.K. L. Qellehsrand S. H,WuQr 8,71 (1965): H. 0. StMham and J. V. A, nS, 2233 (i887); K. K. hnes, J. P. SpBEtraPc.., 22, 125 (1987); L. sebe@ Rw.,W, 249 (1972); ref 11 a d 23. Ch J. 1yilkn. phys., 6% 1974 (18 (28) S. Celwano.
t 1884).
a. -A
and G. '&ana, .S -
@a,
5
(29) A, 8. P. bm,J. Lewb, a d R, S. NyRolm, J. Utm.Sue., 1235 (1962); 3156(1963): 6042(1963). (30)H. D. Stidham arrd J, A. Wn&kf, .,27,997 (lM6); (31) J. R. Fmam, C. CrfabW. a d 6. 435 (1967); J. R. Fenaro, J. Z&w, and W. WomM, Appl. t$ecfme., 29,180 (1989). (32) R. Foglkzo and A. Wak,Ap#. Specbase, 24,601 (187 (33) Q. WW, " E W ~ t w - A m p t w - K ~ x e , " leg, Berfin, lQ81,p 168.
The mean internuclear distances derived from gas-phase electron diffraction patterns are a function of the kample tempkraFure. However, for uniconformational molecules which do not undergo large amplitude motions this dependence is slight, so that the assumption that the sample temperature is equal to the nozzle temperature generally introduces errois which are less than those from other sources inherent in n the amplitudes of vibration are large, or when conformational changes occur with low activas, the meastired root m e h square amplitudes and the relative proportions of conformers are sensitive to the sample temperature, which clearly is less than that of the nozzle. Generalized contour mapa (in diinensionless parameters) have been compute r the density and temperature distributions in free periments, covering a range of heat capacity d-. jete, such as are normally used in electron diffracti Even though the computer programs were written for ideal gases (constant and y) and thus do not strictly conform to the situation in electron diffraction jete, the results do permit an analysis of the kinetic and thermochemical y 9 t e s for typical cases of current interest. We conclude that for unsymmetrical molebulbs with more than,five atoms,vibrational relaxation occura in the jet, but only partial ch tion takes place to an extent determined by the internal contour of the nozzle, even for acti m low as 2 kcal/mol. The critical experimental parameters which have not been adequately controlled in most electron diffraction units are the size of the electron beam as the jet, the displacement of its axis above the nozzle lip, and the internal contour of the nozzle exit section.
qp
ence shows that the measured interatomic distances am lite finite sample spread, whereas analysis For the determination of molecular structures by gdsspreading should increase the measured p h m electron diffraction the aample is injected as a free amplitudes of vibration by AIij e e&, jet through a small hole (0.20.7 mm) from a source preswhere 6 a rij262lL.2 (6 is a measure of the width of srample sure of 1-30 Torr, into an evacuated diffraction chamber, distribution and,'L is the nomle-to-plate distance). Fortugenerally operated a t Torr. The probing electron nately, AI ie relatively insensitive to the exact shape of the y 200 pm in diameter a t the nozzle, distribution function, 88 long as the jet expands symrnetn'distance approximately equal to the calfy aboutsthenozzle axis.2;tb (b) Since the gas sample exjet-crossed-beam technique for mm- pands rapidly upon entering the evacuated diffraction pling has proved ta b4 the simp! viaed, and the chamber its temperature and density decrease, as it passes most free of hrturbing effecta, gh during the . from a fluid flow regime to a free molecule regime. The decades a variety of enclos tested, TOthe measurement and computation of temperature, deneity, is surprising because of the obvious and composition profiles of such )eta have been the subject stic of a free jet. (a) The unavoidable of many studies by those interested in supersonic molecuepreading of the sample reducea the sharpnese of the dif- lar beams.&-**During the past 6 y e m electron fraction pattern. Concurrently, the increase of ambient analpes of crystallites generated in condensed molecular beams have been made for Ar and Xe;l3 similar pressure in the diffraction unit may lead to multiple scattering which has e complex angular dependence, thus con= work on the structure of water polymera is in pmpm.14 eiderably changing the background JevelP Nozzles have COZdimer formation in free Jeta was detected mase a m been dedgned to channel the gas flow, and diffraction trometrically.*6An interesting recent demonstration of the nstructed so as to contain the ejected gas consequences of cooling in supersonicjete was presented by bes, end liquid nitrogen c urfaces Klemperer, et ol,'* They found that from an effusive he region of diffraction.3 H experi- source at 2 6 O , a molecular beam of 2,3-dlchloro-l,3-butadi*L-
I-..---# -a ~ h - - l - - I ~ b - - l a h u
t h l 7Q Un 9II 4074
.ehe’l$wk ~k*;comnporaint,4ndi&tive #ofakbstablii’im-’ :rnei~3;kkd/hblj a b e the’ n o n b h form.*Hmver;.thew wa‘re.ho iaornci~in~a becim f k m a su+honic jet, Mi ‘cause the higher energy apeciatmked.to thkmore stabli coriformation:
mk
an adequate approxima lation distribution of.
that,‘.wMeapproxi’mteco ele&ondiffrektion je developmenb h gm cal,,liinetic.paramatera deecription of wha the:r.qieivoir and, molecdes.
CsllCDltltiOna The numerical ‘method of chicteristics was‘ used tb compute,the Row f!eIds,for p inviscid, ,near-sonic, axially ‘symmetric,.ihotational’free jet dire& into a vacuum. The restrictiona‘on the,fluid are (a) th’at itli equation of state % e form p = pRT; (b) that over the operational tem~riibspecific enthdpy be expresible’ek h(T) = .with cp and y;(= e,$) intiependent of’?‘...The mused wm fi&t :described by Owen .hill;12 it is esselitialIy’the same tis, thme,d bY thod of cmacterbticb W o P d d ‘Anderson ) as a f’iidtion of dimenleads to’the flow Mach sionless coordinates x xlD and R .distance from the nozzle tip; R is the distancb from the nozzle axis, *and ter). Details to supplement the following brief:description are available in a number of sources.12*=2 The method of characteristics is a “boot strap” procedure which leads to a lattice of points, Pii, defined by the intersection of two haracteristic lines (c and. 7 in Figure 11, a t ow Mach numbers (M)are computed as a he x, R dimensionless c sonic flow, if flow conditions are k PjJ+1 a d .Pj+lj, flow conditions may-be&alculated for Pi+1j+1,a t the intersection ofathetwo “ch originating from the known points. The computation begins by finding (e) with respect to the nozzle axis, and the direction a t (n + 1) equally points (we used n = 400) P l j G 0, 1,2,. ,n ) along the leading characteristic line, which is the first of the family. Pi,?(i 1,2, ,,) designates a set of equally,spaced two-dimensional expansion rays that originate at the nozzle lip, and epecify the initial flow con&-
-
..
fluida in thermoc lutions were deve
‘
.
wn, -the interesting gas kinetic $prametere can be calculated at any.point.
(where the subscript zero corresponda to,conditiona at x
0; the flow isjuat sonic at the plane of the n o d e exit).
P ( X ; R)&
= (?‘/To)’‘W)
(2)
that determines the tudes of vibration. In
the Journelol PhplcrlChemlsby. Vel. 78, No. 23,1974
nb&l&t '6f ''&IlMoiis F r $it lendh of travel d b n g that it%% 1ine;'in dimensionless units
Ynd Athe rbot bean..square ahplitudes bkklabd" (shot riQ;id,~~~~.approximatian) for gas' sanjples' a t 0,'at 200, 400°K,:Th&e~are'plottsd ia 8Figure 7. Aimticie'ta the:contribtrtion'zfromthe zero-point vibratioriel amplitudes only the'm des Of the lij =dated with.th8'motion of the gau pairs are affected over this h i e of temperathres. Since the.heat capacity ratio for CzFg is' hemperahire-dependent(y 1.085 and'1.113 at 300 and 2000K,res+tivdy):consider a mean vdue, y = 1.10. Then, the gas'encoun'tered'by a'beah of 'ebctrons~betweeri x = 0.6 to'0.7is a t ki translational temperature Ti=255OK, for the d e m s t plvt of the' sample (Figure Sa). Modt elec'tr6n diffraction unitrc operite with thb electron beam.cov-
-
!.; ..;
J i :
9Z):m&ur@s tht?''@&l:number 'of collisi6hs which" 'an'avc$rag&,zholdeule a t (x;:R),ha&undergone 'afte~.leaving charbcbristic line. .the .* . leading:. ... ......... ..... tot .,.(&
1.
t .
,
%.#.
:..e:
is .a ~"dimdnsionless'time'! elem right member of (5) is the d i s h e. Thus Z& is a "dimensionlees
.Figures 2-6 are "universal soluupstteam from the Macb' disk; as the jet is an order af magnitude greater than the background pressure. Of chum, the source :.piesstjre h d be,sufficiently high 80 ,thaL the' molecular mean'free path at themohleslip is an ordekof magnitude , I@ than the nozzle diameter (invicid fluid flow)?' .(The Rx,not be satisfied under all experimental for electron diffraction experiments, be'cause of h i v Qsowce pressures.) An-erperimbntal.check on , this'dculation'for N z , With' ~ D,I=.0.796 tnmivld PO 10 . Ton,showed that the Mach number generated along the ' axis agreed with the theory.up to'x 3. That point, our calswnde to the'end of the continuum
-
n tb coniider
-
relative:^ tioizle'flow'is
-. prebuie dhip prdduced bp'ttid'
'btrudtureof the
nmzle. It'i2g& td maxidize cox! ub to the nozzle :lip ,by 'using a conical %re; the 'intehal cohtour 'of the 'nozzle is an Important featurd:. Howevei; since hypbdetmic l h i Journalof Physlcal Chemlslry, Vob 78, No. 23.'1074
fraction'practitioners. While a variable y has' hot been incorporated in.%hefree expansion .flow analysis, onemay eaude over the range in*Figuresd6; the gure 7 underscores
To'ass'eas whether the vibrational ternperatureldasely follows %he.gas dynamic translational' thmperatute, one must estimete the average number of ~40llisionsiequired to vibrationilly deexcite .C?Fe.At 298OK sound -dispersion Fora sourp$pr&upe of 10 Torr at dati'show Zid W6 3Q0°K; u = 4.0 A, a i d a nozzle diameter of 0.7 mm, inspectioh'& the plpo and Zht profilea (y = 1.10)indica- that the'moleculeci in the denee core of the sample euffeped -40 collisions; those in the,outer ring axtmaller number (27-16). Since'thie.6 mbre than adequay to maintain vibrationlibrim,' we conclude that the appropriate comparison with experiment is:260-225*# d6#ehdIngeonthe'%maghitudeof x (beam aria):hWb of a reanalpie of the sttucture and dynamics of C$'S bm given .by Gdlahet, Yokozeki, and B8uer.M We conclude that even though no full~,liati~factary analydis hae pt hen presented for the couphd gae dynamic-mction mWlimitedx!am, it is clear that for moletula such ne C2Fa thbre is no eerim difficulty in estitnatting a meanimful sample wibretiond tem-
ed me& co~ipionnurnGri foehatioml were in excdent agreement with dues d tschniqueer: fop HZ(& = 3001, C& (Zmte 161, Con (2= 2.61, etc, Before. one can 'estimate a chemical m h t i o n tiane(ha must ascertain whether the ‘reaction follows firat- .OPwe= ond-order ftinetim; oe pasib& &it o@cup b the ‘efdI-ct€Pv regime. In the following dfecumion we &midem?a d modelifora epefw characteri tentlal, of undqd depthe .[i.e,;> We,mumed that the ~ s l s
’
EiipiEtroii Dlffriction
n d e kmpratur en it. started ita forward motion t ~ ~ a the p d ham. Let G be the difference between the zeropaint vibrational revels in the two conformere (A, B),and € the “battitw” height, measured from the zero-point level of stable conformer (B)to the zero-point level a t the’ tap of the potmtial maximum, Further, 1&gA and #B epecify their raqmctive degeneracies; UA, PB their characterietic frequenclm (kuming that. the orrcillabrs remain simple harmonic up to the top of the barrier);and (OA, cpe the relative fractions of p h space along the reaction coordinate s m i m which can b recognized BIB either
A or B,in the level that just skim the top of the barrier (@A C . I1); 6 m~l/kT. While this ia an oversimplified model it daee incorporab all the elreential features. Note,that the .mofeculee of current inkrest (ethylene chlorohydrin, substituted l,rl=dioxenes,*f’etc.) contaili eight or more atoms and execub lopfrequency vibrations. Hence in applying conventional unimolecular reaction rab theory, one may m u m e that the “etrong collieion” condition applies, and that the flow of energy ‘effet.ive” oscillators ie rapid (dintrakibt S 10-10 8 4 . The number of equivalent clwical ogc re may be estimated uia the the Journrlot PhyakrlChemlshy. Vol. 78, hro. 29, 1971
Goldan-$olly-€bnson correlationm 6,l (classical equiv) = q,i
E m be the mean energy of those moleculea which do react; then .
on the reported Cple et amo , which range from 18 to 22-cal mol-1 deg-1; the 8 to 1.14, The high-preecopreepondiag 7's range fro aure,limit (first order) ragi ..reached when the mean lifetima, imlt,ot Ctitidly eneqized moleculea le subetanIy lorrger than the time tretween collieione (-2 X 10-8 wc for typical jeta wed in electron diffraction unite). Let ThcsJournrlof Physlcel Chemhlry, Vol, 78, No. 23,9074
= k(Em) fi: ?(l + flE&,,)*Dsu .
lOtSSe~" (7) Here 8" ie the effective numbellof Oacillthom and a,, the critical energy (identified with the activat the temperature In the gae ie lowered on rmrvoirsthrough the jet, net convereion A. ManwE. 5 4. Subatitutlon in the abovetqusrtion, or use of the mom oleborate net of graph and table%given by Siv-
7,1{t
exit, .dthe .time the flbw Mwb n u b w grpgwa.fmm ne8v zero ,taunity, d radditlod3060~olliaions in &.jet prior t o ' q a c b the probing &&on beam, t5e ~oleculefl under coneideration will have their :vibrational tempera. nticilly,mked. However, vibr&ioml relaxation relaxation. An uppe does not guaraatse cal kinetics. POPth for tha litter.ie give
. (11) .
.+
O Y O . loo 200 300 400 500 T?(-
man
square atndhdes fw.Cd6 as a
ertz and GOldsblck51 shows r's. S 8, even when (&) is BB high $B 13, r& S 10-10 8' S 10, (BE) * 11.5 gives the aivne mean lifetime. Thus,the'appropriate kinetics for reaction in the nozzle exit and in the jet is that for the,'limiting low-pressure regime, wherein the rate of conveision is determined by the r a b of eneigy transfer in bimolecular cqllisions. translational tenlperature, counters between species wcilators, which contain a total inay use the Sivertz-Gold-=* F(z*; 5 l), x* E @E and 8 = 2Bu. (Actually, this underestr'rn sktion and rotartion eince the relative kinetic ene are not counted.) Essentially e result is obtained from the clmical form
-
-
-
1) = 10, BZ 10, P(E Z Z) = 0.68. For (s 1)= 10,OZ = 5, P(E Z E ) = 0.92. Hence, even for (e +.t)as high 88 17 kd(mo1, there is sufficie rational energy in the
For (s
For M = 80, u = 4 A, at T = 300*K;"i(Z~,~ s 2 X 101' (con centration units in mob cm-3). Asshe a" mean density fol B and A at a b u t ,S Torr; then, for the case (8 8 = 10, and p 0.1, Tchem p! lo'? sec, which r.of 10 lower than the time from the nozzle exit to the ec).' Thie suggests extensive chemical nclueion is dependent on th'e assumed appfiybility of the classical kinetic expression for k f. How. a' quantum-statisti&? .m'odel for the trans gauchc onve$ion led to.essentially the ciame conclusion. A1 300*K, for a plauaible set of molecular'frequencies,and ar M calcula. aisumed barrier of 3 kcaI(mo1, a nt showed tion of the effect'iue unimolecu k 10 Tori that it was proportional to the pr (Le,, system is in the bimolecular ie kuni= 6 x 8eC-l (Tchom e 1 3 x of 1 and.5 kd/mol, Tchem 5 X 10' spectively.
The Relaxation Model The opposite extreme of strongly coupled intramoleculai RRKM theories, is oscillaprs, assumed in the a model in which the moti (here, the rotational angle a pletely decoupled from the r accumulation of sufficient energy for interconversion is a consequence of energetically favorable binary collisions, Le., the molecule executes a brational ladder. We shall n number of collisions with la very little'energy is trans species, but which, none the lators sufficiently to "coupled them," so chat there is a fin i h probability that Borne of the vibrational energy gete lo-
-
mperature to induce majority of binary collisions at the:conformational change €3 A, provided the "strong collidon" condition and 'short dintravib) prevail. The dub i m poinfa pertain to the efficie of energy transfer br collieion; and the de$ree of coup between ss'ciliators in moleculesto which a normal rn alysis is applicable. Inepection of the summary and correlations preaenGd by Lamberts2 show that for more than five atoms, whic efficiency of energy transfer'b 20.1 whcn their lowest molecular frequency is 5200 cm-l; whdn hydrogen is present owest molecular frequency argue that after eufthe nozzle near the
ThsJournalol Physbal Chomlstry, Vol. 78, No,23,lo74
takcih to be 0.10. ir, wi aSeiiin&iiikt th Me+ numb r ,incrimed lin&~y along the: ixmtrsll,a-e'dhm zero at x -10 to x ,+0.07 whaxe M.= t.01. The fidelity of this representation is detePmil6aKi by the &mer, contour a€, the nozzle. Finally, we 'burned &at the' flow was ' ciently rapid, such that there ww no signifiktheat., fei'from the walls to the gfis (thermal b d a n y layer). The estimated travel time through the 2-mm c+el *is.w l madel indicates that chemical re-
'tEie tocat tiansIationcrl. temperature. At xiimple; within the nozzle'wheie . there is no fopwad motion): 'n"+i(nn,]&*'~. e,-fi@; riu4tu]k = e+BhrBand thk bracket in (13) vhishee; However, when the temperature 'dong the' streamline decreams rapidly enough, the terns which specify the vibrational level populatiom lag behind thoee .which' specify the transition ,probabilities. TO evaluate the 'changes, we integra*. inc stream line, s;tarting within'th ion condition (M = 0.1). corresponding expre B in the levels w* gnd o* and (we 4-1) include factors which are not evident in eq 12. Thus dn(w*)/dx(dx/dt) = Kw**l.w*(PAflw*+I + . Kw*.l*w*71w*,1 (Kw*,w*-! 4- K w * , w * + ! ) ~ w * (14) The expremion'for dn (b*)/dx is similar, with cw in the first ,term. I .
-
'
Kw*+l,v* ( P B ) ~ w * + !
(15)
The phase space factors, (PA and c p ~ ,account for the proper partition of species upon their deexcitation from the common conformation into either valley. The folIowing are the equilibrium 'distribution5
that for ndzzlee ;as' currently in use in mast electron diffraction units, when tlie reservoir pressure is greater than 1 Torr, for unsummetrical molecules with more than five atoms, vibrationd rehxation OC: curs in the jet, Then, the appropriate temperature $ w' for calculating Iijk is that read from csntour "IIIIPS, such Figures 2-6. When the objective is to determine the pro; formers as a function of source estimate enthalpy and entropy. sponding conversions, serious' cult td estimate whether chemical relaxation occurs, since that is determirid by an unspe-
written B
-
A
(c,) = c p
+ e [ G t A ) - c;~)] +
-
dimer case, the magnitudes of both and.(C, ) may be very Iarge, and y 1; then there is very littll change in temperature within nozzle flow. On the other hand, such an equilibrium relaxes more rapidly than a conformational change, since the predominant process is association, with high collision crms sectiona, fedgments. We sincerely thank Profemr James son, Engineering and Applied Science at YaIe, for of the methad.of-charackriatics computer proDavid M,Golden (SRI) for the RRKM d c u l a tions, and Professor K. Hedberg for a careful and helpful review of this manuscript. This work was supported in part by the National Science Foundation under Grant No. GP-
.
Here u = 1 for (we +,,l): 2 for (id* equilibrium maintained for all x
+ 21, &. Were local
34060.
I
References and Matee
FOP an illwtrdtive b a w we selectsd ,parametere which match ethylene' chlorohydrin. The integation was etatted et a paint within the nozzle, arbitrarily set a t 1.8 mm ( x = -9) upatreaa from the lip, where the Mslch number wan Fhd JournQlofPhy8/ce/Chrmktry, Vol. 78, Mod23,1974
(1) R. 8. Harvey, F. A. K W , and S. H. eiw, 3. Appb.
(lesa).
m.,P1, 880
(2) 1.1,Karls end J+Ka&, J. CheRt. phys., lS, 963 (1eSO). (3) 8, H. Bew and P. &Hen, J. Fhp. chsm.,88,8317 (Ins). 14) Y. Mortno and Y. Wah, w.chwn.Soc. ,kip., 114 (less). (6) K. K W U , SOC. Sa. tu fl95W m
a
&#.
ttuc
fP
Gas-phtm electron diffraction pattsfns of CZF6 were recorded with the sample reservoir at rdom temperature. Least-squares analysis of .the reduced intensity data gave (DM spnretry) r,(C-C) = 1.645 (6) A, rg(GF) = 1.326:(2) A, and&CF.= 109,7a(0,12)0, with the indicated error estimates. These values *ere compared with corresponding distances reported for an4ogous compounds.Analysis of the torsional mcilbond axis led to a mer dldihedral angle of 67.3(2.7)p'(60° = stslggePed),'whichcormlation about the sponds to an effective shrinkage of 0.004 A for the. lcn$Ct F- F distance. A baiiier height 'to internal rotation of 3.7 kcal/mol wq'derived from the preeen(.djffraction data by taking into a w u n t ample cooling due to the rapid expansion in'the jet.
qc,
The study of fluopine subtitution (CD.and elon molecuk etrudure and reactif& hm beena!. topic of continuing hbrt%t in OUP 1eboratoty.h the c ~ g eof the mbdtutd rn@thmm ethanm, the. C-F bond length ,
--
correlates with the numhr of F substitutions: 1.38-1.39.A, 1.34-1.86 A, and 1,32-1.38 A for the attachment of one, two, and three fluorinm, mpectiwly. The auhstitution effect upon the adjacent C-C bond length, however, is uncertain, Fop gmmplg, a e C-C separation ported fernthe previourm Ieetron diffraction crtudy of hexafluomtbne,! thQJwme/ormyslcrlChsmkrh)r, vor. 7th NO. 23,TO74
