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Determination of Bond Dissociation Enthalpies in Solution by
Photoacoustic Calorimetry
Laarhoven, Lucas J. J.; Mulder, Peter; Wayner, Danial D.
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Determination of Bond
Dissociation Enthalpies in
Solution by Photoacoustic
Calorimetry
LUCAS J. J. LAARHOVEN AND PETER MULDER*
Leiden In stitu te of Ch em istry, Leiden Un iversity, P.O. Box 9502, 2300 RA Leiden , Th e N eth erlan ds
DANIAL D. M. WAYNER*
Steacie In stitu te for Molecu lar Scien ces, N ation al Research Cou n cil of Can ada, Ottaw a, On tario, Can ada K1A 0R6 Received December 24, 1997
Introduction
Th e en th alp y ch an ge th at occu rs in a p h otoin d u ced ch em ical reaction in solu tion can b e q u an tified b y a relatively sim p le tech n iq u e kn own as p h otoacou stic cal-orim etry (PAC), wh ich allows m easu rem en ts to b e p er-form ed u n d er con d ition s (i.e., tem p eratu re, solven t, etc.) relevan t to m ost ch em ical an d b ioch em ical p rocesses. Ph otoacou stic calorim etry was first ap p lied in 1983 to rad ical p rocesses b y Roth b erg et al.,1wh o d eterm in ed th e en th alp y of h yd rogen ab straction from an ilin e b y trip let ben zop h en on e to form th e ben zh ydrol am in e radical p air. Peters an d co-workers2develop ed a tim e-resolved m eth od to d econ volu te th e p h otoacou stic sign al from th e sam p le solu tion in to a d etector resp on se fu n ction (ob tain ed from calib ration ) an d a (tim e-d ep en d en t) resp on se from th e p rocess u n d er stu d y. At ab ou t th e sam e tim e, Griller an d co-workers3 focu sed on th e ap p lication of PAC to th e d eterm in ation of b on d d issociation en th alp ies (BDEs), u sin g an in stru m en t ad ap ted from th at u sed b y Peters, b u t with th e exp erim en tal m eth od sim ilar to th at d e-scrib ed in th is Accou n t.
Bon d stren gth s an d h eats of form ation ,∆fH, are of great im p ortan ce in u n d erstan d in g th e stab ility an d reactivity of reactive sp ecies, su ch as rad icals. In m ost cases, con sid eration of th e en th alp y allows on e to p red ict th e cou rse (selectivity) of a reaction . Wh ile th e b on d stren gth s in m an y sim p le h yd rocarb on s h ave b een m easu red u sin g variou s gas p h ase tech n iq u es4to a p recision of 1-2 kcal m ol-1, th e accep ted ab solu te valu es h ave ch an ged sig-n ificasig-n tly over th e last 30 years. For isig-n stasig-n ce, th e BDE-(C-H) in ben zen e h as risen from 1035to 113.56kcal m ol-1 an d th at of th e b en zylic C-H in tolu en e from 855to 904 kcal m ol-1. Con seq u en tly, m an y BDEs th at were d erived u sin g th ese referen ce valu es ch an ged as well. Desp ite th eir im p ortan ce, BDEs in m ore com p lex sp ecies are m ore d ifficu lt to m easu re an d th u s less reliab le.7Exp erim en tal ap p roach es for th e d irect an d in d irect d eterm in ation of BDEs in th e gas p h ase4,7or in solu tion (electroch em ical cycles8an d PAC) as well as n ew com p u tation al m eth od s su ch as d en sity fu n ction al th eory9h ave led to a d ram atic in crease in th e n u m b er of reliab le BDEs for organ ic an d organ om etallic com p ou n d s. For con sisten cy, all of th e d ata are n orm ally extrap olated to stan d ard state con d i-tion s (i.e., 298 K in th e gas p h ase). Wh ile th is extrap olai-tion allows for com p arison with th e vast store of gas p h ase d ata, som e q u estion s h ave em erged con cern in g solven t effects on th e reaction an d b on d d issociation en th alp ies. For p ractical p u rp oses, m ost ch em ical p rocesses of in ter-est to ch em ists an d b ioch em ists occu r in th e con d en sed p h ase (u su ally in solu tion ) an d th erefore d irect m easu re-m en t of solu tion th erre-m od yn are-m ics p reclu d es th e n eed to assess th e effect of th e solven t.
Th is Accou n t d escrib es th e recen t ad van ces in th e ap p lication of PAC for th e d eterm in ation of b on d d is-sociation en th alp ies (eq s 1 an d 2). Alth ou gh th e exp
eri-m en tal ap p roach is relatively straigh tforward , th e p rop er treatm en t of th e d ata req u ires d etailed in sigh t in to th e fu n d am en tal asp ects of th e tech n iq u e. With ou t th ese con sideration s, large system atic errors an d th u s erron eou s resu lts m ay arise. In th e recen t p eriod , we h ave d evelop ed a d etailed m eth od ology to en su re th at th e PAC en th alp y d eterm in ation s are con sisten t an d th at solven t effects are correctly in corp orated .
The Photoacoustic Response
Ph otoacou stic calorim etry is a th erm od yn am ic m eth od to d eterm in e a b on d stren gth in solu tion . Th e p h ysical b asis for PAC is d ecep tively sim p le; rap id h eat release from a p h otoin itiated p rocess in a lim ited , well-d efin ed volu m e resu lts in a local ch an ge in d en sity, gen eratin g a p ressu re wave th at p rop agates th rou gh th e solu tion at th e sp eed of sou n d . Detection an d q u an tification of th is p ressu re wave is th e b asis of th e tech n iq u e.
Lucas J. J. Laarhoven w as born in 1967. He received his M .Sc. degree (1991) and his Ph.D. degree (1997) from Leiden University. Recently, he assumed the position of a postdoctoral fellow in the physics department of the University of Nijmegen.
Peter M ulder w as born in 1953. He received his M .Sc. degree (1979) from the Delft University of Technology and his Ph.D. degree (1987) from Leiden University. After a postdoctoral period at the National Research Council of Canada, he obtained a permanent staff position at the Leiden Institute of Chemistry. Currently, his research interests include radical processes, hydrogen transfer reactions, and thermochemical aspects of solution and gas phase reactions.
Danial D. M . Wayner w as born in 1958. He received his B.Sc. in chemistry from M cM aster University (1980) and his Ph.D. from Dalhousie University (1984). After postdoctoral w ork w ith Drs. K. U. Ingold and D. Griller he w as appointed to the continuing staff at the National Research Council of Canada in 1986. Currently he is the leader of the M olecular Interfaces Program at the Steacie Institute for M olecular Sciences. His research interests include mechanistic aspects of electron transfer reactions, thermochemical aspects of solution reactions, and organic chemical processes on semiconductor surfaces.
R-H f R•+ H• (1) BDE(R-H) )∆fH(R • ) +∆fH(H • ) -∆fH(RH) (2)
Acc. Chem. Res. 1999, 32, 342-349
With PAC, on ly th e h eat released with in a well-d efin ed tim e in terval is d etected (p rom p t h eat release; vid e in fra). Th e h eat in tegration tim e is d eterm in ed b y th e p rop erties of th e in stru m en t an d th e d etector. Den sity ch an ges d u e to grad u al h eat d issip ation d o n ot con trib u te m easu rab ly to th e p h otoacou stic resp on se. Th u s, th e tim e dep en den ce can b e u sed to ad van tage sin ce it is p ossib le to d iscrim i-n ate agaii-n st “slow” p rocesses su ch as relaxatioi-n from a trip let state or reaction s at or ab ove th e m illisecon d tim e scale.
Th e relation b etween th e h eat release an d th e p h oto-acou stic resp on se h as b een d escrib ed m ath em atically b y ad ap tin g b asic eq u ation s from flu id m ech an ics to th e exp erim en tal circu m stan ces in PAC.1,10-14 Wh ile several rep orts h ave ap p eared over th e last two d ecad es, in wh ich th e d evelop m en t an d ap p lication s of PAC are d escrib ed ,15-19 in th is Accou n t we will h igh ligh t th e p rocedu re by wh ich reaction en th alp ies are retrieved from a p h otoacou stic exp erim en t. Th e p h otoacou stic effect is a con seq u en ce of n on rad iative d eactivation b y in tern al con version , in tersystem crossin g, or a ch em ical reaction of an excited state form ed after ab sorb in g th e p h oton en ergy, Ehν. Eq u ation 3 p rovid es th e relation b etween th e
fraction of ab sorb ed ligh t, fthEhν(1 - 10-A) with A as th e ab sorb an ce, an d th e th erm al en ergy, Eth. Th e resu ltin g tem p eratu re in crease in th e irrad iated cylin d rical volu m e as d eterm in ed b y th e h eat cap acity of th e solu tion , Cp, cau ses th e m ed iu m to exp an d . Th e m agn itu d e of th e exp an sion is related to th e isob aric exp an sion coefficien t of th e solven t, R. If th e th erm al exp an sion is adiabatic (i.e., n o h eat d iffu sion occu rs), th e in crease in volu m e is
p rop ortion al to th e am ou n t of released h eat. Th e volu m e ch an ge in itiates a th erm al sh ock, wh ich is d etected as a p ressu re ch an ge b y a p iezoelectric sen sor (m icrop h on e). Th e m agn itu de of th e observed p ressu re ch an ge is lin early p rop ortion al to th e d isp lacem en t an d th u s to th e in itial h eat release.
Th e ob served p ressu re wave is a m easu re of th e total volu m e exp an sion th at h as occu rred : a com p osite of exp an sion d u e to th e release of ch em ical h eat an d th at du e to th e ch an ge in th e volu m e occu p ied by th e p rodu cts com p ared to reactan ts (∆rV).20Th e form er is th e d esired qu an tity for calcu latin g of th e reaction en th alp y. Th e latter q u an tity, th e reaction volu m e ch an ge, is on ly sign ifican t wh en th e n u m b er of ch em ical sp ecies ch an ges (i.e., wh en th e n u m b er of b on d s b roken is n ot eq u al to th e n u m b er of b on d s form ed ) or wh en large con form ation al ch an ges occu r in m ore com p lex m olecu les, su ch as p rotein s.20-22 Th e d etector can n ot d iscrim in ate b etween th ese two volu m e ch an ges. Th e exp erim en tally ob served p h otoa-cou stic resp on se, Sob s, is d escrib ed b y eq 4, in wh ich c is
an in stru m en tal resp on se factor, fob s is th e ap p aren t fraction of ligh t con verted in to h eat (vid e in fra), an d χsis th e ad iab atic exp an sion coefficien t of th e m ed iu m wh ich eq u als MR/CpF, wh ere M is th e m olecu lar weigh t an d F th e d en sity. Th erefore, it is n ecessary to extract th e valu e of fthfrom th e exp erim en tally d eterm in ed fob s. We d efin e th e m agn itu d e of Sob s as th e p eak-to-p eak am p litu d e of th e first oscillation . A sim p le b lock d iagram of th e in stru -m en t is sh own in Figu re 1. A typ ical tran sd u cer resp on se gen erated b y a p h otoacou stic sh ock wave is sh own in th e in set of Figu re 2.
FIGURE 1. Block diagram of the PAC instrument. The laser pulse passes through a beam splitter w hich sends a small fraction (ca. 10%) of the incident light to a phototrigger and pow er meter to normalize for laser energy fluctuations. The remaining light initiates the photoreaction in the photoacoustic cell. The transmission of the sample is measured w ith a spectrophotometer (the spectrophotometer can be replaced w ith a second pow er meter). Solutions are allow ed to flow slow ly through the cell to ensure that reagents are not depleted. The signals are amplified and collected by a digital oscilloscope and analyzed using a PC.
Eth) fthEhν(1 - 10 -A
) (3)
Sob s) cfob sEhνχs(1 - 10-A) (4)
Bond Dissociation Enthalpies in Solution Laarhoven et al.
Retrieving the Reaction Enthalpy
In th e ab sen ce of rad iative d ecay (i.e., lu m in escen ce), th e h eat released is related to th e ab sorb ed en ergy, Ehν(1 -10-A), th e en th alp y of th e reaction in solu tion ,∆rHsol, an d th e p h otoch em ical q u an tu m yield , Φ (eq 5). However,
th e exp erim en t p rovid es a valu e of fob s, n ot fth, an d p rod u ces on ly a m easu re of th e apparen t reaction en -th alp y, (∆rH)ap p
sol
(eq 6), wh ich still con tain s con trib u tion s
from th e reaction volu m e ch an ge, rein forcin g th e fact th at th e ob served sign al con tain s m ore in form ation th an th e reaction en th alp y alon e. Th e ap p aren t reaction en th alp y is d escrib ed b y eq 6, wh ich d ep en d s on th ree p aram -eters: Φ, ∆rV, an d ∆rH. Kn owled ge of an y two of th ese allows th e th ird to b e d eterm in ed . Sin ce on e n orm ally is in terested in th e en th alp y, in d ep en d en t m easu rem en ts or estim ates of th e q u an tu m yield an d reaction volu m e are im p erative. In d eed , we h ave also u sed th is exp ression to d eterm in e ∆rV for th e p h otod issociation of d i-tert-b u tyl p eroxid e, for wh ich th e en th alp y is well-kn own (vid e in fra).
Th e valu e of fobsis determ in ed by establish in g th e lin ear relation sh ip (eq 4) b etween th e sign al (Sob s) an d th e am ou n t of ligh t absorbed by th e sam p le (1 - 10-A) to yield
a slop e aob s) cfob sEhνχs. In p ractice, th is slop e is ob tain ed b y varyin g th e con cen tration of th e ab sorb in g sp ecies or th e in ten sity of th e in cid en t ligh t. Th e p h otoacou stic resp on se is n orm alized for variation s in th e laser in ten sity b y d ivid in g th e ob served sign al b y th e m easu red laser p u lse en ergy. Th e in stru m en t is calib rated b y com p arin g th e p h otoacou stic sign al from th e sam p le with th at from a com p ou n d th at retu rn s all ab sorb ed ligh t as h eat. A n u m b er of su itab le calib ration com p ou n d s for organ ic solven ts an d aq u eou s system s h ave b een tab u lated else-wh ere.19 We h ave u sed ferrocen e an d 2h yd roxyb en -zop h en on e for p h otolysis at 337 n m (n itrogen laser) in organ ic solven ts. Sin ce th ere is n o accom p an yin g volu m e ch an ge associated with th e calib ration resp on se, fob s) fth ) 1. Th e valu e of fob sfor th e sam p le in q u estion is sim p ly th e ratio of th e slop es for th e sam p le, aob s, an d th e calib ration com p ou n d , acal(fob s ) aob s/acal). Th u s, for an exoth erm ic reaction , m ore en ergy is retu rn ed th an su p -p lied to th e system an d fth(b u t n ot n ecessarily fob s, eq 6) is larger th an u n ity. Great care m u st b e taken to en su re th at th e valu es of c an dχsare th e sam e d u rin g calib ration an d sam p le m easu rem en t. An exam p le of th e resu ltin g p lots is sh own in Figu re 2. Errors can b e m in im ized b y sign al averagin g. It is essen tial th at lin ear p lots of Sob svs (1 - 10-A) are ob tain ed . In ou r exp erien ce, lin ear regres-sion coefficien ts, r2, of 0.9996 are rou tin ely ach ieved , lead in g to an error in (∆rH)solof (1.5 kcal m ol-1.
Bond Dissociation Enthalpies
By u se of reaction s 7 an d 8, th e R-H b on d d issociation en th alp y can b e d eterm in ed sin ce PAC can m easu re th e
FIGURE 2. Typical plot for a photoacoustic experiment w ith a mixture of di-tert-butyl peroxide and phenol (0.1 M ) in benzene. Linear relations betw eenSN(Sobsnormalized for laser energy fluctuations) and absorbed light (1 -T) 1 - 10-A) are show n for the calibration compound
2-hydroxybenzophenone (9) and for phenol (4). The ratio aobs/acal)fobs) 1.056. With eqs 6 and 11, a photon energy,Ehν, of 84.8 kcal mol-1,
Φ ) 0.83, and ∆H(PhOH‚‚‚S) ) 1 kcal mol-1, BDE(O-H) in phenol is 87 ( 1 kcal mol-1. Insert: The actual photoacoustic signal as monitored
by the piezoelectric microphone. The peak-to-peak amplitude of the first oscillation equalsSobs. Other oscillations originate from shock w aves
reflected from the w all of the photoacoustic cell.
∆rH sol )(1 - fth)Ehν Φ (5) (∆rH)ap p sol )(1 - fob s)Ehν Φ )∆rH sol -∆rV χs (6)
en th alp y for th e overall p rocess (reaction 9). It is clear
th at m easu rin g th e en th alp y for th e overall reaction (9) is q u ite a lon g way from actu ally d eterm in in g th e b on d d issociation en th alp y. To ob tain th e BDE in solu tion ,∆rV/ χs(eq 6) n eeds to be in dep en den tly determ in ed. Accordin g to eq 6, a p lot of (∆rH)ap p
sol
vs 1/χs sh ou ld give a straigh t lin e with slop e ∆rV an d in tercep t ∆rHsol. Herm an an d Good m an21 an d Hu n g an d Grab owski23 varied χ
s b y ap p lyin g a h om ologou s ran ge of solven ts or solven t m ixtu res. We m easu red th e q u an tu m yield for th e p h o-tod issociation of d i-tert-b u tyl p eroxid e (reaction 7) in variou s solven ts. Sin ce th e th erm och em istry for th e d is-sociation (∆7H ) 38 kcal m ol-1) is kn own , it was p ossib le to calcu late th e valu es for∆7V/χsfrom eq 6, u sin g th e fob s. We sh owed th at th e∆7V ) 12.4 m L m ol-1, in d ep en d en t of th e solven t.24
A secon d com p lication to overcom e lies in th e fact th at th e p eroxide an d alcoh ol in eq 9 are in solu tion wh ile th eir availab le h eats of form ation p ertain to th e gas p h ase. Th e ch an ge in solvation en th alp y associated with th e con ver-sion of 1 m ol of d i-b u tyl p eroxid e in to 2 m ol of tert-b u tyl alcoh ol in a given solven t can , in p rin cip le, tert-b e m easu red b y solu tion calorim etry. However, it is n ot n ecessary to actu ally m easu re th ese valu es. Ou r research grou p s h ave followed a rath er p ragm atic ap p roach to resolve th is d ifficu lty.24 To retrieve a b on d d issociation en th alp y, a solven t-d ep en d en t correction term , (∆∆sH)ap p, to in clu d e th e reaction volu m e ch an ge (∆rV) an d th e ch an ge in solvation en th alp ies (∆sH), was d evelop ed . By stu d yin g th e reaction of d i-tert-b u tyl p eroxid e with 1,4-cycloh exad ien e (eq 10), we cou ld d eterm in e (∆∆sH)ap pin
variou s solven ts. Th is ap p roach is b ased on th e key assu m p tion th at th e C-H b on d en th alp ies in th e gas p h ase (76 kcal m ol-1)25 an d in solu tion are th e sam e. Accord in gly, th e d ifferen ce b etween (∆10H)ap p
sol
an d th e kn own gas p h ase valu e for ∆10Hga s p rovid es th e solven t correction factor for a p articu lar solven t. We h ave fou n d th ese valu es to b e rem arkab ly con stan t, ran gin g from -9 kcal m ol-1in n on p olar solven ts to -13 kcal m ol-1in p olar solven ts (see Tab le 1). Th u s, a sim p le exp ression for th e b on d en ergy, BDE(R-H)sol, can b e d erived b y collectin g th e kn own h eats of form ation an d th e em p irical correction factor for th e solven t (eq 11). In th is eq u ation , th e
con stan t of 86.0 kcal m ol-1en com p asses th e relevan t gas p h ase h eats of form ation for tert-b u tyl alcoh ol,26a th e h yd rogen atom ,26aan d d i-tert-b u tyl p eroxid e26bof -74.7, 52.1, an d - 81.6 kcal m ol-1, resp ectively, at 298 K.
Solvent Effects on Bond Energies
In th e d eterm in ation of th e solven t correction factors, th e exp licit assu m p tion h as b een m ad e th at th e h eats of solvation for 1,4-cycloh exad ien e an d cycloh exad ien yl are n ot sign ifican tly in flu en ced b y th e n atu re of th e solven t, in agreem en t with gu id elin es p reviou sly su ggested b y Griller an d co-workers.27 Th ese sim p le gu id elin es state th at (1) h eats of rad ical reaction s in n on p olar solven ts will b e th e sam e as th ose in th e gas p h ase an d (2) h eats of free rad ical reaction s in p olar solven ts will d iffer from th ose in th e gas p h ase to an exten t th at reflects th e solvation en ergies associated with th e n et form ation or d estru ction of p olar sp ecies. In d eed , rem arkab ly good agreem en t can b e fou n d for C-H b on d en th alp ies d eter-m in ed in th e gas p h ase an d in solu tion u sin g PAC or electroch em ical m eth ods. Obviou sly, th is assu m p tion does n ot h old for th e tran sform ation of th e p eroxid e in to tert-b u tyl alcoh ol. Th e latter h as an ap p reciatert-b le d ip ole m o-m en t, an d th e h eat of solvation will dep en d on th e solven t u sed . From Tab le 1 it can b e in ferred th at sin ce th e ch em ical volu m e ch an ge rem ain s fairly con stan t, th e ch an ge in ∆∆sH is d irectly related to th e in crease in th e solvation en th alp y of th e alcoh ol.
Th e en th alp y m easu rem en ts b ecom e even m ore com -p licated wh en h yd rogen b on d in g takes -p lace b etween th e com p ou n d of in terest an d th e solven t. As an exam p le, we stu d ied th e BDE(O-H) in p h en ol. Hyd rogen ab straction b y th e tertb u toxyl rad ical on ly occu rs with th e n on -h yd rogen -b on d ed fraction of p -h en ol, an d t-h erefore t-h e m easu red en th alp y ch an ge n ow in clu d es th e solven t/ solu te eq u ilib riu m . Con seq u en tly, th e ap p aren t O-H b on d stren gth of p h en ol is h igh er in aceton itrile th an in ben zen e, du e to an addition al h ydrogen -bon din g en th alp y (Tab le 2).24 However, after in trod u cin g th e kn own en -th alp y ch an ge associated wi-th -th e form ation of a h ydrogen b on d , we were ab le to arrive at on e gas p h ase b on d en th alp y in all solven ts in good agreem en t with th e accep ted literatu re valu e of 87 kcal m ol-1.24
t-Bu OOBu -t 98hν 2t-Bu O• (7)
t-Bu O•+ RH f t-Bu OH + R• (8)
t-Bu OOBu -t + 2RH 98hν 2t-Bu OH + 2R• (9)
BDE(R-H)sol)(∆9H)ap p
sol
2
-(∆∆sH)ap p
2 + 86.0 (11)
Table 1. Solvent Correction Factors, (∆∆sH)app, for
PACa solvent (∆10H)app sol (∆∆sH)appb ∆7V/χsc isooctane -30 -10 5.8 carbon tetrachloride -29 -9 3.2 benzene -29 -9d 3.7 acetonitrile -33 -13d 3.8 ethyl acetate -33 -13 3.8
aReaction 10; average of at least four independent
determina-tions; enthalpies in kcal mol-1. The experimental error is 2 kcal
mol-1.24 bIn the gas phase, the BDE(C-H) of 1,4-cyclohexadiene
is 76 kcal mol-1,25leading to ∆
10Hgasof -20.3 kcal mol-1.c
As-suming an average value of ∆7V ) 12.4 mL mol-1.dSimilar values
has been found for tetralin (-9) and tetrahydrofuran (-13).30
Bond Dissociation Enthalpies in Solution Laarhoven et al.
Time Resolution and Parallel/Consecutive
Processes
Th e tim e resolu tion of a PAC exp erim en t is d eterm in ed b y th e acou stic tran sit tim e τa ) R/υa (R ) laser b eam rad iu s,υa ) sp eed of sou n d in th e m ed iu m ). Braslavski an d Heib el19su ggested a tim e resolu tion (τ
eff) of 1.47τaor 2τa: all h eat released with in th is tim e is in tegrated an d in clu d ed in th e p rom p t h eat release fob s. For a laser b eam wid th of 1 m m an d υavaryin g from 900 to 1400 m s-1in organ ic solven ts,τeffis arou n d 10-6s. Hen ce, th e lifetim e for th e tert-b u toxyl rad ical in th e reaction seq u en ce em p loyed , 1/ (k8[RH]), sh ou ld b e at m ost 0.2τeffto en su re th at m ore th an 99% of th e reaction h eat is d etected . By varyin gτeff(i.e., ch an gin g th e laser b eam rad iu s), on e can cau se differen t p arts of th e exp on en tial decay to fall with in th e p rom p t h eat d om ain wh ich can b e u sed to d eterm in e th e reaction tim e scales.28
Th e su ccess of a p h otoacou stic exp erim en t dep en ds on kn owin g th e reaction rate in relation to th e h eat in tegra-tion tim e. If a reactegra-tion (i.e., th e h eat d ep ositegra-tion ) is too slow, it will n ot b e com p leted b efore th e h eat in tegration tim e lap ses. In th is case, th e ob served sign al is actu ally a con volu tion of th e ch em ical d ecay rate with th e in stru -m en t resp on se fu n ction . On th e oth er h an d, if th e p ri-m ary reaction s are fast en ou gh , su b seq u en t reaction s m ay con tribu te to th e h eat in tegration , ch an gin g th e am p litu de of th e p h otoacou stic sign al. In fact, it is th is effect th at allows on e to u se eq s 7 an d 8 to d eterm in e th e b on d en ergy.
Usin g stan d ard kin etics th eory, th e h eat th at is ex-p ected from a certain reaction or reaction seq u en ce can b e p red icted . Th e p h otod issociation of d i-tert-b u tyl p er-oxid e is in stan tan eou s, resu ltin g in in itial con cen tration s of tertb u toxyl rad icals in th e irrad iated volu m e of ap -p roxim ately 10-6M. Th e rate con stan ts of th e su b sequ en t h yd rogen ab straction s are u su ally kn own from th e litera-tu re. For exam p le, th e ab straction of a h yd rogen atom from p h en ol, with a rate con stan t of 3.3 × 108M-1s-1in b en zen e,29is fast en ou gh to d eliver all reaction h eat (∆8H ) -18 kcal m ol-1) with in th e p h otoacou stic tim e win dow, even at low p h en ol con cen tration s. However, th e abstrac-tion of th e b en zylic h yd rogen from tolu en e (∆8H ) -16 kcal m ol-1), with a rate con stan t of 2.3 × 105M-1 s-1,29
is too slow, even in n eat tolu en e (Figu re 3). With a p h otoacou stic tim e win d ow of 1 µs, on ly fast p rocesses are ob served . Th erefore, even if th e con cen tration of R• were to rise to as h igh as 10-6M, rad ical-rad ical cou p lin g will n ot con trib u te to th e ob served sign al, d esp ite th e d iffu sion -con trolled rate con stan t.
In th e d eterm in ation of th e R-C-H b on d stren gth in tetralin (TET),30 with a low rate con stan t for h yd rogen ab straction , th e tim e lim itation was circu m ven ted b y ad d in g a secon d reactan t, tetrah yd rofu ran (THF), with a kn own b on d stren gth an d a kn own h igh er reaction rate con stan t. Th e resu lt of th is com p etitive h yd rogen atom ab straction p rocess is th at th e lifetim e of th e tert-b u toxyl rad ical rem ain s well with in th e p h otoacou stic tim e d o-m ain . Un der th ese con dition s, th e fraction of th e observed reaction en th alp y from each of th e com p etin g p rocesses is d eterm in ed b y th e rates of th e two in d ivid u al reaction s (eqs 12 an d 13). A p lot of∆9Hsolagain stξ yields a straigh t
lin e with a slop e th at dep en ds on th e differen ce in reaction en th alp y for th e two p rocesses. If th ese en th alp ies are exactly kn own , it is p ossib le to d eterm in e th e kin etics for on e of th e com p etin g reaction s (i.e.,ξ is u n kn own ). On th at b asis, we h ave d em on strated30th at, with a h igh (>2 M) reactan t con cen tration , th e rate con stan t for h yd rogen ab straction is arou n d 40% lower th an th e literatu re valu e. Th e rate con stan ts for reaction 8 are u su ally m easu red b y m ean s of laser flash p h otolysis (LFP) at low su b strate con cen tration s. Th e ap p aren t d eviation can b e ascrib ed to th e op eration of b u lk solven t p rop erties (e.g., activities in stead of con cen tration s). Hen ce, PAC can also b een ap p lied to retrieve rate con stan ts u n d er con d ition s wh ich are n ot accessib le b y con ven tion al m eth od s.
Revised Bond Dissociation Enthalpies
A variety of organ ic an d organ om etallic com p ou n d s h ave b een stu d ied with PAC in ou r lab oratories in th e p ast d ecad e, d em on stratin g th e ap p licab ility of th e tech n iq u e
Table 2. Solution Bond Dissociation Enthalpies, BDE((O-H)sol, for Phenola
solvent (∆9H)app
sol BDE(O-H)sol ∆H(PhOH‚‚‚S) BDE(O-H)
corr sol e isooctane -9.8 86.2 0c 86.2 carbon tetrachloride -5.1 88.0 0d 88.0 benzene -6.5 87.3 1.0 86.3 acetonitrile 0.8 93.0 4.7 88.3 ethyl acetate 0.7 93.0 4.7 88.3 dimethyl sulfoxide 94b 6.6 triethylamine 96b 8.9 solution av 87.4 gas phase 87f
aData from ref 24; all energies are in kcal mol-1. For simplicity, the bond energies are defined with the standard state of the hydrogen
atom being 298 K in the gas phase rather than in solution as was defined in ref 24.bEstimated from the known enthalpy of hydrogen bond formation (Arnett, E. M.; Mitchell, E. J.; Murty, T. S. S. R. J. Am. Chem. Soc. 1974, 96, 3875-3891) by following the procedure in ref 24.cAssumed.dBy definition.eSolution bond energy corrected for hydrogen bonding to the solvent calculated by subtracting from BDE(O-H)solthe enthalpy of hydrogen bond formation between the phenol and the solvent.fArends, I. W. C. E.; Louw, R.; Mulder, P.
J. Phys. Chem. 1993, 97, 7914-7925. ∆9H ob s )ξ∆9H TET + (1 -ξ)∆9H THF (12) ξ ) k8 TET[TET] k8TET[TET] + k8THF[THF] (13)
to retrieve bon d dissociation en th alp ies, reaction volu m es, an d kin etic in form ation . However, som e of th e earlier resu lts sh ou ld b e treated with cau tion sin ce n ot all of th e ab ove con sid eration s were in corp orated in th e d ata an alyses. In th e earlier p u b lication s, reaction volu m e effects an d h eats of solvation were gen erally n ot con sid -ered an d in som e cases th ey were assu m ed to b e n egli-gib le. Tab le 3 lists th e b on d d issociation en th alp ies th at were d eterm in ed u sin g PAC, b y followin g th e b asic m eth od ou tlin ed in th e first p art of th is Accou n t. PAC literatu re d ata31for a n u m b er of ligan d -m etal BDEs are n ot in clu d ed . Wh ere p ossib le, revised b on d stren gth s are given , based u p on th e rep orted valu es for fobs, bu t ap p lyin g th e correct q u an tu m yield (see Tab le 3, footn ote a), th e con stan t 86.0, an d th e solven t correction factor (∆∆sH)ap p accord in g to eq 11.
From th e origin al work of Griller,3 revised b on d d is-sociation en th alp ies of 79 an d 77 kcal m ol-1are ob tain ed for Bu3Sn -H an d 1,4-cycloh exad ien e, resp ectively. Du e to in com p atib ly slow kin etics for th e h yd rogen atom abstraction from dieth yl eth er, we are n ot able to reevalu -ate th e en th alp y of th is p rocess.
In isooctan e, a Si-H b on d stren gth of 90 kcal m ol-1 h as b een rep orted for trieth ylsilan e (en try 4),32wh ich at th at tim e was in lin e with th e kn own h eats of form ation of silan es an d silyl rad icals. Revision lead s to 96 kcal m ol-1, wh ich is in close agreem en t with th e n ow accep ted BDE(Si-H) b on d stren gth of 95 kcal m ol-1.33
Th e rep orted O-H b on d stren gth s7,34(en tries 7 an d 8) in p h en ol are clearly too low. Recon sideration yields a BDE of 87 kcal m ol-1, wh ich is p erfectly in lin e with th e resu lts p u b lish ed a few years later (en try 9).24We also stu d ied th e effect of rin g su b stitu tion on th e O-H b on d stren gth , resu ltin g in a correlation b etween ∆BDE(O-H) an d th e
Ham m ett σ+ con stan t.34 Th is correlation was later ex-ten d ed to a wid er ran ge of p h en ols, in clu d in g th e toco-p h erols.35
In a stu d y of th e R-C-H b on d stren gth in a n u m b er of alcoh ols (en tries 10-14), u sin g p h otolysis of h yd rogen p eroxid e in water as th e rad ical sou rce, Kan ab u sKam in -ska et al.27 sh owed th at th e d ifferen ce in solvation en -th alp ies b etween h yd rogen p eroxid e an d water m u st b e in corp orated in th e an alysis. However, th e ab solu te b on d d issociation en th alp ies are still n ot com p atib le with th e m ost recen t gas p h ase valu es. For com p arison , th e ac-cep ted BDE(C-H) for m eth an ol4is 96.1 kcal m ol-1, wh ile PAC ren d ers a valu e wh ich is 4 kcal m ol-1 lower. It is p rob ab le th at th e reason for th e d iscrep an cy is th e u n kn own con trib u tion of th e reaction volu m e ch an ge in th is solven t m ixtu re.
Du e to th e slu ggish n ess of th e h yd rogen ab straction b y th e h yd roxyl rad ical from CH3CN (en try 15) an d CH3COO-(en try 16), a com p etitive h yd rogen ab straction from h yd rogen p eroxid e takes p lace (eq 14).27However, th e en th alp y for reaction 14 in solu tion is n ot kn own so th e two com p etin g con trib u tion s can n ot b e sep arated at th is tim e.
To d eterm in e th e h eat of form ation of th e b en zoyl rad ical, trieth ylsilan e h as b een in trod u ced as a coreac-tan t,37in ord er to en su re a fast h alogen atom ab straction from b en zoyl ch lorid e (eqs 15 an d 16). Th is p roced u re h as also b een ap p lied to su lfon yl ch lorid es42 an d b en zyl b rom id es.43
FIGURE 3. Release of reaction enthalpy for hydrogen abstraction from 0.1 M phenol (--) and neat, 9 M , toluene (s) as a function of the integration time for the detector. The vertical line at 1 µs denotes the limit of the prompt heat domain (τeff) for photoacoustic calorimetry. The
dotted horizontal line (‚‚‚) represents the final reaction enthalpy w ith toluene.
HO•+ H2O2f H2O + HO2• (14)
t-Bu O•+ Et3SiH f t-Bu OH + Et3Si
• (15)
Et3Si•+ Ph C(O)Cl f Et3SiCl + Ph C(O)
• (16)
Bond Dissociation Enthalpies in Solution Laarhoven et al.
Th e carb on -h yd rogen b on d d issociation en th alp y in 1,4-p en tad ien e38 was fou n d to b e com p atib le with th at ob tain ed from gas p h ase th erm olysis45a(76 kcal m ol-1). Reevalu ation of th e origin al PAC data sh ows th at th e BDEs in th e (su b stitu ted ) p en tad ien es (en tries 20-22) are too h igh (e.g., BDE(C-H) in p en tad ien e: 82 kcal m ol-1). Ad d ition of a tert-b u toxyl rad ical to th e d ou b le b on d s45b is a com p etin g reaction , wh ich m ay occu r to an exten t of 10-20% of th e overall reaction . Th is ad d ition is less en d oth erm al th an th e ab straction from th e m eth ylen e h yd rogen , an d accord in g to eq 11,∆rHsolin creases, wh ich lead s to an overestim ation of th e BDE(C-H). Up on su b stitu tion of th e m eth ylen e grou p b y OH (com p are en tries 20 an d 22), th e rate for h yd rogen ab straction in creases an d th e relative con trib u tion of th e ad d ition
p rocess d ecreases. Th e latter exam p le u n d erscores th e req u irem en t to kn ow th e kin etics in som e d etail in ord er to u se th e PAC tech n iq u e.
Concluding Remarks
Over th e p ast d ecad e, p h otoacou stic calorim etry h as m atu red in to a versatile tool for th erm od yn am ic an d kin etic m easu rem en ts in a b road ran ge of d iscip lin es. It p rovid es fu n d am en tal in form ation con cern in g in ter- an d in tram olecu lar in teraction s an d ch em ical tran sform ation s. Reaction en th alp ies in solu tion on a m icrosecon d tim e scale can n ow b e estab lish ed accu rately b y ad op tin g th e straigh tforward exp erim en tal ap p roach d escrib ed in th is Accou n t. Most im p ortan tly, reaction en th alp ies in solu tion
Table 3. Bond Dissociation Enthalpies, BDE, Determined by PAC in kcal mol-1at 298 K
entry compound solvent BDEa ref BDEarevised
1 (C4H9)3Sn-H isooctane 74 3 78
2 1,4-c-C6H7-H isooctane 73 3 77
3 C2H5OCH(-H)CH3 isooctane 93 3
4 (C2H5)3Si-H isooctane 90 32 96b
5 (CH3)3Si(CH3)2Si-H isooctane 85 32 91
6 ((CH3)3Si)3Si-H isooctane 79 32 84b
7 C6H5O-H benzene 84 2 c 8 C6H5O-H benzene 84 34 87d 9 C6H5O-H various 87 24 87d 10 CH2(-H)OH water 92 27 e 11 CH3CH(-H)OH water 92 27 e 12 (CH3)2C(-H)OH water 89 27 e 13 (CH(-H)OH)2 water 90 27 e 14 (CH2(-H))3OH water 99 27 e 15 CH2(-H)CN water 96 27 e 16 CH2(-H)COO- water 92 27 e 17 DHA (C9-H)f benzene 78 36 g 18 9,9-(CH3)2DHA (C10-H)f benzene 77 36 g 19 PhC(O)-Cl benzene 81 37 87 20 (C2H3)2C(-H)H benzene 77 38 h 21 (C2H3)2C(-H)CH3 benzene 77 38 h 22 (C2H3)2C(-H)OH benzene 69 38 h 23 (CH3)3Ge-H benzene 82 39 87b 24 (C2H5)3Ge-H benzene 82 39 86b 25 (C4H9)3Ge-H benzene 83 39 88b 26 (C6H5)H2Ge-H benzene 79 39 86 27 (C6H5)2HGe-H benzene 80 39 85 28 (C6H5)3Ge-H benzene 80 39 85 29 (CH3S)3Si-H benzene 83 40 87
30 (i-C3H7S)3Si-H benzene 86 40 90
31 (CH3)2NCH2-H benzene 87 41 91i 32 2-oxomorpholinej(C 3-H) benzene 75 41 78i 33 morpholine (C3-H) benzene 91 41 94i 34 piperazine (C2-H) benzene 90 41 93i 35 (CH3)SO2-Cl benzene 70 42 70k 36 (C6H5)SO2-Cl benzene 71 42 71k 37 tetrahydrofuran (C2-H) THF 92 30 92 38 tetralin (C1-H) tetralin 83 30 83 39 C6H5CH2-Br various 61 43 61 40 C6H5NH-H benzene 90 44 90l 41 (C6H5)2N-H benzene 87 44 87m
aReported BDEs in the original papers; where possible, these values have been reevaluated according to eq 11 and employing the quantum yield for the photodissociation of the di-tert-butyl peroxide: Φbenzene) 0.83, or 1/(1 -Φ) ) 2.6 exp(0.48/η) with η the viscosity (in cP) of the medium.24Error margins are 1.5 kcal mol-1.bThe small contribution, within error margins, for side chain hydrogen abstraction is not included.cTime-resolved PAC, deconvolution method.dSubstituted phenols have been studied on several occasions, yielding the following ∆BDEs (kcal mol-1): 4-CN, 5.6; 4-CF
3, 3.2; 4-Cl, 0.4; 4-t-Bu, -1.9; 4-MeO, -5.8; 2,4,6-Me3, -5.5; 2,6-(t-Bu)2-4-Me, -7.7; 2,4-(t-Bu)2, -5.2; 2,6-Me2-4-MeO, -10.1; γ-tocopherol, -7.1; R-tocopherol, -10. See refs 34 and 35.eSee text.fDHA ) 9,10-dihydroanthracene; 9,9-(CH3)2DHA ) 9,9-dimethyl-9,10-dihydroanthracene.gSubstrate concentrations were chosen too low compared to the PAC time window.hValues after evaluation are 82, 82, and 74.0 kcal mol-1, respectively. However, addition of t-BuO•to the
double bond takes place as well, and the two processes cannot be disentangled (see text).iA volume correction of +2.1 kcal mol-1was
already incorporated in the original paper.jA number of substituted oxymorpholines and related compounds have been studied as well.41
kMeasured relative to CCl
4; solvation correction is not necessary.lSubstituent effects in ∆BDE (kcal mol-1): 4-Me, -2.2; 4-F, -0.9. m∆BDE for 4,4′-Me
can b e d eterm in ed d irectly, th u s ob viatin g th e n eed to con vert gas p h ase p rop erties to th ose in solu tion . Fortu -n ately, i-n m ost cases th ere is good agreem e-n t b etwee-n gas p h ase an d liq u id p h ase BDEs. However, th is is n ot th e case for h ydroxylic an d oth er acidic X-H bon ds. Wh ile th is Accou n t h as focu sed on th e ap p lication of PAC for th e d eterm in ation of b on d d issociation en th alp ies, oth er p h ysicoch em ical p rop erties su ch as th e m agn itu d e of h yd rogen b on d in g b etween th e solu te an d solven t or th e ch em ical volu m e ch an ge can b e retrieved b y th e sam e m eth od . In th e fu tu re, we exp ect th e ap p lication of PAC to exten d from m erely fu n d am en tal asp ects of ch em ical reaction s in to areas of ap p lied ch em istry an d b ioch em -istry.
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AR9703443 Bond Dissociation Enthalpies in Solution Laarhoven et al.
