Intermittent growth model

This intermittent growth model was further elaborated [334-341], and ethylene polymerisation systems were devised to involve consecutive equilibria appearing to convert alkylaluminium halide and metallocene first into donor-acceptor complexes [scheme (61)] equivalent to contact (inner) ion pairs and then into separated (dissociated) ion pairs [scheme (62)] [297,338] ... 

Fig. 7 Left-. Reaction scheme of the successive equilibria for the formation of the polymerization active species C. Right. Intermittent growth model involving equilibria between polymerbearing, but inactive, primary complexes CP and active catalyst species C P ...

The funetions in the alkylaluminum aetivated metalloeene eatalyst systems have been deseribed by Reiehert and eoworkers [117 119]. The eoneeptualized point is that eaeh metal-polymer speeies appears to alternate between a dormant and aetive state in whieh the polymer ehain grows. This intermittent-growth model (Fig. 59) was further elaborated by Fink [120, 121] and Eiseh [122, 123] and their eoworkers in extensive kinetie and reaetivity studies (Fig. 59). Conseeutive equilibria appear to eonvert alkyl aluminum and (alkyl) metalloeene halides first into Lewis aeid-base adduets equivalent to an irmer (or contact) ion pair and then into a dissociated (or separated) ion pair. In these dynamic equilibria, only the cation of a separated ion pair appears to be capable of interacting with an olefin molecule and thus to dominate in these equilibria, and can then be termed dormant in this regard [124]. 

EIG. 59 Intermittent-growth model involving equilibria between polymer-bearing, but inactive, primary complexes (C-Pm) and active catalyst species (C -Pn), generated by excess alkyl aluminum halide. 

Two types of crack growth have been considered. One is intermittent, or stop-start crack growth, for which case the crack tip fields applicable to the static crack have been used to develop crack growth models.32 An example of intermittent crack growth in an alumina ceramic is shown in Fig. 10.3,46 and these results are supported also by work in glass-ceramics.8,47 The other mode of crack growth advance is continuous crack growth for which case the HR-fields are taken into account. 

Our results do not support the protein stress model. However, this model may apply in cases where stress is intermittent and results in tissue loss, as observed in the study of crows (Hobson and Clark 1992). Low protein levels throughout life after weaning may have produced overall slow and reduced rate of growth rather than tissue loss. Adult rats fed protein-deficient diets after maturation show systematic losses of nitrogen from most tissues that are in proportion to their turnover rates and masses (Uezu et al. 1983). Perhaps tissue nitrogen isotope enrichment may occur under these conditions. New experiments are needed to evaluate this hypothesis. 

The present model approach has combined three equations to predict the onset of cellular growth during freezing of natural waters (i) constitutional supercooling from morphological stability theory, (ii) an exact diffusive solute redistribution and (iii) an intermittent turbulent solutal convection model. The main results are ... 

The problems encountered in mathematical modeling of tumble/growth agglomeration do not relate to the theories, formulas, and possibilities to solve the ever more complicated equations. With modem computing possibilities, a whole series of assumptions can be introduced into the model equations and responses to certain imaginary process conditions can be predicted. However, the real system often produces unexpected results intermittently or even consistently without offering a clear indication of why such deviations occur. Introduction of new mathematical methods, such as, for example, fuzzy logic or chaos theory, produce more complicated model equations and closer to life results but still are not able to serve as unequivocal bases for control schemes. 

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