Grant: Discovery Grants Program - Individual

Polymer dynamics is a branch of polymer science that studies the diffusivity and viscosity of macromolecules. The topic is of great practical importance as knowledge of the two transport coefficients is required for designing and processing polymers. The Rouse model and the reptation theory are currently used to describe the dynamics of linear macromolecules below and above the crossover molecular weight (Mc), respectively. In the reptation theory, the motion of a linear macromolecule in melts is confined in a tube formed by entanglements. Therefore, macromolecules with molecular weights (M) above the Mc exhibit a much stronger M dependence than those below. However, the entanglement concept is not quantitative. The number of entanglements cannot be measured experimentally and the tube cannot be derived theoretically. The so-called entanglement chain length for a polymer is essentially inferred from its plateau modulus. This is why my research group initiated a project a few years ago, supported by a Discovery Grant, to seek a different approach to analyze polymer dynamics. In particular, we have developed a theory based upon the concept of free volume. The essence of the free volume concept is that the translation motion of molecules requires sufficient amount of empty space in between them (i.e., free volume). Here, the amount of free volume can be quantitatively defined and measured by positron annihilation lifetime spectroscopy. The concept of free volume has been applied successfully to describing the dynamics of small molecules. Over the past few years, we have published a series of papers demonstrating that our newly developed theory is able to predict the existence of the Mc of diffusivity and viscosity, suggesting that polymer dynamics can be portrayed by a single mechanism (i.e., free volume redistribution). Our theory has two advantages. One is that it is not limited to only linear macromolecular structure. It can be easily implemented on polymers with complex macromolecular structures and different sizes. The other is that the only input required is the radial distribution function (rdf) and such calculation is fast. Although our theory is able to estimate diffusivity and viscosity based on the amount of free volume, information about segmental dynamics at different length scales cannot be obtained since rdf is an equilibrium concept that signifies molecular packing. Here, we propose to incorporate the free volume redistribution dynamics in our theory. This is done by including the fluctuation of rdf as described by the well-known van Hove function in our theory. We will then able to extract the corresponding force correlation function, thereby the friction coefficient. The friction coefficient is a key parameter that will allow us to capture segmental dynamics of macromolecules.  This is important as knowing segmental dynamics will help design the desired macromolecular structures needed.