A Brief History of Density Functional Theory Applied to Extracting Information from the Physical Adsorption Isotherm
During the 1980s, considerable progress was made toward a theoretical understanding of fluid behavior in non-homogeneous systems. Particular interest was focused on phase changes in fluids constrained by the presence of walls, capillaries, and slits. A paper that was later to play an important part in defining the application of Density Functional Theory (DFT) to the adsorption isotherm was published in February of 1987 by Tarazona, Marconi and Evans (1) titled Phase Equilibria of Fluid Interfaces and Confined Fluids–Non-local Versus Local Density Functions.
In 1989, Seaton, Walton and Quirke (2) were first to describe a practical method by which model isotherms calculated from mean-field density functional theory may be used to determine pore size distribution from nitrogen isotherms. However, their approach employed the presumption of a specific distribution function.
Researchers at Micromeritics Instrument Corporation realized the disadvantages of presuming the shape of the distribution. It was believed that for DFT to be widely accepted as a general method for reducing the adsorption isotherm, it would need to be independent of any presupposed distribution model.
Work led by James P. Olivier with the assistance of William B. Conklin (3) succeeding in developing a method for determining the pore size distribution in materials that was applicable to the entire range of pore sizes accessible by the adsorptive molecule, and which made no assumptions concerning the functional form of the size distribution. Generalization was accomplished by numerical deconvolution of the isotherm data using a set of pore shape dependent model isotherms calculated from DFT, each member of the set being representative of a unique, narrow range of pore sizes and the entire set covering a wide range of sizes.
Therefore, in 1991, Micromeritics became the first commercial instrument manufacturer to present findings on the use of DFT as a general method to extract porosity information from a physical adsorption isotherm. The presentation was titled Characterization of Porous Solids from Physical Adsorption Data Using Theory of Constrained States and was delivered by Olivier and Conklin at the 7th International Conference on Surface and Colloid Science in Compiegne, France. In this work, adsorption isotherms were modeled using a modified mean field density gradient theory of phase changes in the proximity of surfaces and within narrow pores.
It should be noted that, up to this point in the development of DFT applications to adsorption isotherms, both the original work by Seaton, et al, and the work by Olivier and Conklin that followed used simple local density approximation (LDA) in computing the predicted isotherms. Lastoskie, Gubbins, and Quirke (4, 5) recognized the crudeness of the LDA method and subsequently extended Seaton’s original work by using a refined smoothed density approximation (SDA) described by Tarazona. Since this publication in 1993, focus turned to non-local density approximations.
Olivier and Conklin (6) also were exploring use of the SDA approach and presented their findings at the International Symposium on the Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, held in Kazimier Dolny, Poland, in 1992. The Olivier paper was titled Determination of Pore Size Distribution from Density Functional Theoretic Models of Adsorption and Condensation within Porous Solids.
The next publication from Micromeritics on DFT was by Olivier, Conklin, and Szombathely (7) titled, Determination of Pore Size Distribution from Density Functional Theory: A Comparison of Nitrogen and Argon Results. The paper was presented at the COPS III conference in 1993. This work showed the distribution of surface area and pore volume by size distribution curves elicited by deconvolution from the models and experimental data using a non-negative least squares (NNLS) technique and regularization with non-linear constraint.
By this time, DFT was beginning to be recognized as a significant means for extracting reliable information from the physical adsorption isotherm. In 1993, Micromeritics began providing the “DFT Version 1.00” data reduction package with the ASAP 2000 family of physical adsorption analyzers, instruments capable of collecting high resolution data from the micropore through mesopore regions. A copy of the Forward section of the instruction manual for DFT Version 1.00 is included at the end of this article.
Over the intervening fifteen-plus years since these pioneering works were done, Micromeritics has remained active in the further development of DFT models and applications. The company’s strength in this area was increased in 2008 by the employment of Jacek Jagiello, another early contributor to DFT development. The focus has always been and continues to be to develop practical, valid and useful applications for the use of DFT in extracting information from the adsorption isotherm.
1) Phase equilibria of fluid interfaces and confined fluids–Non-local versus local density functionals; Tarazona, Marconi, and Evans; Molecular Physics, Volume 60, Issue 3 February 1987, pp. 573 – 595
2) A New Analysis Method for the Determination of the Pore Size Distribution of Porous Carbons from Nitrogen Adsorption Measurements; Seaton, Walton, and Quirke; Carbon, Vol. 27, No. 6, pp. 853-861, 1989
3) Characterization of Porous Solids from Physical Adsorption Data Using Theory of Constrained States; Olivier and Conklin; Presented at 7th International Conference on Surface and Colloid Science, Compiegne, France, 1991
4) Pore Size Distribution Analysis of Microporous Carbons: A Density Functional Theory Approach; Lastoskie, Gubbins, and Quirke; J. Phys. Chem. 1993, 97, 4786-4796
5) Pore Size Heterogeneity and the Carbon Slit Pore: A Density Functional Theory Model; Lastoskie, Gubbins, and Quirke; Langmuir 1993,9, pp. 2693-2702
6) Determination of Pore Size Distribution from Density Functional Theoretic Models of Adsorption and Condensation within Porous Solids; Olivier and Conklin; Presented at the International Symposium on the Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids; Kazimier Dolny, Poland, July 1992.
7) Determination of Pore Size Distribution from Density Functional Theory: A Comparison of Nitrogen and Argon Results. In Characterization of Porous Solids; Olivier, Conklin, and Szombathely; Proceedings of the IUPAC Symposium (COPS III); Elsevier Press: Marselle, France, 1993.