62H30 Classification and discrimination; cluster analysis [See also 68T10]
Assessment of the environmental acceptability of refrigerants by discrete mathematics: cluster analysis and Hasse diagram technique
- The recognition of the adverse environmental impact of chlorofluorocarbons (CFCs), mainly used as refrigerants, has lead to look for environmentally acceptable CFC replacements. Main environmental concern CFCs face is their ability to deplete the stratospheric ozone layer, quantified by the ozone depletion potential (ODP). Some of the first replacements mooted were hydrochlorofluorocarbons (HCFCs) and hydrofluorocarbons (HFCs), which contribute to the global warming, quantified by the global warming potential (GWP). ODP and GWP are related to the atmospheric lifetime (ALT), a third indicator. Hence, the environmental impact of a refrigerant may be characterised by a triple of ODP, GWP and ALT values. In this respect, an acceptable refrigerant is a chemical with low ODP, GWP and ALT values. One of the first steps to assess the environmental acceptability of refrigerants is to classify them to find substances with common features. Hence, a supervised and unsupervised classification was performed over 40 refrigerants. First one was a classification based upon elemental composition and functional groups present in refrigerant molecules which leads to: CFCs, HCFCs, HFCs, hydrocarbons (HCs), hydrofluoro ethers (HFEs), chloromethanes (CMs), carbon dioxide, trifluoroiodomethane, dimethyl ether and ammonia. The unsupervised classification was performed using hierarchical cluster analysis. In this case, refrigerants were characterised by three kinds of descriptors: Environmental properties (ODP, GWP, ALT), thermodynamic features related to their refrigeration performance and molecular descriptors derived from their molecular structure. Eight clustering methodologies were applied to each kind of refrigerant descriptors. To assess the stability of these classifications, the cluster index, a method for quantifying classification similarities was developed and further applied to refrigerant results. It was found that environmental descriptors are the only case in which refrigerant classes are stable when varying the classification method. The chemotopological procedure, a method for studying similarity relationships, was applied to the environmental classification of refrigerants. It was found that CFCs are similar to themselves and also to 1,1,1,3,3,3-hexafluoropropane, a HFC. The most similar substances to all CFCs considered were trichlorofluoromethane and 1,1,2-trichloro-1,2,2-trifluoroethane. The other refrigerant families were found to be similar to many other substances, therefore there is no clear affiliation of refrigerants of one family to one certain class. It was found a disagreement between the supervised classification leading to refrigerant families and the three unsupervised classifications (environmental, thermodynamic and molecular ones). Therefore, refrigerant classification into families does not imply same classification based upon environmental properties, thermodynamic features and molecular descriptors. A different refrigerant classification was performed, i.e. the one based upon order relationships of refrigerant environmental properties. In this case the Hasse diagram technique, a method based on partial order theory, was applied to the 40 refrigerants characterised by environmental properties. A parameter free procedure for ordering classes based upon order relationships of their elements was developed. For that purpose, the dominance and separability degrees were introduced, first one indicates the extent to which members of one class hold higher descriptor values than the members of another class; while separability degree quantifies the lack of order relationships between two classes. Dominance and separability degrees were related by a theorem. By the application of dominance and separability degrees to refrigerant families three main classes were detected: problematic substances, gathering CFCs, octafluorocyclobutane and bromochlorodifluoromethane; least problematic ones, collecting HCs, CMs, carbon dioxide, trifluoroiodomethane, dimethyl ether and ammonia; and moderately problematic refrigerants, made from HCFCs, HFCs and HFEs. It was found that some HFEs are not dominated by CFCs, which raises the question on the applicability of these substances as environmentally acceptable replacements. METEOR (Method of evaluation by order theory), a procedure for prioritising descriptors and studying its effect on the order relationships of the objects considered was discussed. When applied to the refrigerants, the effect of prioritising ODP, GWP and ALT in the order relationships of these substances was studied. It was found that pentafluorodimethyl ether, a HFE, is one of the most problematic refrigerants under a large range of priorities of the environmental properties considered. Due to the mathematical generality of the methods here introduced, they are not restricted to the analysis of refrigerants but can be used to the study of different sets whose elements are characterised by various attributes.