Intramolecular interference

To measure the molecular weight of the molecule, we can modilV equation (B 1.9.23) to take into account the intramolecular interference in the dilute solution range. 

Crosstalk has been discussed fairly extensively, as one of a series of interference phenomena that can lead to a different kind of control of molecular transport than has been discussed in Sect. 7.4. It is also possible to observe intramolecular interference effects. For example, with cross-conjugated molecules [163] or benzene dithiol linked in the 1,3 (or meta) configurations [164-171], both are expected to show substantially reduced transport. 

The autocorrelation function (Fig. 2) shows clearly that a representative chain segment embracing about 5-7 CH2-units should be sufficiently long to describe the intramolecular interference modulation in the WAXS-pattern of a PE-melt completely up to distances of approx. 30 A. 

Rgure la shows the observed X-ray total interference term, Qi fQ). The least squares fitting analysis was applied to the observed interference tend in the range of Q 8 A" in order to detennine the intramolecular stmcture of H2SO4 and HSO4" in the aqueous solution. The calculated intramolecular Interference term was evaluated by the sum of intramolecular contributions from H2SO4, HSO4", 804 ", H3O+ and HgO molecules,... 

When molecules are very large, intramolecular interference must be taken into account in calculations of scattered intensities and spectra. We present here a discussion of these effects for large molecules in dilute solution. 

Intramolecular interference is usually negligible for scattering from small molecules since the wavelets scattered from different segments of the same molecule all have essentially the same phase and hence add constructively at the point of observation. However, for large molecules observed at large values of q, the intramolecular interference depends on the distribution and time rate of change of molecular segmental positions. Thus these effects contain information about molecular shapes, shape fluctuations, and molecular rotations. 

Most of the work on intramolecular interference has been concerned with isotropic scattering. The isotropic scattering is large compared to the anisotropic scattering and is hence relatively easy to measure. Thus the bulk of this chapter is concerned with the isotropic scattering. A discussion of the anisotropic scattering is given in Section 8.9. 

Note from Eq. (8.2.4) that 5(0) = 1, as we expect, since there is no destructive intramolecular interference between light waves scattered from different parts of the molecule when q — 0 they all travel the same distance to the point of observation and hence arrive with the same phase. At high values of q, however, there may be destructive interference between light waves scattered from different parts of the molecule, reducing S(q) from its zero argument value. 

In cases where intramolecular interference is negligable (roughly where max q by(z) - b<(o) < 1)... 

If, however, intramolecular interference is important, intramolecular motions may, in some circumstances, affect the spectral distribution of the scattered light. The general condition for such contributions is that the terms containing the MO and by(0) must contribute a time-dependence to S(q, /). Three cases should be distinguished. 

For flexible polymers the structural change due to intramolecular motions must be large enough for the light wave to detect the difference between the various molecular shapes. Only under these circumstances will intramolecular interference affect the lightscattering spectral distributions. An extreme example of this case, the Rouse-Zimm dynamic model of the Gaussian coil, is discussed in detail in Section 8.8. 

As noted above, experimental measurements must be very carefully performed. All measurements must be extrapolated to infinite dilution. In addition, care should be taken to subtract collision-induced scattering from the data, especially for the shorter chain molecules (see Chapter 14). For larger molecules extrapolation to zero q must be done in order to avoid intramolecular interference effects. Local field effects must also be considered when relating the experimental depolarized intensities to <(y2)>. 

Consider the homodyne correlation function, which is proportional to /i(q, t) 2 for a dilute system with negligible intramolecular interference. Then for a polydisperse system... 

Thus by analyzing the homodyne correlation function at small times and computing L(t), one may obtain both z and its variance <( D)2>Z. The assumptions that enter into these equations should be recalled before applying them to any set of experimental data (a) no interactions between scatterers (infinite dilution), (b) no intramolecular interference (small scatterers and/or small q), and (c) polarizability per unit mass of a scatterer independent of the molecular mass (cf. Section 8.5). 

Elastically scattered radiation reaching a detector from different scattering centers in a macromolecule will be subject to interference effects, provided the dimensions of the macromolecule are comparable to or larger than the wavelength of the radiation (22). The Debye scattering function P(u) describes the variation, arisir from intramolecular interference effects, of the scattered... 

Assuming that the particles are small (no intramolecular interference, see Section 9.5.5), that they are independent of each other (ideal gas or infinitely dilute solution), and that there is no loss of light intensity due to absorption. Equations (9-28) and (9-29) may be combined ... 

Under the conditions of no interactions between molecular (infinite dilution), no intramolecular interference (small scattering vector) and no dependence of polarizability per unit mass of molecule on molecular weight then ... 

The upper M limits of S/LALLS in its present form arise from 3 factors. First, it is necessary to stay below c to get a good separation. As M increases, c necessarily decreases and it becomes difficult to measure Cp with a UV detector. Second, as M increases, intramolecular interference begins to affect the LALLS data even at 6 7 scattering angle. The effect is readily calculated if the radius of gyration of the polymer is known. 

Meyerhoff have found it necessary to use a special extrapolation method to eliminate the effects of particle interactions and intramolecular interferences. They point out that neglect of these aspects may introduce errors in the direct evaluation of the polydispersity using these scattering techniques. 

TABLE 8.1 Relations for R, and the Intramolecular Interference Function P(,q,0) for Several Model Structures" (Rayleigh-Gans-Debye Regime)... 

For a homopolymer with a distribution of molecular weights, r (0,c) reduces to wMJM in the limit of infinite dilution and zero scattering angle for >0, the intramolecular interference function P q,c) discussed in the section on static scattering must be included for large enough size to make P(g,c)[Pg.154]

Interest in stratified spheres has been motivated by research on coated nanoparticles. For such a system, with a sphere of radius R of scattering elements of type A, coated by a shell with radius R of scattering elements of type B, PJiq,0) and Pg(g,0) are the intramolecular interference functions for spheres of radius R and R, respectively, Pls rf" (7.0) and via Equations 8.25 and 8.26 are given by [11] ... 

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