Abstract
The diffusion properties at two overall compositions of a ternary aqueous system containing α-cyclodextrin and a double-functional guest molecule, namely di-tert-butyl l-tartrate, have been studied by means of the Gouy interferometry. The experimental data are interpreted in terms of two independent chemical equilibria involving inclusion compounds. The elements of the diffusion coefficient matrix have been expressed as functions of the two equilibrium constants as well as of the diffusivities of the actual species occurring in solution. The reliability of the diffusion coefficients obtained through the Fujita–Gosting–Revzin procedure is also discussed in terms of its dependence on the composition of solutions used in the Gouy experiments.
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References
Szejtli, J.: Introduction and general overview of cyclodextrin chemistry. Chem. Rev. 98, 1743–1753 (1998)
Li, S., Purdy, W.C.: Cyclodextrins and their applications in analytical-chemistry. Chem. Rev. 92, 1457–1470 (1992)
Duchene, D. (ed.): Cyclodextrins and Their Industrial Uses. Éditions de Santé, Paris (1987)
Duchene, D. (ed.): New Trends in Cyclodextrins and Derivatives. Éditions de Santé, Paris (1991)
Szejtli, J.: Cyclodextrins and Their Inclusion Complexes. Verlag der Ungarischen Akademie der Wissenschaften. Akadémiai Kiadó, Budapest (1982)
Szejtli, J., Osa, T. (volume eds.): Comprehensive Supramolecular Chemistry, Vol. 3: Cyclodextrins. Pergamon Press, Oxford (1996)
Auletta, T., De Jong, M.R., Mulder, A., Van Veggel, F.C.J.M., Huskens, J., Reinhoudt, D.N., Zou, S., Zapotoczny, S., Schoenherr, H., Vancso, G.J., Kuipers, L.: β-Cyclodextrin host–guest complexes probed under thermodynamic equilibrium: thermodynamics and AFM force spectroscopy. J. Am. Chem. Soc. 126, 1577–1584 (2004)
Baer, A.J., Macartney, D.H.: α- and β-Cyclodextrin rotaxanes of μ-bis(4-pyridyl)bis[pentacyanoferrate(II)] complexes. Inorg. Chem. 39, 1410–1417 (2000)
Catena, G.C., Bright, F.V.: Thermodynamic study on the effects of β-cyclodextrin inclusion with anilinonaphthalenesulfonates. Anal. Chem. 61, 905–909 (1989)
Clarke, R.J., Coates, J.H., Lincoln, S.F.: Inclusion complexes of the cyclomaltooligosaccharides (cyclodextrins). Adv. Carbohydr. Chem. Biochem. 46, 205–249 (1988)
Eftink, M.R., Andy, M.L., Bystrom, K., Perlmutter, H.D., Kristol, D.S.: Cyclodextrin inclusion complexes: studies of the variation in the size of alicyclic guests. J. Am. Chem. Soc. 111, 6765–6772 (1989)
Godinez, L.A., Schwartz, L., Criss, C.M., Kaifer, A.E.: Thermodynamic studies on the cyclodextrin complexation of aromatic and aliphatic guests in water and water–urea mixtures. Experimental evidence for the interaction of urea with arene surfaces. J. Phys. Chem. B 101, 3376–3380 (1997)
Herrmann, W., Keller, B., Wenz, G.: Kinetics and thermodynamics of the inclusion of ionene-6,10 in α-cyclodextrin in an aqueous solution. Macromolecules 30, 4966–4972 (1997)
Inoue, Y., Hakushi, T., Liu, Y., Tong, L., Shen, B., Jin, D.: Thermodynamics of molecular recognition by cyclodextrins. 1. Calorimetric titration of inclusion complexation of naphthalenesulfonates with α-, β-, and γ-cyclodextrins: enthalpy–entropy compensation. J. Am. Chem. Soc. 115, 475–481 (1993)
Inoue, Y., Liu, Y., Tong, L.H., Shen, B.J., Jin, D.S.: Calorimetric titration of inclusion complexation with modified β-cyclodextrins. Enthalpy–entropy compensation in host–guest complexation: from ionophore to cyclodextrin and cyclophane. J. Am. Chem. Soc. 115, 10637–10644 (1993)
Madrid, J.M., Mendicuti, F., Mattice, W.L.: Inclusion complexes of 2-methylnaphthoate and γ-cyclodextrin: experimental thermodynamics and molecular mechanics calculations. J. Phys. Chem. B 102, 2037–2044 (1998)
Mark, A.E., van Helden, S.P., Smith, P.E., Janssen, L.H.M., van Gunsteren, W.F.: Convergence properties of free energy calculations: α-cyclodextrin complexes as a case study. J. Am. Chem. Soc. 116, 6293–6302 (1994)
Rekharsky, M., Inoue, Y.: 1:1 and 1:2 complexation thermodynamics of γ-cyclodextrin with N-carbobenzyloxy aromatic amino acids and ω-phenylalkanoic acids. J. Am. Chem. Soc. 122, 10949–10955 (2000)
Rekharsky, M.V., Goldberg, R.N., Schwarz, F.P., Tewari, Y.B., Ross, P.D., Yamashoji, Y., Inoue, Y.: Thermodynamic and nuclear magnetic resonance study of the interactions of α- and β-cyclodextrin with model substances: phenethylamine, ephedrines, and related substances. J. Am. Chem. Soc. 117, 8830–8840 (1995)
Tabushi, I., Kiyosuke, Y., Sugimoto, T., Yamamura, K.: Approach to the aspects of driving force of inclusion by α-cyclodextrin. J. Am. Chem. Soc. 100, 916–919 (1978)
Paduano, L., Sartorio, R., Vitagliano, V.: Diffusion coefficients of the ternary system α-cyclodextrin–sodium benzenesulfonate–water at 25°C: the effect of chemical equilibrium and complex formation on the diffusion coefficients of a ternary system. J. Phys. Chem. B 102, 5023–5028 (1998)
Paduano, L., Sartorio, R., Vitagliano, V., Albright, J.G., Miller, D.G.: Measurement of the mutual diffusion-coefficients at one composition of the 4-component system α-cyclodextrin–l-phenylalanine–monobutylurea–H2O at 25°C. J. Phys. Chem. 96, 7478–7483 (1992)
Paduano, L., Sartorio, R., Vitagliano, V., Albright, J.G., Miller, D.G., Mitchell, J.: Diffusion-coefficients in systems with inclusion-compounds. 1. α-cyclodextrin–l-phenylalanine–water at 25°C. J. Phys. Chem. 94, 6885–6888 (1990)
Paduano, L., Sartorio, R., Vitagliano, V., Castronuovo, G.: Calorimetric and diffusional behavior of the system α-cyclodextrin–l-phenylalanine in aqueous-solution. Thermochim. Acta 162, 155–161 (1990)
Paduano, L., Sartorio, R., Vitagliano, V., Costantino, L.: Diffusion-coefficients in systems with inclusion-compounds. 2. α-Cyclodextrin–(dl)norleucine–water at 25°C. Ber. Bunsenges Phys. Chem. Chem. Phys. 94, 741–745 (1990)
Paduano, L., Sartorio, R., Vitagliano, V., Costantino, L.: Diffusion coefficients of the system α-cyclodextrin–n-butylurea–water at 25°C. J. Solution Chem. 24, 1143–1153 (1995)
Ribeiro, A.C.F., Leaist, D.G., Esteso, M.A., Lobo, V.M.M., Valente, A.J.M., Santos, C.I.A.V., Cabral, A.M.T.D.P.V., Veiga, F.J.B.: Binary mutual diffusion coefficients of aqueous solutions of β-cyclodextrin at temperatures from 298.15 to 312.15 K. J. Chem. Eng. Data 51, 1368–1371 (2006)
Ribeiro, A.C.F., Lobo, V.M.M., Azevedo, E.F.G., Miguel, MdG, Burrows, H.D.: Diffusion coefficients of sodium dodecylsulfate in aqueous solutions and in aqueous solutions of β-cyclodextrin. J. Mol. Liq. 102, 285–292 (2003)
Ribeiro, A.C.F., Santos, C.I.A.V., Lobo, V.M.M., Cabral, A.M.T.D.P.V., Veiga, F.J.B., Esteso, M.A.: Diffusion coefficients of the ternary system β-cyclodextrin + caffeine + water at 298.15 K. J. Chem. Eng. Data 54, 115–117 (2009)
Ribeiro, A.C.F., Santos, C.I.A.V., Valente, A.J.M., Ascenso, O.S., Lobo, V.M.M., Burrows, H.D., Cabral, A.M.T.D.P.V., Veiga, F.J.B., Teijeiro, C., Esteso, M.A.: Some transport properties of γ-cyclodextrin aqueous solutions at (298.15 and 310.15) K. J. Chem. Eng. Data 53, 755–759 (2008)
Ribeiro, A.C.F., Valente, A.J.M., Santos, C.I.A.V., Prazeres, P.M.R.A., Lobo, V.M.M., Burrows, H.D., Esteso, M.A., Cabral, A.M.T.D.P.V., Veiga, F.J.B.: Binary mutual diffusion coefficients of aqueous solutions of α-cyclodextrin, 2-hydroxypropyl-α-cyclodextrin, and 2-hydroxypropyl-β-cyclodextrin at temperatures from (298.15 to 312.15) K. J. Chem. Eng. Data 52, 586–590 (2007)
Santos, C.I.A.V., Esteso, M.A., Sartorio, R., Ortona, O., Sobral, A.J.N., Arranja, C.T., Lobo, V.M.M., Ribeiro, A.C.F.: A comparison between the diffusion properties of theophylline/β-cyclodextrin and theophylline/2-hydroxypropyl–β-cyclodextrin in aqueous systems. J. Chem. Eng. Data 57, 1881–1886 (2012)
Huang, L., Allen, E., Tonelli, A.E.: Study of the inclusion compounds formed between α-cyclodextrin and high molecular weight poly(ethylene oxide) and poly(ε-caprolactone). Polymer 39, 4857–4865 (1998)
Weickenmeier, M., Wenz, G., Huff, J.: Association thickener by host guest interaction of a β-cyclodextrin polymer and a polymer with hydrophobic side-groups. Macromol. Rapid Commun. 18, 1117–1123 (1997)
Gref, R., Amiel, C., Molinard, K., Daoud-Mahammed, S., Sebille, B., Gillet, B., Beloeil, J.C., Ringard, C., Rosilio, V., Poupaert, J., Couvreur, P.: New self-assembled nanogels based on host–guest interactions: characterization and drug loading. J. Control. Release 111, 316–324 (2006)
Paduano, L., Vergara, A., Corradino, M.R., Vitagliano, V., Sartorio, R.: Equilibrium properties of the system (dibutyl l-tartrate)–(α-cyclodextrin)–(water) at 25 °C. A 1H NMR and UV study. Phys. Chem. Chem. Phys. 1, 3627–3631 (1999)
Mangiapia, G., Paduano, L., Ortona, O., Sartorio, R., D’Errico, G.: Analysis of main- and cross-term diffusion coefficients in bile salt mixtures. J. Phys. Chem. B 117, 741–749 (2013)
Mangiapia, G., Paduano, L., Vergara, A., Sartorio, R.: Novel method for calculating the diffusion coefficients of a ternary system containing a polydisperse component. Applications to the Gouy interferometry. J. Phys. Chem. B 107, 7216–7224 (2003)
Dunlop, P.J., Gosting, L.J.: Expressions for the solute concentration curves in free diffusion, and their use in interpreting Gouy diffusiometer data for aqueous three-component systems. J. Am. Chem. Soc. 77, 5238–5249 (1955)
Toor, I.H.L.: Solution of the linearized equations of multicomponent mass transfer. II. Matrix methods. AIChE J 10, 460–465 (1964)
Haase, R.: Thermodynamics of Irreversible Processes. Addison-Wesley, London (1969)
Gosting, L.J., Onsager, L.: A general theory for the Gouy diffusion method. J. Am. Chem. Soc. 74, 6066–6074 (1952)
Tyrrell, H.J.V., Harris, K.R.: Diffusion in Liquids: A Theoretical and Experimental Study. Butterworths, London (1984)
Crank, J.: The Mathematics of Diffusion, 2nd edn. Clarendon Press, Oxford (1975)
Cussler, E.L.: Diffusion Mass Transfer in Fluid Systems. Cambridge University Press, Cambridge (1984)
Vergara, A., Paduano, L., Vitagliano, V., Sartorio, R.: Multicomponent diffusion in solutions where crystals grow. Mater. Chem. Phys. 66, 126–131 (2000)
Paduano, L., Vergara, V., Vitagliano, V., Sartorio, R.: Mutual diffusion in presence of chemical equilibrium. Trends Phys. Chem. 7, 209–218 (1999)
Fujita, H., Gosting, L.J.: An exact solution of the equations for free diffusion in three-component systems with interacting flows, and its use in evaluation of the diffusion coefficients. J. Am. Chem. Soc. 78, 1099–1106 (1956)
Fujita, H., Gosting, L.J.: A new procedure for calculating the four diffusion coefficients of three-component systems from Gouy diffusiometer data. J. Phys. Chem. 64, 1256–1263 (1960)
Vergara, A., Paduano, L., Sartorio, R.: Multicomponent diffusion in systems containing molecules of different size. 4. Mutual diffusion in the ternary system tetra(ethylene glycol)–di(ethylene glycol)–water. J. Phys. Chem. B 105, 328–334 (2001)
Carter, J.M., Phillies, G.D.J.: Second-order concentration correction to the mutual diffusion coefficient of a suspension of hard brownian spheres. J. Phys. Chem. 89, 5118–5124 (1985)
Denbigh, K.: The Principles of Chemical Equilibrium. Cambridge University Press, Cambridge (1966)
Albright, J.G.: Theories for the experimental study of isothermal free diffusion in ternary liquid systems involving a chemical reaction. J. Phys. Chem. 67, 2628–2635 (1963)
Leaist, D.G.: Binary diffusion of micellar electrolytes. J. Colloid Interface Sci. 111, 230–239 (1986)
Paduano, L., Sartorio, R., Vitagliano, V., Costantino, L.: Diffusion properties of cyclodextrins in aqueous solution at 25°C. J. Solution Chem. 19, 31–39 (1990)
Paduano, L., Sartorio, R., Vitagliano, V., Costantino, L.: Transport and thermodynamic properties of the systems (d, l)norleucine–water and (l)phenylalanine–water, at 25°C. J. Mol. Liquids 47, 193–202 (1990)
Kim, H.: Diffusion studies of the systems water–succinic acid–urea and water–succinic acid at 25°. Effect of complex formation on the diffusion coefficients of the ternary system. J. Solution Chem. 3, 271–287 (1974)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, New York (2007)
Revzin, A.: Isothermal free diffusion in liquids: calibrations of a new optical diffusiometer, new calculation procedures for ternary systems, and data for the system tetrabutylammonium bromide–water at 25°. PhD thesis, University of Wisconsin, Madison (1969)
Wentworth, W.E.: Rigorous least squares adjustment: application to some nonlinear equations II. J. Chem. Educ. 42, 162–167 (1965)
Wentworth, W.E.: Rigorous least squares adjustment—application to some nonlinear equations. I. J. Chem. Educ. 42, 96–103 (1965)
Miller, D.G.: A method for obtaining multicomponent diffusion-coefficients directly from Rayleigh and Gouy fringe position data. J. Phys. Chem. 92, 4222–4226 (1988)
Albright, J.G., Miller, D.G.: Analysis of free diffusion in a binary system when the diffusion coefficient is a function of the square root of concentration. J. Phys. Chem. 79, 2061–2068 (1975)
Albright, J.G., Miller, D.G.: Analysis of Gouy interference patterns from binary free-diffusion systems when the diffusion coefficient and refractive index have C1/2 and C3/2 terms, respectively. J. Phys. Chem. 84, 1400–1413 (1980)
Acknowledgments
One of us (R.S.) had the opportunity to collaborate with Donald Miller for a long period since the mid 1980s while the other one (G.M.) had the chance to meet him during his last stays in Naples after 2000. Even with different experiences and memories, both of us had the possibility to appreciate Don’s human side, his communication skills, and his high scientific personality. This little contribution is in his memory and honor.
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Mangiapia, G., Sartorio, R. 1:1 and 1:2 Inclusion Complexes of Di-tert-butyl l-tartrate with α-Cyclodextrin: A Diffusion Study. J Solution Chem 43, 186–205 (2014). https://doi.org/10.1007/s10953-013-0124-5
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DOI: https://doi.org/10.1007/s10953-013-0124-5