Dec., 1962
LIATRIX
EFFECTS I N THE GASEOUS H
ATOM-COADENSED
OLEFIX SYSTEM
2677
MATRIX EFFECTS Ih' THE GASEOCS H ATOM-COXDEXSED OLEFIX SYSTEiLI:; SURFACE REACTION---OLEFIN DIFFUSIOK XODEL BY RALPHKLEINAKD MILTOND. SCHEER Xational Bureau of Standards, Washington 25, D. C Received June 4, 196t
The reaction hetween hydrogen atoms, produced in the gas phase, and a condensed film of an olefin depends markedlypn the matrix. This matrix may be either the pure olefin or a mixture of the olefin with a diluent. The model consistent wlth the experimental data is one in which the H atom addition to the olefin occurs as a surface reaction. The olefin is replenished by diffusion from the interior. Two characteristic limiting processes may be distinguished. One involves a diffusioncontrolled, and the other a chemical reaction-controlled rate. The reaction products, that is the monomer to the dimer alkane ratio, depend on the mobility of the alkyl radical formed on the surface.
The reaction between hydrogen atoms, generated on a hot tungsxen filament, and olefin films condensed below LOOOK., has been observed for a variety of terminal unsaturated Several features of this type of system led to a physical model consistent with the experimental ob~ervations.~Hydrogen atoms were assumed to diffuse into the solid. They reacted by terminal addition to give secondary radicals which disproportionated and dimerized to give the stable end prod~cts.~!5 Diffusion of hydrogen atoms into the olefin layer appeared to explain the results obtained. Large differences in the rates of hydrogen atom pick-up by various olefins (the absence of reaction with n-hexene-2 and butene-2, as compared to propene and butene-1, for example) were ascribed to small differences in the activation energies. This was not in agreement with gas phase experiments, where the rates for H atom addition were approximately the same for a variety of olefins, including those with an internal double bond. However, the lower temperature rate measurements would reveal small differences in activation energy that would not have been evident in the higher temperature regions, particularly if the activation energy for the reaction were sufficiently small. Several additional experiments with the hydrogen :Ltom-solid olefin system have indicated that the previously post,ulated model requires modification. It has been found that the immobilizing effect of the matrix, whether it consists of the olefin alone or an admixture of the olefin with inerts, greatly affects the reaction rate as measured by either hydrogen pick-up or saturate formation. We have found that n-hexene-1 appears to be inert a t 77OK. when present in 100% concentration, but shows considerable reaction with atomic hydrogen when diluted with propane, propene, or any other substances which substantially increase diffusion in the solid. The rate of hydrogen uptake by condensed 3-methyl-butene-1 under continuous oxposure of the film to H atoms was rapid initially. The rate decreased in time. If the reaction waq interrupted for a few minutes, the rate increased compared to that immediately before the interruption. Hydrogen atom diffusion into the solid cannot account for these observations, whereas reac(1) R. Klein and &I. D. Scheer, J . A m . Chem. Sac., 80, 1007 (1958). (2) R. Klem and M. D. Scheer, J. Phys. Chem., 6 2 , 1011 (1958). (3) R. Klein, M. D. Scheer, and J. G. Waller, %bid., 64, 1247 (1900). (4) R I . D. Scheer and R. Klein, abid, 63, 1517 (1959). ( 5 ) R. Klein a n d A l D. Pclieer, %bid., 66, 324 (1961).
tion of H at'oms and olefin molecules at the surface of the solid, and replacement of the reactive molecules by diffusion from the interior, is in accord with these experiments. The hydrogen atom diffusion model was suggested by t,he apparent linear dependence of the initial reaction rate3 on film thickness, and by complet'e conversion of the olefin.2 It has now been shown that in a matrix where diffusion is slow (propene in 3-methylpentane, for example) complete conversion is unatt'ainable. The linear dependence behavior with small film thickness is not compelling. EXperimentally it is most difficult to determine initial rates for very t,hin films because the olefin concentration decreases very rapidly as the reaction proceeds even for very short times. There is also the experiment.al difficulty of making a uniformly coherent film for such thin films.
Experimental Results The apparatus used has been described previously .6 Sonv.? niodifications were made so that t,he hydrogen atom concentration coiild be maintained a t a constant value. A reservoir volume was incorporated. This communicated with the reaction vessel through n precision type variablr leak valve. The pressure was kept constant in the r e a c h n vessel by matching the leak rate with the reaction rate during the course of the experiment. A calibrated t,hermocouple gage with a potentiometric recorder was used t o measure t,he hydrogen depletion of the reservoir in time. The deposition process was found to be important for obtaining nniform, reproducible films. The procedure adoptled consist.ed in immersing the Ant bottom of t.he reaction vessel in the refrigerant. The appropriate mixturc was metered through a throttle valve into the reaction vessel. The deposition rate used was such t,hat the film thickness was inrreaved about 1 p/min. The dependence of the rat,e of H atom addition and product yields of Ca and Cq olefins on dilution with various matrices is shown in Tahle I. The effect of the matrix is apparent. Matrices such as propane or butane a t 77°K. give mixtures whose reaction rates vary linearly with olefin dilut,ion. This is not true for diluents such as %-methylpcnt ane or cis-butene-2. Table I1 gives sonic experi1nent)al datja for product analysis in systems of mixed olefins. Thc matrix affects not only thc ratp, hut also the product. distrihution. Figure 1 is a plot, of the prop:rnc and hexane yields as a, function of time when mixtures of propylenc, n-hexene-1 , :md n-butane are deposited together in a film. The striking increase in rate upon dilution with n-butane demonstrates t,he marked matrix effect. Figures 2 and 3 give the hydrogen depleted (at constant hydrogen pressure and tungsten filament, temperature) by very thick films of propylene deposited in n-butane and 3-methylpentane. It is seen that the 71butane environment gives a linear time dependence whilt= the 3-methylpentane matrix shows a t ' / a dependence. (6) 31.D. Scheer and R. Klein, ibid., 66, 375 (1961).
RALPHKLEINAND MILTOND. SCHEER
2678
TABLEI THE DEPENDENCE OF H ATOM ADDITIONA N D PRODUCT
70
YIELDS OF TEE C8AND C4OLEFINSON DILUTION Film thickness = 3 p ; film area = 80 film T = 77"K., W ribbon T = 1800"K., PH, = 150 p ; deposition rate N 50 p/min. Relative rates
2
CS
Olefin isomerization yields C 4 C4 C ~ I trons-Butene4
1.00
8
..
..
0.01
8
..
..*
.80
.. ..
18
2.5
21
2.3
6@
I
tI
Vol. 66 I
I
I
I
I
FILM T = ? 7 ' K FILM A R E P = 8 0 C m 2 FILM THICKNESS;150u W RIBBON T*1600"K ' n-BUTANE N E-P 50
iI
Alkane ratios
Film compn.
Propylene Propylene = 0.01 Butane Butene1 Butene-1 = 0.01 Propane
-
.009
cis-Butene-2 .050 , . a cis-Butene-2 = 0.1 .025 . . a Propane cis-Butene2 = 0.03 .015 . . a Propane cis-Butene2 = 0.01 ,010 , . Propane Propylene = 0.40 .010 . . . 3-Methylpentane Propylene = 0.33 .002 3-Methylpentane _ _ 0 C a is too small to measure relative to low
.. ..
/I
-
I
I
1
I
o
>50
240
4
8
12
v
16
20
24
28 v
Fig. 2.-Time
8
matrices and a range of diffusing substances.* The conclusion that a matrix containing olefin a t temperatures more than half its melting point would show observable rates of H atom addition requires modification. In order to sustain the reaction, the olefin must be capable of diffusing through the matrix a t a relatively rapid rate. I n the matrix isolation experiments, diffusion must be inhibited over distances of the order of molecular diameters. For conveniently observable rates of hydrogen pick-up where reaction occurs on the surface and must be sustained by diffusion of reactive molecules from the interior, diffusion over hundreds of molecular diameters must occur in times of the order of several minutes. This requires temperatures well above T m / 2 . This is illustrated by hexene-1 functioning as its own matrix. At 7 7 O , 7 7 / T m = 0.6, the rate is so low that the reaction as measured by decrease in hydrogen pressure is not observable. At go', 9 O / T m = 0.7, the rate is observable. Additional evidence for diffusional processes in the hydrogen atom-condensed olefin reaction system is the formation of the dimer product of the alkyl radicals. It has been shown previously by isotope tracer studies that disproportionation as well as dimerization occurs.5 The constancy of the alkane ratios (CJC,,)over a wide concentration range was interpreted as demonstrating the absence of the H atom addition to the radical. We have now found that this ratio can be greatly altered in favor of the monomer alkane in a matrix where the diffusion processes are slower. For a 100% propylene film, the propane/2,3-dimethylbutane ratio found in the products is 8. The same ratio is obtained with 1% propylene in butane (Table 11). Ten per cent propylene in cis-butene2 shows a C,/C, ratio of 35. cis-Butene-2 a t 77' provides a rigid environment. The diffusion processes are slowed considerably, diffusion is undoubtedly rate controlling, and some hydrogen atom addition to the alkyl radical occurs. The interpretation of the absence or a t least the small extent of the H atom addition to the alkyl radical in a non-isolating matrix6 is the short life-
15
... C4yields. I
1
300
t iMINUTES1.
Fig. 1.-Matrix
0
5
n-HEXANE
I BO
I t (MINUTES).
PROPANE
I20
30
20
FILM T ' 7 7 ' K ; FILM AREA=B@Cm2 W RIBBONT=1800'K: PH2=150pHg
60
o I
9-
0
P
effect on rate of product formation.
Discussion The rate of the H atom addition to olefins is strongly dependent on the diffusion of the reactive olefin in the matrix in which it is condensed. This correlation is clearly shown in the rate of hydrogen pick-up by propylene, When diluted with butane, a 30% propylene film shows a rate 100 times faster than the same concentration in 3-methylpentane. The latter has been widely used in matrix isolation experiments.' A rule of thumb stated by PimentaP is that reactive species cannot be preserved if the temperature of the matrix substance is higher than approximately Tm/2,where T, is the melting point. This is supported by experiments on a variety of (7) I. Norman and G. Porter, Proc. Roy. SOC.(London), A280, 399 (1955).
(8) A. M. Bass and H. P. Broida, "Formation and Trapping of Free Radicals," Academic Press, New York, N. Y.,1060, Chapter 4.
dependence of reaction with a non-rigid matrix.
Dcc., 1962
TABLE I1 PRODUCT RATIOSFOR H ATOMAUDITION TO MIXEDCSAND C* OLEFINFILMS Film thickness = !j p; film area = 80 cm.2; film T = 77°K.; W ribbon T = 1800°K.,P H , = 150 p ; ~2077,~;deposition rate
-
50
Propylene (1) - 0.84 Butene-1 Propylene = 0.80 (2) Butene-l (Deposited separately; propylene on top) Propylene = 0.10 (3) cis-Butene2 Propylene = 0.11 (4) cis-Butene-2 (Deposited separately; propylene on top) (5) Propylene: cis-butene-2 :butene-1 1 :9 :1 ( 6 ) 3 olefins depo'sited separately in the above order and quantity
--.
C: c4 cs + ca +
-
l/ZCl
c4
olefin conversion
per minute Alkane ratio8
C8
Film cornposition
-
2679
MATRIXEFFECTS IN THE GASEOUS H ATOM-CONDENSED OLEFIXSYSTEM
C1' -
'/nC1
CSC~
Olefin isomerization yields Ca (Butane) trana-Butene2
1 .o
8
18
3.7
2.3
1.1
10
20
3.5
2.0
0.2
35
100
3.4
2.8
2.6
9
16
0.4
2.0
0.1
>50
>50
3.2
2.5
10
18
0.8
1.9
0.01
time of the radical on the surface. The olefin, and correspondingly the alkyl radical, diffuses readily. The alkyl radical, once formed on the surface by the reaction of the H atom with an olefin molecule, readily diffuses one or two molecular layers below the surface, and is removed from further exposure to the atomic hydrogen. However, the alkyl radical recombination and disproportionation reactions still may readily occur. With an immobilizing matrix, the diffusion of the radical is much slower, and the surface Lifetime and exposure to H atoms is longer. Some interesting results have been obtained with mixed olefins in rapidly deposited films (-100 p/min.). Propylene and butene-1, when hydrogenated by H atoms a t 77OK., give propane, butane, 2,3-dinzethylbutane, (C,), 3,4dimethylhexane, (C,), and 2,3-dimethylpentane, (C,). If the propyl and butyl radicals are formed and recombine in a random manner, the ratio C,2/CaC8 is expected to have a value equal to 4 on a purely statistical basis. Table 11, 1, shows this to be the case. The departure of the ratio c72/c6c8from the approximate value of 4 may be used as a measure of the uniformity of mixing of the condensed solid. An attempt was made to condense propylene on top of butene-1 to give a layered structure. This could never be achieved, as shown by Table I I , 2 . Even when the deposition was slow, extending over several hours (-0.1 p/min.), the pseudoequilibrium constant of about 4 was obtained. It must be concluded that the diffusion processes are quite rapid in propene-butene-1 mixtures at 77OK. Departures from the value of 4 were found when propylene was deposited on top of cisbutene-2. The situation can be interpreted by a hill and valley structure of the first deposited butene-2 film. The subsequent deposition of propylene might occur in the valleys, and, ~ 1 the s thickness was increased, present a surface of large patches of propylene, bound by areas of butene-2 or propylene-butene-2 mixtures. Here the c72/cScS ratio of 0.4 (4, Table 11) or 0.8 (6, Table 11) shows
63t
o
o
y
1
I
I
2
Fig. 3.-Time
I 3
I
I
I
I
I
I
4
5
6
7
I
8
9
IO
V'T(MINUTESPZ~ dependence of reaction with a rigid matrix.
a marked lack of uniformity of the surface layer. I n 3, Table 11,both the C3/Caand C4/C8ratios show large increases over that characteristic of loose matrices. It was shown previously that the atom diffusion model leads to a hyperbolic tangent relationship between initial rate and film thickness, with the atom concentration being a maximum a t the surface. Observations of the hydrogen pick-up on a given system may be made as a function of time. Comparison of these results with the model requires the solution of the equations b2H 3x2
D--
bH kH (01) = at
a(o1) - - - - kH(O1) at 2 dHz 1 = -2 dt
so 2
k H ( 0 1 ) dx
where H and 01 represent H atom and olefin con-
RALPHKLEISASD XILTOS D. SCHEEH
2680
centrations a t a distance x from the base of the olefin slab. I n this treatment, the olefin was not assumed to diffuse. From the above dHz/dt could be calculated numerically with the appropriate boundary conditions. The analytical solution is not accessible but it is evident that for small olefin concentration, thin films, and high hydrogen atom concentration, first-order behavior for the total olefin depletion is to be expected. Although first-order behavior may be observed, such a limiting case is non-specific with regard to detailing the mechanism of the diffusion-reaction process. A model consistent with the data is one in which, in contrast to that proposed previously, the H atom addition reaction occurs on the surface. This implies that hydrogen atoms do not diffuse into the solid, and that for the reaction to proceed, olefin molecules in the interior must diffuse to the surface to replenish those which have reacted. Two cases may be considered. In the first, the olefin is a slab, the front surface of which is exposed to hydrogen atoms. The slab thickness is taken as 1 with x = 0 the back surface. The olefin, whose concentration a t x is designated by C, conforms to the set, of equations
bC - = 0 at x dz C
=
=
0
bC
D-
bX
J701. 6G
=
kHoC at x = 0
C = Coatx=
a
Only C(O,t) is required, the quantity of interest being kHoC(O,t). The solution is well known and is
C(0,t) =
Coek2H~2t/D erfc
(kHodm)
It is to be noted that the diffusion of products has not been taken into account. This is of little consequence if the concentrations are dilute, or if the diffusion of the products in the matrix and their interaction with the surface is nearly the same as the reactants. Negligible error is introduced by considering D to be time independent. The rate of reaction is given by
For short t'imes, k _dHz _ _- --HOCo 2 dt
Coatt= 0
If k H o d mis large, then The standard solution of this set is
dHz -=-dt
"-[(;)'/a-
2dn
1 (p)'".. . 2k2HO2
,
+
1
The moles of hydrogen reacted in time t is
Where the ai's are the roots of
dC - = - kHoC a t x = I, so that dt
For small film thickness, large D, and small hydrogen atom concentration, the rate of hydrogen pick-up is approximately equal to kHoC, where C under these conditions is uniform through the film. This result is not very informative. Unfortunately, the form of the solution for the general case is not amenable to a comparison of the experimental results without an independent measure of H o and D. For a second case, the semi-infinite solid, closely approximated by thick deposits, is considered. The applicable equations are
(y"" This expression reduces to
For small values of k H o q D the AHz reduces to kHoCot/2, the limiting case for large diffusion coefficients. The two limiting conditions are represented by the experimental results of Fig. 2 and Fig. 3. Figure 2 is illustrative of a matrix where the diffusional processes are rapid compared to the rate of reaction. The hydrogen depletion is linear in time. This is precisely what is expected, since the surface concentration of olefin will, for a semi-infinite solid, be maintained constant by the rapid diffusion of olefin from the interior. Here
Dec., 1962
PHOTOLI-PI~ OF AZOMETHASE AT HIGHER PI~ESSCRES
2681
the chemical reaction is rate controlling. Figure evidence for the "olefin diffusion with reaction on 3 shows the other limiting condition where the the surface" model. Finally, it may be noted that the initial rate for olefin diffusion process is rate controlling. The hydrogen uptake, after about 4 min., follows a the presently proposed model is directly proporsquare root of time dependence. By equating the tional to the olefin concentration, that is slope of the linear portion of the curve to ( D / T ) ~ W ~ , a value for the diffusion coefficient D = 1 X 10-l2 cm.'/sec. is, derived. This refers to diffusion a t 77OK. of propylene in a matrix of %methylinitial pentane in a molar ratio of 1 to 2 . 5 . If the hydrogen atom-condensed olefin experiment is interrupted at some time 2, the olefin con- The "H atom diffusion into the solid" model gives centration a t the surface will increase in time be- a rate proportional to the square root of the olefin cause of diffusion from the interior. The process concentration for thick films.3 The data' clearly will be strongly dependent on the diffusion coeffi- support the present model in that initial rates for cient of the olefin in the matrix. Calculation of the thick films are linear with olefin concentration. It has nom been established that the mechanism surface concentration with time after the H atom for the reaction between hydrogen atoms, genersupply is stopped follows from ated in the gas phase, and a condensed reactant is one in which the reaction occurs on the surface. The surface concentration is maintained by diffusion in the condensed phase. The rate varies depending on the magnitude of the diffusion processes in the solid. If the diffusion is sufficiently small, the observed reaction rate may drop quickly to and an immeasurably low value after the surface layer has been depleted. Thus the previously X reported large differences in reactivity of various C(O,t - t ) = cn erf d--2D(t - t ) l/,D(t - t ) condensed olefins may be interpreted in terms of diffusion limiting processes. The interpretation of rates in terms of matrix effects and chemical reactivity now permits a quantitative examination of both the surface reactions and diffusion processes. IcH, - t / D exp IC' )Id. Acknowledgment.-We express our thanks to 4D(t - t ) Richard Kelley, who participated in much of the The value of C(0,t - 2) increases from its value of experimental work. Charles Hill and T. J. C(0,t). Thus the interruption experiments with DeCarlo contributed to some of the earlier experi3-methylbutene- 1 are understood. and furnish good ments.
J:
[
+
} (
THE PHOTOLYSIS OF AZOMETHANE AT HIGHER PRESSURES -1 SECOKD ETHLANE-PRODCCIKG RE-4CTIOK BY S. TOBY -4SD B. H. WEBS School of Chemist7 ?J, Rutgers Unwersit?/,New Rrunswick, S e w Jersey Recezved June 11 2968 ~
Azomethane was photolyzed from 25 to 150' in the pressure range 10 to 200 mm. At temperatures above 50" and pressures above CiO mm. the hitherto accepted mechanism breaks down. It is shown that the results can be explained by the postulation of an additional ethane-forming step. This reaction does not involve methyl radicals nor is it a simple unimolecular intramolecular split.
Introduction The photolysis of aeomethane (A) has been studied by Jones and Steaciel in the range 25 to 190' and by Toby' from -50 to +50". The main features of the photolysis may be represented by
(CH,),X2
+ hv +2CH3 + N2
(0)
( 1 ) M. H. Jones and E. W. R . Steaoie, J . Chem. Phys., ai, 1018 (1 953). (2) S.Toby, J . A m . Cham. Soc., 82,3822 (1960).
2CI-I3 + C2Htj
CH3 f (CHd2x+ 2 CH4 fromwhichitfolloa,sthat
+ -CHzN?CH3
(1)
(2)
RcHJRc~K~~/' [A] = k2/kli" The quantity R C H J R C ~ H ~ ' (henceforth /~[A] in this paper denoted by a , units l.'l2 mole-'/* sec.-'/p) thus should be independent of [A]. I n Jones and Steacie's datal1 however, there is a
