Chiens Model

Chien s kinetic model (Chien and Wang, 1990 Chien and Sugimito, 1991), unlike Ewen s model described above is for the systems in which more than one active species is present. The model assumes the presence of different types of active center, chain transfer to MAO, chain transfer by jS-H elimination (see p. 578), and first-order deactivation reactions for active centers. Chien applied the model in the study of ethylene polymerization with Cp2ZrCl2/MAO catalyst and propylene polymerization with Et(Ind)2ZrCl2/MAO and Et(H4lnd)2ZrCl2/MAO catalysts. 

For a system with i types of active centers, the polymerization rate of the /th species is 

Assuming that the catalytic species deactivate according to first order kinetics, the total productivity at time t is 

The value of [C ]o can be taken to be equal to the initial metal-polymer bond concentration, [MPB]o- The metal-polymer bond concentration at time t, [MPB]f, 

T total polymer C5 -pentane soluble, Ce n-hexane soluble, C7 n-heptane soluble, E ether soluble fractions. 

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Chien, K. Y. Predictions of channel and boundary layer flows with a low-Reynolds-nuraber turbulence model. AIAA J., vol, 20, pp. 33-18, 1982. 

As written. Equation 19 Implies a simultaneous loss of two sites of the same type. On a heterogeneous catalyst this is only realistic for adjacent sites, as has recently been suggested by Chien (15). Equation 19 assumes adjacent sites are the same species, which appears consistent with active site structural models appearing in the literature (17-18). Performing the same... 

Chen, B.H., Chen, T.M., and Chien, J.T., Kinetic model for studying the isomerization of a- and (3-carotene during heating and illumination, J. Agric. Food Chem., 42, 2391, 1994. 

Lin, Wen-Shan, Chien-Hsiung Lee, and Bao-Shei Pei, 1989, An Improved Theoretical CHF Model for Low-Quality Flow, Nuclear Technol. 55 294-306. (5)... 

Cheng, HC, Chien, H, Liao, CF1, Yang, YY, and Huang, SY, 2007. Carotenoids suppress proliferating cell nuclear antigen and cyclin D1 expression in oral carcinogenic models. JNutr Biochem 18, 667-675. 

Cells R, Cox L, Hermosin MC, Cornejo J (1996) Retention of metamitron by model and natural particulate matter. Intern J Environ Anal Chem 65 245-260 Chaney RL (1989) Toxic element accumulation in soils and crops protecting soil fertility and agricultural food chains. In Bar Yosef B, Barrow NJ, Goldschmid J (eds) Inorganic contaminants in the vadose zone Springer, Heidelberg, pp 140-159 Charlatchka R, Cambier P (2000) Influence of reducing conditions on solubility of trace metals in contaminated soils. Water, Air Soil PoUut 118 143-167 Chien SH, Clyton WR (1980) Application of Elovich equation to the kinetics of phosphate release and sorption in soils. Soil Sci Am J 44 265-268... 

Kuhl, A. L., R. E. Ferguson, K. Y. Chien, J. P. Collins, and A. K. Oppenheim. 1995. Gasdynamic model of turbulent combustion in an explosion. Combustion, Detonation, Shock Waves. Zel davich Memorial Proceedings. Eds. A. G. Merzhanov and... 

Chien C-B (2010) Morphofino tips, Chien lab, in Zebrafish Model Organism Database (ZFIN), available at https //wiki.zfin.org/dis-play/prot/Morpholino-rtips%2C-rChien-rlab. Accessed 04 Feb 2012... 

The diffusion behaviour of Shirakawa polyacetylene is complicated by its fibrillar morphology and high surface area, so that weight changes depend on pore transport and surface adsorption, as well as on diffusion into the fibrils. Chien 6) has reviewed earlier studies of the diffusion of dopant counter-ions in Shirakawa polymer and has emphasised the wide range of values of diffusion coefficient which are reported and which depend a great deal upon the morphological model chosen to interpret experimental data. 

Huang, Y., Rumschitzki, D., Chien, S. and Weinbaum, S. (1997) A fiber matrix model for the filtration through fenestral pores in a compressible arterial intima. Am. J. Physiol, 272, H2023-H2039. 

Thermo-physical property models taken from Sanderson and Chien (29). 

Note Sanderson and Chien (22) reported 10 outside loop iterations using their conventional algorithm for the same system at the same pressure, but with T specified as 358 K. The number of inside loop iterations was not given. It is notable that each inside loop iteration of their algorithm requires that properties be calculated using the actual thermo-physical property models. 

OH. This model may help to explain the relatively high concentration of 7-keto compared to other OS products present in many food products. Chien et al. (1998) also observed that the epoxides were formed in the greatest amount and increased linearly over the heating period of the kinetic study. They concluded that differences in the heat treatment of cholesterol may greatly affect the formation and degradation rates of 7-OOH. 

J. Y. Chien, S. Eriedrich, M. A. Heathman, D. P. de Alwis, and V. Sinha, Pharma-cokinetics/pharmacodynamics and the stages of drug development Role of modeling and simulation, AAPS J. 7 (2005), E544-E559. 

Yet Chien demostrated that it would be possible to obtain polyethylene with a Q value near the theoretical 2, with the homogeneous (CjH5)2TiCl2—A1(CH3)2C1 catalytic system, only if carefully controlled pseudosteady-state conditions are employed. In fact he showed mathematically that the relatively high experimental polydispersiiy (<,) tfom 2 to 5 in function of reaction time), is a natural consequence of a polymerization kinetic model based on non stationary first order initiation, chain propagation and bimolecular chain termination by recombination. 

Such a different conclusion can be understood by considering the difficulties connected to the experimental determination and the definition of Thiele modulus parameters, such as So and D. According to Chien, S means the catalyst primary particle size with a value of about 10 cm for a-TiCIj instead, in the Multigrain model, Sp seems to correspond to the size of the whole catalyst granule. 

Chien S (2007) Ischemic rabbit ear model created by minimally invasive surgery. Wound Repair Regen 15 928-935... 

In the chain-of-rotators (COR) equation proposed by Chien, Greenkom, and Chao [17], a chain molecule is modeled as joined spheres in which adjacent covalent bonds can rotate. Rotation takes place because the chain is not straight any two adjacent bonds are joined at an angle like the radials from the center of a pyramid to the four comers. Chien et al. found the pressure of rotation by comparing the pressure of Boublik and Nezbeda s hard dumbbell fluid [18] with the pressure of Carnahan and Starling s hard spheres. The rotational pressure found is... 

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