In this study, a fully charged polyelectrolyte brush system is examined by means of molecular simulations. The simulation is conducted using Langevin dynamics to investigate the conformation and swelling of the polyelectrolyte (PE) chains inside a brush system under different conditions such as changing the valance of added salt and changing grafting density of chains.
We observe that addition of the monovalent salt induces the structural change of the PE brush. This is due to the screening effect of salt ions surrounding the PE brushes. In this case, the stiffness of the chain gradually decreases from rod-like regime to coil/globule like regime, upon increasing charge ratio of the solution. Consequently, the thickness of the brush decreases monotonically. In multivalent (divalent and trivalent) salt solution, the structural transition is quite different compared to monovalent case. In the region where charge ratio <1, the height of the brush decreases upon increasing the salt concentration. At =1, the chain reach a minimum height, indicating a critical point. Then in >1, the chains swell due to the electrostatic interaction. A charge inversion occurs because of the condensation of multivalent cations which are tightly bound on the PE chains. The effective chain charge reverses its sign and it is the electrostatic repulsion inside the chains which causes the chain swelling.
We also change the grafting density of the PE brush system to study the brush behavior. The height of the brush decreases with increase in grafting density at a given charge ration in the region <1. At charge ratio =1, the chain attains a minimum height in all the grafting density and the value almost the same in all the grafting densities under multivalent (divalent and trivalent) salt solution. But in monovalent case, the brush continues to collapse. In the charge ratio >1, the brush swells and the swelling becomes stronger with the valance in multivalent salt solution. The results show that the brush height can be controlled by changing the valence of the added salt in the solutions or by changing the chain grafting density.

Table of Contents
Abstract i
Acknowledgements ii
Table of Contents iii
List of Figures v
Chapter 1 Introduction 1
1.1 What is Soft Condensed Matter? 1
1.2 What is polyelectrolyte? 1
1.3 What is Polyelectrolyte Brush? 2
1.4 Motivation: Polyelectrolyte Brush 3
1.5 Paper review 4
Chapter 2 Simulation Model and Method 7
2.1 Coarse-grained Model 7
2.1.1 System 7
2.1.2 Interaction of the particles 8
2.2 Simulation Method 9
2.2.1 Molecular dynamics 9
2.2.2 Langevin dynamics 10
2.2.3 Boundary condition 11
2.2.4 Numerical method 11
2.2.5 Verlet neighbor list 12
2.2.6 Ewald sum 12
2.2.7 LAMMPS 13
Chapter 3 Simulation Parameters 14
Chapter 4 Results and Discussion 15
4.1 Height and Structure of the grafted chain 16
4.1.1 Maximum brush height 16
4.1.2 Structure of the brush 18
4.1.3 Polar angle of the brush 20
4.1.4 Brush thickness 21
4.1.5 End-to-end distance 23
4.2 Total charge distribution 24
4.3 Probability distribution of Polar angle 28
4.4 Distribution of monomer and cation concentration 31
4.5 Surface density distribution of monomer and cation 38
4.6 Comparison and Discussion 51
4.6.1 Stoichiometric charge ratio 51
4.6.2 Shape factor / and Polar angle 53
Chapter 5 Conclusion 57
Bibliography 60

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