Energy & Fuels 1993, 7,42-46
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Use of Einstein Specific Heat Models To Elucidate Coal Structure and Changes in Coal Structure following Solvent Extraction Peter J. Hall* and John W. Larsen Exxon Research and Engineering Company, Route 22E,Clinton Township, Annandale, New Jersey 08801 Received March 16,1992. Revised Manuscript Received October 14,1992
Differential scanning calorimetry (DSC) was used to monitor the specific heat capacities (C,) of coals in the range 100-300 K. The effects of pyridine extraction on the DSC of the coals was measured. Illinois No. 6 and Pittsburgh No. 8 show a decrease in C, over this temperature range and Upper Freeport shows an increase. The DSC results are interpreted in terms of two-component Einstein specific heat models in which one degree of vibrational freedom is easily excited while the other two degrees of freedom require more energy. A plausible physical picture which emerges is the relatively easy excitation of atomic vibrations in only one direction and more difficult vibrational excitation in the other two directions. Following van Krevelen, the easily excited vibration is perpendicular to the "cluster" plane and vibrations in the plane defined by the aromatic "cluster" are more difficult (require a higher temperature) to excite. The pyridine extraction of Illinois No. 6 and Pittsburgh No. 8 coals does not change the lower temperature (perpendicular) vibration but does increase the energy required to excite the in-plane vibrations. This is consistent with an increase in macromolecular association. The effect of pyridine extraction on the Upper Freeport may involve an increase in the fraction of atoms associated with the lower temperature component.
Introduction The macromolecular structure of coal is not constant but changes with solvent contact and temperature. Since it controls diffusion rates and molecular contacts within the coal, this structure and its changes are important in chemical reactions of coals. It is necessary to understand the structure and its changes in order to understand and interpret the reaction chemistries of coal, including conversion. Because of this, a systematic investigation of coal macromolecular structure is underway. Here we report the first results obtained using differential scanning calorimetry (DSC) to investigate the macromolecular structure and its changes. Coals have complex disordered macromolecular structures which contain a wide range of chemical functionalities. A variety of techniques have been used to probe coal macromolecular structures and internal associations.' Most are based upon mechanical (elastic) properties. Another approach is to study the vibrational properties of coals, which will be sensitive to changes in structure and molecular conformation. One such approach is to model the heat capacities of coals. That approach is explored here. The heat capacity of a solid at any temperature is determined by the vibrational spectrum of the atoms in the solid. Essentially, the greater the amount of atomic vibration, the greater the heat capacity. The theoretical maximum of heat capacity is obtained when all of the atoms in the solid are vibrating independently in all three coordinate directions. This is described by the Dulong(1) Green,T. K.; Kovac,J.; Brenner,D.;Imsen, J. W. In CoalStructure; Meyer, R. A., Ed.; Academic Press: New York, 1982.
Petit law.2 Precise knowledge of the heat capacity of a solid depends upon a precise knowledge of the atomic vibrational spectrum. The atomic vibrational spectrum is determined by a number of factors such as the nature of atoms present, their local environment, and the degree and type of chemical bonding present. Spectra are highly complex even for relatively simple crystals. Atomic vibrational spectra of solids can be obtained using inelastic neutron scattering. There has only been one published study of inelastic neutron scattering from This was performed over the momentum transfer range 350-3000 cm-I. There have been no attempts to measure the complete atomic vibrational spectra of coals, but such spectra would be expected to be highly complex, consisting of both molecular and macromolecular componente. Given the inherent structural complexity of coal structure, it is surprising that attempts to model the specific heat capacity of coals4have relied on the Einstein model, which assumes the simplest sort of vibrational spectrum possible. The Einstein model assumes a single vibrational frequency for atoms in a solid.* The vibrational frequency in the Einstein theory represents a mean of the real vibrational spectrum. Using the Einstein model, it is not necessary to measure the real vibrationalspectrum of solids to gain information about the physical state of atoms. The mean atomic vibration is expressed as a temperature, called the Einstein temperature. A low Einstein temperature corresponds to an easily excited vibration which will make its contribution to the heat capacity starting at low temperature. The Einstein temperature can be considered (2) Zemansky, M. W. Heat and Thermodynamics; McGraw-Hilk Tokyo, 1968. (3) Howard, J.; Ludman, C. J.; Tomkinson, J. Fuel 1983,62, 1097. (4) Merrick, D. Fuel 1983, 62,540.
0887-0624/93/2507-0042$04.00/00 1993 American Chemical Society
Coal Structure following Solvent Extraction
as an adjustable parameter and calculated from a fit to specific heat data. There is a straightforward interpretation of Einstein temperatures in terms of structure. The higher the Einstein temperature, the harder atomic vibrations are to excite. In turn, this implies greater or stronger interatomic bonding. If the Einstein model could be shown to be a good approximation to describe the specific heats of coals, then those heat capacities and the derived Einstein temperatures may have some use in coal characterization. van Krevelen noted that at room temperature the specific heat capacities of a range of coals were roughly one-third of the maximum value predicted by the DulongPetit law.5 van Krevelen explained this by assuming that at room temperature coal atoms could only vibrate in one direction, perpendicular to the bedding plane where the binding forces were weaker. The specific heat capacity of coal at room temperature could be derived from a knowledge of the ultimate elemental composition of coal from the equation5 C p = R/a (1) where R is the gas constant and a is the mean atomic weight for coal, obtained from the following (generalized) formula5
where f i is the mass fraction of element i and pi is the atomic weight of element i. Although van Krevelen5 did not calculate the variation of specific heat capacity with temperature, he implicitly used an Einstein type of model by assuming only one vibrational frequency for the coal atoms. The idea of binding forces being weaker perpendicular to the bedding plane than parallel to the bedding plane is necessary to van Krevelen's model and is not well corroborated. A series of careful studies of the anisotropy of the organic structures of coal reveals very little orientation with respect to the bedding plane for coals having less than 89%C (d"f).&* Cody et al.9 have shown that swelling in a variety of solvents is highly anisotropic. Coals tend to exhibit greater swelling perpendicular to the bedding plane than in the bedding plane. They suggested that this might be due to an anisotropy in coal cross-linkage, which was assumed to be greater in the bedding plane. A more recent and reasonable explanation is based on the deformation of coals in the seam resulting in a 'locked-in" strain.1° Cody et al.6 also demonstrated that when the solvent was removed from the swollen coal it did not return to its original shape. Rather, the coals were smaller when measured in their bedding planes and larger perpendicular to the bedding plane. It has been well established that coals display anisotropic mechanical properties with respect to the bedding plane,5 but this occurs primarily in higher rank ( % C > 85% dmmf) coal and may be due to strain. (5) van Krevelen, D. W. Coal; Elsevier: Amsterdam, 1961. (6) Cody, G. D. Jr.; Larsen, J. W.; Siskin, M. Energy Fuels 1989, 3, 544-551. (7) Cody, G . D. Jr.; Larsen, J. W.; Siskin, M.; Cody, C.D. Sr. Energy Fuels 1989, 3, 551-556. (8)Roberta,J. E.;Coleman,K. M.;Alaimo, M. H.;Larsen, J. W. Energy Fuels 1991, 5, 619. (9) Cody, G . D., Jr.; Larsen, J. W.; Siskin, M. Energy Fuels 1988, 2, 340. (10) Tom Carlson, Sandia National Labs. Personal communication.
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We prefer to recast van Krevelen's discussion of free and hindered vibrations relative to the bedding plane in terms of vibrations relative to the planes defined by the planar (largely) aromatic clusters in coals. An atom in a cluster will be more tightly bound in the plane of the cluster than perpendicular to the cluster plane. It should therefore be easier to excite atomic motion perpendicular to the cluster than in the plane of the cluster. As a result, at low temperatures, only one of the three possible vibrations is excited, leading to the behavior identified by van Krevelen, heat capacities equal to '/a of those predicted by the Dulong-Petit law. At higher temperatures, the DulongPetit law should be obeyed. The differences between our view and van Krevelen's are subtle. He postulated strong orientational interactions relative to the bedding plane. In his view, atomic vibrations will be anisotopic with respect to the bedding plane. Our frame of reference is the clusters, which are only slightly oriented with respect to the bedding plane. van Krevelen would predict that inelastic neutron scattering will be anisotropic, different parallel and perpendicular to the bedding plane. We predict it will be essentially isotropic. The ideas of van Krevelen5 were extended by Merrick4 who used a linear superposition of two Einstein models with different Einstein temperatures (8).Merrick4 assumed that coal specific heat capacity varied with temperature ( T ) according to
C, = (R/u)['/gl(81/T) + 2/g2(8,/T)1
(3)
where g(8/T) is the Einstein function, defined by exp(8/T)(8/T)2 (4) ((exp(B)/T) - 112 The Einstein theory predicts C,. The correction to give C,, which is the quantity determined experimentally, is very small for coals, -lo4 J K-l g-l. Merrick found values of 380 and 1800 K for 8' and e2, respectively, and demonstrated that this provided a good model for the observed variation of coal specific heat capacity over the range 273-523 K for two high-volatile bituminous coals. The weightings of l/3 and 2/3for gl(e1) and g2(82), respectively, reflect the number of degrees of vibrational freedom associated with vibration perpendicular to and in the cluster planes. Noting that coals have a range of binding forces holding the macromolecules together, Merrick allowed for a distributed function for the Einstein temperatures. A log-normaldistribution with a mean of 1120K and a standard deviation of 1.7gave the best fit to the data. However, the improvement in prediction was
