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Article

Fuzzy Divisive Hierarchical Clustering of Solvents According to Their Experimentally and Theoretically Predicted Descriptors

1
Department of Inorganic Chemistry, Faculty of Chemistry and Pharmacy, University of Sofia, 1 James Bourchier Blvd., Sofia 1164, Bulgaria
2
Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
3
Department of Analytical Chemistry, Chemical Faculty, Gdańsk University of Technology (GUT), 11/12 G. Narutowicza St., 80-233 Gdańsk, Poland
4
Department of Analytical Chemistry, Faculty of Chemistry and Pharmacy, University of Sofia, 1 James Bourchier Blvd., Sofia 1164, Bulgaria
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(11), 1763; https://doi.org/10.3390/sym12111763
Received: 5 September 2020 / Revised: 30 September 2020 / Accepted: 22 October 2020 / Published: 24 October 2020
(This article belongs to the Special Issue Chemometrics in Assessing Molecular Structures and Properties)

Abstract

:
The present study describes a simple procedure to separate into patterns of similarity a large group of solvents, 259 in total, presented by 15 specific descriptors (experimentally found and theoretically predicted physicochemical parameters). Solvent data is usually characterized by its high variability, different molecular symmetry, and spatial orientation. Methods of chemometrics can usefully be used to extract and explore accurately the information contained in such data. In this order, advanced fuzzy divisive hierarchical-clustering methods were efficiently applied in the present study of a large group of solvents using specific descriptors. The fuzzy divisive hierarchical associative-clustering algorithm provides not only a fuzzy partition of the solvents investigated, but also a fuzzy partition of descriptors considered. In this way, it is possible to identify the most specific descriptors (in terms of higher, smallest, or intermediate values) to each fuzzy partition (group) of solvents. Additionally, the partitioning performed could be interpreted with respect to the molecular symmetry. The chemometric approach used for this goal is fuzzy c-means method being a semi-supervised clustering procedure. The advantage of such a clustering process is the opportunity to achieve separation of the solvents into similarity patterns with a certain degree of membership of each solvent to a certain pattern, as well as to consider possible membership of the same object (solvent) in another cluster. Partitioning based on a hybrid approach of the theoretical molecular descriptors and experimentally obtained ones permits a more straightforward separation into groups of similarity and acceptable interpretation. It was shown that an important link between objects’ groups of similarity and similarity groups of variables is achieved. Ten classes of solvents are interpreted depending on their specific descriptors, as one of the classes includes a single object and could be interpreted as an outlier. Setting the results of this research into broader perspective, it has been shown that the fuzzy clustering approach provides a useful tool for partitioning by the variables related to the main physicochemical properties of the solvents. It gets possible to offer a simple guide for solvents recognition based on theoretically calculated or experimentally found descriptors related to the physicochemical properties of the solvents.

Graphical Abstract

1. Introduction

The large number of different solvents used for many important chemical processes and technologies need special attention since their properties depend on a range of specific chemical and physical parameters such as melting and boiling point, water solubility, polarity, vapor pressure, density, viscosity, and even toxicity and many others.
Solvents can be separated by one of four basic methods: by solvent power (solubility polarity, acidity/basicity, properties/parameters), evaporation rate/boiling point, chemical structure, and hazard classification. Within the latter, this evaluation identifies both physical hazards (e.g., flash point, flammability, or reactivity) and toxicity, etc. The partitioning based on chemical structure groups used three groups: hydrocarbons, and oxygenated and chlorinated solvents [1,2,3].
Parker [1] divides them into: protic, aprotic, and inert according to the dipolarity of the solvent molecules and their ability to act as hydrogen bond donors. One disadvantage of a classification scheme such as this is that the groups are not restraining.
Partitioning of solvents based on physicochemical properties proved to be a significant and challenging problem [2,3,4,5,6]. Special interest provides a new study [7] where a new solvent similarity index is introduced, aiding in discovering the most suitable solvent for specific purposes. The solvent similarity index was calculated based on 261 pure solvents at 298 K, and classification was done for the solvents according to their solvation properties. Pushkarova et al. [8] used, as empirical characteristics of solvent-solute interactions via Taft-Kamlet-Abboud, polarity functions to determine the solvatochromic polarity. The practice of solvatochromic probing is growing rapidly but classification of media based on these values can be difficult. The paper focuses on the artificial neural networks (ANN) for the classification of solvent on the basis of their solvatochromic characteristics. Also, the influence of data variation on the stability of classification has been studied.
In the study of Gramatica et al. [9] a neuron nets approach was used for solvent separation. In general, many other chemometric methods contributed to proper solvent selection for practical needs like regression analysis, factor analysis, or partial least square regression [3,4,5].
Bradley et al. [10] used the Abraham general solvation model to predict the solvent coefficients for all organic solvents. The models were used to propose sustainable solvent replacements for commonly used solvents.
Recent efforts are concentrated on the application of chemometric strategies as suitable tools for classification of solvents (as objects of the analysis) characterized by many properly selected variables (chemical, structural, and physicochemical descriptors [11,12,13,14,15]. The majority of the methodologies are well developed and widely used for classification, interpretation, and modeling purposes like cluster analysis, principal components and factor analysis, artificial neural networks, partial least square regression, and discriminant analysis. A limited number of applications are related to fuzzy analysis [16,17].
Fuzzy clustering and partitioning also finds application in solvents characterization [18].
Fuzzy clustering analysis offers unique opportunities for decomposition of a large data set into a fixed number of similarity groups or clusters. Indeed, the classical cluster analysis (hierarchical or non-hierarchical) could achieve similar results but the strong advantage of the fuzzy partitioning strategy is the opportunity to locate a certain object (or variable) not to a single group of similarity but to calculate a function of membership for each object. Thus, a single object could be attributed to more than one cluster. This makes the interpretation efforts more loosely allowing considering specific distribution of objects into clusters with respective degree of membership. It eliminates ambiguity in interpretation or often unavoidable overlapping of clusters.
The major goal of the present study is to achieve a reliable partitioning of a large number of solvents with broad practical use by application of fuzzy partitioning methodology.
In this study, the fuzzy divisive hierarchical clustering and the powerful fuzzy divisive hierarchical associative-clustering method, which offer an excellent possibility to associate each fuzzy partition of samples to a fuzzy set of characteristics (descriptors), were successfully applied for the characterization of 259 solvents, according to their 15 specific descriptors (experimentally found and theoretically predicted). What is quite new is the partitioning of solvents and their association with different descriptors with high, moderate, and low values. The obtained results clearly demonstrated the efficiency and information power of the advanced fuzzy clustering method in solvents characterization and clustering.

2. Materials and Methods

2.1. Fuzzy Clustering Methods

The application of fuzzy logic for various scientific and technical goals has been commented on for decades [19]. This approach differs from the classical hard clustering where each object of the data set finds its own cluster. Thus, an object either belongs to a defined cluster or is out of it. The application of Fuzzy theory to the problem of finding similarity between objects of interest leads to the conclusion that a particular object can belong simultaneously to more than one cluster, but with different degrees of membership (DOMs) between 0 and 1 [20,21]. In one of the possible approaches to so-called fuzzy c-means clustering (FCM), each cluster is replaced by a cluster prototype [22,23] with a respective center, which contains information about the size and the shape of the cluster. The degrees of membership are computed from the distances of the data point to the cluster centers. These distances are responsible for the value of DOM and determine the cluster properties and shape (point, line, etc.) [24].
There are different algorithms in fuzzy clustering applications, the most used being the binary divisive algorithm and the generalized fuzzy c-means algorithm (GFCM). The fuzzy methods briefly described above and the corresponding software were clearly described and efficiently applied in previous papers [25,26,27,28,29,30].

2.2. Data Set

The dataset consists of 269 solvents. Each solvent was described by 15 variables (molecular descriptors and experimentally obtain properties) shown below in Table 1.
In the present study, the following set of subprograms implemented in the EPI Suite™ version 4.10 were used: MPBPWIN™, WATERNT™, HENRYWIN™, KOAWIN™, KOWWIN™, and BCFBAF™.
The melting point (MP), boiling point (BP), and vapor pressure (VP) within the MPBPWIN™ module in EPI Suite™ were applied to predict the properties of our interests. The MPBPWIN™ estimates melting point by the two methods: (1) the Joback Method (a group contribution method); (2) the Gold and Ogle method MP = 0.5839 * BP (in °K). Boiling point is valued by an adaptation of the Stein and Brown (1994) method, which is also a group contribution method. Vapor pressure is predictable as well by the methods: (1) Antoine, (2) Modified Grain method, and (3) the Mackay method. WATERNT™ estimates water solubility directly using a “fragment constant” method similar to that used in the KOWWIN™ program.
The Henry’s law constant is estimated by the subprogram HENRYWIN™, which calculates (air/water partition coefficient) using both the group contribution and the bond contribution methods.
This KOAWIN™ program evaluates the logarithm of the octanol-air partition coefficient (KOA) of an organic compound with the compound’s octanol–water partition coefficient (Kow) and Henry’s law constant (HLC). For the KOAWIN only a chemical structure was needed for estimation of KOA. In the KOAWIN structures are implemented by the SMILES codes (Simplified Molecular Input Line Entry System). The KOA is possible to be predicted from the octanol–water partition coefficient (KOW) and Henry’s law constant (H) by the subsequent equation:
KOA = KOW(RT)/H
where R is the ideal gas constant and T is the absolute temperature. KOA and KOW are unitless values. H/RT is the unit less Henry’s law constant, also known as the air–water partition coefficient (KAW).
Therefore, the equation to estimate KOA is:
KOA = KOW/KAW
The KOWWIN™ program is for the octanol–water partition coefficient prediction. The basis of prediction in KOWWIN is a “fragment constant” methodology. In this “fragment constant” method, the starting structure is divided and then evaluated.
The comparison with the available experimental data shows a high level of correlation. In such a way, missing data in the large data set could be replaced.

3. Results and Discussion

3.1. Fuzzy Divisive Hierarchical Clustering of Descriptors

The fuzzy clustering of the variables (15 in total) aims to check the following:
  • If the experimental values of the respective variables conform with the calculated one (i.e. if they fall within a fuzzy cluster with high membership function);
  • If the partitioning procedure could determine stable groups of similarity between the variables with high DOM;
  • The procedure is important for revealing information about possible descriptors for classification of the solvents in interest.
In the supplemental information section (Supplement T1) the fuzzy partitioning results for 15 variables are presented. In total, 28 groups are considered. The summary of the final partitioning is shown below:
  • A1—only HLc is included (a typical outlier)
  • A2—MPe MPc BPe BPc Dens WSe WSc VPe VPc HLe logKOWe LogKOWc logKOAc logBCF (the rest of the variables show a high level of similarity with a distinct difference from HLc).
In the next steps of fuzzy partitioning respective groups of similarity based on DOM will be sought.
  • A21—MPe MPc BPe BPc Dens VPe VPc HLe logKOWe LogKOWc logKOAc logBCF
  • A22—WSe WSc
In this partitioning stage, the experimentally found and theoretically calculated values of water solubility are extracted as a group of similarity different from the rest of variables in subgroup A21.
  • A211—BPe BPc
  • A212—MPe MPc Dens VPe VPc HLe logKOWe LogKOWc logKOAc logBCF
  • A2111—BPe
  • A2112—BPc
  • A2121—Dens
At this level of fuzzy partitioning, one finds separation between the experimentally and theoretically found values of boiling points and density. According to the DOM values the differences are small and the similarity between these three variables is significant,
  • A2122—MPe MPc VPe VPc HLe logKOWe LogKOWc logKOAc logBCF
  • A21221—VPe VPc HLe logKOWe LogKOWc logKOAc logBCF
  • A21222—MPe MPc
  • A212211—VPe VPc
The separation of two other groups of similarity is indicated melting point (experimental and theoretical values) and vapor pressure (experimental and theoretical values).
  • A212212—HLe logKOWe LogKOWc logKOAc logBCF
  • A2122111—VPc
  • A2122112—VPe
  • A2122121—logBCF
This stage of fuzzy partitioning reveals a slight difference between vapor pressure (theoretical and experimental values), and a more specific role of logBCF as compared to the stable group of logKOW (experimental and theoretical values) and logKOAc (calculated values).
  • A2122122—HLe logKOWe LogKOWc logKOAc
  • A21221221—HLe logKOWe LogKOWc
  • A21221222—logKOAc
  • A212212211—LogKOWc
  • A212212212—HLe logKOWe
  • A2122122121—logKOWe
  • A21221221212—HLe
  • A212221—MPe
  • A212222—MPc
  • A221—WSc
  • A222—Wse
The fuzzy partitioning carried out for 15 variables characterizing a set of solvents revealed the following fuzzy linkage of the variables:
  • Very good coincidence between experimentally determined and theoretically calculated values of the variables characterizing the solvents; this means that if experimental values of some solvents are missing, calculation substitutes could be successfully used for classification and interpretation goals;
  • HLc was defined as a typical outlier;
  • The group of variables characterizing the distribution between different media (important for toxicity properties determination) is very compact;
  • The parameters characterizing physicochemical properties (MP, BP, WS, and VP) indicate various type of similarity with the other parameters—water solubility is the most distant to the rest of parameters, followed by BP and MP; density is closest to BP; logBCF is slightly different as compared to the rest of “toxicity esteems.”
Additional material could be found in Supplement

3.2. Fuzzy Divisive Hierarchical Clustering of Solvents

To compare the partitions, and the similarity and differences of the investigated solvents, we have to analyze both the characteristics of the prototypes corresponding to the partitions hierarchy obtained by applying fuzzy divisive hierarchical clustering and DOMs of solvents corresponding to all fuzzy partitions. The results presented in Table 2 clearly illustrate the most specific characteristics of each fuzzy partition and their similarity and differences.
The initial two clusters A1 and A2 indicate that one typical outlier is present in the list of solvents—perfluorooctane, whose properties are completely different from those of the other 268 solvents. The further divisive fuzzy clustering indicates the level of the membership function of each solvent into each of the next groups included (22 in total).
Next, Table 2 shows the final fuzzy partitioning with the prototypes of the partitions, ranked solvents for each group and the range of DOM.

3.3. Fuzzy Divisive Hierarchical Associative-Clustering of Solvents and Descriptors

To compare the partitions, and the similarity and differences of solvents, we have to analyze the DOMs corresponding to all fuzzy partitions for both the samples and characteristics (descriptors). The results obtained by applying the fuzzy divisive hierarchical associative-clustering method using the descriptor data are presented in Table 3. By carefully analyzing the fuzzy partitions at each level (partition history/hierarchy) in parallel with the descriptor considered data, the following remarks may be taken. The fuzzy partitioning of the solvents with indication of the descriptors related to each fuzzy partition (cluster) is depicted in Table 3.
For the final goal of fuzzy partitioning of the objects (solvents) was performed by the use of 10 variables (only the experimentally found ones) (Table 4).
The fuzzy partitioning performed reveals the following classes of solvents:
  • Class 1 (WSe): 9 19 38 52 53 54 102 117 157 162 179 202 217 223 259 57 72 83 96 104 107 128
Iodoethane Diethyl glutarate 1,1-dichloroethane Dimethyl phthalate quinoline 2,4-dimethyl-3-pentanone n-butyl acetate 1,2-dichloroethane Glycerol-1,3-Dibutyl ether m-cresol Dimethyl adipate Glycerol-1,2,3-triethyl ether diethyl carbonate Caprylic acid diethanolamide DMEU 1-hexanol 4-methyl-2-pentanone Butylacetate 1-chloropropane 2-chloropropane 2-Methyltetrahydrofuran Diethyl succinate.
Mainly chlorinated solvents and similar ones except for diethyl carbonate and buthylacetate (CHLORINATED SOLVENTS CLASS) with major descriptor WSe (experimental water solubility value; calculated water solubility gives the same separation).
  • Class 2 (Dens): 144 145 184 200 218 227 231 233 234
Bromoethane Di-isopropyl ether Benzonitrile Acetophenone Isobutyl acetate Di-n-propyl ether Carbon disulfide Benzaldehyde Chloroform.
Nonpolar and volatile solvents except for isobutyl acetate (NON-POLAR AND VOLATILE SOLVENTS CLASS) major descriptor DENS (density).
  • Class 3 (VPe): 7 40 63 79 131 146 155 166 205 206 207 209 215 243 247 250 255 257 258 269
Benzene 1,1,1-trichloroethane Dichloromethane Methyl formate Diethyl ether 1,1-dichloroethylene Oleyl alcohol Fluorobenzene Tetraethylene glycol Ricinoleic acid Triethylene glycol Butyl stearate Methyl benzoate 1,1,2,2-tetrachloroethane 1,8-Cineole gamma-Valerolactone Nopol alpha-Terpineol beta-Terpineol PolyEthyleneGlycol 200.
This is a mixture of polar solvents—acids and esters with non-polar ones such as benzene or 1,1,1-TCA (POLAR AND NON-POLAR SOLVENTS MIXED CLASS separated mainly by descriptor vapor pressure experimental values; the calculated value gives the same results).
  • Class 4 (MPe): 81 101 106 185 216 240 260 268
Glycerol triacetate Oleic acid Menthanol Diisooctylsuccinat Dioctylsuccinate Isosorbide dioctanoate DPMU PolyEthyleneGlycol 600.
POLAR SOLVENTS CLASS I defined by descriptor melting point I.
  • Class 5 (logKOA): 11 21 22 87 95 119
2-Pyrrolidone Sulfolane Propylene carbonate N-methylacetamide Glycerol Water
POLAR SOLVENTS CLASS II defined by descriptor logKOA.
  • Class 6 (logKOWe): 10 93 98 126 220 221 244
Phenetole Diisobutyl adipate Geranyl acetate Menthanyl acetate Trichloroethylene Pentyl acetate 1-Octanol.
The grouping was defined properly as a polar solvent except trichloroethylene POLAR SOLVENTS CLASS III defined by logKOW (experimental or theoretical).
  • Class 7 (logBCF): 8 16 25 27 59 69 70 71 92 105 118 127 132 134 239
Ethyl myristate Isoamyle acetate Butyl laurate Methyl abietate 2,6-dimethyl-4-heptanone N,N-dimethylaniline Nitrobenzene Benzyl benzoate Methyl stearate Methyl myristate Dimethyl 2-methylglutarate 1,1,3,3-tetramethyl urea Diethyl phthalate Diethyl adipate Glycerol-1,2,3-tributyl ether.
The group of polar ones, except for nitrobenzene—POLAR SOLVENTS CLASS IV defined by logBCF.
  • Class 8 (HLe): 2 4 36 78 82 90 99 103 116 120 125 130 229
Ethyl laurate Glycerol-1,2-dibutyl ether Acetyltributyl citrate Diisoamylsuccinate N,N-Diethylolcapramide Dibenzyl ether Butyl palmitate Methyl linolenate Methyl ricinoleate Methyl laurate Ethyl benzoate Dibutyl sebacate Anisole.
The group defined by a HIGH MOLECULAR WEIGHT POLAR SOLVENTS defined by HLe (experimental).
  • Class 9 (BPe): 5 6 13 15 17 18 23 24 26 34 35 37 42 43 44 46 47 48 49 50 55 60 61 62 64 66 68 73 74 76 80 88 89 97 108 109 110 111 112 113 114 115 123 124 129 133 135 140 188 267
1 3 12 14 28 29 30 31 32 33 39 41 45 51 56 58 65 67 75 77 84 85 86 91 94 100 121 122 136 137 138 139 141 142 143 147 148 149 150 151 152 153 154 156 158 159 160 161 163 164 165 167 168 169 170 171 172 173 174 175 176 177 178 180 181 182 183 186 187 189 190 191 192 193 194 195 196 197 198 199 201 203 204 208 210 211 212 213 214 219 222
224 225 226 228 230 232 235 236 237 238 241 242 245 246 248 249 251 252 253 254 256 261 262 263 264 265 266
This group is quite large. Most of the solvents are polar except for: carbon tetrachloride, xylenes, and bromobenzene.
Cyclohexanol Isododecane Di-n-butyl acetate 1-chlorobutane Glycerol-2-methyl monoether m-dichlorobenzene p-Cymene Methyl palmitate Isopropylacetate chlorobenzene Isopropyl palmitate 2,6-dimethylpyridine 1-bromobutane Butyl myristate Furfurylic alcohol 1-2,4-dimethylpyridine Dihydromyrcenol 3-Hydroxypropionic acid Benzyl alcohol Cyclohexanone 1,3-Dioxan-5-ol Diisobutyl succinate Glycerol-2-ethyl monoether Toluen Methyl Linoleate.
N,N-Dimethyldecanamide N-methylformamide Cyclopentane Propylene glycol Iodobenzene Glycerol-1,3-dimethyl ether Piperidine o-xylene Aniline Diisobutyl glutarate Tetrahydrofurfurylic alcohol 3-Methoxy-3-methyl-1-butanol p-xylene cis-decaline Dimethylisosorbide mesitylene Glycerol-1,2-dimethyl ether Isopropyl myristate d-Limonene 1,3-Dioxolane-4-methanol Propionic acid N-decane Carbon tetrachloride Cyclopentyl methyl ether N-pentane Triethylamine Propyl formate Ethanol Ethyl acetate 1-Butanol 4-picoline 3-methyl-2-butanone n-Propyl acetate propionitrile Dimethyl sulfoxide 1,3-Dioxolane Cyclohexane Formamide Diethylamine Iso-octane Glycerol-1,2,3-trimethyl ether Dimethyl succinate 1,3-Propanediol Propylene glycol Butyronitrile N,N-dimethylformamide Ethyl formate β-Pinene 2,2,2-trifluoroethanol 3-pentanone Pyridine 2-pentanone n-heptane 3-Butyl-1-methylimidazolium tetrafluoroborate 1-Decanol N-methyl-pyrrolidin-2-one α-Pinene 1,2-dimethoxyethane 2-methoxyethanol Methyl oleate Decamethylcyclopentasiloxane Diethylene glycol Glycerol-2-butyl monoether Tributylamine 1-pentanol EthylHexyllactate Nitromethane.
Tert-butyl alcohol 1,4-dioxane Glycerol-1-ethyl monoether Cyclohexene N,N-dimethylacetamide Ethyl palmitate 5-(Hydroxymethyl)furfural 2-butanone 2-methyl-2-butanol styrene Methyl acetate Pyrrolidine N,N-Dimethyloctanamide Glycerol carbonate Acetone 2-aminoethanol tert-butyl methyl ether Acetylacetone 3-picoline Dipropyleneglycol.
2-pentanol n-butylamine Diphenyl ether 2-propanol Ethylene glycol Ethyl linolenate Methanol Cyclopentyl methyl ether Nitroethane Phenol Isobutyl alcohol Ethylenediamine.
β-Farnesen Tetrachloroethylene Tetrahydrofuran 3-pentanol Methyl 5-(dimethylamino) 2-methyl-oxopentanoate 2,4,6-trimethylpyridine Glycerol-1,3-diethyl ether 2-butanol Acetic anhydride Ethyl linoleate trifluoroacetic acid n-hexane Ethyl lactate Cyclopentanon o-dichlorobenzene 3,3-dimethyl-2-butanone Dimethyl glutarate 1-propanol Glycerol-1-methyl monoether n-octane m-xylene Bromobenzene Choline acetate Ethyl oleate Acetic acid.
Acetonitrile Glycerol-1,2,3-tributyl ether morpholine 3-methyl-1-butanol Acetone 1,4-Cineole Terpineol acetate 2-Furfuraldehyde beta-Myrcene Terpinolene Cyclademol Glycofurol (n = 2) Solketal HMPTA DEGDEE DEGDME Ethyl propionate TEGDME Dimetylsulfoxide.
  • Class 10 (HLc): Outlier Perfluorooctane 20
The solvents underlined above do not strictly belong to logical formation of similarity classes and seem more to be rather odd than reasonable as members of the respective class (polar, non-polar, or volatile solvents determined by specific variables). A careful check of the position of these 12 solvents into the fuzzy partitioning groups indicates that all of them have quite low maximal value of DOM as determined by fuzzy analysis (this values is shown next to the name of the solvent).
The few exceptions found (only 9 out of 259 solvents), namely:
(diethyl carbonate, benzene, nitrobenzene);(o-, m-, p-xylene) and (carbon tetrachloride, bromobenzene, trichloroethylene), are resultant to their low maximal DOM, so their position into one group of similarity is not stable and they could be considered either as members of the group with low probability, or members of a different class.
In Table 5 summarized results according to obtained classes are presented.
The table could be used as a practical guide for selection of type of solvents based on their physicochemical properties.

4. Conclusions

The fuzzy hierarchical clustering of a large group of solvents into 10 classes of similarity made it possible to find patterns of the chemicals with specific properties divided by important descriptors. The fuzzy partitioning method applied helped in finding relationships between solvents of various nature (polar, non-polar, volatile etc.) and the physicochemical variables used. Additionally, the chemometric analysis has proven that if there are missing data of specific descriptors the theoretical calculation of them is possible with very high level of approximate to the experimentally observed and established physicochemical indicators.
Thus, the present study offers a simple methodological approach to the complex problem of solvent partitioning.
In order to understand the similarity and differences of various solvents, fuzzy divisive hierarchical clustering and fuzzy divisive hierarchical associative-clustering were successfully applied. The fuzzy partition hierarchy of solvents and descriptors associated allowed identifying partitions (groups) of solvents with more or less similar characteristics in terms of higher, smallest, or intermediate values of considered descriptors.

Supplementary Materials

The following are available online at https://www.mdpi.com/2073-8994/12/11/1763/s1.

Author Contributions

Conceptualization, M.N.; methodology, C.S.; M.N.; software C.S.; M.N.; validation, M.N., V.S. formal analysis, M.N., M.T., C.S., V.S.; investigation, M.N.; resources, M.N.; data curation, C.S., M.N.; writing—original draft preparation, M.N., C.S., M.T., V.S.; writing—review and editing, M.N., V.S.; visualization, M.N. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Information and Communication Technologies for a Single Digital Market in Science, Education and Security” of the Scientific Research Center, grant number NIS-3317 and National roadmaps for research infrastructures (RIs) grant number [NIS-3318]. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

Acknowledgments

The author M.N. is grateful for the additional support by the project “Information and Communication Technologies for a Single Digital Market in Science, Education and Security” of the Scientific Research Center, NIS-3317 and National roadmaps for research infrastructures (RIs) grant number [NIS-3318].

Conflicts of Interest

The authors declare no conflict of interest.

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Table 1. Molecular descriptors and experimentally obtained properties.
Table 1. Molecular descriptors and experimentally obtained properties.
No.Variable NameCode
1Melting point (experimental)MPe
2Melting point (calculated)MPc
3Boiling point (experimental)BPe
4Boiling point (calculated)BPc
5DensityDens
6Water solubility (experimental)WSe
7Water solubility (calculated)WSc
8Vapor pressure (experimental)VPe
9Vapor pressure (calculated)VPc
10Henry Law constant (experimental)HLe
11Henry Law constant (calculated)HLc
12Octanol/water coefficient (experimental)logKOWe
13Octanol/water (calculated)logKOWc
14Octanol/Air (calculated)logKOAc
15Bioconcentration Factorlog BCF
Table 2. Final fuzzy partitioning.
Table 2. Final fuzzy partitioning.
Final Fuzzy PartitionsPrototypes of Fuzzy PartitionsSolvents (Ranked in Decreasing Order)DOMs Range
Parameters of Prototype
A111111−24.06; −54.87; 233.98; 203.55; 21.61; 8685.76; 1293.07; 1.39; 0.83; 0.00; 0.03 1.20; 1.94; 6.05; 0.98190.6348
A111112−14.24; 188.97; 186.54; 2.09; 18.27; 9376.14; 42.79; 2.64; 0.31; 0.00; 1.53; 0.75; 5.65; 0.58; −77.87202, 259, 217, 162,0.7181–0.4695
A11112−65.36; −50.74; 131.11; 132.12; 43.49; 7923.34; 3573.41; 21.71; 20.30; 0.00; 0.02; 1.75; 1.88; 3.84; 0.39102, 1170.6730–0.2889
A11121−60.21; −53.00; 142.95; 135.46; 42.30; 5004.94; 2542.52; 83.02; 78.23; 0.00; 0.03; 1.84; 1.84; 4.05; 0.5954, 38, 52, 53, 9, 1340.7262–0.2825
A11122−71.27; −76.34; 107.00; 147.22; 122.42; 3417.29; 4425.60; 198.31; 70.84; 0.01; 0.03; 1.78; 1.53; 4.90; 0.33118, 104, 57, 960.8062–0.8062
A1121180.41; −23.42; 319.82; 112.29; 573.17; 4808.29; 3389.89; 6.06; 92.03; 0.00; 0.31; 1.33; 9.59; 0.80; −114.19157, 2230.9574–0.9491
A11212−24.89; 76.99; 154.75; 8.68; 2427.15; 2994.14; 647.18; 53.07; 7.58; 0.00; 1.52; 1.23; 4.64; 0.93; −35.57260, 188, 2310.7190–0.2987
A11221−58.62; 121.52; 135.12; 1.73; 7497.75; 6004.92; 136.19; 103.68; 0.21; 0.00; 1.44; 1.69; 3.73; 0.63; −78.32233, 145, 179, 1440.5978–0.3376
A11222−47.51; 136.10; 138.25; 2.50; 6432.46; 3613.26; 122.45; 59.46; 0.38; 0.00; 1.70; 1.71; 3.92; 0.62; −42.74200, 218, 234, 2270.5407–0.2093
A12111−18.28; −10.51; 184.30; 150.65; 12.53; 31.27; 28.06; 20.28; 13.51; 0.19; 0.83; 1.56; 2.13; 4.38; −3.25136, 129, 115, 55, 17, 110, 6, 67, 80, 49, 97, 112, 26, 109, 124, 86, 44, 23, 193, 68, 87, 135, 58, 45, 5, 75, 50, 37, 46, 33, 114, 133, 65, 29, 18, 149, 197, 254, 11, 238, 95, 84, 81, 88, 22, 100, 28, 77, 94, 56, 31, 121, 122, 32, 208, 41, 30, 1, 90, 240, 36, 111, 47, 89, 185, 2160.9956–0.2976
A1211211116.28; 89.97; 337.65; 355.25; 3.90; 97.01; 4.08; 1.86; 5.41; 0.02; 0.03; 6.00; 7.21; 8.30; 2.0599 103 35 43 116 27 92 78 101 64 119 2680.6005–0.0600
A1211211210.77; 55.33; 305.37; 309.65; 2.75; 95.45; 9.19; 1.95; 1.25; 0.02; 0.03; 5.99; 6.11; 7.37; 2.08123, 8, 24, 25, 71, 66, 105, 1300.6368–0.1414
A12112121118.65; 29.24; 273.01; 219.70; 8.12; 125.43; 5.96; 5.76; 0.99; 0.03; 0.02; 1.72; −0.08; 6.95; −0.2048, 21, 1520.6432–0.0937
A1211212122.70; 30.76; 269.06; 258.53; 3.06; 123.06; 4.16; 2.48; 0.42; 0.03; 0.01; 5.05; 2.10; 7.25; 0.8173, 120, 113, 20.7989–0.3787
A121121224.40; −7.63; 243.97; 239.15; 4.24; 134.37; 21.91; 3.45; 1.32; 0.03; 0.03; 3.57; 3.47; 5.96; 1.1298, 126, 108, 61, 60, 93, 760.7381–0.1055
A121122−14.32; 16.36; 184.44; 149.07; 117.55; 465.95; 353.89; 34.18; 24.34; 0.02; 0.40 2.88; 4.28; 3.77; −5.09253, 13, 106, 170, 34, 125, 62, 10, 42, 132, 15, 40, 690.5034–0.0892
A121211118.33; 218.26; 232.00; 5.49; 20.77; 18.76; 16.13; 3.73; 4.80; 0.02; 1.99; 1.41; 6.44; 1.22; −48.90248, 177, 261, 137, 148, 163, 225, 138, 158, 181, 265, 147, 207, 269, 205, 150, 256, 161, 171, 155, 143, 186, 235, 250, 2390.5992–0.1036
A1212112−19.64; 169.10; 172.41; 7.39; 15.19; 17.95; 15.96; 8.17; 3.94; 0.05; 1.51; 1.24; 5.20; 1.14; −52.63201, 262, 212, 198, 139, 190, 183, 222, 173, 266, 214, 2460.5090–0.1133
A1212121−61.90; 89.25; 97.95; 11.00; 8.68; 14.72; 46.64; 47.82; 5.89; 0.07; 0.48; 0.66; 3.55; 0.87; −25.63156, 264, 169, 224, 182, 154, 153, 219, 141, 164, 180, 2100.5958–0.1890
A1212122−45.95; 126.62; 125.31; 4.78; 6.59; 9.59; 14.37; 13.52; 1.99; 0.06; 0.66; 0.77; 4.30; 0.78; −29.46213, 142, 196, 242, 236, 151, 192,175, 176, 178, 165, 191, 252, 251, 160, 263, 203, 189 226, 204, 241, 194, 2490.7261–0.1019
A12122−43.23; 50.28; 135.60; 63.69; 61.31; 128.10; 130.95; 86.49; 35.51; 0.11; 0.90; 1.75; 3.55; 2.46; −17.62232, 159, 211, 195, 168, 187, 245, 172, 174, 237, 199, 228, 74,167, 85, 267, 51, 14, 230, 91, 39, 12, 3, 255, 63, 131, 79, 140, 257, 244, 1270.9979–0.1005
A1221−45.95; 126.62; 125.31; 4.78; 6.59; 9.59; 14.37; 13.52; 1.99; 0.06; 0.66; 0.77; 4.30; 0.78; −29.46215, 258, 221, 243, 166, 146, 247, 206, 209, 2200.6506–0.3753
A1222−45.48; 37.33; 145.26; 205.85; 747.83; 1979.16; 1053.58; 52.32; 18.56; 0.01; 0.39; 2.23; 2.41; 6.05; −4.474, 82, 16, 70, 229, 7, 59, 184, 128, 83, 107, 720.9676–0.1448
A242.00; −58.65; 105.90; 102.10; 1.73; 3371.80; 0.00; 57.84; 33.90; 0.04; 2,450,000.00; 1.62; 6.17; −1.15; 3.74201.0000
Table 3. The fuzzy partitioning of the solvents and variables (descriptors).
Table 3. The fuzzy partitioning of the solvents and variables (descriptors).
SolventsVariablesDOM SolventsDOM Variables
A1 244 15 10 257 125 132 106 42 140 4 62 220 40 82 34
267 79 131 268 209 92 27 255 230 74 239 167 155 63 170 90 71 76 205 269 130 8 199 25 111 185 105 250 89
216 13 207 159 228 150 101 119 2 69 214 120 152 95 246
11 78 81 240 249 21 137 93 18 116 221 22 181 98 258 253 208 172 174 235 126
245 99 51 148 85 265 114 103 36 87 35 261 24 47 161
43 64 229 45 66 68 147 49 194 41 211 123 138 238 256
186 97 188 225 254 158 171 67 109 26 237 124 143 5 180
23 112 195 44 37 160 183 222 113 80 262 210 139 198
73 169 33 166 135 252 251 197 29 65 176 168 133 88 50
46 86 48 75 164 190 189 60 212 175 108 187 248 61 58 151 213 193 192 149 156
236 153 17 201 178 263 163 196 84 14 100 191 16 142
129 154 6 94 39 173 3 177 264 242 55 224 115 241 182
266 110 165 91 121 122 1 56 32 219 141 30 31 77 28 204
226 203 12 59 136 232 260 70 243 127 215 7 247 206 118 134 157 184 223 146 9 96 231 128 83 52 104 227 53 54 38 72 107 162 202 217
218 259 19 234 200 102 57 233 179 144 145 117
1–10 12–151.0001.000–0.9957
A2 20111.0001.000
A11 218 162 259 234 38 217 202
72 107 54 19 200 53 102 57 233 179 144 145 227 117 104 52 83 9 231 128 96 223
157 184
5–70.9991–0.51670.8819–0.7767
A12 111 13 199 152 214 76 246 89 150 228 18 174 172 245
239 253 159 170 114 47 255 211 41 256 194 137 74 195
237 180 66 23 210 238 230 181 186 49 68 161 126 254 171 45 97 98 143 169 124 87 138 235 109 26 67 261 158 112 5 208 225 147 37 265 44 93 22 85 240 160 222 148 80 164 21 123 139 198 262 36
183 33 64 197 252 251 135 43 65 81 24 187 35 60 103 29 113 46 176 73 133 75 50 86 189 248 88 11 167 190 51 168 212 249 95 99 175 108 48 213 61 78 58 120 151 156
193 149 192 2 116 153 267 236 201 178 163 263 90 17 196 84 100 216 14 191 207 154 142 129 94 6 264 119 177 39 173 3 242 224 101
185 55 130 241 115 182 105 266 165 110 91 121 25 122 250 1 56 32 219 30 141 31 8 77 28 204 226 82 203 12 71 269 205 136 155 232 4 27 92
63 34 268 106 131 62 79 140 257 125 42 10 244 132 15
209 40 220 258 69 221 229 166 16 188 70 59 243 260 127 215 206 247 7 118 146 134
8 9 2 13 14
12 10 15 1 4
0.9999–0.50200.9996–0.8953
A111 19 162 217 202 259 53 102 54 179 38 117 223 52 157 960.9607–0.39610.8819
A112 218 234 200 72 107 227 144
145 57 233 83 104 128 231 96 184
5 7 0.9967–0.30220.9–0.3022
A1121 72 107 57 83 128 104 9670.8–0.27180.7987
A1122 218 234 200 227 144 145 233 231 18450.9–0.21230.7709
A121 106 82 119 105 8 90 71 25 120 2 11 95 101 78 229 81
92 216 221 268 130 125 27 4 257 166 21 116 132 185 69 93 260 22 258 244 10 98 155 220 269 205 59 209 126 16 240 70 243 36 99 250 215 207 7 40 255 127 247 103 239 206 79 131 87 63 118 134 146
13 14 12 10 9
15 1 8 2
0.9–0.34750.9–0.6356
A122 253 88 212 48 228 190 198 61 262 47 252 251 159 197
256 17 248 222 175 263 151 201 213 139 6 108 29 73 236
193 129 60 210 176 100 94 178 113 55 183 196 142 173
58 149 242 115 156 254 163 133 191 195 110 3 192 241 264 39 14 169 224 122,121 164 266 194 1 33 165 160 238 158 167 177 32 37 30 56 154 170 211 189 31 225 219
182 153 168 204 187 5 180 141 91 84 50 65 226 203 12 138 152 171 80 214 28 77 237 86 230 135 41 246 46 174 124 111 89 136 44 232
143 245 42 109 172 75 147 140 66 26 114 23 112 186 123 150 161 97 18 261 15 265 62 13 67 34 199 148 85 68 137 51 45 24 249 49 235 43 188 74 208 76 64 35 267 181
4 30.9–0.51860.9–0.8369
A1211 258 269 205 155 257 215 209 250 207 247 243 166 40 7 255 206 63 131 79 1468 9 20.7318–0.22350.8666–0.5420
A1212 8 105 90 71 25 120 11 82 95 119 2 106 4 130 125 21 78 116 69 132 81 92 27 98 101 93 10 260 59 22 126 99 70 16 216 127 240 36 103 185 87 268 244 229 221 118 220 134 23912 10 13 14 1
15
0.9382–0.28800.9–0.9379
A12121 106 81 240 216 185 260 101 2681
A12122 90 120 25 8 82 2 119 105 4
130 78 95 116 71 125 11 27 69 132 98 93 10 126 59 21
99 22 127 16 70 103 36 229 118 221 92 87 134 244 220 239
12 13 10 14
15
0.8–0.33520.9408
A121221 119 11 95 93 22 21 98 10 126 87 221 244 22013 14 120.9–0.28670.9–0.8168
A121222 25 8 82 105 2 120 130 78 71
90 116 27 132 4 69 99 59 103 16 70 36 127 125 92 118
239 134 229
10 150.8–0.22260.9–0.7336
A1212221
1 119 11 95 22 21 87
140.7–0.34220.9207
A1212222
2 98 10 126 93 221 220 244
13 120.5–0.17330.9–0.5802
A1212221
8 25 132 69 105 71 27 59 127 16 70 118 92 239 134
150.8–0.17200.7326
A1212222
2 120 78 4 82 130 90 116 99 36 103 125 229
100.7–0.11690.8960
A1221
48 61 17 47 73 60 108 113 6 129 55 115 42 140 110 111
89 66 15 62 123 34 37 13 114 88 18 5 267 26 24 188 50 109 80 97 124 112 43 135 35 64 76 49
68 74
40.9–0.33070.9159
A1222 252 251 263 175 212 151 213 190 139 176 173 183
222 228 198 236 242 256 266 241 160 178 196 142 62 253 210 201 156 192,191 264 169 194 226 248
165 219 224 189 163 246 177 225 193 197 149 138 203 158 214 180 170 254 154 141 164 153 182 238
147 159 33 195 204 211 30 94 84 152 237 121 167 91
122 65 171 12 32 3 39 31 58 14 100 28 1 168 265 56 187 143 150 261 77 249 230 161 186 29 148 136 232 137 41 174 245 75 172 86 235 85 208 181 51 67 199 45
30.9–0.35090.8366
Table 4. Solvents included in each class and the respective class descriptor.
Table 4. Solvents included in each class and the respective class descriptor.
ClassSolventsVariables
19 19 38 52 53 54 102 117 157 162 179 202 217 223 259 57 72 83 96 104 107 128WSe
2144 145 184 200 218 227 231 233 234Dens
37 40 63 79 131 146 155 166 205 206 207 209 215 243 247 250 255 257 258 269VPe
481 101 106 185 216 240 260 268MPe
511 21 22 87 95 119logKOA
610 93 98 126 220 221 244logKOWe
78 16 25 27 59 69 70 71 92 105 118 127 132 134 239logBCF
82 4 36 78 82 90 99 103 116 120 125 130 229HLe
95 6 13 15 17 18 23 24 26 34 35 37 42 43 44 46 47 48 49 50 55 60 61 62 64 66 68 73 74 76 80 88 89 97 108 109 110 111 112 113 114 115 123 124 129 133 135 140 188 267
1 3 12 14 28 29 30 31 32 33 39 41 45 51 56 58 65 67 75 77 84 85 86 91 94 100 121 122 136 137 138 139 141 142 143 147 148 149 150 151 152 153 154 156 158 159 160 161 163 164 165 167 168 169 170 171 172 173 174 175 176 177 178 180 181 182 183 186 187 189 190 191 192 193 194 195 196 197 198 199 201 203 204 208 210 211 212 213 214 219 222 224 225 226 228 230 232 235 236 237 238 241 242 245 246 248 249 251 252 253 254 256 261 262 263 264 265 266
BPe
1020HLc
Table 5. Defined classes of solvents with the descriptors.
Table 5. Defined classes of solvents with the descriptors.
NameClassPolarNon-PolarVolatilePolar-VolatileDescriptor
Iodoethane 91 x Wsol
Diethyl glutarate 191x Wsol
1,1-dichloroethane 381 x Wsol
2,4-dimethyl-3-pentanone 541 x Wsol
1-hexanol 571 x Wsol
4-methyl-2-pentanone 721 x Wsol
1-chloropropane 961 x Wsol
n-butyl acetate 1021 xWsol
2-chloropropane 1041 x Wsol
2-Methyltetrahydrofuran 1071 xWsol
1,2-dichloroethane 1171 x Wsol
Diethyl succinate 1281x Wsol
Glycerol-1,3-Dibutyl ether 1571x Wsol
m-cresol 1621 x Wsol
Dimethyl adipate 1791x Wsol
Glycerol-1,2,3-triethyl ether 2021x Wsol
diethyl carbonate 2171 xWsol
Caprylic acid diethanolamide 2231x Wsol
Benzaldehyde 2331 x Wsol
Chloroform 2341 x Wsol
DMEU 2591x Wsol
Dimethyl phthalate 521 x Wsol
Quinoline 531 x Wsol
Butylacetate 831 x Wsol
Bromoethane 1442 x Dens
di-isopropyl ether 1452 x Dens
Benzonitrile 1842 x Dens
Isobutyl acetate 2182 xDens
di-n-propyl ether 2272 x Dens
carbon disulfide 2312 x Dens
Benzene 73 x VPe
1,1,1-trichloroethane 403 x VPe
Dichloromethane 633 x VPe
methyl formate 793 xVPe
diethyl ether 1313 x VPe
1,1-dichloroethylene 1463 x VPe
Oleyl alcohol 1553 x VPe
Fluorobenzene 1663 x VPe
tetraethylene glycol 2053x VPe
Ricinoleic acid 2063 x VPe
triethylene glycol 2073x VPe
Butyl stearate 2093 x VPe
methyl benzoate 2153 x VPe
1,8-Cineole 2473 x VPe
gamma-Valerolactone 2503 x VPe
alpha-Terpineol 2573 x VPe
beta-Terpineol 2583 x VPe
1,1,2,2-tetrachloroethane 2433 x VPe
Nopol 2553 x VPe
PolyEthyleneGlycol 200 2693x VPe
Dioctylsuccinate 2164 x MPe
Isosorbide dioctanoate 2404 x MPe
Glycerol triacetate 814x MPe
Oleic acid 1014 x MPe
Menthanol 1064 x MPe
Diisooctylsuccinate 1854 x MPe
DPMU 2604x MPe
PolyEthyleneGlycol 600 2684x MPe
2-Pyrrolidone 115 x logKOA
Sulfolane 215x logKOA
Propylene carbonate 225x logKOA
N-methylacetamide 875x logKOA
Glycerol 955x logKOA
Water 1195 xlogKOA
Phenetole 106 x logKOW
Diisobutyl adipate 936 x logKOW
Geranyl acetate 986 x logKOW
1-Octanol 2446 x logKOW
Menthanyl acetate 1266 x logKOW
Trichloroethylene 2206 x logKOW
pentyl acetate 2216 x logKOW
Ethyl myristate 87x logBCF
Isoamyle acetate 167 xlogBCF
Methyl abietate 277 x logBCF
Methyl myristate 1057 x logBCF
Butyl laurate 257 x logBCF
2,6-dimethyl-4-heptanone 597 x logBCF
N,N-dimethylaniline 697 x logBCF
Nitrobenzene 707 x logBCF
Benzyl benzoate 717 x logBCF
Methyl stearate 927 x logBCF
Geraniol 2397 x logBCF
Dimethyl 2-methylglutarate 1187x logBCF
1,1,3,3-tetramethyl urea 1277x logBCF
Diethyl phthalate 1327 x logBCF
Diethyl adipate 1347 x logBCF
Ethyl laurate 28x HLe
Glycerol-1,2-dibutyl ether 48x HLe
dibenzyl ether 908 x HLe
Methyl linolenate 1038 x HLe
Methyl ricinoleate 1168 x HLe
Methyl laurate 1208 x HLe
ethyl benzoate 1258 x HLe
Dibutyl sebacate 1308 x HLe
Acetyltributyl citrate 368 x HLe
Diisoamylsuccinate 788 x HLe
N,N-Diethylolcapramid 828 x HLe
Butyl palmitate 998 x HLe
Anisole 2298 x HLe
Triethylamine 19 xBPe
propyl formate 39 xBPe
Cyclohexanol 59x BPe
Ethanol 129 xBPe
di-n-butyl acetate 139 xBPe
Ethyl acetate 149 xBPe
1-chlorobutane 159 x BPe
Glycerol-2-methyl monoether 179x BPe
m-dichlorobenzene 189 x BPe
p-Cymene 239 x BPe
Methyl palmitate 249 x BPe
Isopropylacetate 269x BPe
1-Butanol 289 xBPe
4-picoline 299 xBPe
3-methyl-2-butanone 309 xBPe
n-Propyl acetate 319 xBPe
Propionitrile 329 xBPe
Dimethyl sulfoxide 339x BPe
Chlorobenzene 349 x BPe
Isopropyl palmitate 359 x BPe
2,6-dimethylpyridine 379x BPe
1,3-Dioxolane 399 xBPe
Cyclohexane 419 x BPe
1-bromobutane 429 x BPe
Butyl myristate 439 x BPe
Furfurylic alcohol 449x BPe
Formamide 459x BPe
2,4-dimethylpyridine 469 x BPe
Dihydromyrcenol 479 x BPe
3-Hydroxypropionic acid 489x BPe
Benzyl alcohol 499 x BPe
Cyclohexanone 509 x BPe
Diethylamine 519 xBPe
1,3-Dioxan-5-ol 559 x BPe
iso-octane 569 x BPe
Glycerol-1,2,3-trimethyl ether 589x BPe
Glycerol-2-ethyl monoether 619x BPe
Toluene 629 x BPe
1,3-Propanediol 679x BPe
N-methylformamide 689x BPe
Glycerol-1-butyl monoether 739x BPe
Cyclopentane 749 x BPe
Propylene glycol 759x BPe
Iodobenzene 769 x BPe
Butyronitrile 779 xBPe
Glycerol-1,3-dimethyl ether 809x BPe
N,N-dimethylformamide 849x BPe
ethyl formate 859 xBPe
β-Pinene 869 x BPe
Piperidine 889 xBPe
o-xylene 899 x BPe
2,2,2-trifluoroethanol 919 xBPe
3-pentanone 949 xBPe
Aniline 979x BPe
Pyridine 1009 xBPe
Diisobutyl glutarate 1089 x BPe
Tetrahydrofurfurylic alcohol 1099x BPe
3-Methoxy-3-methyl-1-butanol 1109x BPe
p-xylene 1119 x BPe
cis-decaline 1129 x BPe
Dimethylisosorbide1139x BPe
Mesitylene 1149 x BPe
Glycerol-1,2-dimethyl ether 1159x BPe
2-pentanone 1219 xBPe
n-heptane 1229 x BPe
Isopropyl myristate 1239 x BPe
d-Limonene 1249 x BPe
1,3-Dioxolane-4-methanol 1299x BPe
Propionic acid 1339 xBPe
n-decane 1359 x BPe
3-Butyl-1-methylimidazolium tetrafluoroborate 1369 x BPe
1-Decanol 1379 x BPe
N-methyl-pyrrolidin-2-one 1389x BPe
α-Pinene 1399 x BPe
carbon tetrachloride 1409 x BPe
1,2-dimethoxyethane 1419 xBPe
2-methoxyethanol 1429 xBPe
Methyl oleate 1439 x BPe
Decamethylcyclopentasiloxane 1479 x BPe
diethylene glycol 1489x BPe
Glycerol-2-butyl monoether 1499x BPe
Tributylamine 1509 x BPe
1-pentanol 1519x BPe
EthylHexyllactate 1529 x BPe
Nitromethane 1539 xBPe
tert-butyl alcohol 1549 xBPe
1,4-dioxane 1569 xBPe
Glycerol-1-ethyl monoether 1589x BPe
Cyclohexene 1599 x BPe
N,N-dimethylacetamide 1609x BPe
Ethyl palmitate 1619 x BPe
5-(Hydroxymethyl)furfural 1639 x BPe
2-butanone 1649 x BPe
2-methyl-2-butanol 1659 xBPe
Styrene 1679 x BPe
Methyl acetate 1689 xBPe
Pyrrolidine 1699 xBPe
N,N-Dimethyloctanamide 1709 x BPe
Glycerol carbonate 1719x BPe
Acetone 1729 xBPe
2-aminoethanol 1739x BPe
tert-butyl methyl ether 1749 xBPe
Acetylacetone 1759x BPe
3-picoline 1769x BPe
Dipropyleneglycol 1779x BPe
2-pentanol 1789 xBPe
n-butylamine 1809 xBPe
diphenyl ether 1819 x BPe
2-propanol 1829 xBPe
Ethylene glycol 1839x BPe
Ethyl linolenate 1869 x BPe
Methanol 1879 xBPe
Cyclopentyl methyl ether 1889 xBPe
Nitroethane 1899 xBPe
Phenol 1909x BPe
isobutyl alcohol 1919 xBPe
Ethylenediamine 1929 xBPe
β-Farnesen 1939 x BPe
Tetrachloroethylene 1949 x BPe
Tetrahydrofuran 1959 xBPe
3-pentanol 1969 xBPe
Methyl 5-(dimethylamino) 2-methyl-oxopentanoate 1979x BPe
2,4,6-trimethylpyridine 1989 x BPe
n-propylamine 1999 xBPe
Acetophenone 2009 xBPe
Glycerol-1,3-diethyl ether 2019x BPe
2-butanol 2039 xBPe
acetic anhydride 2049x BPe
Ethyl linoleate 2089 x BPe
trifluoroacetic acid 2109 xBPe
n-hexane 2119 x BPe
Ethyl lactate 2129x BPe
Cyclopentanone 2139x BPe
o-dichlorobenzene 2149 x BPe
3,3-dimethyl-2-butanone 2199 xBPe
Dimethyl glutarate 2229x BPe
1-propanol 2249 xBPe
Glycerol-1-methyl monoether 2259x BPe
n-octane 2269 x BPe
m-xylene 2289 x BPe
Bromobenzene 2309 x BPe
Choline acetate 2329 x BPe
Ethyl oleate 2359 x BPe
Acetic acid 2369 xBPe
Acetonitrile 2379 xBPe
Morpholine 2419 xBPe
3-methyl-1-butanol 2429 xBPe
Acetone 2459 xBPe
2-Furfuraldehyde 2499x BPe
Glycofurol (n = 2) 2549x BPe
Solketal 2569x BPe
HMPTA 2619x BPe
DEGDEE 2629x BPe
DEGDME 2639x BPe
ethyl propionate 2649 xBPe
TEGDME 2659x BPe
Dimetylsulfoxide 2669x BPe
n-pentane 2679 x BPe
Isododecane 69 x BPe
Diisobutyl succinate 609 x BPe
Methyl Linoleate 649 x BPe
Dimethyl succinate 659 x BPe
N,N-Dimethyldecanamide 669 x BPe
Glycerol-1,2,3-tributyl ether 2389 x BPe
1,4-Cineole 2469 x BPe
Terpineol acetate 2489 x BPe
beta-Myrcene 2519 x BPe
Terpinolene 2529 x BPe
Cyclademol 2539 x BPe
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Nedyalkova, M.; Sarbu, C.; Tobiszewski, M.; Simeonov, V. Fuzzy Divisive Hierarchical Clustering of Solvents According to Their Experimentally and Theoretically Predicted Descriptors. Symmetry 2020, 12, 1763. https://doi.org/10.3390/sym12111763

AMA Style

Nedyalkova M, Sarbu C, Tobiszewski M, Simeonov V. Fuzzy Divisive Hierarchical Clustering of Solvents According to Their Experimentally and Theoretically Predicted Descriptors. Symmetry. 2020; 12(11):1763. https://doi.org/10.3390/sym12111763

Chicago/Turabian Style

Nedyalkova, Miroslava, Costel Sarbu, Marek Tobiszewski, and Vasil Simeonov. 2020. "Fuzzy Divisive Hierarchical Clustering of Solvents According to Their Experimentally and Theoretically Predicted Descriptors" Symmetry 12, no. 11: 1763. https://doi.org/10.3390/sym12111763

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