Gaussian coil segment distribution

For polymer melts or solutions, Graessley [40-42] has shown that for a random coil molecule with a Gaussian segment distribution and a uniform number of segments per unit volume, a shear rate dependent viscosity arises. This effect is attributed to shear-induced entanglement scission. 

It follows from Eq. (29) that at x—> 0, Px— 4/x-— oo, corresponds to an infinitely thin straight rod. In the Gaussian coil conformation x tends to infinity and it follows from Eq. (29) that pj tends to unity, corresponding to a model with a spherically symmetrical segment distribution. 

Even in his early works Kuhn has shown that the most probable form of a random Gaussian coil is described by a non-spherical distribution of segments. ... 

Typically in solution, a polymer molecule adopts a conformation in which segments are located away from the centre of the molecule in an approximately Gaussian distribution. It is perfectly possible for any given polymer molecule to adopt a very non-Gaussian conformation, for example an all-trans extended zig-zag. It is, however, not very likely. The Gaussian set of arrangements are known as random coil conformations. 

In the third model the polymer is modeled as a flexible coil while the protein is modeled as a rigid sphere. The second virial coefficients for such a sphere-coil model have been calculated analytically by Hermans (17) who assumed that the segments of the flexible particle do not interact with each other and are Gaussian distributed. The resulting cross second virial... 

Unlikely the previous calculations of AF of the coil-globule transition, where the Gaussian distribution of segments in a macrornolecule was assumed (eg. see Equation 2), Bir-shtein and Pryainitsyn (1987) have applied Fixman s (1962) distribution function valid for the range R Rs... 

In the case of a flexible-coil molecule, even under quiescent conditions, there is no abrupt cut-off of overlap with decreasing concentration, owing to the Gaussian probability distribution of a segment occupying a volume at some distance from the origin. 

For ideal polymer coils, the most significant and distinctive property is the Gaussian distribution of the end-to-end distances. By considering the different segments of the freely jointed chain which are statistically independent and can be represented by a Markov chain, one can derive the correction to the Gaussian distribution of the end-to end distances (see Reference 99). 

In many circumstances it is possible to extend the range of measurements with neutrons to cover more than this low Q limit, and then more detailed models of the structure must be evaluated. Debye [22] has derived a result for the scattering from a Gaussian distribution of polymer segments appropriate to a random polymer coil which is of the form ... 

Random polymer coils are often called Gaussian chains because the probability distribution function (for finding a segment in a given volume element) has a Gaussian shape. For linear Gaussian chains, the r.m.s. radius of gyration is... 

---