X-ray diffraction curves for a system of parallel cylinders with liquid-like order: A model for the diffraction of crazed polymers

As a model for the internal structure of polymer crazes, a system of parallel cylinders with liquid-like order is proposed. X-ray diffraction curves were calculated for such a system with Monte Carlo data for the radial distribution function of the two-dimensional hard-disk fluid at different packing densities. A comparison is made between the present calculations and experimental results of crazed polycarbonate showing a very good agreement. A way of evaluating the average craze fibril diameter with the calculations is also discussed.</jats:p

"A New Approach For Characterizing Oil Fractions, And For Selecting Pseudo-Components Of Hydrocarbons"

Abstract The non-uniqueness of the inversion of physico-chemical parameters to obtain molecular weight distributions for heavy oil fractions is discussed. A method to obtain bounds for the cumulatives of these distributions from the usually available experimental information is presented. The method can be applied systematically using linear programming techniques, and the bounds obtained are mathematically rigorous due to the properties of Tschebychev systems. The method is also used [a calculate bounds for the pseudo-critical properties needed to characterize pseudo-components for equation-of-stare use. These bounds provide a way to select optimal lumping schemes (for a given number of pseudo-components) in a systematic manner. Numerical examples for the bounds obtained and for the optimized lumping procedure are prese1lled. Introduction Equations-of-state are used in reservoir engineering to predict the PVT behaviour of crudes when complete experimental measurements are not available and in compositional numerical simulation. Generally, with a sufficiently large number of pseudo-components, a satisfactory description of the heavy fraction of the fluid of interest can be obtained. However, there are strict limitations on the maximum number of components that can be used in numerical simulation work and the original components have to be lumped into a smaller number of new pseudo-components. One way of determining a characterization for a heavy fraction is to take each distillation cut or identified Cn group on a partially extended analysis as a pseudo-component, determining its pseudo-critical parameter via correlations and completing the match by fitting the known experimental data using the binary interaction coefficients as adjustable parameters. Whitson(1) has presented a review of the many correlations available for this purpose. An alternate approach proposed by Whitson(2) assumes a given functional form with adjustable parameters for the distribution of Cn groups (Cn molecular weights) in the heavy fractions. The adjustable parameters are used to fit the known average properties for the heavy fraction and for the distillation cuts or identified Cn groups. The adjusted distribution together with a set of generalized properties for Cn groups up to CH completes the characterization. The problem of lumping these pseudo-components into a smaller number without losing the predicting power of the equation of state has been addressed by many authors(2–5). This problem has several stages into how many components should one lump?, which components should be lumped together? and how does one determine the EOS constants for the new lumped pseudo-components? In this paper we address the lader two points. Lee et al.(3) have proposed a method in which thermodynamic properties are plotted against the average molecular weight. Similarity of slopes is then used as a criterion to choose the lumping scheme for the mixture. Mehra et al.(4) used a statistical approach based upon the minimization of errors introduced in the prediction of phase saturations using similarity of saturation versus component composition slopes as criteria to select the components to be lumped together. Hong(5) developed a trial-and- error scheme. </jats:sec