Energy & Fuels 2006, 20, 257-261
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Steric Effects on Diffusion into Bituminous Coals John W. Larsen* and Doyoung Lee The Energy Institute, 209 Academic Projects Building, The PennsylVania State UniVersity, UniVersity Park, PennsylVania 16802-2303 and The Department of Chemistry, UniVersity of Tennessee, KnoxVille, Tennessee 37916 ReceiVed June 23, 2005. ReVised Manuscript ReceiVed September 21, 2005
The reactions of maleic anhydride, cis-maleate esters, and acetylenedicarboxylate esters with Pittsburgh No. 8 or Illinois No. 6 coal using o-xylene or o-dichlorobenzene solvent are diffusion controlled. Diffusion is Fickian in all cases. The measured activation energies are between 5.4 and 7.6 kcal/mol. Diffusion rates decrease slowly with increasing alkyl chain length and sharply with branching. Diffusion rates are slightly faster with o-xylene than when o-dichlorobenzene is used.
Introduction Diffusion rates must be considered in any reaction of solids because diffusion may limit both the rate and the extent of reaction. Diffusion through polymers is often very sensitive to molecular size and shape.1 Because of this, diffusion in coals has received some attention but remains largely uncharacterized. Most attention has been given to measurements of coal swelling rates as swelling fluids move into the coal. The resulting expansion of the coal particles is easily measured. Less work has been done on the diffusion of reactive molecules into coals, though it is this molecular diffusion that is often most important for chemical reagents reacting with coals. In this paper we address the diffusion rates of a set of dieneophiles into a pair of bituminous coals. The mathematics of diffusion into coals are well established.2,3 The two extreme cases of diffusion into coals are Fickian and Case II. In Case II diffusion the rate-determining step is movement (relaxation) of the coal’s macromolecular chains. There is a sharp boundary between swollen coal containing the penetrant and the unswollen coal. The concentration gradient is sharp, almost a step function. The mass uptake is linear in time if the sample is a slab. In Fickian diffusion the ratedetermining step is movement of the penetrant through the coal and the concentration gradient is not steep. The mass increase follows the square root of time for a slab sample. The mass increase due to diffusion of a penetrant into a coal follows the general equation
Mt/M∞ ) ktn
(1)
where Mt is the mass increase at time t and M∞ is the mass increase at equilibrium. For Fickian diffusion n ) 1/2 for diffusion into a slab and n ) 0.43 for diffusion into a sphere. For Case II diffusion into a slab n ) 1.0 and for diffusion into a sphere n ) 0.85. When n lies between these limits a mixture of Fickian and Case II diffusion often called anomalous transport (1) Barens, A. R.; Hopfenberg, H. B. J. Membr. Sci. 1982, 10, 283303. (2) Brenner, D.; Hagan, P. S. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1985, 30 (1), 71-82. (3) Ritger, P. L.; Peppas, N. A. Fuel 1987, 66, 815-826.
is assumed to occur. A plot of log Mt/M∞ vs t has slope n and is often used to diagnose the diffusion method. The rates of many reactions of coals are limited by the rate of diffusion of a reacting molecule into the coal.4 To understand reactions of coals and especially to design methods for carrying out coal reactions it is necessary to know the limitations that limited diffusion places on reactions of coals. The goal of this work is to add to our understanding of Fickian diffusion into coals. Such understanding, in addition to being necessary for rationally designed (as distinct from Edisonian) coal reaction chemistry, may provide insight into coal physical structure and interactions. There is not space here for a complete review of diffusion in coals. A brief summary of the diffusion rates of pyridine into coals, usually obtained by measuring the time dependence of coal swelling, will reveal some of the trends and complexities. Different materials have different swelling rates5 as do different density fractions separated by density gradient cantrifugation.6 Heating coals before making pyridine diffusion measurements has complex effects on diffusion rates7 or slows diffusion and increases the activation energy for diffusion (Ea).8 Coals that have been pyridine extracted before swelling exhibit faster swelling (diffusion) rates9,10 than unextracted coals and lower activation energies.10 The variation of swelling rate with coal rank has been investigated several times. Diffusion rates have been reported to show no rank dependence9,11 and to increase with increasing rank.12 There is general agreement that pyridine diffusion in low-rank coals is either Fickian or close to Fickian5,11,12 and as rank increases the importance of Case II (4) Larsen, J. W.; Green, T. K.; Choudhury, P.; Kuemmerle, D. W. AdV. Chem. 1981, 192, 277-291. (5) Shibaoka, M.; Stephens, J. F.; Russell, N. J. Fuel 1979, 58, 515522. (6) Gao, H.; Artok, L.; Kidena, K.; Murata, S.; Miura, M.; Nomura, M. Energy Fuels 1998, 12, 881-890. (7) Olivarse, J. M.; Peppas, N. A. Chem. Eng. Commun. 1992, 115, 183204. (8) Suuberg, E. M.; Otake, Y.; Deevi, S. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 1988, 33 (1), 387-394. (9) Barr-Howell, B. D.; Peppas, N. A.; Winslow, D. N. Chem. Eng. Commun. 1986, 43, 301-315. (10) Ndaji, F. E.; Thomas, K. M. Fuel 1993, 72, 1531-1535. (11) Ndaji, F. E.; Thomas, K. M. Fuel 1993, 72, 1525-1530. (12) Otake, Y.; Suuberg, E. M. Fuel 1989, 68, 1609-1612.
10.1021/ef0501851 CCC: $33.50 © 2006 American Chemical Society Published on Web 10/21/2005
258 Energy & Fuels, Vol. 20, No. 1, 2006
diffusion increases.13 The activation energy for diffusion decreases with increasing rank12 or increases with increasing rank.13 Initial coal swelling is anisotropic,6,14,15 but we have been unable to find reported measurements of diffusion parallel and perpendicular to the bedding plane. Nuclear magnetic resonance (NMR) imaging measurements of pyridine diffusion into a high volatile A bituminous coal particle demonstrates Case II diffusion.16 The kinetics of pyridine diffusion out of swollen Illinois No. 6 coal, also measured by NMR, are Fickian with a large rate decrease when about one-half of the pyridine has been lost.17 These NMR results are consistent with diffusion into glassy coal and diffusion out of a rubbery coal-pyridine system. There are several criteria for choosing a reaction to follow. First, it must be possible to follow the reaction with coals readily. It is desirable to use a reaction whose rate is insensitive to changes in solvent. In this study we use the reaction between coals and dieneophiles. The most studied example of this reaction is the addition of maleic anhydride to coals.18 This reaction remains puzzling because the evidence supports the occurrence of a Diels-Alder reaction between diene systems in the coal with the maleic anhydride, but no coal structure contains enough reactive diene systems to explain the amount of maleic anhydride incorporated. A careful 13C NMR study and IR studies by several research groups show that the maleic anhydride carbon-carbon double bond is destroyed during the reaction.18,19 This would occur during a Diels-Alder reaction. A polymerization reaction would also destroy the double bond and has been suggested.20 Maleic anhydride does not readily form a homopolymer but does readily form copolymers with olefins.21 The report20 that the maleic anhydride-coal adduct loses CO2 readily is consistent with polymer formation. Many maleic anhydride copolymers lose CO2 at relatively low temperatures.22 Olefinic systems can be alkylated by maleic anhydride by an ene reaction, but this reaction is unknown with alkylaromatics or the more attractive possibility phenols.18 Alkylaromatics are alkylated at the benzylic position by maleic anhydride in a radical reaction that is initiated by peroxides or light.23 The reaction between maleic anhydride and coals occurs in the dark (vide supra) and with Argonne premium coals that are free of peroxides. The radicals in coals are not very efficient polymerization initiators24 and are unlikely to initiate benzylic alkylation. Finally, two molecules of maleic anhydride add photochemically to benzene.25,26 The first molecule adds 1,2 in a photochemical process, and this is followed by a 1,4 addition of the second molecule. Coals (13) Hall, P. J.; Thomas, K. M.; Marsh, H. Fuel 1992, 71, 1271-1275. (14) Brenner, D. Fuel 1984, 63, 1324-1328. (15) Larsen, J. W.; Flowers, R. A., II; Hall, P. J.; Carlson, G. Energy Fuels 1997, 11, 998-1002. (16) Cody, G. D.; Botto, R. E. Energy Fuel 1993, 7, 561-562. (17) Hou, L.; Cody, G. D.; French, D. C.; Botto, R. E.; Hatcher, P. C. Energy Fuel 1995, 9, 84-89. (18) Larsen, J. W.; Quay, D. M.; Roberts, J. E. Energy Fuels 1998, 12, 856-863 and references therein. (19) Zheeryakova, G. I.; Kochkanyan, R. O. Khim. TVerd. Topl. 2000, 5, 3-7; Chem. Abstr. 2000, 134, 103014. (20) Stephens. J. F. Unpublished work cited in ref 5. (21) Trivedi, B. C.; Culbertson, B. M. Maleic Anhydride; Plenum Press: New York, 1982. (22) McNeill, Polishchuk, A. Yu.; Zaikov, G. E. Polym. Degrad. Stab. 1992, 37, 223-232. McNeill, I. C.; Ahmed, S.; Gorman, J. G. Polym. Degrad. Stab. 1999, 64, 21-26. (23) Bickford, W. G.; Fisher, G. S.; Dollear, F. G. Swift, C. E. J. Am. Oil Chem. Soc. 1948, 25, 251-254. (24) Flowers, R. A., II; Gebhard, L.; Larsen, J. W.; Silbernagel, B. G. Energy Fuels 1992, 6, 455-459. (25) Angus, H. J. F.; Bryce-Smith, D. J. Chem. Soc. 1960, 4791-4795. (26) Grovenstein, E., Jr.; Durvasula, V. R.; Taylor, J. W. J. Am. Chem. Soc. 1961, 83, 1705-1711.
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are not transparent to UV light, so this reaction is not possible within coals. The existence of “charge-transfer” interactions between maleic anhydride and coals has been suggested27 but is not a reasonable explanation. First, the HOMO-LUMO gap between maleic anhydride and the aromatic units in coal is too large for stabilizing charge transfer to be possible.28 The equilibrium constant for formation of the charge-transfer complex of maleic anhydride with pyrene29 (CH2Cl2 solvent) is 18, with anthracene30 (CHCl3 solvent) it is 2, and with mesitylene31 (CCl4 solvent) it is 3.4. These small equilibrium constants contradict the proposed27 existence of strong coal-maleic anhydride charge-transfer complexes. The identity of the electron donor in coal has never been specified in the papers proposing a stable charge-transfer complex between maleic anhydride and coals. If electrons are transferred to maleic anhydride, the 13C chemical shifts of all the sp2 carbons will change significantly. The chemical shifts of the carbonyl carbons are in the expected positions for a saturated anhydride,18 and so are the IR bands.18 This conclusively rules out strongly stabilizing charge transfer between coals and maleic anhydride. Most complexes that undergo charge-transfer excitations (promotion of an electron from the HOMO of a donor to the LUMO of a complexed acceptor) are not stabilized by charge-transfer interactions.32 Maximum stabilization will occur when the HOMO of the donor and the LUMO of the acceptor are of identical energy and drops sharply as they diverge in energy.33 Ironically, one paper27 claiming the existence of strong coalmaleic anhydride charge-transfer complexes contains data that strongly support a Diels-Alder reaction rather than some of the other possible reactions enumerated above. The experiment done was to react coal with maleic anhydride under DielsAlder conditions and then Soxhlet extract the product with various solvents for long times. Maleic anhydride and maleate esters were found in the extracting solvent. Because the DielsAlder reaction is reversible, this is as expected. Warming the adduct and removing the maleic anhydride to shift the equilibrium are ideal conditions for reversing the reaction. Most of the other possible reactions between maleic anhydride and coals are not readily reversible. This data set, rather than evidence against the occurrence of the Diels-Alder reaction, is evidence that the Diels-Alder is the most likely of the possible reactions so far considered. The other possibility is another reversible reaction that destroys the maleic anhydride double bond. Spectral data, both NMR and IR, are conclusive that the maleic anhydride C-C double bond is converted to a C-C single bond during its reaction with coals. Any explanation must include replacing this double bond by a single bond. Infrared and 13C NMR data rule out ester formation.18 There are several other possible chemical reactions that might do this, but only two require serious consideration: the Diels-Alder reaction and a radical addition reaction, either benzylic addition or copolymerization. The reactivity of the radicals naturally occurring in coals has not been sufficiently studied. We do not know (27) Nishioka, M. Energy Fuels 1991, 5, 523-525. (28) Larsen, J. W. Prepr. Pap.sAm. Chem. Soc., Div. Fuel Chem. 2000, 45 (1), 181-184. (29) Merrifield, R. E.; Phillips, W. D. J. Am. Chem. Soc. 1958, 80, 27782782. (30) Andrews, L. J.; Keefer, R. M. J. Am. Chem. Soc. 1953, 75, 37763779. (31) Barb, W. G. Trans. Faraday Soc. 1953, 49, 143-148. (32) Foster, R. Organic Charge-transfer Complexes; Academic Press: New York, 1975. (33) Dewar, M. J. S.; Dougherty, R. C. The PMO Theory of Organic Chemistry; Plenum: New York, 1975.
Steric Effects on Diffusion into Bituminous Coals
whether they are stable and unreactive or persistent and reactive. It would be most interesting to study the reaction of maleic anhydride with coals from which most of the radicals have been removed. The reversibility of the reaction supports the occurrence of a Diels-Alder reaction, but no coal structure contains enough reactive diene structures to account for the amount of maleic anhydride that reacts. It is not now possible to decide between the occurrence of Diels-Alder or radical addition reactions. For this work the identity of the reaction is not important. We are studying kinetics in which the rate-determining step is diffusion and the identity of the reaction plays no role in the diffusion process. When the steric effects on the amount of reaction that occurs are discussed, the identity of the reaction is important. Different products have different molar volumes and therefore will be subject to different steric constraints.
Energy & Fuels, Vol. 20, No. 1, 2006 259
Figure 1. Time dependence of the reaction of maleic anhydride with Pittsburgh No. 8 coal in o-xylene at 110 °C.
Experimental Section All compounds except diphenyl and di-n-hexyl maleate were commercially available. All solvents and liquids were distilled before use. The preparations of diphenyl and di-n-hexyl maleate are given in the Supporting Information. FTIR spectra were obtained by using a Digilab model 20, and all samples for IR analysis were prepared in a Vacuum Atmosphere glovebox. The coals used have been described.34 Three kinetic procedures were used. The procedure used for reactions carried out below 100 °C has been previously described.34 Reactions at 110 and 125 °C. Coal (1.5 g) and 0.0128 mol of dieneophile were stirred at room temperature in 62.5 mL of solvent. Aliquots (5 mL) were withdrawn by pipet from the vigorously stirred mixture and transferred to small glass vials that were then sealed under nitrogen. These were immersed in a constant temperature oil bath at either 110 or 125 °C. At measured times a sample was withdrawn from the bath, cooled rapidly, and filtered through a Soxhlet thimble. The solid residue was Soxhlet extracted with, first, acetone and then benzene and dried to constant weight in a vacuum oven at 110 °C. The increase in weight with time was used to establish the reaction kinetics. Neither acetone nor benzene is a good extraction solvent for coals. This method depends on the reproducible extraction of only small amounts of coal solubles from the reacted coals. Reactions at 200 and 250 °C. Reactions were carried out in a 250 mL stainless steel autoclave. A mixture of coal (3.6 g), dieneophile (0.031 mol), and 150 mL of the solvent were placed in the autoclave that was immediately closed and stirring started. The autoclave was then purged with dry N2. It took 40-60 min to heat the autoclave to the desired temperature. At measured time intervals 10 mL samples were removed through a dip tube into a calibrated 10 mL test tube. The samples were filtered by using a Soxhlet thimble and worked up as before.
Results and Discussion The reaction kinetics were followed by measuring the weight increase of the samples with time. To do this, individual sealed ampules were opened or a fixed volume of the reaction mixture was withdrawn from a strongly stirred reactor. This slurry of coal was filtered through a Soxhlet thimble, extracted with acetone and then benzene to remove unreacted reagent and solvent, and dried to constant weight under vacuum at 110 °C. This elaborate procedure is quite reproducible. The first question to be addressed is the reaction order. All of the reactions give good plots of weight increase vs t1/2, diagnostic of Fickian diffusion. A representative selection of these plots is shown in Figures 1-4. While the plots shown (34) Larsen, J. W.; Lee, D. Fuel 1983, 62, 1351-1354.
Figure 2. Time dependence of the reaction of maleic anhydride with Pittsburgh No. 8 coal in o-xylene at 125 °C.
Figure 3. Time dependence of the reaction of maleic anhydride with Pittsburgh No. 8 coal in o-dichlorobenzene at 125 °C.
Figure 4. Time dependence of the reaction of dihexylmaleate with Pittsburgh No. 8 coal in o-xylene at 200 °C.
use the measured weight data, the data in the tables are on a mole basis to allow easy comparison between the different reactants. The rate-determining step here is diffusion of the dieneophile, not the chemical reaction and not the rearrangement (swelling) of the coal. The chemical reaction would be first order in dieneophile, and coal rearrangement would give Case II diffusion behavior. Neither of these fit the data. A previous study34 of the reaction of maleic anhydride with these coals swollen in a variety of organic liquids showed that diffusion was Fickian in all cases. In addition to maleic anhydride, maleate esters and acetylenedicarboxylate esters were used. Both react with the coal, and IR spectroscopy shows that the relevant double or triple bond is not present in the product. Their reactions with these coals are consistent with the occurrence of Diels-Alder reactions but are subject to the familiar objection: the apparent absence of reactive dienes in the coal. We emphasize that the subject of this paper is molecular diffusion, so the identity of the reaction that occurs is irrelevant to the conclusions reached here, no matter how interesting it may be for those interested in coal chemical structure and reactivity. Table 1 lists the diffusion rates of maleic anhydride and several maleate esters into Pittsburgh No. 8 coal swollen with o-xylene and the amount of each compound that ultimately
260 Energy & Fuels, Vol. 20, No. 1, 2006
Larsen and Lee
Table 1. Rate and Extent of Reaction of cis-Maleate Esters with Pittsburgh No. 8 Coal in o-Xylene Solvent at 200 °C reactant
slope (mol h-1/2)
maleic anhydride dimethylmaleate diethylmaleate di-n-hexylmaleate diphenylmaleate dineopentylmaleate
8.1 15.3 14.5 11.2 13.4 no reaction
k (h-1/2)
moles incorporated/ 100 C atoms
28 31 28 16 21
3.5 2.0 1.9 1.4 1.6
Table 3. Temperature Dependence of the Reaction of Maleic Anhydride with Coals coal
solvent
T, °C
slope (mol h-1/2)
Pittsburgh No 8
o-dichlorobenzene
75 90 110 125 75 90 110 125 200 250 75 110 125 75 110 125
5.9 9.2 10.5 17.0 5.0 7.7 14.3 21.8 82.1 11.2 4.7 15.1 20.8 8.7 16.5 21.8
o-xylene
Table 2. Rate of Reaction of Acetylenedicarboxylates with Pittsburgh No. 8 Coal in o-Xylene reactant
T, °C
slope (mol h-1/2)
dimethyl dimethyl diethyl diethyl
65 95 65 95
4.0 6.5 3.8 6.7
Illinois No. 6
o-dichlorobenzene o-xylene
Table 4. Activation Energies (Ea, kcal/mole) for Maleic Anhydride Diffusion
reacts with this coal. Equation 1 is followed, so the slope of a plot of Mt vs t1/2 is M∞k and k can be calculated using the observed slope and the value of M∞. Dineopentyl maleate is a special case that will be discussed later. The effect of molecular size on these diffusion rates is small, about 50% difference between the fastest (dimethyl maleate) and slowest measured (di-n-hexyl maleate). Not even diphenyl maleate shows a large decrease. Except when highly branched, size effects on diffusivity are small. The results for the acetylene dicarboxylate esters are similar (Table 2). The most relevant literature data are measurements of diffusion rates of some linear alkylamines into a bituminous (81% C, 74% vitrinite) coal.35 At 30 °C the diffusion of n-propyl- and n-butylamine is anomalous while n-pentyl-, n-hexyl-, n-octyl-, and n-decylamine are all Case II. Diffusion was measured by following the expansion of the solid coal volume. Through n-hexylamine the molar uptake of these amines is constant, consistent with the specific site binding proposed earlier by Green.36 Measuring the weight uptake (this work) and the volume increase may follow two different processes. Alternately, the more basic amines may, by more effectively disrupting coal-coal hydrogen bonds, enhance coal structure rearrangements and foster Case II diffusion. The activation energies for the maleic anhydride and amine diffusion are similar (vide supra). The amount of material incorporated into the coal decreases as molecular size increases, except for diphenyl maleate (Table 1). Because of the two phenyl groups its interaction with the coal is more favorable than the alkylesters, alkyl groups being rejected by coal as shown by solvent swelling measurements.37 To react, especially in a Diels-Alder reaction, the coal network must be expanded. This will take work. The larger the reagent, the larger the required expansion. If the reaction is part of an equilibrium or if the network limits the functional groups that can react by making the necessary expansion impossible, the observed behavior is expected. With linear alkylamines the decrease in uptake occurs only for amines larger than n-hexylamine.35 The lack of reaction of the highly branched dineopentyl maleate is puzzling. We anticipated low diffusion rates because it has long been established that planar molecules diffuse faster in coals than branched ones. However, it is possible to diffuse large molecules into coals. For example, the very bulky ((n-
butyl)3Sn)2O reacted in refluxing toluene reacts with all of the hydroxyl groups in Illinois No. 6 and Rawhide coals.38 The presence of a tert-butyl group on tetralin’s aromatic ring does not inhibit hydrogen transfer from the ring to tetralin.39 The presence of a para tert-butyl group on pyridine reduces the swelling of Pittsburgh No. 8 and other coals compared to unbranched or secondary alkyl groups.40 In none of these cases was the reaction or interaction of the branched molecule blocked. In this case it is blocked. Diffusion into coals seems to be strongly affected by the details of the molecules or reacting system. It is not understood. The acetylene dicarboxylates show essentially the same diffusion rates for the dimethyl and diethyl esters. These rates are, as expected, similar to be slower than the reaction of Pittsburgh No. 8 coal with maleic anhydride. This is best seen by comparing the rates for the acetylene dicarboxylates at 95 °C (Table 2) with the faster maleic anhydride rates at 90 °C (Table 3). Table 3 gives the rate constants for diffusion of maleic anhydride into Pittsburgh No. 8 and Illinois No. 6 coals at various temperatures in the solvents o-xylene and o-dichlorobenzene. Note that at 250 °C the rate constant for maleic anhydride in o-xylene with Pittsburgh No. 8 coal decreases substantially. This temperature is sufficiently high to be causing changes in the coal structure that may affect diffusion. It is also high enough to inhibit some Diels-Alder reactions. We cannot be sure what is occurring. The activation energies derived from these data are given in Table 4 and a typical plot is shown in Figure 5. The most notable feature of the activation energies is that they are low and entirely consistent with Fickian diffusion. The activation energy for Case II diffusion of pyridine into coals has been measured and ranges from 20 kcal/mol in Beulah lignite12 to 9 kcal/mol in a bituminous coal.35 With Case II diffusion the macromolecular chain segments must be separated from each other and many cooperative interactions must be simultaneously disrupted. With Fickian diffusion only the coal-
(35) Ndaji, F. E.; Thomas, K. M. Fuel 1995, 74, 842-845. (36) Green, T. K.; West, T. A. Fuel 1986, 65, 298-299. (37) Larsen, J. W.; Green T. K.; Kovac, J. J. Org. Chem. 1985, 50, 47294735.
(38) Larsen, J. W.; Nadar, P. A.; Mohammadi, M.; Montano, P. A. Fuel 1982, 61, 889-893. (39) Larsen, J. W.; Amui, J. Energy Fuels 1994, 8, 513-514. (40) Larsen, J. W.; Lee, D. Fuel 1985, 64, 981-984.
coal
solvent
Ea
Pittsburgh No. 8
o-dichlorobenzene o-xylene o-dichlorobenzene o-xylene
5.4 7.4 7.6 5.6
Illinois No. 6
Steric Effects on Diffusion into Bituminous Coals
Energy & Fuels, Vol. 20, No. 1, 2006 261
Diffusion in coals remains poorly understood. The general pattern that branching slows diffusion is clear. However, sometimes it blocks diffusion, and other times it does not. Long alkyl chains slow diffusion somewhat but still have good mobility through coals provided they are attached to a group that will give them solubility in coals. How reagent diffusion varies with rank and extent of coal swelling has not been determined. Figure 5. Temperature dependence of the reaction of maleic anhydride with Pittsburgh No. 8 coal in o-xylene.
Acknowledgment. We are grateful to the U.S. Department of Energy for support of this work.
coal interactions necessary to allow the molecule to move a bit farther in the coal must be disrupted. We expect that the activation energy for Case II diffusion will be substantially higher than that for Fickian diffusion. This expectation is met in some12 but not all35 cases.
Supporting Information Available: Preparation details for diphenyl and di-n-hexyl maleate. This material is available free of charge via the Internet at http://pubs.acs.org. EF0501851
