Orientation axis

Thus, the process of PAN transformation under the effect of IR radiation proceeds with considerable self-acceleration. The irradiation of uniaxially oriented PAN films gives a polymer with a distinct anisotropy of optical properties, dichroism in the visible spectral region in particular. Figure 8 presents dichroism curves [D =/(X)] at various angles (ip) between the polarization plane and the orientation axis. The same figure shows the dependence D =f(uniaxially oriented film. 

Fig. 8. Dichroism of electronic absorption spectra of oriented and nonoriented PAN films after IR irradiation, (a) Dependence of optical density ( >) on the wavelength for various values of (angle between film orientation axis and light polarization plane).

An uniaxial mechanical deformation provokes drastic changes in the identation pattern of drawn polymers. Some typical results illustrating the dependence of MH on draw ratio for plastically deformed PE are shown in Fig. 19 a. The quoted experiments 12) refer to a linear PE sample (Mw 80.000) prepared in the usual dumbbell form drawn at a rate of 0.5 cm/min at atmospheric pressure. Identations were performed longitudinally along the orientation axis. Before the neck (A = 1), the... 

Fig. 19a. Microhardness values parallel ( ) and perpendicular (X) to the orientation axis as a function of draw ratio, for PE drawn at different temperatures 60 °C (O), 100 °C ( ) 120 °C (A) 130 °C ( )12 b Microindentation anisotropy of the above drawn samples vs. draw ratio...

These expressions show that a deformed polymer network is an extremely anisotropic body and possesses a negative thermal expansivity along the orientation axis of the order of the thermal expansivity of gases, about two orders higher than that of macromolecules incorporated in a crystalline lattice (see 2.2.3). In spite of the large anisotropy of the linear thermal expansivity, the volume coefficient of thermal expansion of a deformed network is the same as of the undeformed one. As one can see from Eqs. (50) and (51) Pn + 2(iL = a. Equation (50) shows also that the thermoelastic inversion of P must occur at Xim (sinv) 1 + (1/3) cxT. It coincides with F for isoenergetic chains [see Eq. (46)]. 

Fig. 14. Heat (1, 1 ) and heat to work ratio (2, 2 ) for reversible deformation of LDPE at 20 °C 7 81. 1,2 — isotropic sample 1, 2 — cold-drawn sample (A. = 4, deformation along orientation axis). Dotted curves correspond to the equation Q = fiTEe and solid curve 2 to the equation Q/W = 2PT/c with P = 2.4 x 10"4 K 1 and E = 0.1 GPa...

Additionally, one can consider the thermal expansivity in an arbitrary orientation direction. For films, the linear coefficient of thermal expansion at angle (p to the orientation axis is determined by... 

Because Pn may be negative, there may exist such directions in oriented crystalline polymers along which the thermal expansivity is zero. Thermomechanical studies of oriented LDPE, PA and PET have shown that a reversible extension of the films at an angle of 30° to the orientation axis is not accompanied by thermal effects 64), i.e. p30. 0. The dependence of P, on the angle for LDPE is shown in Fig. 22. 

Er = modulus in the longitudinal direction relative to the direction of orientation Et — modulus in the transverse direction — angle between the applied stress and the orientation axis... 

Figure 1 shows a block diagram of UCS J-800KCM together with the orientation axis of the optical and electric components. Specific points of improvement are as follows. 

The results of analytical theory are expressed essentially as averages of the type (A"), where is a dynamical vector, usually an orientation axis of the molecule in which there is embedded a unit vector such as e. ... 

Fig. 11. Nominal stress, CTj, versus extension ratio, for polycarbonate with different values of pre-orientation given by Anj. Samples drawn parallel to the orientation axis Ani = 0.029 (I), Ani = 0.016 (II) unoriented sample Ani = 0 (III) sample drawn perpendicular to the orientation axis Ani =0.017 (IV)...

Fig. 12. Extension ratio, Xj", at intrinsic craze initiation as a function of An, for polycarbonate stretched parallel to the orientation axis...

Fig. 15. Logarithmic plot of the total extension ratios at intrinsic craze initiation (T = 129 °C) and after shear yielding (T = 23 °C) L" and X, respectively versus the extension ratio, Xi, after pre-orientation. Samples have been stretched parallel to the orientation axis...

Let us now concentrate on the T u LUMO of Ceo- Referring to Fig. 12, we want to let the molecule have an orientation (j) with respect to the surface-tip arrangement. Thus, we make new combinations of the basis functions to be associated with laboratory axes (X, Y, Z). The Z-axis will be taken as the normal to the surface, i.e. along the orientation axis and so we take... 

Following an rf pulse, because the tensor orientations of each crystallite are different, the resonant frequency for each crystallite is different and the magnetisation rapidly dephases. This can be envisaged pictorially from the chemical shift interaction. In the static powder pattern the frequency axis could be read as an orientation axis. Then in Figure 2.12 the two sets of spins starting off at A and B have different initial precession rates. The azimuthal phase angle picked up by each of these orientations after a time t is... 

The needle-like crystallites, when packed into a flat sample, will also tend to align parallel to the surface. However, the preferred orientation axis, which in this case coincides with the elongated axes of the needles, will be parallel to the sample surface. In addition to the nearly unrestricted distribution of needles axes in the plane parallel to the sample surface (which becomes nearly ideally random when the sample spins around an axis perpendicular to its surface), each needle may be freely rotated around its longest direction. Hence, if the axis of the needle coincides, for example, with the vector d. then reflections from reciprocal lattice points with vectors parallel to will be suppressed to a greater extent and reflections from reciprocal lattice points with vectors perpendicular to d / will be strongly increased. This example describes the so-called in-plane preferred orientation. 

In Eq. 2.78 the multiplier 7 is calculated as a sum over all N symmetrically equivalent reciprocal lattice points and t is the preferred orientation parameter refined against experimental data. The magnitude of the preferred orientation parameter is defined as t = TJT, where Tx is the factor for Bragg peaks with reciprocal lattice vectors perpendicular, and T is the same for those which are parallel to the preferred orientation axis, respectively. In the case of the ellipsoidal preferred orientation function this parameter is equal to z for the needles (in-plane preferred orientation) and 1/t for platelets (axial preferred orientation). 

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