Z-average mean square radius

Despite the non-random-coil-at-theta conditions, Eq. (9) is commonly referred to as the z-average mean square radius. The cross-term of Eq. (9)... 

The z-average mean-square radius of gyration is defined as... 

The quantity K equals 4it X sin (9/2), where X is the neutron wave length and 9 is the angle of scatter. Thus, the Z-average mean square radius of gyration, R, and the polymer molecular weight, Mj, may be obtained from the slope and intercept respectively of a Zimm plot of [dZ/dn] vs. K. The values of and Rg were evaluated after appropriate subtraction of the scattering from an unlabeled polymer matrix (blank) from the samples containing different fractions of labeled molecules. 

Despite the non-random-coil-at-theta conditions, Eq. (9) is commonly referred to as the z-average mean square radius. The cross-term M, rg)iq of Eq. (9) is a quantity measured directly by fight scattering, at small sin (e/2), as clearly may be seen by expanding the term 1/P(0) in Eq. (1) using the expansion of P(0) ofEq. (3). 

The average R is sometimes called the Z-average mean-square radius (for a distribution of random-flight chain species R is proportional to the so-called Z-average molecular weight... 

The experimentalist measures quite easily the mass concentration p, an average molecular mass (i.e. Afw), an average mean square radius of gyration in the limit of zero concentration (i.e. Rg,z), and an average second virial coefficient A2 To these crude quantities correspond the basic quantities... 

A further remark has to be made when the stars contain polydisperse arms. The radius of gyration is now based on the z-average of the mean square radius of gyration over the molar mass distribution while the degree of polymerization is the weight average Also for this case the molar mass dependence of this radius could be calculated and was found to be [83]... 

Since the mean square radius of gyration requires a z-average but the molar mass a weight average the fractal dimension remains unchanged only if the ratio is independent of the molar mass or close to unity. These conditions are mostly fulfilled with polydisperse linear chains but not for the randomly branched ones. Here this ratio increases strongly with the molar mass. 

The leading parameter that characterizes the distributions of randomly branched samples is an exponent Tthat is defined in the next section. The average procedures for the z-average of the mean square radius of gyration and the weight average molar mass results in the relationship [7]... 

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]...

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