Gyration vector

It has to be mentioned that the radii of gyration of the high molecular weight chains (which are of the order of 300 A) could not be determined in the fiame of the present study. Reaching scattering vectors as low as 10 A" , which would have been required, involves technical difSculties on the spectrometer and very long counting times. 

All experiments were carried out on sample SI. The radius of gyration of an isotropic sample, determined from the Zimm plot in the low scattering vector range, is close to 82 A. 

One can also analyze the rotational relaxation of the adsorbed molecules.140 Figure 27a shows a time sequence of a single molecule with an overlay of the unit vector u(t) defined as the direction of the longer principal axis of the gyration tensor. An instantaneous polymer configuration may be described by an ellipse, and therefore, the simplest conformational change is the rotational motion of an ellipse. The time correlation function of u(t) decays exponentially where zr denotes the rotational relaxation time, °c exp(-f/rr). 

The radius of gyration of any polymer can be determined from the wave-vector q dependence of the scattering intensity at low angles qRg < 1) in the limit of zero concentration ... 

The mean-square radius of gyration is the second moment of the distribution of monomers around the centre of mass of the chain [Eq. (2.44)]. The mean-square radius of gyration of an ideal linear chain with N Kuhn monomers of length b is related to its mean-square end-to-end vector [Eq. (2.54)] ... 

The set of real numbers The rt-dimensional vector space Real part of a complex number Sample-to-detector distance Guinier radius (i.e. radius of gyration)... 

The function p(r) represents the frequency of vector length r connecting small volume elements within the volume of the scattering particle, that is, the protein molecule, with maximum dimension Dmax- As the use of the Guinier approximation for the determination of the radius of gyration, Rg, might lead to errors caused by concentration or aggregation effects, we used the normalized second moment of the pair distance distribution function for calculation of R, ... 

No Debye behavior characteristic of the Gaussian coil has been observed. Such a dependence can be studied by making a Zimm plot in the range qR < 1 with q the scattering vector and R the radius of gyration. 

Molecular conformation is an important subject of concern in liquid crystalline polymers. It is also the basic subject of polymer science. The mean square end-to-end distance or the radius of gyration is often used to characterize the size of a polymer molecule. According to the definition, the end-to-end distance is the sum of each rod s vectors in sequence... 

The radius of gyration is essentially the root mean-square radius of a macromolecule (Tanford, 1961). Let R be a vector locating the center of mass of a molecule and let r be a vector locating segment i with mass mi. Then by definition... 

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