Zero growth rate temperature

Figure 2 s-PP and s-P(P-co-0) Relations between the inverse crystallite thickness, the crystallization temperature and the melting peak. The dashed line represents the 2/(< r )-dependence of a perfect s-PP as obtained by an extrapolation procedure. The arrows indicate the limiting temperatures with zero growth rate. 

Sorrentino, A., Pantani, R., Titomanlio, G. Melting and zero growth rate temperatures of syndiotactic polystryrene. Colloid Polym. ScL, 286(8-9), 983-991 (2008). 

When microorganisms use an organic compound as a sole carbon source, their specific growth rate is a function of chemical concentration and can be described by the Monod kinetic equation. This equation includes a number of empirical constants that depend on the characteristics of the microbes, pH, temperature, and nutrients.54 Depending on the relationship between substrate concentration and rate of bacterial growth, the Monod equation can be reduced to forms in which the rate of degradation is zero order with substrate concentration and first order with cell concentration, or second order with concentration and cell concentration.144... 

Those field studies that include water samples collected during winter months all show undetectable tamarensis concentrations (5, 18, 21). Given the relatively small volumes of water typically collected and counted, this does not preclude the presence of a few cells (the "hidden flora"), but it does indicate that motile populations are extremely small at best. Furthermore, since the growth rate of tamarensis is essentially zero at very low temperatures, the appearance of even a few hundred cells in early spring when waters are still very cold suggests that it is excystment and not division of surviving motile cells that initiates the bloom development. 

Figure 4-6 Interface reaction rate as a function of temperature, pressure, and composition. The vertical dashed line indicates the equilibrium condition (growth rate is zero), (a) Diopside growth and melting in its own melt as a function of temperature with the following parameters Te= 1664K at 0.1 MPa, A5m-c = 82.76J mol K , E/R —30000 K, 4 = 12.8 ms K, and AV c l. l x 10 m /mol. The dots are experimental data on diopside melting (Kuo and Kirkpatrick, 1985). (b) Diopside growth and melting in its own melt as a function of pressure at 1810 K (Tg = 1810 K at 1 GPa from the equilibrium temperature at 0.1 MPa and the Clapeyron slope for diopside). (c) Calcite growth and dissolution rate in water at 25 °C as a function of Ca " and CO concentrations.

Consider recrystallization and grain growth in an infinite thin sheet. Assume that the nucleation rate of recrystallized grains is a linear function of temperature above a critical temperature, Tc, and the nucleation rate is zero for T grain-growth rate, R, is constant and independent of temperature. Suppose that at time t = 0 the sheet is heated at the constant rate T(t) = Tc/2 + /3t. Using Poisson statistics, the probability that exactly zero events occur in a time t is p0 = exp(— Nc))-... 

In the case of some metals such as magnesium below a temperature of 200°C, a thin oxide layer is formed, which resists diffusion of oxygen and as a result an initial formation of oxide is followed by practically zero growth of the oxide. The rate law governing this type of oxide growth is logarithmic.75... 

The carbon atoms arriving at the substrate surface must exceed a certain concentration at the solid-gas interface to reach and exceed the critical nucleus size. Therefore the diamond nucleation density as well as the growth rate are dependent on the relative rates of bulk and surface diffusion of carbon atoms. ° These are different for different substrates. Thus, the nucleation process needs a temperature dependent incubation time which is related to the time required to form critical size diamond clusters on the substrate surface. The nucleation rate, which is initially negligible, reaches a maximum after a certain time period and tends to zero for longer deposition times. ... 

Historically, before the mid-19 " century, the methane concentration was approximately constant at about 0.75 ppm, but it has risen continually since then and had reached almost 1.75 ppm by 1994. In the 1970s, the rate of increase was twice as much as that in the 1980s, and in the early 1990s it temporarily became almost zero. It is not known with certainty why the growth rate decreased and has fluctuated recently, though some scientists have speculated that it is related to the air temperature decreases associated with the explosion of Mt. Pinatubo in the Philippines (Baird, 1999). 

Consider a system where the sintering occurs by gas phase transport. Explain in detail the change in neck growth rate (dx/dt) with sintering temperature by the evaporation/condensation mechanism in vacuum sintering. Draw schematically and explain the change in neck radius with external Ar gas pressure (from zero to several thousand atm) for the same temperature and the same period of time (log x versus log PAr)-... 

Experimental data on melt crystallization are summarized in Fig. 3.67 in form of the linear crystal growth rate, v. All linear crystal growth rates go exponentially to zero when the temperature approaches the melting temperature, pointing to a nucleation which is similar as developed in the Figs. 3.51-61. These experiments, thus, provide strong evidence that some kind of secondary nucleation must be found to account for the crystal growth of macromolecules [27]. 

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