Robert I. Gelb

Acid dissociation of cyclohexaamylose and cycloheptaamylose

Abstract Acid dissociation constants of aqueous cyclohexaamylose (6-Cy) and cycloheptaamylose (7-Cy) have been determined at 10–47 and 25–55°C, respectively, by pH potentiometry. Standard enthalpies and entropies of dissociation derived from the temperature dependences of these pKas are ΔH0 = 8.4 ± 0.3 kcal mol−1, Δ S 0 = −28. ± 1 cal mol −1 0 K −1 for 6-Cy and ΔH0 = 10.0 ± 0.1 kcal mol−1, Δ S 0 = −22.4 ±0.3 cal mol −1 0 K −1 for 7-Cy. Intrinsic 13C nmr resonance displacements of anionic 6- and 7-Cy were measured at 30°C in 5% D2O ( v v ). These results indicate that the dissociation of 6- and 7-Cy involves both C2 and C3 20-hydroxyl groups. The thermodynamic and nmr parameters are discussed in terms of interglucosyl hydrogen bonding.

Acid dissociation of cyclooctaamylose

Abstract Acid dissociation constants of aqueous cyclooctaamylose (8-Cy) have been determined at 15–45°C by pH potentiometry. Standard enthalpies and entropies of dissociation are derived from the temperature dependences of these p K a s. These results are compared to corresponding measurements of aqueous cyclohexaamylose and cycloheptaamylose, and the observed trends are interpreted in terms of complexation of cycloamylose with hydroxide ion. 13 C-nmr spectral measurements are reported for 8-Cy in 99.8% D 2 O solution, and assignments of the observed lines are made with the help of deuterium-induced differential isotopic shift experiments.

Complexation of carboxylic acids and anions by alpha and beta cyclodextrins

A pH potentiometric method is used to measure complex formation constants of aqueous alpha- and/or beta-cyclodextrin with several carboxylic acids and carboxylate anions: butyric acid/butyrate; valeric acid/valerate; hexanoic acid/hexanoate; octanoic acid/octanoate; decanoic acid/decanoate; cyclohexanecarboxylic acid/cyclohexanecarboxylate and benzoic acid/benzoate. Standard enthalpies and entropies of complex formation are calculated from the temperature dependencies of the equilibrium constants. These thermodynamic parameters of the alpha-cyclodextrin complexes largely conform to a correlation based on complexes with other substrate species previously reported. Both standard enthalpies and entropies of formation of beta-cyclodextrin complexes are found to be more positive than the corresponding complexes of alpha-cyclodextrin with the same substrates. These observations lead to insights into the bonding mechanism of cyclodextrin complexation.

Complexation of adamantane-ammonium substrates by beta-cyclodextrin and itsO-methylated derivatives

A spectrophotometric method is used to determine formation constants of complexes ofβ-cyclodextrin, the 2,6-di-O-methylated and 2,3,6-tri-O-methylated derivatives ofβ-cyclodextrin as hosts with adamantan-1-ylammonium, adamantan-2-ylammonium and adamantan-1-ylmethylammonium as substrate species. The spectrophotometric method uses methyl orange anion and acid forms as indicator species. Complexes of the cyclodextrins with these species are determined as well as with the adamantane derivatives. Standard enthalpies and entropies of formation of all complexes are calculated from the temperature variation of the equilibrium constants.β-Cyclodextrin and its 2,6-O-methyl derivative have comparable complex strengths with adamantaneammonium substrates and these strengths are about two orders of magnitude stronger than the corresponding complexes of the permethylated derivative. Thermodynamic parameters are interpreted in terms of differing intramolecular properties of the cyclodextrin complexes.

The complexation chemistry of cycloamyloses: equilibrium constants by novel spectrophotometric methods.

Abstract Formation constants for binary complexes of cyclohexaamylose (Cy) and p-nitrophenol/p-nitrophenolate ( PNP PNP − ) are determined by means of a novel acid-base spectrophotometric analysis. Thermodynamic parameters ΔH0 and ΔS0 are derived from the temperature dependences of these constants in the range 20–40°C. The Cy/PNP/PNP− system is then employed as a spectrophotometric indicator to estimate Cy complex formation constants with acid-base inactive substrates potassium perchlorate and sodium benzoate at 25°C and pH 6.8. The advantages and limitations of these methods in comparison with spectrophotometric analyses relying on the Hildebrand-Benesi equation are discussed.

Biases in summary statistics of slopes and intercepts in linear regression with errors in both variables

Monte Carlo simulations are employed to investigate the bias in linear regression parameters for cases in which both variables are subject to normally distributed errors. Both homoscedastic and heteroscedastic errors are treated. The results show that, in general, the arithmetic mean, geometric mean, and angle mean (tangent of the mean of the arctangents) of the slopes are biased and non-normally distributed. The arithmetic and geometric means of the intercepts are generally biased and non-normally distributed as well. However, for all the cases considered, the medians of the slopes and of the intercepts are found to be unbiased. In view of the non-normal distributions of the slopes and intercepts, a nonparametric method is used to determine confidence intervals for the slopes and intercepts.

Complexation reactions of β-cyclodextrin, per-(2,3,6-O-methyl) cycloheptaamylose and γ-cyclodextrin with phenolphthalein, adamantane carboxylate and adamantane acetate

Abstract A spectrophotometric method is employed to estimate complexation constants of phenolphthalein and its mono- and divalent anions with β-cyclodextrin. Subsequent experiments employ phenolphthalein as an indicator species to determine temperature dependent complexation constants of the adamantane carboxylate and adamantane acetate anions with β-cyclodextrin, per-(2,3,6-O-methyl)cycloheptaamylose and γ-cyclodextrin. Analysis of the data confirms that the stoichiometries of all the complexes are 1:1 and provides values of the conditional ΔH and ΔS for the formation of complexes of phenolphthalein with the cyclodextrins. In addition, values of the thermodynamic ΔH° and ΔS° for the complexes of the adamantane derivatives with the cyclodextrins are obtained. The results indicate that no single interaction mechanism can account for all of the various reactions. Thus, the cyclodextrins cannot be regarded as passive hosts in these reactions. Moreover, the different cyclodextrins interact differently with ea...

Complexation of aliphatic dicarboxylic acids and anions by alpha-cyclodextrin

Inclusion complexes are formed in aqueous solution between α-cyclodextrin and several straight-chain alkanedioic acids (ethanedioic, propanedioic, butanedioic, pentanedioic, hexanedioic, heptanedioic and octanedioic acids), several corresponding anions, several straight-chain alkenedioic acids (cis-butanedioic,trans-butanedioic andt,t-2,4-hexadienedioic acids) and several corresponding anions. Formation constants for these complexes were determined by measuring the effect of complexation on the pH of cyclohexaamylose/acid/base buffer equilibria. Enthalpies and entropies of complexation were calculated from the temperature dependences of the formation constants. The observed trends in the thermodynamic parameters lead to hypotheses about the structures of the complexes.

Application of nonparametric statistics to the estimation of the accuracy of Monte Carlo confidence intervals in regression analysis

Confidence intervals and their uncertainties for nonlinear regression parameters are obtained using nonparametric statistical methods. The confidence intervals are calculated by means of a Monte Carlo procedure. Their uncertainties depend on the confidence level desired and on the number of Monte Carlo simulations of the data set. They are obtained by calculating the uncertainties in the boundaries of the confidence intervals using a generalization of the nonparametric method used to calculate confidence intervals for medians. The method described here provides reliable confidence intervals at relatively low computational expense. It seems especially suited to the statistical analysis of nonlinear regression problems that are difficult to deal with using conventional methods.

Nuclear magnetic resonance spectroscopic method for the estimation of competitive equilibrium constants

Abstract A nuclear magnetic resonance method is described which yields precise estimates of competitive equilibrium constants for systems in which two or more complexing agents compete for common species. Chemical-shift data under rapid exchange conditions are required, but neither analytical not equilibrium concentrations are needed. The method is demonstrated by estimating equilibria of proton exchange between aniline and pyridinium ion, proton exchange between triethylamine and diisopropylammonium ion, and cyclohexaamylose exchange between m- and p-hydroxybenzoic acids. The precisions of the equilibrium constants are similar to or better than those obtained from classical methods and are relatively free from interferences.