Forces , energies , and scaling
From Soft-Matter
Forces
There are four forces recognized by the current "Standard Model"
Interaction | Relative Strength | Range | Long-Distance Behavior |
Gravitation | 1 | Infinite Distance | <math>1/r^{2}</math> |
Weak | <math>10^{25}</math> | <math>10^{-18}</math> m | <math>1/r</math> |
Electromagnetism | <math>10^{36}</math> | Infinite Distance | <math>1/r^{2}</math> |
Strong | <math>10^{38}</math> | <math>10^{-15}</math> m | Constant |
- Four forces (in order of incereasing strength)
- Gravitation
- Strong Force: <math>10^{38} times stronger than the Gravitational Force</math>
- Electromagnetic
- Gravitational
- Molecular forces are electromagnetic
- Covalent
- Electrostatic
- Dipolar
- Dispersion
- In general:
Distance dependence of energies
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.