New Approaches in Coal Chemistry - American Chemical Society

3 Cross-Linked Structures in Coals: Models and Preliminary Experimental Data

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LUCY

M.

LUCHT

and N I K O L A O S A . P E P P A S

School of Chemical Engineering, Purdue University, West Lafayette, I N 47907

Treatment of the structure of bituminous coals as crosslinked macromolecular networks can provide important information on their extraction, swelling and liquefaction behavior at low and high temperatures. A modification of the Flory s t a t i s t i c a l mechanical analysis of Gaussian network chains has been applied to highly crosslinked macromolecular networks of coal for the determination of their number average molecular weight between crosslinks, M , and the coal volume fraction of the swollen samples, U , at equilibrium swelling in pyridine at different temperatures. Three key factors in this analysis are discussed and c l a r i f i e d : the nature of crosslinks in coal, the s i g n i f i cance of the number of repeating units between crosslinks, N, and the nature and significance of the pore structure. Values οf M for coal networks of fixed "aromatic cluster" size, M , obtained by numerical solution of the modified Gaussian chains model are 400-450 for bituminous coals. These values were determined experimentally from physicochemical swelling data of several American coals and compared with relevant experimental data from previously reported studies. c

2,s

c

o

Important t h e o r e t i c a l and e x p e r i m e n t a l c o n s i d e r a t i o n s o f the use o f m a c r o m o l e c u l a r t h e o r i e s f o r the d e s c r i p t i o n o f c o a l n e t work s t r u c t u r e s have been r e c e n t l y a n a l y z e d ( 1 ) . Relevant equations d e s c r i b i n g the e q u i l i b r i u m s w e l l i n g b e h a v i o r of n e t works u s i n g t h e o r i e s o f m o d i f i e d G a u s s i a n d i s t r i b u t i o n o f m a c r o m o l e c u l a r c h a i n s h a v e b e e n d e v e l o p e d b y K o v a c (2) a n d b y P e p p a s a n d L u c h t (3) a n d a p p l i e d t o v a r i o u s c o a l s y s t e m s i n a n e f f o r t to m o d e l t h e r e l a t i v e l y compact c o a l n e t w o r k s t r u c t u r e s (_1,4_). As r e p o r t e d b e f o r e (1), G a u s s i a n - c h a i n m a c r o m o l e c u l a r models u s u a l l y employed i n the d e s c r i p t i o n o f polymer networks (such as the F l o r y

0097-6156/81/0169-0043$05.00/ 0 ©1981

A m e r i c a n Chemical Society

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981.


44

NEW

APPROACHES

IN

COAL

CHEMISTRY

model, 5) are i n a p p l i c a b l e f o r s h o r t , s t i f f chains. Although the modified Gaussian network equations provide an accurate d e s c r i p t i o n of physicochemical phenomena observed i n h i g h l y c r o s s l i n k e d networks (within the assumptions made i n t h e i r d e r i v a t i o n ) , t h e i r a p p l i c a t i o n to a c t u a l c o a l macromolecular s t r u c t u r e s i s a r a t h e r d i f f i c u l t task. Coal h e t e r o g e n e i t i e s are i n part r e s p o n s i b l e f o r t h i s problem. S p e c i f i c a l l y , the nature of the c r o s s l i n k s and the number of repeating u n i t s between c r o s s l i n k s , N, appearing i n the modified Gaussian model equations are not unambiguously defined because of the v a r y i n g s i z e , s t r u c t u r e and chemical composition of the groups involved i n the s t r u c t u r e of the c r o s s l i n k e d chains of c o a l . T h i s c o n t r i b u t i o n deals w i t h some important aspects of c o a l s t r u c t u r e e v a l u a t i o n using modified Gaussian models. Further c l a r i f i c a t i o n of the nature and f u n c t i o n a l i t y of the c r o s s l i n k s i s presented, i n c l u d i n g an a n a l y s i s of refinements i n the math ematical equations f o r the determination of M . Preliminary experimental data of relevance to t h i s a n a l y s i s are a l s o pre sented arid discussed. c

THEORETICAL CONSIDERATIONS E q u i l i b r i u m Swelling Theory A d e t a i l e d development of the modified Gaussian s w e l l i n g equations i s o u t l i n e d elsewhere (1,2). B r i e f l y ^ the procedure i n v o l v e s a n a l y s i s of a macromolecular chain as a set of bond vectors. The d i s t r i b u t i o n and p a r t i t i o n f u n c t i o n s are w r i t t e n i n terms of the end-to-end v e c t o r r and the e q u i l i b r i u m f o r c e f to which the macromolecular chain Is subjected. A specific s e r i e s f u n c t i o n i s used to expand the d i s t r i b u t i o n f u n c t i o n , l e a d i n g to a modified d i s t r i b u t i o n , which i s used to d e r i v e expressions f o r the end-to-end d i s t a n c e as a f u n c t i o n of a p p l i e d f o r c e . These expressions can be used to determine the Gibbs f r e e energy due to e l a s t i c f o r c e s , A G £ . The Flory-Huggins theory i s used f o r the expression of the f r e e energy of mixing of macromolecules w i t h s w e l l i n g agent molecules, A G £ . At e q u i l i b r i u m s w e l l i n g , the excess chemical p o t e n t i a l of the s w e l l i n g agent i n the network i s zero, l e a d i n g to equations r e l a t i n g parameters c h a r a c t e r i s t i c of the macromolecular network to thermodynamic p r o p e r t i e s of the system. Equation (1) developed by Peppas and Lucht (3), i s based on t h i s a n a l y s i s and i t i s a p p l i c a b l e to i s o t r o p i c h i g h l y c r o s s l i n k e d networks. I t can be used to determine important s t r u c t u r a l parameters of the macromolecular network, such_as the number average molecular weight between c r o s s l i n k s , M , and the c r o s s l i n k i n g d e n s i t y of the network, ρ . In the f o l l o w i n g equations ν and V 2 are the s p e c i f i c volume of the " i d e a l i z e d " c o a l network and the molar volume of the s w e l l i n g agent respec t i v e l y , Ό2 i s the e q u i l i b r i u m volume f r a c t i o n of c o a l i n the swollen macromolecular network, χ i s the c o a l network/swelling e

m

x

c

χ

s


3.

LUCHT

AND

Cross-Linked

PEPPAS

Structures

in

45

Coals

agent F l o r y thermodynamic i n t e r a c t i o n parameter at the corres ponding s w e l l i n g temperature and U 2 , s > d Ν i s the number of r e p e a t i n g u n i t s between c r o s s l i n k s . an

^ [ l n ( l - u

2

)

S

)

+

u

2

)

S

+

X

u 2

l

>

s

]


:r- - —

l - ^ / 3 i

3

(D

5 < K . - < s »

ρ

[

χ

= 1/v M

1

+

K .

l

/

3

>

(2)

c

Nature of C r o s s l i n k s i n Coal Experimental observations show that bituminous c o a l s s a t i s f y at l e a s t one important macroscopic c h a r a c t e r i s t i c of a c r o s s l i n k e d network: they s w e l l i n numerous s o l v e n t s without being d i s s o l v e d by them even at h i g h temperatures (1, 6-9), unless thermal degradation or r e a c t i o n occurs. In the development of mathematical models to d e s c r i b e network behavior, c r o s s l i n k s are assumed to be poaltA ( u s u a l l y carbon atoms) or s h o r t btUAQQA ( u s u a l l y of molecular weight much s m a l l e r than M ) whence three or more chains are i n i t i a t e d . Based on recent experimental data on molecular weight d i s t r i b u t i o n s of depolymerized c o a l products (1) and the s t r u c t u r e of f u n c t i o n a l groups i n c o a l (4) we propose a c o a l c r o s s l i n k e d s t r u c t u r e where the c r o s s l i n k s are a bonding r e g i o n , where three or more chains are j o i n e d through a s i n g l e CÙxAtOA. This c l u s t e r i s probably an aromatic or h e t e r o c y c l i c group of molecular weight from 100-400 (10) s i m i l a r to groups proposed by Wiser i n h i s model c o a l network s t r u c t u r e (11). F i g u r e 1 presents a schematic a n a l y s i s of the proposed p h y s i c a l s t r u c t u r e . Although t h i s hypothesis reverses the usual concept of a c r o s s l i n k , the network t h e o r i e s d e r i v e d b e f o r e (1,2) can s t i l l be a p p l i e d as long as the molecular weight between c r o s s l i n k s i s c o n s i d e r a b l y h i g h e r than the molecular weight of a c l u s t e r . The r e a l i z a t i o n that the c o a l c r o s s l i n k s have a f i n i t e volume i m p l i e s that the c a l c u l a t e d values of M u s i n g equation (1) and r e l a t e d expressions w i l l be s m a l l e r than the a c t u a l M^, by a f r a c t i o n , f , of the molecular weight of the c l u s t e r , M , where f i s a constant v a r y i n g between 0 and 1, t a k i n g the value of 0.5 f o r t e t r a functional crosslinks. c

c

Q

Μ

c,actual

β

Μ

Ί

c, c a l e .

+ f M

ο

(3)

In l i g n i t e s , the probably s m a l l extent of c r o s s l i n k i n g should e l i m i n a t e the need f o r c o r r e c t i o n . However t h i s c o r r e c t i o n may be important i n bituminous c o a l s and a n t h r a c i t e s where c r o s s l i n k i n g could be e x t e n s i v e . A c t u a l l y , the e f f e c t of "bulky" c r o s s l i n k s should be i n c l u d e d i n the non-Gaussian model a n a l y s i s



NEW

APPROACHES

IN

COAL

CHEMISTRY

Figure 1. Proposed cross-linked structure in coals: Aromatic ring cluster (d); connecting bond (—); tetra functional cross-link (A); multifunctional crosslink (B).


LUCHT

3.

AND

PEPPAS

Cross-Linked

Structures

in

47

Coals

s i n c e t h i s type of c r o s s l i n k may lead to modified expressions f o r the end-to-end d i s t a n c e . Nevertheless, the approach des c r i b e d above can lead to reasonable determination of M without additional modifications.


c

Repeating U n i t S i z e The number of r e p e a t i n g u n i t s between c r o s s l i n k s , N, a parameter appearing i n equation (1), can be simply d e f i n e d as the jratio of the number average molecular weight between c r o s s l i n k s , M to the average molecular weight of the c l u s t e r s , M . Q

c>

Ν = M /ÏÏ c ο

(4)

A c t u a l l y , i n equation (3) i t i s assumed that M Q = M , where M i s the molecular weight of a h y p o t h e t i c a l r e p e a t i n g u n i t , which i n c l u d e s a c l u s t e r and a connecting bond. T h i s i s a reasonable assumption i n view of the comparatively small s i z e of the connecting bond ( u s u a l l y - C H 2 - , -S-S-, or -0-, (_1)) w i t h respect to the c l u s t e r s i z e and molecular weight. Simultaneous use of equations (1) and (4) can l e a d to the values^ of Mc. For bitum inous c o a l networks, a reasonable value of M of 150 w i l l be used henceforth. r

r

EXPERIMENTAL PART To evaluate the s w e l l i n g behavior and the c r o s s l i n k e d para meters of c o a l networks, s w e l l i n g data were obtained f o r seven American c o a l s s u p p l i e d i n f i n e p a r t i c l e s by the Pennsylvania State U n i v e r s i t y c o a l bank. To e l i m i n a t e experimental a r t i f a c t s , s e v e r a l separations and p u r i f i c a t i o n s were performed p r i o r to s w e l l i n g , according to the general experimental p r o t o c o l reported i n e a r l i e r communications (1,12). The c o a l samples were s i e v e d under n i t r o g e n to 20-30 mesh s i z e using ASTM approved s i e v e s , and they were f l o a t e d i n a benzene/CCl4 s o l u t i o n of d e n s i t y 1.3 gr/cm^ to remove most of the m i n e r a l matter and to i s o l a t e most of the v i t r i n i t e (see a l s o Table I ) . Soxhlet e x t r a c t i o n of the samples was performed i n p y r i d i n e at i t s b o i l i n g p o i n t , and the i n s o l u b l e c o a l matrices (residues) were d r i e d under vacuum to constant weight and r e s i e v e d to 20-30 mesh s i z e . To ensure maximum s o l v e n t removal, the c o a l samples were d r i e d to constant weight under n i t r o g e n at approximately 700 mm Hg and 50-60°C. Swelling was performed at temperatures of 57 ± 2°C. Data were a l s o obtained f o r unextracted samples of 30-40 mesh s i z e at 25°C and 50°C. Swelling was c a r r i e d out i n a sealed chamber i n the pre sence of excess p y r i d i n e vapors at atmospheric pressure and at the temperatures mentioned b e f o r e . Thermodynamic e q u i l i b r i u m was achieved a f t e r 24 hours. Due to the porous s t r u c t u r e of the c o a l samples not a l l the imbibed s w e l l i n g agent c o n t r i b u t e d to the c o a l s w e l l i n g . A c o n s i d e r a b l e p o r t i o n of t h i s solvent

American Chemical Society Library 1155 16th St.

N.

w.

Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; Washington, American 0. Chemical C. Society: 2 0 0 3 6 Washington, DC, 1981.


79.04

83.26

91.14

HVB

HVB

HVC

HVA

Anthracite

266

111

212

341

384 3.23

4.41

13.25

10.62

14.51

19.31

23.89

57 50 25

20-30 30-40 30-40

57

57 50 25

20-30 30-40 30-40 20-30

57 50 25

20-30 30-40 30-40

57 50 25

57 50 25

20-30 30-40 30-40

20-30 30-40 30-40

57 50 25

20-30 30-40 30-40

Only the 20-30 mesh c o a l s were e x t r a c t e d before s w e l l i n g .

78.22

77.30

72.37

Subb

416

67.45

Swelling Conditions T(°C) Mesh Size

.563

.472

.423

.413

.403

.346

.289

χ-Factor (1)

Apparent Swelling Behavior o f Coal Samples

Elemental A n a l y s i s (% daf) 0% C%

Lignite

ASTM Rank

418

P.S.U. Identifi c a t i o n Number

TABLE I :


.975

.723 .671 .709

.661 .512 .553

.638 .501 .553

.677 .495 .545

.625 .459 .465

.636 .435 .440

2,app

Swelling

3.

L U C H T AND

Cross-Linked

PEPPAS

Structures

49

in Coals

remained i n the pores without f u r t h e r c o n t r i b u t i o n to c o a l swelling? An estimate o f the totaZ amount of s w e l l i n g agent imbibed by the porous c o a l p a r t i c l e s can be obtained by c a l c u l a t i n g an appa/i&Kt vaZuZ o f ^2.app by use o f equation (5) which assumes a d d i t i v i t y o f volumes.


V 2,app

V

m /ρ

V V + V c,s c s

r r

K

m/p+m/p c c s s K

'

K

Here m, ρ and V denote weight, d e n s i t y and volume o f the two com ponents, i . e . c o a l and s w e l l i n g agent, which are designated by the s u b s c r i p t s c and s r e s p e c t i v e l y ; then V designates the volume o f the swollen c o a l . An apparent volume degree o f s w e l l i n g , Q pp, can a l s o be determined from equation (6). g

a

Q = 1/U app 2,app

(6)

0

x

Accurate determination of the c o a l volume f r a c t i o n i n the swollen c o a l p a r t i c l e s can be done by c a l c u l a t i n g and excluding the pore volume, Vp, occupied by the solvent during s w e l l i n g . Values o f the p o r o s i t y p, expressed according t o equation (7) i n terms o f the pore volume per dry c o a l weight Ή^, were deter mined from recent s t u d i e s f o r s i m i l a r c o a l s (13). Where no values o f t h i s parameter were a v a i l a b l e , an i n t e r p o l a t i o n o f the p o r o s i t y versus carbon content data (% C, dmmf b a s i s ) was used to determine p. ρ = V /m p

(7)

c

Then the weight of the solvent e ^ e c X t v e t i / MQJLUJIQ be c a l c u l a t e d as,

thd coat can

m* = M - m - ρ V s c s ρ

(8)

K

where M i s the t o t a l weight o f the c o a l sample a f t e r s w e l l i n g . Assuming a d d i t i v i t y o f volumes o f the dry c o a l matrix, V , and the solvent that e f f e c t i v e l y swelled the c o a l , V , i t i s p o s s i b l e to determine the true value of the c o a l volume f r a c t i o n i n the swollen c o a l (excluding the pores), V2 s> by equation (9). c

s

9

V

U

2,s

c " V + V ' c s

m

=

/ p

c c m /p + mVp c e s s

2 s (equation 10) i s the one to be used f o r the determination of A s i n c e i t r e f e r s to the s w e l l i n g of the c o a l matrix, excluding the pore s t r u c t u r e . Use of the value of U2 (from equation 5) i n equation (1) would lead to unacc e p t a D l i v a l u e s of M . T h i s i s an e r r o r f r e q u e n t l y made i n previous s t u d i e s . Determination of the number average molecular weight between c r o s s l i n k s , Μ , was achieved by using equations (1), (4) and (10), using the f o l l o w i n g parameters f o r the c o a l samples and s w e l l i n g agent ( p y r i d i n e ) : p = 1.30 gr/cm , p = 0.982 gr/cm , V = 80.56 cm /mole, ν = 0.769 cm /gr and MQ = 150. The necessary values of the c o a l / s w e l l i n g agent i n t e r a c t i o n parameter χ at 25°C were determined from equation (11), which presents a l i n e a r r e l a t i o n s h i p between χ and the carbon content (on a % daf b a s i s ) .


c

P

C

3

c

3

3

s

x

3

χ = 0.0116 (%C)

- 0.4901

(11)

Over the temperature range of 25-60°C the χ f a c t o r was assumed constant. The a r i t h m e t i c values of χ used f o r t h i s i n t e r p o l a t i o n were derived by s e p a r a t i n g χ i n t o an e n t h a l p i c and an entropie c o n t r i b u t i o n . These terms were c a l c u l a t e d from experimentally determined s o l u b i l i t y parameters of the pure s w e l l i n g agent and the non-swollen c o a l (1, 9). T h i s thermo dynamic treatment does not account f o r e f f e c t s such as formation or d i s r u p t i o n of Η-bonds s p e c i f i c to a p a r t i c u l a r c o a l - s o l v e n t system. Although such models e x i s t f o r simpler or more thoroughly c h a r a c t e r i z e d systems, models which can incorporate solvent s p e c i f i c e f f e c t s i n t o the determination of χ f o r c o a l systems are not a v a i l a b l e to t h i s p o i n t . I t i s p o s s i b l e to use s w e l l i n g agents which do not e x h i b i t s p e c i f i c e f f e c t s ; however, most good s w e l l i n g agents f o r c o a l may a f f e c t the tenuous bonds. RESULTS AND

DISCUSSION

"Apparent" Swelling Behavior Table I summarizes the elemental a n a l y s i s of the c o a l sam p l e s used (as s u p p l i e d by the c o a l bank), the c a l c u l a t e d values of the χ f a c t o r s , the s w e l l i n g c o n d i t i o n s and the experimentally determined values of U2 p p f o r these s t u d i e s . Use of the " i n i t i a l " elemental a n a l y s i s of the c o a l samples (before e x t r a c t i o n and s w e l l i n g ) f o r p l o t t i n g the data i s p r e f e r a b l e here, s i n c e t h i s elemental a n a l y s i s i s r e a d i l y a v a i l a b l e and indepen dent of processing c o n d i t i o n s . A general dependence of the apparent c o a l e q u i l i b r i u m volume a


Cross-Linked

L U C H T A N D PEPPAS

3.

Structures

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f r a c t i o n U2 on the carbon and oxygen content (on a daf % B A S I S ) i s ODSIRVED. F i g u r e 2 shows t h i s dependence of ^2,app the carbon content, obtained w i t h e x t r a c t e d and unextracted COALS a

o

of

V A R I O U S S I Z E S and

at

temperatures of

57°C and

n

50°C R E S P E C T I V E L Y .

Based on the number OF data P R E S E N T L Y a v a i l a b l e , \)2 app ( * d e r i v e d parameter Q p , the apparent degree O F s w e l l i n g ) do not s i g n i f i c a n t l y change i n the range OF 67% to 78% CARBON content. Smooth curves can be f i t t e d to these data FOR the range OF CARBON contents i n v e s t i g a t e d . S i m i l a r behavior i s observed when p l o t t i n g volume f r a c t i o n data f o r s w e l l i n g at 25°C, as i n F i g u r e 3. The same f i g u r e i n c l u d e s experimental v a l u e s of U 2 p p d e t e r mined by Sanada and Honda (8) f o r a s e t of c o a l samples of s i m i l a r range i n carbon content. These data are i n c l u d e d here be cause these authors d i d not make any mention of s u b t r a c t i n g the pore volume i n t h e i r c a l c u l a t i o n s . Therefore, t h e i r calculated values of volume f r a c t i o n s may be apparent volume f r a c t i o n s , 2,appThe dependence of \>2 p p oxygen content of e x t r a c t e d and unextracted c o a l samples (on a daf b a s i s ) i s presented i n F i g u r e 4. The same F i g u r e i n c l u d e s the data of Sanada and Honda (8) and K i r o v et a l (9) f o r comparative reasons. The un e x t r a c t e d c o a l samples do, f o r the most p a r t , show more "apparent" s w e l l i n g , i . e . s m a l l e r values of U 2 pp> than the e x t r a c t e d ones. T h i s behavior may be the r e s u l t of c o l l a p s e of the pore s t r u c t u r e due to e x t r a c t i o n . T h i s s p e c u l a t i o n i s p r e s e n t l y under i n v e s t i gation. an(

t

n

e


ap

> a

u

o

n

t

n

e

a

a

True S w e l l i n g Behavior - E f f e c t of Porous S t r u c t u r e _ The e f f e c t of U 2 , s determined values of M i s shown i n F i g u r e 5, which presents data from numerical s i m u l a t i o n of c o a l s w e l l i n g behavior u s i n g h y p o t h e t i c a l values of χ - f a c t o r s ranging from 0.2 to 0.8. These c a l c u l a t i o n s were done with the same coal__and s w e l l i n g agent parameters as b e f o r e , f o r cluster size M 150. Numerical c a l c u l a t i o n s f o r cluster^ s i z e s between 100 and 300 showed that the c a l c u l a t e d values of Mc were r a t h e r i n s e n s i t i v e to change of M Q (at l e a s t i n the range of "reasonable" values of molecular weights of c o a l c l u s t e r s ) . Values of the t r u e c o a l volume f r a c t i o n i n the swollen c o a l p a r t i c l e s were obtained from the experimental values of Table I f o r c o a l s of s i z e 20-30 mesh swollen i n p y r i d i n e a t 57 ± 2°C. Equation (10) was used to determine these v a l u e s of U2 which are reported i n Table I I . The dependence of the t r u e U 2 on the carbon and oxygen content (on a % daf b a s i s ) i s analyzed i n F i g u r e 6. The data show that w i t h i n the range of 67-83%C the t r u e c o a l s w e l l i n g i s not dependent on the elemental a n a l y s i s . Above 83%C the degree of s w e l l i n g decreases s h a r p l y . _ T a b l e I I a l s o i n c l u d e s c a l c u l a t e d values of M ( f o r c l u s t e r s i z e M = 150) from the c o r r e c t e d (true) v a l u e s of U 2 and the corresponding χ - f a c t o r s . This analysis shows that a c c o r d i n g to our hypothesis of " c l u s t e r - c o n n e c t i n g o

n

t

n

e

c

β

Q

s

s

c

Q

s



NEW

APPROACHES IN COAL

CHEMISTRY

COAL CARBON CONTENT ( % C , dof ) Figure 2. Dependence of apparent coal volume fraction at equilibrium swelling on the carbon content (% C, daf), for various American coals. Experimental values of vi, app for pyridine vapor swelling: 57 ± 2°C, 20-30 mesh (extracted coals) (O); 50°C, 30-40 mesh (unextracted coals) (%).




Cross-Linked

Structures

COAL CARBON CONTENT

in Coals

(% C.dof )

Figure 3. Dependence of apparent coal volume fraction at equilibrium swelling on the carbon content (% C, daf), for various American and Japanese coals. Curve fits the Purdue data (American coals only). Experimental values of v , app for pyridine vapor swelling at 25°C: 30-40 mesh (unextracted coals) (%); Sanada and Honda (1966), 30-60 mesh(U)2



54

NEW

APPROACHES IN COAL

COAL OXYGEN CONTENT

(%

CHEMISTRY

0, daf )

Figure 4. Dependence of apparent coal volume fraction at equilibrium swelling on the oxygen content (% O, daf) of various coals. The three curves represent best fitting of the three sets of Purdue data for American coals. Values for other coals ($,9) are included for comparison. Experimental values of v , app for pyridine vapor swelling: 57 ± 2°C, 20-30 mesh (extracted coals) (O); 50°C, 30-40 mesh (unextracted coals) (A): 25°C, 30-40 mesh (unextracted coals) (%); Sanada and Honda (1966) 25°C, 30-60 mesh O / Kirov et al. (1967) 25°C, 50-170 mesh (A). 2



Cross-Linked

Structures

in

55

Coals


3.

Figure 5. Numerical calculation of the M between cross-links, M , as a function of the thermodynamic parameter χ and the coal volume fraction v . Curves are calculated for ν = 0.769 cm /g, V , = 80.56 cm /mol and cluster size M = 150. n

c

M

3

3

Q


Blaustein et al.; New Approaches in Coal Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1981. .472 .563

.858 .956

.C72

83.26

HVA

341

Anthracite

91.14

3.29

*Samples of 20-30 mesh swollen i n p y r i d i n e a t 57 ± 2°C.

384

.108

400

.423 .819

.142

13.25

79.04

HVC

212 4.41

445

.413

.842

.141

10.62

78.22

HVB

772

380

405

430 .403

.862

.152

14.51

77.30

HVB

266

445

.346

Subb

416

.816

67.45

Lignite

418 .159

c

19.31

M

72.37

χ-factor (1)

410

2.β

True υ

.289

3

(ID (cm /gr)

Porosity ρ

i n Coal Samples *

.832

Elemental A n a l y s i s (% daf) 0% c%

Structure

.123

ASTM Rank

True Swelling Behavior o f C r o s s l i n k e d

23.89

P.S.U. Identifi c a t i o n Number

TABLE I I .


m

3

2

Ut

Os


3.


Cross-Linked

Structures

in

Coals

Figure 6. Dependence of true coal volume fraction at equilibrium swelling in pyridine at 57 ± 2°C on the (O) carbon and (Φ) oxygen contents (%, daf) of various American coal samples.


57

N E W APPROACHES IN C O A L

58

CHEMISTRY

bonds" i n c r o s s l i n k e d c o a l s t r u c t u r e s (see F i g u r e 1 ) , a p p r o x i mately three c l u s t e r s may be found between two m u l t i f u n c t i o n a l crosslinks. Average molecular weights i n the range of 400-500 were determined f o r c l u s t e r s i z e of 150. The c a l c u l a t e d values of M f o r a n t h r a c i t e s are not considerably d i f f e r e n t from the corresponding values f o r other c o a l s . Due to the s m a l l number of a n t h r a c i t e samples t e s t e d no f u r t h e r explanation w i l l be attempted here. I t must be noted that the present a n a l y s i s of M serves only as an approximate i n d i c a t i o n of the expected values of molecular weight between c r o s s l i n k s . I f one r e c a l l s that the values of χ - f a c t o r and p o r o s i t y ρ used here are determined from best f i t t i n g of data by other i n v e s t i g a t o r s f o r s i m i l a r c o a l s i t i s evident that t h i s a n a l y s i s i s subject to e r r o r . Experi mental data f o r χ and ρ are being obtained f o r our c o a l s i n our laboratory. However, t h i s c o n t r i b u t i o n shows__how experimental data can be used to improve determination of M and to p r e s e n t , f o r the f i r s t time, approximate values of t h i s important p h y s i c a l parameter of the c r o s s l i n k e d s t r u c t u r e of c o a l s . F i n a l l y the present a n a l y s i s (see F i g u r e 6) does not i n c l u d e enough experimental data i n the range of 85% carbon, namely the range where Larsen (14) claims that a maximum i n M i s observed. Obviously more data i n t h i s range are needed. However, a s i m i l a r maximum i n s w e l l i n g behavior at 75% carbon claimed by Nelson jit a l (13) i s not apparent when the s t a t i s t i c a l mechanical model developed by Peppas and Lucht (3) i s a p p l i e d to d e t e r mine c r o s s l i n k e d d e n s i t i e s . c


c

c

c

Acknowledgements T h i s work was supported by the Department of Energy, Grant //ET-78-G-01-3382. P r e l i m i n a r y s t u d i e s were a l s o supported with funds from the Purdue Coal Research Center. We wish to acknow ledge very h e l p f u l d i s c u s s i o n s with T . Ruppel of the P i t t s b u r g h Energy Technology Center (PETC). The c o a l samples were k i n d l y provided by the Pennsylvania State U n i v e r s i t y , C o l l e g e of Earth and M i n e r a l Sciences.

REFERENCES 1. 2. 3. 4. 5. 6.

L.M. Lucht, and N.A. Peppas, Amer. Inst. Phys. Confer. Proceed., (in press). J . Kovac, Macromol., 11, 362, (1978). N.A. Peppas and L.M. Lucht, paper presented at the 87th National AIChE Meeting, Boston, August 1979. J.W. Larsen and J. Kovac, in J.W. Larsen, ed., "Organic Chemistry of Coal", ACS Symposium Series, 71, 36, ACS, Washington, D.C., 1978. P.J. Flory, "Statistical Mechanics of Chain Molecules", Interscience, New York, 1969. D.W. van Krevelen, Fuel, 44, 229, (1965).



3.


Cross-Linked

Structures

in

Coals

59

7. I.G.C. Dryden, Fuel, 30, 34, (1951). 8. Y. Sanada and H. Honda, Fuel, 45, 295, (1966). 9. N.Y. Kirov, J.M. O'Shea and G.D. Sergeant, Fuel, 46, 415, (1967). 10. D.D. Whitehurst, in J.W. Larsen, ed., "Organic Chemistry of Coal", ACS Symposium Series, 71, 1, ACS, Washington, D.C. 1978. 11. W. Wiser, ACS Fuel Prepr., 20(2), 122, (1975). 12. N.A. Peppas, Annual report on DOE Grant 3382, (1979). 13. J.R. Nelson, O.P. Mahajan and P.L. Walker, J r . , ACS Org. Coat. Plast. Prepr., 43(2), 337, (1980). 14. J.W. Larsen, Amer. Inst. Phys. Confer. Proceed., (in press). RECEIVED May 5, 1981.


New Approaches in Coal Chemistry - American Chemical Society

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