ALBERT

Notes: Abstract The usual method of tracer analysis for calculating the flow across a biological membrance is based on the assumption that the compartments on either side are well-stirred. Thus, the validity of the rate of flow determination is questionable for cases where the distribution of tracer is not homogeneous. In this study, a mathematical model is developed for the purpose of estimating the effect of slow mixing on the calculation of the flow rate. The model is applied to the measurement of the rate of flow of aqueous humor through the living eye by use of a fluorescent dye as a tracer. A transit time of several minutes for the passage of fluorescein through the posterior chamber and an extended period of nonuniform distribution of fluorescein in the anterior chamber was observed. The effect of slow mixing on the calculated flow rate is compared to rates derived from equations based on the assumption of rapid mixing. Aqueous flow rates determined by the two methods were found to agree to within ≈20%.

Notes: Abstract This paper presents a three-parameter model of the mechanism of dispersion of an indicator in the cardio-pulmonary system, based on the postulates that this dispersion can be described by the one-dimensional diffusion equation and that dispersion continues past the sampling site. The model is tested using indicator dilution curves obtained from dogs, and the coefficient of diffusion is thus measured. It is found that this coefficient increases in magnitude non-linearly with increasing blood speed.

Notes: Abstract Based on the ellipsoid model of the left ventricle and the helicoidal course of the left ventricular myocardial fibers, a theory has been developed for calculating the length of the individual myocardial fibers. Numerical solutions of the final equation show that when the left ventricle is distended, the increase in length of the myocardial fibers is not uniform throughout the thickness of the myocardial wall. It was shown that with increasing dimensions of the left ventricle, the distension of the myocardial fibers becomes smaller as one advances from the endocardium to the middle layer of fibers, whereas it increases as one advances from the middle layer to the epicardial layer. The mechanism by which this effect is brought about as well as its physiological implications are discussed.

Notes: Abstract In an open circuit gas washout determination the output of test substance is shown to be of the form ∑ i=0 ∞ A i λ i k on thekth expiration whereA i 〉0,i=1,2,... and 1 〉 λ1 ≥ λ2...≥ 0 provided the transition from inspiration to expiration has certain symmetry properties with the transition from expiration to inspiration. In general, no direct physical interpretation such as volume for theA t ’s or fraction of retained gas on expiration for the λ i is justified.

Notes: Abstract Previous studies by this author of the mathematical biology of automobile driving have emphasized only the biological aspects, except for such mechanical factors as the size of the car. Otherwise, the ideal case of an inertialess car was considered. In this paper the first step is made toward introducing the effects of the mass of the car and the side-slip of the tires when the direction of driving is even slightly altered and combining these with the previously studied biological aspects. Some tentative comparisons with available data are made.

Notes: Abstract According to the occupation theory of drug receptor interaction, the response is a functionf of the number of receptors occupied by drug molecules. Considerable controversy exists regarding assumptions about this function. Without knowledge of the nature of the function, it is not possible to determine directly the rate constants, and hence the affinity constant, in the reaction between the receptor and an agonist drug. Instead, indirect determinations involving the use of antagonists have been employed, limiting the determination of affinity to those agents for which specific antagonists exist. The present paper discusses a method for the direct determination of affinity of an agonist drug. It is a “relaxation method,” i.e., the equilibrium is perturbed and the kinetics of the restoration process are studied. Assuming only thatf is non-decreasing and approximately linear over a limited domain of concentrations, it is shown that the change in response obeys first order kinetics, permitting a determination of the rate constants from the time course of the restoration process.

Notes: Abstract The basic postulate la, which governs the development of organismic sets, introduced previously (Bulletin of Mathematical Biophysics,31, 159–198, 1969), is generalized so as to contain also the rates of changes of the number and variety of differentQ-relations which determine an organismic set. It is thus brought closer to the Lagrangian principle in physics. It is pointed out that the postulate also provides a criterion of stability of an organismic set.

Notes: Abstract A method is presented in this paper for the in-vivo estimation of the nonlinear pressure-volume relationship of the human aorta. The method is based on nonlinear elastic reservoir theory and utilizes clinical data that can be obtained with a high degree of accuracy, namely stroke volume, end diastolic ventricular volume and aortic pressure trace data. The computational procedure is described and then carried out for six cardiac patients. A method for the estimation of instantaneous left ventricular volume during the ejection period based on the considered nonlinear elastic reservoir theory is also presented. The method is applied for the six cardiac patients cited and the results compared with those obtained for the same subjects by a method of estimation based on linear elastic reservoir theory described in a previous paper by the author (1969).

Notes: Abstract Deakin (1967b) suggested that flow of blood might obey a law of minimal energy dissipation. The present paper presents a simpler derivation of Deakin’s equations pointing out several previously unrecognized features. It is shown that these equations are unlikely to be applicable. In particular, the solution obtained by Deakin and Jones (1968) does not yield a true minimum for energy dissipation. The solution for which energy dissipation is actually minimized is shown to possess features which render it unlikely to apply to a real flow.

Notes: Abstract The Kedem-Katchalsky equation for the flow of a non-electrolyte through a homogeneous membrane is shown to be a first order expansion of an exact integral of the Spiegler-Bearman-Kirkwood frictional equations under the assumption that the partial frictional coefficients, ζ ij , are concentration independent. The equations are solved in terms of volume flow; there are no water-to-volume flow correction terms for the permeability, ω, or the reflection coefficient, σ. The precision of the expansion depends upon the magnitude of the water flow. The frictional coefficientsf sm andf sw are given as functions of the experimentally determined parameters ω and σ; the frictions, are shown to be independent ofL p .

Notes: Abstract As was done by Sinclair and Ross (1969(, we consider a cellular population that consists initially (at time zero) ofN 0 newborn cells, all with the same volumev o. It is assumed that the occurrence of cell division is determined only by a cell’s age, and not by its volume. The frequency function of interdivision times, τ, is denoted byf(τ). If cell death is negligible, the expected number of cells,N(t), will increase according to the laws of a simple age-dependent branching process. The expression forN(t) is obtained as a sum over all generations; thevth term of this sum, in turn, is a multiple convolution integral, reflecting the life history ofvth generation cells (i.e., the lengths of thev successive interdivision periods plus the age of the cell at timet). Assuming that cell volume is a given function of cell age, e.g., linear or exponential, and that cellular volume is exactly halved at each division, it is possible to calculate the volume of a cell with a given life history, and thus the average cellular volume of the whole population as a function of time. If at time zero the volumes differ from cell to cell, the final equation must be modified by averaging over initial volumes. In the case of linear volume increase with age, a very simple asymptotic expression is found for the average cellular volume ast→∞. The case of exponential volume increase with age also leads to a simple asymptotic formula, but the resulting volume distribution is unstable. The mean cellular volume at birth and the second moment of the volume distribution can be calculated in a similar manner.

Notes: Abstract The dynamic response of human musculo-skeletal framework is treated by (i) idealization of the musculo-skeletal framework as hybrid structural networks possessing feedback characteristics and then (ii) employing linegraph-flowgraph procedures for the feedback characterization of the hybrid structural networks. Topological procedures are used in which a “tree” of a network furnishes the skeleton upon which the “linkage” (muscle representing) members provide interaction. Feedback characterization (representing the sensitivity of the skeletal members to the tensile forces) is defined, between the internal “linkage” and “tree” members, by means of the flowgraph. Mikusinski operational calculus is used to facilitate representation of inertia effects by dynamic feedback characterization, with inclusion of initial conditions.

Notes: Abstract The representation of biological systems in terms of organismic supercategories, introduced in previous papers (Bull. Math. Biophysics,30, 625–636;31, 59–70) is further discussed. To state more clearly this representation some new definitions are introduced. Also, some necessary changes in axiomatics are made. The conclusion is reached that any organismic supercategory has at least one superpushout, and this expresses the fact that biological systems are multistable. This way a connection between some results of Rashevsky’s theory of organismic sets and our results becomes obvious.

Notes: Abstract The full implications of a statistical model for growth of a microbial cell population using cell mass as the index of physiological state have been examined by solving the partial differential integral equations resulting from the model. Calculations reveal that a lag phase is predicted during the initial stages of batch growth although no specific cellular mechanism for the phenomenon of lag had been incorporated into the model. The model predicts several situations of batch and continuous growth in which the population density and biomass concentration show opposing trends due to significant variation in the cell mass distribution with time.

Notes: Abstract Information treatment, especially in a natural medium, may be done by a random system: given an input, possible solutions are randomly selected and successively tested until the right one is found and then emitted. This paper is a mathematical study of this type of system and its use as a model of some natural (biological) systems. The theoretical development is illustrated by several examples of possible applications to biological cases. We study, under different assumptions, the distribution of the number of trials needed to treat the input, the distribution of the time for this treatment, and the distribution of the average amount of information treated in a trial or in a unit of time. We consider the case of error, and study some optimal conditions of operation and the occurrence of memory influencing the treatment of an input according to previously processed inputs.

Notes: Abstract The role of some inertial properties of the car, studied previously only for the case when the stimulus for the corrective turn is the perception of the angle between the direction of the car and the direction of a straight lane (Bull. Math. Biophysics,32, 71–78, 1970), is generalized to include such stimuli as the nearness to the edge of the lane and the anticipatory effect for a corrective turn, as well as the combination of all three stimuli. Conditions for stability of driving are deduced and discussed. They now depend on both biological parameters and such parameters as the position of the center of gravity of the car, its mass, and the side slip of the tires.

Notes: Abstract Adistance between two mobiles performing a random walk in one dimension is defined. At a given time this distance is directly related to theprobability of encounter for the mobiles. This definition is used when the motion of the mobiles is a Wiener-Levy process, first in the case of an unrestricted random walk, then if a reflecting or absorbing barrier is introduced.

Notes: Abstract The qualitative effects of anisotropy and nonhomogeneity are considered in the evaluation of left ventricular stresses in the intact heart. Maximum stresses and their location are significantly dependent on the nonhomogeneity factors and to a lesser degree on anisotropy of the ventricular wall material. If the circumferential elastic modulus is assumed to vary in a parabolic manner through the wall thickness, maximum stresses occur within the endocardial layers, a result in qualitative agreement with experimental studies.

Notes: Abstract Under the assumption that there is complete mixing in the dead space a series of equations are given which give the values for a washout test of the functional component of the pulmonary bellows (without a dead space) in terms of the washout values of the bellows with a dead space.

Notes: Abstract Expressions are derived for the overall oxygen consumption and the O2 penetration depth into a tissue section in terms of the basic parameters, of the system under steady-state conditions. The approach differs from many previous analyses in so far as the oxygen molecules are regarded as reaching their sites of chemical assimilation by diffusion through extracellular fluid followed by bulk diffusion into irregular cells of significantly lower permeability. This “two-phase” model would seem to be compatible with the major experimental features of steady-state respiration, and gives a ratio of cellular to extracellular diffusion coefficients of the same low order as that found for inert gases under transient conditions. The greater oxygen penetration predicted by this model is discussed in relation to the survival of ischemic tissue and is shown to be consistent with data for myocardial infarction.

Notes: Abstract Two models for a kidney-ureter system are considered: one model of one vessel in which a traced substance, undergoing exchange between the vessel and an external compartment, is emptying into the ureter; the second model of two approximately parallel, identical vessels in which a traced substance, undergoing exchange between each vessel and an external compartment, is emptying into the ureter. A single impulsive input of label into a vessel is assumed. For mathematical simplicity, the major conditions imposed on each system are: (1) rapid mixing transverse to a vessel axis and no mixing longitudinal to a vessel axis within the plasma; (2) small variation of the specific activity within the plasma in the longitudinal direction to a vessel axis; (3) constant flow rate of urine into the ureter and (4) constant exchange coefficients, tubule flow velocity and traced substance concentrations within individual compartments.

Notes: Abstract We use the concept of a layered wall, where each separate layer is to be homogeneous, isotropic, and incompressible, to derive stress-strain relations for the middle layer muscle ring at the transverse midsection of the left ventricle; a convenient method of formulation is that based on the elastic potential function. The hoop or circumferential stress in all three layers is found using dimensional and mechanical parameters derived earlier. The various parameters are expressed as Fourier series so that their behavior over a complete ventricular cycle is known analytically. The cases of simple elongation and what we termcurvilinear simple elongation are considered for the middle layer muscle ring strain, and the resulting stress-strain relations are derived. The results are compared with an incompressible rubber-like material known as a Mooney material.

Notes: Abstract The Peaceman-Rachford finite difference method is applied to cylindrically symmetric, transient heat conduction problems in biological media. Inhomogeneous media and internal sources which vary in both space and time are permitted. Boundary conditions are satisfied without sacrificing high local resolution by means of an exponentially stretched grid. Computation time on a Philco 2000/210 computer is approximately 5 msec per grid point per time step.

Notes: Abstract The energy cost of the left ventricle is quantitatively analyzed on the basis of the following assumptions: (1) The left ventricle is assumed to be an isotropic, homogeneous elastic, thick, spherical shell. (2) The ventricular wall is made up of a finite number of thin concentric shells. (3) The energetics of the left ventricle is in accordance with the second law of thermodynamics. An expression for the work done during ventricular contraction is derived according to the definition of physical work. The energy liberation during isovolumic contraction is formulated parallel to the concepts of heat production in skeletal muscle during isometric contraction. This expression gives the total work done per stroke in terms of mean systolic pressure, end diastolic volume, stroke volume and wall thickness during diastolic phase.

Notes: Summary For the experiments there have been prepared such microheterogeneous mixtures of isotactic polypropylene with polyethylene and of polyvinylchloride with polyethylene which contained maximum 60 volume per cent of dispersed phase component (iPP; PVC respectively) at 160°C for various diffusion times, whereat with sufficient exactness the tetrahedric lattice model could be applied. From the dependence of the mixture excess volume on dispersed phase volume fraction, calculated from additive and real densities, the volume fraction at the maximum dilatation (Φ m ) was determined. At supposing theFickian course of the mutual diffusion, it was possible to calculate the thickness of the interphase layer. It was stated that for both polymer pairs the diffusion after 15 min had been practically stopped. This phenomenon, which could be explained by the kinetic hindrances during the interpenetration of the different nature polymer segments, is resulting in the deviation from theFickian course of diffusion.

Notes: Zusammenfassung Mit Hilfe einer kontinuierlich arbeitenden, selbstregistrierenden Filmwaage wurden dieF/A-Isothermen verschiedenartig substituierter, auf Wasser gespreiteter Siloxane aufgenommen. Die Substituenten haben einen z. T. erheblichen Einfluß auf das Spreitungsverhalten. Je nach der Charakteristik derF/A-Isothermen lassen sich drei Gruppen unterscheiden. Eine erste Gruppe von Siloxanen verhält sich analog den früher untersuchten Polydimethyl- und Methyl-H-siloxanen und gibtF/A-Isothermen mit wenigstens zwei mehr oder weniger ausgeprägten TransformationspunktenA 2 undB, zwischen denen auch der einzige größere Druckanstieg liegt. Dieser Gruppe gehören mehrere Methylorganosiloxane an. Eine zweite Gruppe ist gekennzeichnet durch Isothermen mit nur einem Transformationspunkt (A 2), dessen Überschreitung bei Kompression zu einem stetigen starken Druckanstieg führt. Dieses Bild zeigen Siloxane mit stark hydrophilen Substituenten. Eine dritte Gruppe schließlich gibt glatt verlaufende, von Transformationspunkten freie Kurven, die bei kurzen Kontaktzeiten mit dem Wasser kaum nennenswerte Drucke erreichen und sich erst bei längerer Kontaktzeit im Verlauf derF/A-Werte der theoretischen Kurve für gasanaloge Filme annähern. Hierher gehören u. a. Siloxane mit höheren aliphatischen sowie mit aromatischen Substituenten. Die Diskussion des Flächenbedarfes in der Transformationsounkten ermöglicht eine Ausdeutung der Molekülorientierungen der Gruppe I, die bei Kompression bzw. Expansion des Filmes durchschritten werden. Wie bei Dimethyl- und Methyl-H-siloxanen sind in weitem Bereich des Flächenangebotes die Moleküle raupenförmig gestreckt, durch Wasserstoff brückenbindungen “Hydratisiert”, der Wasseroberfläche aufgelagert. Der bei Kompression unter Druckanstieg erreichteB-Punkt stellt stets einen dicht gepackten, kondensierten Film dar. Nach seiner Überschreitung werden die Molekülketten vom Wasser abgehoben. Auch die Siloxane der zweiten Gruppe legen sich flach mit den Siloxanketten auf das Wasser auf und werden bei Kompression zu dichtesten Packungen zusammengeschoben, sind aber zufolge ihrer hydrophilen Substituenten so stark “hydratisiert”, daß eine Abhebung “wasserfreier” Ketten von der Oberfläche nicht gelingt. Bei den Siloxanen der dritten Gruppe schließlich fehlen Anzeichen dafür, daß die Molekülketten sich auf Wasser strecken. Die Adhäsionskräfte zur Wasseroberfläche sind schwach, bedingt teils durch den zunehmend paraffinischen Charakter der mit höheren Alkylgruppen substituierten Siloxane, teils durch die Minderung der Basizität des Siloxansauerstoffs durch elektronegative Substituenten. Die Siloxane spreiten demzufolge auch nur langsam. Es ist bemerkenswert, daß diejenigen Siloxane, die sich in der Technik als grenzflächenaktive Silicone bewährt haben, den Gruppen I und II angehören, deren gemeinsames Kennzeichen schnelle Ausbildung monomolekularer Filme mit definierten Ordnungszuständen auf der Wasseroberfläche ist.

Notes: Summary Lange andSchwuger have recently shown that in a homologous series of sodium alkyl sulphates, there is an alternation in theKrafft temperatures between alkyl chains containing odd and even numbered carbon atoms. They found no such alternation in the critical micelle concentrations, and concluded that the micelle core is liquid-like. It is shown here that alternations do exist in the free energies of micelle formation. This observation, in conjunction with some others, suggests that there is some long-range order inside a micelle. The magnitude of the alternation, however, is much less than those observed in heats of fusion of fatty acids or hydrocarbons. The existence of some ‘solidlike’ character in the micelle agrees with previous deductions that the entropy of the chains inside a micelle is likely to be less than that of hydrocarbon

Notes: Summary In this paper is described a simulation technique applicable to the gel filtration of an ionic surfactant in the presence of an electrolyte. The applicability was tested by using sodium dodecyl sulfate as a surfactant and sodium chloride as an added salt. In qualitative aspects, the theoretical elution curves showed good agreements with the experimental ones. Disagreements found between both elution curves seemed to be ascribable to the adsorption of the surfactant on the gel surface which was neglected in the theory.

Notes: Zusammenfassung Im Rahmen von Untersuchungen zur Temperaturabhängigkeit der Löslichkeit von Polymeren in Systemen Polymer/Lösungsmittel/Fällungsmittel hatte sich gezeigt, daß bei Temperaturen unterhalb des θ-Punktes (des binären Systems Polymer/Lösungsmittel) in einem gewissen Bereich das Lösevermögen des reinen Lösungsmittels durch Zugabe geringer Mengen an Fällungsmittelverbessert werden kann. Derartige Systeme sind bereits mehrfach beschrieben worden, jedoch tritt der Effekt weit häufiger auf, als bisher angenommen wurde. Die theoretischen Vorstellungen darüber stellen aber keine befriedigende Erklärung dar. In dieser Arbeit wird eine Interpretation des Effektes unter Einbeziehung der Entropie über den Wert der freien Enthalpie gegeben.

Notes: Summary Stretching of nylon-6 fibers in vacuum results in well-resolved spectrum which is attributed to the secondary radical (I)−CO−NH−ĊH−CH2−.Exposure of stretched fibers to air (oxygen) yield the corresponding peroxy radical $$(II) - CO - NH - CH\dot O_2 - CH_2 - $$ . This reaction is reversible. The radical I is identical with those obtained by γ-irradiating nylon-6 fibers (in vacuum) which remain unchanged on opening to air. In fact, γ-irradiation in air also resulted in the same spectrum. The ease with which oxygen reacts with the radicals in the former and not in the latter case, strongly suggests that in the former case, the radicals are trapped mainly in the amorphous region, whereas in the latter case such radicals are present predominantly in the crystalline region. In stretching the sample the shortest tie molecules located in the amorphous regions and connecting the crystal lamellae are ruptured. Radiation, however, creates radicals indiscriminately all over the sample so that the majority is located in crystalline regions.

Notes: Zusammenfassung Durch stufenweise Dinitrophenylierung von Caseinmicellen und quantitative elektrophoretische Auswertung des nicht umgesetzten Caseinanteils wurde die Komponentenzusammensetzung an der Oberfläche, in der Mittelschicht und im Kern der Micellen festgestellt. Danach ist die Oberfläche besonders reich an γ-Casein, während der Kern bevorzugt β-Casein enthält. Untersuchungen mit η-Caseinfraktionen zeigten, daß γ-Casein offenbar eine wichtige Schutzkolloidkomponente innerhalb des Gesamtcaseins ist.

Notes: Summary Previous studies have indicated that non-ionic surface active agents, such as n-dodecylhexaoxyethylene glycol monoether, confer considerable protection on silver iodide sols to flocculation by inorganic cations. In the present study the effects of hydrolysis of the flocculating cations, lanthanum, aluminium and thorium have been examined. It was found that with the hydrolysed cations the protective action of the non-ionic surface active agent was considerably diminished. It was deduced that the hydrolysed species are more strongly adsorbed than the nonionic surface active agent and either displace the latter from the surface or form species which are large enough to cause flocculation by interparticle bridging.

Notes: Summary A detailed description of several phenomena observed during crystallization in a stirred solution of linear polyethylene is presented. It is found that simple shear flow is incapable of accelerating the formation of primary nuclei at elevated temperatures in 5% xylene solution of linear polyethylene (Marlex). The onset of fibrillar crystal formation is noted when the stirrer speed of the inner cylinder of aCouette instrument exceeds a minimum value which corresponds to the onset ofTaylor vortices. Closed loops of fibrillar crystals occurring periodically around the stirrer, revolve in orbits which coincide with the centers of theTaylor vortices. Turbulent flow seems to be most effective in inducing fibrillar crystallization and a maximum crystallization temperature of 112°C was achieved with the 5% xylene solution of Marlex. A mechanism is proposed for the formation of primary nuclei of bundlelike type which is based upon orientation and deformation of aggregates in regions of elongational flow between the vortices. Solutions of high molecular weight polyethylene (M w=1.5×106) exhibit a pronouncedWeissenberg effect prior to the appearance of the first fibers. Normal stresses lower the rate of stirring inCouette flow at which vortices occur. This may account for the observed fibrillar crystallization of the high molecular weight polyethylene at stirrer speeds which in case ofNewtonian fluids give rise to laminar flow according to theTaylor criterion. Settlement of the fibrous network on the stirrer results from secondary flow.

Notes: Summary The adsorption of ethylene-vinyl acetate copolymer which consists of two different adsorption energy segments from solution onto glass sphere was studied. The adsorption depends on molecular weight and the constant α obtained by application ofUllman's equation is decreased with the increase of molecular weight. The molecular weight dependence of adsorption suggests that the polymer chain adsorbed at solution-solid interface consist of sequences and loop chains. The relation between maximum adsorption and area occupied with adsorbed polymer chain from various solution was discussed, and the solvent dependence of maximum adsorption was explained in the difference of polymer solubility.

Notes: Summary The character of the surface and bulk properties of polyethylene have been considered with respect to adhesion and bond strength. Rupture of adhesion oxidatively activated polyethylene to aluminum has two faces. One of them is an apparent failure at the interface of aluminum-polyethylene which was moderately oxidized and another is the failure at the surface region of polyethylene which was strongly oxidized. In the former case the introduction of polar groups with oxidation is effective for the promotion of bond strength, and from the increasing behavior of bond strength we conclude that the adsorption theory on adhesion is appropriate for the elucidation of adhesion mechanism.

Notes: Summary 1. Bombyx mori silk fibroin is digested by chymotrypsin in lithiumthiocyanate solution in a pH-stat. One of the digestion products, the chymotryptic precipitate (Cp), is further digested by papain in lithium-thiocyanate solution. The influence of lithiumthiocyanate concentration and enzyme: substrate ratio on the rate of digestion are examined. 2. Chymotrypsin is not denatured by a lithiumthiocyanate concentration lower than 1%; at higher concentrations the enzymic activity decreases rapidly. 3. The Cp remaining in solution after digestion of fibroin in lithiumthiocyanate was found to be as inhomogeneous as the chymotryptic precipitate from a water solution of fibroin by ion-exchange and gel chromatography. 4. Concentrations lower than 10% of lithiumthiocyanate do not decrease the enzymic activity of papain markedly. 5. Dinitrophenylation of N-terminal glycine and the hydroxyl group of C-terminal tyrosine of Cp has no influence on the digestion by papain. 6. Peptide fragments from the digestion of Cp and DNP-Cp by papain have an average chain length of 4–5 amino acid residues.

Notes: Summary Two polymer crystallization theories are reviewed and discussed against the background of a revision of general nucleation theory, given in a preceding paper. Since crystallization nuclei, as usually defined, do not exist, the free energy of formation of a nucleus, such as it is applied for the calculation of nucleation frequency or rate of crystal growth, is a misleading concept. The latter quantities must be described as functions of parameters governing the attachment of polymer segments to, and their separation from, the growing crystal. The crystallization of polymers is supposed to proceed via attachment of segments of one or a few polymer repeating units rather than by steps of a whole “fold length” at once. Chain folding as aprerequisite for crystallization must be rejected as being highly improbable; it may be theresult of crystallization. One cannot decide from data on polymer-crystallization kinetics alone which theory is right or wrong, since it is the derived interfacial free-energy parameters that are actually the adjustable parameters of the theory.

Notes: Summary The dynamic mechanical properties of nylon 66 films and fibers have been examined, as a function of annealing and drawing, with a Vibron viscoelastometer. It is found that the α′ transition is little affected by annealing treatments, but increase in orientation causes the transition to move to a higher temperature. Experiments, with X-ray diffraction of samples at elevated temperatures, lead to the conclusion that the triclinic to hexagonal phase change does not contribute significantly to the α′ transition. Samples cut parallel and perpendicular to the drawing direction of nylon 66 film, have been used to show that the curves of dynamic tensile modulus versus temperature, for the parallel and perpendicular directions, cross in the neighborhood of the α′ transition. This observation is discussed in relation to the suggestion that the α′ transition is the glass transition in nylon 66.

Notes: Summary This paper primarily describes the large diversity in morphology of fibrillar polyethylene crystals precipitated from stirred solutions at elevated temperatures. Shish-kebabs crystallized at 112°C from stirred xylene solutions of linear polyethylene exhibit lamellar overgrowths having thicknesses of the order of 150 Å from which it was concluded i. a. that at crystallization temperatures above 100°C only backbones are formed and that the surrounding polymer molecules deposit epitaxially on the substrate at lower temperatures. The variation in the appearance of the overgrowth and the inhomogeneity of the samples can be traced back to irregular stacking and to differences in washability of the fibrillar crystals, these differences being largely due to the non-uniform flow pattern along the various stirrer parts. Unusual lamellar shapes, interconnections, sheets between lamellae, the “veil” on the Shish-kebab noted byKeller andMachin, may well be explained byKeith, Padden andVadimskys mechanism of crystallization-induced orientation of macromolecules between the lamellae and the consequent formation of extendedchain crystals. The lamellar overgrowth appears to be arranged along the backbone according to a logarithmic normal distribution, and the average diameter of the lamellar crystals increases with the average spacing, both being approximately equal in size. The fibrillar crystals end in smooth tapered tails having lengths varying between 5 and 8 μ. These observed fibre ends agree best with the “unroll” model proposed for fibrillar crystal growth in flow fields if on the average each molecule introduces one chain fold and the chain ends are randomly assimilated by the crystal lattice. Linear polyethylene below molecular weight of 50×103 and low density polyethylene did not crystallize in fibrillar habit. whereas copolymers of ethylene and slight amounts of propylene and butylene proved capable of forming fibrillar crystals and isotactic polypropylene yielded smooth and overgrown fibres.

Notes: Zusammenfassung Die 2g1-Kinke wird als Baufehler mit 4 möglichen Lagen im idealisierten PÄ-Kristall elastizitätstheoretisch durch je einen Kräftedipol beschrieben. Die Berechnung des Relaxationsbetrags für den γ-Prozeß in PÄ — Kinkschritt (γII′) und Kinksprung (γII) — ergibt mit h·c=0,0006 Übereinstimmung mit der in (7) verwendeten paraelastischen Abgleitvorstellung und mit dem Experiment. Mittlere 2g1-Kinkblockgrößeh und Defektanteil der thermischen Ausdehnung Δα werden unter der Nebenbedingung konstanter 2g1-Kinkkonzentrationc diskutiert.

Notes: Zusammenfassung Die relaxierten Zustandsänderungen des Netzwerks anorganischer Oxydgläser nach Drucksprung wurden durch Messungen derDK im MHz-Bereich verfolgt. Die zunächst scheinbar widersprüchlichen Erscheinungen an geschliffenen und ungeschliffenen Proben sowie Proben unterschiedlicher Dicke lassen sich widerspruchsfrei deuten unter der Annahme eines Volumen-und eines nur an den geschliffenen Flächen auftretenden Oberflächeneffekts. Der Volumeneffekt bedingt einen zeitlichen Anstieg derDK nach Drucksprung; er liegt bei den 0,1-mm-Proben im Meßbereich und ist bei den dickeren Proben mit ihren niedrigeren Konfigurationstemperaturen zu so langen Zeiten verschoben, daß er sich dem Nachweis entzieht. Der Oberflächeneffekt dagegen bedingt einen zeitlichen Abfall derDK und wird mit Erscheinungen in der Schleifschicht, vermutlich Adsorptions-Absorptions-Gleichgewichten von Wasser, in Verbindung gebracht.