J . Phys. Chem. 1984, 88, 3465-3472 rate (primarily about the tilted axis of ordering), Le., an increased microviscosity (see, e.g., Seelig and Seelig'6,47). The broadening of the spectral lines can be due either to slow-motional effects4s or to a distribution of order parameters.16 Slow-motional effects are, in our model, consistent with decreasing RII(and RL),while a distribution of observed order parameters would result if there is some variation in \k because of a distribution in the number and types of distorted chain conformations induced by the proteins. Thus, our model appears to lead to a rather conventional interpretation of N M R spectra, for continuous variations with protein content and temperature without invoking the two-site point of view of Paddy et al.ls A more complete discussion of these matters should be based upon detailed 2H N M R line shape and relaxation studies using these models (cf. ref 22, 23,48 and references they cite). C. Summary. In summary, we believe our ESR simulations do show that a single phase (or one-site) model is a possible alternative to the more familiar two-site interpretation of ESR spectra involving protein-lipid interactions. It seems reasonable, at this stage, to suspect that the "one-siten model is more appropriate for some cases, while other cases are better characterized by a two (or greater) site model. Our primary point for now is
3465
that careful simulation of ESR spectra, based upon well-conceived microscopic models,50is called for in order to appreciate the range of possibilities consistent with the ESR spectra observed, and then carefully designed experiments are required to distinguish amongst them.51 Acknowledgment. We would like to thank Dr. G. Moro for his extensive help with and advice on the computer programs used in the simulations. This work was supported by N I H Grant GM25862 and by N S F Solid State Chemistry Grant DMR8102047. E. M. acknowledges further support from the Charles H. Revson Foundation. (50) These could include the idea of a coherence length for the range of the distorting effects of the protein on the lipid phase by analogy to liquid crystal theory.27 Such a model would necessarily require inclusion of the translational diffusion of the lipids into and out of the range of the proteins. (51) One such experiment, which leads to significantly increased spectral resolution, is to study well-aligned multibilayers (cf. H. Tanaka and J. H. Freed, to be published). Improved resolution of the spin relaxation can be achieved with the new two-dimensional electron-spin-echo technique (cf. G. Millhauser and J. H. Freed J . Chem. Phys., in press: L. Kar, G. Millhauser, and J. H. Freed, J . Phys. Chem., submitted for publication).
Energy Partitioning in the Reactions of Barium Atoms with Normal and Branched Alkyl Iodides and Dibromoalkanes Kishore K. Chakravortyt and Richard B. Bernstein*t Department of Chemistry, Columbia University, New York, New York 10027 (Received: March 1 , 1984)
Laser-induced fluorescence (LIF) measurements are reported of the vibrational-state distribution of the nascent BaX product molecules formed by the reaction of a Ba beam with a crossed molecular jet of an organic halide RX (X = I, Br). The target molecules were the monoiodoalkanes CH,I, C2H51,n-C3H71,CC3H71,and t-C4H91and the dibromoalkanesCH2Br2,CH3CHBr2, and (CH3),CBr2. For the normal iodide reactions, the BaI vibrational distributions are similar to those observed by Zare et al. for CH31, Le., bell shaped with substantial population inversion. Those for the branched iodides are somewhat skewed. For the dibromoalkanes, the BaBr distributions are similar to those of Schultz et al. for CH2Br2,with skewing for the branched alkanes. The peak of the BaX vibrational distribution v, (and the average vibrational energy of the BaX) increases with the exoergicity of the reaction (and the carbon number of the molecule), with u,,, increasing from 39 to 51 across the iodide series and from 41 to 52 for the bromides. The average BaI vibrational energy ranges from 8.5 to 11.5 kcal mol-'; for BaBr, from 13 to 15 kcal mol-'. The products' relative translational energy distributions deduced from the LIF results all peak at energies of ca. 7 kcal mol-'. Recoil momentum distributions are near Gaussian. For the iodide reactions, utilizing the difference between the energy of the highest populated BaI vibrational state and the total available energy, we can make an estimate of the sum of the average BaI rotational energy and the average internal energy of the product alkyl radical. This sum is found to be small (ca. 6.5 kcal mol-') and essentially constant for all the iodide reactions. On the basis of the LIF intensities, reaction cross sections for the iodides (relative to CH31) are estimated to be 1.6,2.9, 1.9, and 1.5 for C2H51, n-C3H71,i-C3H71,and t-C4H91,respectively. These results, especially for the isomeric propyl iodides, are indicativeof significant steric effects on reactivity.
I. Introduction
The reactions of methyl iodide with alkali- and alkalineearth-metal atoms have been studied extensively by the molecular beam scattering method.' In addition to the early measurements of product (MI) angular distributions: a wide range of molecular beam experiments have been carried out, including measurements of product recoil velocity and energy distributions: collision energy dependence of differential4 and integral reaction cross section^,^ orientation dependence of reactivity: rotational and polarization analysis (via electric deflection) of the MI p r ~ d u c t and , ~ MI vibrational-state distributions, via laser-induced fluorescence (LIF).8 These reactions are found to proceed via the classic "rebound" or impulsive mechani~m.~Thus, the MI product molecules scatter 'Present address: National Semiconductor Corp., Santa Clara, CA 95051. *Presentaddress: Department of Chemistry, University of California, Los Angeles, CA 90024.
0022-3654/84/2088-3465$01.50/0
mainly backward in the center of mass (CM) system and a substantial fraction of the reaction exoergicity goes into trans(1) For a review, see M. R. Levy, Prog. React. Kinet., 10, 1 (1979). (2) (a) D. R. Herschbach, Faraday Discuss. Chem. Soc., No. 55, 233 (1973); (b) R. B. Bernstein and A. M. Rulis, ibid., 55,293 (1973); (c) S.M. Lin, C. A. Mims, and R. R. Herm. J . Phys. Chem., 77, 569 (1973). (3) (a) A. M. Rulis and R. B. Bernstein, J . Chem. Phys., 57, 5497 (1972); (b) C. Ottinger, P. Strudler, S. J. Riley, R. M. Harris, and D. R. Herschbach, data presented in ref 2a; (c) C. M. Scholeen and R. R. Herm, J . Chem. Phys., 65, 5398 (1976). (4) (a) M. E. Gersh and R. B. Bernstein, J. Chem. Phys., 56, 6131 (1972); (b) A. G. Urena and R. B. Bernstein, ibid., 61, 4101 (1974); (c) G. Rotzell, R. Viard, and K. Schiigerl, Chem. Phys. Lett., 35, 353 (1975). (5) (a) M. E. Gersh andd R. B. Bernstein, J . Chern. Phys., 55, 4661 (1971); (b) K. T. Wu,H. F.Pang, and R. B. Bernstein, ibid., 68, 1064 (1978). (6) (a) P. R. Brooks and E. M. Jones, J . Chem. Phys., 45, 3499 (1966); (b) R. J. Beuhler, R. B. Bernstein, and K. H. Kramer, J . Am. Chem. Soc., 88, 5331 (1966): (c) R. J. Beuhler and R. B. Bernstein, J . Chem. Phys., 51, 5305 (1969); (d) D. H. Parker, K. K. Chakravorty, and R. B. Bernstein, Chem. Phys. Lett., 86, 113 (1982).
0 1984 American Chemical Society
3466 The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 lational recoil.1° Increasing the reagents’ translational energy leads to a substantial increase in the products’ translational energy.” Herschbach12 has interpreted the near-Gaussian shapes of the M I recoil momentum distributions, found for the reactions of alkali atoms with a series of alkyl iodides RI, in terms of the R I photodissociation spectra. The model accounts for the fact that the M I momentum distributions are nearly the same for a large number of alkali R I reactions.12 An alternative momentum-transfer constraint model has been developed and applied to these reactions by Levine and co-workers.13 Little is known regarding the energy partitioning into the product radicals. There is indirect evidence” that the CH3 product from the CH31 K reaction is internally excited. It is of interest to note that, in the UV photofragmentation of CH31, Leone and co-workers14observed I R chemiluminescence from the umbrella mode of vibrationally excited CH3 product (up to v = 10 for the v2 mode). This result is consistent with that of Lee and cow o r k e r ~ , deduced ’~ from the translational spectroscopy of the photodissociated CH31. The reaction of Ba CH31was the first of the series to be studied by LIF.8 Zare and co-workers determined the BaI vibrational-state distribution and reported* the average vibrational energy of BaI to be 38% of the total available energy Ea.l. The products’ recoil energy distribution was deduced from angular distribution measurements by Herm and co-workers,2cfrom which the average translational energy of the products could be determined. Taking into account the average rotational excitation of BaI (estimated8to be ca. 1-2 kcal mol-’ and combining all these results, it was inferredlo that the average internal energy of the CH, product is ca. 3 kcal mol-’. While the reaction systematics of the alkali metal-alkyl iodide have been well studied, there appear to be no systematic investigations into the effect of size and structure of the alkyl groups upon the dynamics of the corresponding alkaline-earth reactions. The present study examines the role played by the alkyl group (R) in the product (BaX) vibrational-state distribution and consequently in the energy partitioning and product recoil momentum distribution for the reactions of Ba plus alkyl iodides and dibromoalkanes. Starting with methyl iodide, the variations in the alkyl groups have been achieved by extending the normal carbon chain (methyl, ethyl, and n-propyl iodide) and by branching the carbon bonded to the iodide (isopropyl and tert-butyl iodide). The dibromoalkanes selected are dibromomethane,I6 1,l-dibromoethane, and 2,2-dibromopropane. The L I F experiments yield the degree of vibrational excitation of the BaI and BaBr products as well as the relative reaction cross sections within one series. From these data, the recoil energy distribution ( and thus the recoil momentum) of the products is deduced.
Chakravorty and Bernstein LASER BEAM
‘r
BAFFLE ASSEMBLY\
E‘8
ALKYL HALIDE VAPOR SOURCE
+
GAS I N L E T NEEDLE VALVE
+
+
11. Apparatus
The present LIF experiments were carried out in the detector chamber of the so-called “focusing machine”, previously employed for studying the reactions of oriented molecules.6d A schematic drawing of the experimental arrangement is presented in Figure
(7) (a) C. Maltz, N. D. Weinstein, and D. R. Herschbach, Mol. Phys., 24, 133 (1972); (b) D.S . Hsu, G. M. McClelland, and D. R. Herschbach, J . Chem. Phys., 61,4927 (1974). (8) P.J. Dagdigian, H. W. Cruse, and R. N. Zare, Chem. Phys., 15,249 (1976). (9) D.R. Herschbach, Adv. Chem. Phys. 10,311 (1966). (10)R.B. Bernstein and B. E. Wilcomb, J. Chem. Phys., 67,5809 (1977). (11) (a) A. G.Urena and R. B. Bernstein, J. Chem. Phys., 61, 4101 (1974); (b) E. Pollak and R. B. Bernstein, ibid., 70, 3995 (1974); (c) T. Munakata, Y. Matsumi, and T. Kasuya, ibid., 79, 1698 (1983). (12) D.R. Herschbach, Faraday Discuss. Chem. Soc., No.55,233(1973). (13) (a) A. Kafri, E. Pollak, R.Kosloff, and R. D. Levine, Chem. Phys. Lett., 39,l (1975);(b) H. Kaplan and R. D. Levine, J. Chem. Phys., 63,5064 (1975);(c) ref llb. (14) H. W. Herrmann and S. R. Leone, J. Chem. Phys., 76,4766(1982). (15) R.K.Sparks, K. Shobatake, L. R. Carlson, and Y. T. Lee,J. Chem. Phys., 75,3838 (1981). (16) M. Rommel and A. Schultz, Ber. Bunsenges. Phys. Chem., 81, 139 (1977).
COLLECTION OPTICS Ea BEAMA LASER
N
L
(
F
€
LASER BEAM
INTERSECTION ZONE WOOD HORN LASER BEAM OUT
Figure 1. Schematic view of the apparatus showing inlet jet for alkyl iodide (or dibromoalkane), Ba beam source (beam perpendicular to plane of the drawing), collimated laser beam, fluorescence collection optics, and photomultiplier
(PMT).
1. It consists of three parts: (1) a reaction chamber where ground-state BaI or BaBr molecules are produced by the reaction between a beam of Ba atoms and a capillary jet of alkyl iodides or dibromoalkane molecules, (2) a pulsed tunable dye laser that pumps the nascent BaX product molecules to an excited electronic state, and (3) fluorescence collection optics and a photomultiplier that detects the emission from the electronically excited BaX molecules. The Ba atomic beam was produced by effusion from a Monel oven (slit 6.25 mm X 0.63 mm) resistively heated by tantalum wire windings to a stock temperature of ca. 1000 K. (At this temperature, the source vapor pressure of Ba is ca. 0.05 torr.) The oven was surrounded by a reflecting tantalum heat shield to minimize radiation losses. (The oven temperature was monitored by a number of Chromel-Alumel thermocouples.) The oven with its tantalum shield was mounted on a water-cooled brass surface that also supported a copper collimating plate with a rectangular slit (6.25 mm X 2.5 mm) located 25 mm from the oven slit. The whole assembly was contained in a liquid-nitrogen-cooled cylindrical copper shroud of internal diameter 100 mm. The Ba atomic beam reached the reaction zone after passing through the slit in the oven shroud located ca. 30 mm from the reaction zone. The alkyl iodide or dibromoalkane capillary jet was formed by expanding their neat vapors through a thin copper capillary of 1-mm i.d. A needle valve located outside the vacuum system, connecting the reactant source with the vapor delivery feed line, was used to regulate the flow of the vapors so as to maintain a constant pressure of PD = 1 x torr (nominal ion gauge reading) in the detector chamber during the course of the experiment. A pulsed N, laser (Molectron UV 24), operating at 1 M W peak power and 10 pps, was used to pump a dye laser (Molectron DL 11). A flowing dye system (Molectron DL 260) was used for the dye laser. The output pulses were about 10 ns long, nominally 0.01-nm line width, and approximately Gaussian in radial profile. The laser power was measured with a Molectron pyroelectric joule meter (Molectron j3-05). The BaI product molecules were detected by exciting fluorescence in the C2113,2-X2Z+,Av = 0 band system lying near 537 nm, and the BaBr products were detected via the
Reactions of Barium with Alkyl Iodides and Bromoalkanes
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 3461
(20,201
;P
(40,401-
1
I
I
I
I
I
I
532
I
538
140,401 ~ , l 5 . , 5 ,
r.,i (35,351
I
I
I
I
I
I
I
538
232
I
I
53 2
-
I
I
I
534
A
120.20 I
I
536
I
I
538
(nm)
Figure 3. Same as Figure 2 but for the reactions of Ba with i-C3H71and t-C,H,I.
\
-
, 5
532
I
I
(15,151
, i , -15.51
t
534
536
538
Xlnml
Figure 2. Typical LIF excitation spectra of BaI (C2113,2-XZZ+,Av = 0 sequence) from the RI + Ba reactions (R = CH3, C2HS,and n-C3H7). The numbering of the (v’p”) band heads is indicated.
C2ll,,,-XzZ1+, Au = -1 band system lying near 541 nm. Fluorinated coumarin dye (Exciton) in ethanol was used as the laser medium (peak output at 520 nm, range 490-560 nm). The dye laser pulse energy was ca. 10 kJ. The pulse-to-pulse stability was better than 10%. The fluorescence was observed with a photomultiplier (RCA 7265, 51 mm in diameter, S-20 cathode) in conjunction with a fluorescence collection optics assembly placed at right angles to the Ba beam and the probe laser beam. The collection optics consisted of two biconvex lenses with focal lengths (and diameters) of 62.5 and 50 mm, respectively. Two optically blackened light baffles, with center holes of diameters 18.7 and 6.2 mm, enabled the optics system to image tightly at the reaction zone. On the basis of the geometry, this assembly collected about 5% of the total fluorescence and focused it on the center of the photomultiplier window. The photomultiplier signal was averaged by a boxcar (PAR Model 162 main frame, 153 plug-in), externally triggered by a fast-response photoiodide (Hewlett-Packard 4280), which sensed the exit of the laser pulse from the chamber. To account for the boxcar response time of about 50 ns, the photomultiplier signal was fed to the boxcar input via a long coaxial cable, creating a
delay of ca. 75 ns between the trigger pulse and the signal time of arrival, A gate width of 50 ns was selected; the plug-in time constant was 1 s, and the main-frame time constant was 0.1 s. The output of the boxcar was fed to a strip-chart recorder. The dye laser wavelength was slowly scanned in order to obtain the excitation spectrum. At the peak of the L I F spectrum, the fluorescence intensity was found to be strictly linear in laser pulse energy (and also linear in PD). 111. Results
Figures 2, 3, and 4 present typical recorded LIF spectra (i.e., variation of fluorescence intensity with laser wavelength) for BaI and BaBr from the reaction of Ba with the alkyl iodides R I (RI CH3, C2HS,n-C3H7,i-C3H7,and t-C4H9)and dibromoalkanes R”Br, (R” E CH,, CH,CH, and (CH,),C). The BaI bands for C2113/2-X2E+, Au = 0 sequence of the subsystem are identified by comparison with the published (LIF) spectrum of Ba18 and by calculating the band-head positions (for low u ) based on recently determined vibrational constant^.'^ BaBr peaks were identified in a similar manner by comparison with the published spectrum.18 More recent vibrational constants1lCdo not cause any change in the assignments. As will be detailed in section IIB, BaI molecules formed in the reaction of Ba with methyl, ethyl, and n-propyl iodide exhibit quite similar bell-shaped excitation spectra, except that the peak of the vibrational distributions shifts up one vibrational quantum each in the sequence methyl, ethyl, and n-propyl. The peak shifts to still higher u values for i-C3H71and t-C4H91. BaBr excitation spectra for the reaction of Ba with dibromoalkanes exhibit somewhat similar characteristics. For 1,l-dibromoethane and 2,2-dibromopropane, the BaBr spectrum is only partially resolved (it was not possible to resolve the low vibrational band heads). However, the shift of the peak to higher u values from dibromomethane to 2,2-dibromopropane is readily observable. (17) J. S. McKillop and R. N. Zare, Private communication, 1983. (18) A. Schultz and A. Siegel, J . Mol. Speczrosc., 88, 235 (1979).
3468
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984
Chakravorty and Bernstein
n-C7H71
0 06
f (v") 0 04
0 02
0
0 04
f (v") 0 02
A
0
15
I
V"
542
536
(CH312CBr2
IS
45
,
536
V
to unity. Populations are estimated from LIF spectra such as those
I
542
shown in Figures 2-4 (see text).
X (nm) Figure 4. Typical LIF excitation spectra of BaBr (C2111/2-X2Z+, Av = sequence) from the reactions of Ba with CH2Br2,CH3CHBr2,and
-1
(CH3)2CBr2.
-
TABLE I: Relative Fluorescence Intensities and Reaction Cross Sections for the RI Ba BaI R Reactions
+
RI CH31 C2HJ n-C3H71 i-C3H71 i-C,H,I
+
re1 fluores intens 1.o 0.93 f 0.04 0.85 0.04 0.66 0.04 0.61 f 0.04
* *
sensitivity 1.o 1.7 3.4 f 2.8 f 2.4 f
* 0.2 0.8 0.4 0.3
V'I
Figure 5. Relative vibrational population distributions for the BaX product of the reactions of Ba with the indicated alkyl iodides or dibromoalkanes. The ordinate is the fraction in the state u", normalized
re1 cross section 1.o 1.6 f 2.9 1.85 1.45
0.2
* 0.7
* 0.3 * 0.2
A . Relative Fluorescence Cross Sections. Table I presents relative values of the total fluorescence intensity from BaI formed in the reactions of Ba with alkyl iodides under the so-called "standard conditions": PD= 1 X torr (nominal ion gauge pressure in the detector chamber). The relative fluorescence values are proportional to the areas under the excitation spectra of BaI recorded under identical conditions. The relative fluorescence intensities are related to the relative cross sections via the ionization gauge sensitivities for the alkyl iodides. (The correction from relative product densities to fluxes, which involves ratios of BaI lab velocities, is negligible since these are kinematically constrained to be close to the C M velocities, which vary only slightly over the series.) The ionization sensitivity factors were measured by an expansion procedure.19 The resulting relative cross sections are presented in Table I. Despite the large uncertainties in these values, there is clearly a significant difference in the reactivities of n-propyl and isopropyl iodide toward Ba. E . Products' Internal Energy Distribution. The vibrational and rotational energy distributions of BaX can best be obtained from the excitation spectrum by computer simulation. In this procedure, as employed by Gupta et aLZ0and Munakata et al.,Ilc a calculated excitation spectrum is constructed by assuming a rotational population distribution, making use of the FranckCondon (FC) factors and convoluting with the laser bandwidth function. In the case of BaI, the 6 function approximation for
the Franck-Condon factors has been shown to be satisfactory.21 In the present study, it has been assumed that the C2113/2-X28+, Av = 0 band intensities are proportional to the height of the band heads above the base line. For BaBr, the situation is less favorable since the Av = -1 subsystem accounts for only a minority fraction of the total intensity of the C2nl/z-X22? transition.IlcJ8 The simple assumption has been made that the FC factors within the Av = -1 subsystem are constant and that the heights of the band heads are indicative of relative populations. Unfortunately, this introduces considerable ambiguity in the derived BaBr vibrational distributions. Since the FC factors are expected to increase with v, the low v relative populations may be underestimated. Furthermore, each band in a given subsystem has two heads, e.g., R2 and RZ1for the 2113/2-zZ+ transition. As shown in ref 1IC, the Rz(u,v) head coincides with the Rz1(c-2,c-2) head. The relative intensities of the R2 and Rzlheads depend upon the BaBr rotational distribution. This overlap will adversely influence the accuracy of the derived BaBr vibrational distributions (ascertained via the simple band-head height procedure used here). Fortunately, since the BaBr molecule is the product common to all three dibromoalkane reactions, the error induced by this assumption is of somewhat less importance when comparing reactions within the series. Figure 5 shows the results, in the form of stick diagrams representing the normalized vibrational-state distributions for the products of the Ba reactions with the alkyl iodides and dibromoalkanes. Both BaI and BaBr, in all cases, show substantial population inversion. The peak vibrational level shows a systematic upward shift from CHJ to tert-butyl iodide. C. Products' Recoil Energy Distribution. The translational energy distributions P(E',,) for the products of the reactions were calculated from the BaX vibrational distributions as in ref 10. Estimation of the product recoil energy requires knowledge of the average internal energy content of the product radical, E'lnt(R). Since this is, in general, unknown, the procedure adopted here was to take the highest observed BaX vibrational state to be the indicator of the zero of E',,, Le., to assume E'tr
[E'vdBaX)Imax - E'vlb(BaX)
where [E'v,b(BaX)]maxis the vibrational energy corresponding to (19) K. K. Chakravorty, Ph.D. Thesis, Columbia University, New York, 1984. (20) A. Gupta, D. S . Perry, and R. N. Zare, J . Chem. Phys., 72, 6237 (1980).
(21) H. W. Cruse, P. J. Dagdigian, and R. N. Zare, J . Chem. Phys., 61, 4450 (1974).
Reactions of Barium with Alkyl Iodides and Bromoalkanes
'"
A
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 3469
C2H51
E'+r(kcal mol-')
+
Figure 6. Recoil energy distributions P(E',,) for the BaI R products of the RI + Ba reactions (R CH3, C2H5,and n-C3H7). Circles are based on experimental vibrational populations from Figure 5, with a solid
curve drawn through points. Dashed curves are Gaussian fits with widths AE (as indicated) and maxima at Eo values of 7.0, 7.4, and 7.3 kcal mol-', respectively, for CHI, C2HS,and n-C3H7(scaled to unity at peak).
E',,lkcol mol-')
Figure 7. Same as Figure 6 but for R = i-C,H7 and t-C,H, with E , values of 7.6 and 6.7 kcal mol-', respectively. 0 75
the highest observed state. The maximum allowable value of the average internal energy of the radical is given by
CH3I
0 60
where Erot(BaX) is the average rotational energy of the BaX product (undetermined here). In what follows, the recoil distributions are fitted with two different assumed functional forms. First, the data are fitted to a Gaussian in E'tr Figures 6 and 7 show the distributions for the five alkyl iodide reactions. The dashed-line curves are the Gaussian fits to these distributions. The results for reactions involving branched alkyl iodides deviate from Gaussian to a greater extent than for the reactions involving n-alkyl iodides. Note, however, that the peak in the experimentally derived recoil energy distribution, Eo, occurs a t essentially the same value for all the five alkyl iodides. Figure 9 presents sifmilar Gaussian fits to the recoil energy distributions for the dibromoalkane reactions. The distributions deviate increasingly from Gaussian, from dibromomethane to 2,2-dibromopropane. Once again, the peak recoil energy Eo is essentially the same for all thiee reactions. Figure 10 presents a composite plot for the dibromoalkane reactions. Figures 11 and 12 present product recoil momentum distributions P(p') from the RI reactions (after inclusion of the proper Jacobian factorlo). It is evident that the recoil momentum variable leads to a good fit to the experimental distribution curves in accordance with the inference in ref 10. The Gaussian P(p') fits to the experimental curves for isopropyl and tert-butyl iodide are significantly better than in the recoil energy (E'tr)representation. Figure 13 presents similar fits for the three dibromoalkane reactions. The improvement in the Gaussian momentum fits is once again evident. Table I1 lists estimated values for the energetics for the alkyl iodide reactions. Table I11 reports the present energy-partitioning results for the five alkyl iodide cases. (For the dibromoalkanes, the reaction exothermicities are not known with sufficient accuracy
0
045
x
.- 030 L
W
n
0 15
0 0
5
IO
15
20
25
E;, ( k c a l mol-')
Figure 8. Composite plot of P(E:,), now normalized to unit area, for the five indicated RI + Ba reactions. Solid curves are drawn through the experimental points. TABLE II: Estimated Reaction EnergeticsQfor the RI T R Reactions
RI CH31 CAI n-C3H71 i-C3H71 t-C,H,I
E;.? 1.2 1.2 1.2 1.2 1.2
1.95 1.9, 1.95 2.0 2.0
AD,,^ 19.5 20.5 20.3 21.9 23.9
+ Ba
-
BaI
E..., ~~
22.1 23.7 23.5 25.1 27.1
Energies in kcal mol-'. Estimated, based on temperature of 400 K. 'Estimated, with 75O beam intersection angle. dBased on bond energy literature (details in ref 19). I)
to be useful.) Table IV oresents the values o i peak recoil energy E', (namely Eo),peak recoil momentum po, and the reduced width
3410 The Journal of Physical Chemistry, Vol. 88, No. 16, 1984
'9 fi
Chakravorty and Bernstein I.o
CH2Br2
P(P', 0.5
n 1.0
P(E'tr)
26
0.5
0
0
'-"
'
An-C3H71 Figure 9. Same as Figures 6 and 7 but for reactions of Ba with CH2Br2, CH3CHBr2,and (CH3)&Br2. Eo values are 7.0, 6.8 and 7.5 kcal mol-', respectively. 0.90 CHzBr2 CzH,Br2 x (CHd2CErz
A
0.60
P'(%-I 1
Figure 11. Recoil momentum distributions P(p') for the RI + Ba reactions (R CH,, C2H5,and n-C3H7). Solid curves are Gaussian fits to the experimentally desired points. Width parameters fl are indicated; values of po are listed in Table IV. TABLE III: Energy Partitioning Resultsa for the RI R Reactions Evib-
E,,*:
+
RI
(BaI)'
Ei,,(R)e
CHqI C2H4 n-C6H,I i-C3HlI t-CdHgI
16.1 16.8 17.2 18.7 20.5
8.5 8.9 9.2 10.4 11.5
7.5 7.9 8.0
8.3
9.0
6.6 6.9 6.3 6.4 6.6
& 1.5 & 1.5
1.5 & 1.5 & 1.5
+ Ba
-
BaI
+
fd ffl 0.37 0.38 0.39 0.41 0.42
0.33 0.33 0.34 0.33 0.33
Energies in kcal mol-'. Bal vibrational energy corresponding to highest observed u". cAverage vibrational energy of BaI, from normalized distribution of Figure 5. dAverage products' relative translational energy, from data of Figure 8. eEstimated by difference using E,,, from Table 11. /Average fraction of E,,, in BaI vibration. BAverage fraction of E,,, in products' translation.
E i r (kcolmol-') Figure 10. Same as Figure 8 but for the reactions of Ba with the indicated dibromoalkanes.
parameterlo 0 for all eight Ba reactions.
IV. Discussion Reactions of alkali-metal atoms with alkyl iodide molecules provide a good basis for interpreting the analogous reactions involving alkaline-earth-metal atoms (e.@;.,see ref 2b and 22). In the alkyl iodide + K reactions, the angular distribution of KI product peaks in the backward hemisphere with respect to the incoming K atom. The peaking becomes less pronounced as the size of the alkyl group increases.23 As inferred from the kinematic (22) R. Grice, Adc. Chem. Phys., 30, 247 (1975). (23) (a) G. H. Kwei, J. A. Norris, and D. R. Herschbach, J . Chem. Phys., 52, 1317 (1970); (b) J. L.Kinsey, G. H. Kwei, and D. R. Herschbach, ibid., 64, 1914 (1976).
TABLE I V Summary of the Product Recoil Energy and Momentum Distributions for all the Ba Reactions reagent CH,I C2H4 n-C3HlI I'-C3H71 f-C,HgI
En"
D"b
B'
7.0 7.4 7.3 7.6 6.7
7.5 10.3 12.0 12.8 14.3
0.24 0.26 0.26 0.29 0.36
CH2Br2 CH3CHBr2 (CH3)2CBr2
7.0 6.8 7.5
16.1 16.6 19.6
0.27 0.37 0.38
"Peak recoil energy in kcal mol-I. bPeak recoil momentum in 'Reduced width parameter of Gaussian momentum fits.
A-l.
analysis of the ("class B") angular distribution measurements, there is a marked variation along the series of the reactions regarding the partitioning of the available energy between relative translation and internal excitation of the products.23 Investigation of the reactions of K, Cs, and Rb plus normal and branched alkyl iodides,
Reactions of Barium with Alkyl Iodides and Bromoalkanes
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 3471
For the analogous reactions of Ba plus normal and branched alkyl iodides, the present experiments show that an increasing fraction of the reaction exothermicity is converted to vibrational excitation of BaI with increasing size of the alkyl group. Going from CH31to C4H91,the exoergicity increases by about 4 kcal mol-' (because of the weakening of the C-I bond by the same amount) This increase in available energy is funneled completely into BaI vibration, resulting in an increase of 14 vibrational quanta in the case of t-C4HgI over that of CH31. Thus, it appears that vibrational excitation of BaI is governed by the exoergicity of the reaction and is not directly sensitive to the size and/or structure of the alkyl group. For the reactions of Ba CH31, CzH51,and n-C3H71,the BaI excitation spectra exhibit similar characteristics. The vibrational-state distributions are bell shaped, with considerable population inversion. For the branched alkyl iodide reactions, the BaI vibrational distributions show deviations from the bell shape (Le., skewing), especially for the t-C4H91reaction. The sum of the average internal energy of the product alkyl radical and the average rotational energy of BaI is found (Table 111) to be essentially constant at ca. 6.6 kcal mol-'. This suggests a highly localized, nonstatistical partitioning of the available energy into the products' internal and translational degrees of freedom. These impulsive reactions appear to be over before a statistical distribution of energy into the various vibrational and rotational degrees of freedom of the products can be accomplished. This is consistent with the impulsive model. Reaction of alkali atoms with various methyl halides is initiated by a sudden electron jump from the alkali atom to the methyl halide in the vicinity of the crossing between the covalent and ionic potentials. (The energy difference between the intersection of the two potential curves and the initial energy level of the molecule agrees well with the experimentally determined threshold of the reaction^.^^) After the electron jump from the incoming Ba atom to the I-R molecule, the released energy is highly "directed" and localized along the Ba+-I--R axis. Wu et a1.26investigated the dependence of the reaction cross section on the relative translational energy Et, for the reactions of CHJ with K and Rb. They observed an Arrhenius-like positive energy dependence of the reaction cross section above threshold, a maximum, and then a decline with Et,. For the analogous reactions of Ba plus alkyl iodide molecules, it is expected that the reaction cross section would depend strongly upon Et, (cf. the results for the Ba + CH3Br reactionlk). The present experiments were all at essentially the same E,, but in the absence of knowledge of the energy dependence of the cross sections, it is difficult to interpret the observed relative cross sections. Nevertheless, the substantial differences in the alkyl iodide reaction cross sections (Table I) are very probably attributable to steric effects. Notable is the increase of a factor of nearly 3 between CH31and t-C,HgI and the significantly smaller reaction cross sections for i-C3H71 relative to n-C3H71(at the same E,). The iodine atom is obviously less accessible to the incoming Ba atom for the branched alkyl iodides than for the normal alkyl iodides. It is of interest to note that the steric effect for t-C4H91in reaction with K has been directly observed by Marcelin and Brooksz7using the oriented molecular beam technique.6 The products' recoil energy distribution, as estimated from the BaX vibrational distributions, has been fitted to a Gaussian functional form for most of the reactions of Ba with the alkyl iodides and dibromoalkanes (although there is skewing for the reactions of t-C4H91and (CH3)zCBrz). The peak recoil energy remains fairly constant over the entire series of iodides (and dibromoalkanes); see Table IV. Use of the recoil momentum representation P(p') greatly improves the Gaussian fit to the experimental points. However, in
+
c
0.5
p' loA-ll
Figure 12. Same as Figure 11 but for i-CjHII and t-C,H,I. I.o
P(P7 0.5
0 I.o
P(P') 0.5
n
Figure 13. Same as Figures 11 and 12 but for the reactions of Ba with the indicated dibromoalkanes.
employing velocity analysis of the product, revealed the striking fact that the mean velocity of the metal iodide product in the C M system remained fairly constant for the whole series of reactions. It was concluded that, with increasing size of the alkyl radical, an increasing fraction of the available energy is converted into either vibration or rotation of (at least one of the two) products.24
~~
~~
(24) C. Ottinger, P. Strudler, and D. R. Herschbach, unpublished data (referred to in ref 2a). (25) K. T. Wu, J . Phys. Chem., 83, 1043 (1979). (26) K. T. Wu, H. F. Pang, and R. B. Bernstein, J . Chem. Phys., 68, 1064
, ~ ",.~ .
( I 97Ri
(27) G . Marcelin and P. R. Brooks, J . Am. Chem. SOC.,95, 7885 (1973).
J. Phys. Chem. 1984,88, 3472-3419
3472
contrast to the predictions based on the simple impulsive photodissociation model, the peak recoil momentum values p o follow a systematic upward trend with increased size of the alkyl (or dibromoalkane) group (see Table IV). In the alkali metal-alkyl iodide reactions, it has been shownZathat po values remain fairly constant for Cs RI (R CH3, C2H5,n-C3H7, and t-C4H9) reactions; the variation inpovalues is only ca.12%. It is of interest to note that the model of Levine and co-workers13 does predict a trend in po with the alkyl size (for the alkali metal-alkyl iodide reactions). Table I11 shows that the fraction of total available energy appearing in the products’ relative translational motion remains fairly constant over the whole alkyl iodide series. The partitioning of the remaining energy in the internal degrees of freedom of the products is heavily biased toward the BaI vibrations.
+
V. Conclusions Considerable vibrational population inversion has been observed in BaX (X I, Br) nascent product molecules formed in the reactions of Ba with various alkyl iodides and dibromoalkanes. The extent of vibrational excitation in BaI appears to be directly related to the reaction exoergicity. For the normal alkyl iodide reactions, the BaI vibrational-state distributions are bell shaped, similar to those reported by Zare and co-workers for CHJ, while the distributions obtained for the branched alkyl iodide reactions show significant skewing, especially so for the t-C4H91reaction. The fraction of the available energy of BaI increases with the size of the alkyl group, contrary to statistical (“prior”) expectations. The relative reaction cross sections for the alkyl iodide reactions show wide-ranging variations. If one compares the two isomeric
propyl iodides, n-C3H71shows a significantly greater reactivity than i-C3H71. This is interpreted as a steric effect. From the vibrational-state distributions, it has been possible to deduce the product recoil energy distributions. For the n-alkyl iodide reactions, the P(E’,,) distributions show a good fit to a simple Gaussian functionality in E’v, less so for the branched alkyl iodides. Recoil energy distributions for the reactions of Ba with dibromoalkanes deviate increasingly from a simple Gaussian shape as the size of the alkylene group increases. However, the peak values Eo remain approximately constant (ca. 7.5 kcal mol-’ for the entire series). Using the recoil momentum representation, we can fit all P(p’) distributions with a simple Gaussian functionality. The peak recoil momentum values po increase with the alkyl size (or Ea”,). The sum of the (maximum) value of the average internal energy of the nascent product alkyl radical and average rotational energy of BaI appears to be reasonably constant (ca. 6.6 kcal mol-’) over the whole series of alkyl iodide reactions, which suggests a highly localized (nonstatistical) energy release with the impulse directed essentially collinearly from B a1 to the adjacent carbon atom.
Acknowledgment. We thank Prof. David H. Parker for his help in the initial stages of this study, Dr. Fred Gollob for the ion gauge sensitivity measurements, and Dr. Arunabha Gupta, Dr. Nicholas Van Veen, and Prof. Richard Bersohn for valuable discussions. Thanks are also due to a reviewer for constructive comments. Registry No. Ba, 7440-39-3; CH,I, 74-88-4; C,H,I, 75-03-6; n-C3H,I, 107-08-4; i-C3H71,75-30-9; t-C,H,I, 558-1 7-8; CH,Br,, 74-95-3; CH,CHBr,, 557-91-5; (CH3),CBr2,594-16-1.
Light-Scattering Measurements of Diffusion in Binary Solutions Containing an Associating Component Kevin McKeigue and Erdogan Gulari* Department of Chemical Engineering, The University of Michigan, Ann Arbor, Michigan 481 09 (Received: March 2, 1984)
The effect of molecular association on diffusion in binary liquid mixtures was investigated by light-scattering techniques. Dynamic light-scattering measurements of the mutual diffusion coefficient, D, are reported for the systems methanol/benzene, methanol/CS2, ethanol/benzene, and ethanol/CS2. The measurements were made over the complete concentration range and for temperatures ranging from 20 to 8 0 “C. For the same systems, static light-scattering measurements were used to estimate the average degree of self-association of the alcohols. The strong dependence of D on both concentrationand temperature is found to agree qualitatively with a simple physical model for diffusion which considers the formation of alcohol clusters via hydrogen bonding.
Introduction
A number of different theoretical approache~l-~ have been used in an attempt to describe diffusion in binary liquid solutions. A common limitation of all of these methods is their inability to accurately predict diffusion coefficients in highly nonideal solutions. The rough hard-sphere fluid model of Chandler4 which is currently receiving considerable attention2-’ has been applied (1) R. K. Ghai, H. Ertl, and F. A. L.Dullien, AIChE J., 19, 881 (1973), and references therein. (2) S. J. Bertucci and W. H. Flygare, J . Chem. Phys., 63, 1 (1975). (3) K. J. Czworniak, H. C. Andersen, and R. P a r a , Chem. Phys., 11,451 (1975). ‘ ( 4 j D . Chandler, J . Chem. Phys., 62, 1358 (1974). (5) S. H. Chen, H. T. Davis, and D. F. Evans, J . Chem. Phys., 77, 2540 ( 1982). ( 6 ) D. F. Evans, H. T. Davis, and T. Tominaga, J. Chem. Phys., 74, 1298 (1981).
0022-3654/84/2088-3472$01 S O / O
successfully to interpret mutual diffusion coefficients in ideal2 and moderately nonidea13solutions. However, this model also breaks down when applied to solutions which exhibit strong n~nidealities.~ In describing liquid diffusion, solution nonidealities are often taken into account through the introduction of a thermodynamic factor.8 This approach is based on the assumption that the correct driving force for diffusion is the gradient in chemical potential rather than the concentration gradient. Thus
where D is the observed mutual diffusion coefficient, Do is the ideal Fickian diffusion component, x1 is the mole fraction of (7) S. H. Chen, H. T. Davis, and D. F. Evans, J . Chem. Phys., 75, 1422 (1981). (8) J. C. R. Turner, Chem. Eng. Sci., 30, 151 (1975).
0 1984 American Chemical Society
