Competitive collisional activation in vibrational energy transfer with cyclopropane-1t1-2,2d2. A three-channel system

C;lemiwl Physics 67 (1982) 201-212 North-Holland

Publishing

Coinpwy

COMPETITIVE CQLLrSIQNAL ACTIVATION IN VIBRATIONAL ENERGY TRANSFER WITH CYCLO?ROB~E-ir,-2,Za’,. V.V. KRONGAUZ Depnrtmenr

SYSTEM

and B.S. RABINOVITCH

of Chemi~iry

Received 1S November

A THPJE-tXAPiiEL

BG-19, Ur;iveisiry of Wusizington.Seatrle, Washington 98195, ffS.4

1981

Vibrational enerw transfer ha been studied in a reac*&g system by the method of competitive collisional rcxrion “spectroscopy.” C~clopro~z1e_lr~-2,2d~ provides a three-charmel competitivc system which has several advantages relative to conventional absolute rate techniques for the study of coilisional transition probabilities. It is found in the range 823-1123 K that both collisionel efficiency and the amount of enew transferred from the hot molecule to heIium bath gas molecule decline with rise temperature. This is of great importance for hi& temperature shock tube and laser dccomposition systems.

1. Introduction Chow and Wilson [I] first suggested the advantage of using molecules which have competitive reaction channels in thermal activation system in order to obtain information about gas-gas vibrationa energy transfer in reacting systems. The critical threshold energies index the vibrational levels of the molecules, while the fluxes of different products at each level act as transducers of the populations and provide a kind of chemical “spectroscopy”. An attempt to apply such a system was made by Waage and Rabinovitch [2a] using cyclopropane-1 ,2d2. The first successful study of a two-channel system was made by Klein and Rabinovitch (KR) for cyclopropane-l,ld2 thermal isomerization [2b] to propylene. In the present paper the method is extended to the study of a three-channel system, cyclopropane- 1tl -2,2d2. Successful study of ener_gy transfer in compatitive channel systems prepared by chemical activation has been reported some time ago [3]. The L.indeman mcdel fcrrms the basis for modem theories of the_rmaI unirnolecular reaction. However, hi5 StiOilg collision assumption of singie-step deactivation of excited mclecules, which was necessary for mathematical tractaMity, does not adequately explain the behavior of unimolecular reactions when the 0301-0104~82/0000-0000/S

02.75 0 1982 North-Holland

reactant substrate (A) is highly di!uted by bath gases @I) such as He, Na, etc. An empirical canstant correction parametci, PC < 1, called the co!lisional deactivation efficiency, is frequently used to bring the theory into agreement with experiment; ,!3,’ is equal to the mean number of collisions required to deenergize activated reactant molecules. Johnston [4] first pointed out that & is not a constant with pressure and the form of the pressure dependence of 4 was explored by Tardy and Rabinovitch [S]. They studied the set [6] of conservation equations:

% dt

=

Ri

+ w

Cpi+j~v-

Oni

-

i = 0,

kini

(1.1)

for the steady state,

or

here pij is the probability of coIlisionaI transfer of reactant molecule from energy state j to state i; tzi and ki have their conventional meanings; w is the nonelastic collision rate per molecule; Ri is the rate of. input, other than by collision, to the ith level. The pij are subjected to the ccnstraints of completeness and detailed balance:

pjjiipii = (gi!~j) exp [-(Ei - Ej)/RT]

.

For the low pressure limit of a therrnzl reaction, i.e., w < Xri,unimolecular studies provide dir& information about the energy tran.Y%i process [J]; eq. (1 .I> describes a -random waLk process along the energy axis. Tardy and Rabinovirch solved the master equation numtlricaIIy for various assumed analytical forms of c7. Suitable forms of P as a function oftemper2ture and energy transferred betu.22n molecu!es during collision are partially known [5] and 5zme form of statisticai rlccommodation model appears to apply [7,S]. Two of these forms are used in the present work: the stepladder (SL), a stronger form (itself a simplir?cation of a gaussian form), and exponentiai (EXP), a \vz&zr form. If the energy Lransf2rr2d during collision is AE = k quanta. while the average energy transferred b i&F) = VI quanta. pij = Sr,,k for the SL, and pii = C txp(--k,h) ior the EXP model. After the model for P is chosen, (AE) is used as a fitting parameter in the calculations. The collision efficiency p, [51 is 2 convanj?nt measure of the devi:ition of the behavior of a weak coilider bath gas (WC) from the behavior of a strong collide: (SC) under the experimental conditions cmcloyrd. Several alternsti1.e definitions of 0, are uossible [5] _In the present and earlier [3:9] work, t0, was mgasured,where rhe bar signities a mixture of corxtx~t (high) diiution of substrate by thz bath gas ?! so1nt3 specific value of G: then FE1 =w,~~,/o~~,A$;! = A-z:: whrre WCand SCsrar,d for weak and strong collision conditions, respectively. The form of Ri in eq. (1) depends on the experimental conditions empIoyetl [5,6]. In the present therruai flow studies, Ri is t5e input into the system since the total chemical oui?ut is balanced by the flux into the syst2m;R is the 6oitzmann population vec:or of the Bzpur gas. The molecules that entered the rcxtor acquired the reactor wall temperature in times much shorter (==lCe3) than the residence time of tie reacting mixture in the reac;or. Several difficulties enter into the thermal activation method when emp!oyed in the ordinary way for the measurement of absolute ro:e constants [S]. The col!ision diameter, s_.+~~,necessxy for calculation of w irom pressure is not known in general [IO]. AbsoIute

kinetic data also tend to be imprecise, as well. W2 note, however, that both properly designed chemical activztion [I 11 and thermal techniques [3,5,12] may be used either to measure s&4! or to yield ener,v transfer parameters independenr of a knowledge of sAhI. Such is ZIso objective in the present thermal measurements usir,g collisional activation of competitive intramolecular reaction pathways that occur with i distinct threshold energies, EA. An intramolecular comparison technique was first used successfully some time ago in a study of competitive decomposition of the chemically acrivated alkyd radicals by Rabinovitch et al. [I 11. Earlier two-channel thermal work of KR on cyclopropane-l,ld, was carried out at 773 and 973 K, both with neat cycfopropane-f ,Id2 and with helium bat\ gas. It was extended to the study of krypton as 2 bath gas at 823 and 973 K [9]. The purpose of these studies was tc End the form and the tkmpenture dependence 0fU!3 for different bath gases and to measure co& sion cross sections. It is importe?.t to know the beha&r of C&5’) since both present-day shock tube [ 131 and multiphoton laser methods [ 141 extend the working temperature region for polyatomic molecules above 1000 K. An experimenta know!edge of the temperature dependence of (4E) and p, is also imporiannt in these poIyatomic systems because information about the energy transfer collisional interaction can be deduced from such data. Thus, if d(4E)/dT is positive, some so:t of ILandau-Teller model [ 151 based on a repuIsive interaction can be valid; while attractive forces are presumably more significant if dCAE)/dT < 0 [7,8]. The study of KR showed that both .i?U and (4E) in cyclopropane-I ,I d7 system decline in the temperature range between 773 and 973 K. This supports the previous experimental [16] and theoretical findings [7,8] suggesting the importsnce of the attractive forces in energy transfer in this temperature region and the validity of the assumption of some type of quasi-sta:isticai energy redistribution in the transitional modrn of a collision complex, subject to conservation of angular momentum restrictions. Gaynor et aI. [I 71 recentIy studied the two-channe1 competitive n-propyl iodide system by the very low pressure pyrolysis method. Increase of the number of competitive channels can, in principle, provide a more refined description of the energy transfer process. We report on the successful synthesis and study of the three-channel cy-

K V. Krongcur,

3.S. Rabinovitcit~Competitive

clopropane-I rl -2,2d2 reaction by a -hermal activation technique over the range from 823 to 1123 K. Helium was chosen as a weak collider. The cyclopropane-ItI 2,2dd7 molecule was chosen because (a) T, D and H exhibit a primary isotope effect, thus providing different threshold energ!es; (b) isomerization of this molecule @e gaschromatographically distinguishab!e produc:, for different reaction channels; (c) cyclopropane decomposition is known to be a “clean” reaction concerning which a large amount of information obtained by different techniques over a wide range of temperuture and pressure is available [2b,l3,14]; (d) the study can be made at fall-off values, k/X-, , zs low as 0.01 which improves the accuracy of the theoretical treatment and the power ofthe experimental method.

on Chromosorb

P, 6O/SO mesh, followed by a 3.3 m of a I/Cinch column of 20% squalane on 45/60 mesh chromosorb P to hold back ethylene glycol. The experimental yield of purified cyclopropancIr, -2,2d, was around 5% based on the labelled ethylene. Neglecting isotope effects on the reactions or isotopic exchange during reaction (2.1), the activity of the product was=O.O4 mCi/cm3 at STP, or z 1.9 X IO3 disintegrations(s Torr cm3)-1. Since the activity of the sample is very low, the incidence of doubie tritriation was negligible. A rough estimate gives 3 X iOW5 molts of T-labelled molecules per mole of material. Conformation of the synthesized material was based on chromatographic and mass spectral analysis. 2.2. Apparatus

2. Experimental _.A.. 3 7 Jlaferials

Helium gas (Airco) was a “spectroscopic pure” grade. Cyclopropane-1 ti -2,2d, was synthesized by reaction of CaC2 with HTO in 99% yield, followed by reactions (2.1) and (2.2) according to the procedure in the references cited: HCI HGCT i- CrCl:, ; H2 Cat-IT f CrCI, ;

38% yield [ 181, H,C=CHT

(2.1)

+ Zn(Cu) + CD21z

(CsHs)zO

+

H2C,-FTH

CD?

+ Znl, + Cu; 5% yield [19] .

/1 -0, (L.L,

The tritiated water (New England Nuclear) had an activity of 25.0 mCi/cm3; CD,17 (Merck, Sharp and D&me) was 99% atom D. Re&Gon (2.2) was conducted in a Pyrex vessel at 60°C and 30 atm of monotritiated ethylene. The prodtict was purified by trapto-trap distillation through four consecutive traps at -70, -126, -143, and -196”C, respectively. Unreacted labelled ethylene war recovered from the last trap. Cyclopropane-ItI -2&-J, was collected from the traps at -143 and --I 26°C. It was purified chromatographically on a packed l/2-inch column consisting of 13.3 meters of 30% 3hl _&NO, in ethylene glycoi

203

coilirional actiwTion

arld nm prucedurP

The experiments on thermal isomerization were conducted by a flow mode in a 12 !J spherical quartz reactor. Procedure and apparatus were similar to those of earlier experimen?s and further details may be found in refs. [2b,9]. The reaction mixture, Hejcyclopropanelrl-2,tiz, in the ratio 1000: 1 by pressure, was admitted to the reactor through a 20 cm X 0.1 mm glass capillary. The flow-out of reactor was throttIed by a 2-inch Veeco valve. Before the start of a run, an appropriate amount of the reaction mixture ~42s accumulated in a small volume following a flow restriction capillary. Men the teflon valve at the entrance of the reactor was opened, the pressure in the reactor reached its steady state value almost instantly. The run time varied from 1200-40 000 s. The pressure in t!le reactor was measured on four overIapping (pirani, Hastings, thermocouple) calibrated gauges. It was shown ear!ier With the use of a tracer technique that this reactor is perfectljj stirred under our experimental conditions of temperature and pressure 19,201. The reactor was pumped by a 2-inch oil diffusion pump. Back-streaming of oil from the diffusion pump was prevented by txvvolarge glass traps in series, ‘O&I at 77 K. Reaction products were trapped in a glass trap at 77 K. At the end of a run the throttling valve was closed, the trapped material was removed for analysis, and the mixture left in t!re reactor was discarded. 2.3 Counting and gas ciwornatographfc A gas-flow radiattivity

counter

equipment

similar

to that

of

204

v. v. K~~~,FJz,

&s.

~bino~iic~lCompe;itive

Rowland et al. [21] was uxd. The counter wzs machined from solid brass: the internal diameter of the tubewas l.Scm;thelengthoftheactivepart, 15.4cm; the central vri.re was 0.02 mm stainless steel, ckmped Tzble 1 Molecukr

pzr;Lmetsrs of the activated compIexes 0:

COlfiJfOMl

and stretched at an ixsulated end 1223. The com;tiq vo!ume of the counter was 47 cmj, optimal for good resoluticn by radiochromatography together with good counting efficiency. T%e carrier 92s for the chromato-

cj~loprcpanclf~-2,222

cpcIonrop;mc~t~-2 72, .

CCR~lkzrion

48.97

isomerizotion

34.85

30.20

,\T 7.30 7 7.21

/ 7.13

_

7.89

1

D ’ ‘\ DH2CCDCHT

H;I--‘D

2b)

TH’

2+

69.39

62.77

18.12

.d

IDx TDHCCDCH2

TH,’“D

7.77 2

1

69.48

61.92

17.80

j+

70.5 1

60.93

19.68

1

1+

70.66

60.54

19.48

2

2

73.98

68.88

17.53

1+

73.83

68.90

17.63

Ii3CCTCD2

D2,LiCCTCH2

H ’ ‘\ D,/“T

TH,CCHCD,

Tf;\H

I’

‘\

D;Y _ H I \

‘) Ii is b!~2-

the nunltw ofiso!opi c ?Loms on the double bond; praence and Iwrts-isomer products treated by one complex.

ofT

is indicated by a + sign.

7.66

i

K V. Kron~ntr, B.S. Rabinovitcit/Compere

+.;.;.:I

:‘:“.

”

n+20

235

collMonal acrivarion

n+46

ncao

n+60

time

n i100

L

(min.)

Fig. 1. Anmpleradiochromatogam ofthepmducts ofcyclopropane-lt,-2,2d2 isomerization;fromleft to right: TD2CCHCH2(T); TDHCCDCH~CI)~:tro~~s-D~HCCHCHT~H!;cis-D~HCCHCHT~)plusD~~C~CH~~H);TH~CCHCD~~~nc~H);rmns-DH~CCDCHT(D~; CL--DH2CCDCHT(D); H,CCTCD,(;I). Pmenthetic ntom ti migatory. Retention time is ~18 h. graphic analysis was helium (flow rate 25-30 cm3/min); methane wsx mixed with the helium at the entry into the counter. Counting vo!tage was 2600 V; the proportiona! re@on was from 2500 to 2750 V, when the helium flow was 30 cm3/min and methane flow 22 cm3/min. The scaIer (Nuclear Chicago) was interfaced with a distal printer (United System Carp) ‘&rough a General Electric frequency counter, doubling the main scaler reading. An analog signa! was plotted by a Honeywel! recorder interfaced with the scaler. -4 200 m packed l/S-inch nylon column consisting of 3070 of 3M silver nitrate-ethylene glycol on 45/60 mesh Chromosorb P, fol!owed by a 1/&inch 3.3 m squalane column to retti ethylene glycol, was used for the separation of the isotopic product propylenes. The columns were run at 0°C.

skewed gaussian peaks is extremely difficult, an analog computer (Dunlop Corp. “CurVe Resolver”) was used for peak resolution. By the analysis of mixtures of cis- and trans-propylenes-IdI avaikble in our Iaboratory [23], it was found that cis-propylene-Id1 has a longer retention time than rmrans.This sffects propylene-l fl -2dl -3dl and propylene-Ill-3,

3d7, which exhibit cis- and t.rans-isomerism witfz respect to the

T-atom. A detailed discussion of the isotopic effect on charge transfer between olefins and silver ion is givenin ref. [22]. A typical radiochromatcgram of the propylene products and their resolution is presented in fig. 1.

3. Results and calculations

3.1. Rotalionai gnd vibrational analysis 2.4. Expected products and #leir fder@catiorr Eight distinct products of cycIopropa;le-ifl-2,36, thermal isomerization can be formed as a result of migration of different isotopes. Isomertiation products

and their corresponding activated complexes are diagrammed in table 1. Retention tknes for the propylenes with 0-, I-, and 2deuterium atoms on the double bond were calibrated using commercially availabie samples of propylene, and propylenepropyhe-2dl

ld2 (Sharp, Merck and Dohme Corp.). Since digitai computer simdation of the eight experimentally

The vibration frequencies of the cyclopropaneIt, -2,2d, were found by applying the product rule to the set if frequencies for cyclopropane-l,ld2 given

in KR (2b]. The molecular distances and the bond angles required for moments of inertia calculations were obtained fron? ref. [24] and those for activated complexes from ref. [25]. Thecalculations were made with use of the program of Schachtschneider 1221. The moments of inertia are given in table 1. The set of frequencies (table 2) was compared with a set calculateci by use of the force constants for cyclopropane

Table 1

3.2. Freqr!encyficrors

\‘ibrstiond frequencies vatedcomplexes

for c~c!opropane-lrl-Z,Zd2

Mc!ecu!e

Frequencies (cm-‘)

C~ClOprOp3X-If,-2.2d~

3100,3080,3040,2330,1210,

md

xtiFrequency factors for each path of isomerization were calculated by the absolute rate theory expression log A = log(rlkT/Jz) [Q’jQ)

i700,1~80,1180,1130,1110,

1070,1030,1020, INKI, 980. 900,800,770,590,450 ii-migration

302O(?j,

COr.Ipl?X

1330,1150,1100,1000,970,

Dmiar3tion

3020(3), 2260, 1500, 1300. 1200, 1170,1130, 1000,970,960, 890, 850.800.770,750.420,Jo0(2)

COmp!eX

T-migration

3020(3),2200(23, 1400,1350, 1300, 1030, 1000. 960,970. 900(7), SOO,700, 630.500,4'0; 310

znd a program based on Schachtschneider [Z]. Both sets of frequencies were similar. although not identical;

they gave identical resuks in our stochastic and RRKM calculations of the rate constants since the calculations are not sensitive to the frequency selection, particularly to minor variations, aslong as calculated frequency fxtors and activation energies are made equal to experimental ones 1161. A!though the secondary isotope effects in cyclopropane isomerizntion [18] can be treated (with some uncerrainty), we handled the isomerization of cyc!ouropane-l-t, -2,2d, as a three-cfwmel, rather than a ien- or twel&lw~nel system. For exampie, instead of considering the differences between the complexes formed by tritium migration eirher to the carbon atom bearing two hyJrogens or ta the carbon bearing two deuteriums. WE used an “average‘. complex. This “average” complex had moments of inertia averaged over the two complexes and frequencies calculated usinp the product rule and werage moments of inerria. The same procedure was applied to the activated complexes for D- and H-migration; for H-migrarion, four complexes were “avsr~ged” into one. A similar procedure was used in KR [2b]; three activated complexes were shown, but isomerization of cyclopropane-l,ld2 system.

was treated

realistically

Vibrational frequencies pIe::es are given in t3ble 2.

B.3

1270(2:T 1690.I-NO,

930,900.850,830,800.750. i90,J00,390

as a two-channel

for activated

com-

BjeFot

(1+c-

+&

1-

_=

OiewOi ), 1-

e+i

e+i

A is the frequency factor; d is the reaction path degeneracy and is two for T-migration, four for Dmigration and six for M-migration; Q, Qf are rhe partition functions of molecule and comples, respectively;B, = iwJkT, where vi is the i&h viiiration frequency. Frequency factors for the different temperatures are given in table 3. 3.3. Hi,h pressure results For the use of the present method, one requires the differences in threshoid energies for the different reaction pathways. The difference AE$H = Ei -.Er may be measured from the plot of the ratio of the log ratio k,/kH versus l/T, with CO, bath gas at a diiulion of=l500:1 and at 2-10 atm; where X-Tlk, = (+/&>tQ:lQ~>

ed-QEo/RO.

AEzH = 930 cd/m01 was determined from the slope of the least-squares fitted line throw& the esperimental points (fig. 3) of the graph of versus 1/T. The rario Q;/QL WkTQ:/x-,Q;l was caIcu!ated to be 1.194 at 698 R, 1.195 at 723 K, 1 .I96 at 773 K, 1.195 at SO6 K, and 1 .I95 at 828 K, with use of the frequencies of table 2. For this threechannel reaction system an additional independent check of the difference in the threshold energies for A value

of

Table 3 Log A_~RT for

ihe channels

of cS’clopropane-ltl-3,Z~~

iso-

mwiz~tion

T(K)

T-channel(2) 8)

D-channeK4)

H-channel(b)

823 973 1123

14.69 14.75 14.78

15.03 15.10 15.16

!5.13 15.21 15.27

a) Vnlu~s in the parentheses arc the rextion path “degenera ties”, (i*, nnd 3rd included in A.

V. V. Krongmz. B.S. ,4abinouirclllComperi~~lecollisional activation

207

and collision numbers, z, for different are summarized in table 4.

temperatures

3.5. Fail-off behavior Solution of the master equation for the steady state gives: 1.2

1.3

1.4 k,,

1/Tx103 Fig. 2. Temperature dependence of the ratio of the high pressure rate constants; the solid line is the least-squares fit to experimental data.

the different paths can be made. This aspect is presented below: the difference is sli&ly larger (1000 cal/mol) and the round value 1000 cd/m01 (350 cm-l) was used. The difference AEg*H was determined experimentally by KR to be x600 cal mol-1 for cyclopropanel,ld,, which should be very close to the value for cyclopropane-ltl-2,2dl. The absolute values of the threshold energies are of lesser importance since it is the ratio of rate constants that is used. The value Ei = 64.2 kcal mol-l, measured for the H-migration channel of cyclopropane-l,ld? isomerization, was used in the present work.

,I? ,

= cki,$jf:

i

where the total decomposition rate constant from the ith energy level, i$, is the sum of the rate constant for r reaction channels at level i, ki = Z,Azl k/ ; nlg is an element of the population vector Nss [5], IV = (wi +

k -

wP)-lN”q

,

where I is the unit the collisional Neq is taken as the Lindemannstrong and

matrh, k is the specific rate matrix, transition probability matrix, and input vector. For the Hinshelwoodcollider case, pij = 0 for Ej, Ei > E0

,i”(sc) = wrrfq/(w

+ k,);

P is

= lli”4 ;

E; > E0 ~ Ei
At the high pressure limit, k, = Ziki$‘l/Lilz~; k,,

thus

= qki?lyCin~

3.4. Coliisioll cross sections km The collision diameters, sAbI have been measured from kinetic data by KR with use of their two-channel system. These coilision diameters gave good concordancy with the values of Chart et al. [ 161 esrimated in another way. In the present work, the sAbi values were extrapolated to higher temperatures, using the reduced collision integrals, flfif)‘, where sAbl = uAhI [@$‘I W. Th e LennardJones constants for the calculation ofRg$* are tabulated in refs. [ IO,lfi] ; then uV = 4.81 A; uHe = 2.58 A; (~/k)~~ = 10.2 K; (~/k)~ = 249 K. Collision diameters, collision integrals, iabie 4 Collision parameters for cycloproPnne-helium

qkilli”‘/z

IIF

.

Partial experimental fall-offcurves (log k/k, versus w) (fig. 3) were obtained at 823,973? and 1123 K. Expetiments performed at the lowest pressures were near the second order region (k/k_ = 0.01-0.03; degree of fall-off ]S ] = 1.6-I .7). The contribution of heterogeneous activation to the reaction becomes noticeable below the pressures indicated by the arrows on the fall-off plots. Fig. 3 compares the experimental data with theoretical curves calculated with use of the above expressions and with employment of the stepladder form of?, with different trial stepsizes (AE) as

collisions

T(Io

T*= ~~~~~~~

&”

SAM@)

1ogrfrorr-’

823 973 1123

16.3 19.3 22.3

0.78 0.7: 0.73

3.26 3.18 3.16

6.93 6.87 6.83

s-l)

lc;flE)(u f ICE)-’dE

1 -1

03

X

[J

kg f(E)

E=EAn

(w + kE)-’ dE

1

,

where

here I and m are particular values of z:F(=l) is a centrifugal correction factor [27]; Ezz is the vibrationai ener,y in excess of Eh;f(E) is the ener,T distribution rimction of reacting molecuies; E is the molecular eners level; XP(E,f)’ is a sum of vibrational eigenstates of the activared complex;N*(E) is the density ofvibrational eigenstates of the molecule at energy E.

Fig. 3. Fti-oficu~s at different ternperJUres; as indicated -eht indicate (AiF) (cm-’ ) SL on ihe wsph. Kun-~~rs at the Z_ model; SC-strong collider CCTFL.Solid lines piesent the rsln&ted values. .&-TOWSindicates the due of w at which the wall coUsions contribution to k becomes noticeable.

shown in the figure; the 2,: were evaluated by RRKM calculations with use of the parameters in table 2, as discussed further in section 3.6. Other forms ofP were also used in the earlier work [2b] but it suffices here to use only the SL model for conprtrison purposes. 3.6 Average erlergl: down step (AElper collision; coNisional efficiency is,; tunperuture dependence Theoretical expressions fcr the unimolecular decomposition rate constar,ts along the different channels were given for chemical activation systems by Setsrr and RabinovitcS [Xl. .A general form of the RRiCl! expression of the mte constants ratios for mu!tichannel systems was also given by Tardy et al. in 1967 [! I] for the strong collision case written here in integral farm as Fig. 4. Dependence

of kT/kH on w nt different

temperatures.

?.‘,V. Krortgu:,

B.S. ~binovi:chjComperitile

209

coll~s~on~l activation

In the present work a similar expression for the rate constants ratio was used; however, the strong collision condition was not imposed:

IC

k; tz; dE

7

J

-1

km tP dE EE

E=E,m

5lO

6.0

7.0

log

Fig. 5. k&_~

Cd

versus log w curves at different

temperatures.

3

and pE was computed using eq. (3.1). Plots of ratio of the rate constants for isomerization of cyclopropane-ItI -2,2d2 by the different channels (the isotope which is shifted dun’ng isomerization is indicated by the subscript) are presented in the figs. 4 and 5. The experimental ratios k.,./kH,kD/kH were fitted to a series of theoretical collision rate curves (figs. 4 and 5) calculated for several values of (Ai?). The bestCt values ofCAD are given in table 5 together with estimated errors. The values of (A.E) deduced independently from the k/k,, R,/k, and k&k, ratios are all in satisfactory agreement. It is evident from table 5 that a general tendency for decline of (AE) with temperature exists. The collisior! efficiency p, was evaluated by comparison of the theoreticaI fall-off curve for the strong coliision (SC)case with the, experimental fall-off obtained in the presence of helium (fig. 3). The values are listed in table 5. The PO values can also be computed from the value of (AL’) given in table j with the

Table 5 Summary of average valuez of (M$L

Molecule

V--d2 V-d2t

V-4 V-&f

V V-d,t V

T(Ic)

713 823 973 973 975 1123 117.5

cm-’ 2nd of a,(-) Average UEE)

(AE> (k/& 1

(k+_.J 1

400

400

290

240

250

190

WE) E’= E’

%.Ol (w) b,

Reference

0.49 0.46 0.17 0.25(0.22) d)

0.07 0.056 0.01 0.018

Izbl present work [2bl present ivork

0.23 0.16 0.15

0.015 0.010 0.010

[28a] e) present work [2Sa] e,

(kD/kI<)

350 (170) c)

IS0

)

400 380 i 70”) 190 270(230) d) -70 250 210 2 70 200

a) Estimated error range. b, At fall+ff, k/k, = 0.01, k the range of w used. C) V&e considered doubtiul. dl Parenthetic vahx includes doubtful vlue of column 4. e, Values of ref. [28a] were c&xlated for EXP model and were recalculated

here for zm SL model.

F. V. Kronprmz, B.S. Rabitlo~iiciljCompen’n’l;e

use ofsemiuniversal p!ots given previously [S] for as a function of the dimensionless parameter, is, E’(= C_G)/C?~), where (E? is the average energy of the molxules in the Boltzmann distribution above the threshold energy. Both sets of values arc in a reasonable agreement. 3.7. TJ~csi:old dijfereme

co!!isional acrimion

Similar decline of(llE) in this temperature range has been found for cyclopropane and other molecules in studies oi homogeneous energy rransfer for a number of bath gas, including he!ium, by the diffusion cloud method [28] and in heterogeneous energy transfer studies involving coi!isions of cyclopropane at a seasoned fused silica wall [29]. This trend accords with a quasistatistical model of energy transfer in a collision complex [7,8]. Substrate molecule and bath gas molecule form z collision complex ~vith a binding energy related to the Lennard-Jones well depth, E. The energy of the hot substrate is redistributed among the transitional vibrational modes that are formed in the collision complex. Conservation of total angular momentum of reactant and bath molecule imposes a restriction OP the amount of energy transferred. The average ener= (AE) lost by an energized molecuIe ofreactant during collision, is given by an expression ofthe form,

AEzH

One of the advantages

ol’the three-channel reaction system is the possibility thst it affords for obruining the difference. Ei-Eii. independent of die high pressure acriva:ion energy mesjurernents. The fit of the esperimental data to calculated curves of the plot of kT/kH versus ,CD/kIl: using A.c?~~ 3s a pararncter (fig. 6) gives good confirmation of the measured &rhenius increrrcnt G?T.H = 930 cal mol-l. Based on EA1 = 22450 bm-l anodEt = 22650 cm-l, El = 22500 cm-l (i.e. ilE$” = 250 cm-l = 1000 cal mol-l) gives the best fit to the experimental data. This is the first measurement of the threshold difference for rritium in 3 primary intramolecular kinetic isotouc effect.

4. Discuszion The present data is in agreement with the results of KR. Despite any experimental uncertainty, the decrease oi(AE) Wth rise of temperature found here is very similar to the trend reported by them (table 5).

where P(E,,) is the probability that the transition modes (3. 5 or 6, depending on the complexity of the bath gas, i.e., monatomic, linear or non-linear, respectively) shall contain energy E, after collision if their origina! thermal energy was E, ; Etot = E, + E + E* ; E’ is the internal energy ofthe substrate molecule befcre the col!ision;B(Etll) = N(Erh)esp(-E&/RT). Then (4E) decreases with rise of temperature, since Eti, rises with temperature faster than Et,,. Eq. (4.1) may be illustrated by a simple model of a unimolecular reactant havingrrR internal vibrational modes. In the low pressure region, the (classical) average internal energy of reacting molecules is E, + RT. The activated reactant molecule collides with a monatomic bath gas forming a cotision complex having two transitional bendings and a stretching mode that are active in energy transfer with the pzR original modes. The average energy of the transitional modes is 2RTand the total average internal energy of the complex is E0 f 3RT. Then for this particular condition, the loss of energy after col!ision by the reactant, on a purely statistical basis, is

and dG/dT=(3-7JzR)R/(nR

fornR>

+3)<‘3,

1.

According to this simp!e example, (LIE) decreases with temperature increase fcr other than diatomic molecules. The present study of the temperature dependence of (hE) extends to I123 X which is within the r&on of interest for shock tube and laser multiphoton decomposition studies. The present values agree well with those of KR and with results obtained earlier from diffusion cloud studies (tabie 5j; the data of ref. [28b], which were thought by those authors to etibit some undiagnosed experimental error, seem to beti quantitative diszccord with other results 2nd 2re excluded here. From table 5, the grand overall average energy transferred per collision in the cyclopropanehelium thermal activation system (neglecting the isotopic differences) is: 400 cm-1 at 773 K, 380 cm-l at 823 K, 230 cm-l at 973 K, 210 cm-l at 1123 K, and 200 at 1175 K. Fig. 7 shows the clear trend for the decline of (AE) wit4 increase of temperature of rerlction. There is some indication that the race of decrease of (A,??) irself declines with rise of temperature - in a manner analogous to the behavior found for cyclopropane energy exchange at a surface 1291 and that suggested by Endo et al. [30] for He in triatomic shock tube systems. But this conclusion must be considered tentative, 2s based on existing work. If borne out, it may signify the transition from an accomodation model governed by the attractive potential io 2

London-Teller type ofimpdsive interaction governed by the repulsive potential. In any case, the present work points up rhe uncertainty that attends presentday efforts to calculate collisional effects in high temperature polyatomic molecule systems, 2s well as +he error in extrapolating low temperature collision21 effciency data to higher ternpeatures or of assuming colkionti efficiency to be constant with temperature. We note that the total coilisional efficiency, is,, which is a funcrion of the dimensionless parameter E’, declines with increase in temperature for two reasons: (1) Increase of temperature increases (I?+}, the average enerm of molecules above EO, and increases the severity of the operational test of collisional rfficiency. Tardy and Rabino\itch [jb] noted that for pely weak colliders, fl a l/T”(cr > 2). (2) As the temperzture is raised then, as seen here and in earlier work [2b,27,282], the intrinsic efficiency of energy transfer, i.e.,(AE), 2Iso declines, and fl c: (AEj2 for very weak colliders [S]. This decrease ofcollisional efficiency, as it has been pointed out [5], causes 2 shift of the fall-off curve to much higher pressures than is predicted for strong colliders.

Acknowledgement This work ~2s supported by the National Science Foundation. We thank Professor Arthur Fairhall for the loan of the counting equipment and consultation in the design ofthe proportional counter. We ais0 wish to thank Dr. ME. Berg for assistance in the initial stages of the experiment.

References

BOO

1000

1200

TIKI Fjg. 7, Temperature dependence of (LZ) and sU: 4 MeinRabinovitch; p, data of ref. [28a], and 0, values measured in present woric. No+ that p declines more rzpid!y than does (AEE)which foUo%rsT-l; see text.

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