The spin echo method as a means of determining molecular weight and molecular weight distribution

SPIN ECHO METHOD AS A MEANS OF DETERMINING MOLECULAR WEIGHT AND MOLECULAR WEIGHT DISTRIBUTION * B. V. KUZNETSOV and G. N. MARCHENXO (Received 12 October 1973) The relationship between nuclear spin-spin relaxation times and temperature, molecular weight and viscosity was investigated for a n u m b e r of polymers. The results show that it is theoretically possible to determine M on the basis of viscosity and relaxation time measurements, while M-WD can be determined from the mode of examination of transverse nuclear magnetization vectors.

A WrD• range of problems, including for example th oserelating to types of molecular motion in polymers [1-3] are being resolved b y means of the nuclear spin echo method, and the latter has also been successfully used for measuring coefficients of diffusion of small molecules in high molecular compounds [4], as well as for studies of polymerization reactions [5] and many other processes. There also appears to be much scope for successful use of the method in question in connection with the determination of major parameters of polymeric systems, such as molecular weight and MWD. McCall and his coworkers found [6] that the spin-spin relaxation times Ta of polyethylene and polydimethylsiloxane depend on molecular weight, whereas the mode of extinction of transverse magnetization vectors depends on the breadth of MWD. However practically no systematic studies have been carried out on the lines indicated above. Moreover no adequate information is as yet available on the, relationship between spin-spin relaxation and temperature and the viscosity of polymers, which could well be attributable to a lack of mass produced equipment for the purpose, and to the relative complexity of the latter. Our aim in the worm described below was to investigate spin-spin relaxation time in relation to t h e temperature, viscosity, molecular weight and polydispersity of some polymers. The experiments were performed with chromatographically pure poly(ethylene glycols) (Schuchardt Company, West Germany) with molecular weights ranging from 106 to 4 X 10~. Moreover, we also investigated poly (diethylene glycol adipate) with OH group contents of 0.78 (P]:)GA-1) a n d 4.16% (P]:)GA-2), epoxy resin ED-5, epoxy group content 18%, a n 4 * Vysokomol. soycd. A17: No. 8, 1777-1781, 1975. 2044

2045

Spin echo method as a means o f determining MW and MWI)

poly(vinyl isoprenediol) containing 0-83% OH groups (PDI) and poly(dieneurethane diepoxide) containing 1-98~o epoxy groups (PDI-3A). Binary and ternary mixtures of PEG monofraction were prepared for investigations of T2 in relation to polydispersity. The molecular weights of the mixtures (M w and Mn) were calculated on the basis of weight amounts of the fraction. The apparatus described in papers [5, 7] was used for T~ measurements, and viscosity measurements were based on the Stokes method. The error for single measurements of T~ and y did not exceed :]: 10~o. As can be seen from Fig. 1, T2 is a linear function o f viscosity in t h e coordin a t e s y s t e m selected, a n d the relationship is expressed in a general f o r m as In T 2 = A - - B In t/

(1)

(B=0.8)

The fact t h a t the curves in Fig. 1 are all parallel means t h a t t h e coefficient B is a c o n s t a n t for the studied polymers, whereas t h e m a g n i t u d e of the coefficient A varies w i t h i n fairly wide limits. Of significance is t h e fact t h a t for polymers o f t h e same t y p e the value of A increases with rising molecular weight. in7, [msec]

[~75 [msec]

a

b

8

zt

2

In 1/EcP]

ro3/r

FIG. I. Plots of T2 vs. viscosity (a) and temperature (b) for ED-5 (1), PEG-600 (2), PDGA-2 (3), PDI (4), PDGA-1 (5), PDI-3A (6) and PEG-20,000 (7). I n t h e case o f identical molecular weights A values a p p e a r to be higher for stronger intermolecular interaction. T h e results o b t a i n e d suggest t h a t A depends on t h e t y p e a n d molecular weight of the polymer, whereas B is in e v e r y case a constant. T h e results o f investigations of the t e m p e r a t u r e d e p e n d e n c e of T2 (Fig. lb) show t h a t w i t h i n a fairly n a r r o w t e m p e r a t u r e interval the d e p e n d e n c e in question is expressed b y T2=T2e -E/RT, (2) where E, h a v i n g t h e dimensions o f energy, according to the t h e o r y of nuclear r e l a x a t i o n in liquids [8], characterizes t h e r m a l fluctuations in t h e system.

2046

B . V . KUZl~TSOV and G. Ig. M A ~ r K O

At the same time the temperature dependence of viscosity can be expressed as ~/----~/o"er/Rr,

(3)

where Y is the heat of activation for viscous flow. Substituting expression (3) into (1), and comparing the result with (2), we obtain E E Y-

B - - 0.8

(4)

The temperature dependence of spin-spin relaxation can thus be used as a means of determining heats of activation for the viscous flow of polymers. T A B L E 1. H E A T S BY ~ R

Polymer PDI PDI-3A P D GA - 1 PDGA-2 ED-5 PEG-300 PEG-600

OF ACTIVATIOI~ F O R T H E VISCOUS F L O W OF SOME P O L Y M E R S D E T E R M I N E D AI~'ALYSIS AI~D F R O M T H E T E M P E R A T U R E D E P E N D E l q ' C E OF V I S C O S I T Y

Y (kea] 'mole) viscosity

NIVIR

8.0 13.5 10.2 10.2 15-2

8.3 13.3 10"4 9-9 14.9 7-8 6-9

8.4

Polymer PEG-1000 PEG-1500 PEG-2000 PEG-4000 PEG-6000 PEG-20,000 PEG-40,000

Y (kcal/mole) viscosity

~FI~R

7.4 7.3 7.9 7-1 7-6 7.2 8.8

6.8 7.3 7.9 8.0 7.6 7.5 7.6

The Y values obtained from T2-----f(t) and ~----f(t) plots are given in Table 1. I t will be seen that similar results are obtained b y either method, the slight difference that exists being due to the measurement error. The fact that B ¢ 1 is attributable to the relatively broad correlation time distribution that is found in polymers [2, 9]. Investigations of T2 in relation to molecular weight of P E G (Fig. 2) show that In T2=-C--D In M (5) Moreover, starting at a certain "critical" value of M, marked changes appear in the coefficients C and D. On going on to high molecular weights one finds that starting at M----4000 there is a 2.9-fold rise in the coefficient D, and a 1.7-fold reduction in C. It is noteworthy that the difference in the logarithms (In T | ¢ In T2'o') is not a function of molecular weight, and so the energy E m a y likewise be independent of M. The complex character of the dependence Tz-=f(M) can be attributed to the existence of two types of molecular motion in the polymers. For instance, it was recently demonstrated that a solution of P E G ( M = 3 X 104) in solvent free of resonant nuclei (D20) differs from a solution of the monomer in t h a t it has molecular motion of two types with correlation times differing b y four orders [10]. It appears that when M values are below a critical limit a

Spin echo method as a means of determining MW and MW D

2047

rapid process makes the main contribution to relaxation, whereas with higher M values this is true for a slow process. I n the light of experimental results one can conclude that assuming the dependence of T2----f(M) is known, the spin echo method can be used to determine molecular weight. I t should be noted, however, that major difficulties are involved in experimental determination of the dependence T 2 ~ f ( M ) , which limits the scope of the method quite considerably.

In Ts [ms~] 7

ln~ £=sa:l o

5

3 5

7

9

In PI

11

Fia. 2

tn ~ [cp} Fia. 3

FIa. 2. Plots of TI vs. molecular weight for P E G at 95 (1) and 70 ° (2). Light points denote mixtures of PEI~ monofractions. Fro. 3. Plots of T2 at 95 ° vs. molecular weight and viscosity for P E G (1) and P D I (2). The light points denote the T , and ~ measurements carried out at T ~ 95 °.

To circumvent these difficulties we attempted to derive a single equation relating relaxation times to molecular weight and viscosity values of polymeric systems. The dependence T 2 = f ( M , 7) obtained for P E G at 95 ° (Fig. 3) can be expressed as ln~

Iv1

= f - - K ln tl ,

(6)

where f and K are constant coefficients. I t can be shown by calculation t h a t within experimental error limits the coefficient K is equal to the coefficient B in equation (1). This means t h a t within a molecular weight interval extending at least from 1500 to 4 × 104 correlation (6) is independent of temperature. Certainly, the light points in Fig. 3 referring to temperatures of T2 and ~/measurements other than 95 ° fall satisfactorily on the curve. Regarding the means of determining the dependence T 2 = f ( M , FI) for any actual polymer homologue series if it is correct t h a t coefficient B in the

;:

2048

B. V, KUZ~TSOV and O. N. MAaCrmt~'xO

expression T2=f(~) is independent of the type of polymer, while the coefficient K in expression (6) is equal to coefficient B, then the relationship can be determined if there is only one sample of known molecular weight. The dashed line in Fig. 3 represents the dependence T~=f(M, 7) for P D I (M=4100) based on the foregoing considerations. Thus, when the dependence T~=f(M) is unknown, the process of molecular weight measurement a m o u n t s to the measurement of T2 and t/. The sole requirement is t h a t both these values should be measured at one and the same temperature. in/

\ I\ 150

I 300 T/me, m,~ec

I z/50

~FIo. 4. Mode of extinction of the transverse nuclear magnetization vector for PEG mixtures with M=106 (47 wt.%) and 4× 104 (53 wt.°/o) at 70°: 1--T=m.z;2--T==l.. To determine possibilities of using the spin echo technique as a means o f estimating molecular weight distribution (MWI)) a study was made of the relaxation times of samples t h a t were mixtures of different P E G fractions, I t was found t h a t in the latter case the mode of extinction of the transverse magnetization vector A, contrary to the extinction observed in the monofractions, does not follow the exponential law. TABLE 2. SPrN-sPr~ ~ E ~ o ~ Mwx

10 - s

19"25 23"8 31.0 16-2

Mn×

10 - s

1"72 119 129 13"2

]

"1

TIm~S FOR PEG ~rxTua~s

TSmax, lrlSeC

95° 1660 74 88 485

]

~tmin, n ~ e c

70°

95°

1080 45 37 250

50 39 30 67

I

70° 28 20 16 32

I t can be seen from Fig. 4 t h a t the process of extinction of the transverse magnetization vector for the mixture of two P E G fractions with molecular weights of 106 and 4 × 104 takes place rapidly at first, but this is followed by a marked rise in the extinction time constant. The results of calculation show t h a t for the mixture of two fractions the extinction envelope is the sum of the two

Spin echo method as a means of determining MW and MWD

2049

e x p o n e n t s a n d t h e e x t i n c t i o n constants T2m~o a n d T2m~ (Table 2). H a v i n g ass u m e d t h a t T2m~n corresponds to Mw, a n d T~m,. to Ms, we p l o t t e d t h e results o b t a i n e d on the g r a p h o f the T2-~f(M) plot (Fig. 3). As can be seen from Fig. 2, t h e d a t a for t h e m i x t u r e s are r e a s o n a b l y well described b y correlation (5). Thus, b y measuring T2mlo a n d T2mx t h e Mw/Mn ratios for P E G samples m a y be f o u n d b y means of t h e f o r m u l a

M w / M n ~ e lID In ~ w i t h

Mn>4000

I n conclusion we would p o i n t out t h a t if all the specified relations p r o v e to be correct for o t h e r p o l y m e r homologue series t h e conclusions r e a c h e d in this i n v e s t i g a t i o n could h a v e far reaching practical significance, p a r t i c u l a r l y as t h e viscosity a n d r e l a x a t i o n t i m e m e a s u r e m e n t s involve no great a m o u n t o f work or time. Translated by R. J. A. T=~rD~y REFERENCES

1. M. STOHRER, F. NOACK and J. yon S C ~ Z , Kolloid-Z, und Z. fftr Polyrnere 241: 937, 1970 2. G. I, IWI~HAILOV and V. A. SHEVELEV, Vysokomol. soyed. 8: 1542, 1966 (Translated in Polymer Sci, U.S.S.R, 8: 9, 1700, 1966) 3. U. KINZLE, F, NOALrK and J. von SCHt]TZ, Kolloid-Z. und Z. ffir Polymere 286: 129, 1970 4. R. KOSTFELD and K. GOFFLO0, Kolloid-Z. und Z. ffir Polymere 247: 801, 1971 5. B. V. KUZNETSOV, Ye. A. ASHrKHMIN, M. S. FEDOSEYEV and G. N. MAR~TENKO, Vysokomol. soyed. B18: 164, 1971 (Not translated in Polymer Sci. U.S.S.R.) 6. D. W. McCALL, D. C. DOUGLASS and E. W. ANDERSON, J. Polymer Sci. 59: 301, 1962 7. B. V. KUZNETSOV, Pribory i tekhnika eksperimenta (Experimental Apparatus and Techniques). No. 1, 157, 1971 8. A. ABRAHAM, l~uclear Induction, 1963 9. I. Ya. SLONIM and A. N. LYUBIMOV, Yadernyi magnitnyi rezonans v polimerakh (Nuclear Magnetic Resonance in Polymers). Izd. "Khimiya", 1966 10. G. PREISING and F. NOACK, Kolloid-Z. Lind Z. fiir Polymere 247: 811, 1971