Results and Discussion
6.6 Other Elemental Compounds
The estimation of the various other elemental compounds as well as the new groups introduced is presented in Table 6-18. The proposed method yielded an extremely low deviation for these set of components. With the new groups, the proposed method also suggests the broadest range of applicability from all methods. For the case of silicon, the groups involving electronegative elements produced a higher mean deviation.
Since carbon has similar characteristics as silicon, functional groups incorporated silicon as a possible neighbour, for example, chlorine connected to a carbon or silicon
atom. Although, this maybe accurate for a large number of cases, there are certain cases involving stronger steric effects and a weaker electronegative potential due to the larger molecular weight and radius of silicon as compared to carbon. These cases produce larger deviations which were described preViously (Section 6.2.3).
Table 6-18: Functional analysis of other elemental compounds showing the deviations and number for components of the different models used.
Number of Components Absolute Average Deviation (K)
Compounds Pr JR SB GC MP CR Pr JR SB GC MP CR
Mono-Functional Compounds
Phosphates 4 0 0 0 0 4 4.97 6.98
Arsine 6 0 0 0 0 6 3.17 3.07
Germanium 0 0 0 0 0.00 15.81
Germanium&Cb 3 0 0 0 0 3 1.20 6.03
Stannium 3 0 3 0 0 3 1.14 2.42 1.30
Borates 8 0 0 0 0 8 6.35 5.05
Silicon 37 0 27 0 0 37 5.01 19.82 5.06
Silicon to 0 43 0 0 0 0 40 10.77 10.80
Silicon to F or Cl 80 0 0 0 0 77 9.67 10.12
New Groups
Phosphine 4 0 4 0 0 0 1.65 14.72
Selenium 0 0 0 0 0.00 10.76
Aluminum 2 0 0 0 0 0 5.50
(Proposed method, JR - Joback and Reid, SB - Stein and Brown, GC - Constantinou and Gani, MP - Marrero and PardiIlo, CR- Cordes and Rarey)
The general argument with the estimation of metal compounds would be the predictive capability of these groups, due to the smaller number of components used.
This smaller set generally includes mono-functional compounds and the argument would be based on predictive capability of multi-functional compounds, in particular highly electronegative groups or anions. Since metal groups can act as cations, and with the case of multi-functional compounds involving anions, these compounds are now called ionic liquids. For these set of compounds, there is no vapour pressure.
Thus, the predictive capability of these compounds can be considered good.
6.7 Model Development
The development of the normal boiling point model involved the analysis of the different models proposed in Chapter 5. The results of these models (Section 5.7) are presented in Table 6-19. The analysis was performed on a set of 2557 components excluding the Beilstein data set. For the regression, the criterion for convergence employed was 1xIO-S•
Table 6-19: Average absolute deviation for the different models proposed (Section 5.7)
Average Absolute Average Absolute
Equation no. Error(K) Equation no. Error(K)
5-1 15.5126 5-2 6.6846
5-3 6.9714 5-4 6.6747
5-5 6.6723 5-6 6.7572
5-7 6.6756 5-8 8.7249
5-9 7.0407 5-10 7.0403
5-11 9.8546 5-12 6.6749
5-13 6.9567 5-14 6.9551
5-15 6.6748 5-16 6.6759
5-17 6.6844 5-18 6.6896
The first analysis involving fitting a logarithmic model produced the highest average deviation from all models (Equation 5-
n
The previous method incorporated a model (Equation 5-2) which gives a good description of the dependence of the normal boiling point on molecular size. The model also produced one of the lowest deviations with only three non-linear parameters. The same model was then tested with the molecular weight instead of the number of atoms (Equation 5-3) and produced a slightly higher average deviation. This conclusively proves that number of atoms has a stronger influence than molecular weight on group contribution. The model from the previous method was also tested using the molecular weight in three different forms (Equations 5-4,5-5 and 5-6).Inall cases, these models did not produce a significant improvement (only 0.18% improvement for Equation 5-5) with the inclusion of another physical contribution and a large number of non-linear parameters. Consequently, employing the molecular weight with the number of atoms did not suggest a more meaningfulresult. The model was also tested using a power and logarithmic fit (Equations 5-7 and 5-8). For Equation 5-7, the value of the exponent was extremely close to one. Thus, in this case the average deviation is quite similar to the previous model. For the logarithmic fit, this produced a much higher average deviation. The higher average deviation is a result of the model not being able to predict higher temperature compounds (consider the fit of Constantinou and Gani and Marrero and Gani in Figure 6-1, both methods employing a logarithmic fit). Consequently, the logarithmic fit should not be considered in the model development of group contribution. It was discussed in Chapter 3 (Equation 3-11) that the number of atoms and molecular weight has a linear relationship to the normal boiling point. The testing of these models (Equations 5-9 and 5-10), however, produced a higher mean deviation. The model proposed by Retzekas et al (2002) involved a separate group and physical contribution (Equation 5-11). In this case, theresult was poor because of the competing contributions. The model involving the molecular weight as part of the numerator (Equation 5-12) also produced a similar deviation to the previous model. In other words, the inclusion of the molecular weight as a linear relationship to the normal boiling point did not show any improvement.
The previous model was also tested using various mathematical forms, including a quadratic fit (Equations 5-13 to 5-18). In all cases, there were no significant improvements over the original model. The development of a second set of contributions also produced higher average deviations. However, the regression for these contributions is quite complicated, since there are three different types of regression viz. non-linear, linear and successive approximation. Consequently, the starting values for the simplex algorithm were a major influence on the regression. This now plays a major role when the new simplex is formed. Thus, there were two different types of regression performed. The first type involved leaving the second set of contributions unchanged when a new simplex was built. The second type involved returning the original values when a new simplex was built. Both types were applied to the equations described in Chapter 5. For the case of fitting the second set of contributions instead of the number of atoms,this produced negative contributions for a few groups. Other cases involved, were based on fitting the contributions to the exponent of the number of atoms and summation of group contributions. However,
this also produced higher deviations which can be attributed to the sensitivity of the exponent values.
For all the models tested, the previous model is probably the most feasible. The model only incorporates three non-linear parameters and a readily available quantity viz. the number of atoms. The model produces among the lowest average deviations and by the relationship of the experimental and calculated normal boiling points (Figure 6-7), an exceptional distribution. The relationship provides hardly any large outliers and is independent of the range of temperatures. Consequently, the model will be used for the development of the proposed method. All the results provided in this chapter, are based upon this model.
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Figure 6-7: Relationship of the experimental and calculated normal boiling points for the proposed method.