Energy & Fuels 1990,4, 379-384
catalyst deactivation, while hydrogen gas acts either as a hydride donor to saturate carbenium ion intermediates or as a proton donor to reactivate Brernsted superacid sites. Acknowledgment. We acknowledge Celal Dogan and Joseph L. Fabec for their assistance in the characterization of catalysts. We also thank Dan Fraenkel for discussions. The research was supported by the U.S. Department of Energy under University Research Program Contract No. DE-FG22-87PC79928,
379
Registry NO.2102,1314-23-4; HfO2,37230-85-6; Pt,7440-06-4; hafnium zirconium oxide, 104365-48-2; hexadecane, 544-76-3; heptane, 142-82-5; propane, 74-98-6; ieobutane, 75-28-5; butane, 106-97-8; isopentane, 78-78-4; pentane, 109-66-0; 2,a-dimethylbutane, 75-83-2; 2,3-dimethylbutane, 79-29-8; 2-methylpentane, 107-83-5;3-methylpentane, 96-14-0; hexane, 110-54-3; 2,2,3-trimethylbutane, 464-06-2; 2,2-dimethylpentane, 590-35-2; 2,3-dimethylpentane, 565-59-3; 2,4-dimethylpentane, 108-08-7; 3,3dimethylpentane, 562-49-2; 2-methylhexane, 591-76-4; 3methylhexane, 589-34-4; 3-ethylpentane, 617-78-7.
Coal Solubility and Swelling. 1. Solubility Parameters for Coal and the Flory x Parameter Paul C. Painter,* John Graf, and Michael M. Coleman Polymer Science Program, Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802 Received January 30, 1990. Revised Manuscript Received May 29, 1990
This is the first of three papers that deal with coal solubility and swelling. An association model has been applied to coal, and this predicts that the mixing of coal with certain solvents will be determined by a balance between unfavorable "physical" interactions, measured by a Flory x parameter, and favorable hydrogen bonding interactions. This first paper deals with the determination of x from solubility parameters. Methods based on group contributions and swelling measurements are assessed. The former suffers from large errors while the latter does not give correct values because of large free-volume differences between coal and most solvents. Even though group contribution methods are flawed when applied to coal, they at least appear to give values in the right range.
Introduction The "solubility" &e., the amount of soluble material that can be extracted from a particular solvent at a given temperature) and swelling characteristics of a coal are fundamentally determined by its molecular structure. In order to relate macroscopic properties to molecular characteristics, however, we require a sound theoretical model. A considerable degree of at least qualitative insight'* has been obtained by applying the theories of Paul Flory,'oJ1 particularly those describing polymer solution thermodynamics and the swelling of cross-linked rubbers, and it is now generally accepted that coals can be described as macromolecular networks. Nevertheless, it is also widely recognized that these theories have serious shortcomings, when applied to coal. Perhaps the most crucial of the additional difficulties are that, first, the theories only deal with weak interactions (dispersive forces), which are handled by the assumption of random contacts and the definition of a parameter x. Strong specific interactions, such as the hydrogen bonds that occur in most coals, cannot be accounted for in this manner. Second, the "chains" that are presumed present in coal are probably too short and too stiff to obey Gaussian statistics, so that even if Flory's theories of swelling are correct, and this is an area of some controversy, they would be inapplicable to coal. Flory's work has been modified by various groups to account for these problems. For example, Kovac12has developed a modified Gaussian model that has been ap-
* To whom correspondence should be addressed. 0887-0624/90/2504-0379~02.50 ,I O I
,
plied to the swelling of coal by Larsen et ala5Recent work in this laboratory has been concerned with the use of association models to account for hydrogen b~nding.'~-'~ Our purpose in this series of papers is to put this work together in a comprehensive fashion and examine its strengths and limitations. This will lead us to the prediction of so far unobserved behavior, which ultimately allows a test of the validity of our approach, and to a reassessment of the way we interpret swelling measure(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; Cooper, B. R., Petrakis, L., Eds.; AIP Conference Proceedings 70; AIP New York, 1981. (5) Larsen, J. W.; Green, T. K.; Kovac, J. J.Org. Chem. 1986,50,4729. (6) Lucht, L. M.; Peppas, N. A. In Chemistry and Physics of Coal
Utilization; Cooper, B. R., Petrakis, L., Eds.;AIP Conference Proceedings 18; AIP: New York, 1981. (7) Lucht, L. M.; Peppas, N. A. Fuel 1987,615, 803. (8) Lucht, L. M.; Peppas, N. A. J. Appl. Polym. Sci. 1987,33,2777. (9) Brenner, D. Fuel 1985, 64, 167. (IO) Flory, P. J. Principles of Polymer Chemistry; Comell 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 Prese: Stanford, CA, 1985; Vol. 1-111. (12) Kovac, J. Macromolecules 1978, 11, 362. (13) Painter, P. C.; Park, Y.; Coleman, M. M. Macromolecules 1988, 21. 66. (14) Painter, P. C.; Park, Y.; Coleman, M. M. Macromolecules 1989, 22, 570. (15) Painter, P. C.; Park, Y.; Coleman, M. M. Macromolecules 1989, 22, 580. (16) Painter, P. C.; Park, Y.; Coleman, M. M. Energy Fuels 1988,2, 693.
0 1990 American Chemical Society
Painter et al.
380 Energy & Fuels, Vol. 4, No. 4, 1990 w
Q A1
> 0 K
w z w
F 5 z
0 Io a
E 1000
0
2000
3000
4000
SO00
AE (cal. mole") Figure 1. Calculation of the fraction of interacting units that have energies tAE at three different temperatures.
ments. The first two papers in this series will deal with coal-solvent interactions and how they are incorporated into the theories of swelling presently in use. The final paper will discuss an alternative approach. The interactions between a segment of a coal molecule and a solvent can be categorized as ranging from the relatively weak (e.g., dipole-dipole) to the relatively strong (e.g., hydrogen bonded). This distinction is somewhat arbitrary and is probably best described in terms of the magnitude of energies involved. Figure 1shows the results of a simple calculation using Boltzmann's distribution to determine the fraction of molecules (or, in this case, interacting segments) that have energies greater or equal to at a given temperature. the energy of dissociation (a) Above interaction strengths of about 3 kcalemol-' less than 1% of the interacting units would have sufficient energy to dissociate at any particular instance; this is the realm of the (relatively) strong hydrogen bonding interactions typical of the phenolic OH groups found in coal. Here we cannot assume random contacts of these functional groups. Conversely, below say 1 kcal-mol-', there is a substantial fraction of interacting units that have energies I h E and it is appropriate to assume random mixing and a mean field. Between these two poles, Le., AE values of between approximately 1-3 kcal-mol-', we have an intermediate case where the situation is not clear-cut. In this work we will assume, to a first approximation, that weak and intermediate-strength interactions can be handled by the usual Flory x parameter and that the effect of hydrogen bonding can be included by the use of an association model. Accordingly, the free energy of a coal-solvent mixture will depend upon a combinational entropy term and the balance between the favorable hydrogen bonding interactions and the generally unfavorable x term. This is a crucial point. Because we have separated strong, specific interactions, the value of x will only reflect "physical" forces, (van der Waals, London dispersion forces, interactions between aromatic rings, etc). This, in turn, suggests that again to a first approximation we should be able to estimate its value using solubility parameters from the wellknown relationship
x
= (V*/W[~ 6,12 ,
+P
(1)
where V, is the molar volume of the solvent (a reference volume), 6, and 6, are the solubility parameters of the coal and solvent, respectively, and P is an empirical parameter that usually has a value of the order of 0.34. Note that
in order to apply this equation we now need to consider solubility parameters calculated or measured so as to exclude the effect of hydrogen bonding. These latter effects are handled separately, as we mentioned above. We will defer a discussion of hydrogen bonds to the following paper and concern ourself here only with the calculation of x. For an insoluble network the solubility parameter (6,) can be determined in one of two ways; from group contributions using, for example, the methods of van Krevelen?" Hoy,18 or Small,l9or from experimental swelling measurements. Unfortunately, both these methods involve difficulties and for coals lead to the prediction of very different solubility parameters, even when the effect of hydrogen bonding is minimized or excluded. For example, Larsen et aL5carefully examined the swelling of acetylated coals in non-hydrogen-bonding solvents. An Illinois No. 6 coal and a Bruceton coal both gave a maximum degree of swelling for solvents with solubility parameters in the range 9-10 ( ~ a l - c m - ~ This ) ~ . ~value . would then normally be taken as the proper value for coal, as it would give the minimum value for x. However, a calculation of the corresponding solubility parameters using the atomic contribution method proposed by van Krevelen2 gives values depending upon the precise in the range 11-12 (~al.cm-~)O~, value of the fraction aromaticity assumed for these samples. We found it difficult to determine precisely how van Krevelen obtained his parameters, as his methodology is not described, but on the basis of our calculations we believe it to be prone to large errors and full of broad and perhaps unjustifiable assumptions, as we will discuss in the body of this paper. The obvious choice would therefore seem to be the experimentally determined values. Paradoxically, we believe that van Krevelen's result is at least in the right range and the value determined from maximum swelling is not that corresponding to the value of the solubility parameter for coal. This is not because of any problem with the experiments, but one that has its origins in free-volume or compressibility effects that are ignored in simple theories of mixing. We will now commence our discussion with an examination of van Krevelen's methodology. Calculation of Solubility Parameters Using Group Contributions At first glance it appears to be a trivial task to calculate the solubility parameter of a macromolecule. One only has to consider the groups present in the repeat unit (e.g., -CH2-, -0-, -CH,), refer to tables of molar attraction constants (F)determined by various a u t h o r ~ , ~ Jand ' - ~ ~use the relationship d = CFi/V
(2)
There are two immediate problems in applying this to coal: first we do not know the precise distribution of functional groups; second, there are large differences in the values of the attraction constants reported by different authors and one often does not know the extent of errors involved with the choice of a particular set of parameters. We will first examine this latter problem as it is central to our subsequent discussion. The group contribution method, originally developed by Small,lg was considerably expanded by Hoy18 and van Kre~e1en.l~ In applying the values tabulated by these last two authors to synthetic polymers, however, we encoun(17) van Krevelen, P. W. Roperties of Polymers; Elsevier: Amsterdam, 1972. (18) Hoy, K. L. J. Paint Technol. 1970, 42, 76. (19)Small, P. A. J.Appl. Chem. 1953, 3, 71.
Coal Solubility and Swelling. 1
Energy & Fuels, Vol. 4, No. 4, 1990 38 1
Table I. Atomic Grow Contributions V*, cm3 F*, WUP carbon hydrogen eater oxygen ketonic oxygen ether oxygen aromatic C=C nonaromatic C=C chlorine nitrile nitrogen primary nitrogen secondary nitrogen tertiary nitrogen
mol-’ -10.9 13.9 7.5 23.2 5.5 23.9 23.4 23.7 34.4 0.1 -3.8 -2.8
12
~
y
(cal.cms)0.6mol-’ 7.0 63.5 23.8 281 106 127 116 255 417 187 102 51.8
10
0.68 + 0 . 9 2 ~ RA2 = 0.937
/
0-
tered a number of problems and found various inconsistencies, often associated with the use of an insufficient number of compounds to adequately define parameters for particular groups. We therefore decided to calculate our own group contributions using a data set based on the properties of 255 non-hydrogen-bonding organic liquids.20 In performing these calculations we had the considerable advantage of access to powerful desk-top computers, unavailable when the above quoted work was performed. This allows the calculation of group contributions by matrix methods in a much more interactive manner and lays bare the consequences of unwarranted assumptions and the effects of errors. For a full discussion of these points the reader is referred to the original paper,2obut we note in passing that our results are in good agreements with the seminal work of Small,lg who clearly understood the limitations of the method. Of concern to our studies of coal are errors, which we will consider shortly, and the recognition of a fundamental assumption. In calculating group contributions the molar attraction constants are determined from the experimentally determined solubility parameters of the model liquids multiplied by their respective molar volumes (i.e., I F i = 6V). Accordingly, the subsequent calculation of the solubility parameter for an unknown material must also use group contributions to the molar volumes based upon a correlation using the same experimental data set used to determine the factors Fi. It has been common practice to use molar attraction constants from Hoy or van Krevelen with some arbitrary experimental or calculated molar volume. This is specious. It is necessary to have both molar volume (V*)and molar attraction (F*)values from the same set of model compounds in order to be consistent in calculating the solubility parameter of a macromolecule. This source of error was introduced by van Krevelen2 in his calculation of coal solubility parameters from group contributions. Because the precise distribution of functional groups in a coal could not then (and probably not now) be identified, he determined atomic contributions that could be related to the elemental composition of the coal and then calculated solubility parameters using
6
,
I
6
”
10
8
12
EXPT. SOLUBILITY PARAMETER (cal. cm-3)0*5
Figure 2. Comparison of calculated and observed solubility parameters.
results shown in Table I, which includes both the molar attraction constants and molar volume contributions that must be used in concert in order to limit errors. The values listed do not necessarily have intrinsic meaning when considered on their own; for example, carbon atoms are listed as having a negative contribution to molar volume! They are merely parameters obtained from a best fit of the experimental data, in the least-squares sense, that when taken together give the best correlation of observed and calculated values. These values can now be applied to the calculation of solubility parameters by expressing the molar attraction constants and molar volumes on a “per carbon atom” basis: H 0 ( N + S) 7.0 + 63.5fa + 63.5- + 106- + 51.8-
c
6, =
-10.9
c
o
c
W+S)
+ 12fa + 13.9-HC + 5.5-c - 2.8- c
I
.I
(4)
The symbol f a is the fraction of carbon atoms that are aromatic and for application to coal we have arbitrarily assumed that all oxygens behave as ether oxygens and included the contribution of sulfur atoms (generally small) with nitrogen. The “constitutional” effects, leading to the terms in f a in eq 4, were determined as contributions per “pair” of aromatic C atoms. Their contributions per carbon atom are thus half the corresponding values listed in Table
I.
where NJC denoted the atomic ratios H/C,O/C,etc., and the molar volume per carbon atom was calculated from the molecular weight per carbon atom and the density. Errors were not discussed in this work. We have attempted to reproduce van Krevelen’s values using the matrix method and data set mentioned abovez0and obtained the set of
When reapplied to the original data set, the parameters listed in Table I result in errors of h0.6 ( c a l - ~ m - ~(at ) ~the .~ 95% confidence level) in the determination of solubility parameters (compared to errors of f0.4 when functional group contributions are used20). The calculated and observed values are compared in Figure 2. Furthermore, one might anticipate that the deviation between calculated and observed values would be even greater than f0.6 when the atomic volume and attraction constants are applied to molecules not in this data set (i.e., coals). If we apply eq 4 to an Illinois No. 6 coal and use a value of fa = 0.78 determined by NMR measurements,21 we calculate a value of 6, = 11.4 ( c a l . ~ m - ~ compared )~,~, to a ) ~ . ~ from van Krevalue of about 11.8 ( ~ a l - c m - ~obtained velen’s plot of 6 vs the carbon content of coal. We do not place high confidence in the absolute value of this number,
(20) Coleman, M. M.; Serman, C. J.; Bhagwagar, D. E.; Painter, P. C. Polymer, in press.
(21) Davis, M. F.; Quinting, G. R.; Bronnimann, C. E.: Maciel, G.E. Fuel 1989, 68,763.
6=
C(Ni/C)Fi molar volume per carbon atom
(3)
Painter et al.
382 Energy & Fuels, Vol. 4, No. 4, 1990
r
OH
Figure 3. Model structure for Illinois No. 6 coal, illustrating approximately the distribution of functional groups. Table 11. Group Contributions
-CH, -CHZ-CH-
31.8 16.5 1.9
C6H3 C6H4
41.4
CsH6
-0Obmup
58.8 75.5 5.1
218 132 23 562 652 735 95
6.9 8.0 12.1 13.6 11.1 9.7 18.6
= PIV*.
particularly as it is outside the range of the model compounds used to obtain group contributions. It should be kept in mind that these model compounds contained functional groups that have individual contributions covering a much broader range, however, and we are predominantly concerned with the accuracy of these group contributions. Accordingly, is the value of 6, = 11.4 (cal-~m-~ to) a~ first . ~ approximation a sensible number? It probably is. Consider the model structure displayed in Figure 3. This has a value of fa of about 0.8 and carbon, hydrogen, and oxygen contents of 84%, 6%, and lo%, respectively, close to values for Illinois No. 6 coal (even closer if we replaced about 4 % of the carbons with sulfur and nitrogen). Using the functional group contributions shown in Table 11, taken from a larger subset,20we calculate a value of 6, = 11.5 ( c a l . ~ m - ~(acetylation )~.~ of the OH group results in no appreciable change in this value). The reason is apparent from a consideration of group values of 6 listed in the final column. An ether (or phenolic) oxygen considered on its own would have a solubility parameter of 18.6 (cal.~m-~)~". Benzene rings have values )~.~, upon the between 11 and 13.6 ( c a l + ~ m - ~depending degree of substitution. Naphthalene rings have larger values, as Smalllgdetermined. Counterbalancing this, alkyl groups have solubility parameters between 6.9 and 8 (~al.cm-~)O.~. Even though our knowledge of the distribution of functional groups is not precise, a simple consideration of the aromaticity and oxygen content of Illinois No. 6 coal indicates that a value of 6, in the range 11-12 (~al.cm-~)O.~ is far more reasonable than the value of 9-10 (cal-~m")~.~ indicated by swelling measurements. We reiterate that these differences are not due to hydrogen bonding, as the experiments of Larsen et al.5 and our calculationsmwere conducted so as to eliminate or at least minimize such effects. In addition, the functional groups shown in Figure 3 can be "shuffled" to give other arrangements with little change in the calculated value of 6,. Determination of Solubility Parameters from Swelling Measurements In resolving the differences in the values of 6, given by group contributions and swelling measurements, we first observe that this problem is not unique to coal. Bristow and Watson22found that certain rubbers with solubility )~.~ parameter values of the order of 9-10 ( c a l ~ m - ~gave (22) Bristow, G. M.; Watson, W. F. Trans. Faraday. SOC.1958, 54, 1731.
maximum swelling in a series of n-alkanes with heptane, 6 = 7.4 ( ~ a l - c m - ~ )This ~ . ~ difference . was demonstrated to be due to so-called free-volume effects by Biros et al.,23who applied Flory's equation-of-statetheory2e26 to the problem. It is a relatively straightforward matter to show that such effects also account for the observed maximum in the swelling of coal. We will apply the lattice fluid model of Sanchez and Lacombe2'-% rather than Flory's theory, however. The association formalism we use to describe hydrogen bond interactions13-15and the Sanchez-Lacombe theoryn-zs are both simple lattice models, the latter accounting for free volume by placing "holes" on the lattice, so for future application it is more appropriate to combine these approaches, as we will report elsewhere,3O rather than to somehow graft an association model onto Flory's equations-of-state theory. It is questionable that it is at all appropriate to apply such models to coal, of course, and there are various assumptions that limit their degree of quantitative accuracy even when applied to well-characterized synthetic polymers. Our aim here is to obtain a qualitative understanding of the problems involved in obtaining x from swelling measurements, however, and in this regard we suggest that the model is adequate. There is sufficient evidence to strongly support the proposition that coal is a macromolecular network,lP9so the major assumption is the degree to which lattice models apply to a macromolecule such as coal, which contains aromatic units or clusters that occupy groups of adjacent lattice sites rather than segments that each occupy just one lattice site. In this regard Guggenheim31has analyzed the statistical mechanics of mixing such molecules and found that the Flory approximation still applies reasonably well. We assume this would extend to a macromolecule consisting of chains of such clusters linked by flexible groups. Using the equations of Sanchez and Lacombe,na we then obtain the following expression for x:
or, more succinctly:
p A€* x=-+p'
kT where p and ?1 are the reduced density and temperature (see refs 27-29) and the subscripts 1 and 2 refer to components 1 and 2 of the mixture. The term A€* is given by A€* = ~*11+ ~*22- 2t*12 (7) and is the usual difference in the energy of 1-2 contacts relative to 1-1 and 2-2 contacts. If we make the geometric mean assumption t*12 = (€*11€*22)'/2 (8) then (23) Biros, J.; Zeman, L.; Patterson, D. Macromolecules 1971,4, 30. (24) Flory, P. J.; Orwoll, R. A,; Vrij, A. J. Am. Chem. SOC.1964, 86, 3515. (25) Flory, P. J. J. Am. Chem. SOC. 1965, 87, 1833. (26) Eichinger,B. E.; Flory, P. J. Trans. Faraday SOC.1968,64,2035. (27) Sanchez, I. C.; Lacombe, R. H. J. Phys. Chem. 1976,80, 2352, 2568. (28) Sanchez, I. C.; Lacombe, R. H. Macromolecules 1978, 11, 1145. (29) Sanchez, I. C.; Lacombe, R. H. J. Polym. Sci. Polym. Lett. Ed. 1977, 15, 71. (30) Painter, P. C.; Graf, J.; Coleman, M. M. To be published. (31)Guggenheim, E. A. Mixtures; Clarendon Press: Oxford, 1952.
:r
Coal Solubility and Swelling. 1
Energy & Fuels, Vol. 4, No. 4, 1990 383
The correspondence of this equation to the solubility parameter approach can then be seen immediately by rewriting eq 1on the basis of numbers of molecules rather than moles and transforming the subscripts:
x
1 n-Pentane 2 n-Heptane 3 Cyclohexane 4 o-Xylene 5 Toluene 6 Benzene
Di-Phenyl
8
2
1
The solubility parameters are related to the cohesive energy densities (CED) and hence the lattice fluid par a m e t e r ~ through ~'~~~ 6 = (CED)1/2=
[ 7]1'2 [ $1 =
1/2
7,
(11)
where u* is the average close-packed volume of a segment and generally varies with composition (i.e., u*, # u*~). If we assume there is no dependence of the energies of inetc.) on composition and use the identity teraction (e*,, V1 = u*,/pl, then eq 9 can be obtained directly from eq 10. Accordingly, in the solubility parameter approach we can to a crude approximation identify the parameter with so-called free-volume or compressibility effects, while the (6, - 62)2 term reflects exchange interaction energies that are assumed independent of composition. This is not a good way of looking at the problem as eq 9 shows that free-volume effects contribute to both the energy term (through 3) and the term we labeled 8'. The crucial point is that swelling measurements can give values for the solubility parameter of coal that deviate appreciably from calculated values. We illustrate this by using eq 5 to calculate x for various coal/solvent mixtures. The necessary parameters for the solvents used by Larsen et al.5 were obtained from Sanchez and Lacombe?' while the parameters for coal were calculated from its coefficient of thermal expansion and an assumed value of the solubility ~ . ~value , given by our parameter of 6 , = 11.4 ( c a l . ~ m - ~ )the atomic group contributions.2 The coefficient of thermal expansion for coal in the glassy state is about 1 X according to van Krevelen." Using correlations also listed in van Krevelen's book (aI- as 5 X lo4 and alTs = 0.29, we assume that the value of a in the rubbery state is beand 3 X lo4 (for a TB 600 K). As we will tween l X see, the difference in these values does not affect our calculated results. We also assume that coal-solvent physical interactions are given by the usual geometric mean assumption. The equations necessary for our calculations are29
-
6
0
7
9
10
11
12
SOLUBILITY PARAMETER
Figure 4. Comparison of calculated values of
x for a n Illinois
No. 6 coal and a set of solvents plotted against the values of the solubility parameters for the solvents ( 1 5 =~ 11.4 ~ (cal-~m-~)~,~, a, = 1.5 x 10-5). 5 2 n-Heptane 3 Cyclohexane 4 o-Xylene 5 Toluene 6 Benzene
4-
3-
x
8 Di-Phenyl
2COAL
17
7
6
8
9
10
11
12
SOLUBILITY PARAMETER
Figure 5. Plots of the values of x for the same set of solvents shown in Figure 4, but with 6, = 11.4 ( c a l ~ c m - ~and )~.q ~ =3 x 10-4.
7 0
A
Chl from Soiublllty Paramaera
-
1
iI
04". 6
1
O A 0 0
A 0
O
~ " . ~ " . ~ " ' ~ " . I 7
8
9
10
I
11
SOLUBlLlTY PARAMETER
6 = [c*/u*1'/2p and the equation of state p 2 + P + T[ln (1- p ) + p1 = o
(13)
(14) (where it has been assumed that the degree of polymerization of the coal network m). The result for the set of solvents used by Larsen et al. is shown in Figure 4 (using a1= 1.5 X A coal with ) " ~a minimum a solubility parameter of 11.4 ( ~ a l - c m - ~has value of x and hence a predicted maximum swelling with a solvent that has a solubility parameter of about 10 (~al-cm-~)"~. Using a value of a1= 3 x 10-l gives a predicted maximum swelling that is practically unaltered, as shown in Figure 5. Both are close to the values determined experimentally, which is remarkable considering the as-
-
x calculated from free volume (A)and solubility parameters (0)against the values of the solvent solubility parameters. Figure 6. Plot of the values of
sumptions that have gone into the calculations. Finally, values of x calculated for the Illinois No. 6 coal using the solubility parameter approach (6& = 11.4 ( c a l . ~ m ~ )and ~.~) the lattice fluid model are compared in Figure 6 and plotted as a function of the solvent solubility parameter. Both show the same trend and the values are not that different, again considering the fairly crude assumptions that have gone into both sets of calculations. Conclusions 1. The calculation of solubility parameters by van
Krevelen's atomic contribution method2 is subject to large errors but nevertheless gives values that are apparently
384
Energy & Fuels 1990,4, 384-393
critical solution b e h a ~ i o r . ~ ' - ~ ~ in the right range. We have modified the equation to 4. In applying simple solution theories to coal it would account for those arising from inappropriate use of molar seem to be most appropriate to regard y. as an volumes, but the errors remain at least i0.6 ( c a l ~ m - ~ ) ~ . ~therefore . adjustable parameter, but to reiterate, solubility parame2. The difference in the value of the solubility parameter ters seem to give values that are at least in the right range obtained by this method and from swelling measurements, and may thus be useful in providing an initial estimate of both conducted so as to minimize the contribution of hydrogen bonds, is due to the apparently large free-volume X. differences between coal and most solvents. Acknowledgment. We gratefully acknowledge the 3. Despite its simplicity, the solubility parameter apsupport of the Office of Chemical Sciences, Department proach does give a rough value for x and partly accounts of Energy, under Grant No. DE-FG02-86ER13537, for free-volume effects, as Patterson and co-workers pointed out a number of years ago.= They do not account Registry No. CS2, 75-15-0;pentane, 109-66-0; heptane, 142for composition dependence, however, and free-volume 82-5; cyclohexane, 110-82-7;o-xylene, 95-47-6;toluene, 108-88-3; benzene, 71-43-2; biphenyl, 92-52-4. differences can increase with temperature, leading to lower
Coal Solubility and Swelling. 2. Effect of Hydrogen Bonding on Calculations of Molecular Weight from Swelling Measurements Paul C. Painter,* Yung Park, Maria Sobkowiak, and Michael M. Coleman Polymer Science Program, Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802 Received January 30, 1990. Revised Manuscript Received May 29, 1990
In this paper theories of swelling that have been applied to coal are modified to account for hydrogen bonding. The results of various swelling measurements are analyzed and suggest some important conclusions. First, the calculated molecular weights are low, indicating that even a modified Gaussian would not describe their chain statistics, thus invalidating the model. Second, an analysis of the phase behavior suggests that the phenomenon of gel collapse could be observed in swollen coal networks. Finally, the swollen coal network itself could be phase separated. These last two predictions account for various previously reported experimental observations and suggest new experiments that would test the validity of the analysis.
Introduction It is now widely recognized that the hydrogen bonds that occur between the phenolic OH groups found in most coals strongly influence their solubility and solvent swelling characteristics. This is not to say that dispersion and other "physical" forces are unimportant, but that the thermodynamics of mixing will depend upon the balance between the various favorable and unfavorable coal-solvent interactions. In its original form, the lattice model of Flory'-' that has been most often applied to coal was designed to deal with only weak forces. Hydrogen bonds introduce a number of difficulties, including the effect of nonrandom contacts of the functional groups involved and modifications to the entropy of mixing that are a result of the formation of such strong, specfic interactions. For mixtures of low molecular weight materials, by which we mean relatively small molecules that each contain only one functional group capable of forming hydrogen bonds, association models have proved to be a beautifully simple way of handling these problems. The trick, if such it can be called, is to not even attempt a description in terms of a separate
* To whom correspondence should be addressed. 0887-0624 f 90 f 2504-0384$02.50 f 0
accounting of the energies and entropy changes of orientational specific interactions, but to consider the equilibrium distribution of species present at a given concentration. Take, for example, a simple molecule containing a single OH group. Such a molecule can associate in the form of chains, with an equilibrium distribution of chain lengths. As an example, a chain of phenol molecules with a "degree of polymerization" equal to three is shown in Figure 1. Although at ambient temperatures the bonds between molecules are dynamic, constantly breaking and re-forming at the urgings of thermal motion, in terms of statistical mechanics it is perfectly valid to treat the equilibrium distribution of hydrogen-bonded chains as if they were covalently bonded units. Accordingly, theories developed to describe the random mixing of covalent polymers that have a heterogeneous distribution of molecular weights can be applied. The only difference is that (1) Flory, P. J. Principles of Polymer Chemistry; Cornel1 University Press: Ithaca, NY,1953. (2) Flory, P. J. J. Chem. Phys. 1944, 12, 425. (3) Flory, P. J. J. Chem. Phys. 1946, 14, 49. (4)Flory, P. J.; Rehner, J. J. Chem. Phys. 1943, 1 1 , 512. (5) Flory, P. J.; Rehner, J. J. Chem. Phys. 1943, 1 1 , 521. (6) Flory, P. J. J. Chem. Phys. 1950, 18, 108. (7) Flory, P. J. J. Chem. Phys. 1950, 18, 108.
0 1990 American Chemical Society
