Free radical model

Notwithstanding Platzman s theory, most calculations of radiation-chemical yields in water and aqueous solutions were performed using the free-radical model (see Magee, 1953 Samuel and Magee, 1953 Ganguly and Magee, 1956). The hypothesis was that the recapture time of the electron would be shorter than the dielectric relaxation time. Therefore, recombination would outcompete solvation. 

The product cystine is presumably formed in the recombination of two thiyl radicals. This free-radical model is suitable for formal treatment of the kinetic data however, it does not account for all possible reactions of the RS radical (68). The rate constants for the reactions of this species with RS-, 02 and Cu L, (n = 2, 3) are comparable, and on the order of 109-10loM-1s-1 (70-72). Because all of these reaction partners are present in relatively high and competitive concentrations, the recombination of the thiyl radical must be a relatively minor reaction compared to the other reaction paths even though it has a diffusion controlled rate constant. It follows that the RS radical is most likely involved in a series of side reactions producing various intermediates. In order to comply with the noted chemoselectivity, at some point these transient species should produce a common intermediate leading to the formation of cystine. 

Porter NA, Roe AN, McPhail AT (1980) Serial cydizationof peroxy free radicals models for polyolefin oxidation. J Am Chem Soc 102 7574-7576... 

Savage, P.E. and M.T. Klein, Discrimination Between Molecular and Free-Radical Models oflPhenyldodecane Pyrolysis., Ind. and Eng. Chem. Res., 26,374,1987. 

The purpose of obtaining all this information is to present reasonable free radical models for the primary oxidation and reduction products observed in the irradiated crystals. This begins with, and is usually based on, the precise information about major sites of spin density. There are however, some problems in dealing with all of the small hyperfine couplings obtained from the ENDOR data. This could mean, for example, that one may have problems with establishing precisely what... 

The resonance stabilized benzofuranyl (lactone) radicals can either reversibly dimerize or react with other free radicals. Model experiments have demonstrated that this class of chemistry behaves as a powerful hydrogen atom donor and are also effective scavengers of carbon-centered and oxygen-centered free radicals (21) (see Fig. 5). 

Both Nylon and polycarbonate resins have free-radical models for autoxidation reactions. For Nylons (except Nylon 6 caprolactum and others not of specific form Nylon m,n), the steps in the autoxidation mechanism is shown below. 

Calculate the delocalization energies of the positive ion, free radical, and negative ion of the allvl model. 

Within the predictive capabilities of the models, reactivity is given by bThe larger r- the more reactive the molecule (or ion or radical). Note that the tenriinal carbon atoms in buta-1,3-diene are predicted by Iltiekcl theoiy to be slightly more reactive than the carbon atoms in ethylene. Qualitative eoirelation with experience is seen fur sume alkenes and free radicals in Fig. 7-3,... 

Using an sp hybridized carbon for the carbon that has the unpaired electron make a molecular model of the free radical intermediate in this reaction... 

There are numerous synthetic and natural compounds called antioxidants which regulate or block oxidative reactions by quenching free radicals or by preventing free-radical formation. Vitamins A, C, and E and the mineral selenium are common antioxidants occurring naturally in foods (104,105). A broad range of flavonoid or phenoHc compounds have been found to be functional antioxidants in numerous test systems (106—108). The antioxidant properties of tea flavonoids have been characterized using models of chemical and biological oxidation reactions. 

Biological Antioxidant Models. Tea extracts, tea polyphenol fractions, and purified catechins have all been shown to be effective antioxidants in biologically-based model systems. A balance between oxidants and antioxidants is critical for maintenance of homeostasis. Imbalances between free radicals and antioxidants may be caused by an increased production of free radicals or decreased effectiveness of the antioxidants within the reaction system. These imbalances can be caused by the radicals overwhelming the antioxidants within the system, or by an excess of antioxidants leading to a prooxidant functionaHty (105—118). When antioxidant defense systems are consistently overwhelmed by oxidative reactions, significant damage can... 

Kinetic Models Used for Designs. Numerous free-radical reactions occur during cracking therefore, many simplified models have been used. For example, the reaction order for overall feed decomposition based on simple reactions for alkanes has been generalized (37). 

In the second paper the models were amplified for ethane, 49 reactions with 11 molecular species and 9 free radicals for propane, 80 reactions with 11 molecular species and 11 free radicals. The second paper has a list of 133 reactions involving light hydrocarbons and their first- or second-order specific rates. 

The peroxide decomposes at elevated temperatures to give free radicals, which then abstract a hydrogen atom from the methyl group. The radicals formed then combine to form a hydrocarbon linkage. Results obtained by reacting model systems with benzoyl peroxide and analysing the reaction products are consistent with this type of mechanism. ... 

As an example stereolithography is a 3-D rapid process that produces automatically simple to very complex shaped models in plastic. Basically it is a method of building successive layers across sections of pho-topolymerized plastics on top of each other until all the thin printed layers can be joined together to form a whole product. The chemical key to the process, photopolymerization, is a well established technology in which a photo initiator absorbs UV energy to form free radicals that then initiate the polymerization of the liquid monomers. The degree... 

Takemoto et al.21) synthesized similar types of models, i. e. poly(/3-methacryl-oyloxyethyladenine) 20 (PMAOA), poly(0-methacryloyloxyethyluracil) (PMAOU), and poly(j3-methacryloyloxyethylthymine) (PMAOT), by free-radical polymerizations of /3-methacryloxyethyl compounds of the corresponding base. 

Dannenberg J. J. The Molecular Orbital Modeling of Free Radical and Diels-Alder Reactions Adv. Mol. Model. 1990 2 1-63... 

In the literature there is only one serious attempt to develop a detailed mechanistic model of free radical polymerization at high conversions (l. > ) This model after Cardenas and 0 Driscoll is discussed in some detail pointing out its important limitations. The present authors then describe the development of a semi-empirical model based on the free volume theory and show that this model adequately accounts for chain entanglements and glassy-state transition in bulk and solution polymerization of methyl methacrylate over wide ranges of temperature and solvent concentration. 

A new rate model for free radical homopolymerization which accounts for diffusion-controlled termination and propagation, and which gives a limiting conversion, has been developed based on ft ee-volume theory concepts. The model gives excellent agreement with measured rate data for bulk and solution polymerization of MMA over wide ranges of temperature and initiator and solvent concentrations. 

It can be seen from equation (2) that when y 0 the model falls into the classical expression for the rate of conversion of free radical polymerization. Equation (la) shows that this will be the case whenever all macroradicals have the same high mobility (i.e., as n tends to infinity) or when both entangled and non-entangled radicals have the same termination rate constant (i.e. a is equal to unity). 

Experimental conversion-time data, obtained from the literature, on the bulk free radical polymerization of MMA initiated by AIBN at several temperatures and initiator concentrations, were described by the model. However, the expressions for the rate of conversion and gel effect index were first simplified and rearranged. ... 

Figure 5, Variation of the model parameters Cj (O) and Cb (X) u)ith temperature for the bulk free radical polymerization of MM A initiated by AIBN...

---