Effect of chain flexibility on master curve behavior for diffusion coefficient

Abstract

The diffusion coefficients of simple chain models are analyzed as a function of packing fraction, η, and as a function of a parameter C that is the density raised to a power divided by temperature to look at scalar metrics to find master curves. The central feature in the analysis is the mapping onto an effective hard site diameter, d. For the molecular models lacking restrictions on dihedral angle (e.g., freely jointed), simple mappings of molecular potential to d work very well, and the reduced diffusion coefficient, D*, collapses into a single-valued function of η. Although this does not work for the dihedral angle restriction case, assuming that d is inversely proportional to temperature to a power results in collapse behavior for an empirically selected value of the power. This is equivalent to D* being a single-valued function of C. The diffusion coefficient of a single-site penetrant in the chain systems also is found to be a scalar metric that can reduce the chain diffusion data for a given system to a single master curve.

Microscopic Theory for the Role of Attractive Forces in the Dynamics of Supercooled Liquids

“…The result is consistent with density-temperature scaling [10,22]. The inset also shows that the density scaling exponent is high (∼10), consistent with recent simulations that mapped WCA repulsions to effective hard spheres [23] and as expected based on isomorph theory [10][11][12].…”

“…The inset shows the Arrhenius barriers are nearly identical for both fluids, and grow as βE ∞ ∝ η 9.3 . The high apparent power law exponent (simulation [6] finds ∼5) is expected if the continuous repulsion is replaced by an effective hard sphere potential [10]; our exponent value is in excellent agreement with simulations that explored consequences of the WCA to hard sphere mapping [23]. We have also computed an "onset temperature", T on , defined as when the apparent Arrhenius behavior first fails.…”

“…This avoids replacing Newtonian forces by effective potentials determined solely by pair structure, a ubiquitous approximation [15][16][17][18] that results in theories that are effectively "blind" to the dynamical differences between WCA and LJ liquids [7,9]. The predictions of our approach are in good agreement with isochoric simulations [6][7][8][9]11] and isobaric experiments on molecular liquids [22][23][24].…”

Hidden Scale Invariance in Condensed Matter

“…Some systems obey generalized excess-entropy scaling laws without exhibiting strong WU correlations and classical Rosenfeld excess-entropy scaling. Examples include polar liquids, chains of LJ particles connected by springs, Gaussian-core mixtures, the Widom–Rowlinson model, some tetrahedrally bonded systems, and hard-sphere mixtures. ,,,,,− Why is this? One possible explanation is that the hidden-scale-invariance identity eq may be generalized by replacing the potential energy by a free-energy function defined by integrating out certain degrees of freedom, for instance harmonic springs that model the covalent bonds.…”