Determinations of Average Molecular Weights and Molecular Weight

Chapter 10

Determinations of Average Molecular Weights and Molecular Weight Distributions of Lignin Lignin Downloaded from pubs.acs.org by UNIV OF MICHIGAN ANN ARBOR on 05/19/16. For personal use only.

P. Froment and F. Pla Laboratoire de Génie des Procédés Papetiers Associé au Centre National de la Recherche Scientifique, UA 1100, INPG, Ecole Française de Papeterie B.P. 65 F-38402 St. Martin d'Hères Cedex, France

Three methods of molecular weight determination were investigated and their application to lignins is discussed. V P O gives suitable results for M if adequate thermistor beads are used. Reliable M values are obtained by L A L L S if anisotropy, fluorescence and light absorption are taken into account. Preliminary experiments by on-line S E C - L A L L S are promising but need more investigation. n

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The understanding of the macromolecular properties of lignins_requires information on number- and weight-average molecular weights ( M , M ) and their distributions ( M W D ) . These physico-chemical parameters are very useful in the study of the hydrodynamic behavior of macromolecules in solution, as well as of their conformation and size (1). They also help in the determination of some important structural properties such as functionality, average number of multifunctional monomer units per molecule (2,3), branching coefficients and crosslink density (4,5). Number-average molecular weights are mainly determined by colligative methods, viz. cryoscopy, ebulliometry, vapor pressure osmometry and membrane osmometry. Among these methods, membrane osmometry can only be used for molecular weights higher than 25,000. In the case of lignins, vapor pressure osmometry ( V P O ) seems to be the most suitable and practical method in spite of some experimental difficulties. However, it only allows determinations of M in the range of 100 to 10,000. It follows that there is a molecular weight range of 10,000 to 25,000 which cannot be explored by using these two absolute methods. Size exclusion chromatography (SEC) covers this range and is more and more used to characterize lignins, although much remains to be done in order to achieve comparable absolute results from various laboratories. Indeed, the application of this technique to lignins has until now only given qualitative results owing to problems related to molecular associations and calibration procedures. n

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0097-6156/89/0397-0134$06.00/0 © 1989 American Chemical Society

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Lignin Molecular Weights & Weight Distributions 135

Sedimentation equilibrium and light scattering are the two absolute methods that have been used to determine M of lignins and lignin deriva tives. These methods, together with S E C , cover a wide range of molecular weights. Light scattering is an excellent technique, particularly with the advent of more sophisticated instruments as discussed below (6,7). Thisjpaper deals with a detailed analysis concerning the determination of M , M and M W D of lignins using respectively V P O , low angle laser light scattering ( L A L L S ) and S E C . In addition, recent results obtained by on-line L A L L S - S E C are presented. w

Lignin Downloaded from pubs.acs.org by UNIV OF MICHIGAN ANN ARBOR on 05/19/16. For personal use only.

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Results and Discussion Vapor Pressure Osmometry. V P O is a very practical method for deter mining M values in a wide range of solvents and temperatures. Recently, results obtained with classical pendant-drop instruments showed a signif icant dependence of the calibration constant upon the molecular weight of the standards (8,9). O n the other hand, with an apparatus equipped with thermistors allowing the volume of the drops to be kept constant, this anomaly is not observed (10,11). The thermistors used in this study were of the latter type. As shown in Tables I and II, the corresponding Κ values appeared clearly to be a function of the solvent and temperature but not of the molecular weight of the standards. n

Table I. Influence of Solvent and Temperature on the Calibration Constant with Benzil as Calibrating Compound Temperature (°C) Solvent Tetrahydrofuran Dioxane 2-methoxyethanol

25

435

37

45

60

90

950

3775 2680 1445

4765 2520

5690

Table II. Influence of the Molecular Weight of the Calibrating Compound on the Calibration Constant in T H F at 45°C Calibrating Compound Benzil POE POE Polystyrene

Molecular Weight 210 310 420 1790

K(ohm.mole

x

.kg)

3775 3750 3790 3780

Given the sensitivity of colligative methods to the presence of low molecular weight impurities, particular care was taken to isolate lignin sam ples free of such foreign contaminants. Thus, for example, the extraction

LIGNIN: PROPERTIES AND MATERIALS

136

of a s a m p l e of spruce dioxane l i g n i n for eight hours w i t h d i e t h y l ether p r o duced a n increase of M f r o m 1200 to 3000, the c o r r e s p o n d i n g weight loss b e i n g a b o u t 5%. Conversely, the presence of m a c r o m o l e c u l a r aggregates are not detected adequately b y V P O . A s u i t a b l e change of solvent or a t e m p e r a t u r e increase c a n l e a d t o d i s s o c i a t i o n a n d a c o r r e s p o n d i n g effect o n M . T a b l e s III a n d I V clearly show t h a t t h i s associative p h e n o m e n o n is not relevant i n the case of t w o t y p i c a l samples. n


n

Table III. M

of N a r r o w F r a c t i o n s of Spruce D i o x a n e L i g n i n

n

fractions M (THF) M (Dioxane) n

n

Dl 820 800

D2 970 970

D3 1250 1300

D4 1650 1700

D5 2250 2250

D6 3100 3100

D7 4000 4000

D8 5000 5000

D9 6050 6050

Table I V . M of B l a c k C o t t o n w o o d A l k a l i L i g n i n F r a c t i o n s i n Different Solvents a n d at Several T e m p e r a t u r e s n

2-methoxyethanol Sample F-l F-2 F-3 F-4

w

THF 45°C

25° C

37° C

45°C

60° C

17600 24000 43500 55000

3650 5100 6000 6300

3700 5100 5900 6400

3750 5000 5950 6400

3700 5050 5850 6400

3700 5000 5900 6450

M

I n order to overcome the s o l u b i l i t y l i m i t a t i o n t y p i c a l o f l i g n i n f r a c t i o n s , c h e m i c a l m o d i f i c a t i o n s have been envisaged. O b v i o u s l y o n l y those m e t h o d s g i v i n g n e a r l y q u a n t i t a t i v e recovery are adequate for the p u r p o s e of m e a s u r ing M . T a b l e V shows results related to the a c e t y l a t i o n technique where o n l y a slight increase i n M is observed as expected. n

n

T a b l e V . M of Spruce A l k a l i L i g n i n F r a c t i o n s Before a n d A f t e r A c e t y l a t i o n ( i n 2 - m e t h o x y e t h a n o l at 60° C ) n

M

n

Sample SA-1 SA-2 SA-3

Before A c e t y l a t i o n 2000 2850 3850

After Acetylation 2350 3150 4450

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Lignin Molecular Weights & Weigfit Distributions

137

Light Scattering Photometry. W e w i l l l i m i t o u r discussion t o L A L L S be cause i t constitutes a net i m p r o v e m e n t as c o m p a r e d t o other m e t h o d s of M d e t e r m i n a t i o n . It has the advantage of p r o v i d i n g absolute values of the R a y l e i g h r a t i o b y direct c o m p a r i s o n of scattered a n d t r a n s m i t t e d l i g h t . w


R(e)

(1)

= G(e)G(0)- D(aiy 1

1

where R(9) is the R a y l e i g h r a t i o , G(0) a n d G ( 0 ) are respectively the p h o t o m u l t i p l i e r readings for scattered a n d t r a n s m i t t e d l i g h t , D is the a t t e n u a t i o n used for the measure of the t r a n s m i t t e d l i g h t , a n d the p r o d u c t σΐ is a n i n s t r u m e n t a l factor. A n o t h e r advantage is t h a t , o w i n g to the s m a l l angle between the i n c i d e n t a n d scattered b e a m , the f o r m factor Ρ(θ) is e q u a l to u n i t y . T h e e q u a t i o n r e l a t i n g the R a y l e i g h r a t i o to the m o l e c u l a r weight t h u s reduces t o : Kc/AR(0) = 1/M + 2,4 c (2) W

2

where c is the c o n c e n t r a t i o n ( g . m l " " ) , A2 is the second v i r i a l coefficient, AR(6) is the difference between the R a y l e i g h r a t i o s o f the solvent a n d the s o l u t i o n , a n d Κ is the l i g h t s c a t t e r i n g constant w h i c h , for v e r t i c a l l y p o l a r i z e d i n c i d e n t l i g h t , is given b y : 1

Κ = Av n {dn/dc) \- N2

2

2

A

1

(3)

where η is the solvent refractive i n d e x , dn/dc is the refractive i n d e x i n c r e m e n t of the s o l u t i o n , λ is the wavelength, a n d Ν A v o g a d r o ' s n u m b e r . M is o b t a i n e d b y e x t r a p o l a t i n g Kc/AR(ff) to zero c o n c e n t r a t i o n . Nevertheless, i n order to o b t a i n reliable results w i t h l i g n i n s , fluores cence, l i g h t a b s o r p t i o n , a n d anisotropy m u s t be t a k e n i n t o account. F l u o rescence is easily e l i m i n a t e d by the use of a n adequate interference filter. It is w e l l k n o w n t h a t l i g n i n s e x h i b i t a n a b s o r p t i o n s p e c t r u m w i t h a m a x i m u m i n the near u l t r a - v i o l e t t a i l i n g a l l the w a y i n t o the v i s i b l e . T h e c o r r e c t i o n of a b s o r p t i o n depends o n the geometry of the cell a n d of the s c a t t e r i n g v o l u m e . F o r t u n a t e l y , i n the K M X - 6 i n s t r u m e n t , the scat t e r i n g v o l u m e is at the center of the cell a n d the i n c i d e n t a n d scattered b e a m s are e q u a l l y a t t e n u a t e d . C o n s e q u e n t l y the c o r r e c t i o n of a b s o r p t i o n is reduced to the measure of the i n t e n s i t y of the t r a n s m i t t e d b e a m for each concentration. T h e net effect of a n i s o t r o p y is an enhancement of the scattered l i g h t . T h i s excess s c a t t e r i n g can be e l i m i n a t e d b y m e a s u r i n g the v e r t i c a l a n d h o r i z o n t a l c o m p o n e n t s of the scattered light w i t h a n a n a l y z i n g p o l a r i z e r . These two c o m p o n e n t s are c o m p l e x functions of s i n θ a n d c o s 0 (12). F o r s m a l l values of θ s e t t i n g s i n 0 = O(cos0 = 1) results i n a negligible er r o r . T h e R a y l e i g h r a t i o corrected for anisotropy is t h e n given b y the u s u a l expression: w

AR(e) where AR(9) a n d ARh(6) excess R a y l e i g h r a t i o s .

= ARv(0)

- (4/3)ΔΛή(0)

(4)

s t a n d respectively for the v e r t i c a l a n d h o r i z o n t a l


138

T a b l e s V I a n d V I I give results c o r r e s p o n d i n g t o t w o series of l i g n i n fractions o b t a i n e d w i t h a flow-through reactor (3). ( T h e u n i t s for dn/dc a n d A2 are respectively rnl.g" a n d m o l e . m l . g ~ ) . These results show t h a t L A L L S allows the d e t e r m i n a t i o n of low M values. T h e dn/dc values differ f r o m s a m p l e t o s a m p l e b u t v a r y o n l y s l i g h t l y for a given set of fractions. T h e second v i r i a l coefficient e x h i b i t s no definite t r e n d . N e g a t i v e values i n d i c a t e perhaps some association effects b u t light s c a t t e r i n g alone is not sufficient to a s c e r t a i n t h i s p o i n t . 1

2


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Table V I . L A L L S Results on A c i d i c Organosolv L i g n i n Fractions from B l a c k Cottonwood Fraction Parameter M dn/dc Λ .10 w

2

2

1

2

3

4

5

6

7

8

1500 0.168 2.1

2550 0.159 1.5

4000 0.157 2.8

9000 0.157 1.7

19000 0.156 0.15

29000 0.157 0.11

59500 0.159 0.18

74000 0.157 0.19

Table V I I . L A L L S Results on A l k a l i L i g n i n Fractions from Black C o t t o n wood Fraction Parameter M dn/dc2 Λ .10 w

2

2

1

2

3

4

5

6

7

8

4700 0.187 0

10500 0.184 -1.2

11500 0.188 2.1

17500 0.190 1.4

24000 0.192 1.3

36000 0.191 0.9

43500 0.189 1.7

55000 0.193 1.1

Size Exclusion Chromatography. O n e can define three levels of i n t e r p r e t a t i o n i n S E C . T h e first is a v i s u a l i n s p e c t i o n of the weight f r a c t i o n versus e l u t i o n v o l u m e curve. K n o w i n g t h a t for a pure size e x c l u s i o n m e c h a n i s m the m o l e c u l a r weight decreases w h e n the e l u t i o n v o l u m e increases, t h i s gives a p i c t u r e of the d i s t r i b u t i o n a n d allows a q u a l i t a t i v e c o m p a r i s o n of samples. T h e c a l i b r a t i o n a n d subsequent c a l c u l a t i o n of average m o l e c u l a r weights constitute the second level. T h e t h i r d level refers to the c o r r e c t i o n of c o l u m n d i s p e r s i o n . Because the a i m of t h i s paper is the d e t e r m i n a t i o n of m o l e c u l a r weight averages, a t t e n t i o n w i l l be focused o n the second l e v e l , as s u m i n g t h a t a l l the p r o b l e m s associated w i t h the first one have been solved. T h i s is a n a m b i t i o u s a s s u m p t i o n b u t indispensable for p r o c e e d i n g t o the second l e v e l . F r o m the Q factor (13) to B e n o i t ' s u n i v e r s a l c a l i b r a t i o n (14) a n d the more recent " s o u t h e r n c a l i b r a t i o n " (15), a lot of papers have been devoted to t h i s question. U n f o r t u n a t e l y , the a p p l i c a t i o n of these procedures to lignins has been unsuccessful. T h e best a p p r o a c h is the c a l i b r a t i o n o f the


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c o l u m n s w i t h w e l l characterized l i g n i n samples of b r o a d or n a r r o w d i s t r i b u t i o n (16). A n o t h e r practice is the direct use of the c a l i b r a t i o n established w i t h p o l y s t y r e n e samples. W h e n the exponents of the M a r k - H o u w i n k e q u a t i o n for b o t h polystyrene a n d the sample under s t u d y are the same, t h i s m e t h o d gives " r e l a t i v e m o l e c u l a r weights." If the c o n d i t i o n above is not fulfilled, as for l i g n i n s , there is no s i m p l e r e l a t i o n between the c a l c u l a t e d m o l e c u l a r weights a n d the real ones. F i g u r e 1 shows the c a l i b r a t i o n curves for p o l y s t y r e n e a n d l i g n i n i n the low m o l e c u l a r weight region. E v e n i n t h i s region where the effects of b r a n c h i n g are r e d u c e d , there is no coincidence between l i g n i n a n d p o l y s t y r e n e . W h e n the molecular weight increases the two curves diverge. On-Line SEC-LALLS. T h e p o s s i b i l i t y afforded b y o n - l i n e S E C - L A L L S to c o n t i n u o u s l y calculate the m o l e c u l a r weight of the molecules e l u t i n g f r o m a set of c o l u m n s allows one to overcome the c a l i b r a t i o n p r o b l e m . I n F i g u r e 2 are s h o w n the recorder traces for the v e r t i c a l ( V v ) a n d h o r i z o n t a l ( H v ) components of the scattered l i g h t , the t r a n s m i t t e d l i g h t ( G O ) a n d the c o n c e n t r a t i o n of the effluent ( D R I ) c o r r e s p o n d i n g to a n a c e t y l a t e d o r g a n o s o l v h o r n b e a m l i g n i n . N o t e t h a t these recordings need, at least, three s a m p l e injections. T h e m o l e c u l a r weight averages are c a l c u l a t e d b y s u m m i n g over the e l u t i o n v o l u m e range s p a n n e d b y the s a m p l e , the expression: M

w

( i ) c ( i ) = l / [ t f / Δ Λ ( 0 , i) - 2A ]

(5)

2

where M (i) a n d c(i) are respectively the weight average m o l e c u l a r weight a n d the c o n c e n t r a t i o n of the species e l u t i n g at v ( i ) . K, A a n d AR(0, i) have been defined above. T h e s u m m a t i o n leads to: w

2

M

w

= ( Δ ν / ρ ) Σ { 1 / [ # / Δ Λ ( 0 , i) - 2A ]}

(6)

2

M

n

(7)

=Vc(i)/E[c(t)/M (i)] w

where ρ is the injected weight a n d Av is the e l u t i o n v o l u m e i n c r e m e n t . I n practice A is neglected (17). E q u a t i o n (6) shows t h a t M depends o n l y o n the i n t e n s i t y of the light s c a t t e r i n g signals. T h e value of M calculated a c c o r d i n g to e q u a t i o n (7) is always higher t h a n t h a t o b t a i n e d b y absolute methods. 2

w

n

A glance at curve V v reveals a n i n t e r e s t i n g feature. I n the h i g h m o l e c u l a r weight region ( s m a l l e l u t i o n volumes) there is a s m a l l peak l o c a t e d near the v o i d v o l u m e . T h e absence of equivalent peaks at the same e l u t i o n v o l u m e o n the c o n c e n t r a t i o n detector a n d the h o r i z o n t a l c o m p o n e n t curves indicates the presence of a s m a l l a m o u n t of h i g h m o l e c u l a r weight species i n the s a m p l e . It r e m a i n s to be ascertained i f t h i s h i g h m o l e c u l a r weight component is a f u n d a m e n t a l c h a r a c t e r i s t i c of the s a m p l e or a n a r t i f a c t . Some e x p e r i m e n t s c a r r i e d out i n our l a b o r a t o r y show a t e n d e n c y for t h i s peak t o become reduced w i t h storage t i m e . F u r t h e r e x p e r i m e n t s are needed to elucidate the exact n a t u r e of t h i s p h e n o m e n o n . F o r t u n a t e l y , the effect o n the c a l c u l a t i o n of m o l e c u l a r weight averages is m o d e s t . F o r



140

F i g u r e 2. Recorder traces of on-line S E C - L A L L S e x p e r i m e n t .

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the s a m p l e s t u d i e d the M value is 15000 i n s t e a d o f 12000 w h e n t h e h i g h m o l e c u l a r weight c o m p o n e n t is neglected. T h e M value is 4500 i n s t e a d o f 4000 d e t e r m i n e d b y V P O . L i g h t s c a t t e r i n g is very sensitive t o h i g h m o l e c u l a r weight c o m p o u n d s b u t , o n the other h a n d , low m o l e c u l a r weight components are n o t detected a n d must be e l i m i n a t e d i n order to a v o i d difficulties a n d t o o b t a i n reliable n u m b e r - a v e r age m o l e c u l a r weights as s t a t e d p r e v i o u s l y w i t h V P O . w


n

Conclusion L i g n i n s are p o l y disperse macromolecules whose average m o l e c u l a r weights are r a t h e r l o w . T h e i r d e t e r m i n a t i o n b y means o f absolute m e t h o d s becomes n o w easy o w i n g t o i m p r o v e m e n t s i n techniques, a n d t h i s i n spite o f m a n y p r o b l e m s inherent i n t h e p o l y m e r itself. _ V P O appears t o be the most p r a c t i c a l c o l l i g a t i v e m e t h o d for d e t e r m i n i n g M . Nevertheless, care must be taken c o n c e r n i n g l i g n i n p u r i f i c a t i o n a n d d r y i n g , t h e p u r i t y o f the solvent a n d i n s t r u m e n t c a l i b r a t i o n . O n t h e other h a n d , reliable M values c a n be o b t a i n e d u s i n g L A L L S i f fluorescence, l i g h t a b s o r p t i o n a n d a n i s o t r o p y are accounted for. S E C alone allows o n l y c o m p a r i s o n between l i g n i n samples. T h e c a l i b r a t i o n o f the c o l u m n s s t i l l r e m a i n s a r e a l p r o b l e m . T h e a s s o c i a t i o n of S E C w i t h L A L L S , f o l l o w i n g the procedure described here, is c e r t a i n l y the best a p p r o a c h to d e t e r m i n i n g m o l e c u l a r weight averages a n d the M W D of l i g n i n derivatives. However, there r e m a i n s t o be e x p l a i n e d the appearance of s m a l l a m o u n t s o f h i g h m o l e c u l a r weight fractions. T h i s t o p i c is presently under i n v e s t i g a t i o n . n

w

Experimental Dioxane Lignin. Spruce w o o d m e a l was e x t r a c t e d w i t h a b o i l i n g s o l u t i o n c o m p o s e d of 1000 m l dioxane a n d 10 m l H C 1 (sp. g r . = 1.19) (18). T h e r e s u l t i n g l i g n i n was t h e n S o x h l e t - e x t r a c t e d w i t h d i e t h y l ether a n d f r a c t i o n ated b y S E C ( 4 , 1 8 ) t o o b t a i n n a r r o w fractions. Alkali Lignin. B l a c k c o t t o n w o o d platelets were cooked i n a flow-through reactor w i t h 1.0N N a O H at 160°C flowing at a steady rate o f a b o u t 17.5 m l . m i n (3). T h e effluent was collected as several successive fractions f r o m w h i c h l i g n i n was p r e c i p i t a t e d a n d p u r i f i e d (3). T h e same procedure was a p p l i e d , at 170°C, to spruce m a t c h s t i c k s . - 1

Organosolv Lignins. A c i d i c organosolv l i g n i n was o b t a i n e d f r o m b l a c k cott o n w o o d u s i n g a g a i n a flow-through reactor (3). T h e d e l i g n i f i c a t i o n c o n d i tions were m e t h a n o l / w a t e r ( 7 0 / 3 0 v / v ) i n the presence o f 0 . 0 1 M H2SO4 at 150°C. T h e successive l i g n i n fractions were recovered as described i n R e f . 3. H o r n b e a m chips were cooked i n a b a t c h reactor under t h e f o l l o w i n g conditions: ethanol/water (50/50 v / v ) ; catalyst: M g C l 0.05M on o.d. w o o d ; l i q u o r - t o - w o o d r a t i o : 10; m a x i m u m t e m p e r a t u r e : 170°C for 3 hours. T h e r e s u l t i n g organosolv l i g n i n was recovered as described elsewhere (19). 2

142



Quantitative Acetylation of Lignins. T o a v o i d f r a c t i o n a t i o n o f the l i g n i n s a n d loss o f l o w m o l e c u l a r weight components, w h i c h occur i n t h e u s u a l a c e t y l a t i o n procedures, the q u a n t i t a t i v e a c e t y l a t i o n described b y H . C h u m et al. (20,21) was e m p l o y e d . Vapor Pressure Osmometry. N u m b e r - a v e r a g e m o l e c u l a r weights were e v a l u a t e d w i t h a vapor pressure osmometer ( K n a u e r ) f o l l o w i n g a p r e v i o u s l y described m e t h o d (18). Low Angle Laser Light Scattering Photometry. Weight-average m o l e c u l a r weights were d e t e r m i n e d w i t h a K M X - 6 photometer ( L D C / M i l t o n R o y ) . T h e l i g h t source was a 2 m W v e r t i c a l l y p o l a r i z e d h e l i u m - n e o n laser (A = 632.8 n m ) . T h e i n s t r u m e n t was e q u i p p e d w i t h an a n a l y z i n g p o l a r i z e r t o measure b o t h v e r t i c a l a n d h o r i z o n t a l components o f the scattered l i g h t . Fluorescence was e l i m i n a t e d by the use o f a n interference filter centered at 632.8 n m a n d w i t h a b a n d w i t h of 4 n m . T h e solvent was 2 - m e t h o x y e t h a n o l at r o o m t e m p e r a t u r e . Solvent a n d solutions were clarified b y filtration t h r o u g h a 0.2 μνα pore size teflon filter. T h e refractive i n d e x increments were evaluated at 2 0 ± 0 . 0 1 ° C a n d λ = 632.8 n m w i t h a B P 2000 differential refractometer ( B r i c e P h o e n i x ) . T h e refractive i n d e x o f the solvent w a s d e t e r m i n e d under the same conditions w i t h a n A b b e refractometer. F o r o n - l i n e S E C - L A L L S , a flow-through cell was used. High Performance Size Exclusion Chromatography. S E C was carried o u t o n p o l y s t y r e n e - d i v i n y l b e n z e n e gels w i t h porosités r a n g i n g f r o m 100 t o 1 0 A . T h e solvent, T H F , h a d a flow rate o f 1 m l / m i n . T h e detector was a differe n t i a l refractometer. 4

Literature C i t e d 1. Goring, D. A . I. In Lignins: Occurrence, Formation, Structure and Reactions; Sarkanen, Κ. V . ; Ludwig, C . H . , Eds.; Wiley-Interscience: New York, 1971; Chapter 17. 2. Dolk, M . ; Pla, F . ; Yan, J. F . ; McCarthy, J. L . Macromolecules 1986, 19, 1464-70. 3. Pla, F . ; Dolk, M . ; Yan, J. F . ; McCarthy, J. L . Macromolecules 1986, 19, 1471-77. 4. Pla, F . ; Robert, A . Cell. Chem. Technol. 1974, 8, 3-10. 5. Pla, F.; Yan, J. F . J. Wood Chem. Technol. 1984, 4 , 285-99. 6. Piastre, D. Thèse Docteur-Ingenieur, INPG, Grenoble, 1983. 7. Pla, F.; Froment, P.; Capitini, R.; Tistchenko, A . M . ; Robert, A . Cell. Chem. Technol. 1977, 11, 711-18. 8. Brzezinsky, J.; Glowala, H.; Kornas-Calka, A . Eur. Polym. J. 1973, 9, 1251-53. 9. Marx-Figini, M . ; Figini, R. V . Makromol. Chem. 1980, 181, 2401-7. 10. Kamide, K.; Terakawa, T . ; Uchiki, H . Makromol. Chem. 1976, 177, 1447-64. 11. Burge, D. E . J. Appl. Polym. Sci. 1979, 2 4 , 293-99. 12. Russo, P. S.; Bishop, M . ; Langley, K . H.; Karasz, F . E. Macromolecules 1984, 17, 1289-91.


10.

FROMENT

&

PLA


13. Cazes, J . J. Chem. Educ. 1966, 43, A567-76. 14. Grubisic, Z.; Rempp, P.; Benoit, H . J. Polym. Sci. 1967, 5, 753-59. 15. Hester, R. D.; Mitchell, P. H . J. Polym. Sci. Polym. Chem. 1980, 18, 1727-38. 16. Froment, P.; Robert, A . Cell. Chem. Technol. 1977, 11, 691-96. 17. Kim, C . J . ; Hamielec, A . E . ; Benedek, A . J. Liq. Chromatogr. 1982, 5, 425-41. 18. Froment, P.; Pla, F . ; Robert, A . J. Chim. Phys. 1971, 68, 203-206. 19. Ivanow, T . Thèse, INPG, Grenoble, 1987. 20. Chum, H . L . ; Johnson, D. K.; Ratcliff, M . ; Black, S.; Schroeder, H . Α . ; Wallace, K . Proc. 3rd ISWPC 1985, p. 223. 21. Chum, H . L . ; Johnson, D. K . ; Tucker, M . P.; Himmel, M . E . Holz forschung 1987, 41, 97-108. RECEIVED February 27,1989

Determinations of Average Molecular Weights and Molecular Weight

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