Yamakawa-Fujii-Yoshizaki theory

Bushin et al. [38] and independently Bohdanecky [39] showed that the Yamakawa-Fujii-Yoshizaki theory for [77] can be put in an approximate form as... 

Fig. 5-9. Fit of the Yamakawa-Fujii-Yoshizaki theory to [77] data [41] for PHIC in butyl chloride. Solid line, for Ml = 760 nm , = 35 run, and d = 1.5 nm. Dashed line, for rigid cylinders with Ml = 760 nm and d = 1.5 nm.

The best value of d consistent with the [7/] data was found to be 1.6 ( 0.2) nm. The solid line A in Figure 5-10, calculated with q = A2 nm, Ml = 715 nm, and c/ — 1.6 nm, is seen to fit the data points veiy accurately. Its close fit even for Mw above 3x10 appears to indicate that [77] undeigoes less excluded-volume effect than does (5 ) (compare with Figure 5-3). However, this result is an accident due to the defect of the Yamakawa-Fujii-Yoshizaki theory which overestimates [77] near the coil limit. 

Importantly, Yoshizaki and Yamakawa [25] found that, in contrast to /, [77] of a wormlike cylinder undergoes significant end surface effects until the axial ratio p reaches about 50, on the basis of numerical solutions to the Navier-Stokes equation with the no-slip boundary condition for spheroid cylinders, spheres, and prolate and oblate ellipsoids of rotation. They constructed an empirical interpolation formula for [ y] of a spheroid cylinder which reduces to eq 2.37 for p > 1 and to the Einstein value at p = 1. Then, with its aid, Yamakawa and Yoshizaki [4] formulated a modified theory of [77] for wormlike cylinders which agrees with the Yamakawa-Fujii theory [3] for Lj lq > 2.278 and with the Einstein value at Ljd = 1, regardless of dj2q smaller than 0.1. However, no formulation has as yet been made for L/2q < 2.278 and d/2q > 0.1, i.e., for short flexible cylinders. In what follows, the Yamakawa-Yoshizaki modification is referred to as the Yamakawa-Fujii-Yoshizaki theoiy. 

We further analyzed the [ ] data in terms of the Yamakawa-Fujii-Yoshizaki (YFY) theory originally developed for worm-like chains [67,68]. According to Bohdanecky [69], the YFY theory could be cast in a much simpler form... 

The Yamakawa-Fujii theory neglects the friction on the end surfaces of the wormlike cylinder. Norisuye et al. [23] and Yoshizaki and Yeimakawa [25] estimated them by capping each end of a wormlike cylinder with a hemisphere and a straight spheroid, respectively. The results showed negligible effects on / unless the axial ratio p of the cylinder is smaller than 10, implying that the Yamakawa-Fujii theory of / is applicable down to vety low M. 

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