Investigation of the fold-surface problem in polyethylene single crystals with the nitric acid oxidation technique

Single-crystal preparations of polyethylene were treated with the selective oxidizing agent, fuming nitric acid. The degraded products were examined as regards layer thickness (by low-angle x-ray studies), chemical and weight changes, recrystallization and annealing treatments, and by broadline NMR, as part of a systematic investigation aimed at clarifying the nature of disordered material in single crystals. It emerges that there is a disordered-mobile region along the fold surface of the crystals in agreement with other parallel works along similar lines. In a more detailed analysis we can now decompose the nitric acid attack into components affecting the basal and side surfaces, respectively. Taking into account the recrystallization–annealing observations, we infer that the fold surface is heterogeneous with folds of more than one kind. These results were combined with a preliminary molecular weight distribution study by gel permeation chromatography. Taking into account all the available evidence, we are led to suggest a composite structure where surface looseness, coresponding to long loops and hairs, is superimposed on the more regular folded surface. This model is in the process of being tested. The problems concerning the assignment of a value to the amount of surface looseness are being discussed. In addition, a discontinuity in the thermal behavior of the crystals between 75 and 80°C. has been detected.     

Solution grown polymer crystals

Summary A survey is presented on some front line issues in the field of polymer crystallisation from dilute solution. The major portion of the review is devoted to the discussion of the problem of disorder in the simplest single crystal forms which can be considered as a preliminary for the understanding of the nature and behaviour of the amorphous content in a crystalline polymer. Available evidence for the existence of both disorder and crystallographic regularity along the fold surface is critically reviewed, and the compatibility of theoretical considerations with the various conceivable fold surface models is being analysed. The critical surveying of these issues suggests some obvious ways in which the apparently conflicting claims as regards the nature of the true fold surface could be reconciled, and along which future investigations could be fruitfully conducted. Some exploratory work aimed at the clarification of the disorder problem in single crystals pursued along some new lines in our laboratory is being outlined. In addition, single crystal growth from chemically inhomogeneous molecules (copolymers) is also touched upon.In the second part of the review a brief survey is presented of the research in a newly emerging field concerned with crystals with intrinsically fibrous habit resulting from crystallisation during flow, a topic which opens up new perspectives in the subject of polymer crystals.Finally some rather illuminating pictorial similarities between crystals from solution and the melt are placed in juxtaposition.     

Ab initio SCF Calculation of the Fluoronium Ion: Geometry,electronic structure and vibrational constants

An ab initio SCF calculation of 42 points of the energy hypersurface of the fluoronium ion is presented using a contracted F(5s/3p), H(2s) gaussian basis set. In its equilibrium structure a bond length of 1.812 a.u. and a HFH bond angle of 127.2° are predicted. The calculated vibrational frequencies for H₂F⁺, HDF⁺, and D₂F⁺ are in good agreement with the experimental data.     

Determination of organophosphorus, triazine and 2,6-dinitroaniline pesticides in aqueous samples via solid-phase microextraction (SPME) and gas chromatography with nitrogen-phosphorus detection

Solid-phase microextraction (SPME) represents a very simple and rapid method for the extraction of organophosphorus, triazine and 2,6-dinitroaniline pesticides from aqueous samples without making use of any solvents. The same fiber can be used repeatedly. Moreover, a sample volume as small as 3 mL can be employed with no loss in sensitivity. 34 compounds have been extracted from aqueous samples by SPME using a 85 m polyacrylate fiber. For organophosphorus pesticides, a 100 m polydimethylsiloxane fiber has been used additionally for comparison. The fibers were directly introduced into the heated split/splitless injector of the gas chromatograph and determined using a nitrogen-phosphorus detector. The method was evaluated with respect to the limit of detection (LOD), linearity and precision. The limit of detection (LOD) depends on the compound and varies from 0.005–0.09 g/L. The method is linear over at least three orders of magnitude with coefficients of correlation usually >0.999. For triazines and 2,6-dinitroanilines the coefficient of variation (precision) is <8% while for organophosphorus compounds it may reach values up to 18% (however, if the latter compounds are extracted using the polydimethylsiloxane phase considerably higher precision is achieved). The partitioning of the analyte between the aqueous phase and the polymeric phase depends on the hydrophobicity of the compound as expressed by the octanol/water partitioning coefficient (P_ow). For triazines it was shown that there is a linear dependence of the logarithm of the analyte response on the log(P_ow) i.e. the higher the hydrophobicity, the higher the affinity of the analytes to the polymeric phase of the fiber and the higher the response. Salt addition has a strong effect on the extraction efficiency. This effect increases with decreasing hydrophobicity (increasing polarity) of the compound. The triazines ametryn, atrazine, propazine, simazine and simetryn have been identified in a ground water well sample by SPMEGC/NPD.     

On the use of Helmholtz resonators as sound attenuators

Summary In the present paper a nonlinear acoustic theory is proposed, to accurately describe the properties of a generalized type of Helmholtz resonators. The theory may be used as a layout tool to design sound attenuators for combustion facilities. The present investigation shows that, in addition to the nonlinear effects, the effects due to thermoacoustic boundary layers and the first frequency correction to the Helmholtz approximation should be taken into account, in order to predict the frequency-dependent attenuation properties of Helmholtz attenuators with the accuracy required by typical technical applications. A series of experiments is presented which is used to validate the theoretical predictions.

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Zusammenfassung In der vorliegenden Abhandlung wird eine nichtlineare akustische Theorie vorgeschlagen, mit der das Verhalten einer verallgemeinerten Art von Helmholtzresonatoren beschrieben werden kann. Die Theorie kann als Werkzeug zur Auslegung von Schalldämpfern für Verbrennungsanlagen benutzt werden. Die vorliegende Arbeit zeigt, dass neben den nichtlinearen Effekten auch die Einflüsse der thermoakustischen Grenzschichten und der ersten Frequenzkorrektur zur Helmholtzapproximation berücksichtigt werden müssen, damit die frequenzabhängigen Eigenschaften von Helmholtzdämpfern mit technisch ausreichender Genauigkeit beschrieben werden können. Mit einer Reihe von Experimenten werden die theoretischen Ergebnisse untermauert.

     

Exponential weak Bernoulli mixing for collet-eckmann maps

We prove exponential weak Bernoulli mixing for invariant measures of certain piecewise monotone interval maps studied in [BK] and [KN]. In particular we prove this for unimodal maps with negative Schwarzian derivative satisfying lim , wherec is the unique critical point ofT.     

Local Borel summability of Euclidean 311-1311-1311-1a simple proof via differential flow equations

It is shown how the differential flow equation (or, equivalently, the continous renormalization group) method can be employed to give an astonishingly easy proof of the local Borel summability of the renormalized perturbative Euclidean massive ₄ ⁴ .Supported by NSF grant # DMS-9100383     

Complete solutions of a family of quartic Thue and index form equations

Continuing the recent work of the second author, we prove that the diophantine equation

for has exactly 12 solutions except when , when it has 16 solutions. If denotes one of the zeros of , then for we also find all with .