Aggregation Constants Research Articles

Penetration of dissolved amphiphiles into two-dimensional aggregating lipid monolayers

The review demonstrates the recent theoretical and experimental progress in the understanding of penetration systems at the air–water interface in shich a dissolved amphiphile (surfactant, protein) penetrates into a Langmuir monolayer. The critical review of the existing theoretical models which describe the thermodynamics of the penetration are critically reviewed. Although a rigorous thermodynamic analysis of penetration systems is unavailable due to their complexity, some model assumptions, e.g. the invariability of the activity coefficient of the insoluble component of the monolayer during the penetration of the soluble component result in reasonable solutions. New theoretical models describing the equilibrium behaviour of the insoluble monolayers which undergo the 2D aggregation in the monolayer, and the equations of state and adsorption isotherms which assume the existence of multiple states (conformations) of a protein molecule within the monolayer and the non-ideality of the adsorbed monolayers are now available. The theories which describe the penetration of a soluble surfactant into the main phases of Langmuir monolayers were presented first for the case of the mixture of the moleucles possessing equal partial molar surfaces (the mixture of homologues), with further extension of the models to include the interesting process of the protein penetration into the monolayer of 2D aggregating phospholipid. This extension was based on a concept which subdivides the protein molecules into independent fragments with areas equal to those of phospholipid molecule. Various mechanisms for the effect of the soluble surfactant on the aggregation of the insoluble component were considered in the theoretical models: (i) no effect on the aggregate formation process; (ii) formation of mixed aggregates; and (iii) the influence on the aggregating process via the change of aggregation constant, but without any formation of mixed aggregates. Accordingly depending on the mechanism, different forms of the equations of state of the monolayer and of the adsorption isotherms of soluble surfactant are predicted. Based on the shape of the experimental Π-A isotherms, interesting conclusions can be drawn on the real mechanism. First experimental evidence has been provided that the penetration of different proteins and surfactants into a DPPC monolayer in a fluid-like state induces a first order main phase transition of pure DPPC. The phase transition is indicated by a break point in the Π( t) penetration kinetics curves and the domain formation by BAM. Mixed aggregates of protein with phospholipid are not formed. These results agree satisfactorily with the predictions of the theoretical models. New information on phase transition and phase properties of Langmuir monolayers penetrated by soluble amphiphiles are obtained by coupling of the Π( t) penetration kinetics curves with BAM and GIXD measurements. The GIXD results on the penetration of β-lactoglobulin into DPPC monolayers have shown that protein penetration occurs without any specific interactions with the DPPC molecules and the condensed phase consists only of DPPC.

Determination of the aggregation constants of bile salts by capillary electrophoresis

Capillary electrophoresis has been investigated as a novel experimental method for determination of the aggregation constants of surfactants. The tendency of sodium cholate and sodium taurodeoxycholate to associate was studied in phosphate buffers of pH 8.0 and pH 7.0, respectively. Stepwise aggregation equilibria of bile salt monomers has been described in terms of massbalance equations. The Offord equation was used to model the electrophoretic mobility of the bile salt associates, and the experimental mobility values could be fitted to the model. Interestingly, only even-membered aggregates-dimers and tetramers-besides the monomers were proposed from the results of the curve-fitting for both bile salts. The aggregation constants calculated were (in molar units): cholate logK A2=1.37, logK A4=4.98 taurodeoxycholate logK A2=1.68, logK A4=6.46. From these values, more pronounced aggregation of taurodeoxycholate starting at lower concentrations has been deduced, supporting the back-to-back association model of bile salts.

Equilibrium binding model of bile salt-mediated chiral micellar electrokinetic capillary chromatography.

Optimum concentration of bile salts in chiral separations depends on both the aggregation properties of the surfactant and the stability of the analyte-micelle complexes. An equilibrium model is proposed in which these two effects are treated separately. First the aggregation constants should be determined under the experimental conditions of the chiral MEKC analysis. With these data, the equilibrium concentrations of bile salt aggregates can be calculated at any total surfactant concentration. Using the Offord equation to approximate the mobilities of the enantiomer-bile salt complexes, a model function has been derived to fit the experimental mobilities. The method yields the binding constants of the enantiomers to each aggregate present. Those species are assumed to be important in the chiral recognition process, which have significantly different stability constants for the enantiomers. The method is demonstrated by the chiral separation of R- and S-1,1'-binaphthyl-2,2'-diyl hydrogen phosphate with sodium taurodeoxycholate. Based on the calculated binding constants, tetrameric aggregates are assumed to be the discriminating species, while no significant difference in enantiomer binding to dimers was found.

Equations of State for Langmuir Monolayers with Two-Dimensional Phase Transitions

A generalized Volmer's equation is derived for a multicomponent Langmuir monolayer. This general equation is then used to derive the equations of state for the monolayer of a single amphiphile considering the two-dimensional (2D) main phase transition. A theory developed recently (J. Phys. Chem. 1996, 100, 15478) is extended to incorporate the important case that the area per one amphiphile molecule within the aggregate differs from that characteristic for the nonaggregated amphiphile. The general equation derived involves four parameters, two of which refer to the state of the gaseous monolayer whereas the other two parameters express the 2D aggregation constant and the difference between the area per one amphiphile molecule within the aggregate and the area per one nonaggregated molecule. The experimental Π−A isotherms for Langmuir monolayers of various amphiphiles, either measured by the authors or referred to elsewhere, agree well with the proposed model for physically reliable values of model parameters.

Determination of the distance of nearest approach of coagulated particles in haematite and latex dispersions

Previous investigations [H. Lichtenfeld, L. Knapschinsky, H. Sontag, V. Shilov, Colloids Surfaces A: Physicochem. Eng. Aspects 104 (1995) 113; H. Lichtenfeld, H. Sonntag, C. Dürr, Colloids Surfaces 54 (1991) 267] and the work presented here on the kinetics of the rapid coagulation process by means of our single-particle light scattering photometer led to the conclusion that the deaggregation constants for haematite and latex suspensions are finite values. From this finding, we can conclude that the approach of two particles resulting in aggregation does not lead to contact of the surfaces; it can be prevented by a structural barrier of the dispersion medium. A new way to determine this layer thickness is a quantitative determination of the decay of aggregates (measurement of the velocity constants of deaggregation) together with the determination of the aggregation constants at the aggregation proccess, which are connected to the second virial coefficient.

Characterization of interaction between cephalosporins and charged surfactants using capillary zone electrophoresis

Capillary electrophoresis offers a new way of characterizing the interaction between surfactants and drugs. This interaction was studied using capillary zone electrophoresis (CZE). It was observed that addition of tetraalkylammonium bromide to the electrolyte buffer at different concentrations of dodecyl trimethylammonium bromide (DTAB) led to a change of the migration time ( t m) and of the ionic mobility ( μ) of cephalosporins. For quantitative evaluation, a physicochemical model was developed to calculate the aggregation constants ( k) and the stoichiometric coefficients ( m) between DTAB and cephalosporins. The relative standard deviation of the effective mobilities and of the EOF were estimated.

Transport phenomena of sulfonated dyes into cellulose membrane: Effects of urea on parallel diffusion of mono azo dyes

Effects of urea on transport phenomena of sulfonated azo dyes with different aggregation constants into water-swollen cellulose membrane have been studied at 25–55 °C. The results were analyzed on the basis of a parallel transport theory of surface and pore diffusion. Addition of urea decreased equilibrium adsorption of the dyes onto cellulose and increased the surface and pore diffusivities for the parallel diffusion model of the dye with high aggregation constant. Temperature dependence of the effects was also discussed.

Constant Consumption as Interest on Capital

We consider the concepts of aggregate capital value arising in Solow's constant model. For a traditional concept, we establish as interest on wealth in the sense of the interest flow being the vector product of weighted current values of capital stocks and own interest rates. Consumption can be viewed as maximum sustainable net product. I. Introduction There is a presumption that net-investment-zero, a generalization of investing exhaustible resource rents, as in Hartwick (1977), must be associated with preserving capital intact; see Dixit, Hammond, Hoel (1980). In fact, Solow (1986) set this argument out in some detail. Maintaining capital seems like a reasonable prescription for sutainable development.' Elsewhere sustainable development has been tied to non-declining consumption, following Solow's (1974) constant model.2 There are at least two candidates for capital in maintaining capital intact that can be associated with Solow's (1974) constant model. The two were present in Solow (1986). I mention them below and analyze a new approach to linking constant to capital value as in consumption is interest on capital. Our approach is to make all inputs in current production, flows from explicit stocks. In this extended Solow (1974) model we observe (a) aggregate constant under zeronet-investment and (b) constant is interest on capital in the sense N

Nonmicellar Self-Association of Propantheline Bromide: Effect of the Column Length on the Chromatogram

The self-association behavior of propantheline bromide in a 154 mmol dm-3 sodium bromide solution has been investigated by frontal chromatography on two Sephadex columns and by the surface tension method. Analysis of centroid volume data by asymptotic theory yields the monomer concentration of propantheline bromide as a function of its total concentration. Further analysis of the concentration dependence of the monomer concentration by a multiple equilibrium model provides weight-average and number-average aggregation numbers. The aggregates of propantheline bromide are small and are formed in a stepwise manner without a cmc. Stepwise aggregation constants for propantheline bromide are estimated and are used to predict the aggregate size distribution. Derivative chromatograms support the above results based on the centroid volume data. For instance, the shape of the derivative chromatogram of propantheline bromide at the trailing boundary is closer to that of penicillin V than to that of the surfactant, suggesting that propantheline bromide self-associates in a nonmicellar mode. The dimerization constant of propantheline bromide estimated from the trailing peak volume is close to that obtained from the centroid volume. The shape of the frontal chromatogram is almost independent of the size of the column. This fact indicates that our chromatographic method for investigating the self-association behavior is reliable. The surface tension of the propantheline bromide solution has a transition, albeit diffuse, when plotted against the logarithm of the total concentration and decreases gradually with increasing concentration above this transition. A reasonable molecular area of propantheline bromide on the aqueous surface is obtained by using the monomer concentration, determined by the chromatographic data, in the Gibbs adsorption equation.

Aggregation Behaviour of Some Reactive Dyes

The absorption spectra of aqueous solutions of monochlorotriazine reactive dyes, C.I. Reactive Red 9 and Reactive Orange 13 were measured in the presence of 5, 10, 25 and 50% (v/v) of ethanol, pyridine and dioxane-water mixtures and in varied concentrations of KCl, NaCl and LiCl. The varying position, intensity and shape of absorption bands are interpreted in terms of aggregation and disaggregation of dyes in solutions. The aggregation behaviour of the reactive dyes in solutions and in the presence of additives is related to their apparent deviations from Beer's law and aggregation numbers (N). The aggregation constant (K.) of the monomer/dimer equilibrium is calculated. Dyes in ethanol-water mixtures record a larger aggregation number and aggregation constant than in the presence of pyridine. Dioxane is classified as anon-polar solvent and hence has a more disaggregating influence. The value of the aggregation number and constant are increased with increasing salt conentration and the order of degree of aggregation is KCl > NaCl > LiCl related to the order of ionic radii of K+, Na+ and Li+ ions.

On the interaction of metal extractant reagents. Investigation of the aggregation ofdi(2,4,4-trimethylpentyl)phosphinic acid anddi(n-octyl)phosphinic acid in toluene by vapour-pressure osmometry

The aggregation equilibria ofdi(2,4,4-trimethylpentyl)phosphinic acid (HDTMPP) anddi(n-octyl)phosphinic acid (HDOP) dissolved in toluene have been investigated by vapour-pressure osmometry (VPO) at different temperatures. The experimental data have been treated both graphically and numerically, and the average aggregation numbern as well as the aggregation constant have been determined. The results suggest that dimers are formed and that the dimerization constant decreases with temperature. Finally, the enthalpies for the aggregation ofdi(2,4,4-trimethylpentyl)phosphinic acid anddi(n-octyl)phosphinic acid in toluene have been estimated using thevan't Hoff equation.

Thermodynamic study of the aggregation of azo dyes containing two trifluoromethyl groups in aqueous solutions

The aggregation behaviour of azo dyes containing two trifluoromethyl groups, sodium 5-(3,5-bistrifluoromethyl-phenylazo)-6-hydroxynaphthalene-2-sulfonate, 1, and disodium 4-(3,5-bistrifluoromethylphenylazo)-3-hydroxy-naphthalene-2,7-disulfonate, 3, in aqueous solutions has been investigated by 19F NMR and visible absorption spectroscopy. The visible absorption spectra of the corresponding azo dyes containing two methyl groups, sodium 5-(3,5-dimethylphenylazo)-6-hydroxynaphthalene-2-sulfonate, 2, and disodium 4-(3,5-dimethylphenylazo)-3-hydroxynaphthalene-2,7-disulfonate, 4, in aqueous solutions have also been measured. From the visible absorption spectra, the aggregation number has been estimated to be 2 for all the dyes in the concentration region under examination (1 × 10–5 to 1 × 10–3 mol dm–3) and the aggregation constants have been calculated, the temperature dependence of which led to the determination of the thermodynamic parameters. Consequently, the substituents in the dyes affected entropically the aggregation processes. The aqueous solutions of 1 at concentrations greater than 5 × 10–3 mol dm–3 became gelatinous while those of 2, 3 and 4 did not. 19F NMR spectra have been recorded to elucidate the behaviour of 1 and 3 at the higher concentrations. The 19F NMR spectra of both dyes consisted of one singlet whose shapes did not change with dye concentration. The fluorine signals exhibited a progressive shift to higher and lower magnetic field with increasing dye concentration for 1 and 3, respectively. From this concentration dependence, the aggregation constants and the differences in the chemical shifts between the dye monomers and aggregates have been estimated. The aggregation constants determined by 19F NMR were in fair agreement with those calculated using visible absorption spectra. Furthermore, the differences in the chemical shifts between the dye monomers and aggregates have given important information concerning the relative spatial location between a fluorine atom and an adjacent aromatic ring.

The interactions of metal extractant reagents: VI. Aggregation equilibria of Cyanex 302 and Span 80 in toluene solutions

The aggregation equilibria of the commercial extractant Cyanex 302 in toluene have been studied by vapor pressure osmometry (VPO) at different temperatures. The experimental data, treated both graphically and numerically by means of the CPMIN program, can be explained by assuming the formation of a dimer species of the active component bis(2,4,4-trimethylpentyl)thiophosphinic acid for which the aggregation constants have been determined at 28, 40 and 50°C. The influence of other components of the commercial reagent in the aggregation equilibria have also been considered. The interaction between Cyanex 302 and the non-ionic surfactant Span 80 in toluene has also been investigated by VPO and the experimental results interpreted by the formation of mixed species between both reagents.

Self-Association of Penicillins in Aqueous Solution as Revealed by Gel Filtration Chromatography.

The self-association of penicillin G (PCG) and penicillin V (PCV) in 0.15 M potassium chloride solution has been investigated by frontal gel filtration chromatography (GFC) on Sephadex G-10 columns at 25°C. Analysis of the centroid volume, Vc, of a GFC profile yields the monomer concentration of a penicillin and the weight-average aggregation number, nw. No critical micelle concentration is observed in the Vc vs. concentration profile for PCV. The nw value for PCV is 2 at low concentrations and gradually increases with increasing concentration. PCG forms dimers only below 0.06 M, and provides useful GFC data for the investigation of dimerization. The dimerization constants of PCG and PCV are also evaluated from the concentration dependence of the derivative peak position at the trailing boundary. Stepwise aggregation constants, obtained from non-linear least-squares fitting of the centroid volume data, satisfactorily reproduce observed derivative chromatograms, and are used for calculations of the aggregate size distribution of PCV. The structure-association relationship and the effect of self-association on the bactericidal activity and chemical stability of the penicillins are discussed.

Carbon acidity. 86. Lithium and cesium ion-pair acidities of diphenylamine in tetrahydrofuran. The aggregation of lithium and cesium diphenylamide. A new method for the determination of aggregation constants in dilute solution

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTCarbon acidity. 86. Lithium and cesium ion-pair acidities of diphenylamine in tetrahydrofuran. The aggregation of lithium and cesium diphenylamide. A new method for the determination of aggregation constants in dilute solutionJames A. Krom, Jeffrey T. Petty, and Andrew StreitwieserCite this: J. Am. Chem. Soc. 1993, 115, 18, 8024–8030Publication Date (Print):September 1, 1993Publication History Published online1 May 2002Published inissue 1 September 1993https://doi.org/10.1021/ja00071a013RIGHTS & PERMISSIONSArticle Views211Altmetric-Citations44LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (885 KB) Get e-Alerts Get e-Alerts

Positional effects of a trifluoromethyl group on the aggregation of azo dyes in aqueous solutions

The aggregation behavior in aqueous solutions of monoazo sulfonic dyes containing a trifluoromethyl group at various positions to the azo linkage, and the corresponding dyes containing a methyl group, was investigated by means of 19 F NMR and visible absorption spectroscopy. The visible absorption spectra changed with dye concentration, exhibiting distinct isosbestic points. From this, the aggregation number was estimated as 2 for all the dyes in the concentration region used for the visible absorption measurements and the aggregation constants were calculated. Furthermore, the thermodynamic parameters were determined from the temperature dependence of the aggregation constants

Chromatographic study on stepwise aggregation patterns of zwitterionic derivatives of cholic acid

The frontal chromatogram of the 2-hydroxy derivative (CHAPSO) of 3-[(3-cholamidopropyl)dimethylammonio]-1-propanesulfonate (CHAPS) has been obtained on a Sephadex G-10 column at 298 K. From the centroid volume, Vc, of the chromatogram, the monomer concentration, the weight- and number-average aggregation numbers (nw and nn), the critical micelle concentration (c.m.c.) and the dimerization constant, k2, are evaluated, and furthermore, stepwise aggregation constants, ki, are estimated on the basis of several self-association models. At small aggregation numbers, an odd–even alternation of the aggregation number dependence of ki is found and CHAPSO self-associates cooperatively, whereas it does so anti-cooperatively at high aggregation numbers. The c.m.c. depends on the treatment of the Vc data, and this result suggests that CHAPSO forms small micelles. The derivative chromatogram of CHAPSO and some characteristic values obtained therefrom are markedly different from those of a dye and typical surfactants, and reflect their aggregation patterns. The derivative chromatogram simulated on the basis of the above aggregation models is very similar to the observed one. The differences in limiting aggregation constant k and nw/nn between CHAPSO and CHAPS are explained on the basis of the fact that the head group of CHAPSO is more bulky than that of CHAPS. The micelle size distribution of CHAPSO is calculated on the basis of the above aggregation models. The concentrations of the monomer and each aggregate species will be useful for applications of CHAPSO and CHAPS to the solubilization of membrane proteins as well as for the investigation of the aggregation patterns of bile salts.

Aggregation of Mordant Black 11 in aqueous solution

Spectrophotometry was employed to study the aggregation of Mordant Black 11 (MB-11) in aqueous solution. The aggregation number and constant were determined using the maximum slope method. The aggregation characteristics obtained by this method were then compared with other methods. In addition, the spectral change as a result of dimerization of MB-11 was interpreted in terms of the usual cluster model of water exerting hydrophobic interaction around the dye ions.

Gel filtration chromatographic study on the self-association of surfactants and related compounds

After a brief survey of gel filtration chromatography (GFC) and the self-association equilibrium, it is shown that GFC is a unique tool for investigating the self-association of many substances, such as surfactants, chlorpromazine hydrochloride (CPZ), Methylene Blue (MB) and a sulfobetaine derivative (CHAPS) of cholic acid. The hydrodynamic radius of an aggregate can be estimated with the gel of large pore size, such as Sephadex G-200. This method is utilized for the study of the sphere-rod transition of surfactant micelles. A precise value of monomer concentration can be determined from the centroid elution volume of a frontal chromatogram on Sephadex G-10. This important parameter in self-associating systems allows us to determine the micellar aggregation number as a function of the total surfactant concentration. The derivative chromatogram can be used to detect slight changes in self-association. From these results, it is found that nonionic surfactants form premicelles including dimer and that multiple equilibrium model for micelle formation is more appropriate than mass-action model. The Tanford theory with some modifications appears to fit the concentration dependence of the aggregation properties of surfactants forming small globular micelles and allows us to estimate the stepwise aggregation constant and the micelle size distribution function. The pronounced cooperativity in the self-association of surfactants forms the basis of mass action model and the concept of the cmc, though they are actually approximations even for surfactants. They would be more inadequate, though often used, for the self-association of drugs and bile salts. The stepwise aggregation constant of MB is almost independent of aggregation numbers, which may be expected from the stacking mode of aggregation. The main aggregates of CPZ in 154 mM sodium chloride solution are dimer and 38-mer and its dimerization constant is smaller than that of MB and larger than those of surfactants. The stepwise aggregation constant of CHAPS has the maximum at hexamer and oscillates, depending on odd or even aggregation numbers. Thus, the aggregation pattern of a substance is closely related with the chemical structure of the hydrophobic group of its molecule. The definition of cmc is discussed together with its significance.

The Aggregation of Organophosphorus Acid Compounds in Toluene

The aggregation equilibria of 2-ethylhexylphosphonic acid mono-2-ethylhexyl ester (HEH(EHP)) and di(2-ethylhexyl)phosphoric acid (HDEHP) dissolved in toluene has been investigated by vapor-pressure osmometry at different temperatures. The experimental data have been treated both graphically and numerically, and the average aggregation number n of organophosphorus acids, as well as the aggregation constants, has been determined. The results suggest that dimers are formed and the dimerization constant decreases with temperature. Finally, an estimated enthalpy value for the aggregation of organophosphorus acids in toluene has been calculated by using the van′t Hoff equation.