Tung distribution

The Tung distribution was found empirically. It gives the differential mass distribution of the degrees of polymerization as... 

Important differential mass-distribution functions (probability density function of mass-distribution) are the most probable distribution (Schulz-Flory), the Schulz-Zimm distribution, the Poisson distribution, Tung distribution, and logarithmic normal distribution (Wesslau distribution) [08IUP2]. Methods for the determination of distribution functions of molar mass are listed in Table 4.1.4. 

Tung, L. H., Method of calculating molecular-weight-distribution functions from gel permeation chromatogram, /. Appl. Polym. Sci., 10, 375, 1966. 

Figure 27. Radial Voidage Distribution for FCC Catalyst in a 90 mm i.d. column, 2.25 m above gas distributor (curves computed, points experimental) (Tung, Li andKwauk, 1988).

Tung, Y., Li, J., Zhang, J., and Kwauk, M., Preliminary Experiments on Radial Voidage Distribution in Fast Fluidization, Fourth Nat. Conf. Fluidization, Lanzhou, China (1987)... 

Tung (106) has proposed the combination of sedimentation constant data with those from GPC, so as to obtain a distribution of branching, without fractionation being required. 

Tung,L.H., Runyon,J.R. Molecular weight distribution of standard polystyrene samples by GPC and by sedimentation velocity analysis. J. Appl. Polymer Sci. 17, 1589-1596 (1973). 

This large family is cosmopolitan except for arctic areas, with centers of distribution in tropical America and Africa. It is of major economic importance as the source of rubber, tung and castor oils, a basic food crop (manihot, native to South America and introduced into Africa and southeast Asia), and familiar ornamentals (croton, poinsellia). 

Fractionation Data and Distribution Analysis of HEC After One Hour of Cellulase Attack. The results of the gel chromatographic separation of HEC after one hour of enzymic hydrolysis are given in Table II. These fractionation data did not correspond to any of the distribution functions mentioned by Peebles (41) and by Tung (42). In the middle of the distribution it corresponded to the Lansing-Kraemer distribution functions, but deviations occurred at the low- and high-molecular-weight ends. 

Heat transfer in micrombes with viscous dissipation is investigated by Tung and Bayazitoglu [15]. The temperature jump, is ignored in the calculation of the temperature distribution, but taken into account in determination of the Nusselt number. 

The broadness of the distribution is given by the parameter j, obtained from the slope (tan 0) of the log-normal plot where tan d = 7A/2. The polydispersity ratio (Af /Afp = exp(7 /2) no and x are constants in the distribution function not determinable from the log-normal line. (Special cases of the general distribution function have also been employed, e.g., the Lansing and Kraemer relationship where x = 0 [304] and the Wesslau relationship [305], where x = —1). Fractionation data can also be adequately represented by other exponential distributions such as that of Tung [306] W(n) dn = abn exp(—an ) dn. (W(n) = 1 — exp(—an )). Fig. 14a(c). 

Tung, L. H. Molecular weight-intrinsic viscosity relationship and molecular weight distribution of low pressure polyethylenes. J. Polymer Sci. 24, 333 (1957). 

The relation between W and Ws, the domain wall widths in the bulk and at the surface, can be seen in Figure 8. The effect of the surface relaxation is clearly visible as the order parameter at the surface Qs never reaches the bulk value Qo- The distribution of the square of the order parameter at the surface shows the structure that some of the related experimental works have been reported (Tsunekawa et al. 1995, Tung Hsu and Cowley 1994), namely a groove centred at the twin domain wall with two ridges, one on each side. 

Wesslau [3] and Tung [4]). Often these simple models do not describe adequately the measured distribution of Commerical polymers. Theoretical derivations for the blending of two components with known distributions have been reported 15]. These studies concentrated on the effect of the parameters on the MWD of the blend. 

Calcium(II), which shows no appreciable complexing, has a distribution coefficient of 147 in 0.5 M perchloric acid and 191 in 0.5 M hydrochloric acid. Strelow. Rethc-meyer, and Bothnia [10] also reported data for nitric and sulfuric acids that showed complexation in some cases. Mercury(II), bismuth(III), cadmium(II), zinc(II), and lead(II) form bromide complexes and are eluted in the order given in 0.1 to 0.6 M hydrobromic acid [11]. Most other metal cations remain on the column. Aluminu-m(III), molybdenum(VI), niobium(V), tin(IV), tantalum(V), uranium(VI), tung-sten(VI), and zirconium(IV) form anionic fluoride complexes and are quickly eluted from a hydrogen-form cation-exchange column with 0.1 to 0.2 M HF [12]. 

Table 3 Fatty acid distribution of tung biodiesel.

Fjo 5 4 Hardness distribution in 2024 Al for both gas tung- sten arc welding (GTAW) and friction stir welding (FSW). Source Ref 1... 

Maurice, D.V., Lightsey, S.F., Kuo-Tung, H. Rhoades, J.F. (1991). Comparison of glutathione Stransferase activity in the rat and birds tissue distribution and rhythmicity in chicken (Callus domesticus) liver. Comp, Biochem. Physiol, lOOB, 471-4. 

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