Polyvinyl alcohol (PVA) fibres are prepared by wet, dry and semi-melt spinning methods, and the micro-structural heterogeneity along the radius of the fibers was examined by means of the phase contrast as well as polarization-microscopical observations. Futhermore, those fibres are stripped to various extent according to the Elöd's peeling off method, and then its apparent density, small angle X-ray scattering intensity, crystallinity, crystallite-size, iodine adsorption, birefringence, crystalline orientation and mechanical properties are measured. Cross-sections of the fibres washed in water after coagulating in conc. sodium sulfate bath are apparently homogeneous, but cuticle and skin layers are distinguishable from the core layers by means of phase contrast-microscopical observation. The radial structures and properties of the fibres coagulated in a caustic soda are comparatively homogeneous. Marked skins are formed on the dry spun fibres, while the sections of semi-melt spun fibres are uniform. The effects of spinning conditions on the radial structures of fibres are discussed briefly.
In the preceding paper the results of electron microscopic examination on the precipitates Fcp and Fcplx are reported. The former was obtained from the aqueous solution of silk fibroin (bombyx mori) hydrolyzed by chymotrypsin, the later being obtained when the former was dissolved in cupri-ethylenediamine and dialyzed. Fcp and Fcplx showed the structures of beta-fibroin and alpha-fibroin, respectively. To examin further the structure of alpha-fibroin, the sedimented mat of Fcp 1x was prepared and submited to the X-ray diffraction measurements. A clear fiber diagram was not obtained from X-ray diffraction pattern of a Fcp 1x mat, but were led to assign the following rectangular unit cell to the alpha-fibroin: a=4.59 A (direction of hydrogen bonding), b=7.20 A, c=9.08 A (fiber axis), This unit cell includes one polypeptide chain and the polypeptide molecule may take a helical conformation of four-fold, where the residue translation should be 2.27 A. X-ray diffraction photographs of the mat of Fcp 1x and thin film adilute (0.1%) solution of regenerated silk fibroin shows long periods beginning with a spacing of 48.2 A as well as the ordinaly periods. At the present moment no definite relationship between the two kinds of the period is found. One plausible explanation would be that the log periods are caused by the globular structure formed by folded molecules. Infrared absoption spectra indicates the existence of beta-structure for the Fcp. In Fcp 1x, no sign of the presence of alpha-helix is detected, but the feature of the spectra is close to that of the random coil structure.
The principle of the fluorescence method for the study of rotary diffusion is reviewed briefly. Then, from the fundamental equations, a few modified relationships which are important for the practical use are derived. Discussions are made on the distribution of relaxation time, and the rectangular distribution function of relaxation time is introduced. The mean relaxation time (ρG) is discussed as a function of the degree of polarization of fluorescence (P) or the quantum yield of fluorescence (φ). From these observations it is to be concluded that too small a value of activation energy may be obtained, if the equations of uni-relaxation time are applied to the system having comparatively wide distribution of relaxation time.
Microbrownian motion in polyamide chains is studied by the fluorescence method. In the first place, the validity of the estimation of molecular motion is studied. The relaxation properties of fluorescent polyamide (diamino stilbene-conjugate or DAS-conjugate in contraction) are compared with those of the usual nylon-6 in which free fluorescent dye (auramine-O or diacetylamino stilbene) is dispersed. In the dilute solution they give different relaxation times and the apparent activation energies. However, in the concentrated solution and especially in solids, either sample gives almost the same relaxation time and apparent activation energy. Then, in the next place, the molecular motion and the transition in various types of bulk polyamide are studied using auramine-O as a probe. Transition temperature varies almost linearly with CED of the material, and the extrapolation to polymethylene gives the limiting value much higher than the glass transition temperature of polyethylene. Apparent activation energy also depends on CED. Other properties such as dynamic modulus and X-ray parameters are compared with the fluorescence parameter. The effects of water on the relaxtion properties is also studied. The mechanism of the transition is discussed on the basis of these experimental studies.
In the previous papers, it has been shown that the drafting with false twister has the operation of levelling the sliver by twisting and elongation as well as the opration of collecting fibers for a sliver. This report deals with the general and fundamental analysis of the twists given in the false twist drafting zone. A general equation was obtained for the variations in twists in the false twist zone. In a system of giving false twists at one place, the phenomena were theoretically analyzed (formula (5) and (9)) under conditions that the propagating speed of twists is much faster than the running speed of the sliver, and compared with the experimental results. However, the false twist drafting such as in woollen ring spinning does not give twists at just one place but at two places of a twister tube, at the entrance and exit near a front nip. For such a system, formula (11), (13) and (15) are given. The experimental results are as follows. (1) The propagating speed of twists is much faster than the running speed of a sliver. This agrees closely with the assumption upon which the theoretical analysis is based. (2) The test results on the variations in twists with the elapse of time agreed closely with the figures obtained by theoretical results in either case of giving twists at one place or at two places. (Fig. 3, 6, 9 and 10) (3) In the case of twisting at one place, there are found twists in a zone between back rollers and a twister entrance in steady state, but no twists in the other zone between the twister entrance and a front nip. (Fig. 12) In the case of twisting at two places there are also twists in: a zone between the twister entrance and the front nip. In the case of actual woollen ring spinning there are more twists in the former zone than in the latter. (Fig. 13) (4) Twists are given through the false twist friction between the tube and a sliver, and a considerable slipage can be observed. (Fig. 11)
The boundary value problem of the linear homogeneous differential equation can be completely solved by obtaining eigen-value of the coefficient matrix. However, for the numerical solution, various ideas are also used in practice. One proposal is offered in this paper. It is an application of the difference method in such a way to replace the differential equation by the difference equation with an approximate transition matrix. The boundary value problem is generally expressed as follow It is rquired to determine the unknown under conditions of the given. By using an approximate transition matrix, eq. is rewritten as follows: is used, where N is the dividing number of the time interval T and j (j=0, …, N) the numbering of any lattice point. can be calaulated numerically step by step, thus the boundary value problem is solved. If A(t) is constant in time, eq. simply becomes and the following eq. (5) is derived for the evaluation of error. If it is desired to limit the relative error given within α (α_??_1) then n and N may be determined by eq. (6):