Intramolecular structure factor

The intramolecular structure factor Iin,ra>M given in body-fixed coordinates (M) can be written in terms of atomic scattering factors and the atomic distance distribution, yielding... 

Accounting for molecular conformations or torsional and rotational chain dynamics, it is more useful to calculate the mean intramolecular structure factor in terms of density correlation functions (DCF). The structure factor results simply from a Fourier transform of the corresponding DCF. 

More sophisticated approaches to the evaluation of wfr) exist. Some of them are the technique based on the Yoon-Flory expansion, variations of the Gaussian approximation, and an implementation of the Koyama distribution. Freely jointed chains and rotational isomeric chains have also been used as models of chains. Research is actively pursued on the subject of formulating more realistic closure relationships. In considering the choice of an intramolecular structure factor, a paper by McCoy et al. on model polyethylene melts will be useful. 

Results from the PRISM theory have also been compared with results from molecular dynamics calculations on dense chain liquids of degree of polymerization equal to 50 and 200d The two approaches were compared for the intramolecular structure factor and the intermolecular radial distribu-... 

Another exciting development gets rid of the limitation (i) from the start by basing the approach on theoretical developments in the theory of fluids [44-49, 52, 224-225]. These theories all are based on the concept of the direct correlation function [226] related to the direct interaction between monomers the total correlation function is expressed approximately in terms of the intramolecular structure factor and this direct correlation function, which needs a suitable decoupling approximation, which can be motivated by suitable... 

The same molecular closures proposed for homopolymer blends [68-70] apply to copolymers but the intramolecular structure factor matrix is now non-diagonal. Equation (8.8) becomes [86]... 

The difference in fhe moment of inertia vectors is equal to the difference in the absolute location vectors of the subchains 4 - Sy = 4. The second average is then equal to the scattering fxmction for a single molecule, S i(ij) (Equation 3.7). The total scattering fxmction is then expressed as the product of the center-of-mass structure factor and the intramolecular structure factor ... 

Within the low q limit, the intramolecular structure factor is as given in Equation 3.9, and Equation 5.40 becomes ... 

It is important to note that in calculation of the intramolecular structure factors for input into PRISM theory, one can include as much (or as little) chemical detail regarding the molecular architecture as desired. For questions regarding intermolecular packing on relatively long length scales (e.g., the so-called correlation hole regime corresponding... 

At the most coarse-grained level the polymer is described as an ideal random walk on all length scales. The intramolecular structure factor matrix is Gaussian and given by" = exp(-/c"o- a - yl/6), where... 

Figure 34. Self-consistent PRISM structural predictions for (a) average intramolecular structure factor plotted in Kratky form, and (b) site-site intermolecular radial distribution function for N = 100 hard-core chains at a concentrated solution packing fraction of 0.3. The points are the many chain simulation results and the lines are the PRISM results based on the PY-style solvation potential and the simplified version of the variational generating functional method of Grayce et al. discussed in the appendix of Ref. 47.

Chain contour length Molecular weight The mass per unit length, MIL The weight average molecular weight Avogadro s constant The intramolecular structure factor see Equation 8.14... 

Phv(Q 9 8) The intramolecular structure factor for the vertically polarized component of the scattering with vertically polarized incident light see Eq. 62... 

The scaling region is best analyzed in terms of the ideal chain intramolecular structure factor. If we consider a sphere of radius r which contains m beads on the same chain, then... 

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