Linewidth distribution

If the CONTIN algorithm was running in equal spacing on the logarithmic scale and the linewidth distribution was normalized by the area, then the intensity of scattered light for each fraction P can be expressed as G(lnP ) which is related to G(Pj ) by the relation... 

We shall Illustrate our analysis by using one normalized characteristic linewidth distribution G(T, ) from the CONTIN method based on the experimental intensity-intensity time correlation functlon.measured at scattering angle e = 33, concentration C = 3.44x10 g/ml in MEK at 25°C. With fR - 2.56xll "m and... 

The method of cumulants (12) expands g (x) in terms of the moments of the characteristic linewidth distribution... 

We were also able to obtain a continuous linewidth distribution curve 0(ryv,K) from the regularization approach by inversion of equation (15). The result obtained from the Laplace inversion procedure is a set of delta functions G. K) which approximate the continuous G(ryv,K) curve sampled at equal intervals. The subscript w shall henceforth be omitted in the interest of clarity in notation. In order to obtain a size distribution from G(IL,K) we need to convert both the ordinate and the abscissa (IL) in the following way. 

From the regularization approach we obtained the characteristic linewidth distribution. We converted the ordinate according to... 

The existence of a bimodal linewidth distribution may be attributed to several factors. When a polymer is large, interference between segments of the same chain will give rise to an intramolecular scattering contribution to the linewidth. We have ruled out this possibility since K has a maximum value of 1.2 and is often much less than one in our experiments. Thus, our experiments cannot observe the contributions due to internal motions and they amount to, at most, one to two percent of the total scattered intensity.(lO) We have also made other studies whereby a second faster peak can be attributed to a pseudo-gel motion in semidilute solutions (l ). This explanation is unreasonable because the concentrations of our solutions are very small. We should not have reached the semidilute regime. 

Transformation to Molecular Weight. If the llnewldth distribution represents only translational dlffuslonal motions of a blmodal molecular weight distribution, we may be able to transform the measured linewidth distribution to a molecular weight distribution. The procedure has been outlined In paper IV (]4 ). Briefly, we make use of the Mark-Houwlnk expression relating the diffusion coefficient at infinite dilution (D ), the molec-... 

Figure 12. Flow chart indicating the scheme for deducing measurable properties from the linewidth distribution and molecular-weight distribution and comparing them to the observed, static, and dynamical results (O) measured values and (A) model-dependent, deduced quantities. Parentheses refer to equation numbers and brackets indicate important parameters required for each step. Single arrows indicate direct calculations, double arrows are comparisons, and triple arrows show values that are forced to agree. Gyration radii not capitalized are concentration dependent, the argument, (C), being omitted for clarity.

We have attempted to transform the linewidth distribution to a molecular weight distribution and, in the process, determine the shape of the larger fraction. While actual values of for each fraction are inaccessible, results indicate the smsiller fraction to be on the order of 1.5 x 10 g/mole and the larger one about 1 X 10° g/mole or greater. These values correspond to aggregates of U and 15 or more of the polysaccharide chains. The shape of... 

Dynamic properties of PS/TOL, PS1/PS2/T0L and PS1/PMMA2/T0L semidilute solutions (in which PS, PMMA and TOL denote polystyrene, poly(methyl methacrylate), and toluene, respectively 1" denotes the matrix polymer and 2 , the probe polymer) have been studied systematically by using dynamic light scattering. Unimodal characteristic linewidth distribution was observed for two narrow PS/TOL binary solutions consisting of... 

M /Mn s 1.20. But two modes in the characteristic linewidth distribution appeared in a polydisperse PS/TOL binary solution with = 23 x 10°, Muj/Mn 2.0, which indicated that polydispersity could lead to the observed bimodal behavior in the characteristic linewidth distribution... 

Fig. 2(b). Plot of the characteristic linewidth distribution G(T) vs. f from the CONTIN analysis for LPS80. Only one narrow peak is obtained. 

By using the CONTIN analysis, we obtained one characteristic linewidth with a small variance for the two narrow MWD PS samples and two linewidths for the broad MWD PS sample. Figures 2b, 3b and 4b show the characteristic linewidth distribution of LPS80, LPS100 and LPS230 binary PS/TOL solutions, respectively. Numerical values of the data analysis of binary PS/TOL solutions are listed in Table 5. A is the integrated area of the observed peak for the characteristic linewidth distribution from the CONTIN method of analysis. 

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