Determination of rotary diffusivity of poly(n-propyl isocyanate) by molecular dynamics

Abstract

The rotational dynamics of a nondilute solution of the rodlike polymer poly(n-propyl isocyanate) (PPIC) has been studied on an atomistic model by means of a large-scale classical molecular dynamics investigation. The rotary diffusivity of PPIC in toluene solution has been determined from the Einsteinian diffusion regime of the end-to-end vector on the surface of the unit sphere and has been found to be Dr=10.5x10(5)(+/-2.7) s-1, which falls in the range of the experimental data available. A comparison of molecular dynamics predictions with theoretical and perturbation expansion predictions has also been performed.

Detailed Atomistic Molecular Dynamics Simulations of α-Conotoxin AuIB in Water

“…Alternatively, the diffusivity can be computed from the vector correlation function, 〈e 1 (t) • e 1 (0)〉, which is related to D r through 59 Additionally, a characteristic rotational correlation time can be defined in terms of D r as 59 (other definitions, differing only by a constant factor in the denominator, are also in use), and consequently τ r can be extracted from the 〈e 1 (t) • e 1 (0)〉 vs t curve by fitting eq 5 at short times. 60 The decay of the autocorrelation function 〈e 1 (t) • e 1 (0)〉 is shown in Figure 7 for all individual samples, as well as for the average over the four trajectories using multiple time origins. 53 While the evolution of 〈e 1 (t) • e 1 (0)〉 for each sample shows strong fluctuations characteristic of individual instances of a stochastic While rotational relaxation can be captured within relatively short times, considerably more effort is required for the accurate estimation of translational diffusivity, D t , since it is only in the long-time, Fickian limit that D t can be calculated from mean square displacement of the protein center of mass according to the Einstein equation:…”

“…The precise meaning of “short times” in the previous paragraph is that D r t ≪ 1, so the curvature of the two-sphere manifold | e 1 ( t )| = 1 in which diffusion takes place can be neglected. Alternatively, the diffusivity can be computed from the vector correlation function, ⟨ e 1 ( t )· e 1 (0)⟩, which is related to D r through false⟨ bolde 1 ( t ) · bolde 1 ( 0 ) false⟩ = exp ( − 2 D normalr t ) Additionally, a characteristic rotational correlation time can be defined in terms of D r as τ r = 1 2 D r (other definitions, differing only by a constant factor in the denominator, are also in use), and consequently τ r can be extracted from the ⟨ e 1 ( t )· e 1 (0)⟩ vs t curve by fitting eq at short times …”