One of the more useful formulas for our materials is Equation 1 in Chung et al., 2014 Lab on a Chip 14:2456-68
Assuming uniformly distributed pores in a planar (i.e. ultrathin) membrane, the relationship between pore radius r, porosity p, and the average spacing between pores, Lp-p is:
Where the porosity is a number between 0 and 1 (i.e. not a %).
And another fundamental formula to know is the relationship between pore density, ρ, porosity, p, and pore radius, r.
ρ = p*(π r^2)
For the derivations, think about it. Or take BME442.
Professor McGrath holds a BS degree in Mechanical Engineering from Arizona State and a MS degree in Mechanical Engineering from MIT. He earned a PhD in Biological Engineering from Harvard/MIT's Division of Health Sciences and Technology. He then trained as a Distinguished Post-doctoral Fellow in the Department of Biomedical Engineering at the Johns Hopkins University. Professor McGrath has been on the Biomedical Engineering faculty at the University of Rochester since 2001 where he also served as the director of the graduate program in BME for more than a decade and currently serves as Associate Director of the URNano microfab and metrology core. Professor McGrath also has faculty affiliations with many other programs at UR including the Material Research Program, the Environmental Health and Sciences Center, the Biochemistry and Biophysics program, and the Musculoskeletal Research Center. McGrath's graduate, post-doctoral, and early faculty research was focused on quantitative experiments and mathematical modeling of cell migration covering molecular, cellular, and multi-cellular phenomena. This was true until 2007 when he, along with Professor Philippe Fauchet (now Dean at Vanderbilt) and PhD students Tom Gaborski (RIT) and Chris Streimer (Adarza), discovered a means to self-assembled nanopores in 15 nm thick free-standing silicon and demonstrated the remarkable transport properties of the new material in a Nature paper. This seminal discovery led to the creation of the multidisciplinary Nanomembrane Research Group (NRG) and the founding of SiMPore Inc. in the same year. The NRG and SiMPore have been dedicated to the advancement of ultrathin membrane technologies and exploring all of their potential applications ever since. This blog also dates back to 2007 and has had contributions from more than 100 students, faculty, scientists, engineers, and entrepreneurs. It contains over 2,500 pages and posts logging progress large and small over all these years. Yet somehow it feels like we are just getting started.
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