Oct., 1961
DIFFRA~OMETER ANALYSIS OF LIGHTSCATTERING PATTERNS
1749
AS‘ OPTICAL DIFFllACTOMETER ANALYSIS OF LIGHT SCATTERIXG PATTERNS OBTAINED FROM POLYETHYLENE FILMS BYPHILIPR. WILSON, S. KRIMM AND RICHARD S. STEIN Department of Chemistry, University of Massachuseita, A d e r s t , Mass., and Departmat of Physics, University of Michigan, Ann Arbor, M a . Rscei.ed M a d 1, ZBBf
The opticaldiffraction technique is used to analyze the interpretations of light scattering patterns from polyethylene films. Three caseei are considered: (1) the effect of periodicity in spherulite structure, (2) the effect of spherulite anisotropy, and (3) the effect of internal structure.
Introduction I t has been shown2 that the scattering of light a t low angles is a consequence of the optical anisotropy of volume filling spherulites. The anisotropic scattering patterns obtained with polarized light have been interpreted in terms of the anisotropic distribution of induced dipoles within the spherulite. The variation of the scattering patterns during: the growth and melting of the spherulites has been interpreted successfully in terms of this mechanism. The theory permits one to calculate rigorously the scattering from an isolated t,hree-dinnensional spherulite. The effect of environment, in a close-packiil spherulitic medium is approximated by surrounding t’heisolated spherulite with a medium of constant refractive index cqual to the average refractive index of the spheruiite. A more exact treatment of the effect of surrounding sphe.rulit,cs is prohibitively difficult. In this paper, .the opticaldiffraction analog technique3is employed to assess this effect. Ringed Spherulite Structure.--It is now well established that the concentric rings observed in polyethylene spherulites when examined in polarized light arise from radial peri0dicit.y of crystal A theory of orientation within the light scatt,ering from such an isolated spherulite has been presented.2 This theory predicts that a scattering maximum should occur a t a scatte,ring angle, 0, given by tthe Bragg-type equation = d
sin (8/2)
(1)
where X is the wave length of the light in the medium, and tl is the radial repeat distance of crystal orientahion. This maximum has been observed6J (Fig. 1). The effect of having the spherulite surrounded by others was examined by the optical diffraction analog technique. A full discussion of this method and of the essential (1) Two of the suthors (P. R. W h n and R. 8. Stein) acknowledge support, in part, by 1% contract with the O5ce of Naval Rwenrch and by grants from the Petroleum Research Fund and the Phx Corporation. The third author (9. Xrimm) acknowledges support by the United States Pnblio Health Service. The authors are indebted to Dr. Robert I, Miller. Monsanto Chemical Co.. Plaaticu Div.. Springfield, Mans., for the iniorodenaitometer traces. (2) R. S. Stein and M. B. Rhodea, J . A p p l . Phys., 31, 1873 (1960). in) For a ilrtacription and list of referenceu, see W. Hughes and C. A . Taylor, J . S n Inatr.., 30, 105 (1953). (4) (a) A. ReLler, .I. Polymer Sei., 17, 291 (1955); 39, 151 (19591: ,!;) P, Price, ; 5 d , 37,71 (1059): 39, 130 (1959). (5) H. D. Keith ana P.J. Padden, I h i d , 99, 101, 123(195!3). (ti) R. J. Olnrk, R L. Miller. €2. 3. Stein and P. R. Wilson, ibid.. 48, 275 11960).
(7) R S. Stein and A. Plasa, ibid.. 45, 519 (1960).
features of the diflractometer is given by Hughes and Taylor. a Two drawings were prepared. One represents an isolated spherulite possessing a radial variation of scattering power (arising from either density or orientation variations) and the other (Fig. 2) a close-packed assembly of such spherulites. Diffraction patterns are presented in Fig. 3a and b. Three featbear noting: (1) for the single spherulite, a central ring quite close to the incident beam is seen which is absent in the pattern from the array. This results from diffraction by the entire spherulite and arises because of the boundary between the spherulite and its surroundings. (2) A new ring of greater diameter is observed in the pattern from the spherulitic array. This is a consequence of interspherulitic interference and is a result of the incompletely random distribution of spherulite centers. (3) The larger diameter ring is observable in both patterns. This is the predicted Bragg-type diffraction maximum arising from the inter-ring spacing. Its average position is the same in both patterns. This is more intense and more diffuse in the pattern from the array of spherulites. The increased intensity results from the greater number of contributing spacings while the diffuseness is probably a result of the incomplete rings a t the spherulitic boundaries. The andog patterns differ from the observed scattering maximum in that the maximum occurs as a complete circle rather than an equatorial arc. This has been explained on the basis that it is only the tangential refractive index of the spherulite which is periodic, not the radial. Consequent,ly, periodicity in scattering power occurs only in t.he equatorial regions of the spherulite. The effect upon the scattering patterns of the angular variation of scattering power within the spherulite is discussed in the next section. The Effect of Dif€ering Radial and Tangential Polarizability.-The theory of and calculated scattering patterns for homogeneous isolated spherulites having different radial and tangential polarizabilities have been presented. The predicted scattering patterns bear a resemblance to the actual ones: and the observed angular dependency of scattered intensity is consistent wit,h the microscopically measured spherulite size.2 Again, however, the effect of interspherulitic interference is considered only in an approximate way. A more detailed analysis of this effect may be obtained from optical diffraction studies. Polyethylene scattering patterns obtained with parallel and crossed polarization have been pub-
1750
PHILIP
R.WILSON, s. &IMM
AND l < I C W R D
l,'ig. :j.
Fig. 2.-A close-pneked array of twdimensional spherulites with radial variation io ncattcring power.
lished' (with one polarizer in the incident beam and one in the scattered beam). I n both patterns, most of the scattering occurs at angles less than 3 O from the incident beam. The radial dependency of s c a t t e d intensity is a function of the size and packing of the spherulites, hut the angular d e pendency of intensity is a function of the angular dependency of the induced dipole moment within the spherulite and the component of the scattered light from thia which passes through an analyzer. This dependa, of mume, on the relative orientation
s. STEIN
Vol. 6.5
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