Z-average diffusion coefficient

The exponent a depends on the type of experiment performed, and it has been introduced to allow for a consistent description of the different measurements. a=l for PCS, a=0 for short exposure TDFRS, which guarantees strictly concentration proportional amplitudes, and a=b for long exposure TDFRS. a = 1 leads directly to the z-average diffusion coefficient (D)cM characteristic for... 

D and D are the weight- and z-averaged diffusion coefficients, respectively. Weight averaging is obtained directly by transient electric birefringence. 

For noninteracting particles, Depp presents the so-caUed z-average diffusion coefficient, D) ... 

The initial slope of the plot, F, is now the average time constant, and is related to the Z-averaged diffusion coefficient by equation (1). The degree of curvature of the plot is dependent on the polydlsperslty which can be quantified by the parameter V2/T. ... 

Here the first moment, r, is related to the z-average diffusion coefficient,... 

The same procedure can be applied to the cuiiiulaiits or moiiieiils f7(r). With Stokes-Einstein s formula, the -average hydrodynamic riidius of the inacromolecules is determined from the z-average diffusion coefficient... 

Mes and coworkers compared TDA, DLS, HDC, and SEC and showed that all four methods can be used effectively to determine diffusion coefficients of systems with low polydispersities by measuring a series of styrene acrylonitrile (SAN) copolymers. Although these are polymeric systems, it is possible to apply the findings to supramolecular ensembles. The characterization of samples of low polydispersity was achieved best with TDA and DLS, since they both allow the rapid and absolute determination of the diffusion coefficient. However, TDA has the disadvantage that it is subject to interference due to the presence of low-molecular-mass chromophoric compounds. DLS, on the other hand, is influenced much more by the polydispersity of the sample than TDA. Furthermore, the use of DLS enables direct measurements of the Z-average diffusion coefficient of a polydisperse sample but requires a relatively large amount of the sample and is concentration dependent. Unlike TDA, DLS is especially suited for the analysis of high-molecular-mass systems, such as supramolecular systems, and is not disturbed by the presence of low-molecular-mass impurities. 

Problem 3.8 proves this expansion, hi the absence of distribution, i.e., AF = 0, the second- and higher-order terms disappear, and In gi(T) is a straight line. Cnrve-fitting of the measured hi gi(T) by a polynomial gives an estimate of (F) and (AF ). As found in Problem 3.10, the dififnsion coefficient estimated from (F) for a solntion of a polydisperse polymer is a z-average diffusion coefficient. Often, we nse a simple symbol of F for (F). 

Forced Rayleigh scattering can be used to measure the z-average diffusion coefficient of a PAT in dilute solution. For POT in trichlorobenzene, the diffusion coefficient D = 8 x 10 cm s" and hence the hydrodynamic radius of POT is about 130 A [156]. For copolymers of bithiophene and pyrrole, cyclic voltammetry (cf. Sect. 3.2.1) and UV/vis data support the formation of copolymers, which consist of three distinct oxidizable (dopable) units (i) short blocks of bithiophene units, (ii) short blocks of pyrrole units, (iii) random and alternating groupings of bithiophene and pyrrole [157]. 

The data-acquisition and on-line data-analysis was performed by the Automeasure software, version 3.1 (Malvern). Using a cumulant analysis method the z-average diffusion coefficient D is estimated, from which the inverse z-average diameter di/ is calculated. 

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