Infinitely thin rod

For an infinitely thin rodlike polymer for which d/L = de/Le = 0, we have fi = F 0 = Fx0 = D 0/D = 1, and Eq. (46) reduces to Teraoka and Hay-aka wa s original expression [107] of Dx for rodlike polymers. At high concentrations, the results from the Green function method approach the one from the cage model [107], Teraoka [110] calculated stochastic geometry and probability of the entanglement for infinitely thin rods by use of the cage model, and evaluated px to be... 

In the infinitely thin rod limit, Eq. (50) reduces to Teraoka and Hayakawa s original expression of Dr for rodlike polymers [108]. The latter approaches the equation of Dr derived on the cage model [108, 111] at high concentrations. Teraoka et al. [Ill] estimated pr from calculations of stochastic geometry and probability of the entanglement for infinitely thin rods with the cage model, and obtained... 

The rotational diffusion coefficient can be calculated from Eqs. (50) (52) formulated by the Green function method. The Dr/Dr0 values obtained by Doi et al. for infinitely thin rods should be compared with the theory in which Le = L and D]]0/D, = F,0/F10 = fr = b The theoretical solid curve in Fig. 16b shows a favorable comparison with the simulation data. 

This equation is compared with the exact equation for infinitely thin rods of length L ... 

Thus = 1 for an infinitely thin rod, zero for a sphere, and — i for a flat disc. 

This result could have been written down at once as the infinitely thin rods behave ideally. Between two eonfining walls separated by a distance fiwall prevents contact configurations with the first wall for distanees x>h/2. Hence... 

In the limit D = 0 (and hence q = 0), where the spherocyhnder reduces to an infinitely thin rod, the free volume fraction takes the simple form... 

For short (as compared to the persistence length) chains, L pa, which keep virtually straight configuration, the approximation Piong(q) Prod(q) applies, where the form factor of an infinitely thin rod of length L is given by... 

The effect of length polydispersity on the depletion potential due to infinitely thin rods was calculated by Lang for the low concentration limit hi this case the potential depth and the range inaease independent of the measure for the depletant content However, for logarithmic normal distributions with coefScients of variation, minor effect on the depletion potential. 

Consider an infinitely thin rod, whose linear charge density is A = e A. There may be some salt added and the valence of the counterions is if > 0. Let call r the distance of the counterion from the rod and look at a configuration where the counterion is at ri < ro whereas any other counterion is farther than... 

Wormlike chain of contour length L and persistence length 1 Excluded volume chain of contour length L Infinitely thin rod of length L... 

For an infinitely thin rod of length L, the form factor reads [23] ... 

Figure 6 Theoretical Scattering for Infinitely Thin Rods...

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