Introducing the K-Index: A Descriptor, Predictor, and Correlator of Complex Nanomorphology to Other Material Properties


Morphology is a qualitative property of nanostructured matter and is often articulated by visual inspection of micrographs. Properties of porous materials with technological interest such as mechanical strength, wettability, surface area, gas sorption capacity and thermal conductivity, depend to a large extent on the morphology of their solid frameworks. For deterministic procedures that relate nanomorphology to synthetic conditions, it is necessary to express nanostructures numerically ­­– a process that may have a much broader impact than just in the field of material science.

At present, numerous attempts to infer nanomorphology from quantifiable material properties have focused on mechanical strength, which, therefore, has been assumed as the de facto link between nanomorphology and synthetic conditions. However, as it turns out, many material properties, including density, mechanical strength and the elastic modulus, are not single-valued functions of morphology. That is, two samples with completely different morphologies may have the same value of any of those properties. Thereby, there is a need for a different morphology descriptor.

In a recent publication, a Missouri University of Science and Technology team comprised of Curators’ Distinguished Professor Nicholas Leventis (now retired), Tahereh Taghvaee (PhD candidate), Dr. Suraj Donthula, Parwani M. Rewatkar (PhD candidate), Dr. Hojat Majedi Far and Professor Chariklia Sotiriou-Leventis investigated the possibility of quantifying the preverbal impression from visual inspection of scanning electron micrography (SEM) of a nanostructure, which, they reasoned, is related to its openness and its texture. This openness is quantified by porosity, Π, and texture is oftentimes reflected on hydrophobicity, which, in turn, is quantified by the contact angle, θ, of a water droplet on the surface of a material. The θ-to-Π ratio, henceforth referred to as the ‘K-index’, turns out to be an accurate descriptor, predictor, and correlator of complex nanomorphology to other material properties. Their work is currently published in the research journal, ACS Nano.

In brief, by selecting polyurea aerogels as a model system with demonstrated potential for rich nanomorphology, and guided by a statistical design-of experiments model, they prepared a large array of materials (208) with identical chemical composition but quite different nanostructures. The authors reported that the polyurea samples adopted for the study could be put in eight K-index groups with separate nanomorphologies ranging from caterpillar-like assemblies of nanoparticles, to thin nanofibers, to cocoon-like structures, to large bald microspheres. Various characterization methods including nuclear magnetic resonance, porosimetry, thermal conductivity and quasistatic mechanical compression were applied to all samples. The first validation of the K-index as a morphology descriptor was based on compressing samples to different strains: it was observed that as the porosity decreased, the water-contact angle decreased proportionally, and thereby the K-index remained constant, as it should, because compression brings nanoscopic features closer, but otherwise leaves them intact.

In summary, the K-index was presented as a resilient descriptor and predictor of the diverse nanomorphology of polyurea aerogels, a correlator of nanostructure to material properties, and a quantitative tool for materials design. The nanostructure predictive power of the K-index was demonstrated with 20 polyurea aerogels prepared in 8 binary solvent systems. In the end, the authors went on to identify synthetic conditions and prepare nanoporous polyurea aerogels with any targeted nanomorphology prescribed a priori. Altogether, identification of three-way quantitative relationships among nanostructure, properties, and synthetic conditions is expected to be an essential point of departure for fundamental bottom-up simulations of nanostructure formation.

K-Index: A Descriptor, Predictor, and Correlator of Complex Nanomorphology to Other Material Properties - Advances in Engineering

About the author

Nicholas Leventis received his B.S. in Chemistry from the University of Athens, Greece (1980) and his Ph.D. from Michigan State University with The Late Peter J. Wagner in organic chemistry/photochemistry (1985). In 1992 he completed Harvard University’s one-year Graduate Program in Administration and Management and received the Katie F. Young Award. He was a postdoctoral fellow with Mark S. Wrighton at MIT (1985-1988) and worked for six years in the private sector (1988-1994) before joining as an Assistant Professor the Chemistry Department of the Missouri University of Science and Technology (MS&T), advancing to Associate Professor in 1999 and to Professor in 2007. In 1998 he was a Senior Faculty Fellow at the U.S. Naval Research Laboratory, Washington D.C. During an extended leave from MS&T (2002-2006) Dr. Leventis worked first as a GS-14 (2002-2005), and then as a GS-15 (2005-2006) Civil Servant in the Polymers Branch, Materials Division of the NASA Glenn Research Center, where he established the aerogels research program.

In 1992 Dr. Leventis received the Arthur K. Doolittle Award of the Polymeric Materials Science and Engineering Section of the American Chemical Society for his work on electrochromic polymers. In 2005 he received the NASA Exceptional Scientific Achievement Medal (under the auspices of the President) for “ground breaking research in the development of polymer cross-linked aerogels.” Dr. Leventis has won the Society for American Military Engineers Award (2008) and the Nano50TM Award twice, in 2005 for “Reinforced Aerogels” and in 2007 for “Mechanically Strong, Polymer Crosslinked Aerogels.” In 2010 he was named Curators’ Distinguished Professor of the University of Missouri. He retired from MS&T in June 2019.

Besides nanotechnology, Dr. Leventis’ interests include physical organic chemistry, electrochemistry, polymeric and inorganic materials. He has published over 190 research articles in all major areas of chemistry. He is a co-author or the corresponding author in 14 book chapters, and has co-edited two books on aerogels. He has been awarded over 27 U.S. Patents. His publications and patents have received over 7,750 citations. His h-index is 50.

About the author

Chariklia Sotiriou-Leventis received her B.S. in Chemistry from the University of Athens, Greece (1982) and her Ph.D. from Michigan State University with Professor C. K. Chang in organic chemistry (1987). She was a postdoctoral fellow with Professors Roger Giese at Northeastern University (1987-1989) and William von Eggers Doering (deceased) at Harvard University (1989-1992). She worked for two years at Ciba Corning Diagnostics (1992-1994, 2 patents) before joining as an Adjunct Assistant Professor the Chemistry Department of Missouri University of Science and Technology (MS&T) in 1994, advancing to Assistant Professor in 1995, Associate Professor in 2001 and to Professor in 2005.

Her research interests are in the areas of nanotechnology, synthesis of new organic materials including aerogels, physical organic chemistry as well as supramolecular chemistry. She is the recipient of an award in organic synthesis from Ciba Corning Diagnostics and the Gustel Giessen Advanced Research Award of the Barnett Institute of Chemical Analysis and Materials Science. She has published over 130 articles in high impact factor scientific journals, four book chapters and she has been awarded 16 U.S. Patents. Her publications and patents have received over 4,040 citations, and her h-index is 36. She has also received 12 excellence in teaching awards from MS&T for her instruction in both undergraduate and graduate chemistry courses.


Tahereh Taghvaee, Suraj Donthula, Parwani M. Rewatkar, Hojat Majedi Far, Chariklia Sotiriou-Leventis, Nicholas Leventis. K-Index: A Descriptor, Predictor, and Correlator of Complex Nanomorphology to Other Material Properties. ACS Nano 2019, volume 133 page 3677-3690.

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