Fundamental reactions of free radicals relevant to pyrolysis reactions

Journal of Analytical and Applied Pyrolysis 54 (2000) 5 – 35 www.elsevier.com/locate/jaap

Fundamental reactions of free radicals relevant to pyrolysis reactions Marvin L. Poutsma Chemical and Analytical Sciences Di6ision, Oak Ridge National Laboratory, Oak Ridge, TN 37831 -6129, USA

Abstract Free-radical mechanisms are ubiquitous for pyrolysis of organic substrates. Background information is supplied to assist in the interpretation of such reactions by dissection into the elementary radical-forming, radical-consuming, and radical-interconverting reactions that form the building blocks of overall mechanisms. Particular attention is given to homolysis, hydrogen abstraction, b-scission–addition, and rearrangement steps, and to bond-breaking and bond-forming processes. Since the thermochemistry of such elementary reactions is dependent on the stability of the radicals involved, the major influences of structural changes on radical stability are reviewed. Kinetics of prototypical elementary reactions and their responses to structural changes are rationalized in terms of their Arrhenius parameters. The fundamental relationships between thermochemical parameters and kinetic parameters are summarized, and the use of these to estimate rate constants for cases where data is not available is demonstrated. Some kinetic consequences of the combination of elementary reactions to produce chain reactions are reviewed. Critical structural and kinetic features that determine the selectivity among product types and the response of reactions to temperature and substrate concentration are indicated. © 2000 Published by Elsevier Science B.V. Keywords: Free radicals; Pyrolysis reactions; Homolysis

1. Introduction Free-radical pathways dominate mechanisms for pyrolysis reactions of organic materials. The general reaction conditions — high temperature; gas-phase or relatively nonpolar liquid-phase media; typical absence of strongly acidic or basic catalysts — are favorable for free-radical behavior. Alternatives such as concerted molecular processes and ionic reactive intermediates do occur, but it is unwise to

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accept them without rigorous testing and simultaneous evaluation of alternate radical pathways. We will summarize some of the common elementary radical reactions relevant to pyrolysis and how they combine, often in chain fashion, to produce overall mechanisms. We will sketch their responses to variations in radical and substrate structure, to temperature, and to concentration (or pressure), as these follow from the underlying thermochemistry and kinetics [1]. Radical mechanisms often appear more complicated than alternatives because of the number of elementary steps involved. Whereas concerted decomposition processes will normally involve only a single elementary step and acid-catalyzed decompositions only a few steps, it is not uncommon for a radical mechanism for pyrolysis of a moderately complex molecule, let alone a mixture of substrates, to contain tens or even hundreds of elementary steps. While this might seem to offer considerable latitude in formulating mechanistic hypotheses, it is actually quite constraining. The available data base on prototypical elementary radical steps — their thermochemistry, based on experimental and calculated thermochemical parameters of the species involved, and their corresponding rate constants, again measured or estimated from analogs by thermochemical kinetic approaches — has become extensive enough, and the ability to simulate the kinetic consequences of complex postulated pathways by numerical integration has become accessible enough, that any postulated pathways can and should be rigorously tested in a quantitative sense. Thus in older literature, it is relatively common to find complex proposed reaction networks for which one of the critical steps may now be shown not to be kinetically competent to rationalize the observed facility of the chemical transformation involved. Similarly, simulation of previously proposed mechanisms may often predict co-products, whose experimental absence must now cast serious doubt on the validity of the mechanism. In summary, while it is unwise not to first consider radical pathways for a new pyrolytic process, the quantitative bar for evaluating such hypotheses is continually being raised. Pyrolysis reactions occur not only in the gas phase, for which the largest thermochemical and kinetic data base exists, but also in the liquid or even solid phases. We will make the common approximation that gas-phase equilibrium constants and rate constants for reactions involving carbon-centered radicals are transferable to reactions in relatively nonpolar liquid media. While there is ample basis for this simplification [2], it is likely a poorer approximation for radicals centered on heteroatoms, especially in hydrogen-bonding media where specific complexation may occur. For reactions in condensed phases, one must also remain aware of possible additional diffusional restraints on kinetics that are not present in the gas phase.

2. Thermodynamic and kinetic relationships and constraints Before considering mechanisms, we must remind ourselves that overall thermodynamic constraints must be met. A very common reaction result under pyrolytic conditions is cracking of the substrate to form smaller products: S“P1 + P2. Such

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cracking reactions are typically endothermic and therefore must be driven thermodynamically by the favorable increase in translational entropy associated with the formation of more molecules of product than reactant. Consider the simple prototype: CH3CH2CH2CH3 “CH3CH3 +CH2CH2 The reaction is notably endothermic at all temperatures (DH °298 = 22.5 kcal mol − 1; DH °1000 =21.5 kcal mol − 1 [3]) as the formation of a new CC double bond does not fully compensate for the breaking of a CC single bond. However, with Dn =1, the entropy change is favorable at all temperatures (DS °298 = 33.2 cal mol − 1 K − 1; DS °1000 =31.5 cal mol − 1 K − 1). Thus at ambient temperature, DG °298 = 22.5− (298)(0.0332)= 12.6 kcal mol − 1 and K298 = 5.7E− 10 atm, a very unfavorable value; for n-butane at atmospheric pressure, this would allow only the minuscule conversion of x B 0.0025%. In contrast at an elevated cracking temperature of say 1000K (727°C), the corresponding values will be DG °1000 = 21.5− (1000)(0.0315)= − 10.0 kcal mol − 1, K1000 =153 atm, and x\99%, consistent with observations of high-temperature cracking of alkanes. The dominant source of this dramatic change is of course the ‘T multiplier of DS’ in the DG sum. However along with cracking to form smaller species, pyrolysis is also commonly characterized by formation of species larger than the substrate, e.g. ultimately carbonaceous chars. The example just treated illustrates that condensation reactions are unlikely to occur by simple addition: S+ S “P3, because of the entropy constraint associated with Dn = − 1. There are however more allowed generic processes in which formation of a larger molecule is coupled to release of a smaller one: S+ S“ P4 + P5, such that Dn =0. Consider the simple prototype: PhH + PhH “ PhPh +H2 The relevant thermochemical parameters at ambient temperature are DH °298 = 3.9 kcal mol − 1; DS °298 = −3.6 cal mol − 1 K − 1; DG °298 = 3.9−(298)(−0.0036)=5.0 kcal mol − 1; and K298 =2.3E −4 atm, which would allow x: 1.5%. At elevated temperature, they are DH °1000 =7.2 kcal mol − 1; DS °1000 = 2.2 cal mol − 1 K − 1; DG °1000 = 7.2 −(1000)(0.0022) = 5.0 kcal mol − 1; and K1000 = 8.1E− 2 atm, which would allow x :22%. While this model reaction is thus not particularly favorable, nevertheless it could proceed to a modest extent and would be further assisted if the small product, H2 in this example, were constantly bled from the pyrolysis system. In comparisons of kinetics of elementary reactions involving varying radicals within structurally similar families, it is common to note that the more ‘stable’ a radical becomes, the larger will be the rate constants for those elementary steps that produce it and, inversely, the smaller will be those for steps that consume it; (we will see exceptions below). One objective of the ‘thermochemical kinetic’ formalism [4] that we will follow herein is to quantify how systematic changes in structure and thermodynamic ‘stability’ of radicals affect their kinetic ‘reactivity’. Towards this end, it attempts to relate differential changes in the thermodynamic parameter DH° for a reaction series to differential changes in the kinetic parameter E (or DH*), and similarly changes in DS° to those in A (or DS*).

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For many reactants and products of modest size, values of standard-state heats of formation (DfH °298) and entropies (S °298) have been experimentally determined [3] or can be estimated with acceptable accuracy by group additivity methods [3a,4]. Heats of formation of transient radicals are more difficult to measure but can be determined by combinations of kinetic and spectroscopic data. A growing data base exists for prototypical radicals (see Refs. [5,6] for useful descriptions of methodology and data compilations) and can be extended to analogs by group additivity methods [4]. In addition for smaller radical species, high-level ab initio calculations have now often reached a chemically reliable level for these difficult open-shell species (see, e.g. Refs. [7 – 9] for data compilations). Standard entropies of radicals can generally be calculated by statistical thermodynamic methods from known and/or estimated spectroscopic and structural properties with better accuracy than they could be measured. Reaction thermodynamics at 298 K are then available from the familiar relationships: DH °298 =SDfH °298 (products) − SDfH °298 (reactants) DS °298 = SS °298 (products)−SS °298 (reactants) DG °298 =DH °298 −T(DS °298) K298 =exp( −DG °298/RT) Since pyrolysis reactions feature T 298 K and DH° and DS° values are temperature-dependent, rigorous treatments would also apply the corrections: DC °p,T =SC °p,T (products) −S C °p,T (reactants) ŽDC ° p =(DC ° p,T + DC ° p,298)/2 −298) DH °T :DH °298 +ŽDC °(T p DS °T :DS °298 +ŽDC ° p ln(T/298) which require a knowledge of experimental or calculated heat capacities (C °p,T) for the reactants and products, before one can determine the free energy, DG °, T and equilibrium constant, KT, at the reaction temperature, T, of interest. However, ŽDC ° is typically small, its effects on DH °T and DS °T tend to be compensated in p DG °, and thus most of the T-dependences of DG° and K arise from insertion of the T proper ‘T’ value in the T(DS°) and DG°/RT terms. Thus for the order-of-magnitude comparisons used in this overview, we will approximate DH °T and DS °T by DH °298 and DS °298, recognizing that, in analyzing any specific reaction case, the proper heat capacity corrections should be addressed. For the remainder of this overview, quoted DH° and DS° values will refer specifically to 298 K. It is customary to cast the temperature dependence of experimental rate constants for elementary radical reactions in the Arrhenius form, k= A exp(− E/RT), or log k = log A −E/u, where u= 2.303RT and E and R are in kcal mol − 1 units. Of course, this is an empirical relationship and the A and E parameters are not strictly temperature-independent; in fact, curved Arrhenius plots over extended T ranges are common and extrapolation beyond the experimental T range used must be done

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with care.1 In practice however, such T effects typically introduce uncertainties no greater than those in much of the thermochemical data base. Given this caveat, and the further approximation just noted of ignoring small temperaturedependences of DH° and DS°, the Arrhenius kinetic parameters and the thermochemical parameters are related by the relationships2: DH°: Eforward −Ereverse +(Dn)RT or Eforward : DH°+Ereverse − (Dn)RT

(1)

DS°: R ln(Aforward/Areverse) +(Dn)R[1+ ln(R%T)] or In(Aforward/Areverse) :DS °/R − (Dn)[1+ln(R%T)]

(2)

Therefore, knowing any two of the quantities in either Eqs. (1) or (2) allows calculation of the third. For analysis of a given elementary reaction, we recommend estimating the Arrhenius parameters for that reaction direction (either ‘forward’ or ‘reverse’) which has the larger data base, or which is the less sensitive to structural changes, and then deriving those for the other reaction direction from these thermochemical balance equations. Inversely, it is not uncommon to find cases where all three related quantities, e.g. Eforward, Ereverse, and DH°, are claimed to be ‘known’ from differing sources and experimental methodologies, but application of Eqs. (1) or (2) reveals a major inconsistency, such that at least one quantity must be in serious error. In cases where thermochemical parameters for the transition state of an elementary reaction can be estimated or calculated, it may be more useful to cast the rate constant in the transition-state-theory formalism that involves DH* and DS*: E= DH* + (1 − Dn*)RT A= (kT/h) exp(1 − Dn*) exp{[DS* − Dn*R ln(R%T)]/R} where Dn* = 0 for a unimolecular reaction and − 1 for a bimolecular reaction. The latter equation for estimating A factors is especially useful because entropies of transition state models can often be estimated with useful accuracy or derived from analogous cases. Note for later reference that if DS* =0 for a unimolecular reaction at 800 K, then A : 1013.6 s − 1; larger or smaller A values are diagnostic of ‘looser’ or ‘tighter’ transition state structures [4].

1 It is increasingly common over large temperature ranges to use the 3-parameter form, k= A(T/ 298)nexp(−E/RT). Hydrogen abstraction reactions in particular tend to show curved Arrhenius plots, in part because of the probable occurrence of tunneling at lower temperatures. 2 The need for the Dn correction terms, when there is a net change in the number of molecules between reactants and products, arises because the thermochemical quantities are tabulated for a standard state of 1 atm pressure whereas the rate constants are expressed in concentration units. In this convention, R= 1.987 kcal mol-1 and R’=0.082 l mol − 1 K − 1.

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3. Radical stability We will need a working definition of radical ‘stability’ as a basis for applying thermochemical kinetic considerations to elementary reactions. Although unambiguous information on stability of radicals is contained in their numerical DfH° values, a more useful, albeit less rigorous, methodology involves normalizing such values of DfH° relative to the DfH° values of the stable molecules from which the radicals can be formally derived by breaking a CH bond (RH “ R’ + H’). Thus we will use a ‘bond dissociation enthalpy,’ DH°(RH), normally at 298 K, defined as: DH°(RH) DfH°(R’) + DfH°(H’)− DfH°(RH) Some relevant DH°(RH) values are given in Table 1. We will also use a ‘stabilization energy,’ Es, defined for C-centered radicals as the difference between DH°(CH) for the bond in question and that in the ‘parent’ CH3H; similarly Es values for N-centered and O-centered radicals are referred to NH2H and HOH.3 The major factors that determine the strength of a CH bond in hydrocarbons are the hybridization state of the carbon and the opportunity for resonance delocalization of the unpaired electron in the resulting C-centered radical. Increasing p-character compared with s-character at carbon weakens the CH bond in the bond-strength order: sp\ sp2 \sp3. Thus the DH°(CH) values for HCCH, H2CCHH, PhH, and H3CCH2H, to produce an alkynyl, alkenyl, aryl, or alkyl radical, are 133, 109, 111, and 101 kcal mol − 1, respectively. Further less dramatic stabilization of alkyl radicals occurs as the extent of carbon branching at the radical center increases. Thus the DH°(CH) values for CH3H, CH3CH2H, (CH3)2CHH, and (CH3)3CH, to produce a methyl, prim-alkyl, sec-alkyl, or tert-alkyl radical, are 105, 101, 98.5, and 96.5 kcal mol − 1, respectively. This decrease results from stabilizing interactions of the unpaired electron with the b-hydrogens and also possibly from some release of steric compression in going from a tetrahedral precursor to a trigonal radical [10]. Similarly, the DH°(CH) values for PhCH2H, PhCHRH and PhCR2H to produce a prim-benzyl (see below), sec-benzyl, or tert-benzyl radical, are 88.5, 86, and 84 kcal mol − 1, respectively. The significant bond-weakening effects of delocalization of the unpaired electron into an adjacent p-system can be illustrated by comparing the DH°(CH) values for CH3CH2H, CH2CHCH2H, and PhCH2H, to produce an ethyl, allyl, or benzyl radical, which are 101, 88, and 88.5 kcal mol − 1, respectively. This radical stabilization is described in the literature either by the Es value compared with CH3H or in terms of a ‘resonance [stabilization] energy’, in which case the reference is usually chosen as CH3CH2H so that the degree of carbon substitution at the radical center is held constant. For the family of benzylic radicals, for which the ‘resonance energy’ of the parent PhCH2’ is thus (101–88.5)=12.5 kcal mol − 1, even further 3 Small variations in Es would result if the standard were chosen to be some other formal precursor, R – X, instead of R–H, because DH° responds to structural factors in RX as well as R’.

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Table 1 Thermochemistry of selected radicals (kcal mol−1)a R H’ HCC’ H2CCH’ Ph’ CH3’ CH CH ’ 3

2

(CH3)2CH’ (CH3)3C’ CH2CHCH2’ PhCH2’ Ph(CH3)CH’ Ph(CH3)2C’ Ph2CH’ C6H7’ HC(O)CH2’ CH3C(O)CH2’ HOC(O)CH2’ CH3OC(O)CH2’ HC(O)’ CH3C(O)’ HOC(O)’ CH3O(CO)’ H2NCH2’d HOCH2’ HO(CH3)CH’ CH3OCH2’ FCH2’ ClCH2’ NH2’ CH3NH’ (CH3)2N’ PhNH’ HO’ CH3O’ PhO’ HC(O)O’f CH3C(O)O’f F’ Cl’ Br’

DfH °298

DH298 ° (RH)

Esb

Reference

52.1 135 69 79 35 29 21.5 12.5 41 48.5 41 33 66.5–69.5 50 0–3 −12––10 −61.5––58 −57.5––52.5 9–10 −3 −50 −43 35.5–36.5 −4 −14.5 −3––1.5 −7––8 28 43–45 41.5–42.5 34.5 54–62 9.5 3–4 12 −38 −49.5––51.5 19.0 29.0 26.7

104.2 133 109 111 105 101 98.5 96.5 88 88.5 86 84 79–82 76c 92–95 92–94 94–97.5 93–98 87–88 89 92.5 92.5 93–94 96 94 93–94.5 100–101 100 106–108 99–100 91.5 85–93 119 103–104 87 105 104–106 136.4 103.2 87.5

– – – – 0 4 6.5 8.5 17 16.5 19 21 23–26 29 10–13 11–13 7.5–11 7–12 17–18 16 12.5 12.5 11–12 9 11 10.5–12 4–5 5 0 7–8 15–16 14–22 0 15 32 14 13–15 ––– ––– –––

[5] [5] [5,55] [5] [5] [5] [5] [5] [5] [5,6] [6,56] [6,56] [6,57] [58] [5,8,9] [8,57c] [8,59] [8,59c] [5,7,60] [5,61] [4] [6] [8,9,62] [5,8,9,63] [59c] [6,8] [8,9,60] [8,64] [5,6,65] [6,66] [6] [6,57c,67] [5,6] [5,6,60,68] [6,55,69]e [59c] [6,59c] [5] [5] [5]

a Most values rounded to nearest 1 (or 0.5) kcal mol−1; ranges shown for cases where substantial disagreement still exists in literature. b Relative to CH3’, NH2’, or OH’. c RH is 1,3-cyclohexadiene. d There appears to be minimal further stabilization by substitution of alkyl groups either on the radical center or on the a-nitrogen [62], contrary to earlier indications [6]. e This value is still controversial with another cluster of Es values 2.5 kcal mol−1 higher; cf. [42]. f The variation in theoretical calculations appears particularly large for acyloxy radicals, with DH°298 varying between 100 and 110 kcal mol−1 [7,59b].

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stability is offered by delocalization into larger polycyclic aromatic rings. For example, the additional increments of resonance energy for ArCH2’ when Ar= 2naphthyl, 9-phenanthryl, 1-naphthyl, 1-anthryl, 1-pyrenyl, 1-perylenyl, and 9-anthryl have been estimated to be 1.4, 2.5, 2.9, 4.6, 5.1, 5.6, and 7.8 kcal mol − 1, respectively [11]. Additional stabilization is offered by a second aryl substituent at the radical center, albeit somewhat dampened from the effect of the first; thus the DH°(CH) values for CH3CH2H, PhCH2H, and Ph2CHH, to produce an ethyl, benzyl, or diphenylmethyl radical, are 101, 88.5, and :81 kcal mol − 1, respectively. Similarly, an additional resonance energy increment of : 4 kcal mol − 1 occurs when allyl radical is extended to pentadienyl radical [12]. A particularly relevant example of the latter class for pyrolysis reactions involving aromatics is the cyclic version, cyclohexadienyl (C6H7’), which is readily formed by addition of H’ to benzene. Its significant stabilization is revealed by DH°(CH) = 76 kcal mol − 1 for 1,3-cyclohexadiene. Similarly to the ArCH2· series (see above), additional stabilization occurs for the polycyclic analogs, ArH2·, formed from larger ArH molecules [11c]. (Stabilizing effects of larger aromatic rings are notably smaller for aryl radicals (Ar·) because these are s-radicals localized at the radical carbon center, not delocalized p-radicals like ArCH2’ and ArH2’ [13].) Two classes of radicals containing carbonyl groups, which are accessible from aldehydes, ketones, acids, and esters, are noteworthy. A carbonyl substituent on a C-centered radical, e.g. RC(O)CH2’ and ROC(O)CH2’, provides only about half the resonance stabilization as does an olefinic substituent. (A strong dependence of the extent of resonance stabilization on the relative electronegativities of the three atoms in formally ‘allylic’ systems has emerged recently [14] and reaches an extreme for carboxy radicals, RC(O)O’, for which resonance stabilization compared with an alkoxy standard, RO·, is non-existent.) Second, in contrast with strongly bound vinylic or aryl hydrogens, an aldehydic or formate hydrogen directly bonded to a carbonyl carbon, even though it is sp2-hydridized, is relatively weakly bound (DH°(CH) :90 kcal mol − 1), and RC(O)’ and ROC(O)’ radicals are relatively accessible. Effects of first-row heteroatom substituents on a C-centered radical are illustrated by the DH°(CH) values for H3CCH2H, H2NCH2H, HOCH2H, and FCH2H, which are 101, 94, 96, and 100 kcal mol − 1, respectively. Thus, except for the highly electronegative halogen substituent, the opportunity for 3-electron 2-center delocalization with an adjacent lone pair of electrons offers modest stabilization compared with an alkyl substituent. The strength of bonding of H to first-row heteroatoms in the parent binary hydrides increases steadily and notably across the row, as indicated by the DH°(CH) values for H3CH, H2NH, HOH, and FH of 105, 106–108, 119, and 136 kcal mol − 1, respectively. However, the extent of incremental stabilization provided by replacing an H on the radical center with an alkyl group also increases along the row; thus DDH°(CH3CH2HCH3H) = (101–105)= − 4; DDH°(CH3NHHNH2H) : (100 – 107): − 7; and DDH°(CH3OHHOH) : (103–119) : − 16 kcal mol − 1. As a result, the DH° values for the alkylated analogues, RCH2’, RNH’, and RO’, are remarkably similar at : 101 kcal mol − 1.

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In fact, even H’ falls in this same range (DH°(HH) = 104 kcal mol − 1), as does Cl’ (DH°(ClH) = 103 kcal mol − 1). As with C-centered radicals, significant stabilization of N- and O-centered radicals results from resonance delocalization into an adjacent benzene ring. The ‘resonance energies’ for the analogous C-centered, N-centered, and O-centered radicals are 12.5, 7–14, and 16–17 kcal mol − 1, respectively, defined as DDH°(CH3CH2HPhCH2H), DDH°(CH3NHH PhNHH), and DDH°(CH3OHPhOH). Finally, as noted above, the OH bond strength in carboxylic acids is virtually the same as that in aliphatic alcohols, and carboxy radicals, RC(O)O·, are s-radicals, not stabilized p-radicals.

4. Major elementary reactions We will categorize the elementary radical reactions relevant to pyrolysis as radical-forming, radical-interconverting, and radical-consuming. These become the building blocks to produce actual reaction networks, often of the chain variety.

4.1. Radical-forming reactions 4.1.1. Homolysis The most common radical-forming process is homolysis, the breaking of a covalent bond to form two radicals. As a thermochemical descriptor, we will use a bond dissociation enthalpy, DH°(CC), fully analogous to that for DH°(CH): R1R2 = R1’ +R2’ DH°(R1R2) DfH°(R1’) +DfH°(R2’) −DfH°(R1R2) Of all the elementary processes to be considered, homolysis is the most kinetically sensitive to the stability of the radicals involved, because the highly exothermic reverse reaction, radical – radical combination, is not kinetically activated (in the absence of seldomly encountered major steric effects), i.e. Ereverse = Ec : 0. Hence from Eq. (1), DH°(CC) can be seen to be a reasonable approximator for Eforward =Ehom, and incremental changes in DH°(CC) that reflect changes in stability of the radicals R1’ and R2’ formed are fully reflected in corresponding changes in Ehom. DS° values for homolysis are highly positive, largely as a reflection of Dn =1, but are relatively insensitive to details of structure. Application of Eq. (2) to the fact that combination occurs on virtually every singlet-state radical–radical encounter, i.e. Areverse =Ac :109.5 – 1010 M − 1 s − 1, then leads to typical Aforward = Ahom values of 1016 – 1017 s − 1. A reduction in Ahom of : 100.5 s − 1 accompanies formation of each resonance-stabilized radical, because the loss of an internal rotation in the radical associated with delocalization of the unpaired electron leads to a slightly decreased DS° value [4]. These large A values for homolysis are diagnostic of a significantly positive DS* and a loose transition state. As an example of estimating homolysis rates, consider the typical aliphatic CC bond in n-butane: CH3CH2CH2CH3 “CH3CH2’ + CH3CH2’. From the parame-

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Table 2 Estimated D°(CC) and D°(CX) values (kcal mol−1) in prototypical organic molecules

ters: DH°(CC) = 88.0 kcal mol − 1, DS°= 43.9 cal mol − 1 K − 1 (Table 1 and Refs. [3,4,15]), Dn = 1, and log Ac (M − 1 s − 1)= 10.05 [16], we have, for a typical pyrolysis temperature of 800 K, the approximate predictions: Ehom,800 : DH°− 800R= 88.0− 1.6: 86.4 kcal mol − 1; ln(Ahom/Ac)800 : DS°/R − [1+ ln(800R%)] = 22.1− 5.2: 16.9; Ahom,800 :(10(16.9/2.303))(1010.05): 1017.4 s − 1; khom,800 : 6.2E− 7 s − 1; and t1/2,800 :310 h. Compared with this predicted value of log k (s − 1)= 17.4–86.4/u, a recommended high-pressure-limit experimental value [17] is log k (s − 1)= 16.3– 81.3/u. Thus the disagreement in k800 is a factor of only 2 [18]. Predicted DH°(CC) or DH°(CX) values for typical organic molecules offer a guide for identifying the weakest bond in a multifunctional molecule, and hence the most facile site for homolysis, or for comparing the likely order of homolytic lability in a closely related family of molecules.4 However, it is important to reiterate that the DH° value is a function not only of radical stability (Table 1) but also of structural features in the starting molecule, as expressed in its DfH° value5 [19]. Some illustrative examples are listed in Table 2 in which the estimated DH° values of selected bonds are labeled. The series of hydrocarbons illustrates the typical bond strength of 88 kcal mol − 1 for an sp3 –sp3 CC bond in an aliphatic chain, the significant bond strengthening that accompanies the replacement of an

4 For larger radicals, the DfH° values for prototypical radicals in Table 1 can be adjusted by the group additivity approach [4], so long as the core structural features at the radical center and its direct substituents are maintained. 5 See footnote 3.

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sp3- by an sp2-hybridized carbon, and the bond weakening that accompanies the formation of a resonance-stabilized benzylic (or comparably, allylic) radical. The CH3CH2XCH3 series (X=CH2, NH, or O) illustrates that these prototypical carbon-heteroatom single bonds are slightly weaker than those to carbon; hence, in structurally comparable situations, these also must be considered as homolytic sources of radicals. The CH3CH2XPh series illustrates the significant bond weakening provided by benzylic resonance in all three series. Comparing the various bonds in the XCH2CH2CH2R series of alkane, alkylaromatic, amine, alcohol, ether, ketone, aldehyde, and carboxylic acid illustrates the varying degrees of bond weakening of the a – b CC bond whose homolysis would give varying resonancestabilized radicals, XCH2’. The stabilizing order phenyl\ carbonyl: N-heteroatom\O-heteroatom reflects the Es values in Table 1. The ketone and aldehyde also show a modest weakening of the CC bond at the carbonyl center that results from stabilization of the acyl radical. In contrast, this stabilizing effect is absent from the acid and ester; also note that the CO bond at the carbonyl center in these cases is a relatively strong one, especially in the acid. Homolysis of a CH bond to give a radical and H’ is in principle a fully analogous process, but in practice it is seldom competitive with CC homolysis because of the generally weaker nature of CC bonds (compare the values for CC bonds in Table 2 with those for CH bonds in Table 1). Only in special structural cases where all CC bonds are particularly strong but a particularly weak CH bond exists will it be kinetically significant. An example would be toluene in which the PhCH3 bond (102 kcal mol − 1) is notably stronger than the PhCH2H bond (88.5 kcal mol − 1). In the liquid phase, homolysis rates may be slightly reduced from those in the gas phase by the ‘cage effect.’ The initially formed pair of radicals is briefly constrained by the surrounding solvent and thus has a finite probability of recombining without ever having become freely diffusing in solution. The impact of cage effects will decrease with decreasing solvent viscosity and increasing temperature [20]. It is useful to illustrate the dependence of bond half-life on Ehom. Assume that Ahom =1016.5 s − 1 and that we demand a half-life for homolysis of 1 min. The temperatures needed to achieve this level of reactivity for Ehom values of 110, 100, 90, 80, 70, 60, and 50 kcal mol − 1 are :1305, 1185, 1065, 950, 830, 710, and 595 K, respectively. However, it is critical to distinguish between the rate of homolysis of the weakest bond in a given molecule and the rate of its overall pyrolysis. If chain reactions occur, for which homolysis is simply the initiation step, then the latter may be much greater than the former. For example, for the prototype n-butane sketched above, the fact that it does not in fact survive for hundreds of hours at 800 K results from amplification of CC homolysis by a long-chain reaction.

4.1.2. Molecular disproportionation The encounter of two radicals leads not only to combination as normally the dominant process but also, if at least one contains an H substituent in the b-position, a not insignificant proportion of disproportionation in which this

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hydrogen is transferred to a radical center to form one saturated and one unsaturated product (written below in the reverse direction). Then just as radical-consuming combination has homolysis as its microscopic-reverse radical-forming process, disproportionation must have a reverse radical-forming process, i.e. a reaction between a CH bond in one molecule and a p-bond in another to produce a pair of radicals: RH +R2CCR2 = R’ + R2HCCR2’ This process, variously called ‘molecular disproportionation’ or ‘reverse radical disproportionation (RRD)’, has only recently received much attention in the literature [21]. Its Arrhenius parameters for any structural case can be estimated from its thermochemical parameters, an estimated Ad value,6 and the fact that disproportionation, as for combination, is kinetically unactivated (Ed : 0). As for homolysis, since Ed :0, the full extent of stabilization of the radicals produced is reflected in the Emd value. The critical structural features are obviously the stability of the radical produced at the site where the CH bond is broken and that of the radical produced by formal addition of H’ to the unsaturated reaction partner. Consider, for illustration and comparison to the prototypical homolysis example treated above, the formation of two ethyl radicals, not from homolysis of n-butane, but from the interaction of ethane and ethylene: CH3CH3 + CH2CH2 “ CH3CH2’ +CH3CH2’. The relevant parameters are DH° = 65.5 kcal mol − 1, DS°= 10.9 cal mol − 1 K − 1 (Table 1 and Refs. [3,4,15]), Dn= 0, and log kd (M − 1 s − 1)=9.15 [16] (note that kd/kc =0.13 for this case [17]). The corresponding predictions are: Emd,800 :65.5 kcal mol − 1; ln(Amd/Ad)800 : 5.5; Amd,800 : 1011.55 M − 1 s − 1; and kmd,800 :4.5E −7 M − 1 s − 1. Hence in this formal example, the ratio of the rate of molecular disproportionation to the rate of homolysis in a hypothetical mixture of n-butane, ethane, and ethylene7 is predicted to be: rmd/rhom : 10 − 5.85 exp(20900/RT) ×[C2H6][C2H4]/[C4H10]. This expression illustrates two important factors concerning this potential competition as sources of radicals. First, homolysis, having both the higher E and correspondingly higher A values, will be favored by higher temperatures. Thus for a hypothetical case where the pressures of n-butane, ethane, and ethylene are each 1 atm (n/V: P/R%T), the rmd/rhom ratio would be B 1 for all temperatures \ 605 K but \1 for all temperatures B 605 K. Since this temperature is too low to give significant absolute reactivity for either process, molecular disproportionation could be ignored. However secondly, since molecular disproportionation is bimolecular while homolysis is unimolecular, it will be favored by higher concentrations. Thus if the pressures were all increased to 100 atm, the cross-over temperature would increase to :805 K, well into the range of

6

Unknown Ad values are generally best estimated from the better known Ac values and numerous measured kd/kc = Ad/Ac ratios for the types of radicals involved. 7 Note that this formal example is a minimum estimate of the possibility for molecular disproportionation because n-butane would play the same role as ethane, in fact more effectively because of its weaker sec CH bonds.

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pyrolytic reactivity. Thus molecular disproportionation, though generally unlikely in competition with homolysis, should be considered under circumstances where (a) the reactants (or accumulating products) lack weak CC bonds but do contain favorable unsaturated reaction partners (olefins or aromatics) for this form of hydrogen transfer, (b) temperatures are low, and (c) concentrations of unsaturates are high, e.g. in the later stages of a cracking process.

4.2. Radical-intercon6erting reactions The most numerous classes of elementary radical reactions are those in which one radical is consumed while another is formed. We will consider hydrogen abstraction, b-scission-addition, and rearrangement as the types of radical-interconverting reactions most relevant to pyrolysis.

4.2.1. Hydrogen abstraction A second major contributor to initial activation of organics under pyrolysis conditions, besides homolysis of CC and CX bonds to form smaller fragment radicals, is cleavage of a CH (or less likely XH) bond by hydrogen transfer to an attacking radical (radical metathesis):



d−

d+

n

A’ +HB “ AHB l A H B “AH+B’ 1

2

In the hydrogen abstraction transition state (1l 2), bond making and bond breaking are coupled such that the activation energy required, EH, is only a small fraction of the DH° value of the bond being broken. For example, for the prototypical example: CH3’ +C2H6 “CH4 + C2H5’, which is nearly thermoneutral (DH°= − 4 kcal mol − 1; Table 1), log k (M − 1 s − 1)= log(6)+ 7.95− 11.6/u 8 [17] (it is convenient here to include in the Arrhenius expression a term ‘log n’, where n is the number of equivalent hydrogens available for abstraction, ‘log A’ refers to one of the equivalent hydrogens, and k refers to the rate constant for the molecule as a whole). Thus the activation energy is B 12% of DH° for the CH bond being broken. Hydrogen abstraction is a bimolecular process, which requires collision of two reaction partners, and is thus characterized by a negative DS*; hence its A factors are notably lower than for homolysis. They are however not very sensitive to structure and are constrained to a rather narrow range, typically AH = 108.0 –109.0 M − 1 s − 1 per hydrogen [4,16,17,22,23]. An exception is abstraction by an atom, e.g. 8 The Arrhenius form used here is log k= log(number of equivalent hydrogens) + log A(per hydrogen) −E/u. Conversion of the most recent recommendations for hydrogen abstraction rate constants formulated in the 3-parameter Arrhenius form [17] to the conventional 2-parameter form in the region of 800 K tends to give significantly higher compensating A and E values, e.g. log k (M − 1 s − 1) = log (6)+ 9.3–14.6/u [22]. We have chosen for consistency with other discussions of structural effects herein to select the lower values, but one must be concerned about the extent to which these have in fact been perturbed by tunneling at lower temperatures.

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H’, rather than a polyatomic radical. Forming the transition state in this case involves less loss of rotational entropy and thus DS* is larger, as is then also AH by a factor : 102 [4,16,17,22,23]. However, in either case, the major challenge in estimating rate constants for particular examples lies with EH rather than AH. Several ‘effects’ have been recognized that influence the variation in EH with structure [10,24]. We will focus here on examples where at least center B is carbon (the reverse case can of course be treated by thermochemical balance). Cases where both A and B are heteroatoms exhibit similar qualitative behavior but quantitative reactivity patterns are less well understood [24]. As a starting point, an ‘intrinsic activation energy’, E0, can be defined for thermoneutral identity reactions. These E0 values for C-centered radicals appear to decrease slightly with increasing branching but to increase more significantly for cases involving delocalized radicals, e.g. E0(CH3’ + CH4) = 14, E0(CH3CH2’ +CH3CH3)= 13, E0(PhCH2’ + PhCH3)= 16, and E0(Ph2CH’ + Ph2CH2) =18 kcal mol − 1, respectively [24,25]. Thus resonance delocalization has a larger stabilizing effect in the parent radical than in the hydrogen abstraction transition state. Second, for abstractions that become increasingly exothermic (DH° B0; the corresponding barrier for the reverse endothermic reaction can then be derived by thermochemical balance), for which the transition state would be expected from the Hammond principle to become increasingly more reactant-like, EH tends to be increasingly reduced from the E0 value for that class but by only a fraction of DH° (contrast this situation with homolysis). This dependence was first formalized for sets of structurally similar reactions in the Evans–Polanyi expression: EH =E0 +a(DH°) with 0 BaB 1, more typically a5 0.5 in the exothermic direction [10,26]. Third, when there is a marked difference in electronegativity between A and B, i.e. for hydrogen abstraction from CH bonds by heteroatom-centered radicals such as RO’ or Hal’, the transition state is dramatically stabilized by ‘polar effects,’ described by transition state contributors such as 2. For example, whereas EH(CH3CH2’ + CH3CH3)= 13, EH(Cl’ + CH3CH3) B 1 kcal mol − 1 [27], even though both reactions have comparable DH°. Finally, for the normally planar C-centered radicals, there appears to be a contribution to EH from the need for its partial distortion toward tetrahedral geometry in the transition state; since this penalty is less when the attacking radical is an atom or lower-coordinate heteroatom-centered radical, the latter class shows an inherently greater reactivity, all other factors being equal. For predictive purposes, these ‘effects’ can be combined in various models. For small systems, computationally intensive ab initio theory can now give useful results even for transition states. For more complex systems, various semiempirical methods have been proposed, e.g. the methods of Zavitsas [28]. An efficient, albeit highly empirical method has been suggested recently by Roberts [24] as an elaboration of the Evans – Polanyi equation: E : E0 f + a(DH°)(1 − d) +b(DxAB)2 + g(sA + sB) where f= [D°(A – H)][D°(B – H)]/[D°(HH)]2. A best fit to 65 data sets, including heteroatom-containing systems, to a standard error of 0.5 kcal mol − 1, was: E(kcal mol − 1): 8.99f +0.25(DH°)(1 − d) − 0.49(DxAB)2 + 1.01(sA + sB). Briefly, the first

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two terms are of the Evans – Polanyi form but with a ‘universal’ E0 and further modified to account for differences in resonance stabilization between A’ and the transition state; d = 0 for all radicals except those with resonance stabilization, for which d was set at 0.44. The third term accounts for the ‘polar effect’ as expressed in DxAB, the difference in Mulliken electronegativities of A’ and B’. The fourth term addresses the energy penalty of planar-toward-tetrahedral distortion for those A’ and B’ whose preferred geometry is planar; s is assigned as 2.5 for planar C-centered radicals, but 0 for the normally pyramidal CF3’, 0.5–0.6 for X-centered radicals, and 0 for atoms. The coefficients E0, a, b, and g were derived by data fitting. Some comparative examples of the ‘contributions’ from the various terms illustrate the impact of exothermicity and the polar effect: (a) E(CH3’ + CH3CH3) : 8.81 −1.08 − 0.45 + 5.05 :12.3 (Eexp = 11.6); (b) E(CH3O’ + CH3CH3) : 8.72 −0.63 − 3.73 + 3.13 :7.5 (Eexp = 7.1; note the large negative ‘polar effect’ term; and (c) E(CH3’ +PhCH3): 7.73− 2.31− 0.41+ 5.05: 10.1 (Eexp = 9.5; note the negative ‘exothermic reaction’ term). An important consequence of relative rates of hydrogen abstraction during pyrolysis will be the competition for abstraction of various types of CH bonds from complex substrates. For example for attack of CH3’ on propane, recommended values [29] are log ksec (M − 1 s − 1)= log(2)+ 8.0−9.6/u and log kprim (M − 1 s − 1)=log(6) + 7.9 −11.5/u; thus ksec/kprim = 4.2 at 800 K per hydrogen, or 1.4 per molecule. Recommended values for abstraction by H·, which is 103 more reactive largely because of the larger AH, are log ksec (M − 1 s − 1)= log(2)+ 10.7− 8.0/u and log kprim (M − 1 s − 1) =log(6) +10.3 −9.4/u; thus ksec/kprim = 6.0 at 800 K per hydrogen, or 2.0 per molecule. Thus hydrogen abstraction can be seen to be inherently a rather unselective process which typically produces mixtures of radicals from complex substrates. Under hydropyrolytic reaction conditions where excess H2 is provided (D°(HH) = 104.2 kcal mol − 1), hydrogen abstraction from it by reactive radicals can be competitive with hydrogen abstraction from CH bonds and constitutes the normal mode of H2 activation for reaction. For the near-thermoneutral example, CH3’ +H2, log k (M − 1 s − 1) =8.8 −10.7/u [22], quite comparable to CH3’ + C2H6, log k (M − 1 s − 1) =8.75 −11.6/u [17]. Of course, compared against weaker, more reactive CH bonds, the competitive reactivity of H2 will decrease, as it also will for attack by more stabilized radicals, which necessarily becomes endothermic. Nevertheless, H2 can serve as a significant source of H’ for further reactions, particularly when a large excess of high-pressure H2 is supplied. The kinetic enhancement of hydrogen abstraction by the polar effect makes possible the known phenomenon of homogeneous catalysis of certain pyrolysis reactions by H – X species such as HCl, HBr, or H2S [30]. Consider a generic reaction network in which a near-thermoneutral hydrogen transfer between C-centers, such as step (3), is rate limiting. If the medium contains comparable amounts of an H– X species, the same net transformation could also be achieved by the successive occurrence of steps (4) and (5): R’ + HR1 “RH +R1’

(3)

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R’ + HX “ RH +X’

(4)

X’ +HR1 “XH +R1’

(5)

If E4 and E5 were each significantly less than E3, this 2-step sequence could in fact offer a kinetic advantage, with HX then serving as a non-consumed catalyst. For electronegative X, for which the polar effect lowers E for hydrogen abstraction, this situation is in fact probable, if no additional barriers result from either step (4) or (5) being significantly endothermic. The criterion to avoid the latter is that D°(XH) be very near that of D°(CH) for the specific case involved.

4.2.2. b-Scission-addition A well-known elementary reaction at ambient temperatures is radical addition to an olefin to form an adduct radical, a process central to free-radical vinyl polymerization. Radical addition is significantly exothermic, because the formation of a new CC bond more than compensates for the ‘opening’ of a p-bond, but it entails an unfavorable entropy loss, because Dn = − 1. Thus, as T increases, an unfavorable TDS° contribution to DG° steadily overtakes a favorable DH° contribution, and the directionality of this elementary process is typically reversed in the pyrolysis temperature range, i.e. b-scission occurs: RCH2CHR1’ = R’ +CH2 =CHR1 in which a bond once removed from an existing radical center is broken with concomitant formation of a p-bond and a smaller radical. As a prototype, consider: ’CH2CH2CH2CH3 = CH2CH2 + ’CH2CH3, for which DH°: 22.7 kcal mol − 1 and DS°: 31.4 cal mol − 1 K − 1 (Table 1 and Refs. [3,4,15]); thus DG° is very unfavorable in the direction written at 298 K ( :13.3 kcal mol − 1) but favorable at 800 K (: − 2.4 kcal mol − 1). The reported rate constant is log kb − C (s − 1) =13.55 − 28.7/u [17]. Thermochemical balance then predicts log kadd (M − 1 s − 1) :8.95 −7.6/u for the reverse addition of ethyl to ethylene, compared with reported values of 8.2−7.3/u [17] and 8.5 − 7.7/u [10]. This reasonable agreement serves to illustrate the range of Arrhenius parameters for both processes for all-carbon systems. The Ab value for unimolecular b-scission, typically 1013 – 1014 s − 1 rather than the 1016 –1017 s − 1 characteristic of homolysis, is indicative of a near-zero DS* and a somewhat tighter transition state than that for homolysis. Meanwhile Eb exceeds the enthalpy of reaction by the modest activation energy for addition, Eadd :7 – 8 kcal mol − 1. Note the extent to which the b–g bond has been weakened by the driving force provided by concurrent formation of an olefinic bond in the a – b position; in this example, Eb is only :35% of that for breaking the analogous bond in n-butane itself (see above). Kinetic effects of structural changes along the carbon skeleton are rather modest, but there is too much scatter and A –E compensation in the data base to assess them quantitatively. Selecting comparative values only from compilations by a single author [17], we could note that the reported Arrhenius values correspond to a 2-fold decrease in rate constant at 800 K from 1-butyl to 1-propyl, as the stability of the expelled radical from these prim precursor radicals decreased, although a full

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manifestation of the DEs value of 4 kcal mol − 1 between methyl and ethyl radicals would correspond to a rate factor of 12. Similarly, for sec and tert radicals in which intramolecular competitive b-scissions are possible, the stability of the departing radical appears to be a reliable guide for predicting regiochemical preference [31,32]; e.g. the ratio ethyl:methyl produced from 3-hexyl radical at 773 K is :4. On the other hand, for similar comparisons of expelling the same radical from precursor radicals in differing stability classes, the very limited data appear counterintuitive if only radical stability is highlighted. For example, the expulsion of methyl from 2-butyl [17] radical appears to be slightly faster than that from 1-propyl radical, even though the latter prim radical is less stable. Such comparisons illustrate the dangers of focussing only on individual ‘effects,’ rather than the entire reaction, when all the ‘effects’ are small. This general guidance is demonstrated by the selected data in Table 3 for reaction in the addition direction. Additions of a single radical, methyl, to a series of all-carbon olefins are compared in the upper portion. The enthalpies of reaction (DH °add) (Table 1 and Refs. [3,4,15]), their differential change relative to ethylene

Table 3 Relative thermochemistry and kinetics of radical addition reactions Radical

Olefin

Adduct

DH °adda

D (DH °add)a,b

kadd 363 (rel)b,c

D (DG *add)a,b,c

CH3’ CH3’ CH3’ CH3’ CH ’

CH2CH2 CH2CHCH3 CH2C(CH3)2 CH2CHPh CH2CHCHCH2

CH3CH2CH2’ CH3CH2CH(’) CH3 CH3CH2C(’) (CH3)2 CH3CH2CH(’) Ph CH3CH2CH(’) CHCH2

−23.7 −23.4 −22.9 −34.0 −32.3

0.0 0.3 0.8 −10.3 − 8.6

0.5d 0.6 1.1 23.4 30.8d

0.0 −0.1 −0.6 −2.8 −3.0

Radical

Olefin

Adduct

DH °adda

D (DH °add)a,b

kadd 437 (rel)b,e

D (DG *add)a,b,e

CH3’ C2H5’ (CH3)2CH’ (CH3)3C’

CH2CH2 CH2CH2 CH2CH2 CH2CH2

CH3CH2CH2’ CH3CH2CH2CH2’ (CH3)2CHCH2CH2’ (CH3)3CCH2CH2’

−23.7 −22.6 −21.7 −20.6

0.0 1.1 2.0 3.1

0.5d 0.4d 0.25d 0.1d

3

a

kcal mol−1. Relative to CH3’+CH2CH2. c Ref. [33]. d Divided by 2 for reaction degeneracy. e Ref. [10]. b

0.0 0.2 0.6 1.4

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(D(DH °add)), the rate constants for addition at 363 K relative to ethylene as determined by Szwarc [33], and the conversion of these to differential free energies of activation (D(DG*)) are recorded. Compare the changes from ethylene through propene to i-butene. The danger of seeking a connection between reactivity (D(DG*)= − 0.6 kcal mol − 1) and radical stability alone (DEs = − 4.5 kcal mol − 1 (Table 1)) is made apparent by noting that radical stability and relative enthalpy of reaction (D(DH °add) = +0.8 kcal mol − 1) do not correlate, i.e. the more stable the adduct radical becomes, the less exothermic the reaction becomes. The apparent paradox results not from an improper treatment of the role of stability of the adduct radical but from a failure to simultaneously consider the stabilization of the starting olefin by the added methyl groups. In fact, the D(DH °add) values show that the latter factor is slightly larger, and the ‘effects’ almost cancel. Focussing more properly on D(DG*) and D(DH °add), we conclude that the apparent weak inverse correlation may well be within the combined error limits (as well as the implicit assumption of constant A factors) and that attempting to interpret this would be unwise. Additions of a sequence of increasingly more stable radicals, methyl through tert-butyl, to a single olefin, ethylene, are compared in the lower portion of Table 3. The DEs change of 8.5 kcal mol − 1 for the attacking radical is reflected in a D(DH °add) change of only 3.0 kcal mol − 1 for the overall reaction; hence again radical stability is only one determinant of thermochemistry. The D(DG*) change is even smaller, 1.4 kcal mol − 1, and a significant portion of even this increment may represent increasing steric congestion (see below). Regardless of details, the relative insensitivity of the rate of the addition process to structural changes involving alkyl substituents is clear. The structure-reactivity patterns in additions of methyl are clearer for a comparison of the much larger structural change from ethylene to styrene (or butadiene) (Table 3). Now the much larger DEs value ( − 12.5 kcal mol − 1) overwhelms the substituent effects on the olefins (D(DH °add) = − 10.4 kcal mol − 1). The much smaller D(DG*) = − 2.8 kcal mol − 1 value then again indicates that the rate of the addition process, with an early transition state, responds to the overall thermochemistry in a comparatively insensitive fashion (a small ‘Evans–Polanyi a’). Inversely, the reverse b-scission process is then predicted to be significantly inhibited for benzylic radicals that must expel a non-resonance-stabilized alkyl radical, and enhanced for alkyl radicals that can expel a benzylic radical. For considerations of pyrolysis reactions of more functionalized heteroatom-containing substrates, it is worth summarizing the effects of substituents on the radical addition process, obtained from studies in the liquid-phase organic arena [26b,34], since these are of some use in estimating effects on the reverse b-scission reactions. For C-centered radicals adding to substituted olefins, Giese [34] has summarized the ‘effects’ of substituents at the three possible sites (Tedder [26b] has presented a similar model, albeit with somewhat different nomenclature): XCR2’ +YCHCHZ “XCR2CHYCHZ’ Substituents Z, at the olefinic terminus where the adduct radical center is forming, exert dominantly ‘polar’ effects, i.e. the addition rate constant is increased

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by increasing nucleophilicity of the attacking radical, e.g. methylB prim-alkylB sec-alkylBtert-alkyl, and increasing electrophilicity of the olefin, e.g. CH2CHRB CH2CHPhBCH2CHCO2R (or inversely but less relevant here, increasing electrophilicity of the radical paired with increasing nucleophilicity of the olefin). Substituents Y, at the olefinic terminus where the attacking radical is approaching, exert dominantly ‘steric’ effects, i.e. the rate constant is decreased by steric compression in the area of the forming bond; in comparison, polar effects are less important. Finally, substituents X, on the attacking radical, exert both polar effects, by modulating its nucleophilicity, and steric effects, by increasing non-bonded interactions. Note that for all three cases, radical stabilizing effects appear much less important than the polar and steric effects, i.e. again in this paradigm radical addition is comparatively insensitive to radical stability. The radical expelled in b-scission can also be H·, e.g. for the prototype used above: ’CH2CH2CH2CH3 “CH2CHCH2CH3 + H’ However, its loss is inherently slower than corresponding loss of an alkyl radical, reflective of the greater strength of the CH compared with the CC bond; a value of log kbH (s − 1) =14.0 – 38.3/u [17] has been estimated. These values predict kbH/kbC :100.45exp( − 9600/RT) or 0.007 at 800 K. Therefore, H’ formation typically becomes stoichiometrically significant only for radicals for which alkyl radical expulsion is not possible, e.g. ’CH2CH3, or for which a very strong CC bond would need to be broken, e.g. ’CH2CH2Ph. The barrier for H’ expulsion compared with alkyl radical expulsion would be even higher, were it not for the fact that addition of H’ to a given p-system is notably more rapid than addition of an alkyl radical, with both a larger A value and smaller E value [10]. Even though radical addition becomes thermodynamically unfavorable at higher temperatures, it of course remains kinetically accessible. Thus actual adduct formation is seldom observed, not because the addition step does not occur, but rather because it rapidly reverses before the adduct radical can be trapped, for example, by hydrogen abstraction. Therefore chemically significant consequences of addition can result if the transient adduct radical has available multiple competitive b-scission pathways, one of which is kinetically more favorable than reversal of the formation step. Thus the following generic substitution process at an unsaturated center is possible: R’ +R1HCCR2R3 “ RR1HCCR2R3’ “ RHCCR2R3 + R1’, where R1’ is a more stable radical than R’. A particularly important example is addition of H’ to an aromatic ring to give a cyclohexadienyl radical (3, Scheme 1), which is kinetically very facile with log kadd (H’ +PhH)= 10.6–4.3/u [35]. Such addition is significantly preferred over the (endothermic) abstraction of hydrogen to generate phenyl radical, log kH (H’ +PhH)=9.5–8.1/u [35]. If H’ adds at an unsubstituted ring position, it will simply depart and no net chemistry will have occurred. However, if it adds at the ipso position of an alkylated aromatic, the kinetic preference to break the weaker CC bond intervenes (see Scheme 1) and an alkyl radical will depart (kbC kbH). This two-step hydrodealkylation process, in which the initial kadd is then rate-determining, is an important pyrolytic bond

24

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Scheme 1.

breaking step for alkylaromatics, particularly when H2 is present to serve as the source of H’. Note that whereas abstraction of aryl hydrogens is not kinetically competitive with ipso H’ addition to an alkylaromatic, hydrogen abstraction from the benzylic position is; e.g. for H’ +PhC2H5, kH/kipso : 3 at 921 K [36]. A bimolecular variant of hydrodealkylation has been proposed in certain cases, especially those that involve highly stabilized cyclohexadienyl radicals. In this so-called ‘radical hydrogen transfer,’ an emerging hydrogen atom from one radical is transferred to an unsaturated reaction partner without ever becoming a free H’, e.g.: ’CH2CH3 +CH2CH2 “CH2CH2 + CH3CH2’. However, the process remains controversial [25,37]. Exceptions to the generalization that actual adduct formation is uncommon under pyrolysis conditions must obviously occur during the early stages of the char formation that often accompanies cracking reactions. For example, condensation reactions of model unsubstituted aromatics to produce biaryls have been extensively studied [1]. A key step is likely the addition of an aryl radical to an arene, followed by H’ expulsion from the intermediate cyclohexadienyl radical (3), i.e. Scheme 1 in the reverse direction. The strong CC bond to aromatic carbon makes bH and bC scissions from 3 much more competitive when R=aryl (kbC ] kbH) than for alkylcyclohexadienyl radicals, for which alkyl radical expulsion is dominant. For example, the relative rates of expulsion of Ph’ and H’ from 3 (R= Ph) have been estimated to be similar, 1 – 10 [38], and the balance between phenylation of benzene and hydrogenolysis of biphenyl is effectively reversible depending on H2 and benzene concentrations (cf. the overall thermodynamics discussed earlier). b-Scission processes are also well known for radicals containing heteroatoms. If the heteroatom is at the g-position, a heteroatom-centered radical can be expelled. For example, reported rate constant expressions [17] evaluated at 800 K for the process: ’CH2CH2X “CH2CH2 +X’ fall in the ratio :1:0.1:0.4:100 for X= C2H5, OC2H5, OH, and Cl, respectively. While these individual values may not be highly reliable (the kinetic data base is limited and some of the Arrhenius parameters appear questionable), the generality of the b-scission reaction channel is apparent. If an O heteroatom is at the b-position, a carbonyl compound rather than an olefin is formed (e.g. ’CH2OCH2R“ CH2O+ ’CH2R). The greater bond

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strength differential between a CO and a CO bond, compared with a CC and a CC bond, makes this cleavage thermodynamically more favorable and also appears to contribute to more rapid kinetics compared with a corresponding all-carbon case; for an example involving PhCH(’)XCH2Ph (X= O or CH2), see Ref. [39] This relative reactivity pattern is particularly evident when the heteroatom is at the a-position, i.e. for alkoxy radicals. For example, the rate constants for decomposition of t-butoxy and neopentyl radicals [(CH3)3CO’ “ CH3’ + (CH3)2CO, log kb (s − 1) = 15.0 – 16.5/u [40] and (CH3)3CCH2’ “ CH3’ + (CH3)2CCH2, log kb (s − 1) = 13.9 – 30.9/u [41]] correspond to 105 more rapid cleavage of the alkoxy radical than the alkyl radical at 800 K. Two important variants for O-containing radicals that are rapid at elevated temperatures are decarboxylation of carboxy radicals [RC(O)O’ “R’ + CO2] and decarbonylation (‘a-scission’) of acyl radicals [RC(O)’ “ R’ + CO]. In general, for a given R’ being expelled, decarboxylation is more rapid than decarbonylation. Within each class, the reaction is more rapid for R = alkyl than for R = aryl, reflective of the relative CC bond strengths involved. The comparative radical half-lives at 800 K shown in Table 4 are illustrative.

4.2.3. Rearrangement Intramolecular 1,2-shifts of hydrogen or alkyl groups in radicals are occasionally postulated but are most usually in error since it is clear that they possess a large activation barrier that is typically insurmountable compared with other radical decay pathways. In contrast, 1,2-shifts of aryl groups are common and actually proceed by an addition — b-scission sequence involving an intermediate spirocyclohexadienyl radical intermediate (4). Examples are also well documented in which the migration origin is an O or S atom, such that 1,2-phenyl shift generates an alkoxy or thiyl radical (see Ref. [42] for a recent review). The kinetic data in Table 5 for the classic ‘neophyl rearrangement’ and selected heteroatom analogs illustrate the range of Arrhenius parameters involved (Scheme 2). Intramolecular 1,x-hydrogen shifts for larger x are kinetically competent, especially when x= 5, in which case ‘rearrangement’ is simply an intramolecular hydrogen abstraction involving a favorable 6-membered ring transition state in which angle and conformational strain is minimized, although there is significant loss of entropy from the need to freeze out several internal rotations. Reported rate constants for 1-hexyl“2-hexyl [log k (s − 1)= 9.5–11.6/u] [43] and 3-octyl“2-octyl Table 4 Prototypical rate constants for decarboxylation and decarbonylation of RC(O)O’ and RC(O)’ Process

R

log k (s−1)

t1/2

Decarboxylation Decarboxylation Decarbonylation Decarbonylation

CH3 C6H5 CH3 C6H5

13.3–6.2/u 12.6–8.6/u 12.5–16.7/u 14.6–29.4/u

2 ps 40 ps 8 ns 190 ns

800

Ref. [70] [71] [17,72] [73]

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Table 5 Prototypical rate constants for 1,2-phenyl shifts Process Ph(CH3)2CCH2’ “ ’C(CH3)2CH2Ph PhOCH(’)CH2Ph “ ’OCH(Ph)CH2Ph PhSCH(’)Ph “ ’SCHPh2

DH° (kcal mol−1)

log k (s−1)

t1/2

−5 +5

11.55–11.8/u \11.5–18.0/u

3 ns B200 ns

[52] [42]

0

10.65–21.4/u

10 ms

[74]

800

Reference

Scheme 2.

[log k (s − 1) =9.4 – 11.2/u] [43]) reveal an activation energy fully in line with that expected from intermolecular hydrogen abstraction but a particularly low A value for a unimolecular process, reflective of the entropy loss associated with achieving the cyclic transition state.9 Examples are also documented for x= 4. Reported rate constants for 1-pentyl“ 2-pentyl [log k (s − 1)= 11.1–20.0/u] [44] and 2-octyl“4octyl [log k (s − 1) =10.5 – 17.0/u [43]] reveal an increased activation energy, reflective of some added strain in the now 5-membered-ring transition state, but also a somewhat larger A that has been suggested [43] to result from the advantage of freezing out one less internal rotation compared with the x= 5 case. Examples for x\ 5 have been suggested and are probably feasible but, as already noted, those for x= 3 or x =2 should be considered highly suspect. In addition to unimolecular rearrangement, the same net effect can also be achieved by intermolecular hydrogen abstraction in which a given substrate-derived radical abstracts hydrogen from a different position in the substrate, e.g.: CH3CH2CH2CH2’ +CH3CH2CH2CH3 “ CH3CH2CH2CH3 + CH3CH2CH(’)CH3. It is not unusual to have situations in which a family of isomeric radicals is formed from a given substrate, e.g. by competitive hydrogen abstraction, and in which the kinetically most favorable decay routes to pyrolytic products are associated with one or more of the less readily formed radicals. The importance of this ‘indirect isomerization’ process is then that it allows an ‘escape route’ for the more populous but kinetically less competent radicals. However, it is important to note the linear dependence of the rate of this bimolecular process on the concentration of substrate, such that it will be promoted by high concentrations, while becoming 9 Note that these are indeed 1,5-H shifts, i.e. 1-hexyl “‘5-hexyl’ and 3-octyl “ ’7-octyl’ only the rules of nomenclature could make them appear to be 1,2-H shifts.

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progressively less favorable under more and more dilute conditions. Examples of this phenomenon are described below.

4.3. Radical-consuming reactions 4.3.1. Combination The occurrence of radical-radical combination on almost every spin-allowed gas-phase encounter has already been noted, i.e., Ec : 0 and kc = Ac : 109.5 –1010 M − 1 s − 1. In the liquid phase, combination will typically show Ec : 1–2 kcal mol − 1, a value that reflects the temperature dependence of the viscosity of the medium rather than a chemical barrier. Activated combination processes occur only for the so-called ‘persistent’ radicals, such as the triarylmethyls or dialkylnitroxyls, whose combination would give a product that is very sterically encumbered or contains a very weak bond. 4.3.2. Disproportionation For the encounter of most radicals, combination dominates but disproportionation is non-negligible. The values of kd/kc illustrate the trend for increasing disproportionation as alkyl radicals change from prim to sec to tert: n-C3H7 + nC3H7, 0.15; n-C3H7 +i-C3H7, 0.4; i-C3H7 + i-C3H7, 0.65; i-C3H7 + t-C4H9, 1.3 (both possible olefins formed in comparable amounts); and t-C4H9 + t-C4H9, 2.8 [17]. However, the special propensity of tert alkyl radicals for disproportionation does not extend to benzylic analogs [25b,45], where, for example, even cumyl radicals still largely couple [46].

5. Chain reactions

5.1. Chain kinetics Sets of elementary radical reactions typically combine in chain sequences to accomplish an overall pyrolysis reaction. The minimum requirements for a chain are at least one radical-forming reaction to produce reactive radicals, a repetitive alternation of at least 2 radical-interconverting steps that forms a closed cycle with respect to the radicals involved, and a radical-consuming step to destroy reactive radicals. In chain-reaction parlance, these constitute the ‘initiation,’ ‘propagation,’ and ‘termination’ steps, with the number of propagation cycles that occurs per initiating radical formed being the chain length. With a long chain length, the bulk of the chemical transformation results from the chain propagation steps, while the initiation step(s) maintains a low steady-state concentration of reactive radicals and its rate is balanced by the termination step(s). During pyrolysis of complex mixtures, these functions may be uncoupled, as a given species may participate in only one. For example, initiation may be dominated by a minor component that contains a particularly weak bond for homolysis. Another minor component (or evolving product) may be converted, often by hydrogen

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abstraction, to a particularly stable radical that then dominates termination because propagation rate constants are generally retarded much more by increasing radical stability than are structure-insensitive termination rate constants. For a radical to play a significant role in chain propagation, it must be both formed and consumed in a facile manner; thus effective propagating radicals will tend to have their thermodynamic stability and kinetic reactivity balanced. Remaining aware of these separable roles of various functional groups as initiators, inhibitors, and stoichiometric reactants when chain reactions are involved is critical to understand mechanisms for a polyfunctional material. A very simple example, the pyrolysis of ethane, will illustrate some general principles of chain kinetics.10 The weakest bond to provide initiation is clearly the CC bond whose homolysis produces methyl radicals, which then rapidly abstract hydrogen from ethane. The alternating chain steps are b-scission of H’ from ethyl radical and hydrogen abstraction by H’. Finally, combination and disproportionation of all possible radical pairs are potentially available to terminate the chain: CH3CH3

ki

CH3CH3 “ 2CH3’ “ CH4 +CH3CH2’

Initiation

kb

CH3CH2’ “ CH2CH2 +H’

Propagation step 1

kH

H’ + CH3CH3 “ CH4 +CH3CH2’

Propagation step 2

kt1

2CH3CH2’ “ CH3CH2CH2CH3 (and CH3CH3 + CH2CH2) Termination step 1 k

t12 CH3CH2’ +H’ “ CH3CH3 (and CH2CH2 + H2)

kt2

2H’ “ H2

Termination step 1,2 Termination step 2

The full kinetic form will obviously incorporate numerous rate constants, even in the steady-state approximation, and predicting reactivity based on estimates of the facility of the various steps can appear somewhat daunting. However, certain simplifications can be made by considering the inherent kinetic barriers to each of the propagation steps. Consider the ethane cracking example. At steady state in the limit of long chains, two relationships pertain: (a) the rate of initiation and the rate of termination must be equal, i.e. ki[CH3CH3]= kt1[CH3CH2’]2 + 2 ’ ’ ’ kt12[CH3CH2 ][H ]+kt2[H ] , and (b) the rates of the two propagation steps must be equal to each other and to the overall rate of reaction, i.e. rate − ethane = kb[CH3CH2’] =kH[H’][CH3CH3]. Straight-forward algebra then leads to: 3/2 rate − ethane =k 1/2 / i kbkH[CH3CH3]

{kt1k 2H[CH3CH3]2 + kt12kbkH[CH3CH3]+ kt2k 2b}1/2 but this expression is hardly likely to inspire the non-kineticist to action. But consider simplifications that result from comparing the magnitude of the terms kb 10

Observation of the idealized kinetics, even for simple substrates, seems often more the exception than the rule because of the intervention of additional steps involving impurities and/or evolving products.

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and kH[CH3CH3], which may be considered the ‘pseudo-first-order’ rate constants for the two propagation steps with respect to the two reactive radicals involved, and determining which of these poses the greater ‘kinetic barrier.’ (As defined here, the ‘pseudo-first-order’ rate constant combines the elementary rate constant and the concentration of the substrate, if involved.) If kb  kH[CH3CH3], and if we then also note that kt1 :kt12 :kt2 because of the relative insensitivity of combination rate constants to structure,11 then: rate − ethane :(ki/kt1)1/2kb[CH3CH3]1/2, and the reaction will be half-order in ethane with a rate insensitive to the value of kH. Inversely, if kb kH[CH3CH3], then: rate − ethane :(ki/kt2)1/2kH[CH3CH3]3/2, and the reaction will be three-halves-order in ethane with a rate insensitive to the value of kb. Although quite different in detail, both of these extreme rate laws illustrate the general pattern for chain reactions that involve radical–radical termination: a half-order dependence on the rate of initiation (in this case ki[CH3CH3]), an inverse half-order dependence on the rate constant for termination of the radical involved in the step that poses the greater ‘kinetic barrier’ (either kt1 or kt2), and a linear dependence on the pseudo-first-order rate constant for that step (either kb or kH[CH3CH3]).12 Fortunately, thermochemical kinetic estimates of the magnitudes of the two propagation rate constants and insertion of the concentrations of substrates often allows us to predict which sense of the inequality between the pseudo-first-order terms pertains and therefore which overall kinetic rate law to anticipate. In general, the sense of the inequality will depend both on temperature, with the term with the higher E value being favored by increasing temperature, and on substrate concentration (pressure), if one of the terms depends on substrate and the other does not. For the specific example being used here, we have the estimates: log kb (s − 1): 13.3–39.7/u [17] and log kH (M − 1 s − 1): 11.0–9.6/u [47]. Thus, kb  kH[CH3CH3] will pertain over any typical pyrolysis conditions, and the half-order rate law can be anticipated. For this typical case where the chain rate law has a half-order dependence on the rate of initiation, an inverse half-order dependence on the rate constant for termination, and a linear dependence on a propagation step (rateexp = rate1/2 i ratep/ 11 This is not an ideal example in this regard because termination rate constants involving atoms tend to be larger than those for multiatomic radicals in the high-pressure limit; also for such small species as H’ and C2H5’, termolecular kinetics involving a third body will be significant at realistic experimental pressures. 12 A possibly helpful qualitative view of the origin of these simplifications may be obtained by noting that, since the rates of the two propagation steps must be identical, the chain-carrying radical involved in the step with the smaller pseudo-first-order rate constant must accumulate to a greater concentration than that of the other radical to compensate. Then, given the similarity of termination rate constants, its termination will dominate, and its propagation step can be said to be ‘rate limiting.’

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k 1/2 t ), the experimentally determined Arrhenius parameters will take the form: 1/2 Eexp =Ei/2 +Ep and Aexp =A 1/2 i Ap/A t . The observed activation energy will thus contain only one-half rather than the full value of the activation energy for the initiation step, which will typically be the most highly activated step in the chain. Hence the overall rate may be notably greater, and the temperature dependence less, than might have been anticipated from considering only the initial bond-breaking step. In real practice for structural complex substrates, and especially for mixtures, the number of elementary steps increases very rapidly and explicit integration of the coupled kinetic equations is no longer feasible. Fortunately this is not necessary because of the accessibility of efficient computer codes for numerical integration of such complex sets of coupled differential equations. These allow quantitative evaluation of proposed mechanisms and of estimates of rate constants, and they also provide predictions of reaction responses to temperature and substrate concentration.

5.2. Competitions among radical-intercon6erting reactions In addition to kinetic issues that arise from comparing the two (or more) propagation steps that involve the two (or more) chain-carrying radicals, it is also a common occurrence that a given chain-carrying radical will possess competitive decay channels. The rate balance of these will determine the actual propagation steps that occur and therefore the selectivity among the products that are formed. The dependence of such competitions on reaction conditions is again determined largely by their relative Arrhenius parameters and molecularities. Cracking of linear alkanes [1], which has been studied over broad ranges of temperature (B 600 to \ 1000 K), substrate concentration (subatmospheric pressure to neat liquid or supercritical fluid at kbar pressures), and corresponding residence times (fractions of s to h), offers a fruitful area for illustration because the product mix formed is very different dependent on reactions conditions. At the high end of the temperature range and low end of the concentration range, each molecule of a linear alkane, Cn H2n + 2, gives one molecule of a 1-olefin, Cm H2m [m= 3 to (n−1)], several molecules of C2H4, and one molecule of CH4 or H2. This is the so-called Rice–Kossiakoff behavior [48]; for a specific example of n-hexane, see Ref. [31]. As temperature decreases and/or concentration increases, the product mix shifts toward one molecule of a 1-olefin, Cm H2m [m=2 to (n− 1)], and one molecule of the corresponding alkane, Cn − m H2n − 2m + 2. This is the so-called Fabuss–Smith–Satterfield behavior [49]; for examples, see Ref. [50]. Finally, at the lowest temperatures and highest pressures, the latter product slate is further expanded, as conversion increases, to include alkanes larger than the substrate; for examples, see [50a,51]. Yet this disparate behavior results from a single underlying mechanistic scheme. The substrate is activated by hydrogen abstraction to give a mixture of Cn H2n + 1(’) radicals. Each has available competitive decay channels, which will ultimately lead to different products; (a) unimolecular b-scission, which produces a 1-olefin and a smaller radical (which itself then faces the same competition); (b) unimolecular

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1,5-H shift, which alters the product selectivity from that expected from the selectivity pattern of the initial hydrogen abstraction from substrate; (c) bimolecular hydrogen abstraction from the substrate, which gives an alkane and starts a new chain; and (d) addition to olefinic products, which can lead, after hydrogen abstraction, to alkane products actually larger than the substrate. We illustrate these for the 1-hexyl radical that would be formed, for example, as an initial minor chain carrier by hydrogen abstraction during the pyrolysis of n-hexane; or for a larger substrate, 1-hexyl radical could result from b-scission of a larger precursor radical. Thus: k

b ’CH2CH2CH2CH2CH2CH3 “ CH2CH2 + ’ CH2CH2CH2CH3

k

1,5 ’CH2CH2CH2CH2CH2CH3 “ CH3CH2CH2CH2CH(’)CH3

k

H ’CH2CH2CH2CH2CH2CH3 “ CH3CH2CH2CH(’)CH2CH3

(+ other isomers)

C6H14

’CH2CH2CH2CH2CH2CH3

kadd

“

RCHCH2

CH3(CH2)6CH(’)R

Assessing the relative importance of these competitive processes requires a knowledge both of their Arrhenius parameters and of the concentrations involved. From considerations noted earlier, the Arrhenius parameters will fall in the order Eb  E1,5 :EH \Eadd and Ab A1,5 \AH \ Aadd; the hydrogen abstraction process will have a kinetic dependence on [substrate]; and the olefin addition process will have a kinetic dependence on (evolving) [olefin product]. Thus at the highest temperature and lowest [substrate], the unimolecular, highest-E b-scission will predominate over the bimolecular, lower-E hydrogen abstraction. In this regime such an alkyl radical would then preferentially continue to expel C2H4 and break down all the way to CH3’ or H’ before hydrogen abstraction with substrate occurred, i.e. the Rice – Kossiakoff mechanism. In contrast, at the lowest temperature and highest [substrate], the reverse inequality will pertain. In this regime such an alkyl radical would preferentially be converted to an alkane by hydrogen abstraction from the substrate rather than expelling C2H4, i.e. the Fabuss–Smith– Satterfield mechanism. (Inserting estimated values for these rate constants suggests that the 1,5-shift process would prove to be non-negligible in both regimes.) Finally, at the very lowest temperatures and high concentrations (very slow conversion rates), the olefin addition process emerges as a significant reaction channel [50a,51], because its equilibrium limitations (see above) can be overcome at low enough temperature.

5.3. Reactions through minority radicals It is common for pyrolysis substrates to be activated by competitive hydrogen abstractions to give a family of potential chain-carrying radicals. Yet the nature of the products formed does not necessarily reflect the initial composition of this family if certain members do not possess facile decay channels but rather are converted to other members of the family, either by unimolecular rearrangement or

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by bimolecular hydrogen abstraction from the substrate. Selected examples are illustrative. A major channel in the pyrolysis of tetralin under low-temperature dense-phase conditions [1] is rearrangement to 1-methylindane. Its precursor has been shown [52] to be the sec 2-tetralyl radical, which has a productive 1,2-aryl shift pathway, even though the benzylic sec 1-tetralyl radical is clearly more stable and would thus be formed preferentially in hydrogen abstraction from tetralin. Hence a major part of the pathway to 1-methylindane must be the 3-step sequence shown in Scheme 3. Two cracking stoichiometries are observed for 1,4-diphenylbutane at 673 K: production of (a) ethylbenzene + styrene and (b) toluene +allylbenzene. The ratio of (a):(b), which are clearly associated with b-scission of the two possible isomeric radicals, is concentration dependent [53]. PhCH(’)CH2CH2CH2Ph “PhCHCH2 + ’CH2CH2Ph PhCH2CH(’)CH2CH2Ph “PhCH2CHCH2 + ’CH2Ph Extrapolated to dilute gas-phase conditions, the (a):(b) ratio was : 5.5 and thus corresponds reasonably with the expected preferred formation of the more stable benzylic 1-radical in hydrogen abstraction steps (by PhCH2CH2’ and, to a lesser extent, PhCH2’). However, as concentration increased to the neat liquid substrate, this ratio steadily decreased toward unity. This counterintuitive change must be diagnostic of a steadily increasing proportion of reaction through the 2-radical, which, although less stable, has a considerably more facile b-scission process because of expulsion of the stabilized benzyl radical. This ‘added’ route through the 2-radical is again made possible because the 1-radical, which has a much greater barrier to its b-scission, can begin to ‘escape’ by the exchange reaction: PhCH(’)CH2CH2CH2Ph +PhCH2CH2CH2CH2Ph “ PhCH2CH2CH2CH2Ph +PhCH2CH(’)CH2CH2Ph as the concentration of substrate is increased. An even more dramatic example occurs in the pyrolysis of 1-phenylpentadecane at 673 K [54]. Although numerous

Scheme 3.

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pairs of cracking products can be imagined and were indeed observed in small amounts, two stoichiometries dominated. The second most prevalent product pair, n-tridecane+styrene, is intuitively reasonable because again it is associated with the b-scission of the most stable benzylic 1-radical. The more surprising, most prevalent product pair, toluene+ 1-tetradecene, must result from b-scission of the 3-radical which, of all the 13 sec radicals, has the most favorable b-scission channel because of expulsion of a benzyl radical. Yet these two mechanistic factors alone could not allow a dominance of the toluene + 1-tetradecene product pair unless there were ‘escape’ routes for the 12 other sec radicals that must be formed in amounts comparable to the 3-radical in the activation of the substrate by hydrogen abstraction. Again the bimolecular exchange reactions appear to offer the necessary steps to complete the mechanism.

Acknowledgements Preparation of this overview was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, US Department of Energy under contract number DE-AC05-96OR22464 with the Oak Ridge National Laboratory, managed by Lockheed Martin Energy Research Corporation. References [1] For a more detailed treatment of selected hydrocarbons, see M.L. Poutsma, Energy Fuels, 4 (1990) 113. [2] (a) S.E. Stein, J. Am. Chem. Soc., 103 (1981) 5685. (b) J.M. Kanabus-Kaminska, B.C. Gilbert, D. Griller, J. Am. Chem. Soc., 111 (1989) 3311. [3] Thermochemical parameters for non-radical species were taken from standard sources; e.g. (a) D.R. Stull, E.F. Westrum, Jr., G.C. Sinke, The Chemical Thermodynamics of Organic Compounds, Wiley, New York, 1969; (b) J.D. Cox, G. Pilcher, Thermochemistry of Organic and Organometallic Compounds, Academic Press, London, 1970; (c) E.S. Domalski, E.D. Hearing, NIST Estimation of the Chemical Thermodynamic Properties for Organic Compounds at 298.15 K, ver. 5.2, National Institute of Standards and Technology, Gaithersburg, MD, 1994. [4] S.W. Benson, Thermochemical Kinetics, Wiley-Interscience, New York, 1976. [5] J. Berkowitz, G.B. Ellison, D. Gutman, J. Phys. Chem. 98 (1994) 2744. [6] D.F. McMillen, D.M. Golden, Annu. Rev. Phys. Chem. 33 (1992) 493. [7] E. Sicilia, F.P. DiMaio, N. Russo, J. Phys. Chem. 97 (1993) 528. [8] G. Leroy, M. Sana, C. Wilante, THEOCHEM 74 (1991) 37. [9] M. Lehd, F. Jensen, J. Org. Chem. 56 (1991) 884. [10] J.M. Tedder, Angew. Chem. Int. Ed. Engl. 21 (1982) 401. [11] (a) J.D. Unruh, G.J. Gleicher, J. Am. Chem. Soc., 93 (1971) 2008. (b) R.B. Roark, J.M. Roberts, D.W. Croom, R.D. Gilliom, J. Org. Chem., 37 (1972) 2042. (c) W.C. Herndon, J. Org. Chem., 46 (1981) 2119, (d) S.E. Stein, D.M. Golden, J. Org. Chem., 42 (1977) 839.

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