Kinetic Isotope Effect For Reaction Research Articles

Dependence between the photochemical age of light aromatic hydrocarbons and the carbon isotope ratios of atmospheric nitrophenols

Abstract. Concepts were developed to establish relationships between the stable carbon isotope ratios of nitrophenols in the atmosphere and the photochemical processing of their precursors, light aromatic volatile organic compounds. These concepts were based on the assumption that nitrophenols are formed dominantly from the photo-oxidation of aromatic volatile organic compounds (VOCs). A mass balance model as well as various scenarios based on the proposed mechanism of nitrophenol formation were formulated and applied to derive the time-integrated exposure of the precursors to processing by OH radicals (∫[OH]dt) from ambient observations made between 2009 and 2012 in Toronto, Canada. The mechanistic model included the possibility of isotopic fractionation during intermediate steps, rather than only during the initial reaction step. This model takes kinetic isotope effects for the reaction of the precursor VOC with the hydroxyl radical and their respective rate constants into account, as well as carbon isotope ratio source signatures. While many of these values are known, there are some, such as the kinetic isotope effects of reactions of first- and second-generation products, which are unknown. These values were predicted in this study based on basic principles and published laboratory measurements of kinetic carbon isotope effects and were applied to the mechanistic model. Due to the uncertainty of the estimates based on general principles, three scenarios were used with different values for isotope effects that were not known from laboratory studies. Comparison of the dependence between nitrophenol carbon isotope ratios and ∫[OH]dt with published results of laboratory studies and ambient observations was used to narrow the range of plausible scenarios for the mechanistic model. The results also suggests that mass-balance-based models do not adequately describe the dependence between nitrophenol carbon isotope ratios and ∫[OH]dt.

Stable carbon isotope ratios of ambient aromatic volatile organic compounds

Abstract. Measurements of mixing ratios and stable carbon isotope ratios of aromatic volatile organic compounds (VOC) in the atmosphere were made in Toronto (Canada) in 2009 and 2010. Consistent with the kinetic isotope effect for reactions of aromatic VOC with the OH radical the observed stable carbon isotope ratios are on average significantly heavier than the isotope ratios of their emissions. The change of carbon isotope ratio between emission and observation is used to determine the extent of photochemical processing (photochemical age, ∫ [OH]dt) of the different VOC. It is found that ∫ [OH]dt of different VOC depends strongly on the VOC reactivity. This demonstrates that for this set of observations the assumption of a uniform ∫ [OH]dt for VOC with different reactivity is not justified and that the observed values for ∫ [OH]dt are the result of mixing of VOC from air masses with different values for ∫ [OH]dt. Based on comparison between carbon isotope ratios and VOC concentration ratios it is also found that the varying influence of sources with different VOC emission ratios has a larger impact on VOC concentration ratios than photochemical processing. It is concluded that for this data set the use of VOC concentration ratios to determine ∫ [OH]dt would result in values for ∫ [OH]dt inconsistent with carbon isotope ratios and that the concept of a uniform ∫ [OH]dt for an air mass has to be replaced by the concept of individual values of an average ∫ [OH]dt for VOC with different reactivity.

Dynamics of the active site architecture in plant-type ferredoxin-NADP+ reductases catalytic complexes

Kinetic isotope effects in reactions involving hydride transfer and their temperature dependence are powerful tools to explore dynamics of enzyme catalytic sites. In plant-type ferredoxin-NADP+ reductases the FAD cofactor exchanges a hydride with the NADP(H) coenzyme. Rates for these processes are considerably faster for the plastidic members (FNR) of the family than for those belonging to the bacterial class (FPR). Hydride transfer (HT) and deuteride transfer (DT) rates for the NADP+ coenzyme reduction of four plant-type FNRs (two representatives of the plastidic type FNRs and the other two from the bacterial class), and their temperature dependences are here examined applying a full tunnelling model with coupled environmental fluctuations. Parameters for the two plastidic FNRs confirm a tunnelling reaction with active dynamics contributions, but isotope effects on Arrhenius factors indicate a larger contribution for donor–acceptor distance (DAD) dynamics in the Pisum sativum FNR reaction than in the Anabaena FNR reaction. On the other hand, parameters for bacterial FPRs are consistent with passive environmental reorganisation movements dominating the HT coordinate and no contribution of DAD sampling or gating fluctuations. This indicates that active sites of FPRs are more organised and rigid than those of FNRs. These differences must be due to adaptation of the active sites and catalytic mechanisms to fulfil their particular metabolic roles, establishing a compromise between protein flexibility and functional optimisation. Analysis of site-directed mutants in plastidic enzymes additionally indicates the requirement of a minimal optimal architecture in the catalytic complex to provide a favourable gating contribution.

Kinetic Isotope Effects from QM/MM Subset Hessians: "Cut-Off" Analysis for SN2 Methyl Transfer in Solution.

Isotopic partition-function ratios and kinetic isotope effects for reaction of S-adenosylmethionine with catecholate in water are evaluated using a subset of 324 atoms within its surrounding aqueous environment at the AM1/TIP3P level. Two alternative methods for treating motion in the six librational degrees of freedom of the subset atoms relative to their environment are compared. A series of successively smaller subset Hessians are generated by cumulative deletion of rows and columns from the initial 972 × 972 Hessian. We find that it is better to treat these librations as vibrations than as translations and rotations and that there is no need to invoke the Teller-Redlich product rule. The validity of "cut-off" procedures for computation of isotope effects with truncated atomic subsets is assessed: to ensure errors in ln(KIE) < 1% (or 2% for the quantum-corrected KIE) for all isotopic substitutions considered, it is necessary to use a less-restrictive procedure than is suggested by the familiar two-bond cutoff rule.

Nuclear Quantum Tunneling in the Light-activated Enzyme Protochlorophyllide Oxidoreductase

In chlorophyll biosynthesis, the light-activated enzyme protochlorophyllide oxidoreductase catalyzes trans addition of hydrogen across the C-17-C-18 double bond of the chlorophyll precursor protochlorophyllide (Pchlide). This unique light-driven reaction plays a key role in the assembly of the photosynthetic apparatus, but despite its biological importance, the mechanism of light-activated catalysis is unknown. In this study, we show that Pchlide reduction occurs by dynamically coupled nuclear quantum tunneling of a hydride anion followed by a proton on the microsecond time scale in the Pchlide excited and ground states, respectively. We demonstrate the need for fast dynamic searches to form degenerate "tunneling-ready" configurations within the lifetime of the Pchlide excited state from which hydride transfer occurs. Moreover, we have found a breakpoint at -27 degrees C in the temperature dependence of the hydride transfer rate, which suggests that motions/vibrations that are important for promoting light-activated hydride tunneling are quenched below -27 degrees C. We observed no such breakpoint for the proton-tunneling reaction, indicating a reliance on different promoting modes for this reaction in the enzyme-substrate complex. Our studies indicate that the overall photoreduction of Pchlide is endothermic and that rapid dynamic searches are required to form distinct tunneling-ready configurations within the lifetime of the photoexcited state. Consequently, we have established the first important link between photochemical and nuclear quantum tunneling reactions, linked to protein dynamics, in a biologically significant system.

Computational Studies on the Mechanisms and Dynamics of OH Reactions with CHF2CHFOCF3 and CHF2CH2OCF3.

The dual-level direct dynamics method has been employed to investigate the multichannel hydrogen abstraction reactions of CHF2CHFOCF3 + OH (R1) and CHF2CH2OCF3 + OH (R2) theoretically. The optimized geometries and frequencies of the stationary points and the minimum energy path are calculated at the B3LYP/6-311G(d,p) level, and the energetic information is further refined by the MC-QCISD method. There are two hydrogen abstraction channels for reaction R1 and three hydrogen abstraction channels for reaction R2. And four products, CF2CHFOCF3, CHF2CFOCF3, CF2CH2OCF3, and CHF2CHOCF3, are produced during these two reactions. The enthalpies of formation for the species involved in the two reactions (CHF2CHFOCF3, CF2CHFOCF3, CHF2CFOCF3, CHF2CH2OCF3, CF2CH2OCF3, and CHF2CHOCF3) are calculated via isodesmic reaction. Furthermore, the reaction mechanisms of subsequent reactions of product radicals (CF2CHFOCF3, CHF2CFOCF3, CF2CH2OCF3, and CHF2CHOCF3) with the OH radical are studied at the same level. The rate constants of reactions R1 and R2 are evaluated by means of canonical variational transition-state theory including the small-curvature tunneling correction over a wide range of temperatures, from 250 to 1200 K. Our results show that the tunneling correction plays an important role in the rate constant calculation in the low-temperature range. Agreement between the calculated and experimental data available at 298 K is good. It is found that the fluorine substitution decreases the reactivity of the C-H bond, and as a result, reaction R2 may proceed much easier than reaction R1. The Arrhenius expressions over a wide temperature range are obtained, and the kinetic isotope effects for reactions CHF2CHFOCF3/CDF2CDFOCF3 + OH and CHF2CH2OCF3/CDF2CD2OCF3 + OH are estimated so as to provide theoretical estimation for future laboratory investigation.

QM/MM simulations for methyl transfer in solution and catalysed by COMT: ensemble-averaging of kinetic isotope effects

Sampling of structures from QM/MM molecular dynamics reveals distinct families of reactant-state conformers and yields kinetic isotope effects for reactions in enzyme active sites and in solution, averaged over thermal fluctuations of the environment, that allows meaningful comparison of computed with experimental values.

Laboratory measurements of the 12C/13C kinetic isotope effects in the gas-phase reactions of unsaturated hydrocarbons with Cl atoms at 298 ± 3 K

The carbon kinetic isotope effects (KIEs) in the reactions of several unsaturated hydrocarbons with chlorine atoms were measured at room temperature and ambient pressure using gas chromatography combustion isotope ratio mass spectrometry (GCC-IRMS). All measured KIEs, defined as the ratio of the rate constants for the unlabeled and labeled hydrocarbon reaction k 12/k 13, are greater than unity or normal KIEs. The KIEs, reported in per mil according to Cl ɛ = (k 12/k 13−1) × 1000‰ with the number of experimental determinations in parenthesis, are as follows: ethene, 5.65 ± 0.34 (1); propene, 5.56 ± 0.18 (2); 1-butene, 5.93 ± 1.16 (1); 1-pentene, 4.86 ± 0.63 (1); cyclopentene, 3.75 ± 0.14 (1); toluene, 2.89 ± 0.31 (2); ethylbenzene, 2.17 ± 0.17 (2); o-xylene, 1.85 ± 0.54 (2). To our knowledge, these are the first reported KIE measurements for reactions of unsaturated NMHC with Cl atoms. Relative rate constants were determined concurrently to the KIE measurements. For the reactions of cyclopentene and ethylbenzene with Cl atoms, no rate constant has been reported in refereed literature. Our measured rate constants are: cyclopentene (7.32 ± 0.88) relative to propene (2.68 ± 0.32); ethylbenzene (1.15 ± 0.04) relative to o-xylene (1.35 ± 0.21), all × 10−10 cm3 molecule−1 s−1. The KIEs in reactions of aromatic hydrocarbons with Cl atoms are similar to previously reported KIEs in Cl-reactions of alkanes with the same numbers of carbon atoms. Unlike the KIEs for previously studied gas-phase hydrocarbon reactions, the KIEs for alkene–Cl reactions do not exhibit a simple inverse dependence on carbon number. This can be explained by competing contributions of normal and inverse isotope effects of individual steps in the reaction mechanism. Implications for the symmetries of the transition state structures in these reactions and the potential relevance of Cl-atom reactions on stable carbon isotope ratios of atmospheric NMHC are discussed.

Kinetic isotope effects in the gas phase reactions of OH and Cl with CH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;Cl, CD&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;Cl, and &amp;lt;sup&amp;gt;13&amp;lt;/sup&amp;gt;CH&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt;Cl

Abstract. The kinetic isotope effects in the reactions of CH3Cl, 13CH3Cl and CD3Cl with OH radicals and Cl atoms were studied in relative rate experiments at 298±2 K and 1013±10 mbar. The reactions were carried out in a smog chamber using long path FTIR detection and the spectroscopic data analyzed employing a non-linear least squares spectral fitting method using measured high-resolution infrared spectra as well as absorption cross sections from the HITRAN database. The reaction rates of 13CH3Cl and CD3Cl with OH and Cl were determined relative to CH3Cl as: kOH+CH3ClkOH+CH3Cl/kOH+13CH3Cl}kOH+13CH3Cl=1.059±0.008, kOH+CH3ClkOH+CH3Cl/kOH+CD3ClkOH+CD3Cl=3.9±0.4, kCl+CH3ClkCl+CH3Cl/kCl+13CH3ClkCl+13CH3Cl =1.070±0.010 and kCl+CH3ClkCl+CH3Cl/kCl+CD3ClkCl+CD3Cl=4.91±0.07. The uncertainties given are 2σ from the statistical analyses and do not include possible systematic errors. The unexpectedly large 13C kinetic isotope effect in the OH reaction of CH3Cl has important implications for the global emission inventory of CH3Cl.

Theoretical study of rate constants and kinetic isotope effects for reactions in the ClH 2 system using variational transition state theory

Variational transition state theory calculations have been performed on the BW2 potential energy surface (PES) for abstraction and exchange reactions in the ClH 2 system, and thermal rate constants and kinetic isotope effects are reported. Excellent agreement with two previous QM calculations on BW2 validates the present computational scheme. For abstraction reactions, general good agreement with various experimental measurements is obtained. For exchange reactions like D + ClH → DCl + H, the results on BW2 are in better agreement with experiments than those on G3, as may originate from different topologies of these two PESs in the exchange barrier region.

Carbon and hydrogen isotopic compositions of stratospheric methane: 1. High‐precision observations from the NASA ER‐2 aircraft

Measurements of δ13C and δD of atmospheric CH4 from whole air samples collected in the upper troposphere and lower stratosphere aboard the NASA ER‐2 aircraft during the SOLVE (2000), POLARIS (1997), and STRAT (1996) campaigns are reported. Samples cover latitudes from 1°S to 89°N and altitudes from 11 to 21 km, providing CH4 mixing ratios that range from 1744 to 716 ppbv. Measurements of isotope ratios were made by continuous‐flow gas chromatography isotope ratio mass spectrometry which provides high‐precision analyses on 60 ml aliquots of air. These measurements comprise the first upper atmosphere isotopic CH4 data set to date using this technique and the most extensive with respect to latitude and season in any case. Values of δ13C‐CH4 on the V‐PDB scale range from −47.28‰ near the tropical tropopause to −34.05‰ in the high northern latitude stratosphere. Values of δD on the V‐SMOW scale range from −90.9‰ to +26.4‰. Correlations of isotope ratios with CH4 mixing ratios show enrichment in the heavy isotopes as CH4 mixing ratios decrease due to kinetic isotope effects associated with oxidation by reaction with OH, Cl, and O(1D). Empirical fractionation factors are found to be highly dependent on the range of CH4 mixing ratio considered, increasing with decreasing mixing ratio. Systematic nonlinearity in a Rayleigh fractionation model suggests a range of stratospheric fractionation factors, αCstrat = 1.0108 ± 0.0004 to 1.0204 ± 0.0004 (2σ) and αHstrat = 1.115 ± 0.008 to 1.198 ± 0.008 (2σ), from high to low CH4 mixing ratio, respectively. The variation in α over the range in mixing ratios reflect changes in partitioning between CH4 sink reactions in different regions of the stratosphere. In Part 1, these new high‐precision observations are discussed and compared with other stratospheric and tropospheric isotope measurements. In Part 2 [McCarthy et al., 2003] the observations are compared with 2‐D model results, and implications for the kinetic isotope effects for reactions with OH, Cl, and O(1D) are discussed.

Experimental and theoretical multiple kinetic isotope effects for an SN2 reaction. An attempt to determine transition-state structure and the ability of theoretical methods to predict experimental kinetic isotope effects.

The secondary alpha-deuterium, the secondary beta-deuterium, the chlorine leaving-group, the nucleophile secondary nitrogen, the nucleophile (12)C/(13)C carbon, and the (11)C/(14)C alpha-carbon kinetic isotope effects (KIEs) and activation parameters have been measured for the S(N)2 reaction between tetrabutylammonium cyanide and ethyl chloride in DMSO at 30 degrees C. Then, thirty-nine readily available different theoretical methods, both including and excluding solvent, were used to calculate the structure of the transition state, the activation energy, and the kinetic isotope effects for the reaction. A comparison of the experimental and theoretical results by using semiempirical, ab initio, and density functional theory methods has shown that the density functional methods are most successful in calculating the experimental isotope effects. With two exceptions, including solvent in the calculation does not improve the fit with the experimental KIEs. Finally, none of the transition states and force constants obtained from the theoretical methods was able to predict all six of the KIEs found by experiment. Moreover, none of the calculated transition structures, which are all early and loose, agree with the late (product-like) transition-state structure suggested by interpreting the experimental KIEs.

Kinetic and Thermodynamic Studies of Reaction of *Cr(CO)(3)C(5)Me(5), HCr(CO)(3)C(5)Me(5), and PhSCr(CO)(3)C(5)Me(5) with *NO. Reductive Elimination of Thermodynamically Unstable Molecules HNO and RSNO Driven by Formation of the Strong Cr-NO Bond.

Reaction of H-Cr(CO)(3)C(5)Me(5) with *NO at 1-2 atm pressure in toluene solution yields Cr(NO)(CO)(2)C(5)Me(5) as the sole metal-containing product in addition to N(2)O and HNO(2) as the principle nitrogen-containing products. N(2)O and HNO(2) are attributed to decomposition of the initial product HNO. Kinetic studies yield the rate law d[P]/dt = -k(2nd)( )(order)[HCr(CO)(3)C(5)Me(5)][*NO]; k(2nd)( )(order) = 0.14 M(-)(1) s(-)(1) at 10 degrees C, with DeltaH() = 11.7 +/- 1.5 kcal/mol and DeltaS() = -16.3 +/- 3.5 cal/(mol deg). The rate of reaction is not inhibited by CO. The kinetic isotope effect for reaction of D-Cr(CO)(3)C(5)Me(5) is k(H)/k(D) = 1.7. These observations are consistent with a first step involving direct H (D) atom transfer from the metal hydride to *NO, forming HNO. Also supporting this mechanism is the approximately 150-times slower reaction of H-Mo(CO)(3)C(5)Me(5) and failure to observe reaction for H-W(CO)(3)C(5)Me(5) in keeping with metal-hydrogen bond strengths Cr < Mo < W. Reaction of PhS-Cr(CO)(3)C(5)Me(5) with NO at 1-2 atm pressure in toluene solution also forms Cr(NO)(CO)(2)C(5)Me(5) as the sole metal-containing product. The initial product is the unstable nitrosothiol PhS-NO. Kinetic studies yield the rate law d[P]/dt = -k(1st)( )(order)[PhS-Cr(CO)(3)C(5)Me(5)]; k(1st)( )(order) = 3.1 +/- 0.3 x 10(-)(3) s(-)(1) at 10 degrees C, with DeltaH() = 21.6 +/- 1.2 kcal/mol, DeltaS() = + 3.9 +/- 1.5 cal/(mol deg). The rate of reaction is independent of both NO and CO pressure. The transition state in the first-order process is proposed to involve migration of bound thiolate to coordinated CO, forming Cr(CO)(2) (eta(2)-C(=O)SPh)C(5)Me(5). The enthalpy of reaction of *Cr(CO)(3)C(5)Me(5) and NO yielding Cr(NO)(CO)(2)C(5)Me(5) and CO has been measured by solution calorimetry: DeltaH degrees = -33.2 +/- 1.8 kcal/mol. The Cr-NO bond strength is estimated as approximately 70 kcal/mol and provides the net thermodynamic driving force for the proposed elimination of the unstable molecules HNO and PhSNO.

α-Deuterium kinetic isotope effects in reactions of methyllithium: is better aggregation the cause of lower reactivity?

The values k H/ k D for α-deuterium kinetic isotope effects for the reaction of methyllithium and methylmagnesium iodide with a series of substrates are consistently ca. 10–15% higher for the lithium reagent than for the Grignard reagent. This may indicate a pre-equilibrium between an aggregate and a reactive monomer, with a better fit of the trideuterio monomer in the aggregate. An attempt has been made to compare the equilibrium constants for the aggregation of deuterio and protio methyllithium by studying the metal-halogen equilibrium between methyllithium and methyl iodide.

Secondary beta-Deuterium Kinetic Isotope Effects in Reactions of Grignard Reagents.

Secondary beta-Deuterium Kinetic Isotope Effects in Reactions of Grignard Reagents.

Effect of steps and surface coverage on rates and kinetic isotope effects for reactions catalyzed by metallic surfaces: chemisorption of hydrogen on nickel

The authors present a new parametrization for the embedded-diatomics-in-molecules (EDIM) potential energy function that is significantly more accurate than the previous one for the interaction of two H atoms with a Ni surface or with a third H atom. Thus, it can be used to study lateral interactions of H{sub 2} with H, and it is also parametrized for a system of three H atoms on a Ni surface. In addition, the metal atom parameters are independent of which layer the metal atom is in so there is no ambiguity in studying reactions at steps or kinks. They apply canonical variational transition state theory with semiclassical transmission coefficients to investigate the dynamics of the dissociative chemisorption of gas-phase H{sub 2} molecules on both single-crystal-face and stepped Ni(100) surfaces. They also consider the effect of additional H atoms, and they compare results for clean and partially covered surfaces. They find that classical transition-state recrossing and quantal tunneling effects are very important in the dissociation of H{sub 2} on the clean Ni(100) surface.

Improved potential energy surfaces for the reaction O(3P)+H2→OH+H

We present global 3A′ and 3A″ potential energy surfaces for the reaction O(3P)+H2→OH+H and its isotopic analogs. The new surfaces are based in part on the surface of Lee et al. [J. Chem. Phys. 76, 3563 (1982)] for collinear O–H–H, which is modified to give accurate properties for reactants and products. The potentials for noncollinear O–H–H geometries are based on bending energies of Bowman et al. [J. Chem. Phys. 81, 1739 (1984)] as fit previously and called surface set M2 by two of the authors [B. C. Garrett and D. G. Truhlar, Int. J. Quantum Chem. 29, 1463 (1986)], and the potentials for H–O–H geometries are based on a new interpolation scheme. The new surfaces treat the approach of an O to either end of H2 equivalently. We used improved canonical variational transition state theory calculations with the least-action ground-state tunneling approximation (ICVT/LAG) to recalibrate the classical barrier height to 13.0 kcal/mol. The ICVT/LAG rate constants calculated using the new surfaces are in excellent agreement with experimental values over the temperature range 298–2400 K. Rate constants and kinetic isotope effects for reactions involving D2 and HD also are presented and analyzed. Here again, the theoretical results are in very good agreement with experiments.

Kinetic isotope effect for hydrogen atom transfer from substituted anilines and phenols to the triplet state of anthraquinone

1. The rates of triplet quenching of anthraquinone by substituted anilines and phenols and their OH- and NH2-deuterated analogs have been measured by pulse photolysis in toluene and acetonitrile solutions. 2. In the case of anilines the kinetics of hydrogen atom transfer are determined by charge transfer in the transition state or by the formation of charge transfer complexes as intermediates in these reactions. The kinetic isotope effect for these reactions is increased up to five as the anthraquinone triplet quenching rate constants are decreased as a function of reduced electron-donating ability of substituted anilines. 3. The kinetic isotope effect for hydrogen atom transfer reactions from substituted phenols to the triplet state of anthraquinone reaches a maximum of two and is determined not only by the degree of charge transfer in the transition state but also by the kinetics of formation of an intermediate hydrogen-bonded complex.

Transition State Theory in Isotope and Radiation Chemistry

A short survey of the history of the transition state theory (TST) including new developments is given. In isotope chemistry reaction-kinetic isotope effects can be calculated via TST using the concept of molecular partition functions. Several examples are given. In radiation chemistry TST is applied on particular to ionic reactions. The general procedure is exemplified by ion-molecule reactions.

ChemInform Abstract: TEMPERATURE DEPENDENCE OF BROMINE KINETIC ISOTOPE EFFECTS FOR REACTIONS OF N‐BUTYL AND TERT‐BUTYL BROMIDES

Chemischer InformationsdienstVolume 11, Issue 28 Preparative Organic Chemistry ChemInform Abstract: TEMPERATURE DEPENDENCE OF BROMINE KINETIC ISOTOPE EFFECTS FOR REACTIONS OF N-BUTYL AND TERT-BUTYL BROMIDES J. F. WILLEY, J. F. WILLEYSearch for more papers by this authorJ. W. TAYLOR, J. W. TAYLORSearch for more papers by this author J. F. WILLEY, J. F. WILLEYSearch for more papers by this authorJ. W. TAYLOR, J. W. TAYLORSearch for more papers by this author First published: July 15, 1980 https://doi.org/10.1002/chin.198028113AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume11, Issue28July 15, 1980 RelatedInformation