content_image/362981.jpg content_image/362980.jpg content_image/362979.jpg content_image/362978.jpg content_image/362977.jpg
## Appendix B 

We present the derivation of the expression (3.21) for the time relaxation τ$_{do}$$_{,}$$_{1}$ . Substitu- tion of the equation (3.20) for the irreversible time evolution of the configurational variable Q into the Doi-Ohta relaxation equation (1.7a) gives 

<img src='content_image/362981.jpg'>

Under the assumption of a homogeneous system, integration over the whole system size of the above expression gives 

<img src='content_image/362980.jpg'>

The general expression (3.19) for the coarse-grained friction matrix M (2) $^{′}$, dif gives 

<img src='content_image/362979.jpg'>

which after substitution of the appropriate functional derivatives, M (1) , dif element, and the integration over r$_{4}$ , r ′ $_{1}$, and r ′ 2 becomes 

<img src='content_image/362978.jpg'>

where we have used the assumption of a homogeneous ( M = const. ) and isothermal system, as well as the approximations based on a difference between the Cahn-Hilliard and Doi- Ohta length scales, as in Appendix A. Substitution of the friction matrix element (B4) into equation (B2), gives after using the normalization condition ∫ V d $^{3}$r ′ χ ( r − r ′ ) = 1, the final formula for the Doi-Ohta time relaxation 

<img src='content_image/362977.jpg'>

[1] R. G. Larson, The Structure and Rheology of Complex Fluids (Oxford University Press, New York, 1999). 

