Bounds for the diffusion constant

Upper bound. Next we consider the translational diffusion constant. To calculate Dc, we consider that a weak constant field 

To see the effect of the deformation term d ldR , we have to solve eqn (4.193). The effect can be calculated by a variational principle. It can be shown that for any I that satisfies eqn (4.194) 

Equation (4.199) indicates that the Kirkwood formula (4.198) cor-respon k to the choice of = 1 and is actually an upper bound for Da. 

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Lower bound. A lower bound for the diffusion constant is given in a similar form to eqn (4.189). Let V be the function which satisfies eqn (4.190), then... 

This observation is in accordance with a supposedly rigorous variational bound for the diffusion constant, which states that the Kirkwood value is an upper bound. A much stronger effect (w 30%) was found for the intrinsic viscosity [rf, which measures the polymer contribution to the viscosity p of the solution, relative to the viscosity rjs of the pure solvent. It is experimentally defined as... 

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