Hydrodynamic radius Gaussian chain

Monte-Carlo simulations are applied to estimate the characteristic ratios and p parameters from the RIS models for PE, POM, polybutadiene, and polyisoprene. Here the p parameter is defined as the ratio of the radius of gyration to the hydrodynamic radius. The p parameters of these real chains in the unperturbed state show only a slight dependence on the microconformation in the limit of large molecular weights and are found close to 1.504, which is the value for an idealized Gaussian chain. The estimated p parameters of the real chains appear to be correlated to the chain stiffness and increase with the characteristic ratios. 

One can expect that the parameter of hydrodynamic interaction (2.11) behaves universally for subsequent division of the chain. One can reasonably guess that the quantity (2.11) does not depend on the length of the macromolecule and on the number of subchains. In this case, the hydrodynamic radius of the particle for the Gaussian chain... 

The reason why Aoop is given by Eq. 4.43 is as follows. In Section 3.2.7, we learned that the hydrodynamic radius of a linear chain polymer is given as the reciprocal of the average of where r is the distance between two monomers on the chain. We used the definition to estimate Re for a chain with a Gaussian chain conformation. We can use the same formula to calculate D oop for the cooperative dynamic mode of the blob. It is given by... 

The shape of this Gaussian function is given in Figure 2.10a. Here, rIP R) is plotted against R/Re, where Re = /Ni is the root mean square end-to-end distance for a Gaussian chain. The radius of gyration, root mean square end-to-end distance, and the hydrodynamic radius (in units of Re) are also marked,... 

Figure 2.10 (a) The normalized end-to-end distance probability distribution function for a Gaussian chain. The radius of gyration Rg and the hydrodynamic radius R are shown in units of the root mean square end-to-end distance R. (b) Sketch of the long-ranged segment density profile falling inversely with the radial distance from the center of the chain. 

Fig. 10 Dependence of the hydrodynamic part of the diffusion coefficient, Dh =D — Dq/N, on the hydrodynamic radius for Gaussian chains of lengths = 10, 20, 40, 80, and 160 right to...

Equation [156] underestimates the ratio of Rh/Rg by about 15% ° when compared with the experimental one at the 6 temperature. Similar calculations can be made for Gaussian chains with other architectures. In real chains, the expansion of chain dimension by exduded-volume effects brings about an expansion of the hydrodynamic radius. ... 

In the limit of N—both l h and 1 , scale with the degree of polymerization in the same way as the gyration radius of the Gaussian or swollen coil N"a. Remarkably, for finite-length semiflexible chains, the nondraining condition does not strictly apply. As a result, deviation in the observable N dependence of the gyration radius and those of the hydrodynamic radii... 

---