Studies on biaxial stretching of polypropylene film. IV. Overall orientation during one‐step biaxial stretching and its application to the estimation of the principal refractive indices of isotactic polypropylene

Abstract

Polypropylene film was biaxially stretched in one step in air at 140°C or 152°C, and the deformation was studied optically. A linear relation held between Δnss and vA−½ for vA > 10, at both temperatures, where Δnss is the birefringence with respect to the normal to the film and vA is the degree of stretching expressed as the factor by which the area of the film is increased. Extrapolation of data in this linear region yielded a value of 20 × 10−3 for −Δnss at infinite vA. Since it is presumed that the polypropylene molecules lie completely parallel to the film surface when the film is stretched infinitely, −Δnss at vA−½ = 0 must be just half Δn°, the intrinsic birefringence in the case of completely parallel orientation. Thus, Δn° must be 40 × 10−3. This value was obtained experimentally in uniaxial stretching when the birefringence with respect to the direction of drawing was extrapolated to infinite extension. Similar relations held between np, the average of the refractive indices in the two stretching directions, and vA, and between nss, the index normal to the film, and vA. By similar extrapolations, (1/2)(n′γ + n′β) and n′β = n*α′ were estimated, and thence nα′ was obtained. Here, n′α and n′β are the refractive indices along the c axis (molecular chain axis) and b axis. All these optical parameters refer to a density of 0.900 g/cm3. Hence by applying a density correction to those values, the principal refractive indices and the intrinsic birefringence of polypropylene crystal were evaluated as follows: nα = 1.5522, nβ = n*α = 1.5106 and Δnc° = 4.16 × 10−3, where n*α is the refractive index prependicular to the b and c axes of the crystal.

A new approach to the continuum theory of birefringence of oriented polymers

“…By the substitution of [23] and [24] in [46] we obtain Unfortunately, the usefulness of equation [47] is impaired by the fact that the anisotropy index s is not a priori a known function offo.…”

“…With the values of nl, n~, N, and Sl as given in tables 1 and 2 the polarizabilities of the optical chain segment of the six polymers may be determined by using [23], [24], and [33]. (33).…”

“…Generalized Lorentz-Lorenz relations[23,24] between density ~ and principal refractive indices ni n~ -1 with the anisotropy index s~ as parameter[15]. .…”

Effects of uniaxial stretching and shrinkage on proton spin-lattice and spin-spin relaxation times of isotactic polypropylene

“…The orientation function of the amorphous regions, fa, was calculated from the following formula [10] An = f~ An~ x + f~ An ~ (1 -x) 0 0 where A n, Anc and a na refer to the birefringence of the sample, the intrinsic birefringence of the isotactic polypropylene crystal and noncrystalline molecule, respectively, and x refers to the crystallinity. In this work the values of 41.6 x I0-3 for A n o and 38.1 x 10-3 for An ~ [11] were used.…”

Structure and properties of uni- and biaxially oriented polypropylene films: Part I - Structural characterization

“…The average angle between the c-axis and any coordinate axis, Z, is related to the orientation function by (15) It follows that the dichroic ratio in this case is given by DTM = (2 cT + 1) / (2 cM + 1) (16) In the case of a transition moment vectorM which on the average is randomly oriented in a plane perpendicular to the molecular c-axis (a reasonable approximation for the crystallinity bands at 809 and 1220 cm'), the angle o formed between this vector M and any coordinate axis Z is given by 2 cos2 8Z = 1 -cos2 cZ (17) The dichroic ratio in this case is, therefore, equal to D = k cos2 êT / k cos2 eM = (1 -cos2 0cT / (1 -cos2 0cM (18) which after substitution of Eq. (15), leads to DTM = (1 -cT / ' -cM (19) It can be easily verified that in the particular case of uniaxial orientation, either with respect to the M-axis = -2 or the T-axis cT = -2 f M' Eqs.…”