^{1}, B. J. Edwards

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

^{1}and B. Khomami

^{1}

### Abstract

Nonequilibrium molecular dynamics (NEMD) simulations of a dense liquid composed of linear polyethylene chains were performed to investigate the chain dynamics under shear. Brownian dynamics (BD) simulations of a freely jointed chain with equivalent contour length were also performed in the case of a dilute solution. This allowed for a close comparison of the chain dynamics of similar molecules for two very different types of liquids. Both simulations exhibited a distribution of the end-to-end vector, , with Gaussian behavior at low Weissenberg number . At high , the NEMD distribution was bimodal, with two peaks associated with rotation and stretching of the individual molecules. BD simulations of a dilute solution did not display a bimodal character; distributions of ranged from tightly coiled to fully stretched configurations. The simulations revealed a tumbling behavior of the chains and correlations between the components of exhibited characteristic frequencies of tumbling, which scaled as . Furthermore, after a critical of approximately 2, another characteristic time scale appeared which scaled as . Although the free-draining solution is very different than the dense liquid, the BD simulations revealed a similar behavior, with the characteristic time scales mentioned above scaling as and .

The authors gratefully acknowledge Dr. V. Venkataramani for help with the BD simulations reported in this article. This work was made possible by the National Science Foundation under Grant No. CBET-0742679 by using the resources of the PolyHub Virtual Organization.

I. INTRODUCTION

II. SIMULATION METHODOLOGY

A. NEMD simulation

B. BD simulation

C. Brightness distribution for configurations of chain molecules

III. RESULTS AND DISCUSSION

A. Dynamics of the end-to-end vector

B. Chain configurations and characteristic time scales

IV. SUMMARY

### Key Topics

- Hydrodynamics
- 14.0
- Molecular dynamics
- 14.0
- DNA
- 13.0
- Shear flows
- 12.0
- Tensor methods
- 12.0

## Figures

Representative configuration classes of chain molecules as defined by the brightness distribution of Venkataramani *et al.* (2008).

Representative configuration classes of chain molecules as defined by the brightness distribution of Venkataramani *et al.* (2008).

The mean-square chain end-to-end distance, , for as a function of from the atomistic NEMD (open symbols) and BD (filled symbols) simulations.

The mean-square chain end-to-end distance, , for as a function of from the atomistic NEMD (open symbols) and BD (filled symbols) simulations.

The intermolecular and intramolecular LJ potential energies as functions of .

The intermolecular and intramolecular LJ potential energies as functions of .

Probability distributions of for the five values of designated by the vertical lines in Fig. 2 as calculated in the (a) NEMD and (b) BD simulations.

Probability distributions of for the five values of designated by the vertical lines in Fig. 2 as calculated in the (a) NEMD and (b) BD simulations.

The magnitude of end-to-end vector, , and the orientation angle with respect to the flow direction, , as functions of time for a random chain of the (a) NEMD and (b) BD simulations.

The magnitude of end-to-end vector, , and the orientation angle with respect to the flow direction, , as functions of time for a random chain of the (a) NEMD and (b) BD simulations.

Probability distribution of positive and negative end-to-end vector orientations in the dense liquids (NEMD simulations) at four values of .

Probability distribution of positive and negative end-to-end vector orientations in the dense liquids (NEMD simulations) at four values of .

Probability distribution of representative chain configuration classes in the dense liquids (NEMD simulations) at four values of .

Probability distribution of representative chain configuration classes in the dense liquids (NEMD simulations) at four values of .

Probability distribution of molecules within the three regions of defined in the text for the dense liquids (NEMD simulations).

Probability distribution of molecules within the three regions of defined in the text for the dense liquids (NEMD simulations).

Time cross-correlation functions versus observation time for three values of and the power spectral density versus frequency for two values of that exhibit minima in the cross-correlation function curves in the dense liquid simulations.

Time cross-correlation functions versus observation time for three values of and the power spectral density versus frequency for two values of that exhibit minima in the cross-correlation function curves in the dense liquid simulations.

Characteristic time scales versus . Horizontal line represents the Rouse time. Vertical dashed line represents the value of at which the stress-optical rule begins to breakdown in simulations of . Diamonds represent the time scale of relaxation of the extended molecules and all other symbols represent the time scales associated with the various auto and cross correlations of the end-to-end vector. Solid symbols represent dilute solution data and unfilled symbols denote dense liquid data.

Characteristic time scales versus . Horizontal line represents the Rouse time. Vertical dashed line represents the value of at which the stress-optical rule begins to breakdown in simulations of . Diamonds represent the time scale of relaxation of the extended molecules and all other symbols represent the time scales associated with the various auto and cross correlations of the end-to-end vector. Solid symbols represent dilute solution data and unfilled symbols denote dense liquid data.

Log-log plots of the characteristic time scales, relative to the Rouse time, versus for the NEMD simulations. Note that plots of the characteristic frequencies would possess slopes of opposite sign but of the same absolute values as those presented in the figures.

Log-log plots of the characteristic time scales, relative to the Rouse time, versus for the NEMD simulations. Note that plots of the characteristic frequencies would possess slopes of opposite sign but of the same absolute values as those presented in the figures.

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