^{1}, B. J. Edwards

^{1,a)}, D. J. Keffer

^{1}, H. D. Cochran

^{1}and V. A. Harmandaris

^{2}

### Abstract

We present various rheological and structural properties of three polyethylene liquids, , , and , using nonequilibrium molecular dynamics simulations of planar elongational flow. All three melts display tension-thinning behavior of both elongational viscosities, and . This tension thinning appears to follow the power law with respect to the elongation rate, i.e., , where the exponent is shown to be approximately for and . More specifically, of is shown to be slightly larger than that of and to increase in magnitude with the chain length, while of appeared to be independent of the chain length. We also investigated separately the contribution of each mode to the two elongational viscosities. For all three liquids, the intermolecular Lennard-Jones (LJ), intramolecular LJ, and bond-stretching modes make positive contributions to both and , while the bond-torsional and bond-bending modes make negative contributions to both and . The contribution of each of the five modes decreases in magnitude with increasing elongation rate. The hydrostatic pressure shows a clear minimum at a certain elongation rate for each liquid, and the elongation rate at which the minimum occurs appears to increase with the chain length. The behavior of the hydrostatic pressure with respect to the elongation rate is shown to correlate with the intermolecular LJ energy from a microscopic viewpoint. On the other hand, and appear to be correlated with the intramolecular LJ energy. The study of the effect of the elongational field on the conformationtensor shows that the degree of increase of with the elongation rate becomes stronger as the chain length increases. Also, the well-known linear reaction between and does not seem to be satisfactory. It seems that a simple relation between and would not be valid, in general, for arbitrary flows.

We would like to acknowledge helpful correspondence with Dr. V. G. Mavrantzas in the preparation of this work. This research was supported by the Division of Materials Sciences and Engineering of the U.S. Department of Energy (DOE) at Oak Ridge National Laboratory (ORNL) through a subcontract at the University of Tennessee. This research used resources of the Center for Computational Sciences at Oak Ridge National Laboratory, which is supported by the Office of Science of the DOE also under Contract No. DE-AC05-00OR22725.

I. INTRODUCTION

II. SIMULATION METHODOLOGY

III. RESULTS AND DISCUSSION

IV. CONCLUSIONS

### Key Topics

- Tensor methods
- 19.0
- Hydrostatics
- 16.0
- Viscosity
- 14.0
- Polymers
- 10.0
- Shear flows
- 10.0

## Figures

Comparison of (a) and (b) vs the elongation rate between , , and .

Comparison of (a) and (b) vs the elongation rate between , , and .

Kinetic and potential parts of and vs the elongation rate for (a) , (b) , and (c) .

Kinetic and potential parts of and vs the elongation rate for (a) , (b) , and (c) .

Contribution of each mode to as a function of elongation rate for (a) , (b) , and (c) .

Contribution of each mode to as a function of elongation rate for (a) , (b) , and (c) .

Hydrostatic pressure vs the elongation rate for , , and . The error bars of all the data are smaller than the size of the symbols.

Hydrostatic pressure vs the elongation rate for , , and . The error bars of all the data are smaller than the size of the symbols.

Intermolecular LJ potential energy per united atom vs the elongation rate for , , and . The error bars of all the data are smaller than the size of the symbols.

Intermolecular LJ potential energy per united atom vs the elongation rate for , , and . The error bars of all the data are smaller than the size of the symbols.

Intramolecular LJ potential energy per united atom vs the elongation rate for , , and . The error bars of all the data are smaller than the size of the symbols. The number of united atoms in a chain is for .

Intramolecular LJ potential energy per united atom vs the elongation rate for , , and . The error bars of all the data are smaller than the size of the symbols. The number of united atoms in a chain is for .

Plots of (a) bond-torsional energy per mode, (b) bond-bending energy per mode, and (c) bond-stretching energy per mode vs the elongation rate for , , and . The error bars of all the data are smaller than the size of the symbols. The number of torsional modes in a chain is for .

Plots of (a) bond-torsional energy per mode, (b) bond-bending energy per mode, and (c) bond-stretching energy per mode vs the elongation rate for , , and . The error bars of all the data are smaller than the size of the symbols. The number of torsional modes in a chain is for .

Conformation tensor vs the elongation rate for , , and ; (a) , (b) , (c) , and (d) .

Conformation tensor vs the elongation rate for , , and ; (a) , (b) , (c) , and (d) .

Relationship between the conformation and the stress tensors; (a) and , (b) and , and (c) and .

Relationship between the conformation and the stress tensors; (a) and , (b) and , and (c) and .

## Tables

Elongational viscosities and as functions of elongation rate for , , and . Numbers in parentheses represent the statistical uncertainties in the least significant digits calculated using Eq. (28) of Ref. 27.

Elongational viscosities and as functions of elongation rate for , , and . Numbers in parentheses represent the statistical uncertainties in the least significant digits calculated using Eq. (28) of Ref. 27.

The mean square end-to-end distance of chains and the mean square radius of gyration of chains as functions of elongation rate for , , and . Numbers in parentheses represent the statistical uncertainties in the least significant digits calculated using Eq. (28) of Ref. 27.

The mean square end-to-end distance of chains and the mean square radius of gyration of chains as functions of elongation rate for , , and . Numbers in parentheses represent the statistical uncertainties in the least significant digits calculated using Eq. (28) of Ref. 27.

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