Contin fitting

Small squares denote the deviation of CONTIN fittings. 

Industrialisation lead to mass production with the characteristic feature of the division of the work process into smaller individual steps and the simplest hand movements, which each worker repeated incessantly. Different parts only fit together if they are made according to a standard. For example the inch is used as the unit for HPLC parts almost everywhere in the world, screws on the European continent have metric sizes and in the US the inch still common. 

The more the precision of the instrument, and the more the points for the time unit in the acquired profile, the better the result of the fitting of experimental data. For this reason instruments with a low measure error and connectable to a computer for the automatic and continous aquisition of data are very much prefered. The UV-Vis spectrophotometer is by far the most used instrument in chemical kinetics. It has a good sensitivity and a good control of the temperature. It is connected or easily connectable to a computer and is available nearly everywhere. The absorbance has a very low dependence on the temperature so that, in the used temperature range, its variation can be neglected during the VTK experiments. 

The analysis of the autocorrelation function data by the Coulter Model N4 is carried out by the Size Distribution Program (SDP), which gives the particle size distribution in the form of various output displays (see Section 10.4). The SDP analysis utilizes the computer program CONTIN developed by S.W. Provencher (ref. 467-470 see also Section 10.2). (This program has been tested on computer-generated data, monomodal polystyrene samples, and a vesicle system (ref. 466-468,471).) Since the SDP does not fit to any specific distribution type, it offers the ability to detect multimodal and very broad distributions. 

For both the subdistribution and the GEX fit methods a Marquardt algorithm for constrained non-linear regression was used to minimize the sum of squares error (.10). The FORTRAN program CONTIN was used for the constrained regularization method. All computations were performed on a Harris H-800 super mini computer. 

For bimodal MWDs none of the methods successfully resolved the two peaks for the case where a majority of the molecules were of low molecular weight (Figure 5). However, CONTIN provided the closest solution. For the case where the skewed low molecular weight peak consisted of only one quarter of the total mass, the GEX fit method gave good results. CONTIN showed three peaks, but the agreement can still be considered fair because of the difficulty in discerning two widely separated peaks of this type. As in the unimodal cases, the subdistribution method showed the poorest fits. 

Operator independence. The GEX method is virtually operator independent. The only inputs required before fitting are parameters concerning the precision of the numerical integration and exit criteria for the Marquardt algorithm. The same set of Inputs was used for all five MWDs. Currently the method also requires upper and lower limits on the GEX parameters but a simple modification of the code can eliminate this need. The CONTIN algorithm has several operator and case dependent parameters that have to be chosen before analysis. However, it is fairly stable with respect to bad choices for some of these inputs. The GEX fit method cannot fit multimodal MWDs without prior knowledge of the number of peaks in the distribution. While CONTIN does not impose this limitation it 1s recommended that the number of peaks be specified before analysis. In our experience with CONTIN if this condition is not met the algorithm tends to compute unimodal solutions for multimodal MWDs and sometimes visa versa. 

The subdistribution method is extremely sensitive to operator input and consistently yielded the poorest results of the three methods compared. In general CONTIN yields good results but tends to shift MWDs to higher molecular weights and sometimes produces artifact peaks or shoulders for broad unimodal or multimodal distributions. Of the three methods, the proposed GEX fitting technique seems to provide results that are most consitent with the input distributions and is the most operator independent. CONTIN and GEX fitting are not significantly affected by noisy data. 

That said, the established methods including those not mentioned above have their limits. PATFIT deals with discrete lifetimes. CONTIN [64, 65] and MELT provide continuous distribution of lifetimes. The merits and demerits of MELT and CONTIN were debated extensively [66-68]. Kansy developed an algorithm that can fit both, discrete lifetimes and log-normal distributions of lifetimes [69]. These challenges become increasingly severe as the range of lifetimes included in the data increases. To date, no method has addressed this issue satisfactorily. A number of approaches have been taken to overcome or circumvent the problems. However, their detailed discussion exceeds the scope of this chapter and will be presented elsewhere... 

Figure 6.8-14 Temperature and O2 concentration determination using a computer fit between measured (dotted) and calculated (continous line) spectra.

This same approach could be used both to validate further the presently entrenched continental drift theory and predict from coal and shale analysis of an area of one continent the type of organic deposits which may be present on another fitted but as yet unexplored continent (8). 

---