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A COMPARISON BETWEEN THE KINETIC THEORY OF - page 10 / 25

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In setting up the Liouville equation, we have to take into account the fact that the ith molecule of species will have "beads" which will be indicated by an additional index , and that these beads will be spread out around the center of mass of the molecule. Therefore, the complete phase space will consist of all the bead positions, , and the bead momenta, . We are then concerned with a distribution function that is a function of all the bead positions and momenta; this function will be described by an "equation of continuity" in the complete phase space:

(2.5)

When this equation is combined with Newton's laws of motion for the beads, and , we then get the Liouville equation for the polymer mixture:

(2.6)

where is the Liouville operator.

2b. The general equation of change

When the Liouville equation is multiplied by some property B and then integrated over the entire phase space, we get the general equation of change:

where (2.7; 2.8)

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