Orientation,strain measure,and supramolecular structure in fibre drawing

Summary The discrete, characteristic values of parameterp found in the empirical relation between birefringence (n) and draw ratio () of man-made fibres (1) can be explained by assuming the presence during cold drawing of a fringed-micelle structure forming a physical network.The deformation of this network is assumed to take place according to the differential equation for the orientation derived from , which will be applied to the orientation of the lateral orthogonal axes of the micelles.Parameterp figures as the strain parameter of the generalized strain measure (19) in the solution of .Dependent on the type of polymer, the micelles would have either a fibrillar (prolate) or a lamellar (oblate) shape and be linked by connective chain molecules, like beads on a string, while either in one, or in both lateral directions they would be joined by traversing molecules. The shape of the micelles inferred agree with those published in a survey of morphological observations (28).It has been found that the semi-empirical relation [2] also applies to the deformation and orientation of polymers in the rubber-like state.

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Zusammenfassung Die in der empirischen Beziehung zwischen Doppelbrechung (n) und Streckverhältnis () von Chemiefasern (1) gefundenen diskreten charakteristischen Werte des Parametersp lassen sich durch die Annahme erklären, daß während der Kaltverstreckung eine Fransenmizellenstruktur existiert, welche ein physikalisches Netzwerk bildet.Angenommen wird, daß die Deformation dieses Netzwerks gemäß der aus [1] abgeleiteten Differentialgleichung für die Orientierung, abläuft, welche Gleichung auf die Orientierung der lateralen orthogonalen Achsen der Mizellen angewendet werden wird.Der Parameter p fungiert als der Dehnungsparameter des generalisierten Dehnungsmaßes (19) in der Auflösung von .Abhängig vom Polymertyp hätten die Mizellen dann entweder eine fibrillare (gestreckte) oder eine lamellare (abgeplattete) Form und wären durch Kettenmoleküle miteinander verknüpft, etwa wie Perlen in einer Kette, während sie entweder in einer oder in beiden lateralen Richtungen durch sich kreuzende Moleküle verbunden wären. Die abgeleiteten Mizellen entsprechen in ihrer Form der in der Übersicht über morphologische Wahrnehmungen beschriebenen Konfiguration (28).Es wurde gefunden, daß die halbempirische Beziehung [2] auch auf die Deformation und Orientierung von Polymeren in gummiartigem Zustand anwendbar ist.Bemerkung: Ein einleitendes Referat über dieses Thema wurde vom Autor auf der 9. Europhysics Conference an Macromolecular Physics in Polen im April 1979 präsentiert.

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With 3 figures and 5 tables     

Die Bewegung eines Körpers in einem ringförmigen Potentialfeld

Zusammenfassung Es wird das quantenmechanische Problem eines Teilchens in einem ringförmigen Potential der Art gelöst.

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The motion of a body in a ring-shaped potential

The quantum mechanical problem of a particle in the torus shaped potential is solved.

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Résumé Solution du problème quantique de la particule dans un potentiel toroïdal: .

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Dem Andenken an meinen Freund Karl Heinz Hansen gewidmet.     

The correlation between isothermal and non-isothermal kinetics in thermogravimetry

It is shown that the total differential of the function of the amount of conversion versus temperature and time (=f(T, t)) is equal to zero non-isothermal kinetics at constant heating rate. Hence, the mathematical expression used in the literature for the rate of the non-isothermal transformation, , is not valid.     

A solution of the exponential integral in the non-isothermal kinetics for linear heating

A simple and satisfactorily accurate solution of the exponential integral in the nonisothermal kinetic equation for linear heating is proposed: $$\mathop \smallint \limits_0^T e^{ - E/RT} dT = \frac{{RT^2 }}{{E + 2RT}}e^{ - E/RT} $$      

Studies on the Kinetics of the First Order Autocatalytic Decomposition Reaction of Highly Nitrated Nitrocellulose

The kinetics of the first order autocatalytic decomposition reaction of highly nitrated nitrocellulose (HNNC, 14.14%N) was studied by using thermogravimetry (TG). The results show that the TG curve for the initial 50% of mass-loss of HNNC can be described by the first order autocatalytic equation

An alternative way to analyze quasi-elastic light scattering data for broadly distributed samples

In Quasi-Elastic Light Scattering (QELS), an apparent average hydrodynamic radius can be calculated from the measuredz-average translational diffusion coefficient D _z by using the Stokes-Einstein equation: withk _B,T and being the Boltzmann constant, the absolute temperature and the solvent viscosity, respectively. It is known thatR _{h, app} is not the same as R _{h z} because , especially when a sample is broadly distributed. In order to obtain R _{h z} instead ofR _{h, app}, an alternative way to analyze QELS data is proposed: at first, we manipulate the measured correlation functionb ^1/2|g ⁽¹⁾(t)| into a new function ; and then, we can analyze this new function to obtain an apparent parameter D_app and an apparent distribution width . We have shown that no matter how broadly a sample is distributed, D_app can be easily reduced to R _{h z} , and is directly related to the distribution width. In this report, besides using a simulated time correlation function, we also used two measured correlation functions of a latex dispersion with a broad particle size distibution and a polystyrene standard with a broad molecular weight distribution to demonstrate this alternative way.     

New approximate formula for the generalized temperature integral

A new procedure to approximate the generalized temperature integral $ \int_{0}^{T} {T^{m} {\text{e}}^{ - E/RT} } {\text{d}}T, $ which frequently occurs in non-isothermal thermal analysis, has been developed. The approximate formula has been proposed for calculation of the integral by using the procedure. New equation for the evaluation of non-isothermal kinetic parameters has been obtained, which can be put in the form: $$ \ln \left[ {{\frac{g(\alpha )}{{T^{(m + 2)0.94733} }}}} \right] = \left[ {\ln {\frac{{A_{0} E}}{\beta R}} - (m + 2)0.18887 - (m + 2)0.94733\ln {\frac{E}{R}}} \right] - (1.00145 + 0.00069m){\frac{E}{RT}} $$ The validity of the new approximation has been tested with the true value of the integral from numerical calculation. Compared with several published approximation, the new one is simple in calculation and retains high accuracy, which indicates it is a good approximation for the evaluation of kinetic parameters from non-isothermal kinetic analysis.     

The Decay of Methylene Blue in Alkaline Solution

The decomposition of methylene blue in aqueous alkaline solution is described. The rate equation is of the form: , where k = 9.0 × 10^-4 mol^- [dm³s^-1 at 20°C and] = 0.5 mol dm^-3.     

Criterion of multiplicity of steady states and the explicit expression for bifurcation set in the simplest model of a catalytic reaction with an arbitrary isotherm

The following criterion of multiplicity of steady states (m.s.s.) for the simplest model of an open heterogeneous catalytic system (monomolecular isomerization in CSTR) with an arbitrary isotherm was obtained in this paper:

An estimation of the surface ionization constant of oleic acid in aqueous sodium chloride solution

The zeta potential () measurements and the site binding theory were utilized for calculations of the parameters of the electrical double layer (edl), ionization, and complexation constants for oleic acid-aqueous sodium chloride solution interface. Assuming that is equal to the diffuse layer potential ( _d ) of the edl, the charge of the diffuse part of the edl was calculated from the Gouy-Chapman equation. The intrinsic ionizaiton constant was then determined by an extrapolation method to be . Subsequently, the surface potential ( ₀) was calculated, and it was found that ₀ changes by 50 mV per pH unit (50 mV/pH) or 42.5 mV/pH for 10^–3 and 10^–2 M NaCl, respectively. For further calculations, the integral capacity of the outer zone of the compact part of the edl was assumed to be for both ionic strengths. It was established that the intrinsic complexation constant for the binding of Na⁺ ions with the surface of oleic acid ispK _Na ^int = 2.9±0.5 if the integral capacity of the inner zone of the compact edl (K ₁) is 80 for 10^–3 M NaCl, but 280 for 10^–2 M NaCl. The use of the sameK ₁ value for both ionic strengths gives a differentpK _Na ^int for different NaCl concentrations, and also provides unrealistic surface charge ( _o ) values greaterfor 10^–3 M NaCl than for 10^–2 M NaCl, at the same pH of the solution.     

Approximate sizes of monoatomic negative ions with fractional nuclear charge using electrostatic potentials

Summary Using the criterion that for negative monoatomic ions withN electrons, the location of minimum in the electrostatic potentialV(r) gives an approximate estimate of ionic radii,r _m. Calculations of the latter are reported for quark atoms with fractional nuclear chargesZ=N– andN– , respectively. Quark atoms withN=1–10, 18 and 36 have also been considered.     

Substitution of aqua ligands fromcis-diaqua-bis(bipyridyl) ruthenium(II) by 1, 10-phenanthroline in aqueous medium

The kinetics of aqua ligand substitution fromcis-[Ru(bipy)₂(H₂O)₂]²⁺ by 1, 10-phenanthroline (phen) have been studied spectrophotometrically in the 35 to 50°C temperature range. We propose the following rate law for the reaction within the 3.65 to 5.5 pH range:

Formalkinetische Behandlung des Masseverlustes bei thermischen Abbauprozessen von Polymeren unter nichtisothermen Bedingungen

On the basis of the formal basic relation $$\frac{{d\alpha }}{{dt}} = A \cdot e^ - \frac{E}{{RT}}(1 - \alpha )^n $$ methods of calculating kinetic values from non-isothermal thermogravimetric curves have been critically evaluated. It has been established that in general integral methods are preferable to differential methods. Methods basing on a series expansion of the exponential integral $$\int\limits_0^T {e^ - \frac{{ET}}{{RT}}} dT$$ are applicable without limitations to any cases. It has been concluded that the integral method suggested by Zsakó is the most reliable.     

The kinetics of silylation of hydroxylated silica 1: Aerosil

The kinetics of the silylation of hydroxylated silica, the non-porous Aerosil using trimethylchlorosilane, under various reaction conditions has been investigated by a gravimetric technique and found to follow the law:

A two frequency method for the interpretation of multiple NQR spectra

A new method for the interpretation of NQR spectra is described. The indentification of multiple lines belonging to different transitions \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{1}{2} \to \frac{3}{2}{\rm and}\frac{3}{2} \to \frac{5}{2} $\end{document}is carried out by using the ‘seizure’ of the corresponding low or high frequency transitions in a two-frequency pulse experiment.     

Bounds for the Kirchhoff index via majorization techniques

Using a majorization technique that identifies the maximal and minimal vectors of a variety of subsets of ${\mathbb{R}^{n}}$ , we find upper and lower bounds for the Kirchhoff index K(G) of an arbitrary simple connected graph G that improve those existing in the literature. Specifically we show that $$K(G) \geq \frac{n}{d_{1}} \left[ \frac{1}{1+\frac{\sigma}{\sqrt{n-1}}} + \frac{(n-2)^{2}}{n-1-\frac{\sigma}{\sqrt{n-1}}}\right] ,$$ where d ₁ is the largest degree among all vertices in G, $$\sigma ^{2} = \frac{2}{n} \sum_{(i, j) \in E} \frac{1}{d_{i}d_{j}} = \left( \frac{2}{n}\right) R_{-1}(G),$$ and R _?1(G) is the general Randi? index of G for ${\alpha =-1}$ . Also we show that $$K(G) \leq \frac{n}{d_{n}}\left( \frac{n-k-2}{1-\lambda _{2}}+\frac{k}{2}+\frac{1}{\theta}\right) ,$$ where d _n is the smallest degree, ${\lambda _{2}}$ is the second eigenvalue of the transition probability of the random walk on G, $$k = \left \lfloor \frac{\lambda _{2} \left( n-1\right) +1}{\lambda _{2}+1}\right\rfloor {\rm and}\quad\theta = \lambda _{2} \left( n-k-2\right) -k+2.$$      

The graphical representation of equilibrium for the isothermal and isobaric reactions of ideal gases

The equilibrium for the isothermal and isobaric reactions of ideal gases is investigated in virtue of the intuitionistic figure. The curve is similar to the curve of tangential function which has one inflection and two vertical asymptotes. The equation only has one root ξ _e and it is suitable to find ξ _e by dichotomy. For non-inert substance, when or x_i^0 $$" align="middle" border="0"> , to increase substance i will make an equilibrium shift in the direction to deplete substance i; when {\nu_i} \mathord{\left/ {\vphantom {{\nu_i} {\sum_i {\nu _i}}}} \right. \kern-\nulldelimiterspace} {\sum _i {\nu _i}}> 0$$" align="middle" border="0"> , to increase substance i will make an equilibrium shift in the direction to produce more substance i.     

Crystal structure of paraffins in the triclinic modification

Summary The superpositions of layers of molecules leading to the formation of densely packed paraffin structures with triclinic symmetry were analyzed. The structure of C₁₈H₃₈ crystals consists of dense packing of the layers      

Size Distribution of Nematic Clusters in Oligomer–Polymer Systems

A physical prerequisite for the formation of nematic clusters in olygomer–polymer systems is considered. A simple geometrical model is proposed that allows, based on a kinetic analysis of the process, obtaining the expression for the cluster size distribution function where , K ₁ and K are the equilibrium constants of first and consecutive additions, and a _n and a ₁ are the equilibrium concentrations of clusters and elementary particles (oligomer molecules). The dependence of the distribution function on the intermolecular interaction energy and the chain rigidity is analyzed.