The viscoelastic properties of a series of syndiotactic polystyrene (s-PS) melts with high stereoregularity and different molecular weights (M w = 134–1160 kg/mol) are measured in a wide achievable temperature range (270–310 °C) to determine the entanglement molecular weight (M e ) and flow activation energy (E a ). In addition, four actactic polystyrenes (a-PS, M w = 215–682 kg/mol) and one isotactic polystyrene (i-PS, M w = 247 kg/mol) are also studied to elucidate the tacticity effect on the corresponding properties. Using a reference temperature of 280 °C, the master curves of dynamic storage and loss modulus are constructed according to the time–temperature superposition principle. On the basis of the classic integration method, the M e values are determined to be 14 500 and 17 900 g/mol for the s-PS and a-PS, respectively, which are significantly lower than that for the i-PS, ∼27 200 g/mol, derived from the Wu’s empirical equation. Owing to the difference in M e , at a fixed M w, the viscosity of i-PS is about 1 order of magnitude lower than that of s-PS and a-PS. However, when double-logarithmic plotting of the melt viscosity against the M w/M e is performed, a self-consistent behavior is seen for all the PS used despite of the differences in the M w and chain tacticity; the derived exponent is 3.61. According to the Arrhenius plot, the determined E a for the s-PS is 53 ± 5 kJ/mol, which is apparently lower than that for the other two isomers possessing a similar value of 90–107 kJ/mol.

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ABSTRACT. For many stochastic models, it is difficult to make inference about the model parameters because it is impossible to write down a tractable likelihood given the observed data. A common solution is data augmentation in a Markov chain Monte Carlo (MCMC) framework. However, there are statistical problems where this approach has proved infeasible but where simulation from the model is straightforward leading to the popularity of the approximate Bayesian computation algorithm. We introduce a forward simulation MCMC (fsMCMC) algorithm, which is primarily based upon simulation from the model. The fsMCMC algorithm formulates the simulation of the process explicitly as a data augmentation problem. By exploiting non-centred parameterizations, an efficient MCMC updating schema for the parameters and augmented data is introduced, whilst maintaining straightforward simulation from the model. The fsMCMC algorithm is successfully applied to two distinct epidemic models including a birth-death-mutation model that has only previously been analysed using approximate Bayesian computation methods.

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