Scattering from Random Coil Polymers

Light Scattering from Random Coil Polymers 

Equation 12-37 is the general equation for light scattering from polymers. If you ve jumped from page 367, you should know that the factor P 9) depends upon the shape of the molecule. Our interest is in the most common case of random coils in dilute solution, where P(B) can be simply expressed as a series in 9. It is usual to truncate this series after the second term, giving our final result, shown in Equation 12-38 in all its complex glory. 

Accurate measurements at low angles are not that easy, however, and more often a method described by Bruno Zimm is employed. Examine the scattering equation (Equation 12-38) carefully. A plot of  

Equation 12-38 can be used in a couple of ways to measure molecular weight. One obvious approach is to measure scattering at 9 0, where P(9) -1 (sirrQ/2 = 0) and cos29 - 1, so Equation 12-38 reduces to Equation 12-39  

FIGURE 12-22 Zimm plot of data reported in Margerson and East (see suggestions for further reading). 

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Light Scattering from Random Coil Polymers... 

Apart from their utility in determining the correction factor 1/P( ), light-scattering dissymmetry measurements afford a measure of the dimensions of the randomly coiled polymer molecule in dilute solution. Thus the above analysis of measurements made at different angles yields the important ratio from which the root-mean-square... 

Thus both the numerator and denominator terms in Eq. (41), or in Eq. (44), depend on the concentration. Because of this situation empirical extrapolation of D is particularly hazardous (for random coiling polymers). If F2 is known from osmotic or light-scattering measurements at a series of concentrations, extrapolation according to Eq. (44) will be facilitated. (If such measurements have been carried out, however, the molecular weight also will have been determined.)... 

We now consider the intensity of independent scattering from a random coil polymer molecule, consisting of (N + 1) beads connected by N bonds and obeying the Gaussian approximation (5.12). We assume that the volume of a bead is uu and the volume of the chain is v = (N + l)uu. Each bead thus contributes po u to the... 

The intensity I(q) of scattering from a single random-coil polymer molecule in solution, obeying Gaussian statistics, can be written (see Section 5.2.3.1) as... 

Light scattering spectra of random-coil polymers differ from spectra of colloidal particles random coils have observable internal modes. At small q, polymer and colloid internal modes involve distances small relative to so internal modes do not contribute to the time dependence of 5(, t). At large 5(, t) of a rigid particle reflects only center-of-mass motion, because rigid probe particles lack observable internal motions. In contrast, for large q internal modes of flexible molecules involve motions over distances comparable to and thus contribute directly to S q,t). Except at extreme dilution, interactions between polymer chains affect both polymer center-of-mass motion and polymer internal motions. 

There has been a sharp debate for many years on the best description of the real macroconformation. Much experimental research has been carried out on pure polymers using different techniques (225) [small angle and intermediate angle neutron scattering (226), electron microscopy, IR, etc.]. Yoon and Flory (40, 228-231) and Gawrisch et al. (232) held the view that the probability of adjacent reentry in polymeric lamella is rather low (<50%) and does not justify the validity of such a model. The trajectory of the chain extends across numerous lamellae and its macroconformation is not far from that of the random coil. In the view of Keller and co-workers (224, 233-236) the adjacent reentry, although not complete (3 1 with respect to other possibilities) largely prevails. 

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