Research Interests

Theoretical Studies in Surface Physics, Fractals, and Quantum Dynamics

We study the extraordinary physical properties of solids and materials with a fractal surface.  Many functional properties depend on the surface geometry (rough, porous, convoluted) only through the fractal dimension and related exponents, providing powerful predictions of the response of the surface to different external interactions.  Examples of such interactions are:
 

• Wetting: We study roughness-induced transitions of liquid films from van der Waals wetting to capillary wetting (complete wetting), including metastable film configurations.  Applications have included structure determinations of rough Ag electrodes and porous carbon fibers.  For partially wetting liquids, we study the contact angle on hierarchically terraced surfaces.
• Scattering: We develop models to extract structural information from small-angle X-ray and neutron scattering data and test the models against other experimental data.  Examples are activated carbons crisscrossed by a fractal network of nanopores (with applications for methane storage) and large-scale fluctuations in phase-separated lipid membranes.  In the optical regime, we are interested in the design of surface architectures with optimum light-harvesting properties.
• Diffusive currents: We study diffusion (mass/heat flux) to and across convoluted surfaces, resulting in nonlinear transport by the competition of screening and transfer across the surface.  One investigation focuses on the lung, in which the space-filling surface spanned by the alveoli creates a respiratory system with remarkable optimal performance and error tolerance.  Biomimetic applications explore catalysts tolerant to self-poisoning, control of chemical vapor deposition in device fabrication, and methane transport in and out of carbon nanopores.

In a different line of research we have derived inequalities and a variational principle which give upper and lower bounds for the time evolution of a quantum system without solving the time-dependent Schrödinger equation.  Current work focuses on semiclassical wave-packet propagation and estimates of the decoherence time in quantum computing.

P. Pfeifer and B. Sapoval, "Optimization of Diffusive Transport to Irregular Surfaces with Low Sticking Probability".  Mat. Res. Soc. Symp. Proc. 366, 271-276 (1995).

P. Pfeifer and J. Fröhlich, "Generalized Time-Energy Uncertaintay Relations and Bounds on Life Times of Resonances".  Rev. Mod. Phys. 67, 759-779 (1995).

P.W. Schmidt, F. Ehrburger-Dolle, P. Pfeifer, T. Rieker, Y.M. Kapoor, and D.J. Voss, "Investigation of Aggregate Structures on Length Scales from About 5 to 10,000 Å".  Mat. Res. Soc. Symp. Proc. 407, 399-404 (1996).

P. Pfeifer and K.Y. Liu, "Multilayer Adsorption as a Tool to Investigate the Fractal Nature of Porous Adsorbents".  Stud. Surf. Sci. Catal. 104, 625-677 (1997).

F. Ehrburger-Dolle, T. Rieker, M.T. Gonzalez, M. Molina-Sabio, F. Rodriguez-Reinoso, P. Pfeifer, and P.W. Schmidt, "Oxidation Processes and Fractal Properties of Activated Carbons".  In: Fractals and Chaos in Chemical Engineering, eds. M. Giona and G. Biardi (World Scientific, Singapore, 1997), pp. 27-38.

P. Pfeifer and P.J. Hagerty, "Screening Transition in Diffusion to and across Fractal Surfaces".  In: Fractals and Chaos in Chemical Engineering, eds. M. Giona and G. Biardi (World Scientific, Singapore, 1997), pp. 151-164.

P. Pfeifer, F. Ehrburger-Dolle, T. Rieker, P.W. Schmidt, D.J. Voss, F. Rodriguez-Reinoso, M. Molina-Sabio, and M.T. Gonzalez, "Fractal Networks of Carbon Nanotubes".  In: Carbon '97, Vol. I, eds. P.A. Thrower and L.R. Radovic (Pennsylvania State University, University Park, 1997), pp. 350-351.

P. Pfeifer, "Is Nature Fractal?"  Science 279, 784 (1998).

P. Pfeifer, "Pore Fractals and Invasion Percolation in Activated Carbons".  In: International Symposium on Carbon—Science and Technology for New Carbons, ed. M. Inagaki (Carbon Society of Japan, Tokyo, 1998), p. 160-161.

T.A. Brown, M.D. McBurnett, and P. Pfeifer, "Dynamical Elites on a Lattice".  In: Renaissance in Social Science Computing, ed. O.V. Burton (University of Illinois Press, 1998), pp. 243-258.

S. Gheorghiu and P. Pfeifer, "Standard and Nonstandard Roughness".  In: Proceedings of the 4th Conference on Fractals in Engineering, eds. M. Dekking, J. Lévy-Véhel, E. Lutton, and C. Tricot (Institut National de Recherche en Informatique et en Automatique, Paris, 1999), pp. 272-280.

P. Pfeifer and S. Gheorghiu, "Fractal Respiratory Membranes: Self-Similar Lung vs. Self-Affine Gill".  In: VI Latin American Workshop on Nonlinear Phenomena, ed. G. Raggio (Universidad Nacional de Córdoba, Argentina, 1999), p. 42.

A. Gabke, C. Czeslik, R. Winter, and P. Pfeifer, "Power-Law Fluctuations in Phase-Separated Lipid Membranes".  Phys. Rev. E 60, 7354-7359 (1999).

S. Gheorghiu and P. Pfeifer, "Nonstandard Roughness of Terraced Surfaces".  Phys. Rev. Lett., submitted.

P. Pfeifer, K.Y. Liu, and P.J. Hagerty, "Wetting Transition and Screening Transition on Fractal Surfaces: Critical Phenomena Which Do Not Exist on Flat Surfaces".  Phys. Rev. E., submitted.