Forces , energies , and scaling

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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:
          Force Energy Eqns.gif

Distance dependence of energies

General energy equation. The important scaling is the power-law. n. General Energy Eqn.png
Energy of a volume of particles. The importnat scaling is the sign of the power law. General Total Energy Eqn.gif
Gravitational energy of a volume of particles. The important scaling is the scaling law with volume. Gravitational Eqn.gif

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.

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