Diffusion broadening

As previously stated, GPC is the method of choice for studying polymer degradation kinetics. The GPC trace, as given by the detector output, does not provide the true MWD due to various diffusion broadening processes inside the different parts of the equipment. The first step is to correct for instrument broadening if a precise evaluation of MWD is desired. Even with the best columns available, this correction may change the MWD significantly as can be visualized... 

To solve Eq. 8 to obtain c(s) as a function of s requires Smin and Smax to be carefully chosen and adjusted accordingly inappropriate choice can be diagnosed by an increase of c(s) towards the limits of Smin or Smax- However, a stable solution can only be obtained if the contribution from diffusion broadening is dealt with. 

At this point we can introduce the perturbation procedure based on the fact that c is small. Let us assume that the initial condition is c(x,0) = c08(x), where B(x) is a delta function (—i.e., an initial pulse injection). The principal consequence of a small c is the fact that the bandwidth of the diffusion broadened peak is narrow, going to zero as c vanishes. Thus, we make the approximation that only the region near = 0 in the terms F( + r) and G( + r) is of interest. The resulting value, denoted by Ao( t), therefore satisfies the equation... 

Gilbert, J. R., Design analysis and 3D measurement of diffusive broadening in a Y-mixer, in van den Berg, A., Olthuis, W., Bergveld, P. (Eds.), Micro Total Analysis Systems, Kluwer, Dordrecht,... 

In addition, the cations and anions are being separated by the normal electrophoretic process. Because of the high potential, this separation can be quite fast. The resolution is excellent, because the small diameter of the tube minimizes concentration broadening, diffusion broadening, and heat broadening. The absence of a gel or particles eliminates eddy migration. 

Ismagilov R, Stroock A, Kenis P, Whitesides G, Stone H (2000) Experimental and theoretical scaling laws for transverse diffusive broadening in two-phase laminar flows in microchannels. Appl Phys Lett 76 2376... 

In CE, there are no eddy diffusion or mass transfer effects, only molecular diffusion broadening. The separation efficiency of CE is 10-100 times that of HPLC. 

A particularly interesting series of experiments has recorded the direct observation of diffusion broadening of the Mdssbauer line [60]. A Co/Cu source or a Fe/Cu absorber shows the onset of considerable line broadening between 1000° and 1060°C due to solid-state diffusion, although the data show considerable discrepancies from prediction by a simple diffusion-jump model. 

Figure 5. Emergent front of BSA on aminopropyltriethoxysilane-treated glass beads. The shape of the front should represent the adsorption process and diffusion broadening.

Quasi-elastic scattering—the wavelength (frequency) shifts owing to Doppler effects and diffusion broadening. 

This experiment shows that, although proteins are similar to glasses, they are also very different. The smoothness of the spectral diffusion broadening in the glass reflects the fact that there are no distinguishable hierarchy levels and that it is, under the conditions of our experiment, essentially an infinite system. The protein is finite. There is no smooth distribution of structural states. Within the temperature range accessible... 

Fig. 14. Thermally induced spectral diffusion broadening in mesoporphyrin IX-substi-tuted horseradish peroxidase ( ) as compared to mesoporphyrin IX in a glass (A). Inset shows the long-wavelength range of the protein absorption. The arrow indicates the hole burning frequency [From J. Zollfrank, J. Friedrich, J. Fidy, and J. M. Vanderkooi, Biophys. J. 59, 305 (1991)].

Fig. 8.10 A Gaussian transport process. Above the distribution function C(x,t) of the charge carriers at various times t. C(x,t) is the probability that a charge carrier will be at the position x at time if it was at the position X = 0 at the time t = 0. xjd is the normalised distance of the charge carriers from X = 0, where they were generated, d is the sample thickness (see Fig. 8.9). In Gaussian transport, the transit time tx is defined by x tx)) = d. Below transients of the displacement current l(t)/l(tx). In Gaussian transport, the width of the decay of the transients is governed by diffusive broadening of the charge-carrier packet. For transient (1), the transit time tx is longer than for transient (2).

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