Parodi relationship

With the Miesowicz technique one can measure three combinations of the Leslie viscosity coefficients from Eqs. (9.25) to (9.27). On account of the Parodi relationship, to find all five coefficients, one needs, at least, two additional measurements. In particular, the ratio of coefficients a3/a2 can be measured by observation of the director field distortion due to capillary flow of a nematic. The last combination yi = as — as can be found from the dynamics of director relaxation. 

In conclusion, from the measurements of x the coefficient yi = 0 3 — 012 could be found if the cell thickness and elastic modulus are known. Note that yj coefficient is the most important for applications. Then, using data on the ratio of 0 3/012 we can find 0 3 and ot2 separately. Further, using the known coefficient for the isotropic phase viscosity 0 4 = 2ria, the coefficients 0 5 = 2r[t. — 2ria + 0.2 and ag = 2r]b — 2ria — 0 3 can be calculated and, for the particular nematic liquid crystal, the applicability of the Parodi relationship ag — ag = a2+ 0 3 verified. As to aj it can be found from... 

There exist only five independent viscosity coefficients in nematics, because according to the Onsager theory it could be shown [63] that (Parodies relationship)... 

Parodi, S. and Brambilla, G. (1977). Relationship between mutation and transformation frequencies in mammalian cells treated in vitro with chemical carcinogens, Mutat. Res. 47,53. 

Parodi, P. W. 1981. Relationship between triglyceride structure and softening point of milk fat. J. Dairy Res. 48, 131-138. 

Equation (10-10) contains six viscosities (the orf s). Only five of these are independent, however, since Parodi s (1970) relationship expresses one of the viscosities in terms of the others ... 

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Butyric (4 0) and caproic (6 0) adds occur only at the 5n-3-position. Other adds are also distributed preferentially, e.g. 18 0 at the 5n-l-position. This type of distribution is common to virtually all mammalian milk fats examined except the echidna (Parodi, 1982). The positional distribution of a number of mammalian milk fats (cow, goat, pig, sheep, rat and human) are compared in Table 3.156 (p. 116). The triglyceride carbon number distribution of 76 Australian butterfats (Table 3.157) has been studied (Guyot, 1977 Timms, 1980b), and the relationship below has been observed for triglycerides with carbon numbers 40, 42 and 44 where... 

By invoking Onsager relations, Parodi [48] argues that one restrict the viscous coefficients to satisfy the relationship... 

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

Parodi, PW. (1979). Relationship between trisaturated glyceride composition and the softening point of milk fat. J Dairy Res 46 633-639. 

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