Experimental and Theoretical Studies into the Formation of C4âC6

Article pubs.acs.org/JPCA

Experimental and Theoretical Studies into the Formation of C4−C6 Products in Partially Chlorinated Hydrocarbon Pyrolysis Systems: A Probabilistic Approach to Congener-Specific Yield Predictions Grant J. McIntosh* and Douglas K. Russell School of Chemical Sciences, University of Auckland, Private Bag 92019, Auckland 1010, New Zealand S Supporting Information *

ABSTRACT: This work presents a study of the pyrolytic formation of vinylacetylene and benzene congeners formed from chlorinated hydrocarbon precursors, a complex, multipath polymerization system formed in a monomer-rich environment. (Co-)pyrolyses of dichloro- and trichloroethylene yield a rich array of products, and assuming a single dominant underlying growth mechanism, this (on comparing expected and observed products) allows a number of potentially competing channels to C4 and C6 products to be ruled out. Poor congener/isomer descriptions rule out evencarbon radical routes, and the absence of C3 and C5 products rule out odd-carbon processes. Vinylidenes appear unable to describe the increased reactivity of acetylenes with chlorination noted in our experiments, leaving molecular acetylene dimerization processes and, in C6 systems, the closely related Diels−Alder cyclization as the likely reaction mechanism. The feasibility of these routes is further supported by ab initio calculations. However, some of the most persuasive evidence is provided by congener-specific yield predictions enabled by the construction of a probability tree analogue of kinetic modeling. This approach is relatively quick to construct, provides surprisingly accurate predictions, and may be a very useful tool in screening for important reaction channels in poorly understood congener- or isomer-rich reaction systems.

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INTRODUCTION The chlorinated hydrocarbons represent an important class of environmental pollutant.1−11 The carbon backbones adopted are identical to those observed in the pyrolysis/combustion of hydrocarbons, and like their nonchlorinated counterparts, chlorinated polycyclic aromatic hydrocarbons (Cl-PAHs) tend to form abundantly in pyrolysis and combustion systems. Probable carcinogens, control, and mitigation of the formation of these compounds is of obvious importance, which therefore demands detailed knowledge of the formation of these compounds. However, despite their importance, Cl-PAH formation and that of their precursors is still poorly understood, especially when compared to nonchlorinated analogues. Of fundamental importance is a solid understanding of the formation of the precursors on which (Cl-)PAHs are to be built. In analogy with hydrocarbon systems, it is expected that the formation of the first ring is the rate-limiting step for PAH growth. Almost all models have continued to draw from analogy with hydrocarbon systems,12−15 which are typically C2rich (a consequence of the stability of acetylene), and many hydrocarbon models consist of vinylacetylene and butadiene species reacting by way of radical reactions to aromatic C6structures.16−21 These in turn seed the hydrogen abstraction/ acetylene addition (HACA) pathways widely believed to generate PAH structures.22−27 Indeed, analogues of these processes are found (and are generally the sole C6 formation © 2014 American Chemical Society

routes) in the relatively small body of work that exists concerning chlorocarbons.12−15 As a consequence, the radical mechanisms prevalent in the literature associated with hydrocarbons also underlie the current understanding of the mechanism of chlorinated C4 and, ultimately, C6 growth. The seminal works into the growth of chlorocarbons have been undertaken by Taylor et al.12−15 who performed a series of pyrolysis experiments of highly chlorinated species such as C2HCl3 (TCE) and C2Cl4, with the results interpreted by way of detailed kinetic models. Concerning C4 formation, the authors find that radical channels explained yields well, and that these were initiated by C−X bond rupture in the ethylene units; here, X is almost exclusively a chlorine atom given the lower bond cleavage energy.28 Cl then initiates a radical chain reaction, abstracting hydrogen where present to form C2Cl3 radicals that either decompose to C2Cl2 or react onward with C2Cl2 to form C4Cl5 radicals; these in turn may continue to react or deactivate to give C4Cl4 + Cl. To our knowledge, there are no detailed studies of partially chlorinated products (rapid H-abstraction by Cl in TCE systems leads efficiently and almost exclusively to fully chlorinated products). Received: February 12, 2014 Revised: June 30, 2014 Published: September 1, 2014 8644

dx.doi.org/10.1021/jp5015516 | J. Phys. Chem. A 2014, 118, 8644−8663

The Journal of Physical Chemistry A

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reduces the number of parameters and species needed in comparison to a full kinetic model, and we suggest that the accuracy required (as this is primarily recommended for initial model refinement) and a cancellation of errors that typically arises when competing paths are of the same reaction class (in an analogous fashion to the ideas behind reaction-class transition state theory, RC-TST)44−46 allow this handful of parameters to be easily estimated.

Benzenes were historically thought to form by C2H2 addition to C4H3 and C4H5 radicals;16−21 more recent studies suggest, however, that these are comparatively slow (C3 radical dimers have since received much attention)29−33 and tend to form fulvenes rather than the observed aromatic products.34−37 However, models of chlorinated systems initially adopted the C4 radical channel but have yet to be updated to include 2C3like (or any competing channels, for that matter) channels, which may also be relevant, although these channels were included in works considering C3Cl6 pyrolyses.13 Again, no studies exist, to our knowledge, regarding detailed models for partially chlorinated systems. Despite the good agreement these works achieved,12−15 we have recently speculated that direct analogy with hydrocarbons may be fraught with difficulty,38−41 echoing an earlier warning by Detert et al.42 to the same effect. In particular, we have argued that the low C−Cl bond cleavage energies, which result in a far more rapid observed43 decomposition of key radicals such as C2Cl3 than included in previous models,12−15 should effectively shut down the proposed C4 and C6 growth pathways, at least in highly chlorinated systems. Additionally, we have shown that (in agreement with hydrocarbon systems)34−37 C4Cl3 and C4Cl5 addition to C2Cl2 indeed leads predominantly to fulvene.40,41 We instead propose a number of nonradical channels that are consistent with experimental results for C4H4−xClx and C6H6−yCly formation; this culminated in a 51 species, 144 elementary reaction, kinetic model of TCE pyrolysis (with 376 individual kinetic parameters) in which radical and nonradical mechanisms were placed in direct competition providing solid support for nonradical mechanisms as the dominant reaction channels in C4Cl4 and C6Cl6 formation.41 The generality of these results are yet to be confirmed for C4H4−xClx and C6H6−yCly; the major hindrance is the in greatly increased number of products formed once heteroatoms are introduced. One now has to account for not only the formation of a given carbon framework, but also the relative abundances of homologues (compounds with the same carbon skeleton but vary in the H/Cl substituent content); further, the more detailed models must make accurate congener-specific predictions (congeners being an extension of the concept of isomers, but in which the numbers of H and Cl substituents can vary). As an example of the increasing complexities, to model benzene-based species, one must deal with 7 homologue families and a total of 13 congeners spanning C6H6 to C6Cl6. With the naphthalenes, 9 homologues exist with 76 congeners from C10H8 to C10Cl8. This imposes significant modeling constraints even prior to having to consider multiple competing channels leading to a given product, each generally multistep. A solid understanding of the formation of partially chlorinated PAHs requires a detailed understanding of chlorobenzene formation, which is most effectively achieved by kinetic modeling. With the large number of possible reaction classes, and the increasingly large number of intermediates and products associated with partial chlorination, we propose a simple modeling approach based on probability trees as a means of largely explaining experimental results and providing positive support for the most veracious of the possible pathways. While not an alternative to kinetic modeling, we propose this may be a general approach to screening out unimportant reaction channels in large, multichannel/multiproduct reaction systems for which a solid understanding of the fundamental chemistry is yet lacking. This approach greatly

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EXPERIMENTAL AND COMPUTATIONAL METHODOLOGY A. Chemicals. All chlorocarbons and other compounds used were of analytical grade quality and obtained from SigmaAldrich. These and SF6 (British Oxygen Company) were purified before use by repeated freeze−pump−thaw cycles. Materials were handled on Pyrex vacuum lines fitted with greaseless taps; before use, the line was preconditioned by exposure to the vapor under study and re-evacuated. B. Infrared Laser Powered Homogeneous Pyrolysis (IR LPHP). All static cell pyrolyses utilized the IR LPHP technique. Since this method has been described in detail elsewhere, only a brief description is given here.47−50 Pyrolysis is performed in a two piece cylindrical Pyrex cell (total length 120 mm, diameter 38 mm). The cell allows easy disassembly for sample extraction, with the join biased more toward one end to minimize disruption to the gas flow around the hot zone.51 The two pieces are flanged to allow them to fit against one another, forming an airtight seal with the aid of a rubber O-ring and vacuum grease. The cell is held together with a metal clamp attached across the join, and is enclosed by ZnSe windows. Although ZnSe is opaque to infrared radiation below 500 cm−1, it has several distinct advantages over cheaper materials, such as NaCl. ZnSe is strong and thermally stable, and nonhygroscopic. Most significantly, ZnSe is highly transparent to the CO2 laser radiation. The pyrolysis cell is filled with up to 40 Torr (1 Torr = 133.3 Pa) of the vapor under study and approximately 8 Torr of SF6. The contents of the cell are then exposed to the output of a 70 W free running CW CO2 laser operating at 10.6 μm. The laser power level (which determines the temperature) is generally set close to the threshold required for measurable decomposition of the target compound, with an exposure time sufficient to provide an analyzable yield of products, typically a few percent decomposition. Incident power is controlled by attenuation of the beam exiting the cavity by a variety of different sized apertures. As shown elsewhere,47,50 SF6 strongly absorbs the laser radiation, which is then rapidly converted to heat via efficient intermolecular and intramolecular relaxation. The low thermal conductivity of SF6 ensures that a strongly nonuniform temperature profile is produced in which the center of the cell may reach temperatures of the order of 1500 K while the cell wall remains at room temperature.52 IR LPHP has a number of well-documented advantages. The first of these is that pyrolysis is initiated directly in the gas phase, thereby eliminating the complications frequently introduced by competing surface reaction. Since surfaceinitiated reactions frequently involve free radicals, this factor enhances the role of molecular mechanisms. The second is that the primary products of pyrolysis are rapidly ejected into the cooler regions of the cell, inhibiting their further reaction. In favorable cases, these products may be accumulated for further investigation. One substantial disadvantage of IR LPHP is that the temperature of the pyrolysis is neither well-defined nor easily determined, despite many experimental and theoretical 8645



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approaches;47,50 kinetic analysis and comparison with more conventional methods of pyrolysis are thus difficult. However, an approximate effective temperature may often be estimated by the use of a “chemical thermometer”, i.e., a noninteracting reaction of known kinetic parameters; we apply the concept of an effective temperature in our kinetic models. Further, given the relatively high gas pressures employed in our studies compared to typical IR LPHP experiments, our systems will possess a relatively high thermal conductivity, leading to a flatter temperature profile and a closer agreement with an isothermal temperature approximation. C. Analytical Methods. Gas chromatography−mass spectrometry (GC-MS) analyses were conducted using a Hewlett-Packard 6890 series gas chromatograph interfaced with a Hewlett-Packard 5793 Mass Selective Detector (MSD). Base pressure of the MSD was maintained at 1 × 10−5 Torr by a turbomolecular pump backed by a rotary pump. A “HP5-MS” cross-linked phenyl methyl siloxane gum capillary column (i.d.: 0.25 mm, length: 29.2 m, film thickness: 0.25 μm) was employed. Helium was used as the carrier gas in this GC-MS system. Gas samples from selected experiments were extracted from the pyrolysis cell, via a septum port, with a Hamilton 2.5 mL gastight syringe fitted with a lockable valve. The contents of the cell were at relatively low pressure (20−40 Torr); typically, therefore, after 2.5 mL of the gas sample were extracted, and the syringe valve engaged, the sample was compressed to 0.25 mL to achieve a pressure closer to atmospheric. One drawback of the sample extraction method described above is that products of low volatility are not easily recovered from the pyrolysis cell, and therefore a different method was developed for the analysis of solid deposits. Pyrolysis mixtures in the higher temperature experiments aimed toward chlorobenzene production led to sooty or tar-like black solids. The cell was refilled and more deposits generated prior to sample extraction; typically, three successive fills and pyrolyses were performed to accumulate enough solid for analysis. Toluene (10−20 mL) was then added to an evacuated cell after pyrolysis, and analyte dissolution was aided by around 5 min of vigorous shaking. Finally, to ensure all extractable materials were removed, the cell walls were scraped down with a metal spatula, with all removed solid dropping into the toluene extract. The liquid sample and suspended solid was removed with a Pasteur pipet, and placed into labeled sample vials. The vials were allowed to sit for at least a week to ensure that any extractable material still remaining in the suspended solid had dissolved. The extract was filtered into clean vials prior to GCMS analysis. D. Computational Methodology. The geometries of all stationary points were located with the Gaussian 09 suite.53 The B3LYP hybrid density functional54,55 using the 6-31+G(d) basis set has been employed extensively for geometry optimizations. Zero point energy (ZPE) corrections were computed from harmonic frequencies obtained at the same level of theory as employed for optimization; these were scaled by 0.9806,56 unless otherwise stated. Single-point energies (SPEs) have been computed at the MP2, MP4(SDQ), and CCSD(T) levels, all with the 6-31+G(d) basis set. Due to the expense of these SPE calculations, the M06-2X hybrid functional (recently developed by Truhlar et al.57 and recommended for barrier heights and reaction kinetics, among other applications) has also been utilized extensively. For basis sets, a survey of the gas-phase enthalpies of

isomerization of a number of hydrocarbons (including thermodynamics associated with chlorinated hydrocarbons) has shown that M06-2X/6-311+G(3df,3p) SPE calculations are of comparable accuracy to expensive high level methods such as CBS-QB3 and G4MP2.58 Rate constants have been estimated within the framework of transition state theory. Structural data for pre-exponential factors were obtained from a variety of levels: the role of basis set is explored by B3LYP geometry optimizations with the STO-3G, 6-31+G(d), and cc-pVTZ basis sets, while the computational method is explored in MP2/6-31+G(d) optimizations. The generalized transition state theory rate constant is given by eq 1:59 k(T , s) = κ(T )

kT Q (T , s) −VMEP(S)/ kT e h Φ(T )

(1)

where a generalized transition state is defined at each point s along the minimum energy path (MEP), and is perpendicular to the MEP while intersecting it at s; k and h are the Boltzmann and Plank constants, respectively; Φ(T) is the partition function of the reactants, and Q(T,s) is the transition state quasi-partition function (the imaginary frequency has been projected out). Partition functions are evaluated under rigid rotor and harmonic oscillator approximations. The transmission coefficient is denoted κ(T) and accounts for tunneling effects. We have estimated the transmission factor with the Wigner correction60 for tunneling through the barrier where ω‡ represents the (imaginary) vibrational frequency corresponding to the reaction coordinate, deemed appropriate as this term deviated negligibly from unity. κ (T ) = 1 +

1 ℏϖ‡ 24 k bT

2

(2)

We assume that variational minimization of the rate constants does not lead to a significant improvement, and the rate constants are evaluated only at s = 0 in the current work.

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EXPERIMENTAL RESULTS A considerable number of products are generated during the pyrolysis of the chloroethylenes. The simplest are C4 species (C3 products are conspicuously absent).41 With a view to analyzing C4 species, 20 Torr (summing over partial pressures) of chloroethylenes in 1:0, 1:1, and 0:1 DCE:TCE ratios were pyrolyzed in a series of 8 s exposures, with 30 s cooling between exposures, and using a 7.6 mm diameter aperture. It should be noted that the trans-isomer was the sole C2H2Cl2 species present at the start of each experiment; however, this rapidly isomerized to a near-equimolar composition of mixed cis- and trans-C2H2Cl2 at lower temperatures than are required for the chemistry discussed here, and therefore the distinction is largely omitted from discussion. Products were sampled by way of extraction with a gastight syringe. Partial chromatograms, focusing on the window where the vinylacetylenes elute, are given in Figure 1. While not the sole C4 products, C4H6-based congeners form in negligible quantities, although chlorodiacetylenes form abundantly. The diacetylenes are revealing, especially as they likely form from the vinylacetylenes by H-abstraction and Cl-loss. Further, they are the only C4 products detectable by IR spectroscopy, which allows time-resolved product formation to be easily tracked. Neat DCE and TCE systems produce C4HCl and 8646



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least 30 s cooling in between, and with a small aperture diameter of 3.4 mm) of DCE shows C2HCl formation occurs prior to the appearance of the only spectroscopically observable C4 product, C4HCl, consistent with a C4-formation induction period requiring acetylene production.38,39 This is supported by our previous studies where we noted the suppression of C4HCl formation to give C4H2 instead on the introduction of overpressures of acetylene to the partially reacted DCE system.38,39 Clearly, all results strongly support acetylene dimerization channels in C4 formation. Indeed, the chemistry of the acetylenes themselves is also very revealing in this regard. C2HCl accumulates, but is eventually consumed, in the very low temperature DCE experiments we have just discussed. Under similar conditions, C2Cl2 produced during TCE pyrolyses dimerizes so rapidly to C4Cl4 that dichloroacetylene could not be detected spectroscopically and was only observed during GC-MS analyses of postpyrolysis vapors. On the other hand, neat C2H2 pyrolyses found only a minor degree of acetylene degradation even with 20 s pyrolyses and an aperture 8.4 mm in diameter. However, it is readily consumed in the presence of C2HCl even under much gentler conditions (5 s exposures with an aperture of 4.6 mm in diameter) during the aforementioned experiments in which C2H2 is added to the partially pyrolyzed DCE experiments. These experiments demonstrate that Cl-content has a very significant effect on increasing the reactivity of the acetylenes. Incidentally, our previous studies also show that 2C2 → C4 channels are not perturbed by the introduction of CH2Cl2 in partial pressures equal to that of the chloroethylene,38 probably a consequence of rapid dimerization of key C1 radicals and ultimately chloroacetylene formation, suggesting the C 2

Figure 1. Selected ion chromatograms depicting the isomeric distributions of the major vinylacetylene congeners formed during the pyrolysis of trans-DCE, TCE, and 1:1 mixtures of the two. The three C4H2Cl2 and C4HCl3 isomers and sole C4Cl4 isomer are denoted with the symbols *, †, and ‡, respectively.

C4Cl2, respectively; however, the equimolar DCE/TCE experiments see enhanced C4Cl2 yields. All results are consistent with an acetylene dimerization process, followed by HCl elimination, a trait common to vinylacetylene formation as we will soon discuss. Acetylene-carried channels also seem the most reasonable based on other evidence. Highly resolved temporal trends are relatively easily examined after short pyrolyses followed by an in situ product check with IR spectroscopy; very low temperature pyrolyses (92 pyrolyses at 10 s each, with at

Figure 2. Retention times and identities of C6H6‑xClx, 3 ≤ x ≤ 6, congeners formed in the copyrolysis of trans-DCE and TCE in ratios of (top to bottom) 1:0, 1:1, 1:3, and 0:1. Pyrolyses were performed using three successive fills/heating cycles and a total partial pressure of 40 Torr; a laser aperture diameter of 6.0 mm and pyrolysis duration of 6 × 30 s exposures, with 30 s cooling in between, was employed. 8647



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shown to be well modeled by a binomial distribution based on C2HCl/C2Cl2 trimerization.38,41 Note that while all congeners spanning tri- to hexachlorobenzene are formed, not all members of a particular homologue family are produced in equal abundances. Further, we have previously shown that the relative isomer yields within a given homologue family can be changed if the reagents are changed (for example, the yields of tetrachlorobenzenes differ noticeably from those shown in Figure 2 if C4Cl6 + C2H2 are pyrolyzed);41 this indicates that congener yields are determined predominantly through kinetic, rather than thermodynamic, influences under these conditions.

addition channels may be very important in many chlorocarbons systems beyond just those with C2 precursors alone. We return now to vinylacetylenes, a more congener-rich system than the diacetylenes and which may therefore allow more detailed model testing. In the chromatograms given in Figure 1, retention times of the chlorovinylacetylene congeners are labeled; each chromatogram is scaled such that the height of the dominant vinylacetylene peaks are approximately the same between each run for ease of visualization. Note that single-ion traces are provided (at m/z = 120, 154, and 180 amu, the parent ions for dichloro-, trichloro-, and tetrachlorovinylacetylene, respectively), omitting other products for clarity. Additional chlorovinylacetylene congeners form alongside the parent species, not visible in the single-ion traces, and will be discussed shortly. The pyrolysis of neat DCE leads to the formation of dichlorovinylacetylene (C4H2Cl2) isomers almost exclusively. As shown in Figure 1, the products are dominated by two major isomers in very similar abundances, with a much smaller additional peak at a slightly earlier time. Although not shown, C4H3Cl isomers are also found at earlier retention times, but only in trace quantities. Mixed 1:1 DCE:TCE pyrolyses are also found to produce vinylacetylenes abundantly, although the degree of chlorination shifts to more highly chlorinated structures. Trichlorovinylacetylene (C4HCl3) now becomes the dominant homologue family. As shown in Figure 1, there is a single dominant congener formed; two lesser isomers, of similar concentrations to one another, are also formed. As noted, no other congeners are observed as a single ion chromatogram is presented; however, C2H2Cl2 and C4Cl4 congeners are also formed, albeit less abundantly (each with approximately half the peak area of the dominant C4HCl3 homologue), with the C4H2Cl2 congener profile largely unchanged from that observed in the neat DCE experiments. The relative abundance of the additional homologue families will be explored later in this work. Finally, neat TCE pyrolyses are found to form perchlorovinylacetylene, C4Cl4, as essentially the exclusive vinylacetylene product. This too is consistent with the shift to increasingly chlorinated products as the DCE/TCE ratio changes in favor of TCE. In fact, we have previously shown that the changes noted as the degree of chlorination of the precursors change are very well modeled by a binomial distribution,38,39 assuming the dimerization of chloroacetylenes by an unspecified mechanism. Chlorobenzenes are also produced abundantly during chloroethylene pyrolysis, and are the next family of compounds to be formed (C5-species are, like C3 products, formed negligibly). However, these species are of insufficient volatility to be analyzed by gas-phase sampling techniques. Instead, they have been extracted as dissolved solids by way of toluene washes following 40 Torr of mixed DCE and TCE pyrolyses (aperture diameter, 6.0 mm; duration, 6 × 30 s exposures, with 30 s cooling in between, per fill of reagent). Chromatograms of relevant systems where each homologue family is produced in the highest abundances, are given in Figure 2 (again, single ion runs at m/z = 180, 216, 250, and 286 amu are presented for the pure DCE to pure TCE systems, for the sake of clarity). The degree of chlorination of C6 products as the reaction mixture changes from pure DCE to TCE has recently been studied in detail, where it was found that chlorobenzene homologues also show a distinctive change in the degree of chlorination depending on the precursor mixtures, and this too has been

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THEORETICAL RESULTS A. Ab Initio and TST Results: Vinylacetylene Formation. Computational chemistry is an invaluable tool to modeling chemical systems where detailed experimental study of individual elementary reaction steps is not practical or possible. However, even on restricting the chemistry considered to only mid- to fully chlorinated systems, the number of possible reactions that must be considered quickly becomes prohibitive; this is particularly problematic given the number of potential competing reaction channels (such as radical channels, vinylidenes, and direct acetylene-acetylene pathways), a number of which are probably so slow as to be practically inoperative. We will initially focus on the probable channels in the smaller C4H4−xClx systems before treating the more congener rich chlorobenzenes, and will begin by restricting the likely reaction classes by way of counter-arguments before committing to computational study. The primary mechanism of chlorinated vinylacetylene formation, at least on the basis of studies of perchlorinated systems,12,15 is the interaction of vinyl radicals with acetylene. (Partially chlorinated systems have been the subject of comparatively little study). Chloroacetylene congeners are formed abundantly and rapidly15,39,61−64 during the pyrolysis of chloroethylenes by either chlorine radical carried chain reaction:65−69 (a) CXClCHY + Cl → CXClCY + HCl CXClCY → C2XY + Cl

or unimolecular HCl elimination:

(b) 15,63,65,66,70

Note that reaction a leaves the highly reactive CXClCY vinyl moiety; its propensity for further reaction is dictated largely by the rate constant of decomposition in reaction b. Given the high energies of bond scission in the chloroacetylenes,66,71 reaction via ethynyl radicals is unlikely and therefore conventional mechanisms, based on analogy with hydrocarbons, suggest that reactions proceed primarily via radical− radical recombination of vinyl moieties, or radical−molecule addition between vinyl radicals and either the ethylenes or acetylenes. (Incidentally, this also suggests ethynyl radicals are unlikely to drive diacetylene growth). The first two predict the formation of high yields of butadienes, which is inconsistent with our observations. The last is at first sight a viable mechanism for vinylacetylene formation. To pursue this, however, even when restricted to simply the DCE and TCE systems, there are three vinyl radicals (cis- and trans-C2H2Cl2, and C2HCl3) and two acetylenes (C2HCl and C2Cl2); ignoring 8648



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cis−trans isomers, this reduces the number of possible channels from 9 to 6. We can reduce this further to 4 by assuming that successful product forming interactions are driven almost exclusively by vinyl radical addition to the chlorinated tail of C2HCl, allowing facile Cl-loss and products consistent with the observed pattern of acetylene condensation with HCl elimination exclusively. The remaining reactions are given in Figure 3, and in principle we would require accurate

constant data for C2Cl3 decomposition from accurate combined ab initio calculation and measured decomposition rate data.43 In such a scenario, a rapid accumulation of acetylenes might favor nonradical bimolecular channels involving acetylenes. Vinylidene, CCH2, is a potential candidate for initiating such chemistry. Barriers to the formation of vinylidene, computed by ab initio techniques, are ∼180−195 kJ mol−1;72−75 barriers of 190 and 215 kJ mol−1 are obtained for the easiest rearrangement of C2HCl and C2Cl2, respectively.70,76 (Note, the chlorinated species have been subject to limited study.) It has also been predicted that the barrier for reversion back to acetylene is extremely low76 at 9.9 kJ mol−1, suggesting that the lifetime of CCH2 should be exceedingly short, although higher dimensional quantum chemical calculations77 and experimental observations78 suggest a surprisingly long lifetime. It is unclear whether this stability extends to the chlorovinylidenes. Regardless, our experimental evidence argues strongly against their role as the dominant mechanism in chlorinated systems. In particular, C2Cl2 has the highest barrier to isomerization to vinylidene, and thus should be the least reactive; C2HCl should possess a similar reactivity to C2H2 given similar barriers. This contradicts our experimental results38−40 and the extreme reactivity of C2Cl2 toward polymerization,79−81 revealing a dramatically increased reactivity with chlorination. We have recently proposed an alternative where an acetylenic carbon adds across the triple bond of a second. Figure 5 depicts

Figure 3. Major vinylacetylene products formed via radical channels during pyrolysis of (a) neat DCE, (b) 1:1 mixtures of DCE:TCE, and (c) neat TCE.

thermochemistry and rate data for these shortlisted processes (most readily attained by TST). However, the large number of congeners provides numerous unique testing opportunities for a given reaction mechanism, and simple arguments concerning chlorine distributions can demonstrate in a number of instances where channels are very likely inoperative. For example, only a single C4H2Cl2 isomer is predicted, with two major C4HCl3 isomers suggested (we expect similar rate parameters, and therefore similar yields), neither of which is in agreement with experiment. It should also be noted that, as will be discussed shortly, the β-chlorinated attack pathways should be considerably lower in energy. (Indeed, we find this holds in a wide variety of systems involving C2HCl addition to chlorocarbons radicals).17 However, this channel would promote H-loss over Cl-elimination therefore favoring a more highly chlorinated product than observed experimentally (see Figure 4). Finally,

Figure 5. CCSDT/6-31+G(d)//B3LYP/6-31+G(d) PESs of 2C2H2, 2C2HCl, and 2C2Cl2 molecular dimerization systems. Many structures are omitted for clarity, but chlorinated species follow the analogues of the hydrocarbon system rearrangements.

the general pathways leading from dimerization to vinylacetylene formation. There are a number of potential addition and shift routes, and associated intermediates, even in a restricted C4H2Cl2−C4Cl4 set of relevance to this study, and as such we only present the 2C2H2, 2C2Cl2, and a representative 2C2HCl PESs for the full reaction channel. Energies are computed at the CCSD(T)/6-31+G(d)//B3LYP/6-31+G(d) level (inclusive of ZPEs); missing structures on this PES are merely chlorinated analogues of the C4H4 structures, and are omitted for clarity. Exploring this PES, we find that the initial adduct forms directly in a cycloaddition reaction in the 2C2H2 systems; chlorination leads to stepwise C−C bond formation processes. Further, all rearrangements lead to effective vinylacetylene formation by way of cyclobutadienes once the

Figure 4. Vinylacetylene formation channels via α- and β-chlorinated C2HCl addition to dichlorovinyl radicals.

we suggest that the lower C−Cl bond cleavage energy in the chlorovinyl radicals should initiate far more facile acetylene formation than in hydrocarbon systems, deactivating these radicals and shutting down this pathway; we have demonstrated this explicitly in the case of C2Cl3,41 based on reliable rate 8649



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Table 1. Entrance Barriers for a Number of Possible Acetylene−Acetylene Pairs in the Formation of Chlorinated Vinylacetylenesa

a

All barriers are based on SPEs from a B3LYP/6-31+G(d) optimized geometry, and all use the 6-31+G(d) basis set except for M06-2X energies, which employ a 6-311+G(3df,3p) basis.

Table 2. Pre-exponential Factors (Fitted to the Form B = ATn, in L mol s Units) Computed by Nonvariational TST for a Sampling of Acetylene Dimerization and Diels−Alder Cyclization Transition Statesa

a

Also given are the pre-exponential factors, B, at a representative temperature (1000 K).

least 12 cycloprop-3-ene-methylene carbene intermediates, necessitating at least 12 transition states (asymmetry in these saddle point structures indicates that a rigorous analysis will need to account for many more structures). The energies for the 2C2H2 reaction appear in good agreement with previous studies, suggesting the levels considered here (particulaly CCSD(T) values) are probably adequate for our current purposes.84 One striking observation that Table 1 demonstrates more fully is the significant lowering of energy of these transition states as the degree of chlorination increases. With increased chlorine content, chemistry-driving vinyl radicals (or, presumably, many other key radicals) lose Cl atoms more rapidly shutting down radical channels, a consequence of the far lower barrier to C−Cl bond cleavage43,65,66 relative to C−H cleavage, 85−91 at ∼100−110 and 140−170 kJ mol −1 , respectively. However, in addition to generating more acetylene, higher chlorine content also lowers the barriers to molecular channels, dramatically enhancing their feasibility and suggesting a switch from radical- to nonradical channels. Another important feature of note is the β-stabilization effect. Transition states bearing a Cl atom on the β-carbon are lowered by an amount that, while varying between methods, is largely independent of the degree of chlorination, and is

initial adduct is formed. We have included on the 2C2HCl PES, for completeness, an H-migration step in the initial adduct leading to methylenecyclopropene, which competes with a cyclobutadiene route, and is a key intermediate in the vinylidene channel that has been experimentally observed to yield vinylacetylenes;82,83 however, it is clear from Figure 5 that the cyclobutadiene formation dominates (and indeed we find this is generally the case for all pairs).38 This PES very clearly indicates that chlorination has a significant impact on lowering the entrance barrier to this process, dropping from 236 to 78.5 kJ mol−1 on moving from C4H4 and C4Cl4 structures. However, these PESs also demonstrate the large number of individual shift routes required to fully characterize even a small subset of these molecular channels. To more carefully study the rate limiting bimolecular addition process, we have computed energy barriers and preexponential factors for a number of relevant acetylene pairs (see Table 1). All barriers are computed from B3LYP/6-31+G(d) optimized geometries, with SPEs computed thereafter. Preexponential factors have also been computed at a variety of levels of theory via nonvariational TST; these are given in Table 2, and will be discussed shortly. The structures included represent a restricted sampling, and one can find a total of at 8650



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typically ∼10−20 kJ mol−1 (again, a full survey of all TS geometries will be needed for a rigorous analysis). We have found,38 as will be elaborated on in both this and future works, that this is a general trend seen in the formation of at least vinylacetylenes, benzenes, phenylacetylenes, and naphthalenes. Because of this, a single estimate of the relative energy barriers could in principle be used to characterize the relative contribution of α- and β-chlorinated acetylene addition for a large number of Cl-PAHs, and their precursors, to a first approximation. Note that this difference is relatively constant in spite of sometimes large differences within one structure but at differing computational levels. Rate constants will provide a better estimate of the contributions of each set of pathways. Nonvariational TST has been employed to derive pre-exponential factors at a variety of levels of theory; we have explored various basis sets (STO3G, 6-31+G(d), and cc-pVTZ) at a reference B3LYP level of theory, and method by way of MP2/6-31+G(d) optimized rate constants for a small selection of the pairs given in Table 2. In some cases, rate constants vary considerably with the levels employed; geometries tend to be similar, and the noted differences probably reflect differences in the treatment of vibrational modes (the low-frequency modes contribute heavily to the partition functions and therefore rate constants). However, pre-exponential factors appear almost identical between α- and β-chlorinated routes at a given level of theory. Thus, and given the near-invariant energy difference between competing channels, while absolute rates will require significant study to ensure their accuracy relative rates appear to be easily obtained with little difference between low and relatively highlevel treatments. To summarize, radical-based routes driven by vinyl radicals are unfeasible due to the low bond dissociation enthalpy measured for C 2Cl3 (which we have shown leads to deactivation of radical routes, and which should hold for all chlorinated vinyl radicals)40,41 and the poor isomer description this method provides. Odd carbon-based radical channels are unlikely due to the absence of these products in pyrolysis mixtures. Turning to molecular channels, while vinylidenes are a candidate in nonchlorinated systems, the energy barriers are inconsistent with the known reactivity of C2Cl2 and observed reactivity of C2HCl in our studies. These appear to be superseded by direct molecular adduct formation; barriers in Table 1 and Figure 5 show a significant lowering of the entrance barrier as the degree of chlorination increases, consistent with the reactivity trends of these acetylenes. Further, these barriers are all lower than the isomerization barrier to the vinylidene structure. Accurate kinetics will require, by analogy with CCH2, a solid understanding of the halovinylidene lifetimes; however there is some evidence against vinylidenes in halogenated systems. A number of recent matrix isolation studies into the addition of (usually fluorinated) vinylidene to acetylene has provided very strong evidence for the presence of intermediate species.82,83 Vinylidenes produced photolytically in matrices at approximately 10 K after UV irradiation (λ < 248 nm) undergo rapid addition to the remaining acetylene molecules upon annealing at 30−40 K to form methylenecyclopropene derivatives. Irradiation at 420 nm generally revealed the formation of vinylacetylene and butatriene signals at the expense of methylenecyclopropene. The reaction of difluorovinylidene with acetylene, for example, yields (difluoromethylene)cyclopropene, and following irradiation was shown to give 1,1-difluorobut-1-ene-3-yne.82

Methylenecyclopropene decomposition may be direct, although there is some suggestion it leads first to allenylcarbene, H2C CCR−CR: (R = H, F), which yields butatriene prior to vinylacetylene formation.92 Irrespective of the exact route, intermediate species are clearly feasible in the molecular dimerization of acetylene. Maier and Lautz have also performed a series of UV-photolyses on matrix isolated acetylene mixtures; however, their approach involves excitation of the matrix, not the reagent, and thus inducing nonphotolytic reaction.93 Irradiation of acetylene mixtures in a Xe matrix, particularly with longer wavelength radiation (248 nm), also yields the acetylene dimer, vinylacetylene, without the presence of radicals; however, in contrast with vinylidene-based processes, cyclobutadiene is observed in place of methylenecyclopropene. The latter experiments arguably resemble thermal decomposition more closely than photolysis, and the dominant intermediate in these cases, despite being higher energy than methylenecyclopropenes, is in line with our predictions. Consequently, direct bimolecular adduct formation seems the most likely channel. As noted, with very many structures there are a number of potential reaction channels; however, there are only a few points where the reaction may branch. Consequently, we will explore in a later section a simplified kinetic model to more rigorously check the veracity of these channels in describing our results, or whether further alternatives need to be sought before committing to the derivation of the necessary kinetic parameters required for accurate mechanistic verification. B. Ab Initio and TST Results: Chlorobenzene Formation. These systems have been examined in close detail in our previous work;40,41 as such, we treat these systems only somewhat sparingly here. Again, we can rule out a number of possible reaction channels on the basis of our experimental results. Benzene formation in chlorinated systems has been argued to proceed either via radical channels, particularly the addition of acetylene to chlorinated C 4 H 5 or C 4 H 3 radicals,12,13,15 or the dimerization of C3Cl3 radicals,14 again in analogy with the findings for nonchlorinated systems.17−21,29−37,94−97 However, the potential for Diels−Alder cycloaddition reactions between vinylacetylene and acetylene in benzene formation,98−101 and the results of the studies of vinylacetylene formation in chlorinated systems38,39 prompted the serious consideration of nonradical channels in the formation of chlorinated benzene congeners.40,41 Indeed, our studies of C6 formation40,41 strongly suggested nonradical channels do in fact dominate in chlorobenzene systems; in fact, the linear C6Cl6 product formed during neat TCE pyrolyses (Figure 2) was found to be almost diagnostic of molecular routes. Further, the conventional C4/C2 radical channels are found to lead predominantly to fulvene-based, rather than aromatic, C6 structures.40 This is very similar to what is noted in nonchlorinated systems.37 The slower rates of radical/ molecule processes relative to strictly molecular channels, again a consequence of rapid decomposition of chlorinated radicals, was also largely confirmed for the highly chlorinated TCE system after the construction of a kinetic model requiring 376 individual kinetic parameters, for which around 60 reactions (and approximately 160 individual parameters) were eventually found associated with reactions too slow to influence the global reaction system.41 C3 reactions, on the other hand, are found to be inoperative experimentally due to the absence of odd-carbon products which should form readily in systems where C3radicals are sufficiently concentrated to dimerize to form a 8651



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Table 3. Entrance Barriers for a Number of Possible Failed Diels−Alder Cyclization (Acetylene Dimerization Analogue) Pairs in the Formation of Chlorinated Benzenesa

a

All barriers are based on SPEs from a B3LYP/6-31+G(d) optimized geometry, and all use the 6-31+G(d) basis set except for M06-2X energies, which employ a 6-311+G(3df,3p) basis.

examined. Entrance barriers for a number of pairs are given in Table 3. Unlike the acetylene pairs, we do not provide full PESs leading to benzenes here, as we have considered the C4Cl4/ C2Cl2 pair in full in our previous studies.40 While we refer the reader to this work for the details, we will provide a brief summary of pertinent points. We find the rearrangements provide a facile pathway to the observed products once the initial adduct has been formed, and reaction has a number of similarities with the acetylene dimers. In particular, adduct formation leads quickly to a vinylcyclobutadiene intermediate. Chlorine-assisted ring opening can lead to linear products (although only in perchlorinated systems, where H-abstraction is otherwise favored), and ring closure/opening via a Dewarbenzene-like intermediate leads to the aromatic products.

major product, and due to the improbability of the C3 scheme to reasonably account for the changes in dominant homologue family as the proportion of DCE to TCE is varied; this is again found to be well-fitted to a chloroacetylene trimerization model.41 Of the previously considered models, this largely leaves molecular channels. Out-competed in vinylacetylene formation, we assume (given the similarities in chemistry) that vinylidenes are unimportant here, too. However, Diels−Alder cyclization is an option now, and we must therefore consider both these and direct acetylene addition routes. We first consider the C4 analogues of the previous section to adduct formation between a number of vinylacetylene/ acetylene pairs. The computational expense is in general dramatically increased; thus, only a few relevant pairs are 8652



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Table 4. Entrance Barriers for a Number of Possible Diels−Alder Cyclization Pairs in the Formation of Chlorinated Benzenesa

a

All barriers are based on SPEs from a B3LYP/6-31+G(d) optimized geometry, and all use the 6-31+G(d) basis set except for M06-2X energies, which employ a 6-311+G(3df,3p) basis. NON-DA indicates failed ring closure reactions.

channels should dominate; however, increased chlorine content may lower the barrier to direct addition and, more importantly, inhibits ring closure. Again, while energetically feasible and the sole remaining channels after introducing counter-examples, this is not wholly adequate to truly address the veracity of these pathways. Accurate congener specific yield predictions would be far more convincing. However, it must be stressed how quickly the number of competing channels increases with molecular size, even within a given reaction class; restricted to just the DCE/ TCE systems and the initial Diels−Alder formation transition states, there are eight C4H2Cl2/C2HCl, four C4H2Cl2/C2Cl2, six C4HCl3/C2HCl, three C4HCl3/C2Cl2, and a single C4Cl4/ C2Cl2 pairthis count ignores cis−trans isomers, which would increase the number of pairs considered. With the inclusion of a full pathway for each pair, it is evident that a full kinetic model will be very difficult to construct, with no guarantee that the chosen classes of reactions will be competitive with any potentially competing channels associated with radicals, vinylidenes, or a direct acetylene−acetylene like process. With a large quantity of data amassed in multiple experimental trials, we have a number of cases in which we can argue against alternatives, although we would prefer greater confidence in the proposed reactions beyond simply being the only hypothesized models to withstand counter-example. In the following section, we will demonstrate a simplified approach to obtaining congener-specific yield predictions in kinetically controlled systems that provides a stronger explicit case for the remaining Diels−Alder and direct addition channels. C. Development of a Reaction Probability Tree Framework. While the construction of a full kinetic model is the ultimate goal in understanding, in detail, complex chemical processes,41 this can be extremely difficult to realize in practice in poorly understood systems with little to no prior derived kinetic or mechanistic data. The necessary parameters are often inaccessible by experimental investigation and, given multiple heavy atoms and a high number of potential elementary reaction steps, may be impractical to obtain

Concerning the initial adduct, formation of the relatively stable bridged adduct appears to be a 2-step process, forming the C−C bonds in succession. The second bond formation step has the higher energy and is probably rate-determining, thus we include both the initial barrier and this second C−C bond formation barrier here. Interestingly, we do not observe the strong barrier lowering influence of chlorine with the DFT barriers, although other levels, including our highest level of theory (CCSD(T)/6-31+G(d)//B3LYP/6-31+G(d)) do hint at this trend. This seems to indicate that caution need be applied to these species, likely due to the biradical nature of many intermediates, which arguably require multireference methods for the most accurate barrier estimates. All methods, on the other hand, do reveal the clear barrier lowering associated with β-stabilization of the acetylenes offered by chlorine; this stabilization is observed in both steps, will produce a similar effect (i.e., at ∼40 kJ mol−1 one orientation considerably outcompetes the other) as found in the 2C2 reaction system. As mentioned, Diels−Alder mechanisms are an additional nonradical channel not accessible in the 2C2 system. Tabulated barriers for the formation of the initial adduct are provided in Table 4; again, we do not reproduce a full PES here as we have provided the full pathway for C6H3Cl3 formation in our previous work,40 subsequently demonstrating that all rearrangements provide a facile route to aromatic products. Table 4 reveals that the entrance barrier to the Diels−Alder channel might also exhibit lowering with chlorination, although again not as dramatically as in 2C2. No strong barrier influence is noted on the direction of C2HCl addition (whether chlorine is directed to the vinyl or acetylenic end of the vinylacetylene unit) but we find that as the degree of chlorination increases, the bond length between the acetylene unit and the vinyl end of the C4H4 congeners tends to increase, and in a number of cases ring closure fails altogether leading directly and naturally to our alternative channel. Failed ring closure appears to be the result of steric hindrance as opposed to electronic effects.40 Thus, it appears that on the basis of lower bond energies, Diels−Alder 8653



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Scheme 1. Probability Tree Fragment Depicting the Chances of Following Various Chlorinated Vinylacetylene Formation Channels

construction. This can be justified if we assume errors in energies are largely additive (not unlike the assumption inherent in perturbation theoretical approaches). Similarly, errors in pre-exponential factors are assumed to be multiplicative (not unreasonable, as these are derived as the ratio of molecular partition functions, each separable into the products of translational, rotational, vibrational, and electronic components). Rate constants may therefore take the approximate form

theoretically. In fact, the number of potential reactions one must consider represents one of the major hurdles; typically, all but a small number of the potential reaction channels are too slow to be operative, and are therefore negligible, but this is usually not clear until after they have already been compiled into a working model. Clearly, an inexpensive means to screen inoperative channels and, ideally, strongly support hypothesized pathways, would be extremely beneficial in the construction of models of systems like halogenated hydrocarbon growth. A simple approximate view of a complicated reaction system can be achieved by considering reaction steps as a branching scheme of pseudounimolecular reactions where only parameters necessary to describe branching, and not every elementary step, are required. Unfortunately, such an approach would not provide time-resolved information, nor are absolute yields obtainable, and consequently the absolute rates cannot be derived. However, and with a view to application as a means of screening possible channels, there are several important advantages that this approach offers for large multiple-congener systems that are poorly understood in detail. Only a handful of kinetic parameters need be known only for a small number of steps where the reaction may proceed via two or more routes (branch). Neglect of reverse reactions will also simplify the model dramatically (this is reasonable, at least in the current work, as most elementary reactions tend to be highly exothermic).39,40 We also assume that all branchings involving the same reaction classes do not differ in relative rate; this, too, significantly lessens the number of parameters required, as only the smallest member of the class needs be considered in detail. Ab initio data in the preceding sections indicate the validity of this premise, particularly for the important α- and β-chlorinated acetylene addition channels. Another important advantage is that these probabilistic models should benefit from a cancellation of errors, particularly when branching reactions are of the same class; this is especially useful as this approach is not designed for precise, quantifiable modeling results, but rather an early verification of the veracity of new reaction schemes, further increasing the ease of model

ki = αAi e−Ei +ΔE / RT

(3)

where α and ΔE are errors in A and Ei, respectively, unaccounted for in a TST treatment; we assume these are largely invariant within a class of similar reactions. The probability, P(i), that reaction i occurs is given by P(i) =

ki Ai e−Ei / RT αA e−Ei / RT eΔE / RT = ΔE /i RT = ∑j kj ∑j Aj e−Ej / RT ∑j Aje−Ej / RT αe (4)

where it is clear that, assuming all reactions are similar, the final probability is largely free of any systematic errors introduced by theoretical techniques. For example, low frequency vibrations can correspond to internal (hindered) rotational modes in weakly bound complexes, and should be treated as hindered rotors; TST treatments often ignore this effect, which can be substantial.102,103 However, these terms should largely cancel when rates are considered in a relative sense as they are generally applied as a correction factor to the harmonic oscillator-based vibrational partition function term.104 This cancellation of errors also suggests that a level of theory/ approximation may be used that is much lower than would be required in a full kinetic model requiring absolute, rather than relative, rate constants. This seems justified by the constant energy difference and similar pre-exponential factors between the α- and β-chlorinated modes of addition noted in Table 1 and Table 2, despite sometimes quite different absolute values between computational methods. 8654



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exponential factors for each route, indicates that a value of α = 0.6 is reasonable. Finally, the conversion of the chlorocyclobutadienes to vinylacetylenes presents numerous potential reaction branching possibilities. An initial survey of all H- and Cl-migrations required to initiate decomposition are given in Table 5 for the

The work in the preceding sections has offered counterexamples for a number of competing channels; as such, we have only a small number of branching routes that we must account for. Concerning vinylacetylene formation, while further alternatives may exist, the only set of pathways that were not readily removed by counter-example is the chloroacetylene dimerization channels. To construct a reaction probability tree, we consider first the major product branching steps in the formation of chlorinated vinylacetylenes along with branching probabilities (Scheme 1). The first branches involve the choice of the acetylene base, followed by choice of the second acetylene for dimerization. We assume that only C2HCl and C2Cl2 form from DCE and TCE respectively, in good agreement with our previous findings.38,39 We have weighted reaction branches with a probability p of reacting with C2HCl, and 1-p of undergoing C2Cl2 addition. The value of p is simply assigned by assuming the initial proportion of the parent ethylene reflects the instantaneous proportions of each acetylene; for example, the 75:25 C2HCl3:C2H2Cl2 system implies p = 0.25. While C2Cl2 addition is relatively straightforward, C2HCl exhibits additional branching as the acetylene group of the product may be either α- or β-chlorinated. We have demonstrated here and in previous works that, due to radical stabilization effects associated with chlorine, β-chlorinated addition of acetylene moieties to hydrocarbons is typically ∼20 kJ mol−1 lower in energy than the converse.38,40 At an approximate pyrolytic temperature of 1000 K, this energy difference is enough to slow a reaction by an order of magnitude. Denoting the probability of β-chlorinated addition q, we can estimate the value as q = =

Table 5. H- and Cl-Migration Barriers in Chlorocyclobutadienea E/kJ mol−1

→ → → →

187.1 N.A. (see text) 259.7 254.7

C1 C1 C2 C2

C2 C4 C1 C3

migration from

E/kJ mol−1

→ → → →

231.8 242.0 246.2 238.8

C3 C3 C4 C4

C2 C4 C3 C1

All energies, in/kJ mol−1, are derived from ZPE-corrected DFT/ B3LYP/6-31G(d) level calculations. a

simplest chlorocyclobutadiene; note that this species itself does not appear in our model as the underlying simplifying assumption is that relative barriers should extend readily to all members in a given reaction class. This demonstrates that Cl-shifts are appreciably lower in energy than are H-shifts; as such, these are the only shifts we will consider. Additionally, it is found that Cl-shifts only occur across CC (double) bonds, with C−C bond lengths shortening and CC bond lengths lengthening to double and single bonds, respectively, during optimization; that is, the C1 → C4 converts to the C1 → C2 shift in the course of the optimization. This further restricts the number of shifts one needs to consider when computing branching probabilities. Symmetry also reduces the number of unique shifts; as such, one finds that the two dichlorocyclobutadienes can, under these restrictions, only lead to a single dichlorovinylacetylene product each, thus no additional branching probabilities are ultimately required (see Scheme 1). There are, even after these restrictions, still three possible shift routes open to trichlorocyclobutadiene; these are demonstrated in Figure 6, along with shift barriers. In this case, explicit calculation was required, revealing that the Cl-shift toward the hydrogenated carbon is ∼10 kJ mol−1 easier than to a chlorinated site, presumably due to steric interactions. Labeling the shift to the chlorinated site with a probability β,

rate(β‐Cl) rate(β‐Cl) + rate(β‐H) [C2HCl]2 Ae−E / RT

[C2HCl]2 Ae−E / RT + [C2HCl]2 Ae−(E + 20)/ RT 1 = (1 + e−20/ RT )

migration from

(5)

This assumes both attack pathways have comparable preexponential factors regardless of absolute values (as supported by Table 2), and allows us to estimate the value of q to be 0.92 at 1000 K. Note that analogous values are in principle required for the reaction of C2HCl and C2Cl2, but, as all routes ultimately lead to the same intermediate (trichlorocyclobutadiene) anyway (see Scheme 1), this distinction is ultimately unnecessary. That said, the value of q used for the 2C2HCl reaction we would assume should hold equally well here. In addition to the attack orientation of the C2HCl moiety, the mechanism of conversion of the cycloprop-3-ene-methylene carbene-based intermediates into cyclobutadienes (see Figure 5) in the 2C2HCl system is also important. There are two distinctive rearrangement modes possible in which the radical moiety can bind either to the hydrogenated or chlorinated carbons. These are given probabilities α and (1-α) respectively. DFT/B3LYP/6-31+G(d)//HF/3-21+G(d) (ZPE values are unscaled) calculations show only a slight energy difference, favoring addition to the hydrogen site by ∼3 kJ mol−1 (again, we note such low levels of theory should be adequate given the cancelation of errors demonstrated by eq 4). An analogous calculation to that shown in eq 5, again assuming identical pre-

Figure 6. Cl-shift routes, and barriers to migration, available to trichlorocyclobutadiene. 8655



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Scheme 2. Probability Tree Fragment Depicting the Modification to Benzene Formation Channels to Allow “Failed” Diels− Alder Cyclization Pathways

Scheme 3. Probability Tree Fragment Depicting the Chances of Following Various Chlorinated Benzene Formation Channels

leading to branching probabilities of γ = 0.999 and δ = 0.995. This again makes the same assumptions inherent in eq 5. We now explore the branching associated with the acetylene dimerization analogues which depart from the Diels−Alder channel with a probability value denoted by ω (see Scheme 2). This is the probability that an interacting vinylacetylene/ acetylene pair will follow a non-Diels−Alder path instead of a Diels−Alder channel (the former arises naturally as the failed complete closure of the latter). As this scheme also shows, the parameters along this new pathway are very similar to those already used. Once we move down a non-Diels−Alder channel, we have a probability p or (1 − p) of encountering C2HCl or C2Cl2, respectively; if reaction occurs with C2HCl, it may add to the vinylacetylene through the hydrogenated or chlorinated carbons (probabilities q and (1 − q), respectively); once the acetylene has added, it is found that reaction proceeds without branching until aromatic-based species are formed. (The vinylcyclobutadiene in Scheme 2 ring closes, and the resultant Dewar-benzene ring opens to form the Diels−Alder cycloaddition intermediate structures, analogous to those formed following choices labeled ε and 1 − ε in Scheme 3). From this point, as these reactions are identical to those required in the rearrangement of Diels−Alder formed moieties, we again adopt the probabilities γ and δ (see Scheme 3). Consequently, only a single additional parameter, ω, is required. As eq 5 indicates, branching probabilities are heavily dependent on the energy difference between competing pathways. Our computational work also suggests that there is a significant decreased importance (due to steric hindrances) of the Diels−Alder transition states relative to the acetylene dimerization-like channels as Cl-content increases; we can model this here as a chlorine-dependent energy difference between a Diels−Alder and an acetylene dimerization channel. While this appears to be more a consequence of geometric

we can compute (with an analogous calculation to that in eq 5) an approximate branching probability of β = 0.12. Assuming benzenes grow from vinylacetylene seeds, the semiquantitative prediction of their formation can now be addressed. Complicating matters, in addition to analogues of the acetylene dimerization channels, benzene distributions via Diels−Alder processes must also be considered. An overview of the important branching steps is given in Scheme 2, which also introduces the branching between Diels−Alder and failed Diels−Alder (acetylene dimerization-like channels) with branching parameters specific to Diels−Alder transition states given in Scheme 3. Considering first the Diels−Alder channels, for a given vinylacetylene moiety the probability that C2HCl or C2Cl2 is encountered is, again, p or (1 − p), respectively. In scenarios where C2HCl is encountered, the reaction may branch depending on whether the hydrogenated or chlorinated carbon of C2HCl bonds to the vinylic carbon of vinylacetylene in the Diels−Alder cyclization transition state. Our previous work has found that this difference has little influence on the energy barrier,40 also shown by the values in Table 4, and assuming identical pre-exponential factors (justified in Table 2), this probability (denoted ε) can be taken as 0.5. Following this, two successive 1,2- H- or Cl-shifts are required to move one of the atoms from the double occupied carbon to the unoccupied site (see Scheme 3). Product branching can only occur when the doubly occupied site bears both a chlorine and a hydrogen, and is therefore the only scenario that one must account for. We have given the H-migration branches probabilities labeled γ and δ for the first (migration to an occupied carbon atom) and second (migration to an unoccupied carbon atom), respectively. Our previous work on chlorobenzene formation suggests40 that the chlorine shifts are higher in energy by ∼60 kJ mol−1 in the former, and ∼30 kJ mol−1 in the latter, 8656



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assuming either dimerization or trimerization of acetylenes. The reaction probability tree model implemented here is based fundamentally on such a model, therefore explicitly explaining this so far empirical relationship. As a consequence, modeled homologue yields also follow a binomial distribution when plotted as a function of the fraction of DCE to TCE present in the initial reaction mixture (see Figure 7). Modeled and

considerations (unrealistically long C−C bond lengths in attempts at finding Diels−Alder transition states) than barrier, it can, for the current purposes, be subsumed by an activation energy term if treated as entropic in origin in an isothermal situation. Therefore, modifying this equation to model branching between Diels−Alder and failed Diels−Alder channels (assuming the latter has an order of magnitude greater pre-exponential factor due to the stricter geometry constraints placed on a transition state requiring two bonds be formed simultaneously, in agreement with our previous transition state theory calculations)41 we derive 1−ω =

rate(Diels−Alder) rate(Diels−Alder) + rate(Failed Diels−Alder) [VA][ace]A e−E / RT

=

−E / RT

[VA][ace]A e + 10[VA][ace]A e−(E +ΔE)/ RT 1 = (1 + 10e−ΔE / RT ) (6)

where [VA] and [ace] represent the concentrations of the vinylacetylene and acetylene moieties respectively, E is the barrier to Diels−Alder cycloaddition, and ΔE the additional energy the failed cyclization channels require relative to the Diels−Alder transition state energy. Note that this can be negative, i.e., the failed cyclization channels can be preferred (as in highly chlorinated systems, for example). Therefore, as the barrier to the failed Diels−Alder channel is heavily dependent on the degree of chlorination, the probability ω should also depend on the degree of chlorination; this will be explored in the following section. D. Probability Tree Model Predictions. For ease of visual comparison between theory and experiment we adopt the device of plotting experimental chromatographic data alongside fitted theoretical curves of major products. The chromatographic peaks modeled tend to be rather asymmetric; chromatograms have therefore been simulated with modified Poisson functions of the form given in eq 7:105 ⎤n ⎡ k h(t ) = hmax e−k(t − tr)⎢1 + (t − tr)⎥ ⎦ ⎣ n

Figure 7. Total predicted and experimentally determined homologue yields of (top) vinylacetylene and (bottom) benzene congeners, as a function of the DCE/TCE ratio in the initial reaction mixture. Modeled (solid lines) and experimental (open symbols) data are scaled such that they reach the same maximum; dichlorovinylacetylene yields have been quartered for ease of comparison with the other congener yields.

(7)

The retention time of the fitted peak is given by tr, hmax is the peak height, and k and n are Poisson model parameters. The parameters tr, k, and n are derived exclusively from the shapes and positions of the experimental peaks.105 Thereafter, the peak height parameter hmax, is dictated solely by the predicted relative product yields from our model. Integration of eq 7 yields Area ≈ hmax

2πn k

experimental data are scaled such that the maximum of each curve coincides; dichlorovinylacetylene yields have necessarily been further divided by 4 such that the trichloro- and tetrachlorovinylacetylene yields can be plotted clearly on the same graph. It is clear that these predictions are in very good agreement with experiment for both vinylacetylene and benzene congeners. Somewhat less trivial is the accurate prediction of individual congener yields within a given homologue family. Examining vinylacetylenes first, experiment shows that under conditions where each homologue is favored, there should be two nearly equimolar dichlorovinylacetylenes formed and a single dominant trichlorovinylacetylene with two additional isomers in lesser (near-identical) abundances (Figure 1). Strict confirmation of congener identities is difficult without calibration standards or retention indices by which to identify

(8)

Thus, once n and k have been determined from the peak shapes, the relative height of the fitted curve is determined with eq 8 by equating relative areas to the fractional yields predicted by our probabilistic reaction tree approach. To aid comparisons, we have subsequently scaled the modeled profile such that the experimental and modeled peaks of the dominant congener are the same height. Model predictions are, in general, in very good agreement with experiment. Considering the broader conclusions first, we have previously noted that both vinylacetylene39 and benzene41 homologue families closely follow a binomial distribution 8657



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Figure 8. Predicted (top) trichlorobenzene and (bottom) tetrachlorobenzene congener yields as the energy difference between conventional and failed Diels−Alder pathways (ΔE), and consequently the branching probability ω, vary.

achieved with a barrier difference of 30 kJ mol−1, which is incidentally in agreement with explicit barriers for Diels−Alder and acetylene dimerization channels as we have explicitly computed previously,40 and in reasonable agreement with our highest level CCSD(T) results in Table 3 and Table 4. However, agreement becomes increasingly poor as the energy difference decreases (the failed Diels−Alder channels become increasingly accessible) suggesting less 1,2,3-C6H3Cl3 and predicting products are almost exclusively the 1,2,4-trichlorobenzene congener. This is also in very good agreement with our previous findings, which suggests Diels−Alder cycloaddition should dominate growth here.40,41 On the other hand, tetrachlorobenzene yields are at best fair when we assume that the failed cyclization reactions require 30 kJ mol−1 in excess of what is required in conventional cyclization channels, but becomes increasingly accurate when the relative barrier is decreased. This suggests increasing involvement of acetylene dimerization reactions in C6 growth. This is again in agreement with values in Table 4, noting in particular several Diels−Alder transition states failed to close altogether. Consequently, we can conclude that chlorobenzene formation in high concentration C2/C4 systems occurs primarily through Diels−Alder cyclization when reagents are in a low degree of chlorination, but is aided by an increasing contribution from failed cyclization channels as the degree of chlorination increases. Finally, we note that we have not considered the formation of nonaromatic C6 species in this work. We have previously shown that the important linear C6Cl6 species in particular is formed in an alternative branching of the failed Diels−Alder (acetylene dimerization) channel, and requires a Cl-radical addition to the carbon skeleton to provide facile product formation.40 However, in the partially chlorinated structures considered here, reaction with chlorine would almost certainly result in hydrogen abstraction rather than addition and rearrangement (Cl atoms are largely considered, in most kinetic models, to initiate H-abstraction only),65,66 and

the observed products. However, we can confirm a more circumstantial agreement. Unlike the predictions of the radical channels which predict a single isomer, the molecular routes predict two dichlorovinylacetylene isomers. Furthermore, these are in very similar abundances; with p = 1, we predict 58.4% and 41.6% of the C4H2Cl2 yield to be 1,2-dichloro and 1,4dichlorovinylacetylene, respectively, in agreement with the relative abundances seen experimentally. Similarly, the predictions regarding trichlorovinylacetylenes (again erroneous under the conventional radical model, which suggests two congeners of comparable abundance; see Figure 3) are very well matched in the semiquantitative analysis of the molecular pathways, as modeled using our reaction probability approach. Model predictions indicate 76%, 12%, and 12% for the 1,2,4-, 1,1,2-, and 1,1,4-trichlorovinylacetylenes, respectively, in good agreement with the experimental finding of one dominant isomer with two lesser, but non-negligible, isomers of similar abundances. The predictions of benzene yields build on those of the vinylacetylenes (and therefore any error here will propagate into the benzene model). Yield predictions were made not only as a function of the initial conditions (values of p) but also as a function of ΔE in eq 6, or equivalently ω. The value of ΔE is expected to be high (and therefore ω approaches 1, thereby shutting down non-Diels−Alder channels) in systems with a lower degree of chlorination based on the results of the Theoretical Results Section B. Here, we found barriers and steric factors favor a Diels−Alder channel under such a scenario. Decreasing ΔE to zero (ω → 0.5) will make Diels− Alder and acetylene dimerization-based channels similarly probable, that is, approximate a certain extent of failure of some Diels−Alder transition states to close appropriately, expected as chlorine content increases. To explore this in detail, we present the trichloro- and tetrachlorobenzene congener profiles as this barrier is varied (see Figure 8). Considering the trichlorobenzenes first, we see that very good agreement is 8658



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a decrease in the lifetime of vinyl radicals, predicting a change from radical to nonradical process as the degree of chlorination increases. Not only does this agree with our earlier conclusion, that radical processes are inoperative, but also describes the increasing reactivity of the acetylenes with increasing chlorine content. This last point is, in fact, poorly described by a competing molecular processes involving vinylidene, which therefore also suggests the inoperability of these channels (at least in the mid- to fully chlorinated systems that are the focus of this work). Turning to C6 formation, analogues of these acetylene dimerization processes exist, but Diels−Alder cycloaddition is also possible now. Explored at a variety of computational levels, Theoretical Results Section B shows Diels−Alder cycloaddition has a relatively low barrier (on the order of the barriers required for C2HCl dimerization, which we argue is an active C4 formation channel). Failed Diels−Alder channels, at least in lower degrees of chlorination, possess somewhat higher barriers in midchlorinated systems; however, our highest level, CCSD(T)/6-31+G(d)//B3LYP/6-31+G(d), suggests this barrier lowers as the degree of chlorination increases. More importantly, ring closure transition states cannot be located for sterically crowded Diels−Alder processes, leading naturally to acetylene dimerization analogues. Thus, computational results strongly argue for Diels−Alder cycloaddition (suggested active in some nonchlorinated systems)99−101 but a transition to acetylene dimerization-like processes as the number of chlorine substituents starts to exceed hydrogen; eventually, failed ring closure processes dominate the most highly chlorinated systems. These arguments, we feel, provide a strong basis on their own for the efficacy of nonradical routes in chlorinated systems. However, a simplified analogue of kinetic modeling, the construction of a reaction probability tree, can provide semiquantitative congener predictions that provide stronger support again for these pathways. Described and tested in the Theoretical Results Section D, we find very good predictions for vinylacetylene congeners. Assuming only a molecular acetylene dimerization channel, passing through a chlorinated cyclobutadiene intermediate before leading to the observed vinylacetylene product, we predict two dominant C4H2Cl2 isomers, and one dominant C4HCl3 isomer, in very good agreement with experiment. Note, too, that radical channels predict the opposite (one C4H2Cl2 and two C4HCl3 isomers); see Figure 3. Additionally, this mechanism provides a natural explanation for the thus-far empirical observation that the yields of C4H4−xClx products can be modeled with a binomial distribution assuming bimolecular reaction of C2HCl/C2Cl2, with the concentrations of each determined by the relative concentrations of their respective precursors (see Figure 7). However, while successful rationalization of the major isomer count and the modeling of C4 homologue family yields provide good evidence for the proposed channels, we lack explicit isomer identification in our experimental chromatograms. As with the vinylacetylenes, very good agreement between experiment and theory is found with the chlorobenzenes. The underlying model, an extension of the acetylene dimerization channel for C4 formation gives a natural explanation of the empirical fitting of homologue yields to an initially unspecified acetylene trimerization model (see Figure 7). Previous studies confirm40,41 that, unlike the C4/C2 radical-molecule channel, the molecular dimerization route does indeed predict aromatic (as opposed to fulvene) structures dominate, and provide a

therefore to product degradation. Consequently, C6Cl6 isomers are the only set of compounds where Cl-atom aided isomerization to nonaromatic products is likely to be possible. While in principle these processes could be described quantitatively by this approach, as they are not likely to be a major product forming channel in general, we have not considered them here. However, it is important to note that our previous models show that all C6Cl6 isomers are very well described solely with the acetylene dimer channel, which falls in line with findings here: increased chlorine content leads gradually from Diels−Alder to failed Diels−Alder (acetylene dimerization) channels.

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DISCUSSION AND CONCLUSIONS The high-temperature chemistry of partially chlorinated systems is extremely rich; in addition to adopting the same numerous carbon skeletons of the products and intermediates found in hydrocarbon systems, one must now account for varying degrees of chlorination and the associated sets of congeners. The most definitive tests of reaction mechanisms rely on the construction of kinetic models; however, this is a formidable challenge in the poorly studied chlorinated systems given the number of products one must account for. Focusing model direction on only the most likely channels first would greatly reduce the complexity of this problem. Direct analogy with hydrocarbon systems is a reasonable first guess, and indeed has been attempted12−15 but we have recently suggested that a more accurate treatment shows such channels are almost certainly inadequate. Thus, this study has been performed to narrow the focus of future kinetic work (although we are still restricted currently to relatively small systems such as vinylacetylene and benzene congeners). The most effective first approach is to proceed by counterexample; the complicated product distributions can be used to our advantage here, as all congeners yields should be modeled by only a single model, or a small subset of possible reactions. First, it seems radical-carried channels can be ruled out: the wrong number of isomers in each homologue family is predicted for C4 species following conventional channels; regarding C6 formation, conventional 2C3 radical−radical pathways appear inoperative given the absence of odd-carbon products; and C4/C2 radical-molecule channels predict almost exclusive formation of fulvene structures and exhibit little capacity to describe the formation of the C6Cl6 isomer perchlorohexa-1,5-dien-3-yne during TCE pyrolysis. While this approach removes a large number of possible reactions from consideration, it is not sufficient to assume that as the radical mechanisms tested do not fit the experimental evidence, our previously hypothesized nonradical channels must therefore be operative by fiat. Instead, confirmation requires rigorous testing showing that these channels hold up in the details. We have some positive evidence implicating acetylenes in C4 growth particularly; acetylene based induction periods and controlled congener formation in chlorinated diacetylene growth strongly suggest acetylene dimerization (the diacetylenes likely forming analogously to or, by HCl elimination, subsequently from the more congener rich vinylacetylene species). However, a more general approach to assessing acetylene molecular channels is to determine energetic feasibility. Concerning vinylacetylene formation, Theoretical Results Section A demonstrates direct acetylene dimerization processes experiences a significant barrier lowering as the degree of chlorination increases. Concomitant with this is 8659



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data (necessary for complete knowledge of the importance of certain reaction pathways) but, unlike a full kinetic model, has only a few parameters. For example, the reaction networks in the current study have (see the Supporting Information) on the order of ∼120 unique species and ∼400 individual reaction pathways (requiring on the order of 1000 rate parameters). The reaction probability tree model reduces this to 81 individual pathways requiring only 8 branching parameters. As noted, product yields in this simple model are surprisingly well described given the approximations made here, and the chemistry elucidated here is consistent with in-depth studies by way of ab initio studies and explicit kinetic modeling. As such, given the success of this approach we have extended this technique to the study of chlorinated phenylacetylenes, naphthalenes, acenaphthylenes, and biphenyl species in subsequent works for which the detailed studies performed for vinylacetylene38,39 and benzene38,40,41 congeners is no longer feasible; these results will be provided in future publications.

reasonable and accessible route to perchlorohexa-1,5-dien-3yne, in line with experiment. The current work goes further, confirming that the model is capable of extremely faithful congener-specific modeling, and in doing so suggests additional branching hitherto only intimated in our previous works. Allowing for incomplete closure of the Diels−Alder transition state initiating the acetylene dimerization-like channel, which we speculated was likely to become increasingly important as the degree of chlorination increased (and is the sole channel in C6Cl6 formation) we find extremely pleasing agreement between theory/experiment can now be reached with C6H2Cl4 (Figure 8). C6H3Cl3 predictions become increasingly poor under the same conditions, suggesting agreement is unlikely to be merely coincidental. (That is, our expectation based on computational results is for essentially exclusive Diels−Alder cycloaddition in the C6H3Cl3 system, with acetylene dimerization processes becoming more important). It should also be noted that the benzene model builds on vinylacetylene predictions; thus, while direct congener-specific agreement cannot be assessed, the very good agreement attained for C6 products indirectly confirms the fidelity to congener-specific predictions in the C4 formation channels. The deviations between these and accepted mechanisms should also be discussed, particularly regarding nonchlorinated species to which these mechanisms naturally extend and for which radical-based chemistry is firmly supported. The reason appears 2-fold; first, C−Cl bond cleavage energies are considerably lower than C−H bond energies, and therefore the lifetime of key chlorinated radicals is necessarily many orders of magnitude lower in chlorinated intermediates. As such, reaction-carrying radicals are not likely to participate as extensively as in nonchlorinated systems. Previous works were restricted to crude approximations for the C−Cl bond scission energies in key radicals, which led to barriers far higher (and lifetimes far longer)12,15 than more recent and sophisticated calculations and measurements suggest. As such, the role of radicals in the pyrolysis of small chlorinated hydrocarbons appears to have been overestimated. Additionally, chlorine atoms in the structure of key species appears to stabilize biradicals and carbenes formed in the nonradical channels,38−40 lowering the barriers of important steps relative to those found on a nonchlorinated PES.84,106,107 Consequently, we anticipate that as the degree of chlorination decreases, the importance of nonradical channels is likely to diminish, playing a negligible role (chemistry now favors radical-carried processes) once nonchlorinated species are explored. Aside from a mechanistic study, we have a second aim in this work; namely to introduce and benchmark a far less time- and labor-intensive alternative to kinetic modeling of as-yet poorly understood systems by which to analyze complex reaction systems with many competing channels. Often, several of the potential pathways are found to be unimportant, but only after they have been fully accounted for and simulated. Viewing the system as a probability tree removes the need to measure or compute rate constants for any elementary reactions that do not represent a branching point of the system and, by way of cancellation of errors (as branching probabilities are computed from relative rate constants), allows a number of expense-saving approximations to be applied. Additionally, the use of relative rates suggests that branching probabilities need only be computed once for each class, and not for each individual example. As a consequence, we have a model that, unlike a simple PES search, returns reactant/intermediate concentration

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ASSOCIATED CONTENT

* Supporting Information S

Cartesian coordinates of all stationary points considered and reaction probability trees of all reactions relevant to the formation of chlorinated vinylacetylene and benzene congeners discussed in this work. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Address: School of Chemical Sciences, University of Auckland, Private Bag 92019, Auckland, New Zealand; Tel: +64 9 923 8302; E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the University of Auckland, the Marsden Fund and Lottery Science for grants towards equipment. We also gratefully acknowledge the University of Auckland for financial support of Grant McIntosh through a Guaranteed Doctoral Scholarship. Finally, we are also very grateful for the support provided by the Computational Chemistry Group at the School of Chemical Sciences, The University of Auckland.

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ABBREVIATIONS DCE, dichloroethylene; HACA, hydrogen-abstraction acetylene addition; IR LPHP, infrared laser powered homogeneous pyrolysis; PAH, polycyclic aromatic hydrocarbon; PES, potential energy surface; (RC-)TST, (reaction-class) transition state theory; TCE, trichloroethylene; SPE, single point energy; ZPE, zero point energy

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REFERENCES

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