Theory for Rigid Rodlike Macromolecules with Polydomains

2 Theory for Rigid Rodlike Macromolecules with Polydomains 

When limiting our attention to low-molecular-weight nematics, we may expect that, in general, flow has the following effects (1) it alters the distribution of molecular orientations about the nematic axis (director) and (2) it affects the director itself. In other words, the velocity v(r) and the director n(r) are coupled under flow of nematic solutions. Next, we first present the expressions for stress, then discuss some important features of the Ericksen-Leslie theory, and finally show relationships existing between the six Leslie coefficients and three molecular parameters appearing in the Doi theory. The presentation of the entire Ericksen-Leslie theory (Ericksen 1960 Leslie 1966, 1968, 1979) is beyond the scope of this chapter. 

Stress Expression Ericksen (1960) and Leslie (1966, 1969) derived the following expression  

It can be shown that only five of the six Leslie coefficients are independent because, according to Parodi (1970), the following relationship holds  

Relationships between the Six Leslie Coefficients and Three Molecular Parameters in the Doi Theory By limiting their analysis to the first-order perturbation from the equilibrium state, Kuzuu and Doi (1984) derived the Ericksen-Leslie equation from the Doi theory under weak velocity gradient and obtained the following relationships between the six Leslie coefficients and the three molecular parameters (concentration, molecular weight, and the order parameter) appearing in the Doi theory  

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