The rms radius of gyration

The end-to-end distance is an ambiguous quantity for a branched chain. In such cases, the rms radius of gyration Rg is used as a measure of the polymer 

For linear polymers, there is a very simple relationship between r and 

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Table IV. Adsorbed layer thickness 5 and the rms radius of gyration (S2) 5...

Another measure of the size of a polymer coil is the rms radius of gyration, Rq, defined by... 

In addition to the RMS end-to-end distance, the dimensions of linear chains are often characterized in terms of the RMS distance of a chain segment from the center of mass of the molecule. It is defined as the square root of the average squared distance of all the repeating units of the molecule from its center of mass and is known simply as the RMS radius of gyration, S It is thus given by [14]... 

Problem 3.9 For polystyrene of molecular weight 100,000, calculate approximately the solution concentration below which the Flory-Krigbaum theory should be used. Use the following relationship between the RMS radius of gyration and the polymer molecular weight M 2 x cm. 

Similarly the RMS radius of gyration for perturbed dimensions in real chains, is greater than that for unperturbed dimensions. 

K12 Kim, S., Cotts, P.M., and Volksen, W., On-line measurement of the rms radius of gyration and molecular weight of polyimide precursor fractions eluting from a size-exclusion chromatograph, J. Polym. ScL PartB Polym. Phys., 30, 177, 1992. 

An equivalent measure of the dimensions of a simple chain is the RMS radius of gyration s Y which is the RMS distance of the elements of the cham from its centre of gravity. It can be shown that s Y is related simply to r Y through the equation... 

Other parameters used as a measure for the dimension of a polymer molecule include rms radius of gyration (Rfi, average span the maximum extension averaged in all direction), and Hollingsworth radius ((/ hoii) the radius of the smallest sphere that contains all the segments of a chain). Their relationships, for a random coiled polymer chain, can be summarized as... 

The end-to-end chain distance is a readily conceivable but not a directly measurable quantity. Also, it loses all physical significance with branched chains, which possess more than two chain ends. A related quantity is the radius of gyration. It is directly measurable as the mean square radius of gyration, which is defined as the second moment of the mass distribution around the center of mass. The root mean square (rms) radius of gyration, often simply called radius of gyration, is thus... 

Concentration and molecular weight dependences of the probe radius of gyration Rg for molecular weight P probes in solutions of molecular weight M matrix polymers as functions of matrix concentration c. The fits are to stretched exponentials Rgo exp(—ac"), with the percent root-mean-square fractional fit error %RMS, the materials, and the reference. Materials include EB-ethyl benzoate, PMMA-polymethylmethacrylate, pS-polystyrene. 

However, expansion of the molecular coil due to volume exclusion is not uniform, and is greatest where the segment density is highest. Thus a different expansion parameter is required to account for expansion from the unperturbed RMS radius of gyration... 

Because there are many possible ends in branched polymers, it is customary to use the radius of gyration S) instead of r for such polymers. The radius of gyration is actually the RMS distance of a chain end from the polymer s center of gravity. S is less than the end-to-end distance (r), and for linear polymers = 6S. ... 

FIGURE 3.15 Standard plot of the log of the mean radium of gyration versus log molecular weight for differently shaped macromolecules. Essentially, for a sphere the radius is proportional to the root-mean-square (RMS) radius, and with a slope in the logrg versus log M of 1/3 for rod-shaped polymers, length is proportional to RMS radius and M with a slope of 1 and for random coils the end-to-end distance is proportional to the RMS radius and with a slope of about 0.5-0.6. 

Table 1. Summary of the RMS Deviation, RMS Fluctuation, Radius of Gyration, SASA, Hydrophobic exposed SASA, Solvent Diffusion, Average Distances and Hydrogen...

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