Energy & Fuels 1997, 11, 1103-1104
1103
Comments Regarding the Use of Coal Swelling To Count Hydrogen-Bond Cross-Links in Coals Eric M. Suuberg Division of Engineering, Brown University, Providence, Rhode Island 02912 Received January 2, 1997 Larsen et al.1 recently reported on a method for counting hydrogen-bond cross-links in coals involving examination of the swelling behavior of coals in nonhydrogen-bonding solvents (chlorobenzene and toluene), to which were added small amounts of hydrogenbonding solvents (pyridine and tetrahydrofuran, THF). The hypothesis was advanced that the specifically interacting solvents first titrate the internally-hydrogenbonded functional groups of the coal (mainly hydroxyls). This paper prompted comments by Painter,2 who argued that it is not logical that internal hydrogenbonded sites should be attacked first. He asserted that Larsen et al. have considered the non-configurational entropy in advancing their argument, but it appears Larsen et al.1 were most concerned with configurational entropy as discussed below. Painter further noted that the behavior would be sensitive to whether the coal was above or below the glass transition temperature (Larsen et al. assumed it to be below). This latter issue will not be taken up here, except to note that unswollen coal is universally accepted to be in the glassy state at room temperature. Other issues raised by Painter, as to whether hydrogen bonds can act as effective cross-links in coal and whether ternary phase behavior is possible in swollen coal, will also not be considered here. Larsen et al.1 assumed that the key interactions responsible for the observed behavior are ordinary hydrogen-bonding interactions. The efficacy of the selected hydrogen-bond acceptor solvents (THF and pyridine) is consistent with this assumption. Also, it is well-known that there is an abundance of hydroxyl groups in the coals examined, and they observed that methylation of the groups permitted full swelling in the absence of the hydrogen-bond acceptors. Larsen et al.1 noted, however, that coals contain many more sites capable of interaction with strong bases such as alkylamines, than the numbers of sites that they had determined in this work. Moreover, the number of such amine-titratable sites is in excess of the hydroxyl content of the coals of interest in the present work.3,4 This cautions against assuming a priori that the sites in question are all hydrogen-bonding hydroxyls and other types of electron donor-acceptor interactions may be present. Painter2 challenged the conclusion that the sites with which the hydrogen bond acceptors (bases) interact are internally bonded sites, noting that the overall free energy change associated with interaction would be (1) Larsen, J. W.; Gurevich, I.; Glass, A.; Stevenson, D. S. Energy Fuels 1996, 10, 1269-1272. (2) Painter, P. C. Energy Fuels 1996, 10, 1273-1275. (3) Green, T. K.; West, T. A. Fuel 1986, 65, 298-299. (4) Suuberg, E. M.; Otake, Y.; Langner, M. J.; Leung, K. T.; Milosavljevic, I. Energy Fuels 1994, 8, 1247-1262. (5) Gumkowski, M.; Liu, Q.; Arnett, E. M. Energy Fuels 1988, 2, 295-300.
S0887-0624(97)00004-2 CCC: $14.00
∆g ) ∆gcs - ∆gcc
(1)
in which ∆gcs and ∆gcc are the free energies of coalsolvent bonding and internal hydrogen-bonding interaction c, respectively. This compares with the free energy of interaction with a free site, ∆g′, for which ∆gcc in (1) is zero. Painter defined ∆g in terms of free energy per bonding interaction. Since there exist many possible hydrogen-bonding interactions, there is no unique value of ∆g. Painter reasoned that ∆gcc must always be negative, forcing ∆g′ to be more favorable (negative) than ∆g. This would argue for initial titration of free sites, as opposed to internally bonded sites. This conclusion even appears to be supported by our data showing that a significant enthalpy release can occur prior to much swelling of a coal by a good electron donor.4 Titrametric enthalpies of bases interacting with the same Argonne Premium Coal Samples as used by Larsen et al. are high and decrease with increasing solvent uptake;5 Illinois No. 6 coal gave 70.7 and 54.0 kJ/mol enthalpies for ethylenediamine and n-butylamine, respectively. These values are consistent with hydrogen bonding to strong electron acceptor sites, but cannot be directly compared to other published values, since the experiments involved titration from acetonitrile solution, and no account was taken of the enthalpy of demixing. Still, the latter observations tend to suggest initial interaction with free sites. A selectivity for internally bonded sites could involve a value of ∆gcc close to zero, which would make ∆g ) ∆g′. A value of ∆gcc ) 0 is plausible even in a case in which hydrogen-bonding interactions are dissociated. The definition of ∆g is in terms of a contribution per bonding interaction, and thus ∆gcc is a partial molar type of quantity. If coal were placed in a hypothetical initial dry state in which all hydrogen-bonding interactions were dissociated, at first ∆gcc would be quite large and negative, corresponding to formation of strong hydrogen-bonding interactions with a minimum of structural deformation required. As the more favorable interaction possibilities are exhausted, only progressively less favorable interactions would remain. These would include both enthalpically less strong interactions that require little structural deformation, as well as the enthalpically favorable interactions that require entropically unfavorable (tighter) structural network configurations. The process of forming further interactions stops when the value of ∆gcc becomes zero. In the above situation, the enthalpy of interaction of an hydrogen bond acceptor solvent with a coal would be given by
∆h ) f∆hcb + (1 - f)(∆hcb - ∆hcc)
(2)
where f is the fraction of solvent interacting with “free” © 1997 American Chemical Society
1104 Energy & Fuels, Vol. 11, No. 5, 1997
Communications
sites and ∆hcc is the enthalpy of dissociation of coal/ coal bonding interactions. If f is near zero, as suggested by Larsen et al., ∆h would be small at low amounts of solvent uptake, if the strength of coal/base and coal/coal bonds are comparable (∆hcb ≈ ∆hcc). There is then an apparent dilemma, as the calorimetric results have suggested ∆h to be large. The reason for the apparent discrepancy comes from a failure to conduct a complete enough thermodynamic analysis of the situation. The fact that there is both a base and a solvent involved cannot be overlooked. In the Larsen et al. work, the chlorobenzene plays a major role in assuring a significantly positive entropy of mixing, which they have postulated will drive the process forward to the extent allowed by dissociation of the hydrogen bonds. If Painter’s hypothesis is accepted and the small amount of added base removed from the chlorobenzene solution interacts with free sites in the coal, the free energy benefit would, at most, be given by ∆gmix ) ∆hcb where ∆hcb is the net enthalpy of mixing of the base with the free sites. This net enthalpy is an enthalpy relative to the dilute base solution state and would need to be corrected to some other reference state by proper accounting of an enthalpy of mixing of chlorobenzene and base. This estimate also neglects the unfavorable entropy of adsorption from solution, and the free energy of any elastic deformation of the coal, needed to accommodate the sorbed base. The value of ∆hcb would be at most of order -30 kJ/mol, assuming very strong hydrogen bonds (and neglecting any solution enthalpy effects). The experimental results of Larsen et al. imply a significant increase in mixing entropy, due to the significant uptake of chlorobenzene. Considering the slope of the curves in their Figure 1, and taking a linear approximation to Q ) 1.4, it is possible to estimate that for each mole of base taken up by the coal, about 15 mol of chlorobenzene are also taken up (this value is about half that cited in the paper, because the present value covers a broader range of Q). Using Flory lattice theory for configurational entropy,6 it is possible to estimate that the change in free energy of mixing with chlorobenzene uptake is
d∆Gmix/dNs ) RT[ln(1 - vc) + vc]
(3)
where Ns is the moles of chlorobenzene imbibed by the coal, vc is the inverse of Q (the swelling ratio), R is the gas constant, and T is temperature. In this case, the enthalpy of mixing of chlorobenzene and coal is entirely neglected (i.e., the χ parameter is taken as zero6). One can then use (3) to estimate the free energy change that occurs when adding the base
d∆Gmix/dNb ) (d∆Gmix/dNs)(dNs/dNb)
(4)
It is possible to estimate from (3) and (4), and the slope of Figure 1 of Larsen et al., the free energy change due to the mixing part of the process:
d∆Gmix/dNb ) 15RT[ln(1 - vc) + vc]
(5)
For a typical value of Q ) 1.1 or vc ) 0.909, and T ) 300 K, d∆Gmix/dNb ) -56 kJ/mol of base. This value is greater than the free energy benefit of filling free sites (6) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953.
and shows why the process can be driven in the observed direction. Strictly speaking, the comparison is not yet fair, since there is an elastic free energy penalty for swelling the coal with chlorobenzene. For the assumed Q, there should be no such penalty since, as noted above, the coal structure was not truly relaxed in the dried state. Estimates can be made of the penalty for higher values of Q, using other methods.4 Thus the configurational entropy can make a very large difference in observed behavior, when using a “good” (zero χ) swelling solvent such as chlorobenzene. Neat chlorobenzene cannot swell without the added bases only because it cannot participate in hydrogenbonding interactions. If the same experiment were performed with a different solvent, one that matches poorly with the solubility parameter of the coal, then this needs to be reflected in a modification to (3):
d∆Gmix/dNs ) RT[ln(1 - vc) + vc + χvc2]
(6)
A positive value of χ, as would result from a solubility parameter mismatch, would lead to an unfavorable enthalpy of mixing counterbalancing the favorable entropy of mixing. The higher the value of χ the more unfavorable the mixing process becomes. In this case, there might be no free energy benefit derived from interaction of the base with coal/coal hydrogen-bonding sites, since there is no mixing free energy benefit to be derived by “dissociating” these in order to accommodate a solvent with the poor solubility parameter match. The added electron donor in this case is forced in the direction of interacting with free acceptor sites in the coal. There are two experimental observations that support the above hypothesis. In the calorimetric work cited above,5 strong bases appeared to first interact with free sites. This is because the acetonitrile (δ ) 11.9 cal1/2/ cm3/2) from which the bases were sorbed in the calorimetry study has a poor solubility parameter match with the coal; it is possible to estimate that Illinois No. 6 coal has a solubility parameter of about δ ) 9.5 cal1/2/cm3/2 from the earlier results of Larsen et al.7 This would mean that in order for the coal to imbibe acetonitrile, both an unfavorable enthalpy of mixing of coal and acetonitrile as well as the enthalpy penalty for breaking coal-coal hydrogen-bonding interactions need to be overcome. This penalty is too large for the process to occur spontaneously, and the base adds instead to free sites. A second observation in support of the above hypothesis concerns the data of Figure 1 of Larsen et al.1 In this figure, THF/chlorobenzene is seen to be more effective at swelling of the Illinois No. 6 coal than is THF/toluene. Again, there is a better solubility parameter match between chlorobenzene (δ ) 9.5 cal1/2/cm3/2) and coal than between toluene (δ ) 8.9 cal1/2/cm3/2) and coal, so it is natural to see more uptake of chlorobenzene. In summary, it appears that Larsen et al. have proposed a plausible explanation for their results, which receives quantitative support from simple lattice theory. Verification of their hypothesis awaits further experimental work. EF970004Y (7) Larsen, J. W.; Green, T. K.; Kovac, J. J. Org. Chem. 1985, 50, 4729-4735.
