Scission probability distribution function

Fig. 15.3. Some commonly encountered scission probability distribution functions.

The Gaussian scission probability distribution function, with a preference for mid-chain scission, is frequently encountered in shear-induced mechanochemical degradation. The parabolic distribution, on the contrary, indicates a preference for chain-end degradation. This phenomenon has been reported in the hydrolysis of dextran, as a result of chain branching. 

Applying the TABS model to the stress distribution function f(x), the probability of bond scission was calculated as a function of position along the chain, giving a Gaussian-like distribution function with a standard deviation a 6% for a perfectly extended chain. From the parabolic distribution of stress (Eq. 83), it was inferred that fH < fB near the chain extremities, and therefore, the polymer should remain coiled at its ends. When this fact is included into the calculations of f( [/) (Eq. 70), it was found that a is an increasing function of temperature whereas e( increases with chain flexibility [100],... 

Similarly, with the same type of photocatalyst (Pt/TiC>2 or Fe2C>3) the decomposition of levulinic (4-oxopentanoic) acid in oxygen-free aqueous solution has been investigated in detail (60). In addition to the decarboxylation reaction, oxidative C-C scissions led to propionic and acetic acids (further converted into methane and ethane) and reductive cleavages to acetone and ethanal. The formation of acetone was apparently favoured by higher Pt contents (however product distributions referred to equal illumination durations and not to equal conversions). It was suggested that the variety of products resulted from the presence of two functional groups in levulinic acid. The quantum yield was probably of the order of 5 x IQ-3. 

It can be therefore concluded that the above results of the mechanochemical experiments are directly related to the slowing down of chain mobility upon deterioration of solvent quality. Consequently, these experiments are uniquely useful to study chain dynamics in semiconcentrated polymer solution as a function of the thermodynamic conditions at high shear rates. Hence, these experiments can give information about molecular parameters not being accessible by any other method. For example, one can quote the probability of chain scission along the backbones obtained by the full kinetic analysis of the data (cf. Sect. 3). This distribution of rupture sites is obviously connected with the distribution of strain along the chains, which may be probed by degradation experiments. 

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