2-point pattern

In order to reproduce the observed time dependence of the intensity of the 001 reflection and the 4-point pattern, we here introduce a kinetic model for the structure formation of PET from the oriented glassy states. In the model, we adopt the following assumptions. 

The intensity of the 001 reflection at time t, /ooi (0> is proportional to the number of smectic regions at time t, while the integrated intensity of the 4-point pattern in the SAXS regions, IsAXs t), is proportional to the number of the pre-crystalline regions. Here, the following relations are satisfied ... 

In order to reproduce the observed intensity of the 001 reflection and the 4-point pattern in the SAXS region, we performed a nonlinear least square fit by using Eqs. (2), (6.8)-(6.10), and (14). The solid and dotted curves in Fig. 6.4 were obtained by the above fitting procedure. In Fig. 6.4, it is found that the time evolution of the intensities of both the 001 reflection and the 4-point pattern in the SAXS region can be weU reproduced simultaneously by the present kinetic model. In the next sections, we will discuss the several parameters obtained by the fitting. 

During the isothermal annealing process at 63.6-76.3°C, the intensity of the 001 reflection from the smectic structure has the maximum at a time, while the intensity of the 4-point pattern in the SAXS region increases monotonically with time. 

Although the investigation in this paper mainly concentrated on the time evolution of the 001 reflection and the 4-point pattern in the SAXS region, the measurements of the time dependence of overall diffraction patterns in the WAXS region will be required in order to elucidate the microscopic mechanism of the structure formation in oriented PET. In particular, real-time measurement of the intensity distribution of the meridional reflections of higher order will reveal the detailed mechanism of the structure formation. Real-time relaxation measurements such as dielectric relaxation spectroscopy are also desired for this purpose. 

Lamellar structures or domains in oriented samples Lamellar or domain spacing Lamellar or domain thickness and diameter Tilt angle of the lamellae Misorientation Position of the interference peak along the meridian or the minor axis of the elliptical trajectory of the lamellar reflection Extent of the reflection in meridional and equatorial directions Angular separation of the lamellar reflections across the meridian in 4-point patterns Variation in the meridional width with distance from the meridional axis... 

In oriented systems (fibres or stretched films), the scattered image often appears as a two-bar or a four-point pattern with the scattering maximum at or near the meridian (fibre axis). The one-dimensional scattered intensity along the meridian must be calculated by the projection method using the following fonnalism... 

Determine the limit of detection LOD and limit of quantitation LOQ according to the interpolation at level y = a + CL of the regression line and its lower CL this is sensitive to the calibration-point pattern ... 

Expressions (1) and (2) are called the right difference derivative and the left difference derivative and are denoted by and %, respectively. The difference expressions LjJ" and Ljj" are defined at two points. In other words, these are based on the two-point patterns x, x + h and x — h, X. Moreover, any linear combination of expressions (l)-(2) such as... 

Example Q. Lv = v". An irregular pattern (a non-equidistant grid). Granted two numbers h > 0 and > 0, other ideas are connected with the three-point pattern (x — h-,x,x -f /i+). When /i any such pattern is said to be irregular, since the grid including this pattern turns out to be non-equidistant. Being concerned with new members... 

The operators- Ai and A2 are specified on the regular three-point patterns... 

This operator is defined on the nine-point pattern shown in Fig. 16. The expression for Ai A2 u such that... 

The difference scheme (4) is constructed on the six-point pattern with the nodes... 

We now deal with the family of schemes on the four-point pattern (see Fig. 17e)... 

Although the star point patterns indicated above are optimal from... 

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