Weight Distribution of the Particle Size

From both scattering techniques, PCS and TDFRS, it is possible to determine the rate distribution P(I), or the pk in the discrete case. By means of the Stokes-Ein-stein relation, 

P(r) can be transformed into a distribution of the particle size as defined by the hydrodynamic radius Rh. But only for TDFRS, and not for PCS, a particle size distribution in terms of weight fractions can be obtained without any prior knowledge of the fractal dimension of the polymer molecule or colloid, which is expressed by the scaling relation of Eq. (39). This can be seen from the following simple arguments  

P(r) is the rate distribution as obtained from ket(t) or gj(t). From the continuous form of Eq. (40) it follows that 

For simplicity, normalization factors and proportionality constants have been omitted. Hence, for short and long exposure TDFRS, Eq. (50) reduces to c (Rh) P(r(Rh)) R 2 and c (Rh) °c P(r(RfJ) R 3, respectively. Eq. (50) can easily be generalized for TDFRS with arbitrary exposure times Tp by means of Eq. (32). In the case of PCS, Eq. (50) becomes c (Rh) x P(r(Rh)) R/, 2 l/, ) and c (R )cannot be obtained without knowing b. Fig. 19 shows c (Rh) as obtained from P(D from the insert in the right-hand half of Fig. 16 with Tp = 1.5 s. 

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