The Solubility of Gases in Aqueous Solutions of Decyltrimethyl(cid:173)
`and Cetyltrimethylammonium Bromide
`
`W. PRAPAITRAKUL AND A. D. KING, JR.
`
`Department of Chemistry, University of Georgia, Athens, Georgia 30602
`
`Received August 20, 1984; accepted November 9, 1984
`
`Measurements have been made to determine the solubilities of oxygen, argon, methane, ethane,
`propane, and carbon tetrafluoride at elevated pressures in aqueous solutions of decyltrimethylammonium
`bromide and cetyltrimethylammonium bromide. The solubility of each gas follows Henry's law at all
`surfactant concentrations. Below the critical micelle concentration, the gas solubilities are independent
`of surfactant concentration and closely approximate the corresponding solubilities in pure water.
`Above the critical micelle concentration, the gas solubilities increase linearly with surfactant concentration
`indicating micellar solubilization. The intramicellar solubilities of the individual gases calculated from
`these latter data are found to be comparable to those determined previously with anionic surfactants
`of the alkyl sulfate class suggesting that, with ionic surfactants, the nature of the head group is of little
`consequence in determining the magnitude of intramicellar solubilities. The micellar solubilities of
`CF4 in these surfactants are found to be much smaller than the solubilities of hydrocarbon gases in
`these same micelles indicating that the tendency for mutual exclusion exhibited by fluorocarbons and
`hydrocarbons in bulk solution is also operative in micellar solubilization. These latter data are used
`to further test the applicability of the Laplace pressure model for describing the degree of solubilization
`by various surfactants. © 1985 Academic Press, Inc.
`
`INTRODUCTION
`
`Micellar aggregates present in aqueous so(cid:173)
`lutions of surfactants are capable of solubiliz(cid:173)
`ing nonpolar gases in much the same manner
`as nonpolar solids and liquids. While this
`phenomenon was noted quite early by
`McBain and co-workers (la-c), it has received
`comparatively little attention over the years
`as indicated by the paucity of citations in the
`bibliography contained in Ref. (1). Neverthe(cid:173)
`less, measurements of gas solubility in mi(cid:173)
`cellar solutions are quite useful in that they
`readily provide information about standard
`free energy changes associated with solubili(cid:173)
`zation processes. Since gas molecules are
`small and present at low concentrations in
`these experiments, it can be assumed with
`reasonable confidence that the solubilized gas
`molecules do not perturb the micelles within
`a solution to any appreciable extent thus
`facilitating comparisons between solubiliza-
`
`tion equilibria and the corresponding equi(cid:173)
`libria involving gases dissolved in homoge(cid:173)
`neous bulk phases. It is this feature that
`makes gas solubilization measurements par(cid:173)
`ticularly useful as a means for studying mi(cid:173)
`celles.
`Previous studies in this laboratory have
`examined how the degree of solubilization in
`solutions of ionic surfactants depends upon
`the nature of the gas (lh), the presence of
`amphiphilic additives (Ii), salinity (lj), tem(cid:173)
`perature (1 o ), and the size of the hydrophobic
`portion of the anions of alkyl sulfate class
`surfactants (lm). This paper examines the
`roles that alkyl chain length and head group
`play in determining the extent of solubiliza(cid:173)
`tion. It reports the results of a series of
`solubility measurements involving six gases
`of widely differing properties (02 , Ar, CH4 ,
`C2H6 , C3H 8 , CF 4) in solutions of two cationic
`surfactants, decyltrimethylammonium bro(cid:173)
`mide (OT AB) and cetyltrimethylammonium
`
`0021-9797/85 $3.00
`Copyright © 1985 by Academic Press, Inc.
`All rights of reproduction in any form reserved.
`
`186
`
`Journal oJCo//oid and Interface Science, Vol. 106, No. 1, July 1985
`
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`

`

`GAS SOLUBILITY IN AQUEOUS SOLUTIONS
`
`187
`
`bromide (CTAB) at 26°C. The results of a
`series of solubility determinations for CF4 in
`micellar solutions of sodium dodecyl sulfate
`(SDS) at 25°C are also reported. The gas CF4
`is included in this work in order to ascertain
`whether the extreme positive deviations from
`ideality exhibited by mixtures of fluorocar(cid:173)
`bons and hydrocarbons in the bulk phase
`occur in micelles as well.
`
`EXPERIMENT AL
`
`The method used to determine gas solu(cid:173)
`bilities has been described in detail previously
`(lh). It differs from other common methods
`in that it involves measuring the volume of
`gas released from solutions saturated at ele(cid:173)
`vated pressures. The procedure followed con(cid:173)
`sists of three steps: (i) the solution to be
`studied is allowed to equilibrate with the gas
`of interest at an elevated pressure in a ther(cid:173)
`mostated bomb equipped with a magnetically
`driven stirrer; (ii) the stirrer is stopped and
`
`the solution is allowed to become still where(cid:173)
`upon the pressure is released; (iii) after a
`short delay ( ~ 1 min) in order for thermal
`equilibrium to be reestablished following the
`release of the gas, the magnetic stirrer is
`again activated and the volume of gas released
`from the supersaturated solution is measured
`manometrically at ambient pressure. In this
`manner one determines the number of moles
`of gas released, lln, as the solution proceeds
`isothermally from what was previously an
`equilibrium state at the upper pressure to a
`new equilibrium state at ambient pressure.
`The difference in pressure between these two
`equilibrium states, llP, is numerically equal
`to the gauge pressure recorded during the
`initial equilibration, step (i). The series of
`steps (i)-(iii) are repeated at one or more
`different pressures to establish that the ratios
`lln/ llP are independent of pressure. This was
`found to be the case in every instance so that
`the average values of t:rn/ llP listed in Table
`I can be taken to represent gas solubilities in
`
`Gas Solubilities in Surfactant Solutions Expressed Moles Gas per Atmosphere in 1000 g H 20 at 26°C
`
`TABLE I
`
`Surfactant
`
`Decyltrimethylammonium
`bromide
`
`Cetyltrimethylammonium
`bromide
`
`Sodium dodecyl sulfatec
`
`Surfactant
`concentration
`(m)
`
`0
`0.04
`0.10
`0.20
`0.30
`0.40
`0.50
`
`0.10
`0.20
`0.30
`0.40
`
`0.10
`0.30
`0.50
`
`Gas solubility (m) X l03 '
`
`Ar
`
`CH4
`
`C2H6
`
`C3H8
`
`J.5 J b
`1.52
`1.56
`1.65
`1.72
`1.75
`1.88
`
`1.68
`1.79
`1.92
`2.02
`
`J.55b
`1.50
`1.56
`1.71
`1.93
`2.06
`2.25
`
`1.79
`2.08
`2.41
`
`J.76b
`1.78
`2.07
`2.88
`3.70
`4.53
`5.25
`
`3.39
`4.87
`6.42
`
`J.42c
`1.4
`2.2
`4.3
`6.2
`8.6
`10.4
`
`6.2
`11.4
`15.6
`
`o,
`
`J.4Jb
`1.45
`1.41
`1.46
`1.54
`1.61
`1.66
`
`1.52
`1.58
`1.72
`1.79
`
`CF,
`
`0.27
`0.29
`0.28
`0.36
`0.41
`0.43
`0.45
`
`0.42
`0.42
`0.56
`
`0.37
`0.48
`0.58
`
`a Average errors of solubilities measured in this experiment for 0 2 , Ar, CH4 , C2H 6 , C3H 8 , and CF4 are ±2 X 10-s,
`, and ±2 X 10-5 m, respectively.
`±3 X 10-5
`, ±2 X 10-5
`, ±7 X 10-5
`, ±2 X 10-4
`h Data taken from Ref. (Im).
`c T = 25°C.
`
`Journal of Colloid and Interface Science. Vol. 106, No. I, July 1985
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`

`

`188
`
`PRAPAITRAKUL AND KING
`
`tions of CT AB (and DTAB) were maintained
`at 26°C for these experiments. Previous ex(cid:173)
`periments have shown that the heats of so(cid:173)
`lution of propane in micelles of sodium octyl
`sulfate and SDS are quite small ( 1 o ). There(cid:173)
`fore micellar gas solubilities can be expected
`to be relatively insensitive to temperature so
`that values obtained at 26°C can be compared
`directly with similar data at 25°C, e.g., the
`solubilities of CF4 in SDS in Table I, without
`introducing any appreciable error.
`The solubilities of the various gases dis(cid:173)
`solved in solutions of DT AB and CT AB are
`shown plotted as a function of surfactant
`concentration in Figs. 1 and 2. The data in
`Fig. 1 reveal several features of interest. As
`noted above, the CMC for DTAB is 0.055
`M. Therefore, the fact that the solubilities
`measured for each gas in 0.04 m solutions of
`DT AB are, within experimental error, the
`same as the corresponding solubilities in pure
`water reflects the absence of micelles neces-
`
`11-0
`
`10·0
`
`90
`
`80
`
`0
`
`the respective solutions at a partial pressure
`of 1 atm with Henry's law being satisfied for
`each system.
`The cetyltrimethylammonium bromide used
`in experiments was purchased from Aldrich
`Chemical Company (Cat. No. 85,582-0, Lot
`No. 5814AJ), having a quoted purity of95%.
`The decyltrimethylammonium bromide was
`from Eastman-Kodak Company (Lot No.
`AlOE and AlOF), with no quoted purity.
`The sodium dodecyl sulfate was BDH Prod.
`No. 44244 (Lot No. 9088113C), purchased
`from Gallard-Schlesigner Chemical Mfg.
`Corporation, having a quoted purity of99.0%.
`Each surfactant was recrystallized once from
`2-propanol and dried in vacuo before use.
`Gas chromatographic analysis of the alcohol
`resulting from acid-catalyzed hydrolysis of
`the sodium dodecyl sulfate revealed that the
`SDS was better than 99% pure with respect
`to alkyl chain length. No chemical analyses
`were performed on the trimethylammonium
`surfactants. However, sharp, well-defined
`CMC values of 9 X 10-4 and 5.5 X 10-2 M
`were obtained with the recrystallized CT AB
`and DTAB, respectively, using the surface
`tension method. The close agreement between
`the experimental CMC values and those rec(cid:173)
`ommended in the literature (2) suggests that
`the CT AB and DT AB surfactants used here
`were very pure with respect to chain length
`of the alkyl groups. All gases used were CP
`grade or the equivalent, having quoted puri(cid:173)
`ties of 99.0% or better for the hydrocarbon
`gases, and 99.7% or better for tetrafluoro(cid:173)
`methane, oxygen, and argon. The oxygen
`and argon were obtained from Selox Corpo(cid:173)
`ration while the remaining gases were pur(cid:173)
`chased from Matheson. Doubly distilled water
`was used to make up all solutions.
`
`RESULTS AND DISCUSSION
`
`The gas solubilities determined in these
`experiments are listed in Table I. The Krafft
`temperature of CT AB
`is relatively high
`( ~20°C) (3). Therefore, in order to avoid
`precipitation at higher concentrations, solu-
`
`Journal of Colloid and Interface Science. Vol. 106, No. I, July 1985
`
`~ 7-0
`E
`+-' a
`~ 6-0
`~
`"' ~ 50
`.s
`
`>- 4-0
`C:
`_j m
`5l
`
`::, 30
`_J
`
`!" 0//''"'
`/ I//
`
`0
`
`81/
`-o- CH4
`- - o~ o - o -A r
`2.00-0--1
`8-=e=i'-==8~§=8--8--o- 02
`10 [-
`l-o-o--o--o--o--O- c~
`0 '-------'----L---'------'--'-----'----'---'------'--'----'-----'
`0
`0-1
`0-2
`0-3
`0-4
`0-5
`0-6
`SURFACTANT CONCENTRATION (moles kg-1)
`
`Flo. I. Moles of gas absorbed per atmosphere in 1000
`g of H20 with added decyltrimethylammonium bromide
`shown as a function of surfactant concentration at 26 °C.
`
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`

`GAS SOLUBILITY IN AQUEOUS SOLUTIONS
`
`189
`
`16-0
`
`14-0
`
`12-0
`
`E 10.0
`+-'
`0
`',
`Ol
`.Y
`lll 8-0
`<I>
`0
`~
`>- 6-0
`f-
`_J
`
`iii 3 4-0
`
`0
`<fl
`
`0
`
`o/o/CzH5
`
`0/
`2.0 V --o-- __ 0 _ Ar
`
`-/ /
`
`0-CH4
`
`e---==§=8=8--0-02
`
`l--0--0--0-C~
`
`o~ -~ -~ - -~ -~ -~
`0
`0-1
`0-2
`0-3
`0 4
`0-5
`SURFACTANT CONCENTRATION (moles kg -1)
`
`FIG. 2. Moles of gas absorbed per atmosphere in 1000
`g of H20 with added cetyltrimethylammonium bromide
`shown as a function of surfactant concentration at 26 °C.
`
`sary to induce solubilization. Above the CMC,
`the solubilities of each gas are seen to increase
`with surfactant concentration. The linearity
`of the rising portions of these curves indicates
`that while micelle concentration, hence sol(cid:173)
`ubilization, increases with added surfactant,
`the ability of micelles of DT AB to solubilize
`the various gases is insensitive to surfactant
`concentration, even at concentrations as large
`as 0.6 m. As seen in Fig. 2, the data obtained
`with CT AB exhibit the same characteristics
`although the extent to which the gas solubil(cid:173)
`ities are enhanced by added surfactant is
`much greater, indicating that micelles of
`CT AB solubilize gases more effectively than
`those of DTAB. With the exception of CF4 ,
`the extent to which the individual gases are
`solubilized in the two surfactants increases
`with critical temperature of each gas, as is
`normally the case for solutions in nonpolar
`solvents. 1 CF 4 represents a special case in
`
`1 The critical temperatures of 0 2, Ar, CH4, C2H6, and
`C3H8 fall in the sequence: 154 "" 151 < 190 < 305
`< 370 K. The critical temperature of CF4 is 228 K.
`
`view of the well-known anomalies exhibited
`by solutions of highly fluorinated gases such
`as CF4 and SF6 in hydrocarbon solvents (4).
`If it is assumed that surfactant monomer
`concentration remains effectively constant
`above the CMC, then the slopes of the upward
`rising portions of the solubility data shown
`in Figs. l and 2 can be taken to be ratio of
`solubilized gas molecules to micellized sur(cid:173)
`factant ions present in each solution. 2 The
`solubilized gases constitute a highly dilute
`system so that the mole ratios defined by
`these slopes approximate mole fraction sol(cid:173)
`ubilities of the individual gases in micellar
`DT AB and CT AB at l atm, X~. Micellar
`solubilities thus derived from the upward
`rising slopes of the data of Figs. 1 and 2 are
`listed for each gas in Table II. One-atmo(cid:173)
`sphere solubilities of these same gases in
`water and various normal alkanes are in(cid:173)
`cluded in Table II for comparison.
`The gases' listed in Table II are arranged
`in the order of increasing solubility in hydro(cid:173)
`carbon solvents. The micellar gas solubilities
`for a given surfactant follow the same order.
`The gases are seen to be orders of magnitude
`more soluble in micelles than in water. On
`the other hand, the micellar gas solubilities
`are themselves substantially smaller than cor(cid:173)
`responding solubilities in bulk hydrocarbons.
`Furthermore, in contrast to the individual
`gas solubilities in hydrocarbons, which do
`not vary appreciably from one hydrocarbon
`to the next, the micellar solubility of each
`gas decreases markedly as the length of the
`
`2 Measurements of the electrochemical potential of
`solutions of DT AB using ion selective electrodes by Kale
`et al. (5), show that the activity of the decyltrimethylam(cid:173)
`monium cation decreases by roughly 50% of its value at
`the CMC as the surfactant concentration increases from
`the CMC to 0.6 M. Assuming that this decrease is the
`result of a decrease in monomer concentration accom(cid:173)
`panied by a corresponding increase in micellized ions,
`the discrepancy between the resulting concentration of
`micellized cations and that predicted assuming a constant
`monomer concentration is less than 3% at 0.6 M, the
`highest DT AB concentration used here. The discrepancy
`is expected to be even less with CT AB in view of its
`lower CMC.
`
`Journal of Colloid and Interface Science. Vol. 106, No. I, July 1985
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`

`

`190
`
`PRAPAITRAKUL AND KING
`
`TABLE II
`
`Gas Solubilities at 26°C and I atm (Mole Fraction X 104
`
`)
`
`Surfactants and bulk solvents
`
`Gas
`
`CTAB'
`
`DTAB'
`
`SDS'
`
`Waterb
`
`n-Alkane/carbon No_h
`
`CF4
`02
`Ar
`CH4
`C2H6
`C3H8
`
`9
`10
`13
`29
`155
`480
`
`4
`7
`7
`17
`80
`210
`
`5
`(lOY
`(11 )d
`(19)"
`( I 10)'
`(320)'
`
`0.049 (0.038)'
`0.25 (0.23)'
`0.27 (0.25)'
`0.28 (0.25)'
`0.32 (0.33)'
`0.26 (0.27)'
`
`21.5/7~ J9.7/8K, 20.0/8\ J8.7/10h
`21.611;, 20.9;8;, 21.2w
`25.3/61, 25.0/71, 24.5/81, 24.5/91, 24.8/JOi, 25.5/IY, 25.9/141
`50.8/6k
`325/61, 329/7;, 337 /8;, 336/9;
`J J60/6m, 1160/6", 1170/7", J200/8m, 1230/12", 1265/16"
`
`a Estimated errors: CF4 , ±2 X 10-•; 0 2, Ar, CH4 , ±1 X 10-•, C2H6, ±5 X 10-•; C3H 8 , ±10 X 10-•.
`b T = 25°C, estimated error: ±2 X 10-•.
`cRef. (Im).
`d Ref. (lh).
`'Recommended values from Wilhelm, E., Battino, R., and Wilcock, R. J ., Chem. Rev. 77, 2 I 9 (I 977).
`1 Archer, G., and Hildebrand, J. H., J. Phys. Chem. 67, 1830 (1963).
`c Wilhelm, E., and Battino, R., J. Chem. Thermodyn. 3, 379 ( 1971 ).
`h Wilcock, R. J., Battino, R., Danforth, W. F., and Wilhelm, E., J. Chem. Thermodyn. 10, 817 ( 1978).
`'Thomsen, E. S., and Gjaldbaek, J. Chr., Acta Chem. Scand. 17, 127 (1963).
`1 Clever, H. L., Battino, R., Saylor, J. H., and Gross, P. M., J. Phys. Chem. 61, 1078 (1957).
`k Lannung, A., and Gjaldbaek, J. Chr., Acta Chem. Scand. 14, 1124 (1960).
`1Waters, J. A., and Mortimer, G. A., 'J. Chem. Eng. Data 17, 156 (1972).
`m Thomsen, E. S., and Gjaldbaek, J. Chr., Acta Chem. Scand. 17, 134 (1963).
`"Hayduk, W., Walter, E. B., and Simpson, P., J. Chem. Eng. Data 17, 59 (1972).
`
`alkyl chain of the surfactant ion becomes
`shorter. This suggests that, while the interior
`of a micelle is basically hydrocarbon-like in
`nature, the change in free energy associated
`with bringing a gas molecule from the gas
`phase to the interior of a micelle is more
`positive than for the equivalent process in
`which the gas molecule is transferred into a
`bulk hydrocarbon solvent, with the discrep(cid:173)
`ancy becoming more pronounced as the alkyl
`group of the surfactant ion decreases in size.
`A previous paper on this subject ( l m)
`points out that the trends noted above can
`be reconciled in a quantitative manner by
`invoking a simple model in which the interior
`of a micelle is considered to resemble a
`submicroscopic spherical droplet of oil which
`is compressed by Laplace forces acting across
`the curved micelle-water interface. This
`model was first invoked by Mukerjee (6) in
`order to explain the odd-even alternation in
`free energies of micellization observed with
`
`Journal of Colloid and Interface Science. Vol. 106, No. I, July 1985
`
`sodium alkyl sulfates. The effect of this
`compression is to create a pressure difference
`of PL = 2"(/r between the micelle interior
`and the surrounding aqueous phase, where
`'Y denotes the interfacial tension at the micelle
`surface and r is the radius of the micelle.
`The Laplace pressure acts to raise the chem(cid:173)
`ical potential of a solubilized gas molecule,
`component i, by an amount 2"( V;/r where
`V; denotes the molar volume of the solubi(cid:173)
`lized gas so that the chemical potential of
`gas i residing in the interior of a micelle µ7'
`becomes
`µ7' = µf + RTlnX'{' + 2"(V;/r.
`Here R and T symbolize the universal gas
`constant and temperature while XY' denotes
`the mole fraction of gas i dissolved in the
`micelle, and µf is the chemical potential of
`gas i solubilized in a highly dilute Henry's
`law standard state. To the extent that the
`micelle interior can be treated as ordinary
`
`[1]
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`

`GAS SOLUBILITY IN AQUEOUS SOLUTIONS
`
`191
`
`liquid hydrocarbon, then, in the absence of
`surface tension forces, Eq. [1] reduces to the
`expression for the chemical potential of gas
`i dissolved in a hydrocarbon solvent:
`µf = µr + RTln xr.
`It follows therefore that under equivalent
`conditions of temperature and pressure, the
`logarithm of mole fraction concentration of
`gas i solubilized in a micelle will be less than
`that dissolved in a hydrocarbon by an amount
`2-y V;/RTr, i.e.,
`
`[2]
`
`2-y V; 1
`In X'!' = In Xh - - - -
`RT r ·
`'
`'
`
`[3]
`
`Therefore, if the final assumption is made
`that the micelle radius is proportional to the
`carbon number, nc, of the alkyl chain of the
`surfactant ions making up the micelle, r
`= anc, then Eq. [3] can be rewritten in a
`form that allows direct comparison with ex(cid:173)
`periment:
`
`2-y V; 1
`.
`In X:U = In X? - - - -
`aRTnc
`
`[ 4]
`
`In Fig. 3, the micellar solubilities measured
`in these experiments are compared with those
`determined previously with sodium alkyl sul(cid:173)
`fates, using the functional form suggested by
`Eq. [4]. It is seen that with the exception of
`oxygen which appears somewhat less soluble,
`the micellar solubilities of the gases in CT AB
`and DT AB exhibit the same dependence on
`surfactant chain length as that found previ(cid:173)
`ously with the sodium alkyl sulfates. The
`solubilities shown in this figure represent a
`reasonably large sample of data spanning a
`wide range of the independent variable, n; 1
`•
`Therefore, it can be inferred that the size of
`the alkyl tail is the dominant factor in deter(cid:173)
`mining the extent of solubilization and as(cid:173)
`sociated free energy changes for gases dis(cid:173)
`solved in solutions of these two widely dif(cid:173)
`fering classes of surfactants. This implies,
`within the framework of the Laplace pressure
`model, that the surface tension, 'Y, responsible
`for raising the free energy of solubilizate
`
`-90 ~ -~ - -~ - -~ - -~ - - -
`0.25
`0.20
`0.15
`0.10
`0.05
`0
`
`1/nc
`
`Flo. 3. Logarithm of gas solubilities shown as a
`function of reciprocal carbon number. Open circles:
`sodium alkyl sulfate data from Ref. (Im). Shaded circles:
`alkyltrimethylammonium bromide data from this work.
`Argon data not shown for clarity. Inset: slope of lines vs
`partial molar volumes of individual gases.
`
`molecules is insensitive to the nature of the
`charged head group. A previous study show(cid:173)
`ing that added salt does not affect the degree
`that ethane is solubilized in SDS ( lj) tends
`to support this conclusion.
`The data taken using CF4 provides a par(cid:173)
`ticularly important test of the Laplace pres(cid:173)
`sure model. According to Eq. [1], the factors
`that determine the chemical potential of so(cid:173)
`lubilizate molecules at any particular concen(cid:173)
`tration within the micellar pseudophase are
`the molar volume of the dissolved gas, V;,
`and the standard state chemical potential,
`µr , which is common to the micelle interior
`and bulk hydrocarbon solvents (Eq. [2]). The
`magnitude of the standard chemical potential
`is determined solely by the mean potential
`of interaction between the gas molecule i and
`neighboring solvent molecules. Fluorocarbons
`
`Journal of Colloid and Interface Science. Vol. l06, No. I, July 1985
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`Opiant Exhibit 2311
`Nalox-1 Pharmaceuticals, LLC v. Opiant Pharmaceuticals, Inc.
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`Page 6
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`192
`
`PRAPAITRAKUL AND KING
`
`and hydrocarbons present an unusual situa(cid:173)
`tion in that the extreme mismatch in their
`respective intermolecular potentials leads to
`unusually weak forces of attraction between
`these two types of molecules in the liquid
`phase. This has the effect of increasing µf of
`Eqs. [1] and [2], and acts to suppress the
`solubility of fluorocarbons such as CF 4 in
`hydrocarbon solvents. Therefore, according
`to the Laplace pressure model, this effect
`should influence solubilization in a predict(cid:173)
`able way. Equation [4] predicts that (a) the
`mi cellar solubility of CF 4 in surfactants hav(cid:173)
`ing hydrocarbon-like tails should be unusually
`low and (b) that micellar solubilities of CF4,
`when plotted logarithmically against recip(cid:173)
`rocal carbon number of the surfactant tail
`group, should extrapolate linearly to the cor(cid:173)
`responding value for CF4 in bulk hydrocar(cid:173)
`bons, ln X?, at the origin. However, the
`proportionality constant a and the surface
`tension 'Y are properties of the micelle alone.
`Therefore, the slope of the line defined by
`ln X; vs nz I for CF 4 data should exhibit the
`same linear relationship to the molar volume
`of CF 4 as that found with the other gases.
`Straight lines fitted to the data of Fig. 3 using
`the least-squares method have slopes of-9.4,
`-11.4, -12.0, -13.2, -16.8, and -16.6 for
`0 2 , Ar, CH4, C2H6 , C3H8 , and CF4, respec(cid:173)
`tively. Literature values for the partial molar
`volumes (cm3/mole) of these same gases in
`hydrocarbon solvents are 0 2 46 (7), 56 (8),
`Ar 48 (9), 52 (8); CH4 60 (8, 9); C2H 6 68 (8),
`69 (10); C3H8 93 (8); CF4 89 (9). These
`slopes are shown plotted as a function of gas
`molar volume in the inset of Fig. 3. It is seen
`that the slope generated by the micellar sol(cid:173)
`ubilities of CF4 does indeed fall on the line
`defined by the other gases in accordance with
`the predictions of this model. The slope of
`the line shown in the inset is 0.20 mole/cm3
`•
`Since the proportionality constant a can be
`expected to be the order of 1 A, a slope of
`this magnitude corresponds to a value of 'Y
`= 25 dyn/cm for the tension at the micelle
`surface. Mukerjee, in his original paper on
`this topic (6), suggested that a value of 'Y
`
`Journal of Colloid and Interface Science, Vol. 106, No. I, July 1985
`
`= 20 dyn/cm would be expected for micel(cid:173)
`lized alkyl sulfate ions. More recently, Chris(cid:173)
`tian et al. (lk) have used a somewhat larger
`value of 'Y = 30 dyn/cm in order to account
`for the solubilization of cyclohexane in so(cid:173)
`dium octyl sulfate.
`While the results presented here serve to
`extend the utility of the Laplace pressure
`model for predicting the extent of solubili(cid:173)
`zation of small molecules to cationic, as well
`as anionic surfactants, they also bring to
`focus a problem yet to be resolved. Over the
`years a large body of evidence has accumu(cid:173)
`lated which indicates that below 30°C CT AB
`micelles undergo a change in shape from a
`spherical to a rod-like geometry at concen(cid:173)
`trations ranging from 0.2 to 0.3 M (11). The
`gas solubility data collected here with CT AB
`extend into this concentration regime where
`rod-like micelles are thought to exist. How(cid:173)
`ever, no discontinuities are observed in the
`data shown in Fig. 2, and, as seen in Fig. 3,
`the micellar solubilities of the various gases
`in CT AB appear to be accounted for quite
`well by the Laplace pressure model which
`assumes the existence of spherical micelles.
`This contradiction has been noted before in
`studies involving solubilization of ethane in
`SOS at high salinities ( lj) and remains un(cid:173)
`resolved at this time.
`
`CONCLUSION
`
`The mole fraction micellar solubilities of
`the gases CF4, 0 2 , Ar, CH4, C2H6 , and C3H 8
`exhibit the same dependence on alkyl chain
`length of quaternary ammonium type surfac(cid:173)
`tants as was found previously for surfactants
`of the alkyl sulfate class indicating that the
`nature of the head group is unimportant in
`determining the extent of solubilization in
`ionic surfactants. While factors such as water
`penetration into the micellar interior may be
`invoked to explain low solubilities and the
`strong surfactant chain-length dependencies
`associated with gas solubilization in micelles
`( 12), the Laplace pressure model is able to
`correlate micellar solubilities of a wide variety
`
`Opiant Exhibit 2311
`Nalox-1 Pharmaceuticals, LLC v. Opiant Pharmaceuticals, Inc.
`IPR2019-00685, IPR2019-00688, IPR2019-00694
`Page 7
`
`

`

`GAS SOLUBILITY IN AQUEOUS SOLUTIONS
`
`193
`
`of gases on a quantitative basis. In particular,
`the ability of this model to account for the
`extremely low mi cellar solubility of CF 4 in
`both decyl- and cetyltrimethylammonium
`bromide quantitatively strengthens one's
`confidence in the model, although the prob(cid:173)
`lem of accounting for the nonsphericity of
`cetyltrimethylammonium bromide micelles
`is unresolved.
`
`ACKNOWLEDGMENT
`
`The authors would like to express appreciation for
`support provided by the National Science Foundation
`(NSF) Grant CHE-8218288.
`
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`Journal of Colloid and Interface Science, Vol. !06, No. I, July 1985
`
`Opiant Exhibit 2311
`Nalox-1 Pharmaceuticals, LLC v. Opiant Pharmaceuticals, Inc.
`IPR2019-00685, IPR2019-00688, IPR2019-00694
`Page 8
`
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