, assuming that no mass transfer occurs through the bubble surface in contact with the ceiling of the chamber. For CB in water, the mass transfer area accounts for 6% less than the entire bubble area. In our model such correction can be neglected because the difference of the bubble areas is used for calculation. The theory of solution process of a single gas bubble in liquid was described by Epstein and Plesset in 1950.28 The rate of solution of a single-component bubble was analyzed. In this case the concentration of the gas in the bubble remains constant during dissolution. The approximate mathematical solution of the dissolution problem for spherical bubbles containing only one component was found for a stationary bubble boundary. In this model Epstein and Plesset used the positive constant R: R ) D(Cs - Ci)/F
(3)
where D is the diffusion coefficient of dissolving gas/vapor in liquid, Cs is the dissolved gas concentration for a saturated solution, Ci is the concentration of dissolved gas at the initial time t ) 0, and F is the density of the gas in the one-component bubble. (28) Epstein, P. S.; Plesset, M. S. J. Chem. Phys. 1950, 18, 1505. (29) Einstein, A. Z. Elektrochem. 1908, 14, 235. (30) Einstein, A. Ann. Phys. 1905, 17, 549.
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Adapted to the dissolution process of mixtures of vapors and gases at constant temperature and pressure, this modified constant is the molecular dissolution/diffusion coefficient: R ) Ddiss ) DQ ) D(Cs - Ci)/(C0 - CE)
(4)
where D is the diffusion coefficient of dissolving gas/vapor in liquid, Cs is a dissolved gas concentration for a saturated solution, Ci is the concentration of dissolved gas at the initial time t ) 0, C0 is a starting concentration of the gas in the bubble, and CE is the ending concentration of the gas in the bubble. In our experiments Ci )0. According to the Wilke-Chang correlation31 for diluted solutions, the diffusion coefficient is TxΦBMB DAB ) 7.4 × 10-8 µBνA0.6
(5)
where νA is the molar volume of the solute in cubic centimeters per mole at its normal boiling point, µB is the viscosity of the solution in centipoise, T is the absolute temperature in kelvins, MB is the molecular weight of the solute, and Φ is an “association parameter” for the solvent. The recommended value of ΦB for water is 2.26. Though differently derived, it is possible to define the components of the dissolution/diffusion coefficient Ddiss as a product of a diffusion coefficient D as a kinetic parameter and of a solubility-related dimensionless factor Q as a thermodynamic parameter. It describes the complete dissolution process. Using Ddiss calculated according to eq 2 and the diffusion coefficient D calculated according to the Wilke-Chang equation (eq 5), the factor Q is obtained. The Ostwald partition coefficient of a solute between the gas phase and water in the dilute region is equal to the ratio of the concentration of a solute in water and in the gas phase. This factor Q is equal to the Ostwald partition coefficient only if Ci ) 0 and CE ) 0. Vice versa, one obtains the diffusion coefficient D by use of Ostwald partition coefficients. This model directly connects microscopic quantities and macroscopic observables of the dissolution process.
Results Comparing Dissolution of Different Vapors. By use of the captive bubble device, the dissolution process can be observed in situ, during the entire process, recording changes not only in the bubble volume but also in the surface tension (γ). According to our definition, a substance is soluble in water if it spontaneously enters the bulk of a liquid without any mixing procedures. If a substance adsorbs at the gas/liquid interface but does not enter into the bulk of a liquid spontaneously, it is insoluble. Figure 1 shows the changes in the two parameters, surface tension and bubble volume, versus time for the dissolution process of vapors of hexane and methanol and of three volatile anesthetics, diethyl ether, chloroform, and isoflurane. The concentration of the vapors in the air of the bubble was equal to their vapor pressures at 22 °C (Table 1). Two marginal cases of dissolution could be distinguished. The first one was methanol with quite good solubility in water. Immediately after bubble dosage, the interfacial tension remained constant and was equal to the surface tension of the pure water (Figure 1A). In contrast, the bubble volume decreased immediately and then remained constant. The difference between the dosage volume and that measured at time 0 was 14%, which was exactly equivalent to the vapor pressure of methanol at 22 °C (Figure 1B). The second case was hexane, which is poorly soluble in water according to data found in the literature.31,32 (31) Chemical Engineers’ Handbook.; Perry, R. H., C. C. H., Eds.; McGrawHill: New York, 1995. (32) Scharlin, P.; Battino, R.; Silla, E.; Tunon, I.; Pascual-Ahuir, J. L. Pure Appl. Chem. 1998, 70, 1895.
Figure 1. Dissolution process of vapors of hexane, methanol, and three volatile anesthetics (diethyl ether, chloroform, and isoflurane) in air-saturated water at their respective vapor pressures at 22 °C. (A) Interfacial surface tension change via time; (B)- volume change of vapor-filled bubbles with time.
After bubble dosage of an air bubble containing hexane, the surface tension dropped immediately to about 68 mN/m and remained constant (Figure 1A). Hexane adsorbed at the interface thus changing γ. The adsorption velocity was high because the diffusion of hexane in the gas phase was fast, that is, the diffusion coefficient within a gas is about 4 orders of magnitude higher than that in the liquid. However, changes in the bubble volume were observed neither immediately after dosage nor during the time of the experiment, that is, 900 s. If the formation of a hexane monolayer at the interface with a minimum area demand of 20 Å2/molecule is assumed, the adsorbed hexane amount can be calculated. It is merely 0.015 µL, which is quite small and could not measurably change the bubble volume. The vapor pressure of the hexane was 18%, that is, the absolute amount of hexane vapor is comparable to that of methanol but no changes in volume were observed. Furthermore, no kinetics of the dissolution process could be observed as in the former case of methanol. A small amount of hexane stayed adsorbed at the water/gas interface but did not enter the bulk of liquid. Not low solubility but no solubility of hexane in water was found. The vapors of three inhalation anesthetics represented intermediate cases between methanol and hexane. The solubility of these substances decreases continuously from diethyl ether to chloroform to isoflurane. For all these cases, pronounced kinetics of the dissolution process were observed. The surface tension of pure water, 72.5 mN/m, decreased to 50 mN/m after dosage of isoflurane vapor, to 55 mN/m for diethyl ether, and to 66 mN/m for chloroform (Figure 1A). With elapsing time the surface tension increased again, approaching the equilibrium surface tension of the solvent. As the bubble was captured, the volume decreased as long as the total amount of vapor was dissolved in the liquid phase. The solubility of diethyl ether, 67 g/L at 22 °C, is high compared to that of chloroform, 8.1 g/L at 22 °C, and isoflurane, 2.5 g/L
On the Dissolution of Vapors and Gases
Langmuir, Vol. 23, No. 4, 2007 1819
Figure 2. Dissolution process of anesthetic gases and vapors and nonimmobilizer vapors in air-saturated water at the partial pressure of 22.7 vol % at 22 °C. (A) Interfacial surface tension change of anesthetic vapors via time; (B) Volume change of with anesthetic vapors filled bubbles via time; (C) interfacial surface tension change of anesthetic gases and nonimmobilizers via time; (D) volume change of anesthetic gases and nonimmobilizer filled bubbles with time.
at 25 °C, and so is the partial pressure of diethyl ether (Table 1). Therefore the bubble volume decreases strongly for diethyl ether and approaches the surface tension of water already after some seconds, whereas the difference between the dosage volume and that of equilibrium was equal to the vapor pressure of diethyl ether, that is, 62 vol % (Figure 1B). Similar behavior was observed for chloroform, whereas its dissolution was slower than that of diethyl ether. Still slower was the dissolution of isoflurane: even after 900 s the equilibrium was not yet achieved. The dissolution of different substances was compared for bubbles containing these substances at their vapor pressure, which corresponded to different concentrations (Table 1) but allowed effective control of the measurements and evaluation of the method used. The results show that usage of the captive bubble technique yields precise values concerning the dissolved amount and the kinetics of the dissolution, thus increasing the existing experimental data pool for further development of different dissolution models. This is important for modeling and will be discussed below. Dissolution of Anesthetics and Nonimmobilizers in Water. To find out the specific differences between several substances, the comparison of dissolution kinetics should be carried out at equal partial pressures. Figure 2 shows the time dependence of surface tension for the dissolution process of different anesthetic vapors and gases. The concentration of the vapors and gases in the bubble was 22.7 vol %. The equilibrium surface tension of water decreased dramatically immediately after bubble dosage. A maximum drop of surface tension from 72.5 to 48 mN/m was found for the servoflurane/air mixture (Figure 2A). A minimum decrease from 72.5 to 66 mN/m was observed for chloroform. Although desflurane is least soluble in water, it decreased the surface tension only to 61 mN/m, which is a consequence of its boiling point of 22.8 °C. At 22 °C desflurane behaves more like a gas than like a vapor, and desorption back into the gas phase is increased. During the experiment the surface tension increased
again to the equilibrium value of water, because the concentration of solution was quite low, approximately 0.25 mmol at the end of dissolution. Therefore the original solution is quasi-infinitely diluted. In contrast, the surface tension remained constant after a gas/ air mixture containing bubbles was created (Figure 2C). The dosage of nonimmobilizer vapors of R113 and C5F12 resulted in a decrease of γ to 68 N/m. Thereafter, however, the surface tension increases only slowly, for R113 to 71 mN/m within 1800 s. In contrast, γ remains constant for C5F12 (Figure 2C). R113 was extremely slightly soluble in water, whereas C5F12 did not show any solubility in water. A small amount of each substance was adsorbed at the water/gas interface but did not enter into the bulk of liquid. The volume of the bubble containing inhalational anesthetic vapors decreased smoothly during the dissolution process and approached the equilibrium value, which was reached when all the vapor was dissolved in water (Figure 2B). This was checked by GC analysis for several experiments. Diethyl ether was dissolved faster than all others, followed by chloroform, halothane, enflurane, isoflurane, sevoflurane, and desflurane. The entire amount of vapor was dissolved only after 1700 s for isoflurane, after 2500 s for servoflurane, and after 3500 s for desflurane (end points not shown). The volume of the gas/air mixtures also decreased (Figure 2D) and for N2O approaches the final value after 2000 s. The dissolution process of the xenon mixtures was found to be extremely slow. The final volume was reached after 10 000 s (Figure 2D, end point not shown). Also, the dissolution process of R113 was extremely slow. There was only a decrease in volume of about 3% after 1800 s, that is, only 13% of the vapor was dissolved. The volume change of the mixture containing perfluoropentane differed remarkably from others: the volume was increased. This means that gas dissolved in water was transferred into the
1820 Langmuir, Vol. 23, No. 4, 2007
Figure 3. Dissolution process of xenon in air-saturated water at different partial pressures of xenon at 22 °C: -(s) 100% xenon; (b) 50% xenon; (O) 22.7% xenon in the bubble.
gas phase. The GC analysis showed that there was 21% oxygen in the bubble before but about 25% oxygen after the mass transfer from water into the gas phase. Therefore we concluded that oxygen dissolved in water diffuses into the gas phase, because oxygen is better soluble in perfluoropentane (80 mL of gas/100 mL of liquid) than in water (3 mL of gas/100 mL of liquid). Dissolution of Xenon in Water. The kinetics of the dissolution process at various xenon concentrations within an air bubble is shown in Figure 3. In all cases the bubble volume decreased to a great extent linearly, in contrast to anesthetic vapors or N2O of the same partial pressure (Figure 2B,D). This is a particularity of xenon obviously caused by its low dissolution velocity. Comparing Dissolution Processes at P ) Constant and P * Constant. Figure 4 shows a comparison of the dissolution process of isoflurane and xenon for two different experiments, that is, with the chamber opened to atmospheric pressure (P ) const) and with closed chamber (P * const). The concentration of isoflurane corresponds to its vapor pressure at 22 °C; the partial pressure of xenon was 100%. The aim of the comparison was to ascertain the main effects observed in the two sets of experiments. Therefore, the partial pressures were chosen to get equal amounts of the substances dissolved after 900 s in the liquid phase. For xenon there were no changes in surface tension observed in either experimental case (Figure 4A). γ remained constant at the value of water equal to 72.5 mN/m. At the same time in experiment I the bubble volume decreased versus time, whereas
Wu¨stneck et al.
in experiment II no changes in volume could be observed (Figure 4B). When the chamber was, however, opened to the atmosphere at the end of experiment II, the volume jumped to a value that was approximately equal to that reached in experiment I. This means that in a closed system xenon was dissolved in the liquid phase without any observable changes of either γ or V. In contrast, for isoflurane the surface tension dropped to 50 mN/m in both kinds of experiment immediately after bubble creation. Then γ increased continuously up to the equilibrium value of water, 72.5 mN/m (Figure 4C). In experiment I the volume of the bubble decreased over time, but in experiment II it remained constant (Figure 4D). At the end of experiment II, after connection of the system to the atmosphere, the volume changed in the same manner as for xenon and approached the same value as in experiment I. Isoflurane was dissolved in a closed system (P ) const) even though no volume or area changes were observed. Nevertheless, the surface tension changed in the same manner as in experiment I; only curvature or shape of the bubble was altered. It was not possible to observe the dissolution of a gas, for example, xenon, in a closed system without any pressure compensation, whereas it was possible to observe the dissolution of a vapor, for example, isoflurane, by measuring changes in the surface tension. Discrimination of Anesthetics from Nonimmobilizers. The dissolution process is accompanied by a change not only in bubble volume but also in bubble surface. To demonstrate the typical differences in dissolution behavior of the substances tested, the change in surface tension versus bubble area is plotted in Figure 5. Obviously the tested substances can be subdivided into three groups. Group A consists of the anesthetic gases, in which the surface tension remains constant while the bubble area changes. Group B comprises the anesthetic vapors, for which the surface tension increases whereas the bubble area decreases during dissolution. Group C unifies the so-called nonimmobilizers. Here there is a lack of any dynamics of dissolution and the changes in surface tension depending on the area are negligible. Thus, it is possible to discriminate the nonimmobilizers from anesthetics by comparing their dissolution kinetics. Determination of Dissolution/Diffusion and Diffusion Coefficients. The dissolution/diffusion coefficients Ddiss were
Figure 4. Dissolution process of xenon and isoflurane vapors in air-saturated water at vapor pressure of isoflurane and pure xenon at 22 °C in two different experiments: exp I, chamber opened to atmospheric pressure (P ) constant), and exp II, closed chamber (P * constant). Shown are the interfacial surface tension change with time for xenon (A) and isoflurane (C) and the volume change of bubbles filled with xenon (B) or isoflurane vapor (D) with time.
On the Dissolution of Vapors and Gases
Langmuir, Vol. 23, No. 4, 2007 1821
Table 2. Measured Dissolution/Diffusion and Partition Coefficients in Watera at 22 °C
compd diethyl ether chloroform halothane enflurane isoflurane sevoflurane desflurane N2O xenon
MACb (vol %) 1.9 0.5 0.8 1.7 1.3 2.0 6.0 100 70
MAC (g/L of gas)
measured dissolution coefficient Ddiss × 105 (cm2/s)
diffusion coefficientc D × 105 (cm2/s)
solubility related factor Q
partition coefficient,d water/gas
0.06 0.02 0.06 0.13 0.10 0.17 0.42
Liquids 10.99 7.49 1.10 1.10 0.99 0.66 0.47
0.86 1.00 0.85 0.78 0.77 0.75 0.81
12.79 7.48 1.30 1.41 1.28 0.88 0.58
35.23 7.22 1.41 1.51e 1.25e 1.07 na
1.82 3.85
Gases 0.82 0.16
1.62 1.41
0.51 0.12
0.60 0.12
a Air-saturated water. b Minimal alveolar concentration. c Calculated for dilute solution according to Wilke-Chang correlation. d Taken from refs 32 and 34-36. e Extrapolated from halothane solubility.
Table 3. Measured Dissolution/Diffusion Coefficients of Isoflurane in Watera at 22 °C bubble volume at t ) 0 (cm3) 0.020 0.030 0.040 0.051 0.067
bubble radius as sphere l (cm)
time t (s)
0.169 0.193 0.213 0.230 0.253
850 1000 1350 1550 1850
Figure 5. Change of surface tension versus bubble area during dissolution of anesthetic gases (group A) and vapors (group B) and nonimmobilizer vapors (group C) in air-saturated water at the partial pressure of 22.7 vol % at 22 °C.
determined from eq 2 as explained above. Then, according to eqs 5 and 4, the diffusion coefficient D and the solubility-related quotient Q were calculated. The results and the water/gas partition coefficients are given in Table 2. In the last column, partition coefficients taken from refs 33-36 are shown for comparison. The values of dissolution/diffusion coefficients reflect both processes: dissolution and diffusion. The diffusion coefficients of all vapors were approximately equal to (0.8-1.0) × 10-5 cm2/s. From examination of Ddiss values we concluded that the dissolution process was the prevalent process, especially for diethyl ether and for chloroform. The least soluble sevoflurane and desflurane showed quite small Ddiss values. The diffusion coefficients of both gases were approximately equal to 1.5 × 10-5 cm2/s. The Ddiss value of xenon was much smaller than that of N2O, showing that solubility of xenon is low. For nearly all inhalation vapors and gases, the solubility-related factors Q were in agreement with partition coefficients obtained in the literature. Diethyl ether is an exception. For diethyl ether Q is approximately 3 times lower than the corresponding partition (33) Allott, P. R.; Steward, A.; Flook, V.; Mapleson, W. W. Br. J. Anaesth. 1973, 45, 294. (34) Steward, A.; Allott, P. R.; Cowles, A. L.; Mapleson, W. W. Br. J. Anaesth. 1973, 45, 282. (35) Yang, N. C.; Wang, H. F.; Hwang, K. L.; Ho, W. M. J. Anal. Toxicol. 2004, 28, 122. (36) Eger, E. I., 2nd; Saidman, L. J. Anesth. Analg. 2005, 100, 1020. (37) Duncan, P. B.; Needham, D. Langmuir 2004, 20, 2567. (38) Borden, M. A.; Longo, M. L. Langmuir 2002, 18, 9225. (39) Kabalnov, A.; Bradley, J.; Flaim, S.; Klein, D.; Pelura, T.; Peters, B.; Otto, S.; Reynolds, J.; Schutt, E.; Weers, J. Ultrasound Med. Biol. 1998, 24, 751. (40) Kabalnov, A.; Klein, D.; Pelura, T.; Schutt, E.; Weers, J. Ultrasound Med. Biol. 1998, 24, 739.
1.40 1.38 1.43 1.48 1.30 1.40 ( 0.04
mean a
measured dissolution coefficientb Ddiss × 105 (cm2/s)
b
Air-saturated water. Measured at partial pressure of 34.5 vol %.
coefficient value. It should be noted, however, that diethyl ether is a special case because of its very high solubility in water. By insertion of mechanical energy via intensive shaking during the standard procedure for the determination of partition coefficients, one may enforce the insertion of much more substance into water than otherwise possible. Evaluation of the Dissolution/Diffusion Coefficient Measurements. To test the validity and to evaluate the method for determination of the dissolution/diffusion coefficients, experiments with isoflurane vapor containing bubbles of different size were carried out. The size of the bubbles was changed between 20 and 67 µL, and the concentration of isoflurane was equal to its vapor pressure at 22 °C. The results are shown in Table 3. Satisfactory consistency of the dissolution/diffusion coefficients was obtained.
Discussion The dissolution process of vapors and gases was examined by continuously controlling surface tension, volume, and surface area. All methods used so far for similar investigations37-40 monitor only one parameter in situ, mostly the radius of a dissolving bubble, and model this process according to the Epstein-Plesset equation. In the present paper we have introduced a unique stagnant bubble experimental technique without any bubble manipulation procedures to investigate the dissolution process of partially soluble gases and vapors in liquids. We used the ADSA-CB method in combination with micro-GC to analyze the dissolution process of the anesthetic inhalational vapors, gases, and nonimmobilizers. The captive bubble technique was shown to be a suitable device to characterize the dissolution processes. This technique enables the study of single bubbles of well-defined composition in a
1822 Langmuir, Vol. 23, No. 4, 2007
Wu¨stneck et al.
Table 4. Classification of the Investigated Substances by Their Dissolution Dynamics
well-defined solution environment. Further, the method works extremely fast. One advantage of using the captive bubble technique is that the kinetics of the dissolution is accessible. During vapor dissolution, a change in the interfacial tension γ takes place, but no γ change occurs for gas dissolution. There are two main reasons for this: First, at constant pressure and temperature, the normal density of vapor is much higher than the density of a gas (e.g., 1.47 g/cm3 for CHCl3, 1.2 × 10-3 g/cm3 for air, or 5.4 × 10-3 g/cm3 for xenon). The expected density of the interfacial layer of water is 0.195 g/cm3. Gases may change the density of the interfacial layer only slightly, that is, by several thousandths of a gram per cubic centimeter even for the heavy xenon. Second, gases may desorb to the gas phase because under normal conditions their state is gaseous, whereas the state of vapors is liquid. Consequently, in contrast to vapors, gases are not able to cause a measurable change in surface tension of the pure liquid. Because the normal state of vapor molecules is liquid, desorption of vapor molecules into the gas phase is hampered under normal conditions. The diffusion of gas or vapor molecules into the liquid phase may be quite slow and may become the velocity-limiting step for the dissolution process. New data were obtained to classify different gases and vapors, although in the present work only the mass transfer across the water/gas interface was considered. Depending on the ability of the examined substances to change the surface tension and the bubble volume, they may be divided into five groups (Table 4). The first is the methanol group. These highly water-soluble substances do not change the surface tension and the bubble volume is reduced to the value corresponding to the vapor pressure of the substance. There is no kinetic observable because of the fast dissolution of these vapors in the liquid phase. There is no measurable adsorption at the liquid/gas interface. The second group is formed by anesthetic vapors (chloroform, etc.). The dissolution of anesthetic vapors results in an immediate drop in surface tension followed by a continuous increase of the surface tension up to the equilibrium surface tension of the solvent. This process is accompanied by a continuous decrease of the bubble volume down to an equilibrium value. The process consists of both vapor adsorption at the liquid/gas interface and dissolution in the liquid phase. The third group implies gases (N2O and xenon). Water-soluble gases do not change the surface tension at all. The equilibrium surface tension of the solvent remains
constant. The bubble volume, however, continuously decreases until an equilibrium value is reached. The kinetics of the volume change can be observed. It characterizes the dissolution process only, because no measurable adsorption takes place. The next group is the hexane group. Sparingly water-soluble substances cause an immediate drop in the surface tension, but no changes in the bubble volume can be observed. There is also no kinetic observable. The equilibrium surface tension characterizes the adsorption process. No dissolution takes place. Finally, there is the group of fluorocarbons. The surface tension drops immediately and remains constant. In contrast to all other substances, fluorocarbon vapors are a better solvent for oxygen molecules than water. Therefore the oxygen molecules dissolved in water diffuse from the liquid phase (water) into the gas phase, that is, fluorocarbon vapor, which causes an increase of the bubble volume. The surface tension value characterizes the adsorption of the fluorocarbon at the gas/liquid interface. There is no dissolution of the fluorocarbon in the aqueous phase. The kinetics of the volume change caused by the oxygen dissolution in the gas phase can be observed. This classification (Table 4) is meaningful for the modeling of dissolution processes. The outcome is that the solution of hexane and fluorocarbon in water can take place only if an interface is present or if several molecules of hexane are constituted as an ensemble or aggregate. Solution of hexane in water can be achieved only by shaking with the creation of new interface, but this is not a true molecular solution. Therefore for modeling of the dissolution process it is recommended to use not a single molecule of hexane but several hexane molecules surrounded by water molecules. The common methods to determine the partition coefficients traditionally use measurements exclusively under equilibrium conditions. Substances are shaken vigorously with the solvent until no more of the sample can be dissolved followed by filtering and measuring of the concentration of the solution by HPLC, turbidimetric, potentiometric or other methods. These methods are time-consuming and require much additional equipment. Kinetic aspects of the dissolution process are usually not considered. This kinetics, however, is important for several processes of practical interest. In the present work the dissolution of anesthetic vapors and gases in water was discussed. The knowledge of details of the dissolution process in water and other media may help to better
On the Dissolution of Vapors and Gases
understand the impact of anesthetic substances, and these new data should be considered in the development of new models. Using our simplified model for the dissolution process, the newly introduced dissolution/diffusion coefficients Ddiss, and the known diffusion coefficients, we can estimate the partition coefficients for anesthetics as a solubility-related factor Q. Vice versa, if the partition coefficient is known, one can estimate the diffusion coefficients. All inhalational anesthetics investigated are sparingly soluble in water, showing strong dissolution kinetics. The hypothetical question may be asked: Is there a correlation between the dissolution velocity of anesthetics in water and their anesthetic potency? To answer this question we used the dissolution velocity, that is, the slope of the V/t curves, to calculate the anesthetic potency of several vapors. MAC (minimal alveolar concentrations) values characterize the anesthetic potency. If the known MAC value of chloroform is taken (Table 2), the calculated MAC values of isoflurane, sevoflurane, and halothane are in agreement with clinically relevant values. Indeed, one has to bear in mind that the data presented were acquired at room temperature, while the MAC values are usually measured at 37 °C. In contrast, there is no correlation for diethyl ether. It dissolves very rapidly in water, even though its MAC value is not the smallest. One possible reason for this behavior is that at 37 °C diethyl ether is a gas. This trial shows that it is possible to correlate anesthetic potency with the velocity of dissolution of inhaled anesthetics in water. However, there are no experimental data for comparison with others. The anesthetic potency of hexane is not interpreted here as it is obvious that no correlation can exist because of the absence of solubility of hexane in water. This fact changes completely when the hexane solubility in blood is considered, since this is 5041 to 20042 times higher than its solubility in saline. This means that hexane adsorbs to the components of blood and is delivered with these components in the body. The results of this study show that it is possible to distinguish the dissolution process of gases from those of vapors due to the differences in their surface tension changes. This principal difference is an essential point for the mechanistic understanding of the behavior of gaseous substances at the interfaces during the dissolution process. The so-called nonimmobilizers are scarcely soluble in water or not soluble at all. That there is no change in their surface tension via their bubble surface may help to distinguish the nonimmobilizers among the expected candidates for anesthetic action. Maybe the lack of solubility in water explains the lack of anesthetic action of nonimmobilizers. What is a special feature of xenon among inhalational anesthetics, apart from it being an inert gas? The velocity of xenon dissolution is extremely low and this may be the reason for quite different solubility data of xenon in blood.43 Xenon dissolution data in situ show that the change in dissolution velocity takes place permanently in a proportional range, and therefore one may expect that the exact adjustment of anesthesia with xenon can be realized without any problems. It is well-known in practice that xenon anesthesia does not cause undesirable side effects and it seems to be a safe anesthetic gas.44,45 Further studies (41) Meulenberg, C. J.; Vijverberg, H. P. Toxicol. Appl. Pharmacol. 2000, 165, 206. (42) Eger, E. I., 2nd; Laster, M. J. Anesth. Analg. 2001, 92, 1477. (43) Goto, T.; Suwa, K.; Uezono, S.; Ichinose, F.; Uchiyama, M.; Morita, S. Br. J. Anaesth. 1998, 80, 255. (44) Dingley, J.; Ivanova-Stoilova, T. M.; Grundler, S.; Wall, T. Anaesthesia 1999, 54, 335.
Langmuir, Vol. 23, No. 4, 2007 1823
to define the solubility of xenon will be necessary because of special interest in xenon-induced anesthesia and its neuroprotective physiological activity reported recently.46,47 The examination of dissolution of bubbles filled with gas/ vapor mixtures inside a closed system without any pressure compensation shows that there is no change in volume to observe the dissolution process. The only changing parameter is the surface tension or the shape of the bubble. It is important to take this point into account especially when the processes of dissolution of multicomponent bubbles in the bloodstream are interpreted.39,40 Fluorocarbons are of great interest as agents in the development of contrast media for ultrasound imaging. The mass transport from the liquid to the vapors of fluorocarbon, as found in our study for C5F12, is neither mentioned nor discussed by several authors39,40 investigating the bubble dissolution mechanisms in developments of ultrasound contrast media and stays entirely unconsidered. The dissolution processes in sound-driven bubbles during sonoluminescence are also not fully understood.48,49 The authors49 postulate that at large bubble radius the gas pressure in the bubble is small, resulting in a mass flux into the bubble. Our experimental data contradict this assertion. The Laplace pressure in the 66-68 µL bubble amounts to approximately 60 Pa, which is equivalent to some millimeters’ height of the water column. It is not clear why this pressure difference should cause a mass flux into the bubble. The experiments do not show that any size change causes mass transfer into the bubble. The only driving force for mass transfer is a difference in concentration, and in the case of perfluoropentane the oxygen dissolved in water diffused even from the liquid into the gas phase despite the higher pressure in the bubble than in the liquid. The utilization of surface tension changes during the dissolution process may be important in innovative technical developments. At the end of the dissolution process of vapors and gases the bubble size normally becomes smaller. The smaller bubble has a higher interfacial curvature and thus a higher internal pressure. This effect can be used to design microscale surface-tensionbased bubble valves and pumps. At small scales the surface tension is a main driving force for micromachines,50,51 and the first surface tension driven motor has already been constructed.52 Finally, we conclude that the results described in this paper will increase our understanding of solute-solvent interactions in mass transfer processes. Captive bubble technique is a particularly suitable device to investigate such processes. Acknowledgment. The financial support by the Deutsche Forschungsgemeinschaft (Grant Pi165/12-1) is gratefully acknowledged. LA0622931 (45) Franks, N. P.; Dickinson, R.; de Sousa, S. L.; Hall, A. C.; Lieb, W. R. Nature 1998, 396, 324. (46) Petzelt, C.; Blom, P.; Schmehl, W.; Muller, J.; Kox, W. J. Life Sci. 2003, 72, 1909. (47) Abraini, J. H.; David, H. N.; Lemaire, M. Ann. N.Y. Acad. Sci. 2005, 1053, 289. (48) Brenner, M. P.; Hilgenfeldt, S.; Lohse, D. ReV. Mod. Phys. 2002, 74, 425. (49) Brenner, M. P.; Hilgenfeldt, S. D. L. Nonlinear Physics of Complex SystemssCurrent Status and Future Trends; Parisi, J., Mu¨ller, S. C., Zimmermann, W., Eds.; Springer: Berlin, 1996; p 79. (50) Wapner, P. G.; Hoffman, W. P. Sens. Actuators, B 2000, 71, 60. (51) Lee, J.; Kim, C.-J. J. Microelectromech. Syst. 2000, 9, 171. (52) Regan, B. C.; Aloni, S.; Jensen, K.; Zettl, A. Appl. Phys. Lett. 2005, 86, 123119.
