Thermodynamics of coal solutions - Energy & Fuels (ACS Publications)

Sep 1, 1988 - Interactions of Organic Liquids with Coals: Analysis by Solid-StateC Nuclear .... Paul C. Painter , Yung Park , Maria Sobkowiak , and Mi...
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Energy & Fuels 1988,2, 693-702

693

Thermodynamics of Coal Solutions Paul C. Painter,* Yung Park, and Michael M. Coleman Department of Materials Science and Engineering, The Pennsyluania State Uniuersity, University Park, Pennsyluania 16802 Received February 18, 1988. Revised Manuscript Received May 2, 1988

An association model is used to describe of the free energy related to the changing pattern of hydrogen bonding that occurs in solutions of coal-like *modelnmolecules as a function of composition. Assuming that the other contributions to the free energy of mixing can be approximated by the Flory-Huggins theory, it is possible to calculate the chemical potentials and phase behavior of such mixtures. The model predicts that non-cross-linked coal molecules of low molecular weight and low aromaticity are completely soluble in pyridine but that higher molecular weight, more aromatic molecules phase separate into solvent-rich and solvent-poor swollen-coal gels. Accordingly, repeated extractions would be necessary to remove the bulk of such non-cross-linked macromolecules from a coal sample.

Introduction The most convincing model of coal structure is that of a cross-linked macromolecular network.l* The degree of cross-linking is thought to vary with rank, and this changes the relative proportions of soluble and insoluble material. Some of the most crucial evidence supporting this concept is thus the solubility and swelling behavior of coal. A number of studies have attempted to relate swelling measurements to fundamental network parameters (e.g. ref 3-8 and citations therein) using the theories of polymer physical chemistry,lOJ1but it is widely recognized that there are problems with this approach. These problems are most often associated with the applications of theories originally developed to describe the properties of long, flexible hydrocarbon chains and networks to a material where the chains (or segments between cross-link points) are presumably too short and stiff to obey Gaussian statistics and can also interact through polar forces and the formation of hydrogen bonds. In recent work5J a nonGaussian theory of chain conformations developed by Kovac12has been applied, and Larsen et al.5 also conducted swelling measurements on samples where hydrogenbonding interactions have been eliminated by methylation or acetylation of OH (and presumably NH) groups. The fundamental problem of formulating a reasonable model for the thermodynamics of coal solutions that includes hydrogen-bonding interactions has not been tackled, however, and that forms the subject matter of this paper. The problem is a general one in that contemporary theories of polymer solutions are usually only applicable to mixtures where the interactions between segments are simple van der Waals or London dispersion forces. This d o w s a formulation in a mean field form, A & ) t 4 A b , where Mint is an exchange interaction term, $A and $B are the volume fractions of the components A and B, and their product is proportional to the number of unlike contacts in a solution where there is random mixing. For simple physical forces, AEht is, of course, positive. Polar attractive forces could probably also be handled by a similar approximation, providing that the dipole moments involved are not too strong and are not localized on the surface of the molecules or segments involved. Strictly speaking, the system would not be random, in that unlike segments would have an increased propensity to be adjacent to one

* To whom correspondence should be addressed.

another. These segments would not be associated in the usual sense of the word, however, and Flory'O has argued that for relatively weak interactions the modification in the combinatorial entropy of mixing due to nonrandomness is insignificant (compared to the effects of other approximations). Hydrogen bonds are different and cannot be dealt with by means of a simple approximation. Polymer segments and solvent molecules that interact in this manner are truly associated, and above the Tgthere is a dynamic equilibrium distribution of hydrogen-bonded species. There is a nonrandom arrangement of the hydrogen-bonding functional groups (relative to one another), and a potential function describing the interaction is a complex function of the distribution of charges on the molecules or segments involved and the specific arrangement of molecules in space. Furthermore, the usual lattice treatments of mixtures are based on the assumption that the internal degrees of freedom of each molecule are not seriously disturbed by the proximity of other molecules, so that the system can be treated as an assembly whose partition function is the product of a partition function for translations of the molecules and partition functions for the internal degrees of freedom of each single m01ecule.l~ When polymer segments and solvent molecules become associated through the formation of hydrogen bonds, however, the vibrational and rotational degrees of freedom of each become seriously modified. This can be clearly seen in the infrared spectrum of coal, for example, where OH stretching modes display (1) van Krevelen, D. W. Coal; Elsevier: New York, 1981. (2) van Krevelen, D. W. Fuel 1966,45, 229. (3) Green, T.;Kovac, J.;Brenner, D.; Larsen, J. W. In Coal Structure; Meyers, R. A., Ed.; Academic: New York, 1982. (4) Larsen, J. W. In Chemistry and Physics of Coal Utilization; AIP Conference Proceedings, 70; Cooper, B. R., Petrakis, L., Eds.; AIP New York, 1981. (5) Lamen, J. W.; Green, T.K.; Kovac, J. J . Org. Chem. 1985,50,4729. (6) Lucht, L. M.; Peppas, N. A. In Chemistry and Physics of Coal Utilization; AIP Conference Proceedings 18; Cooper, B. R., Petrakis, L., Eds.; AIP: New York, 1981. (7) Lucht, L. M.; Peppas, N. A. Fuel 1987, 66, 803. (8) Lucht, L. M.; Peppas, N. A. J. Appl. PoZym. Sci. 1987,33, 2777. (9) Brenner, D. Fuel 1985,64, 167. (10) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca: NY, 1953. (11) Flory, P. J. Selected Works of Paul J. Flory; Mandelkern, L., Mark, J. E., Suter, U. W., Yoon, Do.Y., Eds.; Stanford University Press: Stanford, CA, 1985; Vol. 1-111. (12) Kovac, J. Macromolecules 1978,11, 362. (l3).Fowler, R. H.; Guggenheim, E. A. Statistical Thermodynamics; Cambridge University Press: Cambridge, England, 1939.

0887-0624f 88/2502-0693$0l.50f 0 0 1988 American Chemical Society

Painter et al.

694 Energy & Fuels, Vol. 2, No. 5, 1988

large frequency shifts and intensity changes as a result of hydrogen bonding.14 A number of attempts have been made to incorporate hydrogen-bonding interactions into solution theory. One such, where the solubility parameter is separated into nonpolar, polar, and hydrogen-bonding interactions, cannot be successful for the reasons we have stated above. (A solubility parameter formulation assumes random contacts of interacting groups. It is clear from the infrared spectrum of many materials that hydrogen bond, including coal, that there are far more contacts between interacting species than could be predicted on the basis of random mixing.) Other notable attempts include the work of Barker15J6and Tompa,17who used a treatment in which the surface of a molecule is divided into several contact points and the energy of nearest neighbor interactions depends upon the relative orientations of the molecules concerned. This approach is (at least to us) mathematically complicated and introduces a number of parameters that cannot be determined independently but only estimated by a fit to thermodynamic data. As Tompal’ pointed out, it is uncertain how much physical significance could be attached to values so obtained. An alternative approach is the use of association models. This treats the associated complexes, most often linear chains of hydrogen-bonded small molecules, as new, distinguishable, and independent molecular species. The hydrogen-bonding interaction is treated separately from the forces involved in mixing and essentially defines the number and distribution of species present, typically through equilibrium constants that are related to the free energy change corresponding to the formation (or dissociation) of particular types of hydrogen bonds. The hydrogen-bonded “polymers”then mix and interact through simple forces only, a process that can be readily handled by conventional lattice theories. Because the distribution of hydrogen-bonded polymer species changes upon mixing, however, it is necessary to define reference states with great care. Flory18 discussed this in some detail, deriving expressions for the thermodynamic properties of solutions of polymers of different molecular weight. These equations are especially suited to a description of chemical equilibria between polymer species, whether covalently linked or hydrogen bonded, as Flory also pointed 0ut.’~9’~Applying this theory, Kretschmer and Wiebe20developed an association model describing the mixing of alcohols and hydrocarbons that was later extended and applied by a number of other a ~ t h o r s . ~ lBy - ~ assuming ~ that the formation of hydrogen bonds in amorphous polymer mixtures is largely unaffected by the covalent linkages of the interacting units into polymer chains, we have adapted this approach to a description of the mixing of polymers and demonstrated that the equilibrium constants can be determined by infrared measurements.26 In effect, we assumed that the covalently linked chains are randomly Painter, P. C.; Sobkowiak, M.; Youtcheff, J. Fuel 1987, 66,973. Barker, J. A. J. Chem. Phys. 1952,20, 794. Barker, J. A. J. Chem. Phys. 1952,20, 1526. (17) Tompa, H. J. Chem. Phys. 1953,21, 1526. (18) Flory, P. J. J. Chem. Phys. 1944, 12, 425. (19) Flory, P. J. J. Chem. Phys. 1946, 14, 49. (20) Kretachmer, C. B.; Wiebe, R. J. Chem. Phys. 1954, 22, 1697. (21) Hwa, S. C. P.; Ziegler, W. T. J. Phys. Chem. 1966, 70, 2572. (22) Wiehe, L. A.; Bagley, E. B. Ind.Eng. Chem. Fundam. 1967,6,209. (23) Renon, H.; Prausnitz, J. M. Chem. Eng. Sci. 1967,22,299; Errata 1967, 22, 1891. (24) Kehiaian, H.; Treszczanowicz, A. Bull. SOC.Chim. Fr. 1969,18, 1561. (25) Nagata, I. 2.Phys. Chem. ( L e i p i g ) 1973, 252, 305. (26) Painter, P. C.; Park, Y.; Coleman, M. M. Macromolecules 1988, 21, 66.

arranged and there is sufficient segmental flexibility that the interacting functional groups can largely follow their intrinsic proclivities in forming hydrogen bonds. In one sense this assumption is probably unnecessary, in that limitations on the formation and strength of hydrogen bonds will presumably be reflected in the values of the experimentally determined equilibrium constants. To correctly model this latter situation, however, we would have to include a dependence of the equilibrium constants upon the covalent chain stiffness, an unnecessary complication at this stage of our application of association models to the description of hydrogen bonding in coal solutions. In recent work we have generalized our and developed equations describing the phase behavior of mixtures.28 They have proved surprisingly successful in predicting the experimentally observed behavior of various polymer mixture^.^^^^^ Coal is, of course, more complicated, but the same forces are operative and we believe the theory is at least capable of providing fundamental insight and predicting broad trends. Here we will describe a general treatment using “model” coal structures in pyridine solutions as an example. Interactions with other solvents will be considered in future publications.

Theory The association model used in this study is described in detail in recent publications,2628and it would be redundant to reproduce the derivation of equations. An outline of our results as they apply to coal is presented here. There are four topics that need to be considered: the definition of equilibrium constants; the definition of equations describing the stoichiometry of hydrogen bonding; the free energy of mixing; finally, phase behavior. Equilibrium Constants. There are a number of different association models that have been applied to the description of hydrogen bonding interactions in mixtures. We believe the Kretschmer-Wiebe mode120 is the most appropriate as, following Flory,18 it defines the least ambiguous reference state, where the individual species are separate and oriented. This is discussed in more detail elsewhere.n In this model, equal consecutive entropies and enthalpies of association are assumed in forming a hydrogen-bonded chain of n + 1interacting units, from an n-mer, On, and a monomer P1 KB

(1) + PI ==i Pn+1 so that by using Flory’s standard state,18J9the following equilibrium constant can be defined: Pn

Similarly, if we have a competing species, one that can form a hydrogen bond with /3 units but is incapable of hydrogen bonding to itself, we can write K,

Pn

+ CY ==i Pn.

(3) (4)

(27) Painter, P. C.; Park, Y.; Coleman, M. M., submitted for publication in Macromolecules. (28) Painter, P. C.; Park, Y.; Coleman, M. M., submitted for publication in Macromolecules. (29) Coleman, M. M.; Skrovanek, D. J.; Hu, J.; Painter, P. C. Macromolecules 1988, 21, 59. (30) Coleman, M. M.; Lichkus, A. M.; Painter, P. C. Macromolecues, in press.

Thermodynamics of Coal Solutions Table I. List of Symbols chemical repeat unit of non-self-associating molecule chemical repeat unit of self-associating molecule concentration defined as n / V , mol m-3 Gibbs free energy Gibbs free energy of mixing component of Gibbs free energy associated with hydrogen bonding enthalpy enthalpy of formation of a hydrogen bond between B units enthalpy of formation of a hydrogen bond between B and A units association equilibrium constant for formation of a hydrogen bond between B and A units self-association equilibrium constant between B units association equilibrium constant for formation of a hydrogen bond between the “true” interacting units of the B and A chemical repeat units self-association equilibrium constant for that part of the B chemical repeat that can be defined as the interacting unit degree of polymerization of A covalent polymer molecules degree of polymerization of B covalent polymer molecules n-mer number-average hydrogen-bonded chain length of self-associated B units in pure B ratio of molar volumes of A and B chemical repeat units, VA/VB ratio of molar volumes of a and P interacting units, Vu/V, no. of segments in chemical repeat unit A, VA/Vu no. of segments in chemical repeat unit B, V B / V p temp eratu r e volume of one true mole of solution molar volume of chemical repeat unit A molar volume of chemical repeat unit B molar volume of interacting unit of .A chemical repeat molar volume of interacting unit of B chemical repeat a parameter defined equal to KA@oA/r interacting unit of A chemical repeat interacting unit of B chemical repeat lattice coordination no. symmetry no. volume fraction volume fraction of a hydrogen-bonded chain of n B units volume fraction of a hydrogen-bonded chain of n B units and one A unit Flory-Huggins interaction parameter chemical potential Subscripts and Superscriptsa interacting unit property of pure component A,B,Pp, etc. are as defined above.

In these equations @ represents volume fractions and ri is a factor that accounts for the difference in molar

volumes of the interacting units (ri = V,/ Vs). The quantities and are important and represent the volume fraction of “monomers”, i.e. hydrogen-bonding interacting units that are “free”;they are not hydrogen bonded to any other units. Table I summarizes the notation employed in this paper. There are two aspects to the above definitions that need to be considered as applied to coal. First, the self-associating units p are readily identified with phenolic OH groups, while the competing species a would represent solvents such as pyridine, which do not self-associate but are capable of forming hydrogen bonds with an appropriate “donor” functional group. We have used the vague identification “interacting unit” above because in a complex macromolecule such as coal only part of the molecule or average repeat unit forms hydrogen bonds. In simple homopolymers such as the polyurethanes -(ROCONH),-, the interacting unit can, to a first approximation, be identified with the urethane group OCONH, while the remainder of the molecule behaves as inert diluent (in the

Energy & Fuels, Vol. 2, No. 5, 1988 695 sense that it does not hydrogen bond). It does not change the strength (or, more precisely, the free energy) of the hydrogen bonds that do form but can change the number of such interactions, according to its size. For molecules containing a phenolic OH group, however, there is a conceptual difficulty in identifying the “interacting unit”. Is this just the OH functionality or does it include part of the aromatic ring? This is of crucial importance, because association treatments are simple Flory lattice models, and in effect, the size of the self-associating interacting unit defines the lattice cell. Fortunately, the size of the “interacting unit” has been determined in experimental studies of phenol, cresol, etc.,3l and so we do not have make arbitrary assumptions concerning the molar volume of this entity. We can simply define equilibrium constants in terms of chemical repeat units (for simple homopolymers) or “average” chemical repeat units (for complex copolymers like coal) and obtainz7 (5)

where SB is the number of segments in the average chemical repeat unit of the self-associating component (sB = VB/ Vs) and r is the ratio of the molar volumes of the solvent molecule and chemical repeat unit (r = VA/VB). This allows the equilibrium constants KBand KA to be determined experimentally by infrared ~pectroscopy.’~J~ We have noted in our initial publications on the application of association models to the thermodynamics of polymer mixtures that eq 5 and 6 effectively define a transferable equilibrium ~onstant.~’ Providing that the interaction strength is unaltered in a series of similar molecules that have repeat units of different size (i.e. we introduce no unusual steric or electronic differences on going from molecule or molecule), we can use equilibrium constants determined in one system (e.g. phenol) in another (coal) by simply adjusting for differences in the molar volume of the molecules or average chemical repeat units. The second factor that needs to be considered is the assumption that the value of the equilibrium constant is independent of the length of the hydrogen bonded chain, n. There are theoretical reasons for believing that the formation of dimers may be characterized by a different equilibrium constant than the formation of subsequent n-mers (n > 2).32 This can be accounted for in a conceptually simple manner by defining a separate equilibrium constant for dimer formation, although this refinement comes at the expense of more complicated algeIn studies of model urethanes we have found that this is a fine distinction and makes little difference to the calculated stoichiometry and free energy of mixing. For systems containing phenolic OH groups, however, there is good reason to believe that there are also energetic differences between dimer and subsequent n-mer formation, and we have found it necessary to employ the more complicated treatment it calculating their phase behavior.30 Stoichiometry of Association. The equations relating the volume fractions of the components in a mixture to the distribution of hydrogen-bonded species present are simply 0 b t a i n e d ~ from ~ 3 ~ ~mass balance considerations and can be written as (31) Brandani, V. Fluid Phase Equilib. 1983,12, 87. (32) Sarolea-Mathot, L. Trans. Faraday SOC.1963,49, 8. (33) Graf, J.; Coleman, M. M.; Painter, P. C., to be submitted for

publication.

696 Energy & Fuels, Vol. 2, No. 5, 1988

Painter et al.

where x is the usual Flory-Huggins interaction parameter and NAand NB represent the “degrees of polymerization” of the components. This form of the equation is in terms of a free energy per segment. If we allow a solvent molecule to define the lattice cell size, then NA = l and NB would be equal to the molar volume of the coal macromolecule divided by the molar volume of the solvent. Although it is conventional to allow the solvent to define These equations describe the situation where KB is inthe lattice, a definition in terms of the interacting unit of dependent of n and relate the volume fraction of self-asthe coal molecule is, of course, equally valid and makes no sociating species (aB)and solvent (@A) present in a binary difference to the predicted phase behavior. This we will mixture (@A + = 1)to the equilibrium constants KA and consider below. KB and the volume fraction of those units that at equiThe factors for the combinatorial entropy of mixing and librium are not hydrogen bonded, @Bl and a0A. These are AGH are negative and thus favorable to mixing. In this crucial quantities in the calculations of the free energy of formulation x accounts for the “physical” interactions mixing. Because KA and KB can be determined from between the components of the solution and is usually spectroscopic m e a ~ u r e m e n t and s ~ ~@A~and ~ ~ @B ~ ~are ~~~~ positive and unfavorable to mixing. It is the balance known for a particular composition, eq 7 and 8 can be used betwen these factors that should, at least in terms of to calculate a0Aand @B1. The equations have a more general trends, predict the phase behavior of coal solutions. complicated appearance when self-association of species The value of x will be considered below. Expressions B in the form of dimers is characterized by an equilibrium for AGH have been and for the situation where constant (Kz)different from that describing the formation self-association is described in terms of two equilibrium of subsequent n-mers (KB): constants (K, and KB), we can write @n =

-@Bl[

@A

(1 -

2) 2 + LBJ2)][?] +

((1

1

+

= where X = (KA aOA)/r. The degree sign denotes the parameter in the pure state, and

These equations reduce to (7) and (8) when Kz = KB, as they must. We now have the situation where three equilibrium constants, K2,KB, and KA, have to be determined from spectroscopic (or thermodynamic) data. Theoretically,this is readily accomplished by a fit to results obtained over a range of concentrations. In practice, great care must be taken to minimize errors as in certain cases a range of acceptable values for the equilibrium constants can otherwise be determined. We have discussed this problem for the specific case of mixtures of poly(4-vinylphenol) with various acrylates,m while the more general case of self-association of phenol in non-hydrogen-bonding diluents has been the subject of a detailed study by Whetsel and Lady.34 Free Energy of Mixing. Our initial aim is to consider the broad effect of hydrogen bonding on the thermodynamics of mixing. Accordingly, we have chosen a FloryHuggins expression for the free energy to which we simply add a term AGH accounting for the free energy associated with the changing pattern of hydrogen bonding that occurs as a function of solution composition. To our surprise, this model has proved to be far more quantitatively useful than we dared to imagine in predicting the phase behavior of various polymer blend s y ~ t e m s Accordingly, . ~ ~ ~ ~ ~ at this point in our efforts, more sophisticated treatments of mixing, such as those involving free volume, will be largely neglected until the imperatives of quantitative experimental data make them a necessity. We therefore write

(34) Whetael, K. B.; Lady, J. H. In Spectrometry of Fuels; Friedel, H., Ed.; Plenum: London, 1970; p 259.

The corresponding values of roland ro2are obtained by substituting @ O B 1 for @Bl and

A crucial point needs to be made here. The equation describing AGH appears complicated (but once you get used to it, it has an easily understandable structure) and involves a number of parameters. All of these parameters are determined independently from infrared measurements and the equations describing the stoichiometry of the system. T h e y are not determined by a fit to thermodynamic data. Furthermore, once equilibrium constants for a particular type of hydrogen bond (eg. phenol-phenol, phenol-pyridine) have been determined, they can be applied to other molecules containing the same functional group, providing that we do not introduce unusual steric or electronic factors on going from molecule to molecule. As noted above, the equilibrium constants are simply adjusted to account for the difference in size of the interacting chemical repeat units. Phase Behavior. The phase behavior of polymer mixtures is defiied by the position of binodal and spinodal curves. Binodal curves are, of course, calculated by equating the chemical potentials of each component in each phase and solving by numerical methods. In contrast, analytical expressions can usually be determined for the

Energy & Fuels, Vol. 2, No. 5, 1988 697

Thermodynamics of Coal Solutions

spinodal, so curves defining the stability limit are more easily obtained. This remains true when hydrogen-bonding interactions are accounted for by an association The spinodal equation is given b y the condition a2(AG / R T ) =o (16)

aa$

The second derivatives of the Flory-Huggins terms in eq 11 have the familiar form

The second derivative of the expression for AGH is not so easily obtained, but can be shown to be equal to

Analytical expressions have been obtained for the derivative terms by differentiating and arranging eq 9 and 10. These expressions are clumsy, however, and eq 18 is the more illuminating form. The free energy associated with hydrogen-bonding interactions in the mixture is derived in terms of the concentrations of “monomers”, i.e. those units that have no hydrogen-bonded partners whatsoever, through substitution of the condition of equality of the chemical potentials of these “monomers” and their stoichiometric counterpart^.^^^^^ That is PB, = PB PA1 = PA (19) a relationship demonstrated by P r i g ~ g i n for e ~ ~a system in equilibrium. Accordingly, the stability limit should depend upon the balance between the variation of the concentration of these units with composition, a relationship expressed by eq 18. Temperature Dependence. Phase behavior as a function of temperature and composition is simply obtained for this model. We let x have the conventional (1/T)dependence and note that the equilibrium constants, K2,KB, and KA describing B-B and B-A hydrogen bonds depend upon the enthalpy of these bonds h2, h?, and hBA, through the usual thermodynamic relationships:

Hence

$)I

K2 = KO2 ex.(-;(

$-

KB = KoB exp{-;(

$ - h)}

(23)

where To is a reference temperature and hlBis an enthalpy correction term. In the usual range of temperatures accessible to organic macromolecules, the infrared frequency shifts are of the order of 20-40 cm-l, however, which indicates only small changes in enthalpy. The refinement offered by eq 26 therefore seems unwarranted at this stage, where we are interested in predicting broad trends.

Model Structures and Parameters The calculation of the free energy and phase behavior of coal solutions described in the above equations requires a knowledge of parameters that depend upon coal structure. For example, the Flory x parameter should vary systematically with the composition and hence rank of coal. In the model used here, hydrogen-bonding interactions are considered separately from this parameter, which to a first approximation is assumed to arise from simple “physical” forces and is thus calculated by using the solubility parameter approach. Solubility parameters are most accurately applied to nonpolar materials; interactions between polar functional groups can obviously lead to exothermic interactions. Such negative interaction terms are most commonly associated with specific interactions between localized charges, however. Weak nonlocalized polar forces obviously must contribute to the cohesive energies and are thus implicitly incorporated into calculated or measured values of the solubility parameters. For coals that do not contain carboxylate groups, the most likely specific interactions are hydrogen bonds, which we account for in a separate AGH term. Accordingly, we believe that solubility parameters can be used to a first approximation in calculating broad trends. This assumption is supported by the success we have achieved in applying this approach to a description of the phase behavior of synthetic polymers containing phenolic OH, amide, urethane, and carboxylic acid g r o ~ p s . ~ ~ ~ ~ ~ ~ ~ ~ One approach to the calculation of solubility parameters for coal is that described by van Krevelen,2 which empirically relates group contributions to the atomic ratios and fraction aromaticity. Values ranging from 15.2 to about 10.6 (cal/cm3)’I2were determined in this fashion. These values are larger than those determined by Larsen and colleagues5from swelling measurement, but it should be noted that only nonpolar contributions were included in these latter correlations. In order to illustrate trends, we will use a variant of van Krevelen’s method. Rather than consider the effect of varying x purely as a function of composition and aromaticity, we will postulate simple

(24)

(35) Prigogine, I.; Bellemans, A,; Mathot, V. The Molecular Theory Amsterdam, 1957; Chapter XV.

of Solutions;North-Holland

where KO2,KOB, and KOA are the values of the equilibrium constants at the absolute temperature T”. Of course, this assumes that the enthalpy of hydrogen bond formation remains a constant with temperature. We have noted infrared frequency shifts in the NH (and OH) stretching region of the spectra of various polymers”37 and that indicate that this is not so. Accordingly, we can include the linear dependence of enthalpy upon temperature as

(36) Moskala, E.J.;Varnell, D. F.; Coleman, M. M. Polymer 1985,26, 228. (37) Skrovanek, D.J.;Painter, P. C.; Coleman, M. M. Macromolecules 1986,19, 699. (38) Coleman, M.M.; Painter, P. C., various results to be submitted for publication. A summary of this work can be found in nine papers in: Polym. Prepr. (Am. Chem. Soc., Diu.Polym. Chem.) 1988. (39) van Krevelen, P. W. Properties of Polymers; Elsevier: Amsterdam, 1972.

698 Energy & Fuels, Vol. 2, No. 5, 1988 MODEL

Painter et al.

STRUCTURFS

Table 111. Parameters for Structures of Type B Cod PBTBmS 3 rine 4 ring 5 rim 6 rine molar vol, cm3 mol-' 243.8 271.9 300.0 328.1 6,, (cal cm9)'/* 12.5 12.8 12.9 13.1 0.804 0.927 1.04 1.14 XK 7.7 8.6 7.0 6.4 KZ hz,kcal mol-' 5.6 5.6 5.6 5.6 27.6 24.7 22.4 20.5 K B he, kcal mol-' 5.2 5.2 5.2 5.2 193 173 157 144 KA h A , kcal mol-' 8.9 8.9 8.9 8.9 r 0.33 0.30 0.27 0.25 10.2 11.3 12.5 13.7 SB

IYe.€.A

n€!LA

*

I

T2 0

Two rina structures

P

I

CH 2/CH

z T \ 2 J J&

r2

Three rina structures

I

2

T2 0 I

F i g u r e 1. Model structures for "average" coal repeat units. Table 11. Parameters for Structures of TyDe A 3 ring 4 ring coal params 5 ring 6 ring 133.9 162.0 molar vol, cm3 mol-' 190.1 218.2 13.3 13.5 6,, (cal cm-3)1/2 13.7 13.8 1.28 1.46 1.60 1.71 Xle 15.7 13.0 11.1 9.6 KZ 5.6 h2,kcal mol-' 5.6 5.6 5.6 41.5 50.2 35.4 30.8 KB hn, kcal mol-' 5.2 5.2 5.2 5.2 352 291 248 216 K A h A , kcal mol-' 8.9 8.9 8.9 8.9 r 0.61 0.50 0.43 0.37 5.6 6.8 7.9 9.1 SB

hypothetical model structures that allow a visualization of the change in the relative proportions of particular types of functional groups. These are illustrated in Figure 1. Essentially, we assume that coal is a macromolecule consisting of aromatic rings that are linked by aliphatic CH2 and ether bridges. The aliphatic content of the coal can be varied by changing the number of CH2 (and/or CH3) groups present and the number of condensed aromatic rings in a cluster. The precise distribution of functional groups, i.e. whether or not the ether linkage is removed from the postulated (-CH2-0-1 bridge and attached separately to the ring thus making it a trifunctional unit, or making the alicyclic (CH2)4 ring an alkyl (CH2),CH3substituent has very little effect on the calculated solubility parameter, 6,. The prime factors affecting this quantity are the relative proportions of aliphatic and aromatic groups and the fraction of oxygen-containing functionalities. Note that the effect of hydrogen bonding on the calculated cohesive energies is removed by approximating the contribution of OH groups to be equivalent to ether oxygens. The values of 6, calculated for the structures of the type shown in Figure 1 are summarized in Tables I1 and 111, as a function of the number of aromatic rings incorporated into the "average" repeat, and fall within the range determined by van Krevelen.2 Calculations were made by using the group molar attraction constants determined by HoY.~OThe value of x can then be obtained from

x

= 0.3

v* + -[6, RT

- 6J2

(27)

where V , is the molar volume of the solvent and there is a numerical constant (0.3) added to the traditional form of the equation. The initial justification for the addition (40) Hoy, K. L.

J. Paint

Technol. 1970, 42, 76.

of this constant (experimentallydetermined to have values between 0.3 and 0.4) was the supposed inadequacy of the Flory combinatorial entropy expression. Patterson et alS4' subsequently inerpreted this factor as a correction for the difference in free volume between a macromolecule and a solvent. In addition to values of x calculated from solubility parameters, we need to obtain values of the molar volumes of the solvent and hypothetical average coal repeat unit, the number of segments in this unit, sB, defined relative to the phenolic "interacting unit", and the equilibrium constants and enthalpies associated with the various hydrogen bonds that can form. All of these quantities can be obtained from the literature. The molar volume of the solvent pyridine was assumed to be 81 cm3/(g mol), while molar volumes of the average chemical repeat units of the coal molecule were calculated from the individual group contributions listed in van Krevelen's The equilibrium constants describing self-association of phenolic OH groups, K2 and KB,were taken from the detailed study of phenol by Whetsel and Lady% and simply adjusted to account for the difference in molar volumes by using

as shown in a preceding p~blication.~'The equilibrium constant describing hydrogen bonds between phenolic OH groups and pyridine were calculated in the same manner by using values determined for interactions between phenol and pyridine.41* Enthalpies of hydrogen bond formation of 5.2, 5.6, and 8.9 kcal mol-', corresponding to the three equilibrium constants K,,KB,and KA,were obtained from the same literature sources. The values of these parameters are also summarized in Tables I1 and 111. The number of segments in a repeat unit, sB, defined relative to the molar volume of the phenolic OH interacting unit, has been determined for phenol and cresol to be 3.5 and 4.2, re~pectively.~' Adjusting for the calculated molar volumes of the coal repeat units give the values listed in Tables I1 and 111. Calculations The calculation of the free energy per segment according to eq 11 depends upon the definition of a reference volume. In a preceding paper on polymer blends, we found it convenient to use the molar volume of the chemical repeat of the self-associatingp ~ l y m e r * ' as , ~this ~ ~ quantity. For (41)Biros, J.; Zeman,L.; Patterson, D. Macromolecules 1971, 4 , 30. (42) Rubin, J.; Parson, G. S. J. Phys. Chem. 1965, 69, 3089. (43) Cranstad, T. Acta. Chem. Scand. 1962, 16, 807. (44) Singh, S.; Murthy, A. S. N.; Rao, C . N. R. Trans. Faraday SOC. 1966,62, 1056.

Energy & Fuels, Vol. 2, No. 5, 1988 699

Thermodynamics of Coal Solutions

become less negative, increasingly asymmetric, and obviously concave downward over at least a portion of the composition range. A negative free energy of mixing is a necessary but not sufficient condition for mixing, and the -0.0 concave shape of the free energy curves for highly aromatic -0.1 molecules indicates that the solutions become partially & miscible, a phase behavior that can be quantitatively deRT -0.2 scribed by binodal and spinodal curve. Binodal curves are calculated by equating the chemical -0.3 potentials of each component in each phase and solving by numerical methods. Iterating to a “valid” solution can be a difficult process, however. In contrast, analytical 0.0 0.2 0.4 0.6 0.8 1.0 VOLUME FRACTION COAL solutions are available for the spinodal, which defines the stability limit, and these are more easily determined. This Figure 2. Plots of free energy of mixing coal molecules of type A (degree of polymerization = 100) with pyridine. remains true when hydrogen-bonding interactions are accounted for by an association model, as eq 18 demonstrates. Accordingly, most of our discussion of trends will I be based on the spinodal curves, but we have calculated binodals for some specific examples to illustrate the generality of our arguments. Figure 4 shows spinodal curves for pyridine solutions of ... ’. structures of type A (i.e. no acyclic rings and hence a ..... -0.3 -1 c IIue relatively high ratio of aromatic to aliphatic carbon). For -0.4 5 RING a system consisting of four aromatic rings, one of which has a phenolic OH group, linked by methylene and ether -0.5, . , , . ’ bridges, the usual type of inverted U-shaped stability curve 0.0 0.2 0.4 0.6 0.8 1.0 characterized by an upper critical solution temperature is VOLUME FRACTION COAL predicted for low-molecular-weight material (e.g. monoFigure 3. Plots of free energy of mixing coal molecules of type mers, N B = l),as shown in the top left-hand phase diagram B (degree of polymerization = 100) with pyridine. of Figure 4. This curve predicts that solutions would only polymers in solution, however, it is conventional to use the phase separate at temperatures well below the freezing molar volume of the solvent as a reference point. The point of pyridine. As the size of the coal molecule inequations for each are simply related as follows: creases, however, an immiscibility loop appears and is prominent for degrees of polymerization of about 20. This type of phase behavior is often observed in mixtures of coal segment low-molecular-weight materials that hydrogen and it is encouraging that our model predicts such beAGH @B @A@B . - In @A NIn @B + -x + (29) havior. In principle, a solution of the appropriate comr RT B r position would be miscible at high temperatures, become immiscible as the temperature is lowered into the region of the loop, become miscible again at still lower temperatures, and once more immiscible at even lower temperatures. If it could be observed, this would be a classic example of the phenomenon of reappearing phases, a consequence of the changing balance of entropic, physical, where r = v A / VB,the suffix B and A now represent coal and hydrogen-bonding forces with t e m p e r a t ~ r e . Un~~ and solvent, respectively, and NB is the “truen degree of fortunately, the predicted temperature range for this bepolymerization of the coal molecule (i.e. not calculated havior is well beyond the boiling point of pyridine. The relative to the volume of the solvent molecule). Although position of the closed loop is very dependent upon the the magnitude of the values of the free energy differ by relative size of the hydrogen-bonding and physical forces, the factor r , the phase behavior calculated by these two however, so it is possible that other solvents that hydrogen equations is identical, as, of course, it must be. We will bond less strongly than pyridine or have smaller use eq 30 in subsequent calculations. “repulsive” physical interactions could display this intriWe have chosen pyridine as the solvent to illustrate the guing phenomenon in an experimentally accessible temgeneral trends in the thermodynamics of coal solutions perature range. because it is known to strongly hydrogen bond to most coal As the degree of polymerization of this type of coal molecules (i.e. those containing phenolic OH groups) and molecule is increased, the immiscibility loop and the lower has been the solvent of choice for many extraction and lying stability curve expand to meet each other at a double swelling experiments and also in the determination of the critical point,’in this example at a value of N B somewhat molecular weight of soluble material. Some calculated free greater than 30. For higher molecular weight molecules, energies for mixing various hypothetical coal molecules the phase diagram then takes on the classic hourglasswith pyridine are shown as a function of composition in shaped curve of a phase-separated system. In other words, Figures 2 and 3. Figure 2 displays curves calculated for in the range of temperature defined by the boiling and the structures that do not contain acyclic rings; the free freezing point of pyridine, the system will phase separate energy is negative throughout the composition range. into a solvent-rich phase and a solvent-swollen, coal-rich Increasing the relative proportion of aliphatic to aromatic phase. groups results in a larger (more negative) free energy of mixing. Conversely, as the number of condensed aromatic (45) Walker, J. S.; Vause, C. A. Sci. Am. 1987, (May), 98. (46) Walker, J. S.; Vause, C. A. J. Chem. Phys. 1983, 79, 2660. rings in the average repeat cluster increases, the curves COAL-PYRIDINE MIXTURES AT 25°C

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700 Energy & Fuels, Vol. 2, No. 5, 1988

Painter et al. NB=20

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Figure 4. Spinodal curves for coal (type A)/pyridine solutions as a function of degree of polymerization of the coal macromolecule. The plots are for molecules containing four condensed aromatic rings per repeat unit.

This is an intriguing result for a number of reasons. First, it suggests that at least for high-rank coals (number of aromatic rings per repeat greater or equal to four) the observed swelling and solubility properties are not necessarily due to the coal being a cross-linked network (although when we consider the rest of our calculations of phase behavior we will see that this remains the most logical and consistent interpretation). Low-molecularweight materials would be soluble, while a high-molecular-weight molecule would phase separate into a solventrich phase and a solvent-poor (i.e. swollen gel-like coal) phase. The binodals are much closer to the composition limits than the spinodals, so the solvent-rich phase would be relatively dilute (see below). Accordingly, successive extractions would continue to dissolve a portion of the high-molecular-weight material, but it would take many such extractions to obtain an appreciable fraction of soluble material. In this context it is important to note that Vahrman47i48found that extraction of coal with solvents may need to be carried out successively and for long time periods to remove all extractable material, an observation ~~ supported by the work of Bodzek and M a r ~ e c .Vahrman suggested that some molecules are extracted slowly because they are in pores of restricted size. This seems unlikely given the degree of swelling of most coals in solvents like pyridine. An immediate explanation is apparent from the types of phase diagrams we are calculating for coal solutions, however. There is a partition between solvent-rich and solvent-poor phases each time a fresh batch of solvent is used for extraction. Of course if the coal molecules were not cross-linked, this could continue indefinitely, and the above cited work suggests that some limit of extractability is approached. This model also predicts that lower rank coals (i.e. smaller numbers of aromatic rings per repeat unit) would be completely soluble if they were not cross-linked. This is illustrated in Figure 5, which shows binodal as well as (47) Vahrman, M. Chem. Br. 1972,8, 16. (48) Vahrman, M. Fuel 1970,49, 5. (49) Bodzek, D.; Marzek, A. Fuel 1981, 60,47.

spinodal curves for coals (of type A in Figure 1)of different aromaticity, or number of condensed rings per repeat unit or cluster (a degree of polymerization of NB = 100 was assumed in calculating all these curves). When there are three aromatic rings or less per repeat unit, the phase behavior is characterized by classic low-temperature inverted U-shaped curves. For coal molecules of higher aromaticity, hourglass-shaped curves are calculated that predict an increasing partition between a solvent-rich and solvent-poor phase as the number of aromatic rings per repeat unit is increased. As many coals are thought to have between one and three aromatic units per “average”repeat, one must conclude that there are cross-links preventing complete dissolution of the molecules. High-molecularweight and highly aromatic molecules would only be extractable with repeated applications of solvent, however. The coal models considered so far have very high aromatic to aliphatic carbon ratios. The effect of increasing the aliphatic carbon content, through the inclusion of acyclic rings in the model, for example, results in a higher degree of predicted solubility. This is illustrated in Figure 6 where an acyclic ring of four CH2 groups attached to seven aromatic rings serves to render it soluble at low degrees of polymerization. Not until very large molecules (NB 1000) are considered do we find hourglass-shaped phase diagrams. Molecules with smaller numbers of aromatic rings in the repeat unit are completely soluble in pyridine in the experimentally accessible temperature range, reflecting the smaller x parameter for such coals.

-

Discussion The x parameters calculated for some of the model structures used here could be considered unusually large. This is simply a reflection of their very high aromatic carbon contents, however. Most experimental studies of the dissolution and swelling have been made on coals with a higher proportion of aliphatic to aromatic carbon, which have smaller values of x. Although the positive free energy contributions of the physical “repulsion” terms embodied in this parameter are thus overestimated, it should be noted that the negative free energy contributions of hy-

Energy & Fuels, Vol. 2, No. 5, 1988 701

Thermodynamics of Coal Solutions 3 RING

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Figure 6. Spinodal curves for coal molecules (Type B) mixed with pyridine. Seven aromatic rings per cluster were assumed.

drogen bonding are also overestimated, in so much as we assume one phenolic unit per aromatic cluster and neglect the ability of these OH groups to also hydrogen bond to coal ether groups. These factors can be readily accounted for in more detailed calculations, but at this point we are interested in just a general presentation of a model and a demonstration of trends. We simply note here that use of smaller values of x, such as those experimentally determined by Larsen and colleagues for methylated coals,5 would result in phase diagrams that would predict solubility of all non-cross-linked material. Conversely, reducing the contribution of the free energy of hydrogen-bond formation would result in the phase diagrams appearing

more like those calculated for the higher aromaticity, higher molecular weight models. Accordingly, if we consider other solvents that hydrogen bond to phenolic OH groups, such as THF, we would anticipate that the phase behavior would shift in the same unfavorable to mixing direction, because the equilibrium constant describing such interactions is generally smaller than that describing phenolic OH/pyridine hydrogen bonds. Clearly, in future work we must consider the interactions between a range of solvents and "average" coal repeat units constructed from elemental analysis and spectroscopic data. Furthermore, now that we have obtained an expression for the free energy of hydrogen-bond formation, it should be a

Energy & Fuels 1988,2, 702-708

702

straightforward matter to include the contribution of this factor to the chemical potentials and hence obtain expressions that can be used to interpret swelling and molecular-weight measurements with more precision. In conclusion, we have derived expressions for the contribution of hydrogen-bond formation to the free energy of mixing molecules. This has proved successful in predicting the phase behavior of synthetic polymers containing phenolic OH groups,3oand there is no reason to believe that the general approach should not apply to coal. The model predicts that low-molecular-weight, low-aromaticity coal macromolecules should be soluble in pyridine,

indicating that such coals must be cross-linked. Higher aromatic, high-molecular-weight molecules phase separate in solution into solvent-rich and solvent-poor swollen coal gels, however, indicating that many successive extractions would be required to remove the bulk of such non-crosslinked material from a particular sample. Acknowledgment. We gratefully acknowledge the support of the Office of Basic Energy Sciences, Division of Chemical Sciences, Department of Energy, under Grant NO. DE-FG02-86ER13537. Registry No. Pyridine, 110-86-1.

~

Aluminosilicate Sorbents for Control of Alkali Vapors during Coal Combustion and Gasification W. A. Punjak and F. Shadman" Department of Chemical Engineering, University of Arizona, Tucson, Arizona 85721 Received February 1, 1988. Revised Manuscript Received May 10, 1988

Kaolinite is found to be a suitable sorbent for the removal of alkali from hot flue gases. The kinetics and mechanism of adsorption of NaCl vapor on kaolinite were studied at 800 OC under both nitrogen and simulated flue gas (SFG) atmospheres. Under nitrogen, both chlorine and sodium were retained by the sorbent; however, under the simulated flue gas, only sodium was retained. In both cases the adsorption was irreversible. High-resolution scanning Auger analysis of kaolinite particles indicated the formation of a product layer during adsorption. Under the SFG atmosphere the product layer appears to be nephelite, a stable sodium aluminosilicate compound. The rate of adsorption dropped with the increase in alkali loading, and a maximum saturation limit was observed. In the SFG environment this saturation capacity was approximately 5 times greater than that under the nitrogen atmosphere. An analytical model is presented that facilitates the extraction of fundamental kinetic information from experimental results. The model allows for surface adsorption as well as diffusion through both the saturated product layer and pores of the active sorbent.

Introduction A significant fraction of the alkali-metal compounds present in coal are vaporized during combustion or gasifi~ation.'-~The released alkali vapors are the precursors of hot condensates that cause corrosion of various parts of the combustors, gasifiers, and the downstream systems for secondary energy r e c ~ v e r y . For ~ ~ ~example, the corrosion caused by alkali vapors is important in combined cycle processes where the hot flue gases come in contact with turbine materials. In such applications the alkali concentration should be reduced to less than 50 ppb to prevent significant hot corrosion. One of the promising techniques for removal of alkali from hot flue gases is by using solid sorbents. Various studies have considered the feasibility of passing the flue gases through a fixed-bed filter of appropriate sorbents.H This process seems to be quite feasible for application in pressurized fluidized-bed combustion before the turbine section. The use of additives for in situ capturing of alkali during pulverized coal combustion has also received some attention.1° Most of the previous studies have concentrated on the selection of sorbents and the overall feasibility of the

* To whom correspondence should be addressed 0887-0624 I88 12502-0702$01.50 I O I

,

process. The mechanism of adsorption and, particularly, the fundamental kinetics of adsorption are not well understood. In recent years, there have been some studies of the fundamentals of alkali adsorption on various sub(1)Raask, E. Mineral Impurities in Coal Combustion; Hemisphere: New York, 1985; Chapter 7. (2) Huffman, G. P.; Huggins, F. E. In Mineral Matter and Ash i n Coal; Vorres, K. S., Ed.; ACS Symposium Series 301; American Chemical Society: Washington, DC, 1986; Chapter 8. (3) Berkowitz, N. The Chemistry of Coal; Elsevier: New York; Chapter 9. (4) Brio, R. W.; Levasseur, A. A. In Mineral Matter and Ash in Coal; Vorres, K. S., Ed.; ACS Symposium Series 301; American Chemical Society: Washington, DC, 1986; Chapter 21. ( 5 ) Raask, E. Mineral Impurities in Coal Combustion; Hemisphere: New York, 1985; Chapter 17. (6) Lee, S. H. D.; Johnson, I. J.Eng. Power 1980, 102, 397. (7) Lee, S. H. D.; Henry, R. F.; Smith, S. D.; Wilson, W. I.; Myles, K. M. Alkali Metal Vapor Removal from Pressurized Fluidized-Bed Combustor Flue Gas; ANL-FE-86-7; Argonne National Laboratory: Argonne, IL, 1986. (8) Bachovchin, D. M.; Alvin, M. A.; DeZubay, E. A.; Mulik, P. R. A Study of High Temperature Removal of Alkali in a Pressurized Gasification System; DOE-MC-20050-2226;Westinghouse Research and Development Center: Pitssburgh, PA, 1986. (9) Jain, R. C.; Young, S. C. LaboratorylBench Scale Testing and Eualuation of A.P.T. Dry Plate Scrubber; DOE-ET-15492-2030;Air Pollution Technology: San Diego, CA, 1985. (10) Klinzing, G. E.; Blanchere, M.; Weintraub, M.; Shannon, S.; Martello, D., University of Pittsburgh, personal communication.

1988 American Chemical Society