2992
J . Phys. Chem. 1985,89, 2992-2996 the distribution of Stark shifts for d = -6 cm-' is, for all intents and purposes, identical with that for d = -2.5 cm-'. In the above Stark shift calculations it has been assumed that the w2 field is weak. This is reasonable since in the wI(w3) power dependence studies an w2-pulse energy of 0.8 /LJ was used and, furthermore, power broadening of the wfi resonance was not observed for w2-pulse energies as high as 8 pJ (wl-pulse energy of 1 pJ, d = -6 cm-') (vide supra). This absence of power broadening is understandable since the transition dipole of the wvu resonance is that of the wvo(wdv) resonance and also for d = -6 cm-I the average detuning of w 2 from the woturesonance is large, -6'cm-'.
0.4, and 0.58 cm-'. Subtraction of the d = -1.5 and -3.5 cm-' entries in Table V for a given Rabi frequency provides an estimate of the power broadening. Thus, the estimated power broadenings for the experimental Rabi frequencies are sufficiently close to the observed values to assert that a distribution of Stark shifts is a likely explanation for the power broadening. We point out that the calculated values in Table V are in very good agreement with those calculated with eq 24 of OD. At present we are developing a more formal theory for the dynamic Stark effect which is to be applicable to a four-level system possessing inhomogeneously broadened resonances. With our simple model one can understand why the power broadenings for d = -6 and -2.5 cm-' are equal within experimental uncertainty. For d = -6 cm-', w 3 = w1 (*) wdv is the strong interaction since its detuning is +2.5 cm-' and pdU = pvo. The w , ( m ) wvo interaction is approximated as weak since its detuning is -6 cm-'. The pertinent term for the w 3 strong field case contributes to the w f i - A resonance of eq 1 ( p o term) by virture of the equality wA = wdo - wdo. Thus, Stark shifting of wd, leads directly to Stark shifting of the CARS w f i resonance. As expected, our calculations show that the power broadening from
-
Acknowledgment. Ames Laboratory is operated for the U S . Department of Energy by Iowa State University under Contract No. W-7405-Eng-82. This research was supported by the Director for Energy Research, Office of Basic Energy Science. Funding for the laser system used was provided by NSF. Useful discussions with Robin M. Hochstrasser pertaining to line narrowing and dynamic Stark effects are gratefully acknowledged. Registry No. Pentacene, 135-48-8; naphthalene, 91-20-3.
Thermal Explosions of Methyl Isocyantde In Spherical Vessels P. Q. E. Clothier, M. T. J. Clionna, and H. 0. Pritchard* Department of Chemistry, York University, Downsview, Ontario, Canada M3J 1 P3 (Received: July 2, 1984; In Final Form: March 18, 1985)
An improved set of measurements, including a wide variety of consistency tests, on the thermal explosion of methyl isocyanide in spherical vessels from 0.3 to 12.6 L at 350 OC is presented. We also report an accidental explosion which took place with liquid methyl isocyanide at room temperature.
of temperature and pressure, and so the tests which we propose to make will take the form of numerical simulations, to be presented in a separate publication.
The exothermic isomerization of methyl isocyanide to form methyl cyanide possesses a number of attractive features for the testing of the theory of thermal explosions: the reaction is clean, it is unaffected by the presence of many impurities, and it is insensitive to the nature of the vessel surface; as a consequence, it is easily possible to measure explosion limits for this reaction with a reproducibility of f0.01-0.02 torr for critical explosion pressures in the 2-10-torr range. When the use of this reaction was suggested originally,' none of the required thermodynamic and kinetic data were known reliably? but in the intervening years, the enthalpy of the reaction: the thermal cond~ctivity,~ and the rate of reaction up to within 30 OC of the required temperature5 have been measured. Thus, it should now be possible to make a thorough test of thermal explosion theory for this reaction, and it is the purpose of these new measurements to provide reliable experimental results against which to perform these tests. There is, however, one disadvantage to this reaction in performing such tests: being a unimolecular reaction in its falloff region, its rate constant is a function of pressure with an order intermediate betwten 1 and 2, and its activation energy also varies with pressure. Despite the advanced state of unimolecular rgction theory, particularly for this reaction,6 it is still not possible to predict theoretically the variation of reaction order as a function
Experimental Method Spherical Pyrex reaction vessels having volumes from 0.3 to 12.6 L were located centrally in a thermostat; connection between the flask and the external vacuum system was through a straight length of 18-mm-0.d. Pyrex tubing. The thermostat enclosure was in the form of a cube made from insulating material, with an inner dimension of 17 in. Three bare-wire heaters were supported in a space between the outer wall and an inner insulating shield of approximately 15-in. size, and the reaction vessel was totally enclosed (apart from the tube connecting it to the outside) in a metal radiation shield (stainless steel) in the foFm of a 13-in. cube. Two of the heating elements were supplied with a fixed voltage which would maintain the furnace at about 310 OC, and the other element was connected to a Hallikainen Thermotrol controlled by a resistance thermometer located inside the furnace. The air inside the enclosure was circulated by a 5-in. squirrel cage fan running at 1750 rpm, with a capacity (for room temperature air) of about 150 ft3/min-corresponding to a complete circulation of the air more than 40 times per minute; eight thermocouples were located, one near each corner of the controlled space. Since the problems with our earlier measurements4 were in the temperature control,' we needed to establish the accuracy of the
(1) Pritchard, H. 0.;Tyler, B. J. Can. J . Chem. 1973, 52, 4001. (2) Gray, P.; Sherrington, M. E. Spec. Period. Rep.: Gas Kinet. Energy Transfer 1977, 2, 331. (3) Baghal-Vayjooee, M. H.; Collister, J. L.; Pritchard, H. 0. Can. J. Chem. 1977, 55, 2634. (4) Collister, J. L.; Pritchard, H. 0. Can J . Chem. 1977, 55, 3415. (5) Collister, J. L.; Pritchard, H. 0. Can. J . Chem. 1976, 54, 2380.
(7) In the earlier experiment, the use of a Hewlett-Packard recording platinum resistance thermometer as a temperature controller engendered a false sense of confidence in the quality of the result: an electrical feedback occurred in the control circuit, resulting in an offset between the true and the indicated temperature which was different for each flask, and which was zero for an empty furnace.
(6) Pritchard, H. 0. "Quantum Theory of Unimolecular Reactions"; Cambridge University Press: New York, 1984.
0022-3654185 , ,12089-2992101SO10 I
0 1985 American Chemical Societv -
Thermal Explosions of Methyl Isocyanide temperature control beyond any doubt. The output from the multiple thermocouple set, connected in series, was fed to a digital voltmeter and the temperature was recorded at 1-s intervals for long periods. The indicated temperature cycled with a frequency of 30 f 2 s, over a range of f0.004 OC about the mean (except in the case of the 12.6-L vessel where the variation was f0.02 OC, possibly because the largeness of the vessel interfered significantly with the air flow); in addition, there were erratic jumps, which never exceeded f0.1 OC, caused by the opening of the laboratory doors, or occasionally by sudden changes in the airconditioning system. The thermocouples were calibrated at the melting point of lead, and all voltages were referred to a standard Weston cell. The least satisfactory aspects of the temperature control was the existence of a small vertical temperature gradient, which was a little unexpected in view of the speed of movement of the air inside the furnace. The temperature was actually the hottest at the top, and fell at a rate of approximately 0.025 OC/cm; this gradient fell to zero if the heaters were switched off, demonstrating, in fact, that a steady state was achieved with the temperature falling along the path of the air flow. Each experiment was initiated by admitting the methyl isocyanide vapor (either alone or in an appropriately prepared mixture) into the evacuated sphere through an electrically operated Leybold-Heraus N W 10 valve: by adjusting the forepressure very precisely (fO.O1 torr) with a servo-driven Texas Instruments quartz spiral pressure gauge and by opening the valve with a square-wave electrical pulse of known duration (0.185 s) fed from a 50-V dc stabilized power supply, it was possible to admit known amounts of gas into the vessel with considerable reproducibility, and this was a great help in being able to locate the explosion limit within a few shots. Some of the reaction vessels were equipped with a single 0.001-in. Pt/13% Pt-Rh thermocouple at the center, and the difference in temperature between the center of the flask and that of the furnace could be recorded. Pressures inside the vessel were monitored by the use of Pace-Wianko fast response pressure transducer giving an output of approximately 0.1 v/torr. Output from the transducer was fed both to a chart recorder and to a digital voltmeter reading at approximately 60 times per second; calibration of the pressure was made through the use of a 20-mm bore mercury manometer and cathetometer; as in our earlier work, the accuracy of the pressure measurements is about f0.03 torr or f l % , whichever is greater.
Consistency Tests In the earlier work,4 some attempt was made to show that in the temperature range of interest, a free-radical mechanism* which is insignificant at lower temperatures had not become important, thereby negating the extrapolation of reaction rate data from those lower temperatures. The earlier work showed that the addition of small amounts of propylene (radical trap) did not change the explosion limit ~ignificantly.~In the present work, we tried to introduce free radicals into the system to show that they were ineffective in promoting the explosion. Small amounts (up to 5%) of di-tert-butyl peroxide were admixed with the meihyl isocyanide; however, the peroxide decomposed at much too low a temperature, with the result that no methyl radicals were left in the system as the crucial part of the methyl isocyanide self-heating was in progress, and the only observed effect was that of a diluent. Dimethylmercury, on the other hand, was too unreactive, and exerted no more than a diluent effect either. However, diethylmercury did give rise to an effect, but we concluded eventually that this was probably nothing more than a cooperative ignition process. Both ethyl isocyanide and diethylmercury have explosion limits somewhat lower than that of methyl isocyanide at 350 OC, and the latter reaction takes place via a free-radical mechanismg in contrast to the nonradical isocyanide intramolecular isomermization. Curves for the explosion limits of CH3NC/Hg(C2H5)2 (8) Shaw, D. H.; Pritchard, H. 0. Can. J . Chem. 1967, 45, 2749. (9) Gowenlock, B. G.; Polanyi, J. C.; Warhurst, E. Proc. R. SOC. London, Ser. A 1953, 218, 269.
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 2993 as a function of mixture ratio were very similar in form to those for CH3NC/C2H5NC mixtures, indicating that the presence of free radicals in significant concentrations does not give rise to any remarkable effects. Conclusive evidence for the absence of free-radical effects was obtained in two ways, as follows. First, by analysis of the explosion products: in those explosions which are just supercritical, there were no noncondensable products, and gas chromatographic analysis showed the product to be pure methyl cyanide (cf. also ref 3); more than 5% above the critical pressure, small amounts of noncondensables were found, but there is clearly a "window" here in which it is possible to determine the explosion limit free of any uncertainties about the reaction mechanism. Second, in a difference furnace equipped with a set of quartz windows, mixtures of CH3NC with up to 5% of dimethylmercury were examined. The explosion limit of such a mixture was determined in a 0.5-L quartz vessel, and then it was shown that exposure to an intense ultraviolet flash, sufficient to dissociate all of the dimethylmercury, during the induction period did not affect the explosion limit or the induction time for those cases where explosion took place. Some experiments were also conducted to examine the effect of a nonuniform temperature distribution on the explosion limit: an auxiliary nichrome heater and an associated thermocouple were clamped to the outside of a 2-L flask the area of the vessel surface which was heated was about l ' / z in. in diameter. There was no detectable change in the explosion limit until the "hot spot" so created exceeded the bath temperature by 6 OC; theoretical treatment of hot spots, as far as we know, has only been attempted for slab and cylinder geometries.lOJ1 Another similar test was done on geometric uniformity. A pair of 2-L flasks having volumes within 5 mL of each other were shown to give indistinguishable explosion limits. Then one of the flasks was distorted by having an alternating pattern of about 80 bumps and dimples roughly 1 cm in diameter and about 4-mm high blown on its surface; the volume of the flask was unchanged. The explosion limits were remeasured in each flask at 340, 350, and 360 "C, and there was a small, but barely significant, increase in critical pressure of about 0.1 torr in each case for the modified flask; the modified flask also gave consistently longer induction times, but we did not pursue this point sufficiently to be able to state categorically that this was a real effect. A third 2-L vessel was equipped with a 0.001-in. thermocouple at its center, supported from a pair of diametrically opposed lead-in wires of 0.012-in. diameter, each projecting about 1 in. into the vessel. This flask was slightly smaller than the other two, but the differences in radius are so small that there should be no more than 0.04 torr difference between the three vessels in the explosion pressures at the lowest temperature, correspondingly less at the higher ones; within this limitation, we did not find any difference in explosion limit between a 2-L flask with or without a thermocouple (cf. footnote to Table I). An alternative configuration is to mount the thermocouple on a glass stem passed through the neck of the vessel; the glass stem extended to within 5 in. of the center, with the two supporting leads reaching to within 1 and 2 in. of the center, respectively. These tests were performed at only one temperature (350 "C): there was no effect in the smallest (0.3 L) or the largest (12.6 L) flasks, for obvious reasons, but in the 1.5- and 2-L flasks, the critical explosion pressure was increased by 0.1 1 and 0.13 torr, respectively. Among the other consistency tests that were performed previously4 were the placing of thermocouples on the walls to check that no temperature rise occurred there, and the coating of the inside of a flask with a platinum film which could be used for two purposes, one to confirm that no significant temperature rise occurred on the wall and the other to eliminate any considerations in respect of radiative transfer to or from the reacting gas. Also, the usual tests for spurious admission heating effects were made by varying the diameter of the reaction vessel neck and the rate (10) Gray, B. F.; Wake, G. C. Combust. Flame 1984, 55, 23. ( 1 1 ) Zaturska, M. B. Combust. Flame 1984, 56, 97.
2994
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The Journal of Physical Chemistry, Vol. 89, No. 14, 1985
TABLE I: Comparison of Two Independent Sets of Explosion Measurements on Methyl Isocyanide at 350 "C in Spherical Vessels of Various Sizes" series P82 series C84 (T = 350.0 f (T = 350 1 "C) 0.15 "C) longest vessel subsupersubsuper- induction radius,b cm critical critical critical critical time, s 0.86 8.19 8.19 7.84 4.18(0.3L) 7.79 1.04 6.39 6.41 6.50 6.53 4.86 (0.5 L) 1.40 5.20 5.24 5.02 6.29 (1.0 L)c 4.97 4.22 1.72 4.22 4.22 7.34 (1.5 L) 4.20 4.15 1.78 4.13 4.15 7.76(2.0L)d 4.10 3.40 2.05 3.43 3.38 9.22 (3.0 L) 3.39 2.30 3.04 3.06 2.95 10.78 (5.0 L) 2.93 2.23 2.44 2.25 2.19 14.45 (12.6 L) 2.23
*
"All pressures in torr. bNominal volume; radius calculated on the assumption that each vessel is a perfect sphere (cf footnote to Table I of ref 4); the 2-L flask used in this work had volume of 1958 mL. CNotethat ref 1 also gives 5.25 f 0.05 torr for the explosion limit in a another vessel ( r 1.0-L vessel (radius = 6.54 cm) at T = 350.7 "C. = 7.71 cm) equipped with a single thermocouple at the center, the limit lay between 4.01 and 4.05 torr (G80). TABLE 11: Comparison of Three Independent Sets of Explosion Measurements on Methyl Isocyanide in a 2-L Spherical Vessel at a Series of Temperatures" series G80 series P82 series C84 longest temp: sub- super- sub- super- sub- super- induction OC critical critical critical critical critical critical time, s 329 6.67 6.69 6.72 6.78 2.54 339 4.99 5.01 5.07 5.10 5.26 5.27 2.29 359 3.22 3.24 3.26 3.28 3.44 3.45 1.28 369 2.69 2.72 2.84 2.85 1.08 'All pressures in torr. bThe uncertainties in the mean vessel temperature are the same as those shown for the corresponding series of measurements in Table I.
of admission of the gas to the vessel.'* Confirmation that there is no significant heating on admission is now provided by measurements of the central temperature-no rise was detected on admission which exceeded the noise level of the digital-to-analog converter ( f 2 "C); since the lag time of the thermocouple probably exceeds the ' / 6 0 s period between temperature readings, any rise in temperature due to adiabatic compression on entry cannot last for longer than the response time of the thermocouple.
Results The results listed in Tables I and I1 were obtained independently by three operators at different times, and they are signified by a code indicating the date: the quality of the temperature definition improved with time, and only the latest set (C84) was performed with the benefit of automatic digitial recording of the data. Also, there was a slight difference in philosophy between the two earlier sets of data and the latter one in the method of collection: in the former experiments, the initiation was delayed until the temperature indicated on a digital display was within fO.05 OC of the desired value and, without exception, the lowest supercritical pressure exceeded t h e highest subcritical pressure; the closeness between a pair of experiments run under these conditions is shown in Figure 1. In the final set of experiments, however, the experiments were initiated without waiting and, very occasionally, a subcritical and a supercritical result were found at the same pressure (cf. Table I). As the size of the vessel increases, or as the temperature decreases, the induction time lengthens; Tables I and I1 also report the longest induction time observed in any experiment under the given conditions, showing these two effects. Figure 2 shows the &ults of two sets of measurements of induction t h e s in the 12.6-L vessel; the displacement between the two limits of the order of (12) Fine, D. H.; Gray, P.; MacKinven, R. Nature 1969, 223, 393.
L L
0
I-
6-
L
(u
4 -
v)
2-
L 3 v) (u
L
a
0 -
(secl
Time
Figure 1. Comparison of the pressure vs. time traces for a pair of subcritical and supercritical experiments in a 2-L sphere at 350 "C.
IC 3 0
2
3
4
Pressure ( T o r r ) Figure 2. Plot of the apparent induction time vs. pressure of methyl isocyanide thermal explosions in a 12.6-L sphere at 350 "C: vertical dotted line is highest subcritical pressure observed, and circles are measurements made in supercritical experiments, C84; also shown as crosses is a similar set of results from series P82. The indicated value is the time interval between the first point on the preexplosion plateau and the first point of the sharp pressure rise on plots like those shown in Figure 1; it is thus subject to an uncertainty of about s. Our modelling calculations suggest that the valve opening time (Le., -0.2 s) should be substracted from these values to obtain the true induction time.
0.02-0.03 torr (as shown in Table I) is apparent. Qualitatively, these induction times show the correct anticipated behavior,I3 tending toward infinity as pip,,. The temperature-time profiles observed in this work are generally similar to those presented earlier,' with subcritical temperature rises being in the expected range of up to about 41 OC. However, with the benefit of fast digital recording, we can make two qualifications to these standard conclusions. (i) In the supercritical experiments, the recorded temperature rise just above the critical pressure pmis about 550 O C , increasing approximately linearly with pressure to about 605 O C at p = 1 . 4 ~ While ~ ~ . these temperature measurements may be inaccurate due to thermocouple lag, the trend is reasonable because as the induction time becomes shorter, there is progressively less heat loss from the system (and less reactant consumption) before ignition; assuming that all oscillators in methyl cyanide are harmonic, and by computing the specific heat as a function of temperature by standard statistical methods, the maximum possible temperature rise (given that AHrado, = -23.7 k~al-mol:'),~ is a little over 1000 O C . (ii) Very close to the explosion limit, we observed three cases where the central temperature rise did not conform to the expected patterns: (13) (a) Boddington, T.; Feng, C.-G.; Gray, P. Proc. R. SOC.London, Ser. (b) Boddington, T.; Feng, C.-G.; Gray, P. J. Chem. SOC., Faraday Trans. 2 1984, 79, 1299. (c) Boddington, T.; Griffiths, J. F.; Hasewaga, K. Combust. Flame 1984, 55, 297. A 1983, 385,289.
Thermal Explosions of Methyl Isocyanide
The Journal of Physical Chemistry, Vol. 89, No. 14. 1985 2995 3
in one subcritical experiment, a rise of 60 OC was observed, and in two supercritical experiments, rises of 125 and 170 OC were observed; thus, it appears that the transition from subcritical to supercritical behavior is, in practice, a continuous one and we hope to be able to demonstrate this in a more conclusive fashion at a later date.
J?k
~ P C I P To 3RTo - E dTo r2 kuni
(2)
where p = SJ?X/(1.605 X lC5) EQ, (the numerical constant being ~ and n the conversion factor for pcrfrom torr to m ~ l . c m -units), is the order of the reaction; since (2) now contains the ratio 6,/kd, it is independent of the absolute value chosen for kuni.With E = 36 500 cal-mol-' at these p r e s s ~ r e s A, ~= 7.15 X cal.(cm OC s)-I, and assuming the order n = 2, eq 2 gives -0.072 torr O C - I compared with a value of about -0.091 torr OC-' estimated from the results in Table 11; if the order were 1.6, the agreement would exact. An alternative method of examining the rate of change of pcr with To is to plot -R In p",,/F vs. 1/T, whence the slope should be E , the activation energy of the reaction;Is again, with n = 2, the slope is about 37 f 2 kcalemol-I, or if n is allowed to vary with pressure according to theoretical prediction, it is about 34 f 2 kcal-mol-' . Another aspect of existing theory which is reasonably well met is the acceleration of the ignition as a function of the pressure (14) Schneider, F. W.; Rabinovitch, B. S . J . Am. Chem. SOC.1962, 84, 4215. (IS) Fine, D. H.; Gray, P.; MacKinven, R. Symp. (Znt.) Combust., [Prof.], 12, 1968 1969, 545.
P h
Ph
2 -
I -
01 0
"
"
"
"
I
'
5
(P
)
R nj
nj
2
P P
E -$Q kunipcr 6,, = RTo2 A RTo
.-=--(
nj
"b "h
Comparison with Existing Theory The high reproducibility of these experiments gives rise to the expectation that they can be used to provide a good test of existing thermal explosion theory; unfortunately, the obstacle now is the relatively poor performance of existing unimolecular reaction theory in predicting rates in the falloff region outside the temperature range for which falloff curves have been measured. Consider the simplest critical parameter
where E is the activation energy, Q (= -AH) is the exothermicity of the reaction, r is the radius of the vessel, To is the wall temperature, X is the thermal conductivity, pa is the measured critical explosion pressure, and kuniis the predicted unimolecular rate constant at pcr. If conventional strong-collision theory6 is used to predict kunifor pa and To, with the infinite-pressure Arrhenius parameters of Schneider and R a b i n ~ v i t c h , then ' ~ the values of 6,, for the experiments reported in Table I1 rise monotonically from 14.0 to 14.9 with increasing temperature: alternatively, if the randomization model6 is used, 6,, rises monotonically from 9.9 to 10.7; in either case, the variation in 6,, is of the order of f 3 or 4%. This variation could simply arise from the inability of the theory to predict the extent of the shift in the falloff with temperature (or, equivalently, to make a good prediction of the activation energy in the falloff region). The absolute value of 6,, obtained from either calculation is much greater than the traditionally accepted value of about 3.3, but this is simply an artifact of our inability to extrapolate the low-pressure (second-order) rate constant for this unimolecular reaction up into the temperature range of interest. If, instead of examining 6,,, we examine dpa/dTo, this artifact (almost) drops out: we say almost, because if the reaction were at its second-order limit at these temperatures and pressures, this would be true, but strong-collision unimolecular reaction theory predicts a reaction order of about 1.95 at 2 torr, 1.91 at 8 torr, for a temperature of 350 OC; (the corresponding values for the randomization model are 1.65 and 1.61, respectively). Extracting dpcr/dTo from eq 1 yields
s
I?
n j n j
-
P,
>
io
( T o r r ) -IN2
Figure 3. Plots of the C84 induction time data from Figure 2 vs. (p for various trial values of per; notice that from Table I, the true
+);'I2
limit lies between 2.19 and 2.23 torr. 3,
0
I
2
3
Pressure
4
5
6
(Torr)
Figure 4. Plots of times to reach maximum temperature vs. pressure for
the thermal explosion of methyl isocyanide in the 1922-mL spherical vessel at 350 OC. in excess of pcr, shown in Figure 2: for those points for which p > 2.3 torr, there is a reasonable straight line correlation between the induction time and (p- P,.,)-'/~; however, it is not possible to bring the remaining (just supercritical) points into this linear relationship unless pCris assumed to be 2.17 torr, as is shown in Figure 3. This pressure is so far below pa that we can state with complete certainty that ignition would never occur at this pressure in this vessel at this temperature, and that it is at least 0.02 torr below pcr; on the other hand, such a relationship is not expected to hold very close to the critical condition.13c The failure of the square-root plot in Figure 3 is due more to the neglect of reactant consumption rather than simply to mathematical approximations in the derivation: this can be deduced from a plot of the time taken to reach the maximum temperature as a function of pressure, plotted for all pressures in Figure 4-in in this case for the 1922-mL vessel. There is relatively wide scatter at low pressures because the temperature maximum is broad and low; above threshold, the scatter is minimal, since the time to maximum is simply the induction time, which is easily measured. In the absence of consumption, the time taken to achieve the maximum temperature below threshold is infinite, and above threshold, it falls according to a squareroot relationship: the graph in Figure 4 shows a similar general pattern, except in the region of the explosion limit; here, we encounter a rather unexpected behavior that, as the limit is approached from below, it takes longer and longer to achieve the maximum temperature, due to consumption of reactant. The same feature appears in the times to reach maximum temperature in the thermal explosions of compressed wads of bagasse-it takes progressively longer to reach
2996
J . Phys. Chem. 1985, 89, 2996-3000
the maximum as the limit is approached from below, and the induction time then falls again once the system goes above the limit. l 6
Concluding Remarks We have made a thorough reinvestigation of the use of methyl isocyanide for the testing of thermal explosion theory and have performed a large number of consistency tests, none of which shows any signs that would invalidate this system for testing purposes. We have reported sets of experiments, measured independently by three workers at 2-yr intervals, which demonstrate the remarkable reproducibility of this reaction for the determination of explosion limits. Because of the improved temperature monitoring procedures in the latest measurements (C84), they are the ones in which we can place the most confidence. Since Table I1 shows that dp,/dTll,,, -0.1 torr OC-' for a 2-L sphere, the principal uncertainty for the larger vessels in the determination of pcrarises from the pressure calibration; however, dp,,/dTl, varies inversely as 9so that for the 0.3-L vessel, it is -0.35-0.4 torr OC-' at 350 OC, and here the error in the temperature control is dominant. Given the difference in the quality of the temperature control between the two series P82 and C84, all the results in Table I are within acceptable agreement of each other, even including the 0.3 L result. Here, the older result is clearly the less reliable: the longest induction time (0.36 s) was much too short; also, repetition of this experiment with a different sample of methyl isocyanide from that used in the C84 experiment gave 8.17 and 8.18 torr, respectively, for the highest subcritical and lowest supercritical pressures, confirming the correctness of the newer measurements in this case. Thus, we conclude that the recommended values for the critical explosion pressures of methyl isocyanide at 350 OC may be taken to be the mean of the two C84 values given for each case in Table I, with a total uncertainty of about *0.05 torr which allows for small excursions of the temperature from the desired set point, errors in the pressure calibration, and the bracketing range of the limit in those cases where coincidence was not obtained: similar (16) Gray, B. F.; Griffiths, J. F.; Hasko, S.M. J . Chem. Technol. Biotechnol. 1984, 34A, 453.
remarks apply to the data in Table 11. Because of the complication that this reaction is a unimolecular reaction in its falloff region, so that both the reaction order and activation energy are pressure dependent, it is not a simple matter to make the standard tests. Qualitatively, there, appears to be reasonable agreement between theory and experiment insofar as the variation of pcrwith variation in To for fixed r is concerned, but not for the variation at fixed To for different r; also, the square-root relationship for the ignition delay vs. pressure in excess of pm holds quite well once p > l.O5p,, but fails at pressures only slightly in excess of pcr. We hope to be able to resolve these difficulties in numerical simulations of these experiments in a separate publication. Acknowledgment. This work was supported by the Natural Sciences and Engineering Research Council of Canada. We would also like to acknowledge help from John Collister, who performed all of the alkylmercury experiments reported here. Appendix
An Accidental Explosion with Liquid Methyl Isocyanide at Room Temperature. Ever since methyl isocyanide was first prepared by Gautier, it has been known that it explodes when distilled; however, we are not aware of any report that the room temperature liquid itself may explode (except when sensitized by the presence of certain azides17). We had been in the habit of purifying 0.2-mL samples of the liquid by preparative gas-phase chromatography and, over a period of some years, had purified several hundred milliliters in this manner. The desired volume of liquid was injected on to the chromatographic column (inlet port and column at 42 "C) by using a Hamilton CR-700 spring-loaded hypodermic syringe. We presume that the explosion of this 0.2 mL sample of liquid methyl isocyanide occurred as a result of the sudden compression of the liquid by the spring-loaded plunger: the glass barrel (1.2-in. long, 0.3-in. o.d., 0.175-in. id.) was reduced to granules, and the 0.02-in. wall steel sheath surrounding the barrel was expanded from about 3/8 in. to nearly in. diameter at the middle of the viewing slit. Registry No. Methyl isocyanide, 593-75-9. (17) Wohler, L.; Roth, J. F. Chem.-Zrg. 1926, 50, 761.
The Structure of Sodium Dodecyl Sulfate Micelles In Solutions of H20 and D20 N. James Chang and Eric W. Kaler* Department of Chemical Engineering, BF- 10, University of Washington, Seattle, Washington 981 95 (Received: October 9, 1984; In Final Form: April 2, 1985)
The sizes of sodium dodecyl sulfate (SDS) micelles in mixtures of H 2 0 and D 2 0 have been measured at several different ionic strengths and temperatures. The changes in micelle size due to H20/D20substitution are greatest at high ionic strength. Electrical conductivity and light scattering measurements indicate that head group repulsions between surfactant molecules, as well as intermicellar interactions, are the same in H 2 0 and D 2 0 solutions. The conclusion is that a small difference in the strength of hydrophobic bonds between H 2 0 and D 2 0 is responsible for the dramatic changes in micelle size. In addition, the critical micelle concentrations of a homologous series of sodium alkyl sulfates in H20and D 2 0and for SDS in solutions containing various ratios of H 2 0 / D 2 0are reported. Introduction
Many of the physical properties of H,O and ~~0are nearly For example, the surface tensions and dielectric constants of the materials are the same to within 0.5%, and other (1) G. Nemethy and H. A. Scheraga, J . Chem. Phys., 41, 680 (1964). (2) G. A. Vidulich, D. F. Evans, and R. L. Kay, J . Phys. Chem., 71,656 (1 967). (3) M. K. Phibbs and P. A. Gigriere, Can. J . Chem., 29, 173 (1951).
0022-3654/85/2089-2996$01 SO/O
properties such as refractive index, polarizability, and boiling point are all closely matched. The similarity of the two materials has led to the c0"On substitution of D2O for H20 in many experiments, most notably in neutron scatteringe6 and NMR7-9studies. (4) R. Triolo, L. J. Magid, J. S. Johnson, Jr., and H. R. Child, J . Phys. Chem., 86, 3689 (1982). ( 5 ) R. Zana, C. Picot, and R. Duplessix, J . Colloid Interface Sci., 93, 43
(1983).
0 1985 American Chemical Society
