Solubility of Gases in Micellar Solutions
`
`I. B. C. MATHESON* AND A. D. KING, JR.?
`Departments of *Biochemistry and tChemistry, University of Georgia, Athens, Georgia 30602
`Received February 23, 1978; accepted March 27, 1978
`
`Measurements have been made to determine the solubilities of compressed He, O~, Ar, CH4, and
`C~H6 in aqueous solutions of sodium dodecylsulfate (SDS) and cetyltrimethylammonium bromide
`(CTAB) using a simple manometric technique. The solubility of each gas follows Henry's law and
`increases linearly with surfactant concentration above the critical micelle concentration. Values
`for the intramicellar solubility and associated AG for transfer of dissolved gas from water to the
`micellar interior are calculated from the data. The intramiceUar solubility of each gas is found to be
`less than that in a typical hydrocarbon. The discrepancy can be explained using a simple phase
`separation model in which the hydrocarbon-like interior of a micelle is considered to be com-
`pressed by interracial tension at the micelle surface.
`
`INTRODUCTION
`Solubilization of normally insoluble or-
`ganic substances in aqueous solutions of
`colloidal electrolytes plays an
`important
`role in innumerable biological and indus-
`trial processes. As a consequence a great
`amount of research has been devoted to this
`topic as described in several comprehensive
`reviews (1). It is somewhat surprising, how-
`ever, that the role such substances play in
`solubilizing gases and low-molecular-weight
`vapors has received comparatively little at-
`tention, with
`refs.
`(2-7) constituting a
`reasonably complete bibliography on this
`subject. As noted much earlier by McBain
`(lb, p. 45), studies of this nature allow one to
`freely vary the chemical potential of the
`solubilizate under
`isothermal conditions,
`thus providing a sensitive probe for examin-
`ing the equilibria involved in solubilization
`processes.
`This paper reports results obtained at
`25°C with a series of gases having widely
`differing solubilities: He, 02, Ar, CH4, and
`C~H6. Solutions of an anionic surfactant
`(SDS) as well as one of the cationic type
`(CTAB) were used.
`
`EXPERIMENTAL
`The experimental equipment and pro-
`cedures used
`in
`these studies are very
`simple. The apparatus consists of a thick-
`walled cylindrical brass bomb which has an
`observation window on
`the side and
`is
`jacketed such that water pumped from a
`remote constant temperature bath makes
`contact with the major portion of its ex-
`ternal surface. The bomb rests on a variable-
`speed magnetic stirrer, thus allowing the
`agitation produced by a magnetic stirring
`bar in the interior of the bomb to be con-
`trolled externally. The bottom of the bomb
`is constructed so that the water used to con-
`trol temperature passes between the top
`surface of the stirring motor and the pres-
`sure supporting surface at the base of the
`bomb proper, thus preventing conduction of
`heat from the motor assembly to the interior
`of the bomb.
`An inlet line to the bomb is connected to
`a gas manifold through an ordinary needle
`valve, thus allowing the bomb to be evacu-
`ated, loaded with the gas desired, and sub-
`sequently vented to the atmosphere. Bout-
`don gauges, accurate to 0.25% of full scale,
`464
`
`oo21-9797/78/o663-o4645o2.oo/o
`Copyright © 1978 by Academic Press, Inc.
`An rights of reproduction in any form reserved.
`
`Journal of Colloid and Interface Science, Vol. 66, No. 3, October 1, 1978
`
`Opiant Exhibit 2312
`Nalox-1 Pharmaceuticals, LLC v. Opiant Pharmaceuticals, Inc.
`IPR2019-00685, IPR2019-00688, IPR2019-00694
`Page 1
`
`

`

`465
`GAS IN MICELLAR SOLUTIONS
`The dense gas is vented through the mani-
`were used to record pressure. These were
`fold leaving the supersaturated solution
`periodically checked against a dead weight
`under a gaseous environment at atmos-
`tester to ensure their accuracy. An exit line,
`pheric pressure. The solution is allowed to
`also attached to the bomb through a needle
`remain this way for a measured period of
`valve, is connected to a Warburg manome-
`ter filled with water.
`time, usually between 30 sec and 1 min,
`in order to restore thermal equilibrium,
`The solution to be studied is made up in a
`glass liner which makes a close fit with the
`after which
`the valve
`leading
`to
`the
`interior walls of the bomb. A clean stirring
`manometer is opened and the one to the
`bar is added, and the liner containing the
`manifold, is shut. The rate of evolution from
`solution is placed inside the bomb. After
`the unstirred solution is first recorded in
`sealing, the bomb is evacuated to a pressure
`order to correct for gas lost during the period
`somewhat above the vapor pressure of
`allowed for thermal equilibration. The stir-
`water, and the solution is allowed to outgas
`rer is then activated, thus initiating a rapid
`with stirring for several hours. The gas to be
`evolution of gas from the supersaturated
`studied is introduced over the solution at the
`solution. After the gas evolution has ceased
`desired pressure, and the solution is allowed
`as indicated by the manometer, the total
`to equilibrate with the dense gas for a mini-
`volume of gas that escaped from the solution
`mum of 5 hr. The stirrer is then stopped,
`is recorded along with the atmospheric pres-
`and the solution is allowed to become still.
`sure and ambient temperature. Allowance is
`made, of course, for the partial pressure of
`water vapor in converting the volume re-
`corded in the buret to moles of gas.
`The SDS used in these experiments, ob-
`tained from Aldrich Chemical Company,
`Inc., was recrystallized from ethanol and
`dried in vacuo before use. The CTAB
`(Eastman technical grade) was recrystal-
`lized from an ethyl acetate-ethanol mixture
`and also dried in vacuo. All gases used were
`C.P. grade or the equivalent, having quoted
`purities of 99.0% or higher for the hydro-
`carbon gases and 99.5% or better for the
`others. Laboratory-distilled water was used
`without further purification.
`RESULTS AND DISCUSSION
`The data obtained in these experiments
`are the moles of gas released by a known
`amount of solution when the pressure is
`dropped from some initial elevated value to
`atmospheric pressure. The highest initial
`pressures in these experiments were the
`order of 10-15 atm with most data taken at
`pressures half this great. Henry's law can be
`assumed to hold under these conditions so
`that the moles of gas released divided by
`gauge pressure when normalized to the
`Journal of Colloid and Interface Science, Vol. 66, No. 3, October 1, 1978
`
`Solubility
`(moles gas/atm) x 103
`0.54
`0.55
`1.41
`1.47
`1.61
`1.70
`1.51
`1.63
`1.74
`1.82
`1.55
`1.88
`2.09
`1.76
`3.46
`4.99
`1.50
`1.64
`1.82
`1.63
`1.80
`1.97
`
`TABLE I
`Moles of Gas Absorbed per Atmosphere in 1000 g of
`H20 with Added Colloidal Electrolytes at 25°C
`
`Solute
`SDS
`
`Gas
`He
`
`O 2
`
`Ar
`
`Moles solute
`0
`0.300
`0
`0.100
`0.200
`0.300
`0
`0.100
`0.200
`0.300
`0
`0.150
`0.300
`0
`0.150
`0.300
`0.100
`0.200
`0.300
`0.100
`0.200
`0.300
`
`CH4
`
`C~H6
`
`O3
`
`Ar
`
`CTAB
`
`Opiant Exhibit 2312
`Nalox-1 Pharmaceuticals, LLC v. Opiant Pharmaceuticals, Inc.
`IPR2019-00685, IPR2019-00688, IPR2019-00694
`Page 2
`
`

`

`5.00
`
`400
`
`300
`
`200
`
`100
`
`%
`
`(9
`L,J
`8
`
`o:
`
`0
`
`466
`MATHESON AND KING
`same amount of solution constitutes a re-
`ciprocal Henry's law constant. For the pur-
`poses of this study, it proved more con-
`venient to normalize the data to a constant
`amount of water, and the solubilities listed
`in Table I are recorded as moles of gas dis-
`solved per atmosphere in solutions contain-
`ing varying amounts of surfactant dissolved
`in 1 kg of water. Each value listed is the
`average of three experimental measure-
`ments, all taken at different pressures. The
`average error associated with each entry is
`_+0.03 x 10 -~ moles of gas/atm. The ac-
`curacy of these results depends upon the
`fact that the evolution of gas from an un-
`stirred supersaturated solution
`is suf-
`ficiently slow that any correction attributed
`to it is small. In these experiments which
`typically involved the order of 100 ml of
`solution, the rate of gas evolution seldom
`exceeded 0.6 ml/min. The total volume col-
`lected was typically 20-30 ml. Thus the
`correction accounting for gas that escaped
`during thermal equilibration following the
`pressure release amounted to only 1% of
`the recorded volume.
`The solubilities of Table I are shown in
`Fig. 1 plotted as a function of concentra-
`tion of surfactant in micellar form, Cm = m
`-CMC. Here m represents formal sur-
`factant concentration expressed as molality
`and CMC denotes the critical micelle con-
`centration. Values of 8 x 10 -3 and 9 x 10 -4
`m were used as CMC values for SDS and
`CTAB, respectively, in these calculations
`(8). The straight lines shown in Fig. 1 were
`fitted to each set of data by the method of
`least squares, and the resulting coefficients
`are listed in part A of Table II. The intercept
`"b" for each gas represents the solubility
`of that gas in pure water at a partial pres-
`sure of 1 atm and is recast in the more
`familiar mole fraction units in part B of
`Table II: X~2o = b/55.35. A comparison
`with the values recommended by Wilhelm
`et al. (9) for these systems indicates that
`solubilities obtained in these experiments
`are quite accurate. Similarly, if the small el-
`
`/
`
`O
`
`O
`
`C2H6
`
`CH 4
`
`O~
`
`~
`
`~
`
`o
`
`~
`
`
`
`~° :=] 02
`
`0
`
`He
`
`I
`
`[
`0.1 O0
`
`,
`
`,
`
`I
`0300
`
`,
`
`o
`
`) ~
`
`I
`0200
`Crn(MOL B S~lO00g)
`FIG. 1. Moles of gas absorbed per atmosphere in
`1000 g of H20 with added colloidal electrolyte as a
`function of moles of solute in micellar form at 25°C.
`©,
`SDS; E],
`CTAB.
`
`fects expected from salting out and pre-
`micellar equilibria are ignored, the coeffi-
`cient "a" can be identified with the gas
`solubility within the micelle proper, Xm~¢ene.
`g
`These are listed in Table IIB along with
`values for the distribution coefficient, K,
`and corresponding free energy of transfer,
`AG~R =-RTIn K, for each system. The
`AG~a for ethane with SDS obtained here
`(-3.47 kcal/mole) agrees well with that
`found by Wishnia for C2H6 with SDS in 0.1
`M NaC1 (AG~rt = -3.45 kcal/mole (6).
`The gases listed in Table II are arranged
`in order of increasing critical temperature.
`Since they are all nonpolar, one expects an
`increasing contribution of London disper-
`sion forces to the overall potential energy
`
`Journal of Colloid and Interface Science, Vol. 66, No. 3, October 1, 1978
`
`Opiant Exhibit 2312
`Nalox-1 Pharmaceuticals, LLC v. Opiant Pharmaceuticals, Inc.
`IPR2019-00685, IPR2019-00688, IPR2019-00694
`Page 3
`
`

`

`GAS IN MICELLAR SOLUTIONS
`
`TABLE II
`A. Least-Squares Results
`
`S = aCm + b,
`
`S ~
`
`Moles gas/arm
`1000 g H20 + C~ solute
`
`467
`
`Gas
`He
`O~
`Ar
`CH4
`C2H6
`O~
`Ar
`
`b × 103
`a × 10 ~
`Solute
`0.54
`0.0(3)
`SDS
`1.40
`1.04
`SDS
`1.52
`1.06
`SDS
`1.57
`1.8(5)
`SDS
`1.80
`11.1
`SDS
`1.39
`1.4
`CTAB
`1.50
`1.5(5)
`CTAB
`B. Solubilities of Gas~s at 25°C and 1 arm Expressed as Mole Fraction
`
`o-. × 10 ~
`0.03
`0.09
`0.08
`0.3
`0.5
`0.1
`0.09
`
`Gas
`
`He
`02
`A
`CH4
`C2H6
`02
`Ar
`
`Solute
`
`SDS
`SDS
`SDS
`SDS
`SDS
`CTAB
`CTAB
`
`X~o × 104
`
`X~c~ne x 104
`
`0.09 (0.07) b
`0.25 (0.23)
`0.27 (0.26)
`0.28 (0.25)
`0.32 (0.33)
`0.25
`0.27
`
`-0
`10
`11
`19
`111
`14
`16
`
`Standard deviation.
`b Recommended values from Ref. (9).
`
`K =
`
`/gmleelle
`X~,o
`--
`40
`41
`68
`350
`56
`59
`
`-AG~R(kcal/mole)
`
`[gas]mlc+n+
`Kc = -
`-
`
`lgast~o
`
`--
`2.20
`2.20
`2.50
`3.47
`2.38
`2.42
`
`2.9
`3.0
`5.0
`26
`2.8
`2.9
`
`determining the solubility as one proceeds
`down the list. It is seen that, as might be
`expected, the partitioning of gas into the
`micelle is favored as the critical temperature
`increases. A comparison of Ar and 02 solu-
`bilities in SDS to those in CTAB shows that
`CTAB solubilizes more gas than SDS on a
`mole fraction basis.
`Partial molar volumes have been meas-
`ured above and below the critical micelle
`concentration for both CTAB and SDS (10).
`Above the CMC, the partial molar volumes
`for CTAB and SDS are found to be ~ = 365.4
`and 246.4 ml/mole, respectively. Thus with-
`out recourse to any specific model of a
`micelle, one can use these values to convert
`the distribution coefficients of Table II
`based on mole fractions to distribution co-
`efficients based on concentrations: Kc
`= [gaS]mieene/[gas]~2o = K(18/9). A compari-
`son of the values listed in Table II for Ar
`
`and Oz in the two surfactants reveals that
`on a volume basis both Ar and 02 are about
`equally concentrated
`in the micellar in-
`teriors, taken as a whole, of each surfactant.
`In a recent paper (11), Mukerjee calls at-
`tention to the role that Laplace forces play
`in determining intramicellar properties. It is
`interesting therefore to examine these data
`in terms of a simple phase separation model
`in which the micellar interior is considered
`to be a long chain hydrocarbon which is
`subjected to a hydrostatic pressure gen-
`erated by the surface tension forces at the
`curved micelle-water interface. Gas solu-
`bility in such a micellar interior would be
`expected to be less than that in an equivalent
`hydrocarbon at atmospheric pressure.
`Table III lists the solubilities of these
`gases in n-dodecane and various other long
`chain n-alkanes. Experimentally it is found
`that on a mole fraction basis gas solubilities
`Journal of Colloid and Interface Science, Vol. 66, No. 3, October 1, 1978
`
`Opiant Exhibit 2312
`Nalox-1 Pharmaceuticals, LLC v. Opiant Pharmaceuticals, Inc.
`IPR2019-00685, IPR2019-00688, IPR2019-00694
`Page 4
`
`

`

`TABLE III
`Gas Solubility in Hydrocarbons and Laplace Pressures
`Gas
`- AG ~'rt
`~,
`P (atm)
`solvent
`(kcal/mole) (cm3/mole)
`--
`He/Clz
`1.90
`48 a
`319 a, 400 e
`2.63
`56 a, 46 e
`02/C9
`Ar/Ct2
`2.69
`52 d, 48 r 388 a, 420 ~
`CHJC6
`3.08
`60 a , s
`400
`C2H6/C9
`4.12
`68 a, 690
`410
`
`X~ x 104
`2.24 a
`21.2 b
`25.5 ~
`50.8 ~
`336 ~
`
`468
`MATHESON AND KING
`do not change appreciably with size of the
`n-alkane beyond a carbon number of six
`(12). Consequently, the solubilities listed
`can be taken as reasonable estimates of gas
`solubility in the interior of a micelle in the
`absence of any Laplace pressure. It is seen
`that for each gas the solubility and asso-
`ciated free energy of transfer, AG~a, from
`water to hydrocarbon is greater than that for
`the micelle (Table II). Within the framework
`of this model, the difference between the
`free energy of transfer to the micelle and
`that to the hydrocarbon can be equated to a
`positive contribution to the chemical poten-
`tial of the solubilized gas molecule resulting
`from the Laplace pressure of the micelle
`interior, P,
`AG:, = AG~'g- AG,~R
`= RT In (ghg/gm g) -~ PEg;
`Ill
`where bg denotes the partial molar volume
`of dissolved gas, taken to be constant with
`respect to pressure. Values for partial molar
`volumes of the gases are listed in Table IH
`along with the ratio of AGp/bg = P calculated
`for each gas. It is seen that although the
`range in partial molar volumes is not ex-
`tremely great, the values calculated for
`Laplace pressure are remarkably constant
`and assume an average value of 400 arm.
`The Laplace pressure inside a body en-
`closed by a convex surface having a surface
`tension y
`is given by
`the well-known
`formula
`
`a Reference (12).
`0 Thomsen, E. S., and Gjaldbaek, J. Chr., Acta.
`Chem. Scand. 17, 127 (1963).
`c Lannung, A., and Gjaldbaek, J. Chr., Acta. Chem.
`Scand. 14, 1124 (1960).
`a Ng, W. Y., and Walkley, J., J. Phys. Chem. 73,
`2274 (1969).
`e Hildebrand, J. H., and Scott, R. L., "The Solubility
`of Nonelectrolytes," Reinhold, New York, 1950;
`reprinted, Dover, New York, 1964.
`f Walkley, J., and Jenkins, W. I., Trans. Faraday
`Soc. 64, 19 (1968).
`o Gjaldbaek, J. Chr., and Hildebrand, J. H., J.
`Amer. Chem. Soc. 72, 1077 (1950).
`
`the range y/r < P < 2T/r.
`lie within
`to
`Thus taking a radius of 15 2k to be common to
`both types of micelles, one finds that the
`tension at the micellar surface necessary to
`generate 400 atm falls between 30 and 60
`dyn/cm, which are surprisingly high values.
`It should be noted, of course, that any factor
`that serves to reduce gas solubility, for ex-
`ample, water penetration in the micelle, will
`be reflected as an increase in Laplace pres-
`sure as it is treated here.
`There is other evidence of a similar nature
`that suggests that Laplace pressure plays a
`[2]
`P = y[1/ra + l/r2];
`significant role in solubilization phenomena.
`It is well known that for a given surfactant
`where rl and rz denote radii of curvature
`the mole ratio of solubilized paraffin to sur-
`of the surface. In his discussion concern-
`factant decreases with increasing molar vol-
`ing this factor, Mukerjee chose a sphere
`ume of solubilizate; and that among sur-
`having a diameter of 30 A and a surface
`factants having a common head group, the
`tension of 20 dyn/cm as his model, thus
`amount solubilized per mole of surfactant
`estimating a pressure of 250 atm for micelle
`increases with length of the hydrophobic
`interiors. At the relatively high surfactant
`group of the surfactant. It is reasonable to
`concentrations used here, it is likely that a
`expect alkanes larger than pentane to form
`significant fraction of the micelles assume an
`ideal solutions in the hydrophobic interior of
`elliptical shape. Thus one expects
`the
`a micelle. Thus, if the incorporation of
`Laplace pressure encountered in this work
`Journal of Colloid and Interface Science, Vol. 66, No. 3, October 1, 1978
`
`Opiant Exhibit 2312
`Nalox-1 Pharmaceuticals, LLC v. Opiant Pharmaceuticals, Inc.
`IPR2019-00685, IPR2019-00688, IPR2019-00694
`Page 5
`
`

`

`TABLE IV
`Micellar Solubilities of n-Alkanes
`
`KC~2
`
`nh/naoap
`(calc)
`0.14
`0.08
`0.04
`0.01
`
`Hydrocarbon
`n-Hexane
`n-Octane
`n-Decane
`n-Hexadecane
`a Reference (lb).
`
`nh/?l~av
`(exp) ~
`0.18
`0.08
`0.03
`0.00
`
`NaC~8
`
`r/h/n~a p
`(calc)
`0.28
`0.18
`0.12
`0.03
`
`nh/nmap
`(exp) ~
`0.46
`0.18
`0.05
`0.00
`
`469
`GAS IN MICELLAR SOLUTIONS
`the sake of brevity. They are available from
`one of the authors (A.D.K.) upon request.
`ACKNOWLEDGMENT
`The authors would like to express appreciation
`for the support provided by the National Science
`Foundation (NSF Grant No. CHE-7608771).
`REFERENCES
`1. (a) Winsor, P. A., "Solvent Properties of Amphi-
`philic Compounds," Butterworths, London,
`1954; (b) McBain, M. E. L., and Hutchinson,
`E., "Solubilization and Related Phenomena,"
`Academic Press, New York, 1955; (c) Elworthy,
`P. H., Florence, A. T., and Macfarlane, C. B.,
`"Solubilization by Surface-Active Agents,"
`Chapman & Hall, London, 1968; (d) Tanford,
`C., "The Hydrophobic Effect," Wiley, New
`York, 1973.
`2. McBain, J. W., and O'Conner, J. J., J. Amer.
`Chem. Soc. 62, 2855 (1940).
`3. McBain, J. W., and O'Conner, J. J., J. Amer.
`Chem. Soc. 63, 875 (1941).
`4. McBain, J. W., and Soldate, A. M., J. Amer.
`Chem. Soc. 64, 1556 (1942).
`5. Ross, S., and Hudson, J. B.,J. ColloidSci. 12, 523
`(1957).
`6. Wishnia, A., J. Phys. Chem. 67, 2079 (1963).
`7. Winters, L. J., and Grunwald, E., J. Amer. Chem.
`Soc. 87, 4608 (1965).
`8. Mukerjee, P., and Mysels, K. J., "Critical Micelle
`Concentrations of Aqueous Surfactant Sys-
`tems." Nat. Stand. Ref. Data Series, Nat. Bur.
`Stand. (U. S.) NSRD S-NBS 36, Feb. 1961.
`9. Wilhelm, E., Battino, R., and Wilcock, R. J.,
`Chem. Rev. 77, 219 (1977).
`10. Corkill, J. M., Goodman, J. F., and Walker, T.,
`Trans. Faraday Soc. 63, 768 (1967).
`11. Mukerjee, P., KolloidZ. Z. Polym., 236, 76 (1970).
`12. Clever, H. L., Battino, R., Saylor, J. H., and
`Gross, P. M., J. Phys. Chem. 61, 1078 (1957).
`
`solubilizate causes a negligible change in
`micellar radius, the micellar solubility is
`related
`to
`the Laplace pressure quite
`simply by
`
`[3]
`Xi = exp{-Pvi°/RT} ;
`where v~ ° denotes the molar volume of the
`pure alkane. Data for the solubilities of
`alkanes in SDS or CTAB are not known to
`these authors. However, solubilization data
`are available for several alkanes
`in the
`closely related
`surfactants, potassium
`laurate and sodium stearate (lb). These are
`listed in Table IV along with values esti-
`mated with Eq. (3) using P = 400 atm for
`the C12 soap and 280 atm = (12/18) 400 for
`the C18 soap. The agreement between calcu-
`lated and experimental values is remarkable
`considering the simplicity of this model.
`Supplementary material available. Tabu-
`lated values for the individual solubility
`measurements have not been included, for
`
`Journal of Colloid and Interface Science, Vol. 66, No, 3, October 1, 1978
`
`Opiant Exhibit 2312
`Nalox-1 Pharmaceuticals, LLC v. Opiant Pharmaceuticals, Inc.
`IPR2019-00685, IPR2019-00688, IPR2019-00694
`Page 6
`
`