K parameter

Some suggested values of the h and k parameters are shown in Table 7.4. 

System Reference Temperature Range(K) Parameters Values Using EoS... 

The rate constants in the reactions (29) may be conveniently envisaged as elements of symmetric matrix k. In order to calculate the statistical characteristics of a particular polycondensation process along with matrix k parameters should be specified which characterize the functionality of monomers and their stoichiometry. To this end it is necessary to indicate the matrix f whose element fia equals the number of groups A in an a-th type monomer as well as the vector v with components Vj,... va,..., v which are equal to molar fractions of monomers M1,...,Ma,...,M in the initial mixture. The general theory of polycondensation described by the ideal model was developed more than twenty years ago [2]. Below the key results of this theory are presented. 

The values obtained at the convergence for k, Pval parameters and the atomic net charges are reported in Table 5. In these two refinements, the k parameters are... 

On the carbons, nitrogens and oxygens expansions up to octapole level were introduced, whereas the expansions were limited to quadrupole level for the hydrogen atoms. All atoms were given a k expansion/contraction parameter for the spherical monopole term, and all atoms except the hydrogens were given k parameters to expand or contract the non-spherical poles. The k and k values on 0(1) and 0(3), on N(l) and N(3), on C(l) and C(3) and on 0(21) and 0(22) were constrained to be equal. 

These minimums reflect the fact of an acquisition of excess electron charge by the fluorine atoms in the crystal and their existence is a consequence of a specific dependence ESP of negative charged atom on the distance (Fig.8). The reliability of existence of two-dimensional minimums in crystals is confirmed by direct calculations of the ESP by the Hartree-Fock method. An analysis shows the more negative charge of isolated ions (deeper negative minimum of potential). At the same time the minimum position shifts to the nucleus. The K-parameter influences the characteristics of the minima only marginally. 

Kawamoto, K. and Urano, K. Parameters for predicting fate of organochlorine pesticides in the environment (I) octanol-water and air-water partition coefficients, Chemosphere, 18(9/10) 1987-1996, 1989. 

The atomic dipole moment is dependent on eight variables the net charge of the atom, derived from Pvab the k parameter, the atomic coordinates, and the three population parameters P10, P11 + and Pu. If we are interested in the error in the magnitude of the molecular dipole moment /r,otal, and we omit columns of D which contain only zero s, D will be a 1 x 8N matrix, where N is the number of... 

To reduce the effect of extinction and to eliminate possible correlation between the charge density and extinction parameters, the six strongest reflections were eliminated from the refinement. Because the 3s shell of Na is barely populated, its k parameter cannot be refined separately in such a refinement. In the NaF study, this problem was circumvented by assignment of a common k value to the L and M shells of Na. 

Marathe and Trautwein (1983) quote values of 5.09 and 5.73 au-3 from Hartree-Fock calculations on Fe2+ (3d6) and Fe3+ (3d5), respectively, showing that the radial contraction (i.e., the k parameter in the diffraction formalism) has a pronounced effect on the 3(J values. 

In subsequent work by the same authors, non-neutrality of the standard atoms was allowed by addition of a transferable PD valence-shell monopole population, with neutrality being maintained by a slight adjustment of the hydrogen charges, and k parameters refined after the transfer (Pichon-Pesme et al. 1995b). 

The general strategy of equating parameters to statistics is of course not restricted to moments. Reliance on sample percentiles (e.g., sample median) can lead to estimators that are not excessively sensitive to outliers. In general, to fit a distribution with k parameters, k parameters must be equated to distinct sample statistics. 

Excitation spectra of Mn " enable us to calculate the crystal field force A and Raka parameters B and C. The relative position of the ground level Aig (S) and excited levels 4Eg G) and Eg(D) does not depend on A. Using the frequencies of electronic transitions from the ground level to those excited levels (ks and k ), parameters B and C may be calculated based on formulas ... 

Fig. 4.3. The ft-K parameter plane showing loci of changes in local stability or character for the model with the exponential approximation (a) full plane (b) enlargement of region near origin showing, in particular, the locus of Hopf bifurcation (change from stable to unstable focus) and the locus corresponding to the maximum in the ass(/r) curves (broken line).

Fig. 4.8. The h k parameter plane showing changes in local stability and character for y = 0.1 (a) full parameter plane (b) enlargement for small /r and k showing locus of Hopf bifurcation (transition from stable to unstable focus and (as broken lines) the loci for the maximum and...

Fig.. 10.13. The regions of stability of different spatial forms in the pi-K parameter plane for...

Use QRRK theory to calculate kan as a function of pressure for the decomposition of azomethane at T = 563 and 603 K. Parameters needed for the calculation are given in Section 10.4.4, in the discussion of Fig. 10.7. Plot calculated rate constant in units of 1/s versus pressure (in atm) include in the same plot a comparison with experimental data of Ramsperger [326], which can be found in the data file azomethanedata.csv. 

Electron transfer kinetics from the triplet excited state of TMPD to PA in polystyrene has been monitored by phosphorescence emission decay in ref. 85. The rate constant has been found to be invariant over the temperature interval 77-143 K. Parameters ae and ve calculated from the phosphorescence decay using eqn. (12) were found to be ae = 3.46 A and vc = 104 s 1. 

Unfortunately another factor complicates the measurement of true crystallite size. The K parameter is also a function of both crystallite size and of lattice distortion. We recently studied the effect of crystallite size and distortion on the K parameter using optical transform methods with simulated lattice images drawn by a computational method (26). The Scherrer K parameters given in Table X may be used to obtain a true number average crystallite size by any of the methods quoted, but will only be valid for crystallites with a number average size in the range 8 to 15 layer planes and a lattice distortion of 4-6%. The mixed function method (3) appears to give the best estimate of true crystallite size (K = 1.0) and the Hosemann method (4) the best estimate of lattice distortion. 

Nylon Fibers. Table VI shows that PA 66 fibers are different, that heat treatments of 2 seconds at 220°C, with shrinkage allowed, do not modify the crystallinity. Such modification requires annealing for 3 minutes, with shrinkage allowed. The real crystallinity of PA 66 fibers is higher than that of PET fibers, but in contrast with results obtained with PET fibers, heat treatments decrease the k parameter. 

Thence next-nearest neighbor exchange interactions appear, as well as modifications to the nearest-neighbor interactions. Additional structure-dependent modifications to the nearest-neighbor interactions occur if the e(i x j) and e(y x k) parameters are distinguished. Such modifications we pass over here and use simply a second-order nearest-neighbor interaction parameter... 

---