Size dependence of transport coefficients of thin and long asphaltene molecules as determined using a mode-coupling theory approach

Rotational diffusion coefficients (Dr) and viscosities (η) of rigid rod molecules consisting of N beads were first revisited for the situation at low density. Starting from this, the transport coefficients at high density condition were expressed in terms of different density pair correlation functions, such as intermolecular radial distribution function and structure factor. This was attained using a mode-coupling theory approach to approximate the intermolecular force–force correlation function, and thus the friction coefficient. As these density pair correlation functions are dependent on N, they determine how “entangled” the rigid rod molecules are, and therefore reproducing the crossover in the log –log plot of transport coefficients with N. It was found that there are crossovers in transport coefficients from Dr∼N−2.3 and η∼N2.3 at low N to Dr∼N−6.5 and η∼N6.5 at high N. The strength of N dependence is mainly determined by the competition between available free space and the compressibility of the system.