Die Makromolekulare Chemie 108 (1967) 285-287 (Nr . 2520)

From the Institute of Chemistry, University of Napoli, Italy

Kurzmitteilung

An Absolute Method €or the Determination of Crystallinity in Polymers

By PAOLO CORRADINI *, EZIO MARTUSCELLI *, and MICHAEL A. MARTYNOV ** (Eingegangen am 5. April 1967)

The general relation of the integrated intensity Ii of a diffraction line

(1)

where j = the multiplicity, A = the absorption factor, P = the polarization f,actor, L = the LORENTZ factor, ni = the number of unit cells in the ir- radiated volume and Voi = the volume of a unit cell. Replacing ni by

of substance is ni

voi Ii - jAPL IFTI -

where Mi = the total weight, Moi = the weight of the unit cell content and pi = the density, one obtains for the ratio of two integrated intensities I, and I,

provided tha t the general conditions of measurement (primary beam intensity, slit system, sample geometry, wavelength etc.) are kept con- stant. For the mixture of two substances the absorption factors of both components are equal to tha t of the whole mixture. Using the expressions for polarization factor and monochromatic LORENTZ factor for powder method one obtains Eq. (111) in the form

1 (1 + cos2 2 0 \ I, - j lvi , IF:^ \ sin20 cos o ,Il p, W, I, j,V& IF:( ( 1 + cos2 2 0 p1 W,

-- - _

sin2@ cos 0

where Wl, W, = the weight fractions of the components in the mixture. Formula (IV) relates the absolute intensity of any given diffraction maximum of the component 1 to its concentration in the sample and to tlhe intensity and concentration of the component 2. -

”) Sez. VII, Centro Nazionale di Chimica delle Macromolecole del C.N.R. Istituto Chimico,

*’[) On leave from Leningrad State University, Leningrad (USSR), with a felloship of the Via Mezxocannone 4, Napoli (Italy).

italian government.

285

P. CORRADINI, E. MARTUSCELLI, and M. A. MARTYNOV

For the mixture of a partially crystalline polymer and a completely- crystalline standard substance the difference between the ratio of the absolute intensities of any diffraction maximum calculated according to the formula (IV) and tha t obtained by experiment must be pro- portional to the percentage of crystallinity of the polymer. If p and s indi- cate polymer and standard substances respectively and x i s the crystalli- nity of the polymer then Eq. (IV) becomes

1 + cos2 2 0

I, jpV& IF;I sin20cos0 , ps W, Is j8Vip IFiI ( 1 + cos2 2 0 ) pp W,

X (V) - _ 1 -- sin2@ cos 0

We tried to prove it for isotactic polypropylene1) (Escon, melt.ind. 1.8) and polyethylene2) (Hercules, melt.ind. 0.65). Adamantane3) (CloH16), urotropine4) (C,H,,N,), and p e n t a e r y t h r i t ~ l ~ ) (C,H,,O,) were used as completely crystalline standard substances. A number of unoriented samples was prepared from the mixtures of the polymers with the stand- ards with different weight fractions of the substances. We tried to satisfy all the conditions required for powder mixtures preparation (details will be reported later). A Norelco Geiger-counter X-ray spectrometer with filtered Cu-Ka radiation was used to obtain X-ray diffraction curves. The crystallinity data for the polymers were compared with those obtained by means of the HERMANS and WEIDINGER method6). Our results are re- ported in Table 1.

Table 1. Intensities ratio and crystallinil

Mixture

Poly-propylene- urotropine

Polypropylene- adamantane

Polypropylene- pentaerythritol

Polyethylene- adamantane

Indices of the reflections

Poly- mer -

110

110

110

110 200 200 110

Stand- ard

110

111

110+ 002

111 111 002 002

1, 1 s

calcd. Iccording

-

to (IV)

0,208

0,298

0,250

0,758 0,252 0,748 2,240

data fa

X 1, IS

meas- ured

-

0,087

0,138

0,118

0,53 0,20 0,56 1,53

polymers and standards

Crystallinity (yo)

X

41,7

46,3

47,2

69,8 79,2 74,8 68,2

average for the POlY- mer

--

I 45,6

by HERMANS- WEIDINGER

method

44,5

76,5

286

Determination of Crystallinity in Polymer

The differences in the measured averages in the fifth column are due to experimental errors in the measurements performed in this work and to errors in the measurement and putting on an absolute scale of the intensi- ties in the original papers on the X-ray structure determination of the sub- stances used in the course of this work. The influence of the errors in the determination of structure factors on the measurements of crystallinity can be minimized by using several lines and different standards. The effects of thermal vibrations of the atoms and lattice imperfections can also be minimized by measuring the intensities of the lowest order lines.

The good agreement with the data of HERMANS and WEIDINGER con- stitutes an absolute check of the validity of the method proposed by these authors.

Our method can be applied to every polymer with known structure. Later we shall report also the results obtained by this method for nylon-6, nylon-66, isotactic polystyrene and poly-4-methyl-pentene-1.

From a theoretical point of view, it appears to be possible not t o mix the standard substance with the polymer if the absorption factors are known. One can apply the method to separate samples of polymer and standard keeping all conditions of measurement constant.

The principle of the method can also be used for putting the intensities of the reflections of polymers on an absolute scale.

We thank Dr. W. RULAND of Union Carbide, Brussels, for having crit- ically read the manuscript of this paper and for many helpful suggestion.

G. NATTA, and P. CORRADINI, Nuovo Cimento, suppl. 15, 10 (1960) 40. *) C. W. BUNN, Trans. Faraday SOC. 35 (1939) 483. 3, C. E. NORDMAN and D. L. SCHMITKONS, Acta crystallogr. [Copenhagen] 18 (1965) 764;

W. NOWACKI, Helv. chim. Acta 28 (1945) 1233. 4, P. A. SHAFTER, J. Amer. chem. SOC. 69 (1947) 1557. s, F. S. LLEWELLYN, E. G. COX, and T. H. GOODWIN, J. chem. SOC. [London] 1 (1937) 883. 6, P. H. HERMANS and A. WEIDINGER, Makromolekulare Chem. 44-46 (1961) 24; 50

(1961) 98.

287