BRANCHING IN POLYETHYLENE
The principal purpose of this paper is to present the current status, as viewed by the authors, of our knowledge of branching in polyethylene and the effects of branching on its properties. Another purpose is to present some speculative material, and some challenging observations, in an attempt to stimulate, in some measure, future work on the structure and chemistry of polyethylene. In endeavoring to achieve these aims, the authors have drawn heavily upon their own work and liberally from the literature, particularly the published results of R. B. Richards and his collaborators. Polyethylene resins are made by polymerizing ethylene at elevated temperatures and high pressures.’, The polymer molecules formed under these conditions are branched hydrocarbon chains3* 4 . 6 * and their average molecular size varies from approximately 50 carbon atoms per molecule, for the greasy products, to more than 1000 carbon atoms per molecule for rigid resins. The degree of branching in polyethylene has been shown to play an important role in determining the properties of the resin.’ In fact, it is now generally recognized that degree of branching and molecular weight are the most important molecular variables in polyethylene resins. In this paper, degree of branching is defined as the number of branches per 100 carbon atoms, and the number of branches per molecule is defined as the number of -CH3 groups per molecule more than two. Although some chains and branches are terminated by vinyl groups (-CH=CHJ, the concentration of these is very small compared to the concentration of methyl groups. Side chain methylene groups (RR’C=CHZ) may be regarded as short branches but, as such, represent not more than 15 per cent, and generally a much smaller proportion, of the total number of branches. As a result, this configuration is not considered significant for the purposes of this paper.
Quantitative x‐ray studies of order in amorphous and crystalline polymers. Quantitative x‐ray determination of crystallinity in polyethylene
Various quantitative scattering relationships for polymers have been examined experimentally in order to test their validity as assumptions in the x-ray determination of crystallinity. These are (a) the proportionality between the scattered intensity and the pt value of the specimen (p is the density and t the thickness of the material), (b) the relationship between equal pt values for two different specimens of the same material and the corresponding scattering masses in the beam, (c) the scattering from equal masses of a polymer in the amorphous or crystalline states, and (d) the values of the total scattered intensity from equal masses of different polymers. It has been demonstrated, at least in the case of polyethylene, that the percentage of crystalline material in a polycrystalline polymer can be determined quantitatively by means of x-ray diffraction methods. The method used in this study, viz., a comparison of the amorphous scattering from the sample with that from a completely amorphous sample, has been applied to an investigation of the temperature variation of crystallinity in unstretched and stretched polyethylene. The comparison between the x-ray and density results for the case of the unstretched material has been pointed out. The technique has also permitted a determination of the orientation of the crystallites. By means of these methods, it has been shown that the x-ray diffraction results are in essential agreement with previous stress-birefringence data on stretched polyethylene; and that the nature of the stretchng process is different at high and at low elongations.
Robust solutions of inverse problems in electromagnetic non-destructive evaluation
Non-destructive testing (NDT) is the application of physical measurement technology based on energy interaction with the material and its nonconformities. The material's response is sensed by transducers and sensors which?in most cases?scan the component and document the results in inspection images. However, NDT measures a physically defined quantity or even an intrinsic property. The difference between non-destructive evaluation (NDE) and NDT is in the interpretation of the inspection data. NDE has to discuss the inspection results in terms of quality elements and characteristics which are relevant to describe the fitness of the material for use. In the case of macroscopic defects these are the kind of defect (cracklike, globular) and its size and orientation to the main stress directions; in the case of material property determination the parameters are mainly mechanical properties. Therefore, in NDE one has to solve inverse problems. The solution of inverse problems based on mathematical procedures such as integral equations is a strong developing discipline and most of the articles prepared for this special issue of the journal have the objective of discussing the latest state of the art in that field. However, practical NDE needs robust and quick solutions which are to be applied mainly online. Therefore, we present here inversion procedures based on multiple linear regression algorithms applied to inspection data. We describe the calibration procedure to fit the free parameters of the model functions and give examples of practical applications in industry.