Brownian dynamics simulations of the self- and collective rotational diffusion coefficients of rigid long thin rods

Abstract

Mega-electron-volt proton irradiation on supported and suspended graphene: A Raman spectroscopic layer dependent study J. Appl. Phys. 110, 084309 (2011) Gel formation and aging in weakly attractive nanocolloid suspensions at intermediate concentrations J. Chem. Phys. 135, 154903 (2011) Waiting time dependence of T2 of protons in water suspensions of iron-oxide nanoparticles: Measurements and simulations J. Appl. Phys. 110, 073917 (2011) The effects of shape and flexibility on bio-engineered fd-virus suspensions J. Chem. Phys. 135, 144106 (2011) Quantitative measurement of scattering and extinction spectra of nanoparticles by darkfield microscopy Appl. Phys. Lett. 99, 131113 (2011) Additional information on J. Chem. Phys. Here this theory is put to the test by comparing it against computer simulations. A Brownian dynamics simulation program was developed to follow the dynamics of the rods, with a length over a diameter ratio of 60, on the Smoluchowski time scale. The model accounts for excluded volume interactions between rods, but neglects hydrodynamic interactions. The self-rotational diffusion coefficients D r ͑ ͒ of the rods were calculated by standard methods and by a new, more efficient method based on calculating average restoring torques. Collective decay of orientational order was calculated by means of equilibrium and nonequilibrium simulations. Our results show that, for the currently accessible volume fractions, the decay times in both cases are virtually identical. Moreover, the observed decay of diffusion coefficients with volume fraction is much quicker than predicted by the theory, which is attributed to an oversimplification of dynamic correlations in the theory.

Isotropic-nematic spinodals of rigid long thin rodlike colloids by event-driven Brownian dynamics simulations

“…This model was successfully applied to measure the self and collective rotational diffusion coefficients in dilute and semidilute rod solutions. 24 But when focusing on concentrated systems of hard rods, some disadvantages of this model appear. As a result of the random displacements and reorientations, sometimes considerable overlaps and even crossings cannot be prevented, irrespective of the smallness of the time step ␦t.…”

“…͑B11͒ in Appendix B of Ref. 24, we obtain the N-particle Smoluchowski equation Eq. ͑13͒ given above.…”

“…Since incorporating hydrodynamic interactions leads to complicated and slow programs, but does not affect the location of the spinodals, we here prefer a simpler and more approximate approach, leaving for future work the assessment of the importance of hydrodynamic interactions on the dynamics. Although recent studies 24,25 of the self and collective rotational dynamics of rods show that this method works well for dilute systems, it unfortunately turns out that the interaction potentials cause unsurmountable difficulties when performing prolonged simulations of the dense and highly elongated rods needed for a stable nematic phase. We therefore introduce here an event-driven Brownian dynamics algorithm, combining the dynamics equations of traditional fixed time step BD with the collision-based time step commonly used in simulations of hard bodies.…”

Hydrodynamics and Brownian motions of a spheroid near a rigid wall

“…22 Many examples of numerical simulations on Brownian non-spherical particles are reported in the recent literature. Brownian dynamics simulations of unbounded suspensions of rod-like particles [23][24][25][26][27] and arbitrarily shaped particles [28][29][30] have been carried out for different volume fractions, ranging from dilute to concentrated regimes, although interparticle hydrodynamic interactions are often neglected. The inclusion of hydrodynamic interactions gives rise to "corrective terms" in the Brownian dynamics.…”

Efficient simulation of noncrossing fibers and chains in a hydrodynamic solvent

“…10,11 Already at surprisingly low concentrations, uncrossability in such systems leads to a temporary and anisotropic "cage" or tube from which the rod or fiber can only escape through anisotropic motion ͑reptation͒ 12 or through collective motion, as exemplified by the collective reorientation observed in sheared concentrated rod suspensions. [13][14][15] Besides the mutual uncrossability constraint, the dynamics of rods and fibers are also influenced by Brownian forces ͑due to random collisions with solvent molecules͒ and hydrodynamic interactions ͑HIs͒ mediated by the solvent. The role of HIs in entangled suspensions of Brownian rigid rods and semiflexible fibers has remained, with a few exceptions, largely unexplored.…”