Nonlinear-response theory for steady planar Couette flow

Material functions of liquid n -hexadecane under steady shear via nonequilibrium molecular dynamics simulations: Temperature, pressure, and density effects J. Chem. Phys. 130, 084904 (2009) We report for the first time rheological and structural properties of liquid decane, hexadecane, and tetracosane using nonequilibrium molecular-dynamics ͑NEMD͒ simulations under planar elongational flow ͑PEF͒. The underlying NEMD algorithm employed is the so-called p-SLLOD algorithm ͓C. Baig, B. J. Edwards, D. J. Keffer, and H. D. Cochran, J. Chem. Phys. 122, 114103 ͑2005͔͒. Two elongational viscosities are measured, and they are shown not to be equal to each other, indicating two independent viscometric functions in PEF. With an appropriate definition, it is observed that the two elongational viscosities converge to each other at very low elongation rates, i.e., in the Newtonian regime. For all three alkanes, tension-thinning behavior is observed. At high elongation rates, chains appear to be fully stretched. This is supported by the result of the mean-square end-to-end distance of chains ͗R ete 2 ͘ and the mean-square radius of gyration of chains ͗R g 2 ͘, and further supported by the result of the intramolecular Lennard-Jones ͑LJ͒ potential energy. It is also observed that ͗R ete 2 ͘ and ͗R g 2 ͘ show a different trend as a function of strain rate from those in shear flow: after reaching a plateau value, ͗R ete 2 ͘ and ͗R g 2 ͘ are found to increase further as elongation rate increases. A minimum in the hydrostatic pressure is observed for hexadecane and tetracosane at about ˙͑m 2 / ͒ 1/2 = 0.02. This phenomenon is shown to be associated with the intermolecular LJ potential energy. The bond-bending and torsional energies display similar trends, but a different behavior is observed for the bond-stretching energy. An important observation common in these three bonded-intramolecular interactions is that all three modes are suppressed to a small value at high elongation rates. We conjecture that a liquid-crystal-like, nematic structure is present in these systems at high elongation rates, which is characterized by a strong chain alignment with a fully stretched conformation.

Section: Introductionmentioning

confidence: 99%

Rheological and structural studies of liquid decane, hexadecane, and tetracosane under planar elongational flow using nonequilibrium molecular-dynamics simulations

Baig

Edwards

Keffer

et al. 2005

“…By repeating the procedure by which SLLOD was established as the correct NEMD algorithm for PCF, 2 we have now established that p-SLLOD ͑and not SLLOD͒ is the rigorous NEMD algorithm for PEF. We have also shown that p-SLLOD is the rigorous NEMD algorithm for any arbitrary flow field, reducing to SLLOD for PCF.…”

Section: Discussionmentioning

confidence: 99%

“…2 According to the discussion above, instead of studying the Newtonian evolution of f l , we can instead examine the evolution of the canonical distribution function, f 0 , under the p-SLLOD dynamics represented by Eq. ͑7͒.…”

Section: Determination Of the P-sllod Viscous Stress Tensor From mentioning

confidence: 99%

“…2,3. Thus, in this paper, we develop the nonlinear-response theory of the p-SLLOD algorithm under the imposition of an arbitrary steady-state flow field ͑including PEF͒ from two perspectives, and compare the respective results for the stress tensors at the end of the analyses. In the first perspective, which follows the analysis of Evans and Morriss, 2 we develop the nonlinear response of the system based on an analysis of the mechanical response of the canonical ensemble to the imposed flow field-see Secs. II-IV.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An examination of the validity of nonequilibrium molecular-dynamics simulation algorithms for arbitrary steady-state flows

Edwards

Baig

Keffer

2005

Nonlinear-response theory of nonequilibrium molecular-dynamics simulation algorithms is considered under the imposition of an arbitrary steady-state flow field. It is demonstrated that the SLLOD and DOLLS algorithms cannot be used for general flows, although the SLLOD algorithm is rigorous for planar Couette flow. Following the same procedure used to establish SLLOD as the valid algorithm for planar Couette flow ͓D. J. Evans and E. P. Morriss, Phys. Rev. A 30, 1528 ͑1984͔͒, it is demonstrated that the p-SLLOD algorithm is valid for arbitrary flows and produces the correct nonlinear response of the viscous pressure tensor.

“…This relation was first derived for Hamiltonian systems by Yamada and Kawasaki in 1967 9 and for the thermostatted dynamical systems by Morriss and Evans in 1984. 10 Due to the poor statistical convergence of Eq. ͑2͒, however, debate about the validity of this expression for thermostatted systems continued until 1995 ͑Ref.…”

Section: Introductionmentioning

confidence: 99%

Different approaches for evaluating exponentially weighted nonequilibrium relations

Reid

Cunning

Searles

2010

The Kawasaki identity ͑KI͒ and the Jarzynski equality ͑JE͒ are important nonequilibrium relations. Both of these relations take the form of an ensemble average of an exponential function and can exhibit convergence problems when the average of the exponent differs greatly from the log of the average of the exponential function. In this work, we re-express these relations so that only selected regions need to be evaluated in an attempt to avoid these convergence issues. In the context of measuring free energies, we compare our method to the JE and the literature standard approach, the maximum likelihood estimator ͑MLE͒, and show that in a system with asymmetric work distributions it can perform as well as the MLE. For the KI, we derive an analog to the MLE to compare with our relation and show that these two new relations improve on the KI and are complimentary to each other.