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

It can be seen the while the strong force is (as it is named) the strongest of all the forces, having a highly unusual linear dependance on separation (force increases with distance), the distance over which the force acts is on the scale of a femtometer, or typical size of a nucleus. Same goes for the weak force. Thus these forces are completely negligible for describing physics that happens outside the nucleus. The gravitational force, while interacting with all massive bodies, and even light is however, much weaker than the all other forces, and thus is only appreciable for very massive neutral bodies.

Thus we are left with the electromagnetic force as the lone force responsible for almost all physics when considering structure of matter. It should be noted that gravity can of course not be excluded completely since it has can have an effect on the distribution and density of particles in a liquid or gaseous mixture.


Molecular forces

Molecular Forces (forces dominating on the length scales of nanometers to centimeters) are all are electromagnetic in nature.

  • 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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