Secondary growth equations

Equations 4 to 6. Initially, tip growth occurs, yielding fibers with a tubular structure and diameters comparable to those of the catalyst particles (<15 nm). Subsequent side growth adds multiple secondary growth rings and increases the diameter [7], The iron particles become encapsulated in the fiber tips after thickening. 

Variation of Shape Factor. Three typical variations In the shape factor of MgSOi 71120 crystal are shown In Figure 1. The factors show the results obtained from three experiments of crystal growth In the solution without gas admittance at a supersaturation degree (AC) of 1.78 kg m , and a temperature of 298.2 K. In this solution, secondary nuclei(4) were hardly found. The curves connecting the points In the figure were determined by Fourier series equations to... 

Equation (6) predicts a logarithmic growth of the concentration of defects without any saturation. To obtain the saturation effect, which has been experimentally observed by the authors themselves [17], a hypothetical secondary reaction was introduced. The defects of this model were discussed earlier, while we note only that in the initial stage the relationship (6) qualitatively resemble the previous ones. This also has been used in interpreting... 

The isotherms obtained in dilatometric measurements of the crystallization rate could be fitted with an Avrami (3) type equation only by assuming the existence of a secondary crystallization process much slower than the rate of spherulitic growth observed microscopically, and by taking into account the experimentally determined form of the nucleation rate. The nucleation rate was found to be a first-order process. Assuming that the secondary crystalliza-... 

We ve mentioned that the thickness, f, of the secondary nucleus must be bigger than /V if it is to be stable to further growth say by an amount (5/, therefore using Equation 10-36 we can write (Equation 10-40) ... 

For now, let s just focus on the secondary nucleation part of the equation for the growth rate (Equation 10-43) ... 

Because there is no growth during the stationary phase, it is clear that Equation (7-112) caimotbe used to account for substrate consumption, nor can the rate of product formation be related to the growth rate [e.g.. Equation (7-113)], Many antibiotics, such as peniciUin, are produced in the st onary phase. In this phase, the nutrient consumed for growth has tecome vulually exhausted and a different nutrient, called the secondary nutrients, is used for cell maintenance and to produce the desired product. Usually, the rate law for product formation during the stationary phase is similar in form to the Monad equation, that is,... 

Similarly, any compound consuming the acyllactam growth centres (e.g. primary and secondary amine [162, 170]) decreases the rate of polymerization. So far, the rate coefficients 21 of the addition of the first lactam anion to the growth centre have been estimated only for a few monomers. In most cases, however, the published rate coefficients were calculated from the second order rate equation... 

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