Growth Rate Determination

AFM is now utilized to relate microscopic measurement of step velocity to macroscopic face growth rates (Malkin et al. 1996). Such data can be collected at a very rapid rate but does require some familiarity with the technique and access to a research caliber AFM. Likewise, microcalorimetry may be utilized to extract crystal growth rates at a very rapid rate, provided the protein s heat of crystallization is sufficient to yield a measurable signal (Darcy and Wiencek, 1998). Both of these techniques can provide growth rates over a wide range of conditions within days, as opposed to months by more traditional video microscopy techniques. 

---

In addition to induction time measurements, several other methods have been proposed for determination of bulk crystallization kinetics since they are often considered appropriate for design purposes, either growth and nucleation separately or simultaneously, from both batch and continuous crystallization. Additionally, Mullin (2001) also describes methods for single crystal growth rate determination. 

The overall linear growth rate determined from these data is given by the following empirieal expression (Jones and Mydlarz, 1989)... 

The formation of a complex between the propagating end and one or more molecules of monomer can have two extreme consequences. If the incorporation of a monomer molecule from the solvation shell of the cation is the growth-rate determining step, the propagation becomes a unimolecular reaction and the rate of polymerisation becomes of zero order with respect to monomer concentration. Such a model was developed by... 

Rapid gelation Growth rate determining process... 

In this expression, i is current density, p is density, n is the number of electron equivalents per mole of dissolved metal, M is the atomic weight of the metal, F is Faraday s constant, r is pit radius, and t is time. The advantage of this technique is that a direct determination of the dissolution kinetics is obtained. A direct determination of this type is not possible by electrochemical methods, in which the current recorded is a net current representing the difference between the anodic and the cathodic reaction rates. In fact, a comparison of this nonelectrochemical growth rate determination with a comparable electrochemical growth rate determination shows that the partial cathodic current due to proton reduction in a growing pit in A1 is about 15% of the total anodic current (26). 

The concentration of A ions available for growth may be calculated using eqns. (149) and (146). Similarly, the concentration of B ions may be calculated and the growth rate determined from the product [A][B], i.e. 

It is well known that anthropogenic radionuclides such as radiocaesium and plutonium together with natural Pb are accumulated in sediments and can be used for the dating/growth rate determination of the sediments. The flux of these radionuclides depends on factors, such as physical and chemical properties, biological factors etc,. Water dams along rivers will stop the water flow and might act as effective traps by sedimentation processes and accumulate material that otherwise would be transported to the sea. 

For most aerobic fermentation processes, maintenance of absolute sterility is critical to cell growth and biomass production. Culture growth rate determines susceptibility to culture contamination. Mammalian cells divide in a day, while microbials divide in an hour or less. The difference in growth rate makes slower-growing mammalian cell cultures more susceptible... 

Kadko, D. and Burckle, L.H., 1980. Manganese growth rates determined by fossil diatom dating. Nature, 287 725-726. 

Ang, H-M. and Mullin, J.W. (1979) Crystal growth rate determinations from desupersaturation measurements nickel ammonium sulphate hexahydrate. Transactions of the Institution of Chemical Engineers, 57, 237-242. 

Garside, J., Mullin, J.W. and Das, S.N. (1973) Importance of crystal shape in crystal growth rate determinations. Industrial and Engineering Chemistry Process Design and Development, 12, 369-371. 

Fig. 1. Growth rate ( ) and turgor pressure ( ) changes with respect to meristem temperature for 3-leaf slender (sin/sin) and wild-type seedlings. Growth rates determined using high-resolution displacement transducers connected to emerging leaves and turgor pressures measured by pressure probe for individual meristem cells. Bars indicate SEM...

Table 19.20. Result of the pure mode with [19.EC. 1] as growth rate-determining step...

---