Scaling parameters chain radius

This has also been studied experimentally and theoretically by the Saclay group.Let us start from the good solvent side, at a fixed concentration c = and progressively reduce the excluded volume parameter i = a (1 - 2 )- When u a (athermal solvent), the scaling formulas of Chapter III hold. When v becomes much smaller than a , the single chain radius/ decreases and the overlap concentration c = N/R increases. To make this more precise, we use the Flory formula for / as a function of v [eq. (1.38)]... 

In equation (5.33), as previously defined, An is the second virial coeffi-cient of the / -biopolymer component on the molal scale (cm mol- ) and RGl is the radius of gyration of the / -biopolymer component. For a flexible polymer chain the value of the penetration parameter y/ lies in the range 0.6-0.7, while for a semi-rigid/worm-like polymer we have y/ - 0.3 (Tanford, 1961). The shorter the polymer chain, the closer is its effective conformation to that of the equivalent hard sphere. 

A 13.2.1 Choice of The parameter determines the momentum region where the observables cross over from being governed by scales r Rg or r 1 to being dominated by r l/q < Rg, R B. The radius of gyration Rg is defined by the small momentum behavior of the (normalized) density correlations of an isolated chain... 

This model shows that the radius of polymer particle follows simple scaling relationships with the key parameters in the system x1/3, [comonomer]02/3, [macromonomer]01/2, and [initiator]0 1/2, where [ ]0 means initial concentration. These equations also predict that the particle size and stabilization are determined by the magnitude of In addition the surface area occupied by a hydrophilic (PEO) chain follows x 1/3 in the case of azeotropic copolymerization, x=Xj. This means that the PEO chain conformation for chains grafted onto the polymer particles change with grafting density. 

It is pertinent to point out here that a corresponding universal scaling relationship is found [Aral et al., 1995 Tominaga et al., 2002] between ur and an, the chain expansion parameter for the hydrodynamic radius determined from translational diffusion. However, the scaling observed deviates substantially from the QTP theory when the latter is constructed using the Barrett equation for an [Barrett, 1984] ... 

This equation coincides with the OSF expression " " for the chain s bending rigidity in the presence of the electrostatic interactions. The new feature in comparison with the OSF result is the existence of the second length scale charaaerized by the parameter /I2 " It is worth pointing out that at low salt concentrations (large values of the Debye radius), the dependence of... 

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