Application of NMR spectroscopy in molecular weight determination of polymers

Eur. Polvm. J. Vol. 22, No. 12, pp. 1001 1008, 1986 Printed in Great Britain

0014-3057,86 $3.(10+ 0.00 Pergamon Journals Lid

A P P L I C A T I O N OF N M R S P E C T R O S C O P Y IN MOLECULAR WEIGHT DETERMINATION OF P O L Y M E R S SUBHASH C. SHIT a n d SUKUMAR MAITI*

Materials Science Centre, Indian Institute of Technology, Kharagpur 721302, India (Received 20 January 1986)

Abstract Determination of molecular weights of polymers by ~H-NMR spectroscopy is discussed. A brief survey of application of NMR; both ~H and 13C, in the analysis of monomer sequence, copolymer composition, polymer microstructure, end-group and relaxation phenomenon is also made. NMR offers an elegant and simple yet fairly accurate method for determination of molecular weights of polymers.

INTRODUCTION N M R spectroscopy is now well established as an important technique for characterization of polymers [1-3]. Characterization of polymers by N M R spectroscopy includes determination of monomer sequences in the macromolecule [4-II], copolymer composition [12 13], monomer reactivity ratios [14], block copolymer sequence [15, 16], polymer microstructure including stereoregularity [17-24], relaxation phenomena and end-groups [28]. Formerly many such analyses were carried out by pyrolysis gas chromatography, radiometric methods and isotope analysis, i.r. spectroscopy and chemical titrimetric methods for end-group analysis. Some of these methods are of doubtful quantitive validity, others are time consuming involving elaborate experimental techniques. N M R methods for polymer characterization offers a simple, convenient and rapid method of analysis, Determinations of molecular weights of polymers are usually done by vapour pressure or membrane osmometry, light scattering photometry, sedimentation equilibrium technique or gel permeation chromatography. Although viscometryis the mostwidely used technique for molecular weight determination, it is a secondary method requiring the prior deterruination of K and ~ for the polymer solvent pair used for the viscosity determination. Some of these methods require certain procedures or materials. For example, light scattering photometry requires specially purified dust-free solvents, and gel permeation chromatography needs standard polymer samples having M w / Mn close to unity for calibration. Recently N M R spectroscopy has been utilized for molecular weight determination of polymers [29-38]. Like all other analyses by NMR technique, this is a simple, fairly accurate and rapid method. We report here a brief state-of-the-art on the application of *Present address: Plant Polymer Research, Northern Regional Research Centre, U.S.D.A., Peoria, IL 61604,

U.S.A. 1001

N M R spectroscopy in molecular weight determination of polymers and discuss some of our results. 'H-NMR VS '3C-nMr For organic compounds and polymers, ~3C-NMR is increasingly used for structure elucidation [39 -48]. ~3C-NMR possesses obvious advantages over IH-NMR particularly in monomer sequence analysis because the latter has weaker signals and consequently less sensitivity than the former to comonomer sequence effects. For determination of branching in polymers, however, both N M R techniques are equally applicable [41] although it was thought earlier that 13C-NMR has some limitations particularly when the branches are larger than ethyl or propyl. IH-NMR offers in some analyses of polymer structure and composition advantages over ~C-NMR spectroscopy. These are (a) signal intensities of JH-NMR remain unaffected by different nuclear Overhauser effects; (b) similarly signal responses are also insensitive to dipolar relaxation rates; (c) chemical shifts of certain groups in ~H-NMR spectroscopy are better resolved; and (d) the signal-to-noise ratio in general is better in ~H-NMR [44]. The disadvantages of ~H-NMR arise primarily from small chemical shifts in stereoregular configurations, microstructures (head-to-head and head-to-tail monomer linkages), molecular weight changes and compositional differences etc. Chemical shifts due to such molecular effects in ~3C-NMR are about 20-30 times those of ~H-NMR. Another liraitaticn of ~H-NMR is overlap which causes littlc or no peak resolution in many polymers. Nonavailability of suitable solvents and/or poor solubility of polymers in NMR solvents are other drawbacks. They could be largely overcome by solid state ~3C-NMR techniques. Both N M R methods have advantages and liraitations. One technique cannot completely replace the other. These two, and in fact other nuclear (such as 31p, ~gF)magnetic resonance spectroscopies should be complementary.

1002

SUaHASHC. Star and SUKUMARMAITI MOLECULAR WEIGHT DETERMINATIONBY 'H-NMR SPECTROSCOPY

Principle for ~,1, determination Currently there is growing interest in the use of ~H-NMR for determination of molecular weights of polymers. The principle lies in the fact that, in the ~H-NMR spectrum of a polymer, the whole molecule is reflected in terms of the occupied area of the protons of the monomer units at a particular chemical shift. Since each proton of a given monomer occupies a fixed area with respect to the standard proton, the total number of such protons at a fixed chemical shift can be calculated from the peak area for the particular shift. From the total number of protons available from a particular monomer, the number of repeat units of the polymer can easily be calculated. For determination of the molecular weight of a polymer, the following three conditions should be satisfied by the ~H-NMR spectrum of the polymer: (1) The peak area of intensity due to the same kind of protons at a particular chemical shift in the ~H-NMR spectrum should be additive. (2) Overlapping of peaks for protons in different groups should be absent. There is a chance of overlapping when the molecular weight of the polymer is large. This limitation is, however, absent in 13C-NMR because of the wide range of chemical shifts, (3) Resolution of protons of the different segments of a copolymer should be similar. However, different resolution patterns of the protons of the comonomers are frequently observed, Because of these limitations, determination of molecular weight of polymers by ~H-NMR spectroscopy is limited to polymers of relatively low molecular weight (A~tn < 20,000).

total number of protons in the polymer is calculated. Percec et al. [30] used this method to determine the DP of the ct, fn-dihydroxy polyethersulphone (Fig. la). He obtained 1H-NMR spectra of 3,5-dinitrobenzoyl terminated polyethersulphone (Fig. lb) and 4-cyanobenzoyl terminated polyethersulphone (Fig. lc). The three aromatic protons of the 3,5-dinitrobenzoyl group were used as internal standard for determination of M. of (la). In both end-groups, actually six protons are of this type. Similarly two protons of the 4-cyanobenzoyl group are used as internal standard. DP was calculated from the following relationship by proton NMR integration:

D'--~+l=IcH3/l(~rom~tic)

6/

g

(when the 3,5-dinitrobenzoyl end-group is used as internal standard) Similarly,

~-~+ l=Icn3/ll,ro__m~tic, 6 / 4 (when the 4-cyanobenzoyl end-group is used as internal standard) where I indicates the peak intensity at the particular chemical shift of the respective protons present in the group (Table 1). The DP of the copolymer (Fig. ld) prepared by polycondensation of 1,4-dichloro-2-butene with bisphenol A was calculated by the same authors with the help of the following equations (here 2-terminal allylic protons are used as internal standard. The total number of protons of this kind is four) [31]. The D----Pnvalues obtained by ~H-NMR peak integration method agree well with the values obtained independently by GPC.

Methods Jor determination of ~'I, There are three methods for determination of /~n of polymers via. (1) by introducing characteristic end-groups with known number of protons, (2) by using a specific single group with a fixed number of protons as internal standard, and (3) by expressing the peak areas due to two or three specific types of prominent protons at corresponding chemical shifts in terms of the total number of such protons and solving the equations. Method I. After introducing a group with known number of proton at the end of a polymer, the intensity of the various protons in the monomer unit of the polymer at different chemical shifts is cornpared with that of the known proton and thus the

b-P=tlcn--cn/IcH2c'] - / / ' \

2

/

2

4 ]

or

= [/IcH20[/lcH2o \ D-fi

- ! \

4 /

4 ]

or

=/I-"/IcH2o\ll't:n3/~ ~

\ 6 /

4 J

or ( ~ / ~ ) DP--

- 1

m

Table 1. ~H-NMRassignmentused for DP calculation Chemical shift range of 6 ppm

Polymer in Fig. 1 (a) (b) (c) (d)

CH3 1.6 1.6 1.6 1.6

~H2CI . -4.52

Ortho to C-~-N aromatic ~ H 2 0 - - --CH~-----CH-- protons Phenylene . . . . . . . . --8.2 -4.08 6.05 -6.9

Ortho to nitro aromatic protons 9.2 ---

NMR spectroscopy of polymers

~

R

CH3

o

1003

7

H /~X /~X J /~XI s-~L ) ) - - o - - ~ ))---c---~( )z~i-O--R J, X ~ / X ~ J IH,X~/|o c J

0

o

Ea] R~H O2N R~

(O>

/----

COCk

[b]

O2N R ----- NC ~ - - ~ - - - C O C L

ct c.2 c . = c . c . 2 o

[C]

c

oc.2c,

cHc.2o-/

CH3

o c . 2 c . = c.cH2 CL

y-

',~/

I

k~/Jo

CH 3

rd] Fig. 1. (a) ~,eo Dihydroxy terminated aromatic polyethersulphone. (b) ~,e3 Di(3,5-dinitrobenzoyl) terminated aromatic polyethersulphone. (c) ~,~o Di(4-cyanobenzoyl) terminated aromatic polyethersulphone. (d) Polymer prepared from bisphenol A and 1,4-dichloro-2-butene.

Method 2. When a polymer contains a single group with a fixed number of protons, these protons may b_~e used as internal standard for determination of DP from the 1H-NMR spectrum. For example, the terminal OCH 3 group (methoxy protons) was used for the determination of DP of the copolymer (Fig. 2a) rp_Le.pared from L,L-lactide and E-caprolactone [48]. DP of the copolymer (Fig. 2a) calculated from the intensity of the end-group signal was in good agreement with DP calculated from monomer/initiator ratio according to the following relation

DP =

M x % conversion I x 100

Method 3. Sometimes the peaks in the ~H-NMR spectrum of a polymer are so prominent (Table 2)

that they can be clearly expressed in terms of the number of protons of the monomer at corresponding chemical shift [32]. For example DP can be calculated for polymer (Fig. 2b) as shown below: P~ = 4n P2 = 4(3n + 2) P3 = 6(n + 1) P = peak intensity or area, n = number of repeat units DP. The Mn values obtained from GPC were lower than those obtained proton NMR analysis, i.e. by calculation ofn from the above equations. It is claimed this difference arises from impurity of the polyether sulphone.

CH3 I

H -(-OC~CO--O--CH2--CH2--CH2--CH2-.-.-CH2--CO4~-nOCH

3

i-a]

(P2) cH3

c.3

cH3

L

\o/ (P~)

t

(P3)

[b] Fig. 2. (a) Copolyester prepared from LL-lactide and E-caprolactones. (b) 2,c~ Dihydroxy terminated aromatic polyethersulphone.

1004

SUBHASH C. SHIT and SUKUMAR MAITI Table 2. Number of protons (three types) in structural unit of polyethersulphone NMR peak

Pi

Type of proton

P2

Ortho to sulphone (aromatic protons)

Number of protons under each peak area

Ortho to ether and ortho to propyl (aromatic protons)

4

12

P3 Methyl protons

6

EXPERIMENTAL

(one end hydroxyl and the other N,N'-diethyl amine terminated) (Fig. 3a) by the use of the standard protons (methyl protons) peak integration method. Polyethylene terephthalate (PET) with one end hydroxy The ~H-NMR spectrum of polyethylene terephthalate terminated and the other end diethyl amine terminated was (Fig. 4a) exhibits the following peaks: a simple sinprepared by the procedure already published [34]. glet, centered at 8.1 ppm due to four aromatic pro~,to-Dihydroxy terminated PET-Ill polyester was prepared from terephthaloyl chloride and ethylene glycol by main- tons present in the repeat unit of the polyester chain. taining their stoichiometric ratio in the presence of pyridine. Protons of the - O C H 2 - C H 2 - O - moiety give a singlet Polyethylene isophthalate (PEI) with two hydroxy end- at 4.6ppm; a peak at 1.3 ppm corresponds to six groups was prepared by condensation of isophthalic acid methyl protons. There is also a quartet at 2.4 ppm and excess ethylene glycol [33]. Both the polyesters (PET due to the four - N - C H 2 protons. In the following and PEI) were purified by reprecipitation from DMF solu- discussion, I is the peak intensity at the particular tion in methanol. DMSO (E. Merck, India) was kept over chemical shift of the particular proton present in anhydrous MgSO4 for 24hr and then distilled under re- group as shown. duced pressure. Pyridine was dried by the usual procedure. The both end acetylated polyethersulphone polymer and Dp_/(aro__matic)/iCH 3/r ABA block copolymer of aromatic polyester amide (pre4 / 6 pared frOmsegment terephthaloyl~,e~.dicarboxyChloride and p-aminophenol)poly-aS A /lcn 3 end and terminated _ I(ocn24:H2-o) 4 (butadiene-coacrylonitrile) rubber (CTBN) as middle segment B were used as obtained by following the published procedure [36, 37]. All other reagents were used as received. However the/~tn values of two PET polyesters (PET-I and PET-II) (Table 3) obtained by ~H-NMR peak Techniques integration method were not compared by other The 90 MHz ~H-NMR spectra of the polymers PET and independent method. But the inherent viscosity value PEI were recorded on Varian EM-390 spectrometer using of PET-III (Table 3) of about 1152 molecular weight DMSO-d6 as solvent and TMS as standard. The ~H-NMR (~tn) as determined from the following equation spectra of acetylated polyethersulphone (one end hydroxy 1+ r and the other end amine terminated) and aromatic DP=-polyesteramide CTBN rubber based triblock ABA co1- r polymer were also recorded on the same instrument using CDC13 as solvent and TMS as standard. End-group analyses (where r is the mole ratio of terephthaloyl of PEI and PET-Ill were done according to the method chloride to ethylene glycol) described for the determination of ~n [33]. indicates that the M. values of PET-I and PET-II Viscosity measurements were performed on 0.5% (w/v) (Table 3) by IH-NMR technique are correct. The Mn solution of both type of polyesters (PET and PEI) in N-methyl-2-pyrrolidone at 30°C using an Ubbelohde sus- of the PET-Ill was also determined by end-group pended level viscometer, analysis. The fixed amount of PET-Ill was acetylated with an acetic anhydride-pyridine mixture in DMSO media and the subsequent titration of the reaction RESULTS AND DISCUSSION mixture with methanolic NaOH of known strength Recently Shit and Maiti determined the molecular (N) gives the hydroxyl number from the following weight of polyethylene terephthalate (PET) polyester relationship.

Materials

CH3CH2 > N -('- c- ~ ' - ) ~ T nCII-OCH2CH2I0 I CH3CH2

O

O Eel]

HO-- CH2-- CH2-- O4- ~ ~ O ~ r - - ~ -- O-- CH2-- OH2-- O-)'ffH O ~ O [b]

Fig. 3. (a) Mono diethyl amine terminated polyethylene trephthalate (PET). (b) ~,o) Dihydroxy terminated polyethylene isophthalate (PEI).

NMR spectroscopy of polymers

a' H O - - CI'12--CH~-0-4- C - - ~ C - - O

-- CH2--CH2-- 0 .)--H

IIbL.y.P II 0

c"

0

ClinCH2\ ru-t~u / ~r~3 ~'r~z

10

N -(- C "t/O~r C --0 C H2 --CH20-~_ H II ~ / II m 0 0

I

I

1

1

I

I

I

I

I

9

8

7

6

5

4

3

2

1

ppm 8

Fig. 4. (a) M o n o diethyl a m i n e terminated trephthalate ( P E T ) . (b) ~,o) D i h y d r o x y terminated polyethylene isophthalate ( P E I ) .

Hydroxyl equivalent

sharp singlet at 8.3 ppm, a broad singlet at 8.0 ppm

(strength of methanolic NaOH in normality) =

x (titre blank - titre sample) Sample weight (PET-III)

Then the Mn of PET-III was calculated from the following relationship 2 x 1000 M'o=-Hydroxyl equivalent Similarly M', ofc~,~o-hydroxy terminated polyethylene isophthalate (Fig. 3b)was determined from ~H-NMR spectrum (Fig. 4b) analysis by using the terminal protons of the OH group as an internal standard. A

and a multiplet at 7.5 ppm are due to three kinds of aromatic protons a', b' and c' respectively. A singlet peak of very low intensity at 4.9 ppm is due to OH protons in the terminal group of polyester molecules (Fig. 4b). Another sharp singlet was found at 4.6 ppm due to -OCH2CH 2 0 protons. The following relationship was used for the determination of Mn of PEI. DP + 1 . A(ocH, . . . CH, O~ /A (OH) 4 / 2 where A is the area at a particular chemical shift for the respective protons present in a group. Mn obtained by this ~H-NMR method was in good

Table 3. Physical properties of polyesters (PET and PEI)

Polyester PET-I PET-II PET-I I I PEI

~. (~H-N M R) 2880 2112 -2000

(Theoretical)

(End-group analysis)

Inherent viscosity

--

--

0.17

/1~

1152 --

--

0.13

1200 1940

0.08 0.09

1006

SUBHASH C. SHIT and SUKUMAR MAITI

agreement with the value calculated from end-group analysis (Table 3). The JH-NMR technique has been used for molecular weight (Mn) determination of aromatic polyethersulphone prepolymers. The polymer is synthesized by the activated nucleophilic displacement reaction between bis(4-chlorophenyl) sulphone and bisphenol-A in the presence of sodium methoxide and p-amino phenol in anhydrous conditions. The details of synthesis have been described [36]. For N M R analysis, this polyethersulphone prepolymer was acetylated to obtain the following polymer,

The following relationship was used for the calculation of DP of polyether sulphone. IICH3-C)/6 DP = I~cH3-co)/6 where I indicates the peak integration of the respective methyl protons of CH3CO and CH3-C groups. The /~r obtained from 1H-NMR spectral analysis (M, = 1768) agrees well with the value from nitrogen analysis ( ~ t = 1900) of the following ABA copolymer of molecular weight 7122 (/l~t determined from vapour pressure osmometry). (See Scheme on page 1007.)

CH3

,,

0

CH3

O

The IH-NMR spectra of the polymer is shown in Fig. 5. The appearance of two almost symmetrical peaks at 2.03 ppm and 2.07 ppm indicates that the

~"/F ( ~ - - - ~ O

~1- 0 ' - - ' ~

Triblock (ABA type) copolymers, having aromatic polyesteramide segment as the hard A block and polybutadiene-co-acrylonitrile as the soft B block, were prepared by interracial polycondensation [37]. The copolymers have the following structure:

NH ""~m~1- Xp- C-(-" ]] NH - - < ~

O

O

O - ~1~

0

~ -~n

0

O

CN polymer contains the CH3__ C _ [] O

The degree of polymerization of the polyesterimide segments at both the terminal ends of the copolymers (i.e. m + n ) and the number of poly(butadiene-coacrylonitrile) block (i.e. p) in the copolymers were calculated from ~H-NMR spectra of the copolymers by the following relationships. 12 x I l re+n= 9xl 3 12 x 12 p _ _ _ /3 x 100

group at one end and the __NH__C__CH 3 II 0 group at the other end. These two methyl proton peak integrations in the ~H-NMR spectrum were used for the calculation of D---Pof polyethersulphone.

°

~L ~

I0

"l

9

-

6

7

CH3,

i

6

-In

i"

5

'i

t,

0

3

2

I

ppm

Fig. 5. LH-NMR spectrum of ct,o~-diacetyl terminated aromatic polyethersulphone.

0

m

L

9

I

X --

0

H

0

roll 0

II

I 8

I 7

~

H

I G

0

ppm

~/

5

I

ICH3CH2

II

0

-~ ~O--C-~C~-C-)-N 1 k~/ II k ~ / i i A n xCH3CH2

CHz--CH----CH--CH~)~'5 CI-I2--CH

0

k~/I

~

I

CN

I I,

L

I 3

I 2

\

I 1

CH3

0

Fig. 6. ~H-NMR spectrum of diethyl amine terminated polyesteramide and poly(butadiene-co-acrylonitrile) rubber based ABA copolymer.

10

II k'~JII

ClinCH2

~

0

..~C-~C~¥C--O-~C~N-)-C--X~-C

/--~

CH3CH2.

CIH3

CH 3

_jm

,O -,.<:

K

Z

1008

SUBHASH C. SHIT and SUKUMAR MAITI

where I~, 12 a n d 13 are peak intensities o f p r o t o n s of the a r o m a t i c region at 7-8.4 ppm, double b o n d region at 5.4 p p m a n d methyl region at 1.3 ppm, respectively in the 1 H - N M R spectrum o f d i e t h y l a m i n e t e r m i n a t e d A B A c o p o l y m e r (Fig. 6).

Acknowledgement--Financial

support under grant No.

HCS/DST/814/80 from the Department of Science and Technology, New Delhi is gratefully acknowledged.

REFERENCES I. F. A. Bovey and G. V. D. Tires. Fortschr. HochpolymForsch. 3, 139 (1963). 2. K.C. Ramey and W. S. Brey. J. Macromolec. Sci., Rev. Macromolec. Chem. 1, 263 (1967). 3. F. A. Bovey. High Resolution NMR of Macromolecules. Academic Press, New York (1972). 4. R. Yamadera and M. Murano. J. Polym. Sci., Polym. Chem. Edn 5, 2259 (1967). 5. P. A. Curnuck and M. E. B. Jones. Br. Polym. J. 5, 21 (1973). 6. R. W. Lenz and S. Go. J. Polym. Sci., Polym. Chem. Edn 12, 1 (1974). 7. Z. Jedlinski, D. Sek and B. Dziewiecka. Eur. Polym. J. 13, 871 (1977). 8. D. Sek. Eur. Polym. J. 13, 967 0977). 9. Y. G. Urman, S. G. Alekseeva and I. Y. Sianim. Vysokomolec. Soedin. Ser. A. 19(2), 299 0977). 10. J. H. Mackey, V. A. Pattison and J. A. Pawlak. J. Polym. Sci., Polym. Chem. Edn 165, 28 49 (1978). l l. M. Danielewicz and D. Sek. Eur. Polym. J. 15, 639 (1979). 12. R. J. Zdrahala, E. M. Firer and J. F. Fellers. J. Polym. Sci., Polym. Chem. Edn 16, 689 (1977). 13. T. Hamaide, N. Marriaggi, J. L. Foureys, P. Le, Perchee and A. Guyot. J. Polym. Sci., Polym. Chem. Edn 22, 3091 (1984). 14. N. Grassie, B. J. D. Torrance, J. D. Fortune and J.D. Gemmell. Polymer 6, 653 (1965). 15. N. Ogata, K. Sanui and S. Kamiyama. J. Polym. Sci., Polym. Chem. Edn 16, 1991 (1978). 16. R. A. Newmark. J. Polym. Sci., Polym. Chem. Edn 18, 559 (1980). 17. W. Kawai. J. Polym. Sci. Part A-I, 6, 137 (1968). 18. C. Aso, T. Kunitake and Y. Ishimoto. J. Polym. Sci. Part A-1. 6, 1168 (1968). 19. F. A. Blouin, R. C. Chang, M. H. Guinn and H . J . Harwood. Polym. Prepr., Am. Chem. Soc., Div. Polym. Chem. 14(1), 25 (1973).

20. R. E. Bockrath and H. J. Harwood. Polym. Prepr., Am. Chem. Soc., Div. Polym. Chem. 14(2), 1163 (1973). 21. L. B. Stroganov, N. A. Plate, V. Zubov and S. Yu. Fedorova. Vysokamolec. Soedin. Ser A, 16(11), 2616 (1974). 22. Y. Mori, A. Ueda, H. Tanzawa, K. Matsuzaki and H. Kobayashi. Makromolek. Chem. 176(3), 699 (1975). 23. T. Okada and T. Ikushiga. J. Polym. Sci., Polym. Chem. Edn 14, 2059 (1976). 24. P. Pino, G. P. Lorenzi, U. W. Suter, P. G. Casartelli, A. Steinman, F. G. Bonner and J. A. Quirega. Macromolecules 11, 625 (1978). 25. A. E. Woodward. J. Polym. Sci. C8, 137 (1965). 26. K. Hatada, H. Ishikawa, T. Kitayama and H. Yuki. Makromolek. Chem. 178(9), 2753 (1977). 27. K. Hatada, T. Kitayama, Y. Okamoto and K. Ohta. Makromolek. Chem. 179(2), 485 (1978). 28. J. C. Bollinger and C. Aubineau. J. Macromolec. Sci. Chem. A l l , 1177 (1977). 29. C. D. Eisenbach, H. Schnecko and W. Kern. Makromolek. Chem. 176, 1587 (1975). 30. V. Percec and B. C. Auman. Makromolek. Chem. 185, 617 (1984). 31. V. Percec and H. Nava. Makromolek. Chem., Rapid Commun. 5, 318 (1984). 32. D. Gagnebien, P. J. Madee and E. Marechal. Eur. Polym. J. 21, 289 (1985). 33. S. C. Shit, B. M. Mahato, M. M. Maiti and S. Maiti. J. appl. Polym. Sci. 31, 55 (1986). 34. S. C. Shit and S. Maiti. Unpublished work. 35. A. Pourdgavadi, P. J. Madec and E. Marechal. Eur. Polym. J. 20, 305 (1984). 36. S. C. Shit and S. Maiti. Unpublished data. 37. S. C. Shit and S. Maiti. Unpublished data. 38. G. E. Niznik and D. G. Legrand. J. Polym. Sci. Polym. Symp. 60, 97 (1977). 39. D. M. Grant and E. G. Paul. J. Am. chem. Soc. 86, 2984 (1964). 40. M. W. Dutch and D. M. Grant. Macromolecules 3, 165 (1970). 41. L. F. Johnson, F. Heatley and F. A. Bovey. Macromolecules 3, 165 (1970). 42. W. O. Crain, J. A. Zambelli and J. D. Roberts. Macromolecules 4, 330 (1971). 43. V. D. Mochel. J. Polym. Sci. A-l, 10, 1009 (1972). 44. L. P. Lindeman and J. Q. Adams. Analyt. Chem. 43, 1245 (1971). 45. J. C. Randall. J. Polym. Sci., Polym. Chem. Edn 11,275 (1973). 46. G. A. Gray. Analyt. Chem. 47, 546A (1975). 47. J. C. Randall. J. appl. Polym. Sci. 22, 585 (1978). 48. H. R. Kricheldorf, J. M. Jonte and M. Berl. Makromolek. Chem. Suppl. 12, 25 (1985).