Charged Rouse Chains in an Electric Field at Equilibrium

4 Charged Rouse Chains in an Electric Field at Equilibrium 

We now turn our attention to a dilute solution of charged Rouse chains at equilibrium in a constant electric field of intensity E- bead 1 has an electric charge — q and bead N has a charge + q, so that the chain has a dipole moment = ql-jQ . The intramolecular and external potentials are given by 4) = Q ) and E)- Then the normalized equilibrium 

15 The Mass-Flux Vector and the Dilfusivity Tensor (DPL, Sect. 18.4) 

The quantity j,(l) comes from combining the first and fourth terms in Eq. (6.11). The contribution j,(2) comes from the second and fifth terms in Eq. (6.11), recognizing that the v inserted into Eq. (15.3) does not contribute because of ZvW R = 0. The first two terms in j,(3) come from the second term in Eq. (6.11), and the last term in j,(3) comes from the sixth term in Eq. (6.11). To obtain the last form of Eq. (15.4) we make use of the fact that for any symmetrical tensor A 

We first consider the ].( ) term for arbitrary bead-spnng models in which all beads have the same mass m and the same fnction coefficient C then we investigate the i (2) term for the Rouse chain model. Next we give a derivation of a stress-diffusion relation for the simplified model of Hookean dumbbells (that is, a Rouse chain with N = 2), which makes use of the j ,(2) term. Then, we show how the use of the jj(3) term leads to a different result. These discussions and Appendix B are helpful in understanding the nature of the series expansions and some of the problems associated with them, because they are not expansions in a physical parameter. 

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