Trace Analysis Research Centre

The theoretical principles and practical implementation of a new method for multivariate data analysis, maximum likelihood principal component analysis (MLPCA), are described. MLCPA is an analog to principal component analysis (PCA) that incorporates information about measurement errors to develop PCA models that are optimal in a maximum likelihood sense. The theoretical foundations of MLPCA are initially established using a regression model and extended to the framework of PCA and singular value decomposition (SVD). An efficient and reliable algorithm based on an alternating regression method is described. Generalization of the algorithm allows its adaptation to cases of correlated errors provided that the error covariance matrix is known. Models with intercept terms can also be accommodated. Simulated data and near-infrared spectra, with a variety of error structures, are used to evaluate the performance of the new algorithm. Convergence times depend on the error structure but are typically around a few minutes. In all cases, models determined by MLPCA are found to be superior to those obtained by PCA when non-uniform error distributions are present, although the level of improvement depends on the error structure of the particular data set. © 1997 John Wiley & Sons, Ltd.

The characteristics of baseline drift are discussed from the perspective of error covariance. From this standpoint, the operation of derivative filters as preprocessing tools for multivariate calibration is explored. It is shown that convolution of derivative filter coefficients with the error covariance matrices for the data tend to reduce the contributions of correlated error, thereby reducing the presence of drift noise. This theory is corroborated by examination of experimental error covariance matrices before and after derivative preprocessing. It is proposed that maximum likelihood principal components analysis (MLPCA) is an optimal method for countering the deleterious effects of drift noise when the characteristics of that noise are known, since MLPCA uses error covariance information to perform a maximum likelihood projection of the data. In simulation and experimental studies, the performance of MLPCR and derivative-preprocessed PCR are compared to that of PCR with multivariate calibration data showing significant levels of drift. MLPCR is found to perform as well as or better than derivative PCR (with the best-suited derivative filter characteristics), provided that reasonable estimates of the drift noise characteristics are available. Recommendations are given for the use of MLPCR with poor estimates of the error covariance information.

Two new approaches to multivariate calibration are described that, for the first time, allow information on measurement uncertainties to be included in the calibration process in a statistically meaningful way. The new methods, referred to as maximum likelihood principal components regression (MLPCR) and maximum likelihood latent root regression (MLLRR), are based on principles of maximum likelihood parameter estimation. MLPCR and MLLRR are generalizations of principal components regression (PCR), which has been widely used in chemistry, and latent root regression (LRR), which has been virtually ignored in this field. Both of the new methods are based on decomposition of the calibration data matrix by maximum likelihood principal component analysis (MLPCA), which has been recently described (Wentzell, P. D.; et al. J. Chemom., in press). By using estimates of the measurement error variance, MLPCR and MLLRR are able to extract the optimum amount of information from each measurement and, thereby, exhibit superior performance over conventional multivariate calibration methods such as PCR and partial least-squares regression (PLS) when there is a nonuniform error structure. The new techniques reduce to PCR and LRR when assumptions of uniform noise are valid. Comparisons of MLPCR, MLLRR, PCR, and PLS are carried out using simulated and experimental data sets consisting of three-component mixtures. In all cases of nonuniform errors examined, the predictive ability of the maximum likelihood methods is superior to that of PCR and PLS, with PLS performing somewhat better than PCR. MLLRR generally performed better than MLPCR, but in most cases the improvement was marginal. The differences between PCR and MLPCR are elucidated by examining the multivariate sensitivity of the two methods.

Abstract Adsorption studies indicate that paraquat, diquat, and thionine are bound on bentonite by amounts greater than the measured cation-exchange capacity (CEC) of the clay. Methylene blue, new methylene blue, and malachite green are bound by amounts equal to the CEC. The unipositive organocations form aggregates on the clay surface. Aggregation increases with ionic strength and increases the apparent adsorption capacity by 25%. The aggregates are removed by washing with distilled water. Desorption studies show that the dyes are irreversibly bound, whereas the dipositive organocations are reversibly bound. Ionic strength variation reduces adsorption by 15 and 36% in the monovalent and divalent organocation-clay systems, respectively. In the clay-divalent organocation systems adsorption is greater on Na-saturated clay than on K-saturated clay. Adsorption is unchanged over the pH range 4.5–8.5 and decreases steadily below pH 4.0. Changes in adsorption due to changes in temperature are small. The study indicates that ionic strength is the most important variable in clay-organocation interactions.

The combination of HSLC and fluorigenic labelling with the use of a new fluorescence detector is discussed. The experiments were carried out with N-methyl carbamate insecticides labelled with dansyl chloride. Detection limits between 1–10 ng per 4 µl injection are reported and the method is suitable for quantitative analysis. With a reproducibility of 3% relative standard deviation, linear calibration plots up to 600 ng per injection are obtained. The applicability of the method to environmental sample analysis is demonstrated with soil and water analysis of the carbamates Mesurol and Carbofuran without preliminary clean-up.

Abstract These recommendations are a vocabulary of basic radioanalytical terms which are relevant to radioanalysis, nuclear analysis and related techniques. Radioanalytical methods consider all nuclear-related techniques for the characterization of materials where ‘characterization’ refers to compositional (in terms of the identity and quantity of specified elements, nuclides, and their chemical species) and structural (in terms of location, dislocation, etc. of specified elements, nuclides, and their species) analyses, involving nuclear processes (nuclear reactions, nuclear radiations, etc. ), nuclear techniques (reactors, accelerators, radiation detectors, etc. ), and nuclear effects (hyperfine interactions, etc. ). In the present compilation, basic radioanalytical terms are included which are relevant to radioanalysis, nuclear analysis and related techniques.

The application of trilinear decomposition (TLD) to the analysis of fluorescence excitation-emission matrices of mixtures of polycyclic aromatic hydrocarbons (PAHs) is described. The variables constituting the third-order tensor are excitation wavelength, emission wavelength, and concentration of a fluorescence quencher (nitromethane). The addition of a quencher to PAH mixtures selectively reduces the fluorescence intensity of mixture components according to the Stern-Volmer equation. TLD allows the three-way matrix to be decomposed to give unique solutions for the excitation spectrum, emission spectrum, and quenching profiles for each component. The availability of spectra and calculated Stern-Volmer constants can aid in the identification of unknown components. Preprocessing of the data to correct for Rayleigh/Raman scatter and primary absorption by the quencher is necessary. Both three-component (anthracene, pyrene, 1-methylpyrene) and four-component (fluoranthene, anthracene, pyrene, 2,3-benzofluorene) synthetic mixtures are successfully resolved by TLD using quencher concentrations up to 100 mM. Results are compared using both alternating least-squares and direct trilinear decomposition algorithms. The reproducibility of extracted Stern-Volmer constants is determined from replicate experiments. To illustrate the application of TLD to a real sample, a chromatographic cut from the analysis of a light gas oil sample was used. Analysis of the TLD extracted spectra and quenching constants suggests the presence of three classes of polycyclic aromatic hydrocarbons consistent with data from a second dimension of chromatography and mass spectrometry.

The efficacy of smoothing first-order data as a preprocessing method for multivariate calibration is discussed. In particular, the use of symmetric smoothing filters (such as Savitzky–Golay filters) is examined from the perspective of calibration performance, in contrast with past studies based on univariate signal-to-noise improvement. It is shown mathematically that in the limit of a perfect calibration model (i.e. all the errors derive from the measurement uncertainty in the unknown sample), no gains in multivariate calibration performance can be made by the application of symmetric smoothing filters. The proof is corroborated by simulated multivariate calibration procedures, namely principal component regression (PCR). Real experimental data are also used, yielding similarly supportive evidence in favor of the theoretical result. On occasion, marginal performance enhancements (less than a factor of two) are observed in both the simulated and real data. The conditions under which these enhancements are likely to occur are discussed. The recently introduced multivariate calibration technique of maximum likelihood PCR (MLPCR) is also applied using the measurement error covariance information determined from the applied filter matrix. MLPCR is shown to be invariant in calibration performance, even under extreme filtering conditions. Copyright © 1999 John Wiley & Sons, Ltd.

The behavior in atmospheric pressure chemical ionization of selected model polycyclic aromatic compounds, pyrene, dibenzothiophene, carbazole, and fluorenone, was studied in the solvents acetonitrile, methanol, and toluene. Relative ionization efficiency and sensitivity were highest in toluene and lowest in methanol, a mixture of molecular ions and protonated molecules was observed in most instances, and interferences between analytes were detected at higher concentrations. Such interferences were assumed to be caused by a competition among analyte molecules for a limited number of reagent ions in the plasma. The presence of both molecular ions and protonated analyte molecules can be attributed to charge-transfer from solvent radical cations and proton transfer from protonated solvent molecules, respectively. The order of ionization efficiency could be explained by incorporating the effect of solvation in the ionization reactions. Thermodynamic data, both experimental and calculated theoretically, are presented to support the proposed ionization mechanisms. The analytical implications of the results are that using acetonitrile (compared with methanol) as solvent will provide better sensitivity with fewer interferences (at low concentrations), except for analytes having high gas-phase basicities.

Iridium and 26 other elements were determined in shale from the Cretaceous-Tertiary boundary at the locus classicus (for iridium anomalies) at Woodside Creek, New Zealand. Iridium, gold, copper, cobalt, chromium, nickel, arsenic, molybdenum, and iron were enriched in the basal 2 millimeters of the 8-millimeter shale parting as compared with the rest of the stratigraphic column. No other shale partings in the column had anomalous concentrations of any element when the data were expressed on a carbonate-free basis. The boundary material showed striking compositional similarities with the Stevns Klint Danish boundary shale. Elemental concentrations were in general much higher in the New Zealand material than in nonboundary shales from elsewhere in the world. The high concentration of iridium (153 nanograms per gram) in the basal layer of the boundary, together with the enrichment of other siderophile elements supports the idea of an extraterrestrial source for much of the material. The iridium/gold ratio of 2.1 is also in accordance with such a source. The iridium content of the basal layer is higher than for any other marine boundary shale obtained on land. The integrated iridium value is 187 nanograms per square centimeter of boundary surface.

Binding of diquat and paraquat to humic acid, at low concentrations of adsorbates and adsorbents, is described under various conditions. Ionic strength and variations in size and charge indicated that binding interaction was mainly electrostatic in nature. Scatchard plots indicated that two binding sites were involved. The stability constants in all cases were of the order of 105 to 104, and the number of binding sites per 100 equivalent weights was in the range of 3 to 23. The nature of the binding sites did not correlate well with the known functional groups on humic acid. Variation in pH suggested that hydrogen ions competed strongly with the herbicides for the binding sites on humic acid. Temperature was shown to exert a small influence on the binding of diquat and paraquat.

Small-particle silica gels have been used as an adsorbent for high-speed liquid chromatography in an investigation of the application of fluorigenic labelling for the analysis of aromatic hydroxy compounds. The test compounds were mono- and dihydroxybiphenyls and the fluorigenic agent was dansyl chloride. Fluorescence and UV detection are compared. Calibration curves are linear and the relative standard deviation for ten concentrations (1 – 250 ng) is 1.0 ± 0.5% for peak height and 1% or less for peak area. Spiked urine samples were investigated to test this method.

The application of maximum likelihood multivariate calibration methods to the fluorescence emission spectra of mixtures of acenaphthylene, naphthalene, and phenanthrene in acetonitrile is described. Maximum likelihood principal components regression (MLPCR) takes into account the measurement error structure in the spectral data in constructing the calibration model. Measurement errors for the fluorescence spectra are shown to exhibit both a heteroscedastic and correlated noise structure. MLPCR is compared with principal components regression (PCR) and partial least-squares regression (PLS). The application of MLPCR reduces the prediction errors by about a factor of two over PCR and PLS when a pooled estimate of the measurement error covariance matrix is employed. However, when only the heteroscedascity is incorporated into MLPCR, no improvement in results is observed, indicating the importance of accounting for correlated measurement errors.

Abstract Algorithms for carrying out maximum likelihood parallel factor analysis (MLPARAFAC) for three‐way data are described. These algorithms are based on the principle of alternating least squares, but differ from conventional PARAFAC algorithms in that they incorporate measurement error information into the trilinear decomposition. This information is represented in the form of an error covariance matrix. Four algorithms are discussed for dealing with different error structures in the three‐way array. The simplest of these treats measurements with non‐uniform measurement noise which is uncorrelated. The most general algorithm can analyze data with any type of noise correlation structure. The other two algorithms are simplifications of the general algorithm which can be applied with greater efficiency to cases where the noise is correlated only along one mode of the three‐way array. Simulation studies carried out under a variety of measurement error conditions were used for statistical validation of the maximum likelihood properties of the algorithms. The MLPARAFAC methods are also shown to produce more accurate results than PARAFAC under a variety of conditions. Copyright © 2003 John Wiley & Sons, Ltd.

Abstract The quantitative in situ determination of pi-complexed pesticides by reflectance spectroscopy is discussed and quantitative results and stability studies obtained on cellulose and silica-gel thin-layer plates are presented. Detection limits are in the microgram region, with the linear working range for the Mobam-CNTNF complex chosen as an example being 1–10 meg on cellulose and 3–10 meg on silica gel. The complexed pesticide may be recovered following quantitative determination for mass spectral confirmation. The method shows particular utility in studying the degradation of pesticides.

Research Article| September 01, 1986 Stratigraphic occurrences of iridium anomalies at four Cretaceous/Tertiary boundary sites in New Zealand Robert R. Brooks; Robert R. Brooks 1Department of Chemistry and Biochemistry, Massey University, Palmerston North, New Zealand Search for other works by this author on: GSW Google Scholar C. Percy Strong; C. Percy Strong 2New Zealand Geological Survey, P.O. Box 30368, Lower Hutt, New Zealand Search for other works by this author on: GSW Google Scholar Julian Lee; Julian Lee 3Applied Biochemistry Division, Department of Scientific and Industrial Research, Private Bag, Palmerston North, New Zealand Search for other works by this author on: GSW Google Scholar Charles J. Orth; Charles J. Orth 4Los Alamos National Laboratory, Los Alamos, New Mexico 87545 Search for other works by this author on: GSW Google Scholar James S. Gilmore; James S. Gilmore 4Los Alamos National Laboratory, Los Alamos, New Mexico 87545 Search for other works by this author on: GSW Google Scholar Douglas E. Ryan; Douglas E. Ryan 5Trace Analysis Research Centre, Department of Chemistry, Dalhousie University, Halifax, Nova Scotia B3H 4J1, Canada Search for other works by this author on: GSW Google Scholar Jiri Holzbecher Jiri Holzbecher 5Trace Analysis Research Centre, Department of Chemistry, Dalhousie University, Halifax, Nova Scotia B3H 4J1, Canada Search for other works by this author on: GSW Google Scholar Author and Article Information Robert R. Brooks 1Department of Chemistry and Biochemistry, Massey University, Palmerston North, New Zealand C. Percy Strong 2New Zealand Geological Survey, P.O. Box 30368, Lower Hutt, New Zealand Julian Lee 3Applied Biochemistry Division, Department of Scientific and Industrial Research, Private Bag, Palmerston North, New Zealand Charles J. Orth 4Los Alamos National Laboratory, Los Alamos, New Mexico 87545 James S. Gilmore 4Los Alamos National Laboratory, Los Alamos, New Mexico 87545 Douglas E. Ryan 5Trace Analysis Research Centre, Department of Chemistry, Dalhousie University, Halifax, Nova Scotia B3H 4J1, Canada Jiri Holzbecher 5Trace Analysis Research Centre, Department of Chemistry, Dalhousie University, Halifax, Nova Scotia B3H 4J1, Canada Publisher: Geological Society of America First Online: 01 Jun 2017 Online ISSN: 1943-2682 Print ISSN: 0091-7613 Geological Society of America Geology (1986) 14 (9): 727–729. https://doi.org/10.1130/0091-7613(1986)14<727:SOOIAA>2.0.CO;2 Article history First Online: 01 Jun 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Robert R. Brooks, C. Percy Strong, Julian Lee, Charles J. Orth, James S. Gilmore, Douglas E. Ryan, Jiri Holzbecher; Stratigraphic occurrences of iridium anomalies at four Cretaceous/Tertiary boundary sites in New Zealand. Geology 1986;; 14 (9): 727–729. doi: https://doi.org/10.1130/0091-7613(1986)14<727:SOOIAA>2.0.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGeology Search Advanced Search Abstract Three new iridium anomaly sites have been discovered in Cretaceous/Tertiary boundary sequences in New Zealand. These are at Needles Point, Chancet Rocks, and Waipara, where integrated iridium deposition values were 165, 211, and 7 ng/cm2, respectively. In contrast to the previously reported Woodside Creek stratigraphic sequence that had an iridium anomaly of 187 ng/cm2, a ferruginous boundary clay is absent in the three new sites, though the base of the Tertiary is marked by limonite staining. The relatively weak anomaly at the Waipara section is probably due to extensive bioturbation coupled with a high sedimentation rate at the time of deposition. The discovery of these additional boundary rock sequences in New Zealand negates suggestions that the Woodside Creek iridium anomaly was a fortuitous occurrence caused by unusual weathering conditions. The integrated iridium deposition values at these three new sites of somewhat different geology support the previously reported high iridium level for Woodside Creek, which until now was the only iridium anomaly on land in the Southern Hemisphere. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Abstract Vanadium concentrations were determined by neutron activation analysis in samples of epiphytic lichens and tree foliage collected at sites along 10 transects in the vicinity of three oil-fired power plants in eastern Canada. The vanadium concentrations in plants decreased exponentially with increasing distance from the power plants. Substantially larger concentrations of vanadium occurred in lichen tissues than in tree foliage. Lichens clearly are more suitable for bio-monitoring environmental contamination with vanadium near oil-fired power plants.

Abstract Residues of polychlorinated biphenyls (PCBs) and organochlorine pesticides were determined in several species of commercial fish from the Great Lakes and compared to the total organic chlorine determined by neutron activation analysis. The mean organochlorine contents ranged from 44 to 138 ppm (lipid basis) and were 5 to 72 times higher than the contents of PCBs and organochlorine pesticides. Marine fish also contained a large proportion of unidentified organic chlorine. The unknown material in the Great Lakes fish was found to chromatograph with the high molecular weight lipid fraction by gel permeation chromatography.

Research Article| October 01, 1985 Weathered spheroids in a Cretaceous/Tertiary boundary shale at Woodside Creek, New Zealand Robert R. Brooks; Robert R. Brooks 1Department of Chemistry, Biochemistry and Biophysics, Massey University, Palmerston North, New Zealand Search for other works by this author on: GSW Google Scholar Paul L. Hoek; Paul L. Hoek 1Department of Chemistry, Biochemistry and Biophysics, Massey University, Palmerston North, New Zealand Search for other works by this author on: GSW Google Scholar Roger D. Reeves; Roger D. Reeves 1Department of Chemistry, Biochemistry and Biophysics, Massey University, Palmerston North, New Zealand Search for other works by this author on: GSW Google Scholar R. Cleland Wallace; R. Cleland Wallace 2Department of Soil Science, Massey University, Palmerston North, New Zealand Search for other works by this author on: GSW Google Scholar James H. Johnston; James H. Johnston 3Department of Chemistry, Victoria University, Wellington, New Zealand Search for other works by this author on: GSW Google Scholar Douglas E. Ryan; Douglas E. Ryan 4Trace Analysis Research Centre, Dalhousie University, Halifax, Nova Scotia B3H 4JI, Canada Search for other works by this author on: GSW Google Scholar Jiri Holzbecher; Jiri Holzbecher 4Trace Analysis Research Centre, Dalhousie University, Halifax, Nova Scotia B3H 4JI, Canada Search for other works by this author on: GSW Google Scholar John D. Collen John D. Collen 5Department of Geology, Victoria University, Wellington, New Zealand Search for other works by this author on: GSW Google Scholar Author and Article Information Robert R. Brooks 1Department of Chemistry, Biochemistry and Biophysics, Massey University, Palmerston North, New Zealand Paul L. Hoek 1Department of Chemistry, Biochemistry and Biophysics, Massey University, Palmerston North, New Zealand Roger D. Reeves 1Department of Chemistry, Biochemistry and Biophysics, Massey University, Palmerston North, New Zealand R. Cleland Wallace 2Department of Soil Science, Massey University, Palmerston North, New Zealand James H. Johnston 3Department of Chemistry, Victoria University, Wellington, New Zealand Douglas E. Ryan 4Trace Analysis Research Centre, Dalhousie University, Halifax, Nova Scotia B3H 4JI, Canada Jiri Holzbecher 4Trace Analysis Research Centre, Dalhousie University, Halifax, Nova Scotia B3H 4JI, Canada John D. Collen 5Department of Geology, Victoria University, Wellington, New Zealand Publisher: Geological Society of America First Online: 01 Jun 2017 Online ISSN: 1943-2682 Print ISSN: 0091-7613 Geological Society of America Geology (1985) 13 (10): 738–740. https://doi.org/10.1130/0091-7613(1985)13<738:WSIACB>2.0.CO;2 Article history First Online: 01 Jun 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn Email Permissions Search Site Citation Robert R. Brooks, Paul L. Hoek, Roger D. Reeves, R. Cleland Wallace, James H. Johnston, Douglas E. Ryan, Jiri Holzbecher, John D. Collen; Weathered spheroids in a Cretaceous/Tertiary boundary shale at Woodside Creek, New Zealand. Geology 1985;; 13 (10): 738–740. doi: https://doi.org/10.1130/0091-7613(1985)13<738:WSIACB>2.0.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGeology Search Advanced Search Abstract Three types of spheroids are found in the iridium-rich shale layer at the Cretaceous/Tertiary boundary at Woodside Creek, South Island, New Zealand. Two of the types (A and B) consist mainly of microcrystalline goethite, whereas the third type (F) contains an appreciable quantity of hematite. There is a strong correlation between the iridium content of the spheroids and their matrices and the concentrations of other siderophiles such as chromium, cobalt, iron, and nickel. A similar pattern was observed for the chalcophiles arsenic, copper, and zinc. It is suggested that spheroids of types A and B are weathering products derived from diagenetic pyrite clumps and that type F, which contains hematite, represents a further stage in the weathering process and was derived from goethite. The original pyritic material could have readily scavenged arsenic and other siderophiles from the sea-water column under organic-rich reducing conditions at the end of the Cretaceous, and the siderophiles including iridium could have been incorporated into the original meteoritic material. It was concluded, therefore, that types A, B, and F spheroids are weathering products and do not represent original meteoritic material. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

Multivariate data analysis tools have become an integral part of modern analytical chemistry, and principal component analysis (PCA) is perhaps foremost among these. PCA is central in approaching many problems in data exploration, classification, calibration, modelling, and curve resolution. However, PCA is only one form of a broader group of factor analysis (FA) methods that are rarely employed by chemists. The dominance of PCA in chemistry is primarily a consequence of history and convenience, but this has obscured the potential advantages of other FA tools that are widely used in other fields. The purpose of this article, which is intended for those who are already familiar with the mathematical foundations and applications of PCA, is to develop a framework to relate PCA to other commonly used FA methods from the perspective of chemical applications. Specifically, PCA is compared to maximum likelihood factor analysis (MLFA), principal axis factorization (PAF) and maximum likelihood PCA (MLPCA). Similarities and differences are highlighted with regard to the assumptions and constraints of the models, algorithms employed, and calculation of scores and loadings. Practical aspects such as data dimensionality, preprocessing, rank estimation, improper solutions (Heywood cases), and software implementation are considered. The performance of the four methods is compared using both simulated and experimental data sets. While PCA provides the most reliable estimates when measurement error variance is uniform (homoscedastic noise) and MLPCA works best when the error covariance matrix is explicitly known, MLFA and PAF have the distinct advantage of providing information about measurement uncertainty and adapting to situations of unknown heteroscedastic errors, eliminating the need for scaling. Moreover, MLFA in particular is shown to be tolerant to deviations from model linearity. These results make a strong case for increased application of other FA methods in chemistry.