Lennard-Jones potential minimized

In summary, the Lennard-Jones potential is a mathematical model used to describe the potential energy between particles in a system. It is minimized through energy minimization and has significance in understanding equilibrium states and thermodynamic properties. The minimization is affected by initial conditions and parameters, and it is related to the force between particles as the negative gradient of the potential energy function.
  • #1
terp.asessed
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3

Homework Statement


At what distance r is the Lennard Jones potential minimized?

Homework Equations


Typical graph of Lennard Jones potential, U(r) vs. r/σ

The Attempt at a Solution


I thought that from looking at the graph, r = ∞ for potential minimization. However, the answer turned out to be (2)1/6σ. Could someone explain?
 
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  • #2
terp.asessed said:
I thought that from looking at the graph, r = ∞ for potential minimization.
Why? Zero is not the minimum.

However, the answer turned out to be (2)1/6σ. Could someone explain?
You should have the function definition given somewhere. Finding the minimum is simple mathematics.
 

1. What is the Lennard-Jones potential?

The Lennard-Jones potential is a mathematical model that describes the potential energy between two interacting particles in a system. It is commonly used in molecular dynamics simulations to study the behavior of atoms and molecules.

2. How is the Lennard-Jones potential minimized?

The Lennard-Jones potential is minimized through an iterative process known as energy minimization. This involves adjusting the positions of the particles in the system to find the lowest possible energy state.

3. What is the significance of minimizing the Lennard-Jones potential?

Minimizing the Lennard-Jones potential allows us to study the stable equilibrium states of a system and understand the interactions between particles. It is also important in determining the thermodynamic properties of a system.

4. What are the factors that affect the minimization of the Lennard-Jones potential?

The minimization of the Lennard-Jones potential is affected by the initial positions and velocities of the particles, the size of the system, and the parameters used in the potential function.

5. How does the Lennard-Jones potential relate to the force between particles?

The Lennard-Jones potential is directly related to the force between particles, as it is the negative gradient of the potential energy function. This means that at the minimum potential energy state, the force between particles is zero.

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