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The problems relating to multivariate classifications carried out on matrices of constrained data are examined with reference both to row-sum constraints (closed, or compositional data) and to constraints concerning the ratio between variables (radial, or V-shaped data). As regards the use of principal component analysis (PCA) with closed data, the two opposite drawbacks observed previously with raw data and after a log row centering (or Aitchison's transform) are confirmed. It is demonstrated, in particular, that classifications based on raw closed data give too much weight to major variables, while those based on log row centered data to minor and trace variables. In consideration of this, a ‘unified’ procedure is proposed, which simultaneously processes with principal component analysis the two kinds of data above. Such a procedure seems to obviate the cited drawbacks and to give correct classifications. These results have been obtained using both simulated and real data, the latter referring to a set of archaeological glass finds. The problem of the influence of responses below the detection limit on the classifications is also examined, together with some aspects relating to the classification of radial data.

The problem of the presence and of the treatment of values below the detection limit (or 'less than' values) is examined, for some real cases of unsupervised pattern recognition of samples. The experimental data refer to archaeological glass fragments of the seventh and eighth centuries AD and to ceramic shards of Roman epoch and of different provenances. Increasing amounts of less-thans are progressively introduced into the original data by a particular procedure and the less-thans treated each time with three different substitution methods (i.e. substitution with constant values, with randomly distributed values and with values obtained by principal component analysis). A subsequent multivariate classification of the samples by various techniques and an evaluation of the corresponding results, allows one to evaluate and to compare the effectiveness of the three methods of treatment of less-thans.

On the basis of the results of previous studies, the problem of multivariate classification in the presence of the so-called radial or V-shaped data has been briefly re-examined. Taking into account that the radial data, in the absence of preliminary transformations, usually lead to classifications of samples meaningless from a chemical point of view, five different data transformations have been evaluated and compared in the case of both hypothetical and real samples (real samples, in particular, consisted of archaeological ceramic shards to be classified on the basis of provenance). The following transformations have been used: closure to 100, log row centering, log double centering, row centering, and double centering. The transformed data were then classified by means of hierarchical clustering and principal component analysis (PCA). It has been demonstrated that only the first three transformations lead to correct classifications of radial data, and the causes of this fact have been explained.

When it is not possible to analyze an exactly reproducible amount of sample (or whenever samples contain indefinite amounts of extraneous materials) it is customary to normalize the data by making, for example, the sum of the concentrations obtained for each sample equal to 100. Although the data normalized (or ;closed') in such a manner have been criticized, it is empirically shown that closure is appropriate in order to compare and classify samples of the type indicated above.

Multivariate thermodynamic data of proton dissociation of 84 aromatic acids in aqueous medium have been processed with factor analysis. It is demonstrated that the concept of latent factor allows quantitative and rigorousdeterminations of the number and of the importance of the causes of different acid strengths.

Thermodynamic data of proton dissociation of 75 organic acids belonging to four classes (protonated amines, aliphatic carboxylic acids, benzoic acids, phenols) have been processed by multivariate chemometric techniques. The variables consist of conventional thermodynamic quantities (Gibbs function, enthalpy, entropy) and of partial components of these quantities (internal and external, electrostatic and nonelectrostatic components). The above data refer to the aqueous medium, at 25 °C and I = 0 mol dm−3. The Gibbs function of deprotonation in the gas phase and the Hammett σ constant have also been considered. Multivariate techniques include Principal Component Analysis, Factor Analysis, and feature selection. Factor Analysis and related concepts have proved to be useful in defining the causes of differences in acid strengths and their respective importance. Keywords: acid dissociation data, chemometrics of; chemometrics of acid dissociation data; factor analysis of acid dissociation data; principal component analysis of acid dissociation data; thermodynamics of acid dissociation.

A set of quantitative analytical data for 13 rivers belonging to the basin of the Tanaro (Piedmont region, north-western Italy) has been processed by multivariate statistical techniques. The original matrix, which refers to the year 1990, consisted of 20 chemical and physico-chemical variables, determined at 44 sampling sites. The following methods have been used for the treatment of the data: cluster analysis (unsupervised pattern recognition), factor analysis, variable selection by Fisher weights. A comparison has also been made between the data referring to 1990 and to 1978 in order to investigate the evolution of the environmental situation for the Tanaro basin after such a lapse of time. This comparison has been carried out by processing the 3-D matrix which collects the data of the two different periods.

Supervised and unsupervised pattern recognition techniques were used to classify 48 sherds of Roman pottery (terra sigillata), analysed by inductively coupled plasma atomic emission spectrometry and atomic absorption spectrometry for seven major and minor elements (Al, Fe, Ca, Mg, K, Ti and Mn). Hierarchical agglomerative clustering and principal component analysis were used to classify the studied material into compositional groups which could account for different centres of production; soft independent modelling of class analogy (SIMCA) was used to solve questions regarding doubtful assignments. The results indicate that, in the case study, a throughout statistical treatment can allow one to discriminate wares produced in different geographical areas on the basis of the seven elements accounted for.

A set of quantitative analytical data for the rivers Bormida and Tanaro in the Piedmont region (north-western Italy) has been processed by multivariate statistical techniques. The aim consists in evaluating the usefulness of these methods, compared with usual univariate techniques, in the investigation of surface water pollution phenomena. The experimental data consist of 19 chemical and bacteriological variables determined at 31 sampling sites. The following methods have been used for the treatment of the data: cluster analysis (unsupervised pattern recognition), principal component analysis, non-linear mapping, multivariate feature selection. The treatment has been proved to be useful in determining the various factors of pollution together with their mutual importance and correlation in evaluating the general degree of pollution of rivers, and in rationalizing the data collection by eliminating variables with low information content.

Forty-five sherds of Roman pottery, 21 terrae sigillutae and 24 common wares excavated in Augusta Praeroria, were analysed for 12 elements by atomic absorption and emission spectroscopy. Hierarchical agglomerative cluster analysis, principal component analysis, and non-linear mapping were performed on the analytical data in order to classify the objects in groups which could account for different provenances; soft independent modelling of class analogy (SIMCA) and K nearest neighbours (KNN) were used for solving doubtful assignments. The classification results indicate that local productions of terra sigillatu can be easily distinguished from the imported ones, and that common wares have compositional patterns which differ from those of both local and imported terrae sigillatue.

Twenty-one sherds of Roman terra sigillata from Augusta Praetoria (Aosta, Italy) have been analyzed by atomic absorption and emission spectroscopy. Ca, Ba, Ti, Cr, Mn, Fe, Cu, and Al were determined by atomic absorption spectroscopy with electrothermal atomization in graphite furnaces; Mg and Sr were determined by inductively coupled plasma emission spectroscopy; Na and K by flame emission spectroscopy. The data obtained have been processed by different methods of multivariate analysis, such as cluster analysis, principal component analysis, and nonlinear mapping. The results indicate that at least three compositional groups can be identified among the studied sherds, probably reflecting different geographical provenances.

In this paper copper(II) complex formation in aqueous solution with a series of nucleosides (adenosine or guanosine) or nucleotides 5'-monophosphate is studied by means of potentiometry, visible spectrophotometry and ultraviolet circular dichroism. A chemical model has been formulated for each binary system (at T= 25 degrees C and I = 0.1 M), with particular attention to the interaction in the basic field. A spectrum (both visible absorption and ultraviolet circular dichroism) for each complex with a significant percentage of formation (in the adopted experimental conditions) has been calculated, allowing structural details to be hypothesised. The interaction with deprotonated alcoholic group(s) of the ribose moiety has been found to be fundamental in determining the co-ordination chemistry of each ligand considered while cases of co-operation between the purine and ribose donor(s) were also considered. Confirmations were also obtained by an investigation on the corresponding 2'-deoxy compounds as ligands.

Taking into account that the problem of the best pretreatment of data for factor analysis has not yet arrived at generally accepted solutions, it has been tried to estimate, by an empiric procedure, the goodness of the results of repeated factor analyses with different pretreatments, conditions and statistical distribution of variables. Sets of multivariate data for river waters have been constructed firstly, after fixing the number and nature of the latent factors corresponding to the sources of pollution. A series of R-mode factor analyses has then been performed on these data, using various pretreatments (autoscaling, logarithmic transformation and their combinations), various factor rotations (rigid and oblique) and methods of computation of significant factors (40 data processing on the whole). Factor analyses have also been performed on real data of the Po river in the Piedmont region. Comparisons between the results obtained by factor analysis and the actual situation of the systems investigated have made it possible to draw some conclusions on how to proceed in order to obtain realistic results with this chemometric technique.

Multivariate chemometric techniques (principal component analysis, factor analysis, feature selection) have been applied to thermodynamic data of equilibria in different solvents. Eight fundamental reactions in various water-cosolvent mixtures have been considered, at 20 °C (63 equilibria in total). Possible advantages deriving from these techniques, in comparison with the use of traditional univariate methods, are briefly examined. In particular, it is shown that two factors account for 97.8% of variance in the data.

Enthalpies of complex formation of fumarate, itaconate, maleate and succinate with calcium have been determined by direct calorimetry. By using the stability constants of the literature, Gibbs function and entropy were also obtained. The present data refer to the aqueous medium at T = 25°C and I = 0.5 mol l−1. In spite of the trans-configuration of fumarate, examination of the present thermodynamic results indicates a probable bidentate behaviour for this ligand, as a consequence of a charge-transmission due to the carbon-carbon double bond. The lower stability of the fumarate complexes in comparison with those of its cis-isomer seems due to different solute-solvent interactions, while the metalligand bond strength seems similar in both cases. On the other hand the present results seem to indicate for the itaconate complexes a structure similar to that of maleate and succinate, without charge transmission.

Heats of complex formation of the borate ion with the carbohydrates D-galactose, D-glucose, D-fructose, D-mannose, and L-sorbose have been determined by direct calorimetry. By means of the equilibrium constants the corresponding Gibbs functions and entropies were also obtained. The present data refer to the aqueous medium, at T= 25 °C and I= 0.1 mol dm–3. Examination of the results indicates a leading role, in several cases, of solute–solvent external factors (e.g. desolvations of the borate ion) in determining the different stabilities of the complexes. Amongst various factors for the ligands, some appear of minor importance, while the contribution of others (such as the strength of the borate—hexose C–O–B bonds) is fairly constant throughout one series. The present data seem also to confirm the presence of the furanose cyclic form of the carbohydrate in the complex.

Enthalpy of association of hexacyanoferrate(III) ion with Mg(II), Ca(II), Sr(II), and Ba(II) cations has been determined by direct calorimetry. Using the equilibrium constants, Gibbs function and entropy were also obtained. Measurements were carried out in aqueous medium at 25 °C and ionic strength I = 0.1 mol L−1. Examination of the thermodynamic quantities obtained and calculation of the distance of closest approach between cation and anion show the presence of different desolvation processes for the metals studied. More particularly, solvent-separated ion pairs in the case of magnesium and contact pairs in the case of barium seem to be present. The presence of desolvation processes is uncertain for calcium and strontium. The ΔH0 and ΔS0 values show also an important influence from solvent-destructuring processes on ion pair formation.

A calculation method of the electrostatic and the nonelectrostatic parts of thermodynamic quantities of reaction, previously proposed and applied to association reactions in aqueous medium, is applied, in the present work, to reactions in mixed solvents. The aim of the present treatment is to clarify the importance of the various factors (dependent and independent of the dielectric constant) through which the solvent affects complex stability. The method is applied to ΔG0, ΔH0, and ΔS0 data of literature for proton–ligand and metal–ligand reactions in several water–methanol, water–ethanol, and water–dioxane mixtures. The conclusions of the present study seem to confirm a leading role of solvation equilibria in determining different stabilities of complex in different solvents, while a minor role is assigned to the dielectric properties of the solvent.

The chelating material described has iminodiacetate functional groups chemically bonded to commercial cellulose filters in order to preconcentrate trace metals in aqueous samples. The ions investigated were Cd(II), Co(II), Cu(II), Hg(II), Ni(II), Pb(II)and Zn(II). The influence of pH on the uptake efficiency was studied. While mercury(II) ion was very poorly retained, the capacity values for the other investigated cations were between 171 and 218 μmol g−1 of filter. Preconcentration factors of about 100 are easily achieved from solutions containing 100 μg of each metal in one liter. Recovery factors for a single ion were within 96 ± 5% and better than 90% for multicomponent mixtures, when measured by d.c. plasma emission spectrometry.

The procedure is based on decomposition of thiosulfate, with formation of sulfur, in the presence of 0.5 mol l −1 nitric acid. Thiosulfate is determined in the range 15–100 mg l −1 , with a relative standard deviation of 5.4% and a mean relative error of 3.2%. These data are of the same order of magnitude as those obtained for the earlier silver/1,10-phenanthroline method. The present method has the advantage of being almost completely free from interferences; the only interference observed (sulfide) is easily eliminated.

Heats of association of thiosulphate ion with a set of metal ions in aqueous solution have been determined by direct calorimetric method. The measurements have been performed at ionic strength 0·5 and at 25°C. The examination of the values of the thermodynamic parameters seems to suggest that while Zn2+, Mn2+, Ca2+ and Cd2+ ions give mainly contact ion pairs, Co2+ and Ni2+ form solvent separated ion pairs.

A calculation method of the electrostatic and nonelectrostatic parts of thermodynamic quantities of reaction, previously proposed and applied to complex-formation reactions of aminic and carboxylic ligands, is applied, in the present work, to association reactions of several other ligands. In particular, to check its reliability, this method is applied to ΔG0, ΔH0, and ΔS0 data of literature for the formation of metal–anion pairs and for associations of metals with ligands containing pyridine nitrogen, ethereal oxygen, or thioethereal sulfur. Experimental data referring only to aqueous solutions are considered. The results obtained by this method are in agreement, in most cases, with those expected for the reactions examined. Therefore, it seems reliable and useful for a more significant interpretation of conventional thermodynamic parameters.

The proposed nephelometric determination of thiosulfate in aqueous solution is based on precipitation of the slightly-soluble salt of thiosulfate with bis(1,10-phenanthroline)silver(I) cation from an aqueous ethanolic medium. Thiosulfate is determined in the range 3–70 mg l −1 , with a relative standard deviation of 2.6% and a relative accuracy of 2.5%. The method is simple and convenient. Iodide and thiocyanate interfere, but sulfite does not, even at 200 mg l −1 , which is an advantage over the usual iodimetric method.

Enthalpy and entropy of complex formation of picolinate and dipicolinate anions with Ni2+, Cu2+, Zn2+ in aqueous medium were determined by direct calorimetry, and by using the stability constants in the literature. The data refer to 25°C and I = 1 (NaNO3). The experimental results show the presence of the Jahn-Teller distortion for the copper complexes. The causes are also discussed of the weak basicity of the pyridine nitrogen towards hydrogen ion and of its comparatively strong coordinating properties towards metal ions.

Molar heats for the reaction of nickel(II) with sulphur-containing amino acids,S-carboxymethyl-L-cysteine andS-carboxyethyl-L-cysteine, have been determined by thermometric titrimetry. The data refer to aqueous solutions at 25°C andI=2.0m. From these enthalpies and equilibrium constants, the corresponding entropies have been calculated. The present thermodynamic data are complementary to previous spectrophotometric data in explaining the structures of the complexes. In particular, the importance of solute-solvent external factors in determining different stabilities for successive steps of complex-formation is stressed.

A HPLC method for the separation of phenol derivatives has been developed either on a RP Phenyl-bonded or an alkyl C18 -bonded columns. Derivatization with diazotized sulphanilic acid allows a reversed-phase chromatography with spectrophotometric detection at 370 nm. The method sensitivity permits detection down to 0.08- 0.15 ng of phenols. In particular structure-retention time relationships are discussed.

ΔH° and ΔS° of complex formation of Ni2+, Zn2+ and Cd2+ with dithiodiacetate and 3,3′-thiodipropionate anions, and of Cu2+ with 3,3′-thiodipropionate, have been determined by direct calorimetry, knowing the formation constants from the literature. The measurements were carried out in aqueous solution, at 25°C and I = 1 (NaNO3). The examination of the thermodynamic quantities indicates that the stability of this type of complexes is mainly determined by the following factors: the dimension of the chelate ring, the metal-sulphur bond strength and its nature (i.e. the presence or absence of an inner-sphere interaction). Cu2+ with thiodipropionate seems to be affected by a strong Jahn-Teller distortion, which is accompanied by the displacement of an unexpectedly high number of water molecules from the cationic sphere.

The heat of reaction of the anion of furan-2-carboxylic acid with cobalt(II), nickel(II) and copper(II) cations has been determined by direct calorimetry. By means of the equilibrium constants, Gibbs function and entropy were also obtained. The measurements were carried out in aqueous medium at 25 °C and an ionic strength I=1 mol dm−3 (NaNO3). The data obtained seem to indicate a bidentate character of this ligand, with the participation of both carboxylate and heterocyclic oxygen in complex formation. The behaviour of furan oxygen towards 3d metals is compared with that of thiophen sulfur and pyrrole nitrogen.

ΔH° and ΔS° have been determined, by direct calorimetry and by using published stability constants, for the association of Co(II) and Cu(II) with sulfate and peroxodisulfate anions. The results refer to an aqueous medium at T = 25°C and I = 0.5 M. Their examination seems to indicate, for the associations of sulfate, an outer-sphere ion pair formation in the case of cobalt, and an inner-sphere in the case of copper. This is in agreement with previous results for bivalent anions with a tetrahedral structure. By contrast, the desolvating ability of peroxodisulfate seems to be different from that of sulphate.

Enthalpy and entropy values have been determined, by direct calorimetry, for the association of Co(II), Ni(II), Cu(II) and Zn(II) ions with pyrazole in aqueous solution. The results refer to 25°C and I = 1 M. The significance of the thermodynamic quantities obtained is discussed.

Enthalpies for the reaction of borate with 1,2-ethanediol, 1,2-propanediol, 1,2,3-propanetriol and d-mannitol have been determined by thermometric titrimetry. From these enthalpies and equilibrium constants taken from the literature, corresponding entropies have been calculated. The data refer to aqueous solutions at 25 degrees and I = 1.0M (NaNO(3)). The results indicate reasons for the differences in the stabilities of the complexes.

The enthalpies of the first step of complex formation of 1-methylimidazole with CoII, NiII, CuII and ZnII have been determined by direct calorimetry. By means of the equilibrium constants, the Gibbs functions and entropies were also obtained. The measurements were carried out in aqueous medium, at 25 °C and an ionic strength I=1 mol dm−3 (NaNO3). The present results and the previous thermodynamic data for associations of pyrazole and imidazole are used to infer the quality of the metal-ligand bonds and particularly their π-character.

Heat and entropy of reaction of copper(II) with galacturonate and glucuronate anions have been determined by calorimetry. The measurements were performed in an aqueous medium at 25 °C and ionic strength I=1 M (NaNO3). The results indicate a bidentate action of the two ligands towards copper. The carboxylate group as well as the oxygen atom of the ring, the latter by means of an outer-sphere electrostatic bond, seem to interact with the cation.

Reference proteinaceous binding media of the kinds historically used in painting (specially prepared for this study) and samples collected from ancient polychrome works of art were analysed by gas chromatography – mass spectrometry. The data have been processed by several multivariate chemometric techniques, such as cluster analysis, principal component analysis, factor analysis and SIMCA technique in order to classify the binding media of the ancient works of art on the basis of the proteinaceous material used. The characterisation of ancient samples was possible by the joint use of SIMCA technique and factor analysis. The latter, in particular, has made it possible to point into evidence the presence of at least two latent factors. The first factor seems to be connected with the chemical composition of the painting media, while the second factor is likely to be connected with ageing processes.

Enthalpies of association of nitrate and chlorate with manganese(II), cobalt(II), nickel(II), copper(II), and zinc(II) have been determined by direct calorimetry in an aqueous medium at 25 °C and ionic strength I= 1 mol dm–3. The corresponding entropy values have been obtained by using known values of the association constants. The thermodynamic parameters suggest formation of ion pairs of the outer-sphere type, and also indicate the importance of electrostatics in determining the association processes.

Heats and entropies of complex formation of the thiophen-2-carboxylate ion with Ni2+, Cu2+, Zn2+ and Cd2+ have been determined by direct calorimetry, the formation constants being known from the literature. The measurements were carried out in aqueous medium at 25�C and an ionic strength of 1. The values of the thermodynamic quantities for thiophen-2-carboxylate, compared with those for (ethylthio)acetate and (phenylthio)acetate obtained previously, indicate a greater tendency for aromatic sulfur to form bonds with the above metals than for aliphatic sulfur. The causes of this behaviour are discussed.

Homo- and hetero-nuclear complexes of copper(II) and cadmium(II) with L-histidylglycine have been investigated by potentiometry, visible spectrophotometry, and calorimetry in aqueous medium, at T= 25 °C and I= 0.1 mol dm–3(KNO3). Gibbs functions obtained by potentiometry, combined with calorimetric enthalpies, gave the entropies of formation of the complex species. Experimental data have been obtained for the following species (L–= histidylglycinate anion): HL, H2L+, H3L2+, [CuL]+, [CuL2], [CuLH]2+, [CuL2H]+, [Cu2LH–1]2+, [Cu2L2H–2], [CdL]+, [CdL2], [CdLH]2+, [CuCdLH–1]2+, [CuCdLH–2]+. In general, the structures predicted on the basis of the spectrophotometric and thermodynamic results are in good agreement.