Growth rate equations of lamellar polymer crystals

2018 ◽  
Vol 1 (4) ◽  
Author(s):  
Wenbing Hu
Keyword(s):  
Growth Rate ◽  
Rate Equations ◽  
Polymer Crystals

A polycentric growth model of gallium arsenide epitaxial layers from the gas phase with simultaneous diffusion, adsorption and chemical reaction

1988 ◽  
Vol 53 (12) ◽  
pp. 2995-3013
Author(s):  
Emerich Erdös ◽  
Jindřich Leitner ◽  
Petr Voňka ◽  
Josef Stejskal ◽  
Přemysl Klíma
Keyword(s):  
Growth Rate ◽  
Gallium Arsenide ◽  
Epitaxial Growth ◽  
Gas Phase ◽  
Surface Reaction ◽  
Quantitative Description ◽  
The Other ◽  
Rate Equations ◽  
Impact Interaction ◽  
Partial Pressures

For a quantitative description of the epitaxial growth rate of gallium arsenide, two models are proposed including two rate controlling steps, namely the diffusion of components in the gas phase and the surface reaction. In the models considered, the surface reaction involves a reaction triple - or quadruple centre. In both models three mechanisms are considered which differ one from the other by different adsorption - and impact interaction of reacting particles. In every of the six cases, the pertinent rate equations were derived, and the models have been confronted with the experimentally found dependences of the growth rate on partial pressures of components in the feed. The results are discussed with regard to the plausibility of individual mechanisms and of both models, and also with respect to their applicability and the direction of further investigations.

Analyzing growth in cell cultures. I. Calculating growth rates

1986 ◽  
Vol 64 (1) ◽  
pp. 233-237 ◽  
Author(s):  
Susan R. Singer
Keyword(s):  
Growth Rate ◽  
Relative Growth Rate ◽  
Growth Rates ◽  
Rate Equations ◽  
Constant Growth Rate ◽  
Relative Growth ◽  
Relative Growth Rates ◽  
Growing Cell ◽  
Absolute Growth ◽  
Plant Tissue Cultures

Growth is the major parameter used to assess novel phenotypes derived from plant tissue cultures. Any quantitative analysis of growth must have an explicit rational basis. Frequently this criterion is not met. For example, the calculation (W2 − W1)/W1(W1 = initial weight; W2 = final weight) approximates neither linear nor exponential growth. Yet, it is a common method of analysis, as is the related calculation W2/W1. When absolute growth values provide insufficient information, meaningful relative growth rate equations can be utilized. Relative growth rates should be evaluated as ln (W2/W1)/(t2 − t1) for t = time, thereby yielding a constant growth rate for exponentially growing cell lines. Linear growth (root growth, for example) can be approximated by 2(W2 − W1)/((W1 + W2)(t2 − t1)). All methods of analysis we have encountered assume that relative growth at a given instant depends on total mass. The possibility exists that growth may actually be proportional to mass raised to some power less than one. For example, growth could be limited to a thin outer shell of a spherical callus. Then the relative growth rate would equal 3(W21/3 − W11/3)/(t2 − t1). Data can be seriously distorted when inappropriate calculations are used. Such distortions are exacerbated when comparisons are made. In all cases an adequate assessment of growth kinetics for each cell line and each treatment is essential.

A quantitative model of epitaxial layers growth from the gas phase with a simultaneous participation of diffusion, adsorption, and chemical reaction

1986 ◽  
Vol 51 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Emerich Erdös ◽  
Jiří Laitner ◽  
Josef Stejskal ◽  
Přemysl Klíma
Keyword(s):  
Growth Rate ◽  
Gas Phase ◽  
Epitaxial Layer ◽  
Chemical Nature ◽  
Quantitative Description ◽  
Physical Nature ◽  
Rate Equations ◽  
Layer Surface ◽  
Active Centre ◽  
Rate Controlling Step

For a quantitative description of the epitaxial growth rate of gallium arsenide, a model has been proposed including two rate controlling steps, namely one step of physical nature and the other one of chemical nature. As the step of physical nature, the diffusion of gaseous components between the gas phase and the epitaxial layer surface has been considered, and from the steps of chemical nature the adsorption of gaseous components on the epitaxial layer surface and a heterogenous surface reaction have been taken into account. According to the kind of the chemical rate controlling step, five mechanisms have been proposed, where a one - centre model was used in all cases, i.e. the idea that the rate controlling step takes place under participation of one active centre. For all the mechanisms considered, the pertaining rate equations have been derived, which were confronted with the experimentally found dependences of the growth rate on partial pressures of components in the feed. The results are discussed both from the view point of plausibility of individual mechanisms and from the point of view of their applicability and of the next research direction.

Evaluation of topology-dependent growth rate equations of three-dimensional grains using realistic microstructure simulations

2018 ◽  
Vol 6 (2) ◽  
pp. 026523
Author(s):  
Asad Ullah ◽  
Musarat Shaheen ◽  
Asad Khan ◽  
Matiullah Khan ◽  
Khalid Iqbal
Keyword(s):  
Growth Rate ◽  
Three Dimensional ◽  
Rate Equations ◽  
Dependent Growth

Cavity Growth Simulation in 2.25Cr–1Mo Steel Under Creep-Fatigue Loading

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Takashi Ogata
Keyword(s):  
Growth Rate ◽  
Grain Boundaries ◽  
Cavity Growth ◽  
Fatigue Loading ◽  
Growth Behavior ◽  
Rate Equations ◽  
Modified Model ◽  
Growth Simulation ◽  
Creep Fatigue ◽  
Cavity Growth Rate

High temperature components in thermal power plants are subjected to creep-fatigue loading where creep cavities initiate and grow on grain boundaries. Development of a quantitative evaluation method of cavity growth is important for reliable maintenance of these components. In this study, a creep-fatigue test was carried out at 600°C on 2.25Cr–1Mo steel in a scanning electron microscope, and continuous observation of cavity growth behavior during the test was made. Based on the cavity growth observation, existing cavity growth models were modified and the simulated results using the modified model were compared to the observed cavity growth behavior. From the observation, spherical shape cavities initiate and grow up to their length of 2μm on the grain boundaries at the initial stage of damage, and then these cavities change their shape to cracklike and grow until their length reaches around 10μm. Finally, cracklike cavities coalesce with each other to form one microcrack along a grain boundary. It can be concluded that cavity growth rates are controlled by diffusion and power law creep under constrained conditions, based on the theoretical consideration of cavity growth mechanism. Through these discussions, a new cavity growth model was proposed by modifying conventional models. Both spherical and cracklike cavity growth rate equations were derived from the modified cavity growth model. It was indicated that the measured cavity growth rate was well predicted by the growth rate equations, derived from the modified model, and a cavity growth simulation result corresponds to the change in the maximum cavity size with number of cycles under the creep-fatigue loading.

Treatment of Pulping Wastewater by Aerobic Granular Sludge Reinforceed with Mixed-Culture Community

2013 ◽  
Vol 807-809 ◽  
pp. 1135-1139
Author(s):  
Hong Lei Chen ◽  
Gui Hua Yang ◽  
Jia Chuan Chen ◽  
Qin Wu ◽  
Yu Liu
Keyword(s):  
Growth Rate ◽  
Reaction Kinetics ◽  
Mixed Culture ◽  
Granular Sludge ◽  
Aerobic Granular Sludge ◽  
Rate Equations ◽  
Microbial Process ◽  
Spectral Signal ◽  
Kinetics Of ◽  
Aerobic Sludge

Pulping wastewater was further degraded with original aerobic sludge and reinforced aerobic sludge, respectively. The results showed that the UV-vis spectral signal of wastewater treated by reinforced sludge was more weaker than that of treated by original sludge, which indicated biodegrability of aerobic sludge was optimized after reinforcement. For original sludge, COD of wastewater was decreased from 629 mg/L to 203 mg/L, and chroma decreased from 118 C.U. to 91 C.U. COD of wastewater which treated by reinforced sludge was reduced to 146 mg/L, and chroma dropped to 72 C.U. Meanwhile, the reaction kinetics of aerobic microbial process was studied, and the growth rate equations of two kinds of sludge were established. Keywords: pulping wastewater; aerobic sludge; kinetics; bioaugmentation

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