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Early data exist for polymethylene (PM), prepared by Lewis acid-catalyzed polymerization of diazomethane, that is in principle even less branched than HDPE; however, these materials have typically not been well characterized.
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(b) Data at 480 °C from ref 7a are not included in Figure 1 because of uncertainty about the conversion factors from area % to mol %.
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0344147655
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A similar disparity between GC and FIMS data would result if the loss of transfer efficiency for higher-c products in GC runs were highly selective for condensation/sorption of ENEs compared with ANEs.
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n, additional steps involving positional isomeric radicals are of course involved.
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150
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In step 1b, "Y" is some irregularity such as an allylic C-C bond adjacent to unsaturation, a branch point, a head-to-head rather than head-to-tail sequence, trace peroxides incorporated during radical polymerization, or terminal initiator residues.
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156
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0344579091
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The hypothesis of exclusive nonchain in-cage operation of steps 1, 6a, and 6b (ref 44) and the accompanying suggestion that transfer is not important in "static" systems but may become so in "flowing" systems contain the unlikely implicit assumption that macroscopic mixing can disrupt a molecular-level cage.
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85052276618
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•.
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Inversely, the mere presence of monomer in the volatiles does not diagnose UZ because it can also be formed in step 4d.
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165
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85052274905
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note
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• and allyl radical were kinetically equivalent.
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166
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0345010096
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note
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i" term (ref 40a).
-
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167
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0345441180
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note
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•, which has typically been ignored in the literature, must also be considered since it will be formed in equivalent amounts in step 1 and exclusively by step 3b for quaternary-center polymers.
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168
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0344147651
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note
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169
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0345441179
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0344579090
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• would be the more prevalent radical for termination (see text).
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176
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0345010095
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note
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While they used backbone rather than TV end-group allylic homolysis as the initiating event, they included specific (but not quantitatively stated) rate constant enhancement factors both for abstraction of allylic hydrogens and for β-scission steps that generated allylic radicals.
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177
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0344147649
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i-2)].
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(a) Further indirect evidence for long KCL at least for allylic end-group homolysis is the only modest selectivity to propylene which should be the ultimate transfer product from allyl radical (refs 47a, 56, and 63a). Willmott (ref 7a) did suggest a correlation between the modest amount of propylene formed and the extent of terminal unsaturation in the starting PE.
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242
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0345441164
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note
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This idealized statistical result is unlikely to be fully rigorous for small c values for which specific mechanistic anomalies associated with end groups would become nonnegligible.
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243
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0344579083
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note
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In contrast to the "smooth" curves in Figure 2 for the range c ≈ 12-25, plots (not shown) of data from Faravelli and coworkers (ref 30b), limited to the ENEs from HDPE at 600 °C (x = 1) and 500 °C (x < 1), show significant minima centered at c = 17, which were not predicted by their model (see text). The ANE:ENE:DIENE patterns described in Table S4 do not suggest any unusual maxima in ANEs or DIENEs to counteract these atypical minima.
-
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244
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245
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All time units and concentrations are relative for assumed first-order behavior; all derived values of s are also only of relative, not absolute, significance for this scaling exercise.
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246
-
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0344579071
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note
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Mole and weight fraction calculations assume that the molecular mass of P(n) scales as n.
-
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247
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85052277688
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note
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18n).
-
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248
-
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0344147639
-
-
note
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1/2 = (In 2)/18 = 0.0385.
-
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249
-
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0345010078
-
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note
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This scaling result is qualitatively the same as that portrayed in Figure 2 of ref 35a.
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252
-
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0344579070
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note
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evap ∝ -n, led to qualitatively identical trends in simulation output.
-
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253
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0345010077
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note
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From pyrolysis-FIMS results (see above), Lattimer (ref 78) proposed BB with a very large number of serial shifts required before β-scission; e.g., the maximum near c = 36 would require 8-9 shifts.
-
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255
-
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0344147640
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-
2-5 gases when T was increased from 415 to 600 °C and suggested that it was largely a primary ("early") product because it did not increase further as t at 600 °C was increased from 1 to 10 min; however, the pyrolysis was likely already complete after the 1 min run.
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s• is reasonable, a source of selectivity for attack adjacent to a branch site is not obvious.
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263
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0344579062
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Only 2-propyl, 2-butyl, and 3-pentyl are inaccessible for x = 4-6.
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264
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0344147635
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Expressions given in three-parameter Arrhenius format to accommodate curved Arrhenius plots over large T ranges were converted to two-parameter format at a median pyrolysis T of 773 K; the error introduced for k values then calculated at, say, 673 or 873 K, is trivial compared with the likely absolute errors.
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265
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0344147634
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773 would become 3.9, in perfect accord with thermochemical balance. Therefore we made this small adjustment, arbitrarily divided between log A and E.
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β,733(s,p) for 2-pentyl, which is 2.5-fold larger than predicted by the Yamauchi expression (ref 172).
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10.20) exp(-17000/RT) for 2-octyl → 4-octyl at much lower T (385 K) (ref 180), which would correspond to a 4.5-fold larger value if extrapolated to 773 K.
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note
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14(p,s) does not.
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287
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0345441153
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1.3-fold higher still; calculations of E at the level of theory used were not considered chemically reliable.
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Interestingly, the probabilities increased again for x = 9-14 to small but nonnegligible values. This approach also suggested that an alkyl branch on the chain modestly promotes the achievement of the cyclic transition state.
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0344147630
-
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note
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All the models and calculations noted conclude that 1,3-shift is of trivial importance because of the major increase in strain associated with a four-membered ring. The ethyl SCBs in PE are generally ascribed to an indirect mechanism (ref 5b) not involving a 1,3-shift, although this is not universally accepted (ref 60).
-
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303
-
-
0345010069
-
-
note
-
14.
-
-
-
-
306
-
-
0345441148
-
-
note
-
-4T (ref 197); extrapolation of this correlation leads top values that are ≈0.06 units higher near 750 °.
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307
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33947479449
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(b) Chiang, R.; Flory, P. J. J. Am. Chem. Soc. 1961, 83, 2857. Gubler, M. G.; Kovacs, A. J. J. Polym. Sci. 1959, 34, 551. Quinn, F. A., Jr.; Mandelkern, L. J. Am. Chem. Soc. 1958, 80, 3178.
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note
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313
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0345441151
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Evidence for diminished reactivity of polystyrene and polypropylene in solution toward the tert-butoxy radical, a moderately chemically activated example, compared with small-molecule models remains surprising. The authors of this study (ref 201) considered a true "polymer effect" in which hydrogens in the interior of a polymer coil were shielded from the attacking radical; such an "effect" is again not likely relevant to a melt.
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314
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Niki, E.; Kamiya, Y. J. Org. Chem. 1973, 38, 1403. Niki, E.; Kamiya, Y. J. Chem. Soc., Perkin Trans. 2 1975, 1221.
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0344147629
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P (ref 204b), and similar differences have been claimed for styrene (ref 204c).
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Zetterlund, P.B.1
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324
-
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0344579049
-
-
note
-
If the PnR involved in forming PENEn happened to be a near-end PmR (formed either by direct transfer from P, 1,x-shift within PnR, or further transfer between PnR and P), there would be an added contribution from the resulting ΣENEr and ΣPENEm that is not included in this definition. However, for large MW and hence m ≪ n, this correction is trivial and any ENEs so formed would be statistically distributed without any of the specificity characteristic of BB.
-
-
-
-
325
-
-
0344579055
-
-
note
-
β(s,Me).
-
-
-
-
326
-
-
0344579056
-
-
note
-
1,x-Shifts and β-scissions in both directions are included in this generic ratio, although some of these processes may not be structurally allowed for small m.
-
-
-
-
327
-
-
0345441146
-
-
note
-
The chosen lower limit of c = 3 purposely excludes the ENE2Z formed from UZ, and the chosen upper limit of c = 20 minimizes perturbations caused by the truncation of the PmR series at m = 30.
-
-
-
-
328
-
-
0344147624
-
-
note
-
-1) at 500 °, and hence the differences will be slightly larger/smaller at lower/higher T.
-
-
-
-
329
-
-
0344147625
-
-
note
-
1x values were characterized by a major increase in the amount of truncation as the population of PmR with m > 30 became for the first time nontrivial.
-
-
-
-
330
-
-
0344147626
-
-
note
-
16 set to zero of course gave even sharper maxima. However, minor amounts of volatiles were still formed at other than the "magic" c values; these are derived from successive formation of Ar1R, Ar6R, ... and β-scission of the latter.
-
-
-
-
331
-
-
0345441147
-
-
note
-
Because of the truncation at c = 25, the actual "wt % RS" will be somewhat larger because the RS contribution extends further toward higher c values than does the BB contribution. For the most conservative assumption that no BB products occur for c > 25 (the simulation begins to become statistically unreliable at this point because of the truncation at m = 30), the actual wt % RS values over the c range to 1-100 (the RS contribution becomes vanishingly small for c > 100) would be 32.6, 64.3, and 77.1 wt % rather than 25, 50, and 75 wt %.
-
-
-
-
332
-
-
0029329141
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Ranzi, E.; Faravelli, T.; Gaffuri, P.; Sogaro, A. Combust. Flame 1995, 102, 179. Ranzi, E.; Dente, M.; Pierucci, S.; Biardi, G. Ind. Eng. Chem. Fundam. 1983, 22, 132.
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0344579054
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note
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Numerous other sources for rate constant assignments are available (ref 215), including several used to model the pyrolysis of hexadecane (refs 162d, 202, and 216), but none provide a complete set.
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Ristori, A.1
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0035795515
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Doue, F.; Guiochon, G. J. Chim. Phys. Physiochim. Biol. 1968, 65, 395. Doue, F.; Guiochon, G. Can. J. Chem. 1969, 47, 3477, Depeyre, D.; Flicoteaux, C. Ind. Eng. Chem. Res. 1991, 30, 1116, Khorasheh, F.; Gray, M. R. Ind. Eng. Chem. Res. 1998, 32, 1853. Ristori, A.; Dagaut, P.; Cathonnet, M. Combust. Flame 2001, 125, 1128. Watanabe, M.; Adschiri, T.; Arai, K. Ind. Eng. Chem. Res. 2001, 40, 2027.
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Watanabe, M.1
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346
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0345010062
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note
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exp = 0.082, and v = 0.110 for Phillips HDPE are not likely statistically different, given our derivation of the values from reading graphical data from the original publication.
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347
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0345010061
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note
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1x ratios. For example, repeating the exercise in Table 7 for case 3 in Table 6, that with the highest selectivity for 1,5-shift, would give the best match at of course a higher proportion of unselective RS, specifically 84 wt % RS with s ≈ 0.072.
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348
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0345441139
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note
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As a possible example of the latter phenomenon for polypropylene, see ref 78.
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