(475g) Rheological and Structural Studies of Liquid Decane, Hexadecane, and Tetracosane under Planar Elongational Flow Using Nonequilibrium Molecular Dynamics Simulations

1.
Introduction

There exist two important standard flows
in rheology¹: shear flow [e.g.,
planar Couette flow and Hagen-Poiseuille flow] and elongational flow [e.g., uniaxial elongational flow (UEF),
biaxial elongational flow (BEF), and planar elongational flow (PEF)]. In
contrast to shear flow, it is extremely difficult to perform real experiments
in elongational flow, and thus only a few experimental data are available for
this flow field.¹ Research is still in progress toward developing
improved experimental apparati and methodologies for measuring elongational
viscosities.¹ In this regard, without a doubt, the computational
feasibility of simulating elongational flows would be tremendously helpful.

With the help of Kraynik and Reinelt's²
discovery of the temporal and spatial periodicity of lattice vectors in PEF, it
has been possible, in principle, to perform nonequilibrium molecular dynamics
(NEMD) simulations of PEF without any limit of simulation time. Recently,
however, Todd and Daivis³ have reported an aphysical phase
transition after a certain time interval in NEMD simulations of PEF when using
the so-called SLLOD algorithm, which has been extensively used in NEMD
simulations over three decades, especially for shear flow. As shown by the
present authors⁴ very recently, the instability comes from the SLLOD
algorithm itself due to its inconsistency of the fundamental principle, i.e.,
Newtonian dynamics. All these problems have been completely resolved by the
present authors⁴ using the so-called proper-SLLOD (or p-SLLOD)
algorithm.

2. Technical approach

In our previous work⁴ using
the p-SLLOD algorithm, we demonstrated its fundamental correctness by applying
it for a simple WCA fluid. In the present work, we extend our simulation
methodology for NEMD simulations of PEF from simple fluids to relatively short
complex fluids. We explore three alkanes, C₁₀H₂₂
(decane), C₁₆H₃₄ (hexadecane) and C₂₄H₅₀
(tetracosane), which previously have been studied under shear flow.^5-7
Thus, an advantage of choosing the three alkanes is to compare NEMD simulation
results of PEF and those of shear flow, i.e.,
compare zero-elongation-rate viscosity and zero-shear-rate viscosities. An NEMD
simulation for these alkanes under shear flow was previously carried out by Cui
et al.;⁶ therefore, it
appears to be most appropriate to choose the same state points as those used by
Cui et al.,⁶ for
comparison: the temperature, T=298 K,
and the density, r=0.7247 g/cm³, for decane, T=323 K and r=0.7530 g/cm³ for hexadecane,
and T=333 K and r=0.7728
g/cm³ for tetracosane. Exploring these states by NEMD simulations,
we employed 200 molecules for decane, 162 molecules for hexadecane, and 100
molecules for tetracosane. The potential model employed for our systems is
essentially the same as that used by Cui et
al.⁶ for shear flow. The model was proposed by Siepmann et al.,⁸ and is known as the
SKS united-atom model, with the exception that the rigid bond is replaced by a
flexible one with harmonic potential

3. Results and Discussion

Two elongational
viscosities, h₁ and h₂, were separately calculated with
appropriate rheological definitions. For all three alkanes, h₁ and h₂
showed tension-thinning behavior as elongation rate increased. It was observed
that h₁ and h₂ are, in general, not identical to each
other, indicating that two independent viscometric functions actually exist.
Consistent with the theoretical prediction, h₁
and h₂ appeared
to converge to each other at low elongation rate, i.e., in the Newtonian regime. For the three alkanes, the zero-elongation-rate
viscosities calculated in this work agreed well with the zero-shear-rate
viscosities reported by Cui et al.⁶
Another interesting similarity between shear^6,7 and planar
elongational flow was found in that for both flows there exists a minimum in
the hydrostatic pressure at constant density vs. strain rate for these alkanes.

The mean square
end-to-end distance of chains <R_ete²> and the mean
square radius of gyration of chains <R_g²> showed
different trends from those in shear flow. After reaching a plateau value,
<R_ete²> and <R_g²> were
shown to increase further as elongation rate increases. This phenomenon has
been interpreted by conjecturing that chains are fully stretched at high
elongational rates. This conjecture was well supported by examination of the
intramolecular LJ energy.

The effect of
elongation flow on three bonded intramolecular interactions (i.e.,
bond-stretching, bond-bending, and torsion) was investigated in detail with
further help of the distribution functions. The bond-bending and torsional
energy showed a similar trend to each other, but a different behavior was
observed in the bond-stretching energy. An important observation common in
these three interactions was that all three modes were suppressed to small
values at high elongation rates. We conjecture that a liquid-crystal-like,
nematic structure, characterized by a strong chain alignment with a fully
stretched conformation, exists in systems at high elongation rates.

4. References

¹F.
A. Morrison, Understanding Rheology
(Oxford University Press, New York, 2001).

²A.
M. Kraynik and D. A. Reinelt, Int. J. Multiphase Flow 18, 1045 (1992).

³B.
D. Todd and P. J. Daivis, J. Chem. Phys. 112,
40 (2000).

⁴C.
Baig, B. J. Edwards, D. J. Keffer, and H. D. Cochran, J. Chem. Phys. 122, 114103 (2005).

⁵S.
T. Cui, P. T. Cummings, and H. D. Cochran, J. Chem. Phys. 104, 255 (1996).

⁶S.
T. Cui, S. A. Gupta, P. T. Cummings, and H. D. Cochran, J. Chem. Phys. 105, 1214 (1996).

⁷R.
Khare, J. de Pablo, and A. Yethiraj, J. Chem. Phys. 107, 6956 (1997).

⁸J.
I. Siepmann, S. Karaborni, and B. Smit, Nature 365, 330 (1993).