Radius of gyration root-mean-square

The procedure is obviously a very simple one, but suffers from the fact that the success rate diminishes very rapidly as the pore radius becomes smaller. The root-mean-square radius of gyration of... 

Figure 3. Partition coefficient of freely jointed chains between the bulk solution and a cylindrical pore. The chains have different numbers of mass-points (n) and different bond lengths, and are characterized by the root-mean-square radius of gyration measured in units of the pore radius. See text for details.

For a statistical coil, the product of polymer intrinsic viscosity and molecular weight is directly proportional to the cube of the root-mean-square radius of gyration RG 77137... 

Debye scattering deals with the situation wherein the relative size parameter is large. Since the root mean square radius of gyration of the particle, (s2)1/2, is a... 

An estimation of the local ligand concentration, [N]coii> could be achieved by assuming free movement of the ligands in the interior of a sphere with radius i, the root mean square radius of gyration of the polymer chain ... 

Fig.6 Temperature dependence of z-average root-mean square radius of gyration ((Pg>) and average hydrodynamic radius ( Rh)) of copolymers NIPAM-co-VP/60/5 and NIPAM-co-VP/30/5 in water, where the weight average molar masses are 2.9 x 106 and 4.2 x 106 g/mol, respectively [56]...

Experimental Assessment, The most direct experimental assessment of the persistence length may be obtained from the root-mean-square radius of gyration measured by light scattering. The analytical expression for the unperturbed Rq of a. wormlike chain has been given by Benoit and Doty (5) ... 

A method for calculating observables resulting from incoherent excitation transport among chromophores randomly tagged in low concentration on isolated, flexible polymer chains is described. The theory relates the ensemble average root-mean-square radius of gyration ) of a polymer coil to the rate... 

Due to the sensitivity of electronic excitation transport to the separation and orientation of chromophores, techniques which monitor the rate of excitation transport among chromophores on polymer chains are direct probes of the ensemble average conformation (S). It is straightforward to understand qualitatively the relationship between excitation transport dynamics and the size of an isolated polymer coil which is randomly tagged in low concentration with chromophores. An ensemble of tagged coils in a polymer blend will have some ensemble averaged root-mean-squared radius of gyration,... 

Problem 4.18 For the polystyrene sample in Problem 4.17 calculate (a) the second virial coefficient, (b) the root mean square end-to-end distance, and (c) the root-mean-square radius of gyration. 

Several parameters, most of which are interrelated and can be estimated in terms of each other, are utilized to describe the conformational properties of polymer chains [1,2]. These quantities include the steric hindrance parameter a, the characteristic ratio Cx, the persistence length Ip, the statistical chain segment (or Kuhn segment) length lk, the root mean square radius of gyration Rg (often briefly referred to as simply the "radius of gyration"), and the molar... 

The interfacial thickness of PP/PA/PP-MA system was estimated by ellipsometry to be thick, Al = 40 nm, much larger than the coil size of the component polymers, viz. the root-mean-square radius of gyration = 3.7 10 nm... 

The limited success of this relation was attributed by Stockmayer and Fixman to the fact that the root-mean-square radius of gyration is not directly related to the hydrodynamic behavior of the macromolecule when the molecular shape is changed by branching, since the form of the distribution of the parts of the molecule about its center of mass is also altered. As a result, the flow of solvent through the molecule is too complex to be related to the simple radius of gyration. From such considerations, Stockmayer and Fixman obtained a relation of the form... 

Challa et at. [115, 129, 130] particularly examined the effect of chain length on the oxidation rate of disubstituted phenols. Consequently, several copolymers containing styrene and amine units were synthesized. By application of the following expression for the root-mean-square radius of gyration of a macromolecule. 

Can the wormlike model fit other data It was argued above that the Kuhn-equivalent approximation to the xanthan chain (M=10 ) is 50 freely jointed links each 100 nm long. For this chain, the root mean square radius of gyration s can be estimated ... 

The left-hand side of the equation is the third power of the root-mean-square radius of gyration of the molecule (proportional to the volume or size of the molecule). The right-hand side contains the product of the molecular weight M of the polymer and the intrinsic viscosity [> ]. is a proportionality constant. Braoit et at. (4) found that he could obtain a univer curve for aU polymers when he plotted the product of the intrinsic viscosity and the molecular weight against the dution volume. 

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