Monte Carlo simulations epimerization

A general method has been developed for the estimation of model parameters from experimental observations when the model relating the parameters and input variables to the output responses is a Monte Carlo simulation. The method provides point estimates as well as joint probability regions of the parameters. In comparison to methods based on analytical models, this approach can prove to be more flexible and gives the investigator a more quantitative insight into the effects of parameter values on the model. The parameter estimation technique has been applied to three examples in polymer science, all of which concern sequence distributions in polymer chains. The first is the estimation of binary reactivity ratios for the terminal or Mayo-Lewis copolymerization model from both composition and sequence distribution data. Next a procedure for discriminating between the penultimate and the terminal copolymerization models on the basis of sequence distribution data is described. Finally, the estimation of a parameter required to model the epimerization of isotactic polystyrene is discussed. 

Isotactic polystyrene was epimerized to various extents by reaction with KOtBu in hexamethylphosphor-amide solution at 100°. The 13C-NMR spectra of the epimerized samples and of polystyrene in 9 1 trichlorobenzene nitrobenzene-d6 solution at 150° were recorded and analyzed using stereosequence distributions that were calculated for the samples by Monte Carlo simulation of the epimerization process. 

Monte Carlo Simulations. The epimerization reaction was simulated using the Monte Carlo program we described earlier(17). A 5000 element array was allocated to store information about the configurations of monomer units at various positions in a 5000 unit polymer chain. The positions were indexed in such a way that the polymer could be considered cyclic. This was done to avoid end group effects. The configurations (R or S) at individual sites were indicated by 0 or 1 values. The polymer chain was made isotactic by giving all elements of the array initial values of 0. 

Epimerized Isotactic Polystyrene Samples from Aromatic C—1 Carbon Resonances and Calculated by Monte Carlo Simulation... 

Figures 1-6 compare observed aromatic C-l carbon resonance spectra with simulated spectra based on the heptad chemical shifts given in Table VI and on heptad stereosequence concentrations calculated by Monte Carlo simulation of the epimerization process, using V=0.65. The simulation spectra reproduce the general features of the observed spectra very well and can be considered to be in at least semi-quantitative agreement with the observed spectra. The agreement between observed and simulated spectra might be improved if spectra with higher S/N ratios were employed and if additional parameter adjustments were made. It seems, however, that the heptad assignments developed in this work are reasonably correct.

Table III. Correlation of A-F Aromatic C-1 Carbon Resonance Areas Measured for Polystyrene and Epimerized Isotactic Polystyrene Samples with Stereosequence Distributions Calculated by Monte Carlo Simulation (V=0.65)...

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