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; differences can increase with temperature, leading to lower benzene, 71-43-2; biphenyl, 92-52-4.
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. 0887-0624f 90 f 2504-0384$02.50f 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
Coal Solubility and Swelling. 2
A
Figure I. Hydrogen bonds linking three phenol molecules. the distribution of hydrogen-bonded chain lengths is a strong function of both concentration and temperature. Flory2i3described how this could be handled through the careful choice of reference states. An expression for the free energy of mixing small molecules that hydrogen bond then follows directly by using Flory’s equations to describe the mixing of the equilibrium distribution of “chains” found at a particular concentration in diluent and then subtracting an expression for mixing with one another the (different) equilibrium distribution of chains found in the pure self-associating material (Le., the chains are treated as distinguishable species according to their chain length and an expression for mixing these various chains ivith one another is determined, following Flory2). The free energy change due to changes in hydrogen bonding are thus accounted for in terms of an overall configurational free energy expression that includes the combinatorial entropy of mixing. An important consequence of this approach is that “physical” interactions (e.g., van der Waals forces) between the segments of these randomly mixed chains can be treated in the same manner as equivalent covalent chains, using, for example, the Flory x parameter. The separation of hydrogen bonding and weaker interactions is thus a natural consequence of the model. Equally important, equilibrium constants, defined according to F l ~ r ycan , ~ be used to define the distribution of species and can be determined by infrared spectroscopic measurement^,"'^ although in some systems such measurements are not always easy. In its simplest form, therefore, this approach does not require the use of any adjustable parameter in addition to x. Although the application of association models to small molecules is well-established (a review of this field can be found in the book by Acree14), a formal extension of the theory to a description of the thermodynamics of polymer solutions or blends has only recently been attempted. In a series of papers we have described our approach to this problemasgand successfully demonstrated that the model is at least capable of predicting broad trends in the phase behavior of a number of different In the (8) Painter, P. C.; Park, Y.; Coleman, M. M. Macromolecules 1989,22, 570. (9) Painter, P. C.; Park, Y.; Coleman, M. M. Macromolecules 1989,22, 580.
(10) Coleman, M.M.;Lichkus, A. M.; Painter, P. C. Macromolecules 1989,22, 586.
Energy & Fuels, Vol. 4, No. 4, 1990 385
original formulation of the theory, however, we essentially assumed that the formation of hydrogen bonds is unaffected by the linkage of the functional groups involved into covalent chains. An expression for the free energy of mixing can then be obtained by adding the result obtained for low molecular weight molecules to a Flory-Huggins expression for polymers. A correction term is added because certain free energy contributions per segment are counted twice, once as a member of a covalent chain and once as a member of a hydrogen bonded chain. More recently, we have employed a Flory lattice model to obtain a more rigorous deri~ati0n.l~We determine the probability that a mixture of the non-hydrogen-bonded chains would spontaneously occur in a configuration equivalent to that found in the hydrogen-bonded system. The result we obtained in this manner is the same as that previously derived. Having derived what we believe to be a reasonable model for the description of hydrogen bond interactions, our concern becomes its application. We recently reported an initial study of coal, but our discussion was limited to the solution thermodynamcs of “model” coal structures.16 Here we will consider how the model can be applied to “real” coals and extend our application to the swelling as well as solubility characteristics of these materials. A preliminary and abbreviated report of this work was presented at a recent American Chemical Society meeting.” Theory In order to obtain an understanding of the effect of hydrogen bonding on coal solution and swelling behavior, we need to consider how such strong interactions modify the free energy of mixing and its derivatives with respect to composition. The fundamental equations have been presented e l ~ e w h e r e , ~and ~ ~here J ~ our concern is the peculiarities of their application to a material as complicated and heterogeneous as coal. For clarity of presentation we will therefore consider a simplified form of the equations, using the symbol AGH to represent the contribution of hydrogen bonds to the overall free energy. The equations are presented in their complete form in the Appendix. The free energy of mixing is given by
where @A and aBare the volume fractions of components A and B, x is the usual Flory-Huggins interaction parameter, limited here to a description of “physical” (non-hydrogen bonding) forces, while AGHIRT is the contribution to the free energy of mixing from the change in the number and type of hydrogen bonds that occurs as a function of composition. The quantities xA and XB are the “degrees of polymerization” of the components A and B, actually equal to the molar volume of these molecules divided by a reference molar volume. If component A is a solvent and B a polymer, it is usual to use the molar volume of the solvent (VA)to define the lattice cell size, so that xAwould be equal to 1. In using association models it is more convenient (Le., simplifies the algebra) to use the “repeat” unit of the macromolecule to define the reference volume (VB) and we therefore use
(11) Coleman, M.M.;Hu, J.; Park, Y.; Painter, P. C. Polymer 1988,
2.9., 1R.59. __ - - - -.
(12) Coleman, M.M.;Lee, J. Y.; Serman, C. J.; Wang, Z.; Painter, P. C. Polymer 1989,30, 1298. (13) Serman, C. J.; Xu, Y.; Painter, P. C.; Coleman, M. M. Macromolecules 1989,22, 2018. (14) Acree, W. E. Thermodynamic Properties of Nonelectrolyte Solutions; Academic Press: New York, 1984.
(15) Painter, P. C.;Graf, J.; Coleman, M. M. J. Chem. Phys. 1990,92, 6166. (16) Painter, P. C.; Park, Y.; Coleman, M. M. Energy Fuels 1988,2, 693. (17) Painter, P. C.; Park, Y.; Coleman, M. M. Prepr. Pap.-Am. Chem. SOC.,Diu. Fuel Chem. 1989, 34 (2), 559.
Painter et al.
386 Energy & Fuels, Vol. 4 , No. 4, 1990
AGH @B @A@BX AGM @A @pB + -+ =In @A + --In RT r RT (2) XB r where r = VA/ V,. This opens up the question of what is
a “repeat” unit for coal, or if indeed such a thing can be defined. Coal is, of course, extraordinarily heterogeneous,and in the ordinary sense a polymer repeat unit cannot be defined. That is not what we are doing here, however. As long as the OH groups of coal are randomly distributed, then all we require is the definition of an average unit or segment per OH group. This is not for the purpose of defining coal to be a polymer of such units but only a device for computational convenience, as we will show. Scott18 demonstrated more than 30 years ago that the “physical” interactions of a copolymer of any degree of heterogeneity could be described by a solubility parameter that is a volume fraction average of the contributions of its constituents. We can therefore, in principle, use the method of van Krevelen,19 as modified in the preceding paper,20to calculate the parameter 6& As we made clear, we have little confidence in the precise value of ad so determined but believe it is at least in the right range. Our purpose here is not to try to predict accurately the phase behavior of any specific coal sample but to consider broad trends and try to obtain some fundamental insight into structure and the balance of molecular forces that determine behavior. The group contribution method, with all its limitations, should still predict the correct trend in the value of x as, for example, we consider the systematic changes in aromaticity and oxygen content that occur as a function of rank. In order to calculate x from the solubility parameters, however, we also need to define a reference volume for the coal that can correspond to any arbitrarily defined segment (because we will simply calculate the free energy change per segment upon mixing). Van Krevelen19calculated his solubility parameter in terms of the molar volume of a coal “molecule” per carbon atom, Vc/C, using (3)
where C’is the weight percent carbon in the sample and d is the density. In the same fashion we define a molar volume per OH group as Vm 1600 -.=(4) OOH ObHd where O b His the weight percent oxygen in the sample that is present as OH groups (ObH and d are known or measurable quantities). This allows us to calculate the free energy contribution from hydrogen bonding interactions per molar volume of the average coal segment containing one OH group. As discussed in the preceding paper, the x parameter is then calculated from solubility parameters using
x
VB
= ~ [ 6 , , , - 6J2
+ 0.34
(5)
where 6, is the solubility parameter of the solvent. The definition of a “segment”of a coal molecule per OH group, therefore merely serves to place the calculations of x and AGH on a common scale of unit volume, VB. As long as (18) Scott, R. L. J. Polym. Sci. 1952, 9, 423. (19) van Krevelen, D. W. Fuel 1965, 45, 229. (20) Painter, P. C.; Graf,J.; Coleman, M. M. Energy Fuels, preceding paper in this issue.
the OH groups in coal are more or less randomly distributed, our definition of an arbitrary segment is conceptually sound and presents no problems. Given the above method for calculating x, the calculation of the free energy of mixing, phase behavior, and the chemical potentials depends upon the determination of AGH and its derivatives with respect to composition. Thwe equations appear at first sight complicated, but they have an easily understandable structure. Their derivation has been presented elsewhere,8v9J5and the results are also presented in the Appendix. In our discussion of swelling we will need to determine the contribution of hydrogen bonding to the chemical potential of the solvent. We let this have the symbol (AGH)A. The Flory-Rehner equation: as derived by Kov a ~ ?and ~ applied to coal by Larsen et al.,14 is then further modified to give
+ PBVA/N@B’/~ (1- @B) + @B + x @ B 2 + (AGH)A/RT] PBVA@BlJ3
Mc =
-[ln
(6)
where we maintain our previous of letting the subscript B represent the self-associating component (coal) while the subscript A represents the “competing” species (solvent). Mc is the number-average molecular weight between cross-link points, and N represents the number of cluster^"^ or “repeat units” between cross-link points. In our discussion of the phase behavior of hypothetical coal solutions we require the spinodal, given by the second derivative of the free energy with respect to composition. In this case we use volume fractions as our variable and obtain (d2(AG/R‘I?)/d@~2.8,9,15 In the calculation of the contribution of hydrogen bond interactions to these derivatives, the crucial quantities are the experimentally determined equilibrium constants describing self-association of the functional groups within the coal (e.g., OH-OH hydrogen bonds) and those describing the competing coal-solvent hydrogen bonds. The free energy expression, equations describing the stoichiometry of hydrogen bonding, and experimental infrared spectroscopic measurements are linked by the important volume fraction quantities @Bl and @A1, the fraction of B (coal) segments and A (solvent) molecules that at equilibrium have no hydrogen-bonded partners whatsoever, at any instant of time. The equilibrium constants describing the self-association of coal were not determined directly. It is a consequence of the lattice model8 that equilibrium constants for a particular functional group determined in one molecule can be transferred to a different molecule with the same functional group by simply adjusting according to the molar volume:
KBvg = a v h (7) Using values determined for phenol and cresols (KbVk) , we can thus calculate appropriate values for a coal segment (This result has worked extremely well in defined by predicting the phase behavior of blends of poly(viny1phenol) with various polyacrylates and polyesterslO).The values of the equilibrium constants describing the selfassociation of phenol have been determined by Whetsel and Lady.21 (This splendid paper, published in Spectrometry of Fuels a number of years ago, anticipates our use of association models for coal and has the almost
vB.
(21) Whetsel, K. B.; Lady, J. H. In Spectrometry of Fuels; Friedel, H.,
Ed.;Plenum: London, 1979; p 259. (22) Murthy, A. S. N.; Rao, C . N. R.Appl. Spectrosc. Rev. 1968 2,69. (23) Kovac, J. Macromolecules 1978, I I , 362.
Coal Solubility and Swelling. 2
Energy & Fuels, Vol. 4, No. 4, 1990 387
-
forgotten virtue of tabulating all data obtained, in this case, in both the near- and mid-IR regions. We were thus able to check all calculations and determine the appropriate values of the equilibrium constants.) We have expanded our treatment of self-association to also account for the hydrogen bonds that can form intramolecularly between coal OH and ether oxygens. This is conceptually straightforward and comes at the expense of a minor increase in the algebraic complexity of the equations. The equilibrium constants describing interactions between phenolic OH groups and ethers, and indeed, between OH and most of the functional groups found in solvents commonly used to swell coals, are tabulated in the literature (e.g., see the review by Murthy and RaoZ2). We are fortunate that interactions involving both alkyl and phenolic OH groups have been so widely studied.
Results and Discussion Coal Solubility. An understanding of the solubility of a coal in various solvents can be obtained by a calculation of hypothetical phase diagrams. They are hypothetical in the sense that we assume that the coal is not cross-linked but is simply a macromolecule. This macromolecule could be highly branched and with an extremely high molecular weight, but within the limitations of the simple lattice model applied here, its equilibrium properties can be determined. This, in turn, allows an understanding of why a particular solvent is capable of extracting more (or less) soluble material than another and, as we will see, provides some fundamental insight into the variation of swelling behavior with temperature. According to our association model, solution behavior is determined by the balance of forces. The first is the combinatorial entropy, given by the first two terms of eq 2, and the second is the change in free energy due to the change in the pattern of hydrogen bonding, given by the last term in eq 2; both of these terms are negative and favorable to mixing. The third component is the x parameter, reflecting “physical” forces, and is positive and unfavorable to mixing. In order to obtain a one-phase system, it is not a sufficient condition that the overall free energy be negative; the second derivative of the free energy with respect to composition must also be positive. The points at which this latter quantity is zero, determined as a function of temperature, define the spinodal or the stability limit. It is this limit that we will use as a guide to phase behavior. In a preliminary communication of this work17we calculated theoretical (spinodal) phase diagrams as a function of coal rank. The value of x was estimated using van Krevelen’s method.lg As noted above, we have little confidence in the precise value so calculated for any particular coal, but the trend with rank makes sense in terms of what we known about the structure of coal and the value appears to be in the right range.20 As the oxygen content of coal falls, ad should decrease, but this is offset a t higher rank by increasing aromaticity.20 The value of Gcod should therefore, go through a minimum. Simultaneously, the number of coal OH groups available for hydrogen bonding to solvent decreases with increasing carbon content. The balance of these forces is such that we predict that if they were not cross-linked, low-rank coals should be soluble in pyridine at ambient temperatures but that phase separation should occur as the carbon content of the coals under consideration i n ~ r e a s e s . * ~ J ~ Spinodals for three coals are reproduced from our preliminary publication” in Figure 2, illustrating this trend. Here, we will also examine three different coals in more detail, as the predicted phase diagrams will play a major
COAL(78.3YoC) PYRIDINE MIXTURES
ONE PHASE
100
0.2
0.0
0.6
0.4
0.8
1.0
VOLUME FRACTION COAL
-
COAL(84.7%C) PYRIDINE MIXTURES
T(”C)
,:lO -50
.. .,:,-,
:
50]
,
T:PHASr
.
,100 0.0
0.6
0.4
0.2
.
1 1.0
0.8
VOLUME FRACTION COAL
.. .. .
150-
100500-50-
-100
-
-
200
=
0.0
TWO PHASE
.
I
0.2
I
0.4
.
.. .. . I
0.6
,
,=. 0.8
1.0
VOLUME FRACTION COAL
Figure 2. Calculated phase diagrams (spinodals)for three coals mixed with pyridine. The carbon content of the coals varies from 78.3 to 90.1%, and additional details are given in ref 17. Table I. Parameters for Coal at 25 ILL No. 6 PSOC 207 PSOC 402 cm3 mol-’ 212 VE,cm3 mol-’ 308 6,, (~al-cm-~)~.~ 11.7 VB,
Kz
h2,kcal mol-’
KE hE, kcal
KB h g , kcal
mol-’ mol-’
8.95 5.6 20.9 5.0 28.6 5.2
239 256 11.8 7.95 5.6 18.5 5.0 25.4 5.2
246.11 275 11.9 7.72 5.6 18.0 5.0 24.7 5.2
role in our discussion of swelling measurements. The calculated spinodals of these coals, Illinois No. 6, PSOC 207, and PSOC 402, are shown in Figures 3, 4, and 5, respectively. The parameters used to calculate these phase diagrams are listed in Tables I and 11. For Illinois No. 6 coal we illustrate the spindoals obtained for mixing with three different solvents, pyridine,
Painter et al.
388 Energy & Fuels, Vol. 4, No. 4, 1990
2oo-r a -
COAL(PSOC402)-PYRlDlNE MIXTURE
COAL(ILLINOIW6) SOLVENT MIXTURES
5
150
2oo
O
150
D
O
D
O
D
*
I 1
loo$
3
*** ** t **
D O
D
Y
BENZENE
IO
-
500 1
,
.
-50
,
-100
0.0
0.2
0.4
0.6
0.8
.
~
1.0
VOLUME FRACTION COAL
Figure 5. Calculated spinodal for PSOC 402 mixed with pyridine.
pable of hydrogen bonding with functional groups of the first. The situation where the second component also self-associates presents a number of algebraic difficulties that we have yet to tackle. Consequently, this precludes 200 a consideration of solvents such as methanol, or perhaps even N-methyl-2-pyrrolidinone(NMP), which may self150 associate through very strong dipolar interactions. In 100 general, however, we would expect that these solvents would not be as miscible as pyridine, in that now two sets 28 **..* o^ 50 of self-associatinghydrogen bonds would have to be broken 2 to form one coal-solvent hydrogen bond; i.e., AGH would I0be smaller. In this context it is interesting to note the -50 recent results of Iino et al.25who used a mixed solvent of NMP and CS2to obtain enhanced swelling and extraction , , -100 - ' yields. This combination might fortuitously bring the solvent solubility parameter into the right range, while limiting any self-association of NMP due to the presence of the polar cosolvent. The calculated spinodals for PSOC 207 and PSOC 402 Table 11. Parameters for Solvents at 25 OC in pyridine show progressively increasing values of the V,, cm3 KA,kcal h,, kcal 6,, (cal. upper critical solution temperature (maximum value of the solvents mol-' mol-' mol-' cm-3)O.b inverted U) relative to Illinois No. 6 coal, a trend that pyridine 81.0 285 8.9 10.6 largely reflects the increasing value of x calculated for this 5.76 9.9 THF 74.3 89.5 coal/pyridine series. To reiterate, although the precise 58.9 4.03 9.9 acetone 74.3 5.76 7.5 45.2 diethyl ether 101.7 positions of these curves are obviously affected by the 2.03 11.8 23.6 acetonitrile 55.4 errors in calculating 6cd, we believe that this predicted 1.41" 1.25 9.1 benzene 82.2 trend in behavior should be reasonably accurate. The calculated phase behaviors indicate that if these " Weak H bonds between OH groups and T electrons have been proposed. coals were not cross-linked they would be completely soluble in pyridine, at least at elevated temperatures. This tetrahydrofuran (THF), and benzene. For pyridine, we remains true even if we assume very high molecular predict a typical inverted U-shaped stability curve with weights for the coal molecules (the contribution of the an upper critical solution temperature near 25 "C. Mixcombinatorial entropy from the coal is very small for the tures with THF and benzene are predicted to be far less degree of polymerization xB assumed in these calculations miscible, with the stability limits calculated to be near the (xB = 100); changing this value to 1000 to 10OOO has only two composition extremes. An examination of Table 11, a minor effect on the calculated spinodals, as illustrated which lists the solvent parameters utilized here, together in our preceding p~b1ications'~J~). Accordingly, we believe with some values for other solvents, immediately demonthat these results strongly support the present generally strates why. Pyridine forms much stronger hydrogen held view that, at least up to a certain carbon content, coals bonds than the other solvents listed (as measured by the are composed of cross-linked networks which also contain equilibrium constant K A ) ,and in addition, its solubility molecules that have a distribution of finite molecular parameter is closer to the range we estimate represents the weights and molecular architecture. The predicted phase most likely value for this coal (6 = 11-12 ( c a l - ~ m - ~ ) ~ . ~ )diagrams . also help explain various other observations Thus, favorable interactions (coal-olvent hydrogen bonds) concerning the solubility of coals in pyridine. Depending are maximized and x is minimized. This is an important upon the coal, extracts obtained by Soxhlet extraction can point; correlation of coal swelling to a single parameter, have portions that become insoluble at room temperature, chosen so as to represent x or some measure of the strength as the two-phase region is entered upon cooling. The of favorable interactions, can be misleading. It is the extent of this will obviously depend upon the molecular balance of favorable and unfavorable forces that is imweight of the extract. Also, these results indicate that portant. One additional observation needs to be made. As we have pointed out in our preceding p~blications,8~~J~" (24) Larsen, J. W.; Green, T. K.; Kovac, J. J . Org. Chem. 1985, 50, the model is presently limited to the consideration of 4129. systems where one component hydrogen bonds to itself, (25) Iino, M.; Takanohashi, T.; Ohauga, H.; Toda, K. Fuel 1988,67, while the second does not but has a functional group ca1639.
0
I
1
I
I
-
.
I
Coal Solubility and Swelling. 2
Energy & Fuels, Vol. 4, No. 4, 1990 389
EXTRACTABILITY OF COALS IN PYRIDINE
EXTRACTABILITY OF ROCKY MOUNTAIN COALS IN PYRIDINE
u-
E E
e
0
P
5
I
5 t
cy . o . 90
I
oJ 65
'
75
70
BO
85
,
74
I
,
76
78
8 0
82
84
8 6
8 8
CARBON CONTENT IN COAL,%wl dmmf
9 11
CARBON CONTENT IN COAL,%W dmmf
PERCENT OF OXYGEN AS OH IN PYRIDINE EXTRACTS FROM ROCKY MOUNTAIN COALS
Figure 6. Extractability (wt % soluble material) in pyridine of a set of coal samples.
I
10
EXTRACTABILITY OF USA COALS IN PYRIDINE
7 4
76
78
80
82
86
84
8 8
CARBON CONTENT IN COAL,%wt dmmf 65
70
75
8 0
85
90
95
Figure 8. Extractability and w t % 0 as OH of a set of Rocky
Mountain US. coals.
CARBON CONTENT IN COAL,%wt dmmf
EXTRACTABILITY OF POLISH COALS IN PYRIDINE
PERCENT OF OXYGEN IN USA PYRIDINE EXTRACTS 8
I
1.c
I
u-
E
E
8'
'0
5 w
65
70
75
8 0
85
90
80
95
CARBON CONTENT IN COAL, %wt dmmf
Figure 7. Comparison of the pyridine-soluble weight fractions of a set of US.coals (Rocky Mountain coals excluded) and the w t % 0 as OH groups. Each factor plotted as a function of coal %
8 2
84
8 6
8 8
CARBON CONTENT IN COAL,%wl dmmf
PERCENT OF OXYGEN AS OH IN PYRIDINE EXTRACTS FROM POLISH COALS
c.
repeated extractions may be necessary to obtain the bulk of the soluble material. If at the temperature of extraction we are in the two-phase region, the soluble material will partition into a solvent-rich (extractable) phase and a coal-rich residual phase. This equilibrium will be reestablished at each successive extraction, with the amount of material extracted becoming smaller and the total extracted asymptotically approaching its upper limit. This assumes that the extractable material can diffuse out of the network, which for highly branched (but not crosslinked to the network) molecules may not be true, a topic we will address in the following paper. The Pyridine Extractability of Coal and Cross-Link Density. With the aid of the above theoretical analysis we can now examine some experimental data. This allows us to make some qualitative observations concerning the cross-link density of coal before we proceed to a discussion of swelling measurements. For the purpose of spectroscopic analysis we have exhaustively extracted a large number of coal samples with
5 8
d W
0
78
80
82
84
8 6
88
CARBON CONTENT IN COAL,% wt dmmf
Figure 9. Extractability and wt % 0 as OH of a set of Polish
coals.
pyridine using a Soxhlet apparatus. The details of this work will be reported elsewhere,%but here we will consider the weight fraction of extractable material plotted as a function of rank, shown in Figure 6. The pronounced scatter in the data is similar to that observed by van Krevelen,n with the outer envelope of the points reaching (26) Sobkowiak, M.; Painter, P. C. To be published.
Painter et al.
390 Energy & Fuels, Vol. 4 , No. 4, 1990
a maximum near a carbon content of 86%. It is intriguing to note that if we now separate the data according (approximately) to geographic origin, reflecting the geological history and age of the coals, much cleaner plots and distinct curves are obtained, displaying a clearly identifiable maximum in the amount of material extracted, as shown in Figures 7-9. The position of the maximum varies somewhat from set to set, but it is now clear that the "extractability" of a coal with pyridine varies in a very systematic manner with carbon content and must surely reflect corresponding variations in structure. Also shown in Figures 7-9 is the percent oxygen as OH, determined from infrared analysis of the acetylated parent coals.26 Significantly,the amount of material extracted goes to zero at approximately the same point that the amount of oxygen present as OH groups also goes to zero. On the basis of the theoretical analysis presented above, this is precisely the trend we would anticipate. At low carbon contents the value of x is large (because of the corresponding high oxygen content), but so is the favorable contribution from AGH. The latter contribution is much larger than the former, so that if the system were not cross-linked, it should be single phase. With increasing carbon carbon content, the contribution from hydrogen bonding decreases a t a faster rate than the decrease in x, so that single-phase mixtures are only predicted to occur at increasingly higher temperatures. At some value of percent carbon, the distribution of functional groups becomes such that x starts to increase, while the number of OH groups available for hydrogen bonding continues to decrease. At this point the phase diagram appears like an hourglass (i,e,,the stability limit lines lie at the composition extremes) over the experimentally accessible temperature range, indicating phase separation into a solvent-rich and solvent-poor phase, with only small amounts of one component dissolved in the other. Given this analysis, and based on the results we have obtained with synthetic polymers, we have a good deal of confidence in predicting such then one must conclude that low-rank coals are highly cross-linked with only small amounts of extractable material, or possibly with larger amounts of potentially soluble material that is so highly branched it is inextricably trapped in the network (see paper 3 in this series). As we consider coals of higher carbon contents (about 80-86% C), the degree of cross-linking and/or the degree of branching must decrease. For high-rank coals (>go% C) it is possible that there are no cross-links at all; the high aromaticity and lack of functional groups that can interact favorably with a solvent simply render it insoluble. Alternatively, the degree of cross-linking, after passing through a minumum, again increases. Our model is not presently capable of distinguishing between these last two possibilities. This preliminary discussion now sets the stage for a consideration of estimates of cross-link density, or molecular weight between cross-link points, from swelling measurements. The Swelling of Coal. Before we consider the analysis of swelling data, we wish to clear up what we consider to be some misconceptions concerning the role of hydrogen bonds as "cross-links" in coal. In a certain sense our objection can be considered a matter of semantics, but we believe that this leads to a lack of a proper understanding of the fundamental processes at work. In a liquid hydrogen bonds are dynamic, constantly breaking and re-forming at the urgings of thermal motion. The same dynamic state (27) van Krevelen, D. W. Coal; Elsevier: Amsterdam, 1981.
M,
12000
I
8000
4
6000
I
1 0
100
200
300
600
500
400
MO
Figure 10. Plot of Mcvs Mo(see text) for Illinois No. 6 coal as a function of various assumed values of the coal solubility parameter (&). The effect of hydrogen bonding was ignored in making these calculations.
600
0
3 0 0 , ' t 0
100
,
200
300
,
,
400
,
I
500
,
600
MO
Figure 11. Plot of Mcvs Mofor Illinois No. 6 coal (accounting for hydrogen bonding).
exists in a polymer above its TB' Nylon in the melt flows like a liquid, even though the majority of its functional groups remain hydrogen bonded at any instant in time.% Below the glass transition the macromolecules are "frozen" in place and there is insufficient mobility to permit attainment of the equilibrium distribution of hydrogen bonds reflecting the given temperature. The hydrogen bonds present still break and re-form, albeit over a longer time scale. They are not quasi-permanent cross-links and short-range rearrangements are still feasible. In the presence of a solvent the Tgis depressed. Thus a glassy network can becomes "rubberyn, as apparently coal can in the presence of s 0 l v e n t , 2 ~and ~~~ equilibrium can be established. Hydrogen bonds, per se, do not therefore prevent the network from reaching an equilibrium swollen state. Nonetheless, maximum swelling will only occur if the polymer and the solvent exist in a single phase. The phase behavior of binary coal-solvent systems is a crucial factor that has not been addressed in previous studies of the swelling of coal. We now turn our attention to an examination of the results obtained by Larsen et al." and Lucht and Peppas31 in their studies of coal swelling. Our aim here is an exploration of the general validity of using modified rubber elasticity theory, so we will not (and as of now, cannot) deal with the recent important observation of Cody et al.= that, in its mined state, coal is strained and the initial swelling is anisotropic. Larsen et al.24studied the swelling of an extracted but otherwise unreacted Illinois No. 6 coal in (28) Skrovanek, D. J.; Painter, P. C.; Coleman, M. M. Macromolecules 1986, 19, 699. (29) Brenner, D. Fuel 1985,64,167. (30) Green, T.;Kovac, J.; Brenner, D.; Larsen, J. W. In Coal Structure; Meyers, R. A., Ed.; Academic Press: New York, 1982. (31) Lucht, L. M.; Peppas, N. A. Fuel 1987,66,803. (32) Lucht, L. M.; Peppas, N. A. AZP Conf. R o c . 1981, 70,28. (33) Cody, G. D.; Larsen, J. W.; Siskin, M. Energy Fuels 1988,2,340.
Energy & Fuels, Vol. 4, No. 4, 1990 391
Coal Solubility and Swelling. 2
200f 0
'
I
100
'
I
200
1
I
300
.
I
'
400
v
I
'
500
600
MIa
Figure 12. Plot of &fcvs Mo for PSOC 207 (accounting for
hydrogen bonding).
1000
4
-
m
D
l
60% 80°C
600
made concerningthe form of the temperatuer dependence of the parameters over this fairly limited range. An explanation is immediately apparent if we examine the calculated solution-phase diagrams shown in Figures 4 and 5, however. Materials similar in chemical composition to PSOC 207 and 402 are predicted to have upper critical solution temperatures near 75 and 125 "C, respectively, these values being subject to the errors, particularly in x , discussed above. Of course these phase diagrams are calculated on the assumption that the macromolecular units are not cross-linked. For network structures we also have to consider contributions from a chain extension of deformation term, which opposes mixing. Consequently, the balance of forces can be such that there is a phase boundary between a swollen and "collapsed" network. Clearly, if the swollen network is at a temperature above some upper critical value, Le., in the single-phase region, the coal should swell to the limit imposed by the nature of the network. Below this transition, however, there is a two-phase region and as the phase boundary is crossed one would expect that solvent would be expelled from the network, to an extent determined by the phase behavior of the coal-solvent system. Swollen polymer networks can undergo a transition known as gel c o l l a p ~ ea, phenomenon ~~~~ that apparently depends upon the balance between the various solution and elastic forces at any particular temperature. The transition can be continuous or discrete. The plots shown in Figures 12 and 13 suggest that this is precisely what we are observing in coal. PSOC 207 shows a small change in swelling and hence calculated molecular weight on going from 35 to 60 "C but a large difference on going from 60 to 80 "C. In contrast, the changes for PSOC 402 appear to be more evenly spaced. We suggest that the discontinuity in behavior for PSOC 207 is due to expulsion of solvent from the swollen coal network at the lower temperatures. Our association model predicts this trend remarkably well; an examination of the calculated solution-phase behaviors, shown in Figures 4 and 5, indicates that PSOC 207 has a upper critical solution temperature in the range of these experiments, although we must keep in mind the errors in calculating x and the fact that we should include elastic forces in accounting for the phase behavior of the gel. Lucht and Peppas31 proposed, among other interpretations, that this variation in swelling could be due to a greater dissociation of hydrogen bond interactions at higher temperatures. This certainly occurs, but a distinction between the types of hydrogen bonds present was not made, and this is crucial. In the unswollen coal network it is the hydrogen bonds between segments of the coal network that must be broken to enhance swelling, not those that may occur between coal OH groups and the solvent (e.g., pyridine). In the presence of an "inert" (i.e., non-hydrogen bonding) solvent the fraction of OH-OH hydrogen bonds, a number that is easily calculated,p10only decreases significantly at high concentrations of the solvent and this would occur only at degrees of swelling that in practice are never achieved. Figure 14 shows the results of such a calculation for an Illinois No. 6 coal, but keep in mind that this is for an assumed single-phase system. In marked contrast, pyridine strongly hydrogen bonds to coal OH groups and for the degrees of swelling considered here (volume fraction of coal in swollen network between 0.35 and 0.5) there are practically no OH-OH hydrogen bonds remaining, as also illustrated in Figure 14. In-
'""1
200 0
100
200
300
400
500
600
M O
Figure 13. Plot of hydrogen bonding).
Mcvs Mofor PSOC
402
(accounting for
pyridine. Using3 swelling ratio of Q = 2.4, we obtained the plots of the M,, the number-average molecular weight between cross-link points against Mo, the assumed molecular weight of a coal cluster, shown in Figure 10. The KovacZ3equation as used and hydrogen bonding was left unaccounted for. Results were obtained for four different assumed values of ad, ranging from 9 to 12, and display the large sensitivity to x noted by Lucht and pep pa^.^^ These results are dramatically altered if we now include the effect of hydrogen bonding, using eq 6. The effect of variations in x is now greatly reduced, as _canbe seen from Figure 11, and the calculated values of M,are now much smaller. This is a consequence of the large contribution of hydrogen bonding to the chemical potential of the solvent; i.e., the (AGH)A term dominates the x term. A calculated molecular weight of about 500, or "degree of polymerization" of about 2-3 clusters, between cross-link points is determined assuming Mo.This appears to be too small to be reasonable given the assumptions of the model for coal swelling, but we will defer a discussion of this point until after we consider some additional data. Lucht and Peppas31 have also studied the swelling of various coals in pyridine, including PSOC 207 and PSOC 402. These swelling measurements were conducted at three different temperatures, 35,60, and 80 "C, and the results of applying eq 6 to their data is shown in Figures 12 and 13. It can be seen that there are distinct differences in the calculated values of the molecular weight between cross-link points, with much larger values being determined at high temperatures. Unlike Lucht and Peppas,3l we allowed x to have its usual 1/T dependence, while the variation ofJhe values of the equilibrium constants, and hence (AG,),, with temperature was determined through the usual van't Hoff relationship.8 Accordingly, it is not the temperature dependence of the solvent chemical potential that is responsible for such large differences. Only small variations might be expected due to the errors inherent in the various assumptions that are
(34) Tanaka, T. Phys. Rev. Lett. 1978,40,820. (35) Erman, B.; Flory, P. J. Macromolecules 1986, 19, 2342.
Painter et al.
392 Energy & Fuels, Vol. 4, No. 4, 1990 1.0
,
I
swollen coal gels at low temperatures. Lucht et al.= have observed a Tgfor PSOC 418/pyridine mixtures near 150 "C. Clearly, this is a t odds with the generally rubberlike behavior of swollen samples observed by Brenner.% The Tg of the parent coal was determined to be about 310 "C. If we use Couchman's method3'ta for determining the Tg of a mixture wlACp, In Tgl+ w2ACp, In Tgz In Tg = (8) WlACp, + WZACp,
1.0
and estimate the heat capacity increment AC for coal and pyridine from the S i m h a - B ~ y e rrelationskip ~~ TgACp = 115.5 J / g (9)
0.0
0.6 0.4 0.2 0.0 0.0
0.2
0.4
0.6
0.6
VOLUME FRACTION COAL
* igure 14.
Plot of the fraction of Illinois No. 6 coal OH-.OH hydrogen bonds plotted as a function of composition at 25 "C for TI 'inert" solvent (non-hydrogen bonding, e.g., benzene) and for ,,jridine. The parameters used are listed in Tables I and 11. creasing the temperature changes this very small number of coal OH-.OH hydrogen bonds in the pyridine-swollen network only very slightly (the above calculations assumed a temperature of 25 "C, but a t a coal volume fraction of 0.5 there are only minor differences upon increasing the temperature to 80 "C). Accordingly, it is not a change in the number of hydrogen bonds or their strength that is responsible for the changes in swelling (in pyridine) with temperature. If we now consider the values of the degree of swelling obtained at the highest temperature to be the most accurate, the predicted molecular weight between cross-links is now more reasonable, but still small in terms of the inherent limitations of the model (modified Gaussian). If we further assume that the molecular weight of an average "cluster" is of the order of 200, this model predicts that the number of such clusters between cross-links is of the order of 3 for these coals. We must, therefore, question whether it is at all appropriate to apply Flory's theory to coal, even in the modified form expressed by eq 6. We will suggest an alternative in the following paper. Consequences a n d Predictions The first consequence of the analysis we have presented above is that it appears likely that at least some, and perhaps most, pyridine swollen coal networks undergo a phase separation in an exprimentally accessible temperature range. We therefore predict that we should observe the phenomenon of gel collapse in these coals. This transition is not sudden in the sense of occurring over a narrow time frame, but is sharp in the sense that a t the critical point small changes in temperature or solvent will cause a large change in swelling, once equilibrium has been attained.34 A further consequence of our findings is that even if modified theories of rubber elasticity can be applied to coal, the swelling measurements that provide the fundamental parameters for the calculation of M cmust be conducted at temperatures above any such transition point. Having included the effect of hydrogen bonds, we find that the modified Flory theory of swelling leads to the calculation of smaller molecular weights than if we had simply not accounted for them. This result will remain true regardless of any deficiencies in our association model, as an examinaqion of eq 7 will quickly reveal. The contribution of (AG,), is negative (or zero if there is no change in hydrogen bonding, but this would mean that there is no mixing). Accordingly, the size of the denominator in eq 7 will always be increased once any contribution from hydrogen bonding is determined, by whatever method. As a result, M , will have a lower calculated value. An additional possibility that arises from our analysis is that there might be a second observable Tgfor certain
then using a value of Tg2= 127 K for pyridine, we calculate that the glass transition of a homogeneous mixture, say 50% by weight coal, should be of the order of 166 K, or -107 "C. It is well-known that strong interactions can lead to significant deviations from the Couchman relationship, but not, we believe, to a difference of 250 "C. If, however, the swollen coal network is microphase separated into two swollen phases in equilibrium with pure solvent, and the analysis of swollen networks by Erman and F10ry~~ demonstrates this possibility, then two Tis might be observed, one closer to the value of coal and the second closer to the value for the solvent, depending upon the composition distribution. This possibility, together with that of gel collapse, are experimentally testable predictions of our analysis. Acknowledgment. We gratefully acknowledge the support of the Office of Chemical Sciences, Department of Energy, under Grant No. DE-FG02-86ER13537. Appendix We adopt here the nomenclature listed in our preceding publications, to which the interested reader is referred.8,9J6 Certain new quantities are introduced and will be defined here. Essentially, our equations need to be modified to account for hydrogen bonding between coal OH and ether groups. Previously, only self-associationbetween phenolic groups in competition with the formation of hydrogen bonds with the OH groups and solvent were considered. We let KE be the equilibrium constant describing the formation of a hydrogen bond between coal OH and ether oxygen groups. Then in pure coal the equations describing the stoichiometry of the system are @OB = @B,r02[1 + x O 1 ] (AI)
@"E =
@El[l
+ KE@"Blr0l]
(A2)
where @E is the volume fraction of ether oxygen containing segments in the coal, defined in terms of an arbitrary segment containing a phenolic OH group as @'E
= @B
% 0 as ether oxygen % 0 as phenolic OH
]
643)
The factor Xol is given by
xol= KE@"E,/r@
(A4)
where @OE, is the volume fraction of ether groups that are not hydrogen bonded and re is the ratio of the molar volume of the ether and OH-containingsegments (see body (36) Lucht, L. M.; Larson, J. M.; Peppas, N. A. Energy Fuels 1987, I , 56. (37) Couchman, P. R. Macromolecules 1978,11, 1156. (38) Couchman, P. R.; Karasz, F. E. Macromolecules 1978, 11, 117. (39) Simha, R.; Boyer, R. F. J. Chem. Phys. 1962, 37, 1003.
Energy & Fuels 1990,4, 393-397
of paper for a discussion of this concept). Note that these molar volumes are defined such that @OB + E'@ =1 (-45)
393
nition is perfectly valid as long as the functional groups are distributed randomly. The contribution of hydrogen bonding to the free energy of mixing is now given by
In a mixture we now have @B = @B,rz[l @E
=
@S
= @S,[l
@E,[1
+
+ xz]
+ KE@B,r11 + KS@B,r11
(A6)
(A7)
-AGH -
- aBIn
RT
(2)+
In
(3) + 5 In as, + rS
@'E1
(A8)
where = KE@El/re
(A9)
X2 = Ks@s,/re
(A10)
and the subscript S represents solvent and was given the subscript A in our preceding p a p e r ~ . ~ * ~ J ~ Again, note that @B + @ E + @s = 1 (All) i.e., we have simply divided the coal into two types of segments, the first of which contains one OH group and the second of which contains one ether oxygen. The molar volume of each follows from the composition. This defi-
I"
In
fiOBb
aB+ @E In @E + @A In @A re
PA
The chemical potentials and spinodal can be obtained from this equation by numerical calculation or by analytical solutions, derived in the same manner as in previous papers.*l9J6 Registry No. THF,109-99-9; pyridine, 110-86-1; acetone, 67-64-1; diethyl ether, 60-29-7; acetonitrile, 75-05-8; benzene, 71-43-2.
Coal Solubility and Swelling. 3. A Model for Coal Swelling 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
In this paper we propose a model for coal swelling based on a process called disinterspersion. This allows a calculation of the "molecular weight" or number of aromatic "clusters" between cross-link points under the assumption that rigid chains swell with little or no change in average conformation up to a limit imposed by the geometry of the network. Sample calculations are presented and suggest that for an Illinois No. 6 coal the "molecular weight" between cross-link points is small.
Introduction In the first two papers in this series we considered the thermodynamics of mixing coals with solvents, extending the application of the Flory lattice model's so as to include the effect of hydrogen bonding. This allowed us to determine the effect of such interactions on the chemical potential of the solvent and hence the degree of swelling of a network. The theories of swelling that have been are well-known to be severely limited in their application to coal, but have nevertheless been considered useful as a qualitative and comparative probe of structure. In the same manner, we find that a qualitative consideration of the balance between various contributions to the thermodynamics of mixing and the "elastic" free energy leads us to predict that in various solvent-swollen coal samples we may be able to observe the phenomenon of gel collapse. The detection of this transition as a function of temperature and/or solvent composition would then be
* To whom correspondence should be addressed. 0881-0624/90/ 2504-0393$02.50/0
an additional experimental probe of molecular structure, providing that we can apply an appropriate statistical mechanical model. Therein lies the rub. Not only are Flory's theories and their modifications seriously compromised when applied to a material such as coal, recent experimental evidence indicates that there may be a fundamental flaw in the basic model4 and it cannot be accurately applied to even ideal networks. The use of swelling data to obtain even a rough estimate of coal structural parameters would thus seem to be a hopeless task. Strangely enough, it is the relatively stiff and presumably short nature of the "chains" present in coal, characteristics that preclude an application of any ideal network theory, that allows the application of an alternative approach, (1) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953. (2) 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. (3) Kovac, J. Macromolecules 1978, 1 1 , 362. (4)Neuburger, N.A.; Eichinger, B. E. Macromolecules 1988,21,3060.
0 1990 American Chemical Society
