Finite Element Results Interpretation:

After a fitting session has converged, the finite element analysis will result in data that can be used to calculate molecular weights or partial specific volumes, if the molecular weight is know from a different source.

Press on the Model Results button in the model control window to see the possible models that would be consistent with the calculated parameters. Make sure to click on Update for 20o,W before modeling any results in order to correct all data for the proper buffer, temperature and vbar values. You can also update the models from within the modeling window. Three hyposthetical models are presented:

In addition, the frictional coefficient f, the frictional ratio f/f0, the volume of the particle, the radius of the minimal sphere and the frictional of the minimal sphere are shown. The minimal sphere is the sphere that has the same volume as the modeled particle.

Special considerations:

How reliable are these calculations? The reliability of these hypothetical models is dependent on the adequacy of the model used for the finite element fit. If the model used for the nonlinear least squares fit can be used to accurately describe the underlying physical system, the models are all equally likely. Of course, there exists no information that would tell you which of these three models is the most likely. The frictional information derived from the finite element fit is degenerate, in the sense that many different models can be used to explain the frictional coefficient ratio f/f0 observed. Therefore, these data can only be used to suggest a possible interpretation of the system at hand.

How adequate a particular fitting model is, is very difficult to determine. In the first place, it is of course required that the data were fit with a fitting model wich produces residuals that scatter randomly about zero. In general, it can be stated that if the same model can be used to fit the same system under many different conditions such as different run speeds, concentrations and run durations it is quite likely that the model describes adequately the system under investigation. Therefore, it is recommended to fit multiple run conditions of the same system, and if possible, in a single global fit (this functionality is available in the future release of the Beowulf version of the UltraScan software).

If the same model can be applied to all run conditions, the confidence in the resulting parameters is higher than if only a single run condition is examined. A special case is found if the frictional ratio, f/f0, is equal to unity. In such a case it is possible that the sample is spherical in shape. Even though a unity value for f/f0 is indicative of a spherical shape, it is also possible that the model which produced a unity f/f0 ratio is the result of an incorrect fitting model.

In the most obvious case even a ratio less than unity is possible. In this case a warning message is printed and the model used to arrive at the values can be considered invalid since there is no physical possibility for this to occur. In that case the frictional ratio will be printed in red to alert the user to the problem. Such a ratio will most likely occur because a heterogeneity in the sample has been compensated for by a too large diffusion coefficient. In the worst case scenario a gaussian distribution of particle sizes will produce a boundary spreading that can be compensated quite well with a larger diffusion coefficient, since a larger diffusion coefficient will also produce a similar boundary spreading. Especially in the case of noisy data or low concentrations of secondary components, this error may occur quite readily.

www contact: Borries Demeler

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Last modified on January 12, 2003.