^{1}, Jorge Castillo-Tejas

^{2}, Octavio Manero

^{3}and Juan F. J. Alvarado

^{1,a)}

### Abstract

Equilibrium and non-equilibrium molecular dynamics were performed to determine the relationship between the static structure factor, the molecular conformation, and the rheological properties of chain molecules. A spring-monomer model with Finitely Extensible Nonlinear Elastic and Lennard-Jones force field potentials was used to describe chain molecules. The equations of motion were solved for shear flow with SLLOD equations of motion integrated with Verlet's algorithm. A multiple time scale algorithm extended to non-equilibrium situations was used as the integration method. Concentric circular patterns in the structure factor were obtained, indicating an isotropic Newtonian behavior. Under simple shear flow, some peaks in the structure factor were emerged corresponding to an anisotropic pattern as chains aligned along the flow direction. Pure chain molecules and chain molecules in solution displayed shear-thinning regions. Power-law and Carreau-Yasuda models were used to adjust the generated data. Results are in qualitative agreement with rheological and light scattering experiments.

The financial support of CONACYT (Project Nos. 100195, 83501, 104672, and 129962) is gratefully acknowledged.

INTRODUCTION

METHODOLOGY

Model and simulation

Structure factor

Rheological models

Material functions

RESULTS AND DISCUSSION

Equilibrium molecular dynamics

Non-equilibrium molecular dynamics

Rheological characterization

Structure of the Lennard-Jones solvent

Structure of the chain molecules in solution

Evolution of the static structure factor

CONCLUSIONS

### Key Topics

- Shear rate dependent structure
- 19.0
- Solvents
- 19.0
- Polymers
- 18.0
- Shear rate dependent viscosity
- 17.0
- Shear flows
- 14.0

## Figures

Particle interactions scheme. Dark circles correspond to beads in the chain molecules. Light circles represent solvent particles. Non-bonded particles, including solvent and beads, interact with truncated and shifted Lennard-Jones potential while bonded chains are represented by a FENE + Lennard-Jones potential.

Particle interactions scheme. Dark circles correspond to beads in the chain molecules. Light circles represent solvent particles. Non-bonded particles, including solvent and beads, interact with truncated and shifted Lennard-Jones potential while bonded chains are represented by a FENE + Lennard-Jones potential.

Structure factor projections on the x-y plane at . There is isotropy in all cases: (a) 0.0, (b) 0.1, (c) 0.5, and (d) 1.0 solutions.

Structure factor projections on the x-y plane at . There is isotropy in all cases: (a) 0.0, (b) 0.1, (c) 0.5, and (d) 1.0 solutions.

Shear viscosity vs. shear rate for the 0.0 (●), 0.1 (▽), 0.5 (▲), and 1.0 (□) solutions. Power law model fits well the simulated data in the shear thinning region, while the Carreau-Yasuda model fits the behavior of simulated data in the whole range of shear rates.

Shear viscosity vs. shear rate for the 0.0 (●), 0.1 (▽), 0.5 (▲), and 1.0 (□) solutions. Power law model fits well the simulated data in the shear thinning region, while the Carreau-Yasuda model fits the behavior of simulated data in the whole range of shear rates.

First normal stress coefficient vs. shear rate for the 0.1 (▽), 0.5 (▲), and 1.0 (□) solutions.

First normal stress coefficient vs. shear rate for the 0.1 (▽), 0.5 (▲), and 1.0 (□) solutions.

Second normal stress coefficient vs. shear rate for 0.1 (▽), 0.5 (▲), and 1.0 (□) solutions.

Second normal stress coefficient vs. shear rate for 0.1 (▽), 0.5 (▲), and 1.0 (□) solutions.

Ratios of the second and first normal stress coefficients vs. shear rate for the 0.5 (▲) and 1.0 (□) solutions.

Ratios of the second and first normal stress coefficients vs. shear rate for the 0.5 (▲) and 1.0 (□) solutions.

Absolute value of the first normal stress difference vs. shear rate for the 0.0 (●), 0.1 (▽), 0.5 (▲), and 1.0 (□) solutions.

Absolute value of the first normal stress difference vs. shear rate for the 0.0 (●), 0.1 (▽), 0.5 (▲), and 1.0 (□) solutions.

Structure factor patterns on the x-y plane of the pure solvent at shear rates of (a) and (b) . Both cases display isotropic behavior.

Structure factor patterns on the x-y plane of the pure solvent at shear rates of (a) and (b) . Both cases display isotropic behavior.

Structure factor patterns on the x-y plane of the 0.1 solution at shear rates of (a) and (b) .

Structure factor patterns on the x-y plane of the 0.1 solution at shear rates of (a) and (b) .

Structure factor patterns on the x-y plane of the 0.5 solution at shear rates of (a) and (b) .

Structure factor patterns on the x-y plane of the 0.5 solution at shear rates of (a) and (b) .

Structure factor patterns on the x-y plane of pure chains at shear rates of (a) and (b) .

Structure factor patterns on the x-y plane of pure chains at shear rates of (a) and (b) .

Evolution of the structure factor patterns on the x-y plane as a function of the shear rate at the shear-thinning region for the pure chain molecules. (a) , (b) , (c) , (d) , (e) and (f) . Peaks appear as the shear rate increases. The scattering pattern changes are due to molecular organization.

Evolution of the structure factor patterns on the x-y plane as a function of the shear rate at the shear-thinning region for the pure chain molecules. (a) , (b) , (c) , (d) , (e) and (f) . Peaks appear as the shear rate increases. The scattering pattern changes are due to molecular organization.

Mean square radius of gyration as a function of shear rate. The increasing in the value of this parameter with the shear rate evidences the alignment of the chains along the flow. Symbols differentiate chain mass fraction in the solution: 0.1 (▽), 0.5 (▲), and 1.0 (□).

Mean square radius of gyration as a function of shear rate. The increasing in the value of this parameter with the shear rate evidences the alignment of the chains along the flow. Symbols differentiate chain mass fraction in the solution: 0.1 (▽), 0.5 (▲), and 1.0 (□).

Scheme to represent the relation between the static structure factor, the chain conformation, and the shear viscosity for the pure chain molecules (melt). The three-dimensional snapshots show the alignment process of the chain molecules with the flow as the shear rate increases. For the sake of clarity not all chains used in calculations are include in the three-dimensional snapshots. Note also the changes in the structure factor patterns as the shear rate increases.

Scheme to represent the relation between the static structure factor, the chain conformation, and the shear viscosity for the pure chain molecules (melt). The three-dimensional snapshots show the alignment process of the chain molecules with the flow as the shear rate increases. For the sake of clarity not all chains used in calculations are include in the three-dimensional snapshots. Note also the changes in the structure factor patterns as the shear rate increases.

## Tables

Dimensionless variables and parameters used in simulation.

Dimensionless variables and parameters used in simulation.

Parameters of Power-Law and Carreau-Yasuda models that fit simulation data.

Parameters of Power-Law and Carreau-Yasuda models that fit simulation data.

Comparative table of some rheological parameters.

Comparative table of some rheological parameters.

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