# Thermodynamic Scaling of the Shear Viscosity of Lennard-Jones Chains of Variable Rigidity

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## Abstract

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## 1. Introduction

## 2. Models and Theory

#### 2.1. The Lennard-Jones Chains Fluid Model

#### 2.2. Simulation Context

#### 2.2.1. Numerical Methods and Parameters

#### 2.2.2. Viscosity Modeling and Thermodynamic Scaling

## 3. Results

#### 3.1. Fully Flexible LJ Chains Model for Alkanes

#### 3.2. Semi-Rigid LJ Chains Model for Alkanes

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

LJ | Lennard-Jones |

NEMD | Non-Equilibrium Molecular Dynamics |

NIST | National Institute of Standards and Technology |

TS | Thermodynamic Scaling |

## References

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**Figure 3.**Shear rate effect on the differences of the normal stresses for ${\rho}^{*}=0.95$, ${T}^{*}=3$, ${N}_{c}=4$. (

**a**) Normalized differences of the normal stress ${N}_{1}$ versus shear rate, (

**b**) Normalized differences of the normal stress ${N}_{2}$ versus shear rate.

**Figure 4.**Reduced residual viscosity versus $\frac{{\rho}^{*\gamma}}{{T}^{*}}$ for fully flexible chains, semi-logarithmic scale.

**Figure 6.**Impact of the length chain on ${\gamma}_{Nemd}$ (LJ fully flexible chains) and ${\gamma}_{Alkanes}$.

**Figure 7.**Evolution of the $\gamma $ parameter with the chain length ${N}_{c}$ for fully flexible Mie chains. Comparison with ${\gamma}_{Alkanes}$ using Equation (10).

**Figure 8.**Thermodynamic scaling for the viscosity on LJ chains (${N}_{c}=4$) of different rigidities, semilogarithmic scale.

**Figure 9.**Rigidity influence, ${\left({k}^{*}\right)}^{0.5}$, on the parameter $\gamma $ for a LJ chain of length ${N}_{c}=4$.

**Figure 10.**Evolution of ${\gamma}_{{k}^{*}=0}$, ${\gamma}_{{k}^{*}=5}$ and ${\gamma}_{Alkanes}$ with the chain length ${N}_{c}$. For alkanes, ${N}_{c}$ is the equivalent chain length of Equation (10).

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**MDPI and ACS Style**

Delage Santacreu, S.; Hoang, H.; Khennache, S.; Galliero, G.
Thermodynamic Scaling of the Shear Viscosity of Lennard-Jones Chains of Variable Rigidity. *Liquids* **2021**, *1*, 96-108.
https://doi.org/10.3390/liquids1010008

**AMA Style**

Delage Santacreu S, Hoang H, Khennache S, Galliero G.
Thermodynamic Scaling of the Shear Viscosity of Lennard-Jones Chains of Variable Rigidity. *Liquids*. 2021; 1(1):96-108.
https://doi.org/10.3390/liquids1010008

**Chicago/Turabian Style**

Delage Santacreu, Stephanie, Hai Hoang, Samy Khennache, and Guillaume Galliero.
2021. "Thermodynamic Scaling of the Shear Viscosity of Lennard-Jones Chains of Variable Rigidity" *Liquids* 1, no. 1: 96-108.
https://doi.org/10.3390/liquids1010008