Polymers gyration, Root mean square

Synthetic, nonionic polymers generally elute with little or no adsorption on TSK-PW columns. Characterization of these polymers has been demonstrated successfully using four types of on-line detectors. These include differential refractive index (DRI), differential viscometry (DV), FALLS, and MALLS detection (4-8). Absolute molecular weight, root mean square (RMS) radius of gyration, conformational coefficients, and intrinsic viscosity distributions have... 

Root-mean-square end-to-end distance, which effectively takes account of the average distance between the first and the last segment in the macromolecule, and is always less that the so-called contour length of the polymer. This latter is the actual distance from the beginning to the end of the macromolecule travelling along the covalent bonds of the molecule s backbone. Radius of gyration, which is the root-mean-square distance of the ele-... 

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... 

Effect of PVA Molecular Weight on Adsorbed Layer Thickness. Figure 4 shows the variation of reduced viscosity with volume fraction for the bare and PVA-covered 190nm-size PS latex particles. For the bare particles, nre(j/ is independent of and the value of the Einstein coefficient is ca. 3.0. For the covered particles, rired/ t increases linearly with tp. Table IV gives the adsorbed layer thicknesses calculated from the differences in the intercepts for the bare and covered particles and determined by photon correlation spectroscopy, as well as the root-mean-square radii of gyration of the free polymer coil in solution. The agreement of the adsorbed layer thicknesses determined by two independent methods is remarkable. The increase in adsorbed layer thickness follows the same dependence on molecular weight as the adsorption density, i.e., for the fully hydrolyzed PVA s and... 

The constant in Equation (5.112) cannot be readily evaluated using scaling theory. Our transformation applies equally well to the radius of gyration or the root mean square end-to-end length, only the numerical constant changes. We would like to be able to apply this idea to the role of concentration in semi-dilute and concentrated polymer regimes. In order to do this we need to define a new parameter s, the number of links or segments per unit volume ... 

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 ... 

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. 

For random coils, is directly proportional to the contour length. If n is the number of main chain atoms in the chain, = an. The parameter a is relatively insensitive to environment (21), and has been calculated for a number of polymers from strictly intramolecular considerations using the rotational isomeric model (22). The root-mean-square distance of segments from the center of gravity of the coil is called the radius of gyration S. The quantity S3 is an approximate measure of the pervaded volume of the coil. For Gaussian coils,... 

Measurements of hydrodynamic thickness LH have been performed by many investigators and, in most cases, the measured LH were almost twice the radii of gyration of polymer coils in bulk solution. It is desirable to clarify the theoretical relationship between LH and the root-mean-square thickness of the adsorbed polymer layer. Some progress in this direction has been made recently. 

In spite of all the recent success which can be traced to the three techniques, SANS, SAXS, SALS, there are serious limitations in their scope Q). For instance only average values, such as root-mean-square end-to-end distance and radius of gyration of a polymer chain can be extracted from these techniques. In other words, these techniques cannot provide information on the actual conformation or dimension of the individual polymer chain. Also since all three techniques are indirect, the analysis of the raw data is not straightforward and requires various manipulations and faith in existing theories to draw conclusions. Finally with regard to SANS, it must be noted that only a limited number of facilities in the U.S.have this capability, thus restricting its use. 

A radius of gyration in general is the distance from the center of mass of a body at which the whole mass could be concentrated without changing its moment of rotational inertia about an axis through the center of mass. For a polymer chain, this is also the root-mean-square distance of the segments of the molecule from its center of mass. The radius of gyration is one measure of the size of the random coil shape which many synthetic polymers adopt in solution or in the amorphous bulk state. (The radius of gyration and other measures of macromolecular size and shape are considered in more detail in Chapter 4.)... 

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,... 

Another useful parameter is the radius of gyration P, which is a measure of the effective size of a polymer molecule (it is the root mean-square distance of the elements of the chain from its centre of gravity). 

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... 

---