Effective step length

The erratic motion of a chromatographically migrating molecule resembles a random-walk process. In order to apply random-walk ideas to chromatography, we must identify the effective step lengths and step numbers associated with the molecular migration. This is the main task to follow. 

If / and /x are the effective step lengths (monomer length) for the random walks parallel and perpendicular to the ordering direction (in the isotropic phase / =/x= o)> respectively, and under the assumption that the deformation occurs without a change of volume, the following relation is obtained for the elastic component of the free energy in the nematic phase... 

We introduce a very important static property, the effective step length of the chain... 

I have estimated very roughly as f TT sn absurdly large value for a physical system, but remembering that is a Kuhn effective step length and all the other factors omitted the value is not surprising. 

Hie mesh size d is assumed to depend only on the effective spacing of obstacles in the medium and thus on the polymer concentration alone. We do not mean to imply that d would necessarily be of the order of the distance between chains (a few An troms in undiluted systems). Its effective value should be somewhat larger than this, since d must also reflect a certain amount of local freedom for mutual rearrangement of iKighbors in real systems. Nevertheless, like the primitive path step length a of Doi and Edwards, d should be independent of the large scale molecular structure. 

For A = 1 this is known as the augmented Hessian (AH) method. It was first proposed by Lengsfield , and used with various modifications by several authors . It can easily be proved that H —el is always positive definite if e is the eigenvalue obtained by solving Eq. (33). It can also be shown that the AH method is quadratically convergent . A value A > 1 has the effect of further reducing the step length x. In fact, as shown by Fletcher and... 

---