Structural parameters fractions

Once P(F ° ) and P(Fg° ) have been calculated, it is possible to calculate a number of network structure parameters including the weight fraction of sol, wg, and the "effective" crosslink density. A given polymer or crosslinker will be part of the sol only if all of its groups are attached to finite chains. Thus, the weight of the sol is given by... 

It should be emphasized that for Markovian copolymers a knowledge of the values of structural parameters of such a kind will suffice to find the probability of any sequence Uk, i.e. for an exhaustive description of the microstructure of the chains of these copolymers with a given average composition. As for the composition distribution of Markovian copolymers, this obeys for any fraction of Z-mers the Gaussian formula whose covariance matrix elements are Dap/l where Dap depend solely on the values of structural parameters [2]. The calculation of their dependence on time, and the stoichiometric and kinetic parameters of the reaction system permits a complete statistical description of the chemical structure of Markovian copolymers to be accomplished. The above reasoning reveals to which extent the mathematical modeling of the processes of the copolymer synthesis is easier to perform provided the alternation of units in macromolecules is known to obey Markovian statistics. 

H2 + CH4, D2, P2 + Tetralin, GO + H2O were selected and reduction was conducted by varying the reaction time. Each isolated fraction was subjected to ultimate analysis, H-NMR, C-13 NMR, molecular weight measurement and the structural parameters were calculated. The results of the study of these structural parameters in the course of the reactions were evaluated and the reaction mechanisms thereof are discussed below. 

In this contribution, we report equilibrium modulus and sol fraction measurements on diepoxidet-monoepoxide-diamine networks and polyoxypropylene triol-diisocyanate networks and a comparison with calculated values. A practically zero (epoxides) or low (polyurethanes) Mooney-Rivlin constant C and a low and accounted for wastage of bonds in elastically inactive cycles are the advantages of the systems. Plots of reduced modulus against the gel fraction have been used, because they have been found to minimize the effect of EIC, incompleteness of the reaction, or possible errors in analytical characteristics (16-20). A full account of the work on epoxy and polyurethane networks including the statistical derivation of various structural parameters will be published separately elsewhere. 

Chapter 13 - It was shown, that limiting conversion (in the given case - imidization) degree is defined by purely structural parameter - macromolecular coil fraction, subjected evolution (transformation) in chemical reaction course. This fraction can be correctly estimated within the framework of fractal analysis. For this purpose were offered two methods of macromolecular coil fractal dimension calculation, which gave coordinated results. 

Moreover, the objective function obtained by minimizing the square of the difference between the mole fractions calculated by UNIQUAC model and the experimental data. Furthermore, he UNIQUAC structural parameters r and q were carried out from group contribution data that has been previously reported [14-15], The values of r and q used in the UNIQUAC equation are presented in table 4. The goodness of fit, between the observed and calculated mole fractions, was calculated in terms RMSD [1], The RMSD values were calculated according to the equation of percentage root mean square deviations (RMSD%) ... 

Table 1 presents as an example the experimental dependences of kinetic parameters of the reaction, structural parameters of the network and some physico-mechanical characteristics on the molar fraction of monofunctional molecules in the reactant mixture, which is specific of FTD in the given case. As can be seen, the presence of monofunctional molecules, even in minor amounts (only 3-10%), exerts a strong influence on the kinetic and physico-mechanical parameters. 

Table 1. Dependence of the kinetic parameters of the reaction, the structural parameters of the network and the physico-mechanical properties of polyurethane elastomers on the molar fraction of OH groups in the monofunctional reagent21...

Finally, the alicyclic fraction of H.i should be discussed. This structural parameter can be calculated from ... 

Transannular interaction between the silicon and the nitrogen atoms in Si- and C-substituted silatranes is strongly proved by numerous X-ray studies5-7 13-15,18-22,29. Table 1 provides structural parameters for a large fraction of the approximately 60 crystal-lographically determined structures of 1-substituted silatranes which are mainly collected in a recent review29. 

Crystallinity and disorder are important structural parameters for understanding relationships between structure and physical properties. Flaws and distortions are the main features that limit the ultimate properties of textile fibers. Some of these crazes, cracks and voids are revealed under the electron microscope, either on the surface or in cross sections stained with heavy metals (J, 2). However, these staining techniques (that reveal the main morphological features) make it much more difficult to determine the degree of distortion of the crystalline fraction. Theoretically, line profile studies permit separation of effects due to crystalline size from those due to structural distortions. However, the lack of peaks in semicrystalline fiber x-ray patterns hinders that approach. 

With such an understanding on system complexity in mind, the DBS model is composed of two simple force balance equations, respectively, for small or large bubble classes, and one mass conservation equation as well as the stability condition serving as a variational criterion and a closure for conservative equations. For a given operating condition of the global system, six structure parameters for small and large bubble classes (their respective diameters dg, dL, volume fraction... 

The C60 molecules were found to be executing large amplitude reorientations at room temperature, so that large anisotropic thermal displacement factors of the C60 carbon atoms were found. The thermal displacement parameters for some of the C60 carbon atoms at room temperature are, in fact, so large that the C60 atomic coordinates may well represent only an average over one or more disordered structures involving fractional atomic occupancy. On the other hand, the TDAE N and C atomic coordinates are well-defined already at room temperature. 

It should be emphasized that for the Markovian copolymers, the knowledge of these structure parameters will suffice for finding the probabilities of any sequences LZ, i.e., for a comprehensive description of the structure of the chains of such copolymers at their given average composition. As for the CD of the Markovian copolymers, for any fraction of Z-mers it is described at Z 1 by the normal Gaussian distribution with covariance matrix, which is controlled along with Z only by the values of structure parameters (Lowry, 1970). The calculation of their dependence on time and on the kinetic parameters of a reaction system enables a complete statistical description of the chemical structure of a Markovian copolymer. It is obvious therewith to which extent a mathematical modeling of the processes of the synthesis of linear copolymers becomes simpler when the sequence of units in their macromolecules is known to obey Markov statistics. 

Mixtures of hydrocarbons are assumed to be athermal by UNIFAC, meaning there is no residual contribution to the activity coefficient. The free volume contribution is considered significant only for mixtures containing polymers and is equal to zero for liquid mixtures. The combinatorial activity coefficient contribution is calculated from the volume and surface area fractions of the molecule or polymer segment. The molecule structural parameters needed to do this are the van der Waals or hard core volumes and surface areas of the molecule relative to those of a standardized polyethylene methylene CH2 segment. UNIFAC for polymers (UNIFAC-FV) calculates in terms of activity (a,-) instead of the activity coefficient and uses weight fractions... 

COAL STRUCTURE PARAMETERS (weight fraction DMMF)... 

Structural parameters were obtained for the fractions of HVL-P using elemental composition, molecular weight and PMR data. 

Table V shows yields and structural parameters of SP-300 fractions. These fractions were black solid materials like the feed coal, as compared to dark-brown viscous liquids of the HVL-P fractions. The overall average molecular weight of SP-300 was more than three times that of HVL-P. SP-300 fractions have much larger R, RN and //cl than HVL-P fractions. The //cl values disclosed that there were, on the average, 2.8 aromatic clusters per molecule in SP-300, as compared to 1.1 aromatic clusters per molecule in HVL-P. Thus SP-300 fractions are high molecular weight materials,in which the degree of depolymerization is relatively low. This in turn suggests that SP-300 has retained more of the original structures of the parent coal than has HVL-P.

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