Lennard-Jones Potential V(r) (Condensed Matter)

In summary, on page 6 of the provided lecture notes, it is mentioned that the potential between atoms or ions is described by an equation with integer exponents p and q. These exponents determine the behavior of the potential and can vary depending on the type of atoms or ions involved. For example, for two neutral, inert gas atoms, p=12 and q=6, while for two oppositely charged ions, q=1 due to the inverse-square-law for charged particles.
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http://www.ph.qmul.ac.uk/phy108/CM2005_week2_Lecture3_Interatomic%20Forces2.pdf
Page 6, I've understood all of the notes so far. But it just randomly goes into this, what/where did these p's and q's come from? What do they mean?

Can't find anything that I can understand online!
 
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It is found (experimentally, I think) that the potential between atoms or ions has the behavior given by the 1st equation on page 6, where p and q are integer exponents in that expression. That's pretty much it, they are just the exponents that describe the potential. For two neutral, inert gas atoms, p=12 & q=6 describes the potential. For an ion + neutral atom, p and q will be something else. For two oppositely charged ions, we know that q=1 because of the inverse-square-law for charged particles.

Hope that helps.
 

Related to Lennard-Jones Potential V(r) (Condensed Matter)

1. What is the Lennard-Jones potential V(r)?

The Lennard-Jones potential V(r) is a mathematical function used to describe the potential energy between two atoms or molecules in a condensed matter system, such as a solid or liquid. It takes into account both the attractive and repulsive forces between the particles, resulting in a curve that resembles a shallow bowl.

2. How is the Lennard-Jones potential calculated?

The Lennard-Jones potential is calculated using the equation V(r) = 4ε[(σ/r)^12 - (σ/r)^6], where ε is the depth of the potential well and σ is the distance at which the potential is zero. These values are specific to the type of atoms or molecules involved and can be determined experimentally or through theoretical calculations.

3. What does the shape of the Lennard-Jones potential curve represent?

The shape of the Lennard-Jones potential curve represents the potential energy between two particles as a function of their separation distance. The well at the bottom of the curve corresponds to the minimum potential energy, or the most stable state, between the particles. As the particles get closer or farther apart, the potential energy increases due to the attractive and repulsive forces between them.

4. How does the Lennard-Jones potential affect the behavior of particles in a condensed matter system?

The Lennard-Jones potential plays a crucial role in determining the behavior of particles in a condensed matter system. It governs the intermolecular forces between particles, which can affect properties such as melting point, boiling point, and viscosity. It also determines the equilibrium distance between particles and influences the overall stability of the system.

5. Can the Lennard-Jones potential be used to model all types of interactions in a condensed matter system?

No, the Lennard-Jones potential is a simplified model that is only applicable to systems with non-polar molecules or atoms. It does not take into account more complex interactions, such as hydrogen bonding, dipole-dipole interactions, or ionic interactions. In these cases, more advanced potential energy functions must be used.

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