Quantitative Description of Oxidative Degradation of Brown Coal in

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Energy & Fuels 1999, 13, 1230-1238

Quantitative Description of Oxidative Degradation of Brown Coal in Aqueous Phase on the Basis of Bethe Lattice Statistics Jun-ichiro Hayashi* and Tadatoshi Chiba Center for Advanced Research of Energy Technology (CARET), Hokkaido University N13-W8, Kita-ku, Sapporo 060-8628, Japan Received June 9, 1999. Revised Manuscript Received September 9, 1999

The present study has been undertaken to clarify the mechanism of an aqueous-phase oxidative degradation of a brown coal and to examine the applicability of lattice statistics for a quantitative explanation of the degradation. In this paper, first, changes in carbon type distribution as well as those in contents of oxygen functionalities, caused by the oxidation, are analyzed, and the results demonstrate the validity of the previously proposed mechanism of the oxidation: (1) The oxidation depolymerizes the coal by eliminating aromatic clusters; (2) When a cluster is eliminated, the inter-cluster bridges that connected the cluster are converted into peripherals of the neighboring clusters, and carboxyl groups are formed at the ends of the peripheral chains; (3) The elimination of the cluster also accompanies the deactivation of the neighboring clusters due to the formed carboxyls. The relationships among the loss of clusters, that of bridges, and amount of carboxyls formed are quantitatively explained by general lattice statistics assuming that each cluster is bonded to 2.2 bridges on average. Second, a structural model of the coal is developed in order to explain the increase in the solvent-extractable material by the degradation. The model describes the macromolecular structure of the coal as a mixture of Bethe lattice with a coordination number Z ) 2.2 (the site occupation probability p0 ) 1) and solvent extractable material. The model is found to predict the observed increase in the mass fraction of DMF extract quantitatively as a function of a corrected site-occupation probability, and also to present the molecular mass distribution of the material consistent with that observed by a laser desorption-ionization mass spectrometry.

1. Introduction Despite its “nonpolymeric” macromolecular structure with a variety of chemical elements, bone structures of the organic portion of coal may be simply approximated by lattice models, as done in recently developed pyrolysis models.1-3 The models characterize the structures in terms of the concentrations of the structural elements (aromatic clusters of mono- and fused rings carrying peripheral groups and bridges of alkyl groups and ethers connecting clusters) and the coordination number of the clusters that is indispensable to quantitative description of the lattice and is defined as the maximum number of bridges that might be connected to a cluster.4,5 Since the degradability of coal is governed by the concentration of bridges relative to that of clusters as well as the thermal or chemical stability of bridges, the applicability of lattice models to the description of coal structure can be examined by analyzing characteristics of coal deg* Author to whom all correspondence should be addressed. Telephone: +81-11-706-6850. Fax: +81-11-726-0731. E-mail: [email protected]. (1) Niksa, S.; Kerstein, A. R. Fuel 1987, 66, 1389. (2) Grant, D. M.; Pugmire, R. J.; Fletcher, T. H.; Kerstein, A. R. Energy Fuels 1989, 3, 175. (3) Fletcher, T. H.; Kerstein, A. R.; Pugmire, R. J.; Solum, M. S.; Grant, D. M. Energy Fuels 1992, 6, 414. (4) Stauffer, D. Introduction to Percolation Theory; Tailor & Francis, London, 1985. (5) Stockmayer, W. H. J. Chem. Phys. 1943, 11, 45.

radation. The analysis requires measurable structural changes with the progress of degradation, namely, an increase in the fraction of low-molecular-mass components released from macromolecules along with a decrease in the bridge concentration. The relationship between these changes is a function of molecular configuration and thus could be described quantitatively by assuming a certain lattice with an appropriate coordination number. Recently, an oxidation in weakly alkaline aqueous phase6,7 was found to solubilize low rank coals to a considerable extent even at temperatures below 100 °C. Hayashi et al.7 oxidized a brown coal at 85 °C in a 0.5 N Na2CO3 aqueous solution in a closed reactor, through which atmospheric oxygen gas was bubbled. The mass fraction of solvent-extractable material in the coal increased from 0.15 to 0.97 as the oxidation progressed. Analyses of the products revealed that aromatic carbon was selectively oxidized into carboxyls in the residual solid, those of water-soluble nonaromatic acids and carbon dioxide, while aliphatic carbon was minimally involved in the reaction. They proposed a reaction mechanism that the oxidation converted aromatic carbons bonded to bridges into peripheral carboxyl groups (6) Hayashi, J.-i.; Matsuo, Y.; Kusakabe, K.; Morooka, S. Energy Fuels 1997, 11, 284. (7) Hayashi, J.-i.; Aizawa, S.; Kumagai, H.; Chiba, T.; Yoshida, T.; Morooka, S. Energy Fuels 1999, 13, 69.

10.1021/ef990117c CCC: $18.00 © 1999 American Chemical Society Published on Web 10/16/1999

Oxidative Degradation of Brown Coal in Aqueous Phase

Figure 1. Elimination of aromatic cluster and conversion of inter-cluster bridge into carboxyl group by oxidation.

on the neighboring clusters, and also converted the other aromatic carbons into nonaromatic acids or carbon dioxide. According to this mechanism as illustrated in Figure 1, the oxidation decomposes the macromolecular network of the coal by eliminating clusters as sites and converting bridges as bonds into peripherals. The elimination of a cluster (indicated by 3) accompanies the formation of carboxyl groups at the chain ends of the neighboring clusters (1, 2, and 4). If the mechanism is valid, the extent of the degradation can be quantified by determining the amounts of lost bridges and clusters from those of formed carboxyls and oxidized aromatic carbon, respectively. In addition, the number of carboxyls formed as peripherals is expected to be equal to that of bridges which were bonded to eliminated clusters. The present study has been undertaken to examine the validity of the above-described mechanism of the oxidation and the applicability of general lattice statistics to the analysis of the degradation characteristics. This paper reports the results of the examination and that a model assuming a Bethe lattice4,5 describes the degradation quantitatively. 2. Experimental Section Morwell brown coal was treated in 5 N HCl aqueous solution, and ion-exchangeable metal cations were removed. The acid-treated coal was oxidized at 85 °C for 1-12 h in an aqueous solution of Na2CO3. During the oxidation, atmospheric oxygen gas was continuously bubbled into the suspension. After being cooled to ambient temperature, the suspension was acidified to a pH of 1.0 by adding 5 N HCl aqueous solution. The residual solid was separated from the acidified solution by centrifugation and washed repeatedly with distilled water until no chlorine ion was detected in the washing. The acidified solution and washings were found to contain aromatic acids and nonaromatic acids such as oxalic, acetic, formic and glycolic acids. The aromatic acids were recovered by a liquid-liquid extraction with 2-butanone and then merged into the solid residue as an “oxidized coal”, while the nonaromatic acids were analyzed by HPLC. The oxidized coal was vacuum-dried at 80 °C. Details of the experimental procedure are described elsewhere.7 The oxidized coal sample obtained through the oxidation for X h is hereafter referred to as SX. The oxidized coals were analyzed by a CP/MAS 13C NMR, and the carbon type distributions of the individual samples were determined. Details of the mea-

Energy & Fuels, Vol. 13, No. 6, 1999 1231

surements, peak assignment, and curve resolution of spectra were reported previously.7 The concentrations of carbonylic, carboxylic, and phenolic groups were measured by means of oximation, ion exchange, and acetylation,7 respectively. The samples were also subjected to exhaustive extraction with various single and mixed solvents at ambient temperature under ultrasonic irradiation. The mass fraction of extract for all the samples was found to be expressed as a function of the Hildebrand solubility parameter (SP) for the solvents having Gutmann’s donor number of 20 or greater7 and to be the largest at SP around 12 cal0.5 cm-1.5. Thus, the mass fraction of solvent-extractable material was defined as that of material extracted with dimethylformamide (DMF; SP ) 12.2 cal0.5 cm-1.5 and DN ) 26.6). Molecular mass distribution of the extracts was measured by a laser desorption-ionization mass spectrometry (LD/MS) on a spectrometer (Japan PerSeptive, model Voyager RP-DE). The extract sample was dissolved in DMF together with or without a typical matrix reagent, 1-(4-hydroxyphenylazo)-benzoic acid (HABA) that was used to assist the ionization of the extract. The mass ratio of the matrix to the extract was 10 or greater. The matrix, as well as sinapinic acid and gentisic acid, has been found to be effective for laser-ionization of coal extracts and pitches which often contain heavy materials having molecular mass up to the order of 105 in m/z 8,9. The spectra were observed in a linear mode under the following conditions: accelerating voltage, 25 kV; mass range, 50-100000; pressure, 1-2 × 10-7 Torr. A nitrogen laser operating at 337 nm was used for the laser desorption. The laser was scanned across the sample coated on a target slide, and spectra were summed from up to 64 or 128 laser pulses. For each of the measurements, the laser power was set at a value slightly above the threshold for the appearance of the spectrum assigned to the extract, to avoid the fragmentation of molecules. Preliminary measurements revealed that the molecular mass of the extracts is distributed from 100 to 8000. Also, the spectra obtained in the absence of the matrix were as intensive as those using it. 3. Results and Discussion Calculation of Amount of Lost Bridges and Clusters. Table 1 lists the fractions of different types of carbon found in the oxidized coal samples: fCO (carbonylic carbon), fCOOH (carboxylic carbon), fOH (phenolic carbon), fa-e (aromatic carbon bonded to ether), fa-C (aromatic carbon bonded to carbon), fa-H (protonated aromatic carbon), fa-O (aliphatic carbon bonded to oxygen other than methoxy carbon), fal-OCH3 (methoxy carbon), fal-RCH2 (methylene or methin carbon at a position to aromatic carbon), fal-CH2 (methylene carbon at β position), fal-RCH3 (methyl carbon at R position), and fal-tCH3 (methyl carbon at remote position). These fractions are indicated in the unit of mol-C per 100 mol-C in S0, the initial acid-treated coal. The fractions of total aromatic and aliphatic carbons, referred to as fa and fal, respectively, are defined as

fa ) fa-e + fa-OH + fa-C + fa-H fal ) fal-O + fal-OCH3 + fal-RCH2 + fal-CH2 + fal-RCH3 + fal-tCH3 + fal-acids

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Hayashi and Chiba

Table 1. Fractions of Different Types of Carbon sample

fCO

fCOOH

fa-e

fa-OH

fa-C

fa-H

fal-O

fal-OCH3

fal-RCH2

fal-CH2

fal-RCH3

fal-tCH3

total

S0 S1 S2 S3 S4 S6 S9 S12

6.8 5.7 5.9 6.6 6.3 7.2 5.8 6.6

3.4 4.7 5.1 5.6 5.9 6.1 7.0 7.0

5.4 6.7 3.7 4.5 2.7 3.6 4.1 3.6

10.9 10.1 10.4 9.0 9.1 9.0 8.3 7.6

31.2 28.0 31.5 30.8 29.6 29.8 27.3 26.1

8.0 6.8 6.9 6.3 6.4 6.1 6.6 5.9

1.5 1.8 1.6 1.5 1.7 1.5 2.4 2.6

2.6 2.6 2.8 2.7 2.6 2.6 2.4 2.4

13.1 14.2 13.0 12.7 11.6 13.6 12.9 12.6

8.2 7.7 7.9 8.2 12.1 9.4 11.1 8.6

5.3 4.8 5.1 5.0 5.0 4.7 4.6 5.2

3.6 3.6 3.5 4.0 3.4 2.6 2.8 2.5

100.0 96.5 97.5 96.9 96.3 96.3 95.2 90.5

Figure 2. Fraction of different types of carbon, fa, fal, fCOOH, and fa-b, as a function of oxidation time.

fal-acids is the fraction of aliphatic carbon contained in the nonaromatic acids: acetic, glycolic, malonic, and pyruvic acids. fCO, fCOOH and fa-OH were measured by the chemical analysis as mentioned in the Experimental Section. fa-e was calculated by the difference between fa-OH and the fraction of oxygen-bonded aromatic carbon that was determined by the NMR. Figure 2 shows fa, fal, and fCOOH as a function of the oxidation time. fa decreases monotonically with time while fal remains unchanged. fCOOH increases as the oxidation progresses. The figure also shows the change in the fraction of aromatic carbon bonded to bridges, fa-b. The fraction is given as the difference of the summed fractions of carbon- and etheric-oxygen-bonded aromatic carbons according to Solum et al.,10 namely, fa-C and fa-e, from (8) John, P.; Johnson, C. A. F.; Parjer, J. E.; Smith, G. P.; Herod, A. A.; Li, C.-Z.; Kandiyoti, R. Rapid Commun. Mass Spectrom. 1993, 7, 795-799.

those of carbons at chain ends: fCOOH, fal-OCH3, fal-tCH3, and fal-RCH3, and is calculated.

fa-b ) fa-C + fa-e - (fCOOH + fal-OCH3 + fal-tCH3 + fal-RCH3) The decrease in fa-b with time indicates the loss of bridges by the oxidation, and total amount of bridges is calculated from a simple stoichiometry by

Nb )

fa-b 2

(1)

(9) Herod, A. A.; Li, C.-Z.; Parker, J. E.; Phillip, J.; Johnson, C. A. F.; Smith, G. P.; Humpley, P.; Chapman, J. R.; Kandiyoti, R. Rapid Commun. Mass Spectrom. 1994, 8, 808-814. (10) Solum, M. S.; Pugmire, R. J.; Grant, D. M. Energy Fuels 1989, 3, 187.


Figure 3. Relationship between ∆fCOOH and ∆Nb.

The loss of bridges, ∆Nb, is here defined as

∆Nb ) Nb (for S0) - Nb (for SX) On the basis of the proposed mechanism of the oxidation as illustrated in Figure 1, ∆Nb is expected to be equivalent to the amount of formed carboxylic groups on a molar basis, which is defined as the difference of fCOOH from that of S0 and denoted as ∆fCOOH. Figure 3 plots ∆Nb against ∆fCOOH and demonstrates a one-toone relationship between them. This relationship is consistent with the proposed mechanism. When aromatic clusters are eliminated by the oxidation of aromatic carbon involved in them, the amount of eliminated clusters, ∆Nc, would be expected to have a linear relationship with that of aromatic carbon lost by the oxidation, ∆fa*:

∆fa* ∆Nc ) na where ∆Nc and ∆fa* are expressed in the units of molcluster/100 mol-C in S0 and mol-C/100 mol-C in S0, respectively. In the equation, ∆fa* is a little smaller than the observed loss as the difference of fa from that of S0 (referred to as ∆fa) from that of S0 due to the formation of a small amount of quinones that never contributes to the elimination of clusters. The details of calculation of ∆fa* was described in our previous report.7 The ratio of ∆fa* to ∆fa was in the range from 0.9 to 1, while no systematic relationship of the ratio with the oxidation time was found.7 Another parameter, na, is the average number of aromatic carbon atoms per cluster. The number can be estimated from the abundance of bridgehead carbon relative to total aromatic carbon. As Solum et al.10 proposed, the fraction of bridgehead carbon (denoted as fa-bh) can be defined as the difference between the fraction of carbon-bonded aromatic carbon, fa-C, and the sum of the fractions of nonaromatic carbon bonded to aromatic carbon. fa-bh is given by the following equation assuming that all carbonyls and carboxyls are bonded to aromatic carbon, and in addition, that no a,amethylenes and quinones are present.

fa-bh ) fa-C - (fCOOH + fCO + fal-aCH2 + fal-RCΗ3)


Figure 4. ∆fCOOH and ∆Nb as a function of loss of aromatic clusters, ∆Nc.

From this equation, fb-ah of S0 was calculated as 2.9 mol-C/100 mol-C in S0, which amounts to only 4.8% of fa. fb-ah for the other samples was also found to account for at most 4% of the corresponding fa. The appreciably small values of fa-bh, as described in detail in the previous report,7 indicate that the assumption of monoaromatic rings, in other words, na is 6 mol-C/mol-cluster, is reasonable for the all samples. ∆Nc is thus expressed as

∆Nc )

∆f*a 6

The same relationship as above holds between fa and Nc.

Nc )

fa 6

(2)

Applicability of Lattice Statistics to Explanation of Structural Changes. Figure 4 shows ∆Nb and ∆fCOOH as a function of ∆Nc. Both of ∆Nb and ∆fCOOH are related linearly with ∆Nc at a slope of about 2.2. This means that 2.2 bridges are lost when an aromatic cluster is eliminated by the oxidation, and hence that each of the lost clusters was bonded to the same number of bridges in average. Moreover, the linear relationship itself should be noted when the mechanism of the oxidation is considered. As illustrated in Figure 1, the elimination of a cluster accompanies the formation of carboxyl groups at the chain ends of the neighboring clusters. As we described in the previous paper,7 aromatic rings carrying carboxyls generally have oxidation reactivities orders-of-magnitude smaller than those without carboxyls. Therefore the neighboring clusters may behave as inert ones after carboxyls are formed, while they also lose bridges initially connected to them. Thus, the elimination of clusters would proceed forming deactivated clusters that accumulate during the oxidation. For a macromolecule or lattice consisting of clusters and bridges, of which initial concentration of intercluster bridges is nb,0 () 2Nb,0/Nc,0), the degradation is supposed to be caused by the elimination of clusters (or sites). In the case that all of the clusters have the same

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Hayashi and Chiba

Figure 6. Schematic representation of Bethe pseudo lattice with coordination number of 3.

Figure 5. Observed and calculated nb as a function of Nc/ Nc,0.

reactivity (Case I), the bridge concentration at a given extent of degradation, nb, follows:

nb ) nb,0

( ) (

)

∆Nc Nc ) nb,0 1 Nc,0 Nc,0

(3)

since the rate of decrease in Nb relative to that in Nc, dNb/dNc, is proportional to the bridge concentration as

dNb 2Nb ) ) nb (nb ) nb,0 when Nc ) Nc,0) dNc Nc Here, Nc/Nc,0 is the ratio of remaining clusters to that before degradation and is a measure of the extent of cluster elimination. On the other hand, when the degradation involves the above-described deactivation processes (Case II), the average number of bridges bonded to a remaining “reactive” cluster is independent of Nc/Nc,0, and is equal to nb,0. Then, when a cluster is eliminated, the number of bridges lost is always nb,0, and the following relationship holds:

nb )

2Nb 2{Nb,0 - nb,0(Nc,0 - Nc)} ) ) Nc Nc nb,0{2(Nc/Nc,0) - 1} (Nc/Nc,0)

the change in nb by eq 4 not only provides the initial bridge concentration but also allows us to analyze other characteristics of the degradation based on lattice statistics. In this section, an examination is performed on the applicability of a particular type of statistical lattice to describing changes in the fraction of solventextractable material and its molecular mass distribution as a function of the extent of cluster (site) elimination. Bethe lattices are statistical ones and each of the lattices has an infinite number of sites and is defined by the coordination number (Z) and site occupation probability (p, 0 e p e 1) that is the number fraction of occupied sites to the total sites. When two sites neighboring to each other are both occupied, they are recognized to be connected by a bridge. The lattices are dendroid and thus no loops are allowed therein. The absence of loops is unlikely for actual networked macromolecules, but this gives a fairly good approximation11 of the gel formation observed in polymerization of multi-functional monomers. This characteristic also provides analytical solutions of states of the lattices as a function of the parameters, Z and p, and this simplifies the description of the averaged structure of the coal by a Bethe lattice as shown below. Figure 6 schematically illustrates a Bethe lattice with Z ) 3. For a Bethe lattice with Z and p, nb is expressed as

nb ) Z × p (4)

The degradation in Case II results in nb smaller than that in the degradation in case I at equivalent Nc/Nc,0, which is easily derived by comparing eq 3 with eq 4. Figure 5 shows the observed nb as a function of Nc/Nc,0 together with a line drawn on the basis of eq 4 assuming nb,0 ) 2.2. The observed change of nb is seen to be well explained by eq 4 assuming Case II degradation. Equation 4, as well as eq 3, is applicable to arbitrary lattices. Therefore, the results shown in Figures 3, 4, and 5 reveal that the changes in fCOOH, Nc, and Nb are reasonably well explained on the basis of the proposed oxidation mechanism, and are also quantitatively described by assuming a lattice with nb,0 of 2.2, while leaving other parameters such as the coordination number unknown. Introduction of Lattice Statistics to Further Analysis of Degradation. The above explanation of

When the degradation of the lattice occurs obeying the mechanism of Case I, the probability p and corresponding bridge concentration, nb, are related as follows.

nb p ) nb,0 p0

(5)

where p0 is the site-occupation probability of the initial lattice with nb,0 ) Z × p0. The lattice statistics can also describe the distribution of degree of polymerization. The probability for an occupied site to belong to m-mers consisting of m sites and (m - 1) bridges is given as

Fm(p) ) mbmps(1 - p)t

(6)

where mbm is the total number of configurations possible for m-mers. s and t are respectively the number of bridges involved in an m-mer () m - 1) and the number (11) Flory, P. J. J. Am. Chem. Soc. 1941, 63, 3091.


Figure 7. Fraction of site belonging to m-mers as a function of site-occupation probability, p.


Figure 8. nb as a function of p in Case I and Case II and graphical transformation of p into p*.

of unoccupied sites that are neighboring to the sites of the m-mer.

Table 2. p/p0 and Corresponding p*/p0

s)m-1 t ) m(Z - 2) + 2 Fm(p) is essentially the same as the fraction of m-mer with regard to the occupied sites. It is also known that each Bethe lattice has its critical site-occupation probability, pc, above which so-called “gel” having infinite number of sites, exists in the lattice;

pc )

When p is below pc, no gel exists in the lattice and therefore the total fractions of finite-sized molecules, Ff(p), is steadily unity. On the other hand, when p > pc, Ff(p) is given by

Ff(p) )

∑ Fm(p) )

m)1

() pr

Z/Z-2

p

where pr is a root that satisfies the following equation:

pr(1 - p)Z-2 ) p(1 - p)Z-2 The lattice with pc > p > 1 involves finite-sized m-mers and gel while that with p ) 1 consists solely of gel. Figure 7 shows the fractions of finite-sized m-mers as a function of p for the Bethe lattice with Z ) 3. Fi-j(p) indicated in the figure is defined as m)j

Fi-j(p) )

p/p0a

p*/p0

S0 S1 S2 S3 S4 S6 S9 S12

1 0.950 0.938 0.919 0.864 0.902 0.835 0.801

1 0.947 0.934 0.912 0.843 0.891 0.802 0.751

p/p0 equals Nc/Nc,0.

present oxidation, the elimination of a site results in the loss of nb,0 bridges. Then, nb at a probability p is expressed as

1 Z-1

∞

a

sample

∑ Fm(p)

(7)

m)i

Further details of the Bethe lattice statistics are well explained in the literature,1,4,5 and are therefore not described here. Equation 5 gives the relationship between the changes in nb and p, and this equation is applicable to the description of Bethe lattice degradation only when the elimination of sites occurs randomly as in Case I. In Case II, where the elimination of a site accompanies the deactivation of the neighboring sites as observed in the

{1 - 2(p0 - p)/p0} nb ) nb,0 p/p0

(8)

Equation 8 is directly derived from eq 4 since p/p0 ) Nc/Nc,0. As shown in Figure 8, nb in Case II is smaller than that in Case I at the same probabilities; in other words, p in Case I is smaller than that in Case II at the equivalent nb. In essence, degradation of lattices is brought about by the elimination of bridges and its extent is defined by the decrease in the bridge concentration, i.e., nb. Hence, for description of Case II degradation by eq 6 that is originally available for Case I, p in Case II is needed to be transformed so that eq 5 as a function of the transformed probability gives nb/ nb,0 equivalent to that given by eq 8 as a function of p. The transformed probability, p*, is determined graphically as seen in the figure and expressed as

p* )

p0{1 - 2(p0 - p)/p0} p/p0

(9)

Thus, if the macromolecular structure of the coal can be assumed to be a Bethe lattice, its degradation caused by the oxidation would be described by using p*. Table 2 lists p/p0 and corresponding p*/p0 of the oxidized coal samples. Quantitative Explanation of Degradation Characteristics Assuming Coal as a Bethe Pseudo Lattice. Two different Bethe lattice models are applied

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Figure 9. Fraction of DMF extractable material, YDMF, as a function of normalized probability p*/p0 and its comparison with F1-40(p) predicted by model A assuming different combinations of Z and p0 with Zp0 ) 2.2.

Hayashi and Chiba

Figure 10. Fraction of DMF extractable material, YDMF, as a function of normalized probability p*/p0 and its comparison with F1-40(p) predicted by model B assuming different values of Z.

to the quantitative explanation of changes in the fraction of extractable material caused by the oxidation and in molecular mass distribution of the material. The first model, model A, assumes the following: (1) The initial coal, S0, contains 15% of DMF extractable material on a dry-ash-free mass basis. Thus the coal consists of the solvent extractable material and nonextractable macromolecular network, both of which materials are involved in a Bethe lattice with pc e p0 e 1 and Z ) nb,0/p0. nb,0 () Zp0) is given as 2.2 according to the experimental result shown in Figure 5. (2) The solvent extractable material, experimentally given as DMF extract, consists of m-mers with m ranging from 1 to 40. The basis of this assumption is mentioned below. The model A predicts the mass fraction of solvent extractable, referred to as Ye, as a function of the site probability.

Ye ) F1-40(p) Figure 9 compares Ye as a function of the normalized probability, p/p0, with the observed mass fraction of DMF extract, indicated by YDMF,obs plotted against p*/ p0. It is seen that any of the combinations of Z and p0 satisfying their product of 2.2 cannot predict the observed increase in YDMF. Though not shown, other combinations of Z and p0 with Zp0 ranging from 2.0 to 3.0 were also examined and none of them were found to give Ye in agreement with the observed YDMF. Thus, the model A is not applicable to the explanation of the observed degradation characteristics. Different from the model A, model B assumes (1) S0 consists of solvent extractable and nonextractable materials. The extractable material is comprised of m-mers with m ranging from 1 to 40, while the nonextractable material is a Bethe lattice with p0 ) 1 and nb,0 ) Z. Thus the initial extractable material is not involved in the Bethe lattice. (2) The fraction of the m-mers as Ye and that of the Bethe lattice in S0 are 0.85 and 0.15, respectively, which is based on the observed YDMF for S0 as 0.15. (3) The concentration of bridges for the e ) is 1.8, which extractable material (referred to as nb,0 was determined by analyzing a 13C NMR spectrum of

Figure 11. LD/MS spectra of DMF extracts from S0, S3, S6, S9, and S12.

the DMF extract from S0 on the basis of eqs 1 and 2. (4) When a site is eliminated, the probability for the site belonging to the initial Bethe lattice is 0.85 while that to the initial m-mers is 0.15. This is based on the assumption that the clusters initially involved in the nonextractable material and those in the extractable material have equivalent reactivities to the oxidation. In addition to the above, the second assumption for model A is considered also in model B. Model B predicts Ye as follows:

Ye ) 0.85F1-40(p) + 0.15 Figure 10 compares calculated F1-40(p) as a function of



Figure 12. Molecular mass distribution of solvent extractable on molar basis predicted by model B and mass spectrum of DMF extract from S6.

p/p0 with YDMF. It should be noted that Ye strongly depends on Z agrees best with YDMF when Z ) 2.18. In model B, the initial bridge concentration, namely nb,0 is given as

nb,0 ) 0.85Z + 0.15nb,0e and is calculated as 2.1 using Z ) 2.2. This value of nb,0 is in good agreement with that determined from the results shown in Figure 5, i.e., 2.2. Here, the validity of model B is further examined by comparing the molecular mass distribution of the solvent extractable material predicted by the model with that observed. Figure 11 illustrates LD/MS spectra of DMF extracts from S0, S3, S6, S9 and S12, which were observed without the matrix reagent. The spectra reveal that the molecular mass is distributed widely over the range from 100 up to 8000 and that compounds with molecular mass of 250-350 are the most abundant. Moreover, the distribution seems not to vary with the extent of the oxidation so significantly. The distribution of molecular mass could be converted into that of degree of polymerization, by giving the average molecular mass of the monomeric unit. The average molecular mass, Mm, is easily be estimated as

( )( )

Mm ) 12na

100 100 ≈ 200 fa,0 Wc,0

indicating that the degree of polymerization of the extracts ranges from 1 to approximately 40. This is the basis of that F1-40(p) is considered in the abovedescribed models. Figure 12 shows the molecular mass distribution predicted by model B assuming Mm ) 200 together with the observed mass spectrum of the extract from S6. The predicted distribution at p ) 0.90 is approximately in agreement with that of the DMF extract with p* ) 0.89. It is also seen in the figure that

the predicted distribution little depends on p in the range from 0.75 to 0.95. This is consistent with the observed distribution for the extract insensitive to p. As mentioned above, model B can reasonably describe the observed increase in the fraction of DMF extractable material and its molecular mass distribution as a function of the fractional loss of aromatic clusters that are recognized as sites of the Bethe lattice. The coordination number estimated by the model, 2.2, may provide a simplified macromolecular structure of the coal, in which 80% of the clusters are connected to two bridges while the rest, 20%, of those are connected to three bridges. If the latter clusters can be recognized as the cross-linking (or branching) points in the macromolecular network, the model estimates that the average number of repeating units between the points is about five. Conclusions The present study has been carried out to clarify the mechanism of an aqueous-phase oxidative degradation of a brown coal and then to examine the applicability of lattice statistics for quantitative description of the degradation. Through the analyses of the structural changes of the coal caused by the oxidation, the following conclusion can be drawn. The oxidation depolymerizes the coal by eliminating aromatic clusters. When a cluster is eliminated, the bridges that have been connected to the cluster are converted into peripheral chains of the neighboring clusters, and carboxyl groups are formed at the ends of the peripherals. The elimination of the cluster also accompanies the deactivation of the neighboring clusters due to the formed carboxyls. The mechanism of the oxidation allows us to describe the relationships;

∆fCOOH ≈ ∆Nb

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∆fCOOH ∆Nb ≈ ) nb,0 ≈ 2.2 ∆Nc ∆Nc which are predicted by general lattice statistics. Model B, which assumes that coal is a mixture of a fully developed Bethe lattice with Z ) 2.2 and p0 ) 1, and solvent extractable material with nb,0 ) 1.8, reasonably predicts the observed increase in the fraction of DMF extractable material. The model can also predict the extract’s molecular mass distribution semiquantitatively as a function of p*, the site-occupation probability available for the description of Case II degradation mechanism. Acknowledgment. This work was supported by a “Research for the Future Project” (Coordinator: Prof. M. Iino, Tohoku University) grant from The Japan Society for the Promotion of Science (JSPS), through The 148th Committee on Coal Utilization Technology. The authors are grateful to Dr. T. Yoshida of the Hokkaido National Industrial Research Institute (HNIRI) for his useful advice on the analysis of 13C NMR spectra. Nomenclature Symbol f: fraction of a particular type of carbon determined by NMR or chemical analysis [mol-C/100 mol-C in initial coal] Fi-j: total fraction of oligomers ranging from i-mer to j-mer in Bethe lattice Mm: average molecular mass of monomeric unit [-] Nb: molar amount of bridges [mol/100 mol-C in initial coal]

Hayashi and Chiba Nc: molar amount of clusters [mol/100 mol-C in initial coal] na: average number of aromatic carbon atoms per cluster [molC/mol-cluster] nb: average umber of bridge-bonded aromatic carbon atoms per cluster [mol-C/mol-cluster] neb,0: nb for DMF extract from S0 p: site occupation probability in Bethe lattice [-] p*: corrected site occupation probability defined by eq 5 [-] Ye: mass fraction of solvent extractable material in initial or oxidized coal predicted by model [-] YDMF: observed mass fraction of DMF extract in initial or oxidized coal [-] Z: coordination number of Bethe lattice [-] Subscript 0: sample S0 or initial (before degradation) COOH: carboxylic carbon CO: carbonylic carbon a: total aromatic carbon a-b: aromatic carbon bonded to bridge a-bh: bridgehead carbon a-C: carbon-bonded aromatic carbon a-e: etheric-O-bonded aromatic carbon a-H: protonated aromatic carbon a-OH: phenolic carbon a-O: O-bonded aromatic carbon al: total aliphatic carbon al-O: etheric-O-bonded aliphatic carbon excluding methoxy carbon al-OCH3: methoxy carbon al-RCH2: methylene or methin carbon at R position to aromatic carbon al-CH2: methylene carbon at β or remote position al-RCH3: methyl carbon at R position al-tCH3: methyl carbon at remote position EF990117C

Quantitative Description of Oxidative Degradation of Brown Coal in

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