Schulz Method Research Articles

Analytical Successive Solutional Fractionation of Macromolecules

A detailed theoretical comparison between the efficiencies of the analytical successive solutional fractionation (SSF) and analytical successive precipitational fractionation (SPF) was made under various conditions of the average molecular weight of original polymers, the molecular weight distribution (MWD), the initial polymer volume fraction, and the total number of fractions by using a computer simulation technique. The results were compared with the experimental results obtained for an atactic polystyrene solution in methylcyclohexane. The limit of applicability of the Schulz method and Kamide methods as analytical procedures was obtained.SSF proved successful for evaluating the total profile of MWD of the original polymer. In particular, the combination of SSF with the Kamide method furnished the most accurate procedure for evaluating MWD curve of the original polymer under ordinary conditions. The operating conditions suitable for determining Xw/Xn of the original polymer were, however, extremely limited as compared with those in the preparative fractionation.

Determination of angles between blocks from the topographs obtained by the Schultz method

The paper presents the analysis of formation of the image of non-perfect crystals in the Schulz method. Methods are suggested to determine the angles between blocks by using either `singular' points or the displacement of characteristic lines. Accuracy of these methods is discussed.

The nature of the structural imperfections in the alternate extension and compression of molybdenum single crystals

The structure of Mo crystals in the early stages of fatigue were studied. It was found that the broadening of the peaks on the oscillation curves in the early stages of fatigue is associated with the strengthening of the material, ending in the formation of a relatively small number of subboundary barriers whose orientation is determined by the crystallographic elements of slip in the single crystals. This process is outwardly similar to polygonization, but, in contrast to thermally activated polygonization, it is the result of slip and not of the climbing of the dislocations. The distance between the subboundaries is not uniform along the length of the specimen. Consequently the Schulz method is sensitive to the appearance of structural inhomogeneity in the early stages of fatigue.

Molecular weight distribution of cellulose by fractionation in cadoxen solutions

The fractionation of cellulose in cadoxen solutions has been carried out by precipitation with aqueous propanol. The reproducibility of the method has been tested by means of parallel fractionations, and shown to be good, for both research and routine work. The fractionation data have been analysed using Beall and Schulz methods, and the results compared.

Effect of molecular weight distribution of the original polymer on separation characteristics in successive precipitational fractionation

AbstractAn attempt has been made to confirm the validity of conclusions deduced in the previous papers in which a single sample with a specific molecular weight distribution, was mathematically fractionated. Polymers with a SCHULZ‐ZIMM distribution and WESSLAU distribution (ratio of the weight‐ to number‐average degree of polymerization, X̄w/X̄n = 1,05–5) were brought into a solution, which was cooled to cause precipitation according to the simulative procedure of KAMIDE and SUGAMIYA. The molecular weight distribution (MWD) of the fractions is approximately symmetrical and can be expressed by the normal distribution function, irrespective of the MWD of the original polymer. If the MWD of the original polymer is highly skew in the lower molecular weight region, the fraction, separated from a comparatively concentrated solution at very small p, yields a doubly‐peaked MWD (p is the amount of fraction expressed as weight ratio). As the width of the MWD of the original polymer increases, the MWD of the higher order fraction becomes narrower and X̄w of the fraction decreases rapidly in the fractionation process. The standard deviation, σ' for the polymer in the polymer‐rich phase is larger than that in the polymer‐lean phase, regardless of the type and breadth of the MWD of the original polymer, and the order of fractionation, provided that the fraction size is small. When the initial concentration is not exceedingly low, the KAMIDE method is by far preferable to the SCHULZ method for estimating accurately the MWD of the original polymer from the fractionation data. In a given fractionation run the log‐log plot of polymer concentration in a precipitate vs. X̄w can be approximated by a straight line.

Computer simulation of successively solutional refractionation of macromolecules

AbstractA successively solutional refractionation (SSRF) method, analogous to the successively precipitational refractionation (SPRF) method proposed by KAMIDE et al., has been simulated for a 1% solution of polymer having a SCHULZ‐ZIMM distribution (the ratio of the weight‐ to number‐average degree of polymerization, X̄w/X̄n = 2,0) with X̄w = 300. The combination of the number of the fractions, i, with the number of the sub‐fractions per each fraction, j, as expressed by (i˜j), were chosen so that ij was 15, such as (15˜1), (5˜3), and (3˜5). The fractionation efficiency decreases in the order: (15˜1), (5˜3), (3˜5), (0˜15), where (0˜15) denotes the simple successive solutional fractionation which yields 15 fractions as a total number of the fractions. The (3˜5) and (5˜3) type refractionations were found to be very effective, except for a few initial fractions, to obtain fractions with X̄w/X̄n≤1,1. The two methods, i.e., the SCHULZ method and KAMIDE et al. method, for evaluating the cumulative molecular size distribution of the original polymer were compared with each other by using the refractionation data (X̄w and the amount of the subfractions). The SCHULZ method is apparently advantageous over the KAMIDE et al. method. SSRF is concluded to be suitable not for analytical purposes, but for preparative purposes.

Evaluation of the Iron-o-Phenanthroline Procedure For Determining S02in Turbine Exhaust Gases

Several wet chemical methods have been used or suggested for the determination of SO2 concentrations in air pollution work. These include the iron-O-phenanthroline procedure reported by Stephens and Lindstrom, the Scaringelli-modified West-Gaeke method and the Schulze method. This paper describes a laboratory study to evaluate the usefulness of the iron-o-phenanthroline procedure and is directed to individuals concerned with the analysis of gases from the exhaust of gas turbine engines and other combustion processes, including stationary power plants. The variables considered were: range of usefulness in terms of concentration of SO2, efficiency of collection, effect of contaminants, specifically oxides of nitrogen, olefin and aldehyde and effect of storage prior to spectrophctometric measurement. The Stephens-Lindstrom method was found to be suitable for measuring higher levels of SO2 concentrations. It can accurately measure amounts totalling 6000 µl of SO2 and above whereas the other mentioned methods ...

Role of concentration dependence of polymer/solvent interaction parameter in the polymer fractionation by successive precipitational method

AbstractThe successive precipitational fractionation was carried out very accurately by an electronic computer assuming that polymer/solvent interaction parameter χ depends significantly on the concentration of the solution. The polymer‐rich phase was separated by lowering the temperature of a solution of a polymer having the most probable size distribution with the number‐average degree of polymerization X̄ = 150. The procedure for the simulation of the fractionation, proposed by KAMIDE, OGAWA et al., was improved to be applied to the case when the concentration dependence of χ cannot be neglected. As the concentration dependence of χ, as expressed by p in χ = χ0 (1 + p vp), increases, the partition coefficient χ between the polymer‐lean phase and polymer‐rich phase, and the volume ratio R of these two phases increase, and the breadth in the distribution of the degree of polymerization of the fractions obtained decreases. In particular, the contents of the low P regions in the first few fractions are remarkably small, if p is positive. However, the general features of the P distribution of the fractions are not influenced so much by introducing the concentration dependence of χ. The two methods proposed so far, i.e., the SCHULZ method and the method of KAMIDE et al., were applied to the evaluation of the P distribution in the original polymer from the fractionation data, and the results were compared with each other. The latter method is proved to be preferable to the former also in the case of p ≠ 0. The breadth in the P distribution of the fractions obtained becomes narrower as the intial concentration decreases and p increases. The effect of the amount of the fraction on its P distribution is dependent only slightly of p. The fractionation efficiency is determined solely by σ, irrespective of p.

Simulation of successive precipitational refractionation of macromolecules by electronic computer

AbstractAn attempt has been made to study the following refractionation method proposed by KAMIDE and his coworkers: The first fraction precipitated from a solution of a comparatively high initial concentration is divided by refractionation into several subfractions. The polymer‐lean phase obtained in the last refractionation stage is returned to that in the first fractionation step. As above described, the fractionation followed by the refractionation is repeated adequate times. Taking the FLORY‐HUGGINS theory as the basic principle, the hypothetical refractionations were performed by an electronic computer for a 1.0% solution of the polymer having the most probable distribution (the number‐average degree of polymerization X̄n = 150). The combination of the number of the fractions, i, with the number of the sub‐fractions per each fraction, j, as expressed by (i∼j), was chosen so as ij to be 15, such as (15∼1), (5∼3), (3∼5). The sub‐fractions showed a P distribution qualitatively similar to that obtained by a simple successive fractionation. The fractionation efficiency decreases in the order: (0∼15)0.1, (15∼1)1.0, (5∼3)1.0, (3∼5)1.0, (0∼15)1.0, where (0∼15) stands for the simple successive precipitation which yields 15 fractions as a total number of the fractions, and the suffix 0.1 or 1.0 refers to the initial concentration expressed by volume per cent of a dilute solution, from which the first fractions are separated. The (3∼5) and (5∼3) type refractionations were found to be also sufficiently effective with the exception of a few initial fractions to obtain fractions with X̄w/X̄n ≤ 1.1, where X̄w is the weight‐average P. The total numbers of separating steps necessary for these refractionation procedures are not so different from those of a simple successive fractionation.In addition, the method of KAMIDE et al. was compared with the SCHULZ's method by evaluating the cumulative weight P distribution of the initial polymer using the refractionation data (X̄w and the amount of the sub‐fractions). The method of SCHULZ underestimates both the smaller and larger P regions. On the other hand, the method of KAMIDE et al. slightly overestimates the smaller P region but gives the accurate distribution in the larger P region.

Relations entre lórientation de monogristaux de fer, leurs mecanismes de deformation par laminage et la nature des textures de laminage

The plastic deformation by cold-rolling of large monocrystalline iron samples can be analysed in terms of a triaxial stress system. The rolling textures have been experimentally determined by means of an X ray technique (Schulz method) for monocrystalline iron samples with various orientations; the results show that single and double glide deformation is preponderant and important enough to explain the origin of the various components of polycrystalline iron rolling texture, namely: {100} 〈110〉, {112} 〈110〉, {111} 〈112〉. It has been possible too, to discriminate the various cristallographic planes parallel to the rolling plane for one family, and the various possible rolling directions for one given orientation of the rolling plane.

Polymer fractionation. II. The analytical problem

AbstractComplete fractionations into 5, 10, and 20 fractions were calculated by a numerical method based on the Flory‐Huggins theory in order to evaluate various procedures for determining the molecular weight distribution from fractionation data. If the initial distributions are wide, the differential distribution cannot be accurately reconstructed, not even if each fraction is characterized by two average molecular weights (instead of one, as is customary). In addition to this inadequacy in the evaluation procedure there are the experimental errors which further detract from the accuracy of the result. The integral distribution can, in some cases, be approximated fairly well by means of the Schulz method, provided that the polymer is separated into many fractions with narrow distributions. However, the integral distribution thus obtained does not reflect details in the differential distribution. Polymer fractionation does not appear to be a suitable procedure for accurate determination of the differential distribution. From the assembled material, a thermodynamic method has been derived which seems to hold out better prospects. It should enable the differential distribution to be directly determined from a detailed analysis of the liquid–liquid phase relationships, provided the free energy of mixing function of the system is known.

A critical consideration of the molecular weight distribution of narrow‐distribution polymers

AbstractNumerical fractional solution was applied to a narrow‐distribution polymer having SCHULZ‐ZIMM type distribution (xn = 2000, xw/xn = 1.05) by using a solubility equation based on FLORY‐HUGGINS' theory. Fractions obtained by a series of ten trials overlap extensively with each other and have xw/xn values comparable to the initially given one. Application of the usual SCHULZ method to the data obtained gave a distribution far narrower than the initially given one especially in the lower molecular weight region. On the other hand, a reasonable distribution was obtained when the fractionation data were analyzed in terms of the new method proposed by HOMMA et al. This seems to justify the proposal of HOMMA et al. and their results obtained by sedimentation velocity method.

Improvement of Accuracy in Representation of Conventional Pole Figures

AbstractIn the conventional pole figure, an accurate representation can be attained by correcting the observed X-ray diffraction intensity for any change in diffraction geometry and by comparing this with the correctly established standard intensity. For the intensity corrections, ASTM has prescribed the method of Decker et al. In practice, however, the validity of the correction formula is uncertain, since the prerequisite is difficult to attain for parallelism of an incident beam of sufficient intensity. For the standard intensity, it is desirable to take the intensity obtained with the randomly oriented material of the same composition. However, in most cases an arbitrary unit has been taken because of the difficulty in getting a truly random and uniform sample. Under these circumstances, it is first necessary for an accurate representation of pole figures to make a random sample of uniform thickness for the standard. The authors have obtained satisfactory standard samples by sintering the randomly oriented iron powder made from iron chloride and made use of them to check the method of intensity correction. Satisfactory results are obtained in the randomness tests, such as the comparison of the relative intensity diffracted from the crystal planes parallel to the sample surface and the fluctuation of diffraction intensity during α rotation.In the reflection case by the Schulz method, the (110) reflection intensity of a random sample, by Co Kα radiation, is independent of the tilting angle up to 50°. The other reflections do not give a constant intensity for the wide range of the tilting angles because of dispersion of the diffracted beam due to the wider separation of Kα doublet in the higher reflection angle and the wider irradiated area at the lower angles. In the transmission case Schulz's correction formula is in good agreement with the observed values for the various diffraction lines and the samples of various µt, while the Decker-Harker formula does not give the absorption change with α-rotation even by an incident beam of ⅙° divergence. In both cases, an accurate determination of pole densities is made by comparing the diffraction intensity of the standard sample substituted in place of the test specimen and by correcting the absorption change due to the difference of µt between the standard and test sample, which affords good coincidence in the overlapped region. The pole figure obtained by the above method furnishes an accurate prediction of plastic and elastic anisotropy in sheet metals.

Study of the treatment of polymer fractionation data

AbstractThe fractionations of a hypothetical 250‐component system and an actual polymer were simulated by computations on a digital computer. The results indicated that Schulz's method of treating polymer fractionation data is acceptable if the fractions obtained are reasonably sharp. When extremely low molecular weight materials are present in the polymer, the computation shows that one must be very careful in computing the M̄u/M̄n ratio. A comparison of the computation result with the experimental result of a linear polyethylene fractionation indicates that the Flory‐Huggins' theory describes the liquid‐liquid phase separation of polymer solutions well.

魚類の血液ヘモグロビンに関する研究-I

Oxy-and met-hemoglobin crystals were obtained from the blood of several kinds of fish, i.e., Thunnus orientalis (immature), Katsuwonus vagans, Cyprinus carpio, and Seriola quinque-radiata, etc., by SCHULZ's method, by DRABKIN's method or by the modification of the latter (Fig. 1), and studied spectrophotometrically. The spectra of various derivatives of these hemoglobins were then compared with those of horse hemoglobin prepared for reference (Fig. 2, Table 1), and it was found that there are neither so marked specific differences between fish and horse hemoglobins, nor between fish hemoglobin as seen increases of myoglobins of fish and higher vertebrates.