(774f) Systematic MD Simulation Studies of the Glass Transition Temperatures of Styrene-Based Oligomers and Polymers

Following early molecular dynamics simulation studies, in which it was observed that calculated volume-temperature curves of supercooled monatomic [1] and chain molecule [2] liquids exhibit behavior similar to that observed in experimental dilatometry experiments, with a characteristic change in slope over a temperature range identifiable with the glass transition, there has been considerable interest in using MD simulations to predict the transition temperature Tg of a wide variety of polymers.

Two potential obstacles to the successful and routine application of simulation for the prediction of Tg include the extremely high effective cooling rate, and the quality of force field parameters used in simulations, especially where, as is often the case, chemically complex materials are involved.  With regard to the former, it has readily been demonstrated by experiment that the measured Tg increases with increasing frequency consistent with the view of the phenomenon as reflecting the temperature at which there is a falling out of equilibrium of various modes of molecular motion in relation to the time scale of the measurement. Since cooling rates in typical MD simulations may correspond to perhaps a few tens of degrees per nanosecond (i.e. &gt; 10¹⁰ K/s), the <i>a priori</i> expectation is therefore that Tg measured in a simulation may be some tens of degrees higher than an experimental value measured by a standard technique such as dilatometry, in which the effective measurement frequency is almost zero. Indeed there is evidence from simulations of chemically simple molecules such as the model glass former ortho terphenyl, for which it could be demonstrated that the force field used gave accurate representation of the PVT behavior of the liquid, that the 'molecular dynamics' Tg appears to be about 70-80 degrees higher than experiment [3].  On the other hand, there are reports of MD Tg values much closer to experiment for higher molecular weight polymers, albeit modeled using less thoroughly tested force fields.

One approach to furthering our understanding of the true significance of the Tg measured in simulation of organic materials involves taking advantage of observations made more than 60 years ago by Fox and Flory that the Tg of chain molecules varies with molecular weight [4], initially changing rapidly before eventually reaching a critical chain length beyond which changes are no longer observed.  Following this early work, a number of researchers reported measurements of Tg of a variety of types of oligomers [5].  In the present work we report on molecular dynamics Tg predictions on two of these systems, namely oligomers of styrene and &alpha;-methyl styrene.  In order to accomodate the long simulations required to explore factors such as cooling rate effects, we have used the LAMMPS simulation program from Sandia National Laboratories [6], and furthermore we have first refined the nonbond parameters of the PCFF force field and demonstrated its ability to predict accurately equation of state and cohesive behavior of related small molecules. We then proceed to compare predicted liquid and glass thermal expansion coefficients and molecular dynamics Tgs of the oligomers with the experimental data.  Finally we will discuss differences between simulation and experiment in regard to features such as the width of the glass transition region.

[1] see, for example, Clarke, J.H.R., J. Chem. Soc. Faraday Trans. 2 <b>75</b>, 1371 (1979); Fox, J.R. and Andersen, H.C., Ann. N.Y. Acad. Sci. <b>371</b>, 123 (1981).
[2] Rigby, D. and Roe, R.-J., J. Chem. Phys. <b>87</b>, 7285 (1987).
[3] Goldberg, A. and Rigby, D. presented at the AIChE Annual Meeting, Salt Lake City, Nov 2007.
[4] Fox, T.G. and Flory, P.J., J. Appl. Phys. <b>21</b>, 581 (1950).
[5] see, for example, Ueberreiter, K. and Kanig, G., J. Coll. Sci. <b>1</b>, 569 (1952); Cowie, J.M.G. and Toporowski, Eur. Polym. Journal <b>4</b>, 621 (1968)
[6] Plimpton, S., J. Comp. Phys. <b>117</b>, 1 (1995).