J . Phys. Chem. 1986, 90, 671-677 011j
4,
Ch A
Figure 6. Plots of transition enthalpies against the ratio of TsA h/TCh-I for compound I (a),compound I1 (O), cholesteryl alkanoates (J. Y . C. Chu, J. Phys. Chem., 79, 119 (1975)) ( O ) , and cholesteryl w-phenylalkanoates (J. L. W. Pohlmann, W. Elser, and P. R. Boyd, MI. Cryst. Liq. Cryst., 20, 87 (1973)) (0). Numbers indicate the carbon numbers in the alkyl chains.
parameter u (interaction strength) which was in some way proportional to the ratio of the molecular length of the hard-core portion to the layer spacing in a smectic A phase, and is a criterion for the thermal stability of the smectic A phase. He found that some SA-N transitions become second order; Le., the latent heat for the transition vanishes.
671
In Figure 6 are plotted the latent heats for the SA-Ch transitions ~ ~ - the ~ , latent heats for cholesteryl against the T S ~ - C ~ / Twhere w-phenylalkanoates and cholesteryl alkanoates are also plotted for comparison. The latent heats for the cholesteryl w-phenylalkanoates and cholesteryl alkanoates tend to converge on the solid line and intersect at 0.92. Although the value is different from the predicted value (0.87) by McMillan, the smectic properties roughly follow the McMillan theory. Similarly, the latent heats on the dotted line in Figure 6 for the present compounds tend to decrease with increase in the ratio. The ratios of TSA-Ch/TCh-I for compounds Ia and Ip are 0.69 and 0.77, respectively, at which the latent heat for the former is ca. 100 J mol-’ and 80 J mol-’ for the latter, suggesting the second-order nature of the SA-Ch transitions. As far as we know, the second-order-type transition from SA to Ch (N) phases in nonpolar liquid crystals is rare, though S,d-N and SA1-N transitions in polar liquid crystals frequently show the second-order nature.2’ The dotted line intersects at 0.77, which is quite small compared with the predicted value by McMillan. On the other hand, the latent heats for the present compounds show remarkable deviations from the dotted line. For example, the latent heats for Ij and IIj are 2.15 and 4.43 kJ mol-’, while the ratios of TSA, Wt%q&
50 Wl%C,,E6
0
10 20 y10/C,2Es 87 13
30
LO &
50
4%
60
70
I
90 1W n-Decmn./C,,E, 67 13 80
Figwe 3. Vertical sections through the phase prism of the system H,O-n-decaneC,E, with increasing amphiphilicity of the amphiphile. Left: scction erected m the cmter line of the Gibb triangle (HP:oil = 1:l); right: d o n erected on a line parallel to the H 2 ~sidel at an amphiphile concentration in the "groove".
amphiphilicity is frequently expressed in terms of the HLB value which, for nonionic amphiphiles, is evaluated from . . HLB = 20(MH/M) where MHis the molar mass of the hydrophilic group and M the total molar mass of the amphiphile. Figure 3 demonstrates, however, that the HLB value cannot be an appropriate measure for the amphiphilicity. This is quantified in Table I, in which we have listed both T and c ~ as. obtained from Figure 3. Since mole fractions are the more appropriate composition variable when
considering molecular interactions, we have also listed the mole fractions of H,O and the amnhiohile. . . . as well as the molar ratio between the two. As one can see, the number of H,O molecules solubilized by each molecule of the amphiphile increases with increasing amphiphilicity of the amphiphile from about 2 to about 106, although the HLB value of all five amphiphiles is about 12, and the mean temperature T i n all five systems is about SO OC. Last but not least, a theory must account for the fact that the position of the three-phase body and, accordingly, that of the groove on the temperature scale, i.e. T, changes considerably
Kahlweit et al.
674 The JOurMl of Physical Chemistry,Vol.90,No. 4, 1986
TABLE I: H@-m-oeU~€4+E,( x ~ d x , = 7.91) CtE, C,E, C6E, C8E, C,,E, CllE6
T,'C
C .
wt % 58.9 47.4 29.6 19.7 10.6
35.5 57.0 50.7 52.0 55.0
X H ~ '
0.640 0.790 0.850 0.869 0.880
XC,E;
XH~O/XC~E:
0.279 0.109 0.042 0.020 0.008,
2.3 7.3 20.2 42.9 106
'Mole fraction. b M ~ l aratio. r though systematically as one varies the oil or the amphiphile within a homologous series, Le., as one varies i, j , and k.
-k
Effect of 1, j . and k on Tof the TbreePbase Body Let us first consider the effect of the hydrophobicity k of the oil on T. For this purpose we reproduce Figure 2 from ref 5 which shows (Tu- TI) for the n-alkanes with different classes of CEE,, including recent results for CloE,(Figure 4). The upper boundary of each cusp represents the dependence of Tu on k, the lower boundary that of T p Both drop with decreasing hydrophobicity of the oil. Tu,however, drops a little faster than T,. As a consequence, (Tu- TI) shapes a cusp for each amphiphile which appears to evolve from a tcp at low k. Due to the high vapor pressure of these short-chain alkanes it is, unfortunately, not possihile to reach these tcp's at 1 bar hy merely decreasing the carbon number of the n-alkanes. In order to reach them one has, in addition, to increase the prssure as was demonstrated in Figure 11 in ref 5. We emphasize, however, that one can reach the tcp by decreasing k even at 1 bar, if one chooss less hydrophobic oils like the phenylalkanes as the homologous series (Figure 7 in ref 5).
From Figure 4 it follows that the position of the cusp on the temperature scale is determined mainly by the interaction of H20 and the amphiphile for which Tsis a measure: the higher To, the higher Tfor a given oil. The slope of the cusps, on the other hand, appears to he determined mainly by the interaction hetween the oil and the amphiphile for which T, is a measure: the higher k, Le., the higher T, for a given amphiphile, the higher T. One further observes that the slope decreases slightly with increasing chain length of the amphiphile. Let us now consider the effect of i and j on (T. - TI) for a given oil. In this case one may change either i at constant j, or vice versa. In Figure 5 we have replotted some data from Figure 4 for n-octane as oil. The cusp declining to the right is that for increasing i at constant j = 4 (lower abscissa), the cusp declining to the left is that for decreasing j at constant i = 8 (upper abscissa). In both cases the cusps appear to approach a tcp. Whether the tcp lies above the melting point of the mixture depends on the outcome of the "race* between Tuand Tp If the Tudrop is much it may catch up with TIabove the melting point steeper than TI, (cusp declining to the right), whereas if the drops is only slightly steeper, the tcp lies helow the melting point (cusp declining to the left). This result shows that the chance to reach a tcp hy changing the amphiphile within a homologous s c r i e s f o r a given oil-is higher, if one increases the hydrophobic group at constant hydrophilic group, instead of vice versa. Figure 6 shows the fishes for the series C,E,. As one can see, and cm,"decrease as one approaches the tcp. both (Tu- TI) Since the theory of near-tricritical systems6 predicts for the relation between the width of the three-phase interval and the distance from the tcp
AT
E
-
(T. - TI) ( T - Ttcp)3/2
where Tq is the temperature of the tcp at that pressure, we have plotted (An2/) vs. T for the system H20aane-C,E,. The result is shown in Figure 7. The straight line, evaluated from the first three points
AT = 0.0616(T ~
(6) Gfiffths, R.B.1.Chont. Phys. 1974,60,195.
See also: Creek, J. L.;
Knobler, Ch. M.:Scott, R. L. 1.Chem. Phys. 1981, 74, 3489.
-k
Figure 4. Three-phase temperature intervals (Tu- TI)for H,C-n-alkanes-C,E, (i = 4, 6, 8, 10, 12).
describes the experimental results sufficiently well, which supports our working hypothesis that the phase behavior of these ternary systems is determined to a more or less good approximation hy
Tricritical Points in Ternary Systems
The Journal of Physical Chemistry, Vol. 90, No. 4. 1986 675
r
-j
100 I 90
-
0
2
\
L
6
8
~
1
~~
I
H,O - n-Octane - CiEj
80 S[OCl 70 -
0 10 20 H20/n-OcIone 1.1
30
LO
50 Wl%C.E,
60
70
60 -
50 LO
201
30 20
LuI
~
Hpn-Octane 1 1
----,
-
80
3
I -1
Figure 5. Three-phase temperature intervals (Tu- TI) for H,O-n-octaneC,E,. Cusp declining to the left for C,E, l j = 3, 4, 5: upper abscissa). Cusp declining to the right for C,E, (i = 6, 8, 10, IZ; lower
abscissa). the universal scaling laws for near-tricritical systems. For this particular system one thus finds a tcp at about 8 OC and an amphiphile with an amphiphilicity between Ct2E4and C14E4as the pivot point. From Figure 6 one may again evaluate the mole fractions of the amphiphile at cmin,x ~ Figure , ~8 shows the results plotted
vs. T. Figure 9 shows the corresponding results for increasing carbon number k of some n-alkanes, with C8E4as the amphiphile. From these results it follows that all models of the microstructure which assume a monomolecular layer of the amphiphile separating stable hulk domains of H 2 0 and oil must a m u n t for the fact that even with amphiphiles with constant headgroup area 0’ = 4) T, (Tu - TI), as well as cmin depend strongly on the parameters i and k. This also holds for amphiphiles with a more compact and, furthermore, more rigid head group like n-alkyldimethylphosphine oxides.’
Figure 6. Vertical sections through the phase prism of the systems H,O-n-octaneC,E, (i = 6, 8, 10, 12).
10
H,O - n-Octane - CiEL
A T 4
How To Reach a Tricritical Point With this information we are now in a position to predict how to reach a tcp by changing either the oil or the amphiphile within a homologous series. Let us first consider a change of the oil. In this case the procedure is rather simple. If the ternary system-with a given amphiphil-hows a connected critical line (Figure 2, left), one has to raise T. by increasing the hydro. phobicity of the oil. Since this has no effect on T,, the ‘bending tension” of the critical line will increase until it eventually breaks as was demonstrated in ref 5 for the system H,C-phenylalkanes-C4E2. If, on the other hand, the system shows a broken critical line with a three-phase body (Figure 2, right), one has to lower T, hy decreasing the hydrophobicity of the oil until the end points of the two critical lines cp. and cp, connect with each other. If, as in the case of n-alkanes as oils, the latter procedure is limited hy the high vapor pressure of the short-chain oils, one has, in addition, to increase the pressure.
‘:..._ .;I
(7) Papisehil, K.-H. Dlngmuir, in press.
CIOEL 0
Tc
Figure I. (Tu-
C12EL
vs.
-
LOiI”C1
60
7 for H,@n-oetane-C,E,
80
(i = 6, 8, IO, 12).
Let us now consider a change of the nonionic amphiphile with a given oil. In view of Figure 5, here the appropriate procedure is to change i at constant j . If the system shows a connected critical line, one may attempt to break it by decreasing i; if it shows a broken critical line with a three-phase body, one has to increase i (at constant j). A third path to reach the tcp is to add an appropriate electrolyte. In our discussion4of the effect of electrolytes on the phase behavior of ternary systems we distinguished between “lyotropic” salts, the addition of which widens the upper A 4 loop, and “hydrotropic”
616 The JourMl of Physical Chemistry, Vol. 90. No. 4, 1986
Kahlweit et al.
.17
50
,101
LO
IL
H,O
w‘
-
n-Octane
- C,E,
-salt
20
NaC,2H25SOLISDS)
.08.06 -
t
.u.02 -
-0
n-
Fwn 8.
”
-
10 20 30 LO 50 60 70 80 f LOCI cmtn(in mole fraction xC&; left ordinate) and molar ratio (right ordinate) for the systems H20-n-octaneC,E4.
xH2,,/xC,,,
.-.05_r
w, xu
t
.OL
-
.03-
HO ,
‘C8E \L
%@/+
k=6/8\10 /+
.02-
c
,011
XC8E‘
01 0
1
nonionic omphiphile IC,E,I
/
- C, -
10 20 30 LO
-
2 3 4 w t % salt Figure 10. Three-phasecusps for the system H,(tn-octan&,E,salt. Laww cusp for NaCl as lyotropic salt with tricritlcal pomt at a ‘negative” salt wncentration. Upper cusp for SDS as hydrotropic salt with tricntical pint within the pseudoternary phase prism.
0
/
electrolyte
12
“aXH20’XC&
‘ T hydrophobicity C ,
J O
50 60 70 80
-i IT1 Figure 9. cdn (in mole fraction xcBy; left ordinate) and molar ratio
xH,o/xcI,, (right ordinate) for the systems H,C-n-alLanes (k)-C8EI. salts, the addition of which makes it shrink. Accordingly, one may reach the tcp of a ternary system with a connected critical line by adding a lyotropic salt. This lowers Ts and thus increases the ‘bending tension-of the critical line until it breaks. This was demonstrated by Lang and Widoms with the system H,Obenzene-ethanol-(NH4)2S04, and thereafter by us with the systems H,Dalkanes-2-methyl-2-propanol or I-propanol-NaCl (see Figure 14 in ref 3). Instead of breaking a connected line one may as well mend a broken line by adding a hydrotropic salt which raises T,. As a consequence, the end points of the two critical lines approach each other; (Tu- T I )both rises and narrows until the two end points merge at the tricritical point (see Figure 8 in ref 4). The counteracting effects of a lyotropic and a hydrotropic salt are demonstrated in Figure 10, which represents a combination of Figures 1 and 8 in ref 4. It shows the three-phase cusps vs. salt concentration for the system H,O-octane-C,E,. At zero salt concentration one finds the interval (Tu-Tl) of the ternary system. As one adds a lyotropic salt (NaCI), the three-phase interval is both lowered and widened, thus shaping a cusp the tcp of which lies outside the (pseudoternary) prism at a ‘negative” salt concentration and can be ‘pushed” into the prism by increasing the pressure. As one adds a hydrotropic salt (SDS), on the other hand, the threephase interval is raised and narrowed until the system reaches its tcp at about 31 OC inside the prism at 1 bar. A similar cusp was found by Kunieda and Arai9 in the system H,O-n-
tetradecantn-C4b-n-CsH17S03Na. Figure 11 summarizes the results of this section. It shows in the center the three-phase temperature interval (Tu - TI)of a ternary system A-B-C. Its phase behavior evolves from four (8) L a y . I. C.: Widom, 8. Physic8 A (Amrerdam) 1975. 8 I A , 190. (9) Kunieda, H.:Arm, R. Bull. Chem. Soe. Jppn. 1984.57. 281.
011 IC,)
Figure 11. Three-phase temperature interval (Tu- TI)of B ternary Sptem (center) as evolution from four tncritioll points (schematic). For discussion see text.
different tricritical points. These can be reached, at least in principle, either by increasing the pressure, by decreasing the hydrophobicity of the oil within a homologous series, by increasing Ci at constant Ej of the amphiphile C,E,, or by adding an a p propriae hydrotropic salt, in particular, an ionic amphiphile. Since the thermodynamic properties of the (central) ternary system are functions of state, this suggests that the scaling laws which govern the evolution of its phase behavior from any of these tricritical points must be equivalent if expressed in the appropriate order parameters.
How To Study the Microstructure of the Solutions The bodies of the heterogeneous phases show a pronounced groove (Figure 3 left) which ascends like a waist from T Ion the water-rich side to T. on the oil-rich side. This suggests that one could cut a vertical section through the prism erected on a line parallel to the A-B-T plane of the prism, i.e. at a constant concentration of the amphiphile just a little higher than cmin.The right column of Figure 3 shows these sections for the five systems on the left. As one can see, one finds a narrow channel of an optically isotropic, strongly scattering homogeneous phase from the water-rich to the oil-rich side of the prism, ascending temperaturewise with increasing oil concentration. The existence of these channels permits the study of the properties of the homogeneous solution close to the body of heterogeneous phases as it changes from an “oil-in-water” to a ”water-in-oil” emulsion. Such measurements, though not exactly along that channel, have been performed, e.&, by Nilsson and Lidmanlo when studying the self-diffusion in ternary systems by NMR. We are, at present, collecting data from low-angle X-ray and static and dynamic light scattering, kinetic @- and T-jump), conductivity, and dielectric (IO) Nilsson, P. G.; Lindmsn. B. J. P h y ~ Chem. . 1983.87.4156.
J. Phys. Chem. 1986, 90,677-683
677
measurements, varying again i, j , and k. The results will be published in forthcoming papers. Together with the features of the macroscopic phase behavior summarized in the preceding sections, these data may then serve as basis for a consistent theory of the microstructure of these ternary systems.
periments, to Mr. D. Luckmann for drawing the figures, and to the Max-Buchner-Stiftung and the German Federal Ministry for Research and Technology (BMFT) for financial support.
Note Added in Proof: Since this paper was submitted, we have shown that the phase behavior of quinary systems of the type H2mil-nonionic amphiphil-ionic amphiphil-alt evolves from a tricritical line that spans across five-dimensional space at 1 bar.”
(1 1) Kahlweit, M.; Strey, R., paper presented at the workshop “Progress in Microemulsions” at Erice, Oct 1985; to be submitted for publication in J . Phys. Chem.
Acknowledgment. We are indebted to Mrs. H. Frahm, Mr. B. Faulhaber, and Mr. T. Lieu for their assistance with the ex-
CHEMICAL KINETICS Mass Spectrometric Investigation and Computer Modeling of the CH,-02-0, from 480 to 830 K
Reaction
G . Rotzoll Institut fur Technische Chemie, Universitat Hannover, 3000 Hannover I , Federal Republic of Germany (Received: February 20, 1985; In Final Form: June 30, 1985)
The reaction of methane with ozonized oxygen was investigated in a molecular beam source reactor, consisting of a heated 1-mm-diameter alumina flow tube equipped with a 0.2-mm nozzle. Typical values for pressure and residence time were 600 mbar and 16 ms, respectively, and the temperature range covered was from 480 to 830 K. The gas mixture expanding from the reactor was transformed into a molecular beam and analyzed by a mass spectrometer. H20, CO, CH20, CH30H, H202,CO,, and C H 3 0 0 H were found as reaction products. The experimental results could be fairly well modeled by a reaction mechanism consisting of 47 elementary reactions with 21 species. A kinetic sensitivity analysis and investigation of the reaction pathways yields the main mechanistic features of the reaction. The reaction is initiated by the thermal decomposition of ozone. Very important in the reaction are secondary reactions of ozone with methyl radicals and hydrogen atoms. Besides that, radical-radical reactions of methyl and methylperoxy radicals play a dominant role in the course of the reaction.
Introduction Ozone can initiate oxidation reactions of alkanes at temperatures where, in the absence of ozone, reaction progress would only be very ~ l o w . I - ~ The simplest alkane reaction, the reaction of methane with ozonized oxygen, was studied by Schubert and Pease: Dillemuth et al.,’ and Kleimenov and Nalbandiang The experiments of the first two groups were carried out in static systems at low temperatures and rather long reaction times. Products observed by infrared absorption analysis were CO, C02, HCOOH, and H 2 0 . The disappearance of ozone was analyzed in terms of a second-order reaction with methane, resulting in an activation energy of about 15 kcal/mol. The only conceivable elementary reaction between CH4 and 03,however, as pointed out by Atkinson and Carter: is ~~~~~~~
( 1 ) Dardin, V. J.; Albright, L. F. Ind. Eng. Chem. Proc. Des. Develop. 1965, 4, 6 1 . (2) Caprio, V.; Insola, A,; Barbella, R. Combust. Inst. Europ. Symp. 1973, 99. (3) Caprio, V.; Insola, A,; Lignola, P. G. Combust. Inst. Europ. Symp. 1975, 85. (4) Caprio, V.; Insola, A.; Lignola, P. G. Combusr.Sci. Technol. 1979, 20, 19. ( 5 ) Caprio, V.; Insola, A.; Lignola, P. G. Combusr. Sci. Technol. 1984, 35, 215. (6) Schubert, C. C.; Pease, R. N . J . Am. Chem. SOC.1956, 78, 2044. (7) Dillemuth, F. J.; Skidmore, D. R.; Schubert, C. C. J . Phys. Chem. 1960, 64, 1496. (8) Kleimenov, N. A.; Nalbandian, A. B. Proc. Acad. Sci. USSR, Phys. Chem. 1958, 122, 667.
0022-3654/86/2090-0677$01.50/0
CH4
+ O3
-
CH3
+ OH + O2
AH = 27 kcal/mol
The activation energy of this hypothetical reaction can be expected to lie even above 27 kcal/mol, thus being higher than the activation energy for the thermal decomposition of ozone, which equals 23 kcal/mol.1° A direct reaction between CH4 and O3is therefore severely in doubt. More in line with the thermodynamic facts, the results of Kleimenov and Nalbandian,8 obtained in a flow system at 423 K and residence times of 6 to 32 s, were interpreted in terms of the thermal decomposition of ozone with subsequent reaction of 0 atoms with CHI. This conclusion was arrived at by noting that the ozone decomposition temperature coincided with the temperature at which the oxidation of methane proceeded at a measurable rate. These authors also reported methyl hydroperoxide and formaldehyde as the principal reaction products, completely different from the results obtained by Schubert and Pease and Dillemuth et al. None of the studies mentioned has resulted in an analysis of the overall reaction in terms of elementary reactions. The objective of the work presented in this article therefore is to provide a better and, above all, more quantitative understanding of the ozone-initiated methane oxidation. The experimental ar(9) Atkinson, R.; Carter, W. P. L. Chem. Rev. 1984, 84, 437. (10) Baulch, D. L.; Drysdale, D. D.; Duxbury, J.; Grant, S. “Evaluated Kinetic Data for High Temperature Reactions”;Butterworths: London, 1976; Vol. 3.
0 1986 American Chemical Society
