Kinetics depolymerization

This theory clearly predicts that the shape of the polymer length distribution curve determines the shape of the time course of depolymerization. For example Kristofferson et al. (1980) were able to show that apparent first-order depolymerization kinetics arise from length distributions which are nearly exponential. It should also be noted that the above theory helps one to gain a better feeling for the time course of cytoskeleton or mitotic apparatus disassembly upon cooling cells to temperatures which destabilize microtubules and effect unidirectional depolymerization. Likewise, the linear depolymerization kinetic model could be applied to the disassembly of bacterial flagella, muscle and nonmuscle F-actin, tobacco mosaic virus, hemoglobin S fibers, and other linear polymers to elucidate important rate parameters and to test the sufficiency of the end-wise depolymerization assumption in such cases. 

Figure 1. Mixing device for microtubule depolymerization kinetic studies requiring prompt dilution while minimizing shearing forces that may alter the polymer length distribution.

A typical fit of the theoretical depolymerization kinetics to the experimentally determined rate behavior for dilution-induced depolymerization is illustrated in Fig. 2... 

The generality of the end-wise depolymerization kinetic model is indicated by the comparison of the observed and predicted time-courses of cold-induced microtubule disassembly (Fig. 3). See Self-Assembly Protein Polymerization... 

Modification of depolymerization kinetics and release Endosomal escape Nonviral gene delivery Boron neutron capture therapy Fusogenic liposomes, increase transfection efficiency... 

Boyd, R. H. Theoretical depolymerization kinetics in polymers having an initial most probable molecular weight distribution. Journal of Chemical Physics 1959 31 321. 

The simulation of lignin liquefaction combined a stochastic interpretation of depolymerization kinetics with models for catalyst deactivation and polymer diffusion. The stochastic model was based on discrete mathematics, which allowed the transformations of a system between its discrete states to be chronicled by comparing random numbers to transition probabilities. The transition probability was dependent on both the time interval of reaction and a global reaction rate constant. McDermott s ( analysis of the random reaction trajectory of the linear polymer shown in Figure 6 permits illustration. 

McDermott, J.B., Libanati, C., LaMarca, C., and Klein, M.T. A Stochastic Model of Depolymerization Kinetics 1. Development Approach, (in press)... 

Simha, R Wall, L. A., Some aspects of depolymerization kinetics. Journal of Polymer Science, 6(1), pp. 39-44 (1951). 

To reconcile these differences, we have proposed that pretreatment models should combine reaction with mass transfer and solubility limitations so that the concentration gradient between the solid and the liquid phases is taken into account. Furthermore, we have applied depolymerization kinetics to account for the production of sugar monomers and oligomers observed during the hydrolysis of cellulosic biomass, particularly at low acid levels. Some aspects of these studies will be summarized in this chapter. 

As for other forms of silica, equations for the polymerization-depolymerization kinetics and equilibrium have been formulated by Stober (195) to explain solubility behavior. 

Industrial Engineering Chemistry Research 40, No.2, 24th Jan.2001, p.509-14 KINETICS OF DEPOLYMERIZATION OF POLY(ETHYLENE TEREPHTHALATE) IN A POTASSIUM HYDROXIDE SOLUTION Ben-Zu Wan Chih-Yu Kao Wu-Hsun Cheng... 

Intrigued by the finding that Eca PLs exhibit notable differences in their kinetics, HPAEC analyses were carried out to examine the products from the depolymerization of PGA and 31% esterified pectin. After 18 h of incubation with PGA, PL1 and PL2 had produced mainly di- and trimers. Similariy, main products of PL3 action were trimers, followed by dimers. Moreover, it was the only enzyme found to produce monomers from unesterified substrates with a degree of polymerization >3. Using 31% esterified pectin as a substrate, similar end products were released by the PLs as from PGA. In addition to the products described, traces of tetra- up to octamers were detectable. While PL1 and PL2 released di- and trimers at almost... 

Since the depolymerization process is the opposite of the polymerization process, the kinetic treatment of the degradation process is, in general, the opposite of that for polymerization. Additional considerations result from the way in which radicals interact with a polymer chain. In addition to the previously described initiation, propagation, branching and termination steps, and their associated rate constants, the kinetic treatment requires that chain transfer processes be included. To do this, a term is added to the mathematical rate function. This term describes the probability of a transfer event as a function of how likely initiation is. Also, since a polymer s chain length will affect the kinetics of its degradation, a kinetic chain length is also included in the model. 

Polymerization occurs very quickly and the process is controlled via kinetic effects rather than thermodynamic ones. The net result is that the molecular weight distribution of the product does not match the thermodynamically stable one. If the chains were not capped with monofunctional phenols, the polymer chains would depolymerize, allowing the monomers to rearrange themselves at elevated temperature to approach the thermodynamically stable... 

In general, the structure of sol gel materials evolves sequentially as the product of successive and/or simultaneous hydrolysis and condensation and their reverse reactions (esterification and depolymerization). Thus, in principle, by chemical control of the mechanisms and kinetics of these reactions, namely the catalytic conditions, it is possible to tailor the structure (and properties) of the gels over a wide range. For example, stable silica xerogels of tailored particle dimensions, pore morphology, density and porosity, from relatively... 

Besides the main depolymerization reactions, side reactions should also be considered in the kinetic description of a PET recycling process. This is emphasized by the results obtained from a PET extrusion model [85] shown in Figures 2.19-2.23. The complete set of reactions summarized below in Table 2.10 have been used, but shear effects have not been taken into account. Chain degradation, accompanied by a significant reduction of intrinsic viscosity, occurs even within residence times of a few minutes. Carboxyl end groups, vinyl end groups and acetaldehyde are formed in amounts depending on residence time, temperature and initial moisture content of the PET flakes. 

Wang, D.-C., Chen, L.-W. and Chiu, W.-Y., Kinetic study on depolymerization by glycolysis of poly(ethylene terephthalate) with bisphenol A, Angew. Makromol. Chem., 230, 47-71 (1995). 

Fig. 5. Kinetics of brain microtubule depolymerization following rapid dilution. (A) Time course of the disassembly reaction with experimental data represented by the data points and the theoretical progress curve indicated by the solid line. (The inset to A shows that the process can be fitted to a simple decaying exponential for part of the depolymerization reaction.) (B) Microtubule length distribution for the sample subjected to rapid dilution in A. (Reproduced from Karr et al. (1980)./. Biol. Chm. 255, 8560-8566.)...

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