Nanopattern formation of two dimensional weakly charged telechelic gels by self-assembly

DESCRIPTION:

This project shows the nanopattern formation of a two-dimensional weakly charged telechelic gel by self-assembly due to the competition of electrostatic repulsions and Van der Waals attractions. In this telechelic gel, all end points (red particles in the simulation) are adsorbed onto a planar surface to make a two dimensional system. Each red particle is a course-grained monomer (CGM) representing a short hydrophobic chain, where there is no excluded-volume interaction to simply the system (in a sense, we can think of those hydrophobic chains as floating above the planar surface). Each CGM is connected to each of four neighbor CGMs by a harmonic spring (except for CGMs at corners and edges, which are connected to two and three CGMs respectively). All CGMs are equally partially and negatively charged, and mediated by monovalent counterions with the same size of CGMs to neutralize the systems (blue particles in the simulation). In our system, there is no explicit solvent. The solvent effect is implicitly included by adjusting the interaction parameters of the molecules.

In all simulations, the diameter of particles, σ, is used as the length unit, and k_BT is used as the energy unit, where k_B is the Boltzmann constant, k_B = 1.38x10^-23J/K (If you want to know more about how to convert the length and energy units to the conventional SI units, please check the end-note). The spring strength between CGMs is 0.1 K_BT/ σ;² , which is equivalent to the elastic constant of a hydrophobic Gaussian chain with 30 segments. The charge of each CGM is 0.3e (where e is the charge of one electron, 1.602x10^-19C), which implies the charge fraction of hydrophobic backbones is 1.0%. There are electrostatic interactions between all particles. In addition, there are Van der Waals attractions between CGMs due to the hydrophobicity of the backbones when they are in a poor solvent (meaning that CGMs are attracted to each other, but not the solvent). This is represented by a cut-and-shifted Lennard-Jones (LJ) potential, which has the form:

where r_c =2.5σ, which is the cutoff distance. Here, ε describes the strength of the attraction between CGMs, a larger value means stronger attractions, and a poorer solvent. The excluded-volume interactions between counterions and counterions and between CGMs and counterions are purely repulsive, which is represented by a Weeks-Chandler-Anderson (WCA) potential. It has the same form as cut-and-shifted LJ potential with the cutoff r_c =2^1/6σ.

From our results, we find that the gel will be swollen when the attractions between CGMs are weak, such as the strength of attraction ε = 1.0 K_BT (movie), because the electrostatic repulsion dominates. As the Van der Waals attractions increase, the gel will shrink until the attraction is in balance with the electrostatic repulsions between CGMs, and different sizes of nanopatterns are formed and percolated, such as ε = 3.0K_BT (movie).

FOR CLASSROOM:

These simulations are for college students. As computing power increases, more computer simulations have been widely used for scientific research. This is one example of the theoretical study of the nanopattern formation in a two-dimensional weakly charged polymer gel by self-assembly. We apply a molecular dynamics simulation method (using the LAMMPS simulation package) to study the equilibrium structure of the gel at different conditions. The basic idea in molecular dynamics simulations is to simulate the evolution of the system by integrating Newton 's equations for each particle given the initial conditions (system size, temperature, interaction parameters between each particle, and the initial positions and velocities of each particle). From the resulting trajectories, we can study the properties of the system as a function of time. These simulations can be used in physics, material science and computer science classes as an example to explain the underlying physics and introduce the simulation methodology. Several simulations are also available to introduce the three common states of pure substances depending on the temperature at a certain density. These can serve as background material for this self-assembly simulation, or a stand alone introduction to different phases (solid, liquid, or gas) of matters. In these simulations, the interaction between particles is a cut-and-shifted LJ potential, which is a good approximation for interactions between noble gases (such as He, Ne, Ar etc.). At a low temperature T=0.2 (movie), substances are in the solid state. Molecules vibrate around their equilibrium positions. They can't move a long distance without the application of an external force. At a moderate temperature T = 0.5 (movie), substances will be in a liquid state (click for the simulation, where molecules move faster than those in solid state (Note: Here molecules look more likely to form droplets instead of a continuous liquid because there is no simulated gravity in the simulations). At a high temperature T = 2.0 (movie), substances will be in the vapor state, where molecules move around very fast and occupy the whole containment area.

A swollen polymer gel with ε = 1.0K_BT

A nanosegregated polymer gel at ε = 3.0K_BT, made by VMD.

An example of the solid state at low temperature

The liquid state at a moderate temperature

The vapor state at a high temperature

So how do you convert the simulation units (which are unitless) to the conventional SI units?

If we take for example that the working temperature is 300K, and the diameter of our CGM particle is 5 nm. Then, the attraction strength between CGMs is 1.24x10^-20J (which is equivalent to 7.48 KJ/mol) when σ = 3.0K_BT. The cluster size is about 3 times of the size of CGM. This means the size of the self-assembled nanopattern is about 15 nm.

Acknowledgement:

Dongsheng Zhang would like to thank Fei I Yeh, Jim Chen and John Ireland for stimulating discussions and technical support to prepare this showcase.

These software packages were used to create these simulations:

• VMD - Visual Molecular Dynamics
• LAMMPS Molecular Dynamics Simulator