Solubility of nanoparticles: nonextensive thermodynamics approach

We show in this study that the concepts of nonextensive thermodynamics, introduced in a previous work, can be used to express the variations of the solubility of nanoparticles and porous materials according to their mass by power laws, without the need to resort to fractal dimensions. This results in the demonstration of the Ostwald–Freundlich relation. Our approach is based on a thermodynamic description involving the introduction in the internal energy expression of an extensity, χ. χ is an Euler's function of the particle mass with a homogeneity degree, m, which can be other than one; m is the thermodynamic dimension of the system. We use this approach to simulate various behaviours, and show that an increase in solubility can be either higher or lower than that envisaged by the Ostwald–Freundlich relation.

[1]  J. Cervera,et al.  Calculation of the wetting parameter from a cluster model in the framework of nanothermodynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Mireille Turmine,et al.  Nonextensive Approach to Thermodynamics: Analysis and Suggestions, and Application to Chemical Reactivity , 2004 .

[3]  Daniel Y. Kwok,et al.  Contact angle interpretation in terms of solid surface tension , 2000 .

[4]  A. Shirinyan,et al.  Phase diagram versus diagram of solubility: What is the difference for nanosystems? , 2005 .

[5]  Mireille Turmine,et al.  Drop size effect on contact angle explained by nonextensive thermodynamics. Young's equation revisited. , 2007, Journal of colloid and interface science.

[6]  Correct thermodynamic forces in Tsallis thermodynamics: connection with Hill nanothermodynamics , 2005, cond-mat/0501396.

[7]  M. Strømme,et al.  Solubility of fractal nanoparticles , 2007 .

[8]  T. L. Hill,et al.  Extension of the thermodynamics of small systems to open metastable states: an example. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[9]  D. Avnir,et al.  An isotherm equation for adsorption on fractal surfaces of heterogeneous porous materials , 1989 .

[10]  Peter Pfeifer,et al.  Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces , 1983 .

[11]  W. L. Jorgensen,et al.  Prediction of drug solubility from structure. , 2002, Advanced drug delivery reviews.

[12]  P. Letellier,et al.  Melting point depression of nanosolids : Nonextensive thermodynamics approach , 2007 .

[13]  V. Garcia-Morales,et al.  Microcanonical foundation of nonextensivity and generalized thermostatistics based on the fractality of the phase space , 2006 .

[14]  D. Avnir,et al.  Thermodynamics of gas adsorption on fractal surfaces of heterogeneous microporous solids , 1990 .

[15]  Raymond Defay,et al.  Ètude thermodynamique de la tension superficielle , 1934 .

[16]  J. Delaney,et al.  Physical and Molecular Properties of Agrochemicals: An Analysis of Screen Inputs, Hits, Leads, and Products , 2003 .

[17]  Daniel Y. Kwok,et al.  Contact angle measurement and contact angle interpretation , 1999 .

[18]  On phase changes in nanosystems , 2006 .

[19]  Nissim Garti,et al.  Microemulsions as transdermal drug delivery vehicles. , 2006, Advances in colloid and interface science.

[20]  On the definition of physical temperature and pressure for nonextensive thermostatistics , 2001, cond-mat/0106060.

[21]  Yongbai Yin,et al.  Adsorption isotherm on fractally porous materials , 1991 .

[22]  C. Tsallis.  Entropic nonextensivity: a possible measure of complexity , 2000, cond-mat/0010150.