Forces , energies , and scaling

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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:

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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).

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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.

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