Difference between revisions of "Forces , energies , and scaling"
From Soft-Matter
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== Forces == | == Forces == | ||
| − | * Four forces | + | |
| − | ** | + | |
| + | There are four forces recognized by the current "Standard Model" | ||
| + | {| class="wikitable" border = "1" | ||
| + | |- | ||
| + | |'''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 | ** Electromagnetic | ||
** Gravitational | ** Gravitational | ||
Revision as of 01:56, 23 September 2008
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
| 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.
