Mean radius of gyration

VSTR = O Connell characteristic volume parameter, cm /g-mol ZRA = Rackett equation parameter RD = mean radius of gyration, A DM = dipole moment, D R = UNIQUAC r Q = UNIQUAC q QP = UNIQUAC q ... 

MEAN RADIUS OF GYRATION, ANGSTROMS DIPCLF MOMENT, DEBYES... 

MEAN RADIUS OF GYRATION OF COMPONENT I I A I. CRITICAL TEMPERATURE OF COMPONENT I (DEGREES K). TEMPERATURE OF MIXTURE (DEGREES Kl. 

Mean radius of gyration, 1/2 Entropy change with deformation. 

Fig. 4.2. Mean radius of gyration plotted versus the mean hydrodynamic radius for different micelle shapes according to theoretical predictions (solid lines). Circles give experimental quasi-elastic light scattering results for SDS micelles at different temperatures in 0.6 M NaCl. (From Ref.34 )...

Mean Radius of Gyration. The mean radius of gyration, R, of the pores can be obtained from the so-called Guinier plot (20) ... 

For this, the inverse 1/RGZ of the mean radius of gyration must fall in the middle of the observation window defined by (15.1.22). The result is obtained, for instance, with chains of radius Raz 200 nm. In order to visualize the three correlation ranges, it is convenient to represent the scattered intensities in the form... 

The characteristic ratio CL for is related to the ratio Cy, for the mean-square radius of gyration (Eq. [7]). For a random (freely jointed) chain, CL = 6C. Therefore, there is a relation between the persistence length, the mean end-to-end distance, and the mean radius of gyration in the limit of long chains. Through this relation, we appreciate that Rq) can also be used to describe polymer flexibility. 

In the physical chemistry of polymers, the degree of branching is described by the g-factor, which is defined as the ratio between the mean radius of gyration of the branched chain and that of the linear chain of the same molecular mass... 

On the other hand, many sharp fractions are available with several homologous series of random coil molecules. Common parameters to indicate the size of random coils are the root-mean-square of end-to-end distance, mean radius of gyration and the radius of the hydrodynamically equivalent sphere. Various discussions have been presented in the previous works with regard to the appropriate choice of the parameter or the correction factor for it (ref. 14, 25, 27, 29, 30, 31, 34). These discussions, however, have all ignored the wall effect described above and hence their significance is limited. 

As reflected in size measures such as the mean radius of gyration i g or mean-square end-to-end distance an isolated polyelectrolyte chain in dilute solu-... 

Rg The root mean radius of gyration calculated as the root mean square distance of the elements making up the relative to a chosen reference such as an axis or the centre of gravity. 

For the application system involving acetic acid in Chapter 9, the above representation in Eq. (2.3) is not accurate enough. The reason is that acetic acid can exhibit association leading to dimerization in the vapor phase. Hayden and O Connell used the virial equation of state tmncated after the second term. They developed a correlation for the second virial coefficient of polar, nonpolar, and associating species based on the critical temperamre and pressure, the dipole moment, and the mean radius of gyration. Association of like and unlike molecules is described with the adjustable association parameter. Pure component and binary values for the association parameter are available in the Aspen Physical Property System. For detail calculations in the vapor phase, please refer to the above Hayden and O Connell paper and also to Aspen Physical Property System. ... 

For a Gaussian coil P(0) is related to the mean radius of gyration of the polymeric chain (S) by ... 

Fig, 9.34 The mean radius of gyration as a function of membrane size L for membrane with n monomers between each vertex. Here n = 0 ( ), = 1 ( ) and n = 8 ( ). Note that the compact membrane (n = 0) has the same slope as the perforated membranes. The slope of each line is 1.0. 

The average structural properties at finite temperatures can be characterized well by the mean end-to-end distance and the mean radius of gyration (iigyr)(7), as shown... 

Mean end-to-end distance (/ ee> and mean radius of gyration Rg, of the42-mer. From [40]. 

Figure 8.2 shows the specific heat, as well as the derivatives of the mean end-to-end distance and of the mean radius of gyration with respect to the temperature,... 

Mean radius of gyration (%> as a (unction of the temperature T for the sequences20.1-20.4 (solid curves), 20.5,20.6 (long dashes), and for the homopolymer /I20 (short-dashed curve). From [189]. 

In Fig. 8.7, the mean radii of gyration as a function of the temperature for the sequences from Table 8.1 are shown in comparison with the homopolymer. For all temperatures in the interval plotted, the homopolymer obviously takes more compact conformations than the heteropolymers, since its mean radius of gyration is always smaller. This different behavior is an indication for a rearrangement of the monomers that is particular for heteropolymers the formation of the hydrophobic core surrounded by the hydrophilic monomers. Since the homopolymer trivially also takes in the ground state a hydrophobic core conformation (since it only consists of hydrophobic monomers), which is obviously more compact than the complete conformations of the heteropolymers, we conclude that hydrophobic monomers weaken the compactness of low-temperature conformations. Thus, homopolymers and heteropolymers show a different phase behavior in the dense phase. Homopolymers fold into globular conformations which are hydrophobic cores with maximum number of hydrophobic contacts. Heteropolymers also form very compact hydrophobic cores which are, of course, smaller than that of the homopolymer due... 

The relaxation time xr specifies the time required for a chain molecule to diffuse over a length comparable to its own size, Rm is a mean radius of gyration, fD is the Debye function for a Gaussian chain, and Xs is the Flory-Huggins interaction parameter x at the mean-field spinodal temperature Ts(m.f.). 

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