# Forces , energies , and scaling

## Forces

There are four forces recognized by the current "Standard Model"

 Interaction Relative Strength Range Long-Distance Behavior Gravitation 1 Infinite Distance [itex]1/r^{2}[/itex] Weak [itex]10^{25}[/itex] [itex]10^{-18}[/itex] m [itex]1/r[/itex] Electromagnetism [itex]10^{36}[/itex] Infinite Distance [itex]1/r^{2}[/itex] Strong [itex]10^{38}[/itex] [itex]10^{-15}[/itex] m Constant

• Four forces (in order of incereasing strength)
• Gravitation
• Strong Force: [itex]10^{38} times stronger than the Gravitational Force[/itex]
• Electromagnetic
• Gravitational
• Molecular forces are electromagnetic
• Covalent
• Electrostatic
• Dipolar
• Dispersion
• In general:
``` ```

## Distance dependence of energies

 General energy equation. The important scaling is the power-law. n. Energy of a volume of particles. The importnat scaling is the sign of the power law. Gravitational energy of a volume of particles. The important scaling is the scaling law with volume. Comments on the energy as a function of volume?

Since many properties that depend on interaction energies, such as boiling point, do not change with volume n must be at least 4 at long ranges (Manoharan Notes 2006). Van der Waals attractions go as ~r^-6 at long ranges, ionic interactions go as r^-1, but are screened at long ranges, and hydrogen bonds go as r^-2, but are short ranged (Manoharan Notes 2006).

## Why do we care about kT?

The second law of thermodynamics says the entropy increased (lowering free energy)when a constraint is removed.

• Consider a volume change in a gas at constant number.
• Consider a change in number of a gas at constant volume.
• Consider molecules held together by bonds as the activation to dissociation * is decreased.
• Consider a densely packed liquid crystal solution when the density is lowered.
• Consider a polymer pulled to a fully extended state.