The major research thrusts in our program include: (1) multi-scale modeling of physical systems, integrating information from the quantum to the continuum levels, (2) experimental and computational scanning probe microscopy, (3) fundamental developments in the characterization of viscoelastic behaviors involving multiple retardation times through atomic force microscopy (AFM), and (4) application of quantum computing to study electronic structure.
1. Multi-scale modeling of physical systems, integrating information from the quantum to the continuum levels
Many physical systems are difficult or prohibitively expensive to characterize experimentally due to factors such as sophisticated equipment requirements, small scales, or elusive behaviors. In such cases, computational modeling offers a viable alternative to obtain high quality information at a much lower cost and/or in a reasonable amount of time. In order to obtain accurate results, each phenomenon must be treated at its proper time- and length-scale with the correct method, and information obtained across different scales must be rigorously integrated. In some cases, the simulation requires additional layers, such as modeling of the controls system of an instrument like the atomic force microscope (AFM), which can be operated using a wide variety of imaging modes. Over the years we have specialized in this type of modeling for systems involving physical phenomena that range from the quantum to the continuum level, often combining computation and experimentation in our studies. A representative example is the feasibility study of imaging sub-atomic features with AFM, which combined computational quantum mechanics with AFM dynamics (Nano Lett. 2011, 11, 5026). A second, relevant example was the study of a photodetector based on a molybdenum telluride strip that was subject to strong dispersion forces from the substrate, which introduced strain that changed its bandgap (Nature Photonics 2020, 14, 578; led by our former colleague, Prof. Volker Sorger).
2. Experimental and computational scanning probe microscopy
The first bimodal AFM method (Garcia et al., Appl. Phys. Lett. 2004, 84, 449) introduced a family of techniques involving the simultaneous excitation of the AFM cantilever at more than one frequency, expanding the number of information channels acquired during a single 2D sample scan. The various excitation frequencies can be used to drive either a single cantilever eigenmode or multiple eigenmodes. Our objective is to develop new techniques, primarily through the excitation of multiple cantilever eigenmodes, that allow simultaneous performance of multiple characterization tasks. An example is trimodal AFM (ACS Nano 2013, 7, 10387), which allows simultaneous topographical imaging, compositional mapping and control of the tip-sample indentation, thus offering new capabilities for the subsurface visualization of soft matter. We have also explored tetra- and pentamodal imaging modes (Beilstein J. Nanotech. 2014, 5, 1637) for the study of viscoelastic materials that have multiple characteristic times. We dedicate a significant portion of our efforts to computationally model the subtleties involved in the AFM measurement process, which are often neglected during routine characterization. This is useful in terms of correctly interpreting experimental results, in terms of predicting behaviors and capabilities for future experimental verification or implementation, and in terms of identifying challenges and complexities that offer new research opportunities. We have modeled a variety of AFM methods, including amplitude-modulation (J. Phys. Chem. B 2004, 108, 13613; J. Phys. Chem. B 2005, 109, 11493), frequency-modulation (Meas. Sci. Technol. 2007, 18, 592; J. Phys. Chem. B 2007, 111, 2125; J. Phys. Chem. C 2007, 111, 10029), various modes of multifrequency AFM (Measurement Sci. & Technol. 2010, 21, 125502; ACS Nano 2013, 7, 10387), band excitation (Nanotechnology 2012, 23, 015706; Small 2012, 8, 1264) spectral inversion (Nanotechnology 2010, 21, 075702), higher-harmonics imaging (Nano Lett. 2011, 11, 5026; Appl. Phys. Lett. 2012, 100, 163104; J. Phys. D: Appl. Phys. 2013, 46, 155307), Kelvin probe force microscopy (Beilstein J. Nanotech. 2018, 9, 1272), single-impact viscoelastic characterization (based on band excitation, Sci. Rep. 2018, 8, 7534; Sci. Rep. 2019, 9, 12721), and quasi-static viscoelastic characterization (details provided below, in the description of the next project).
3. Fundamental developments in the characterization of viscoelastic behaviors involving multiple retardation times through AFM
Numerous emerging nanoscale technologies are based on viscoelastic materials, such as polymers and biological structures, whose behavior depends on their prior deformation history. Exploration of these materials with scanning probe microscopy methods can lead to a deeper understanding of the relationships between their nanomechanical properties and their performance in actual scientific and engineering applications. We are thus interested in developing routes towards the measurement of meaningful viscoelastic quantities (e.g., retardation times, frequency dependent loss angle and moduli, time dependent compliance, etc.) from AFM data, through existing experimental procedures such as tapping mode AFM, static force spectroscopy, and multifrequency AFM. Our approach involves (i) the development of tailored mathematical expressions and numerical fitting techniques based on rigorous models, such as the generalized Maxwell viscoelastic model (J. Pol. Sci B: Pol. Phys. 2017, 55, 804), (ii) computational modeling of realistic time-intensive viscoelastic behaviors (Beilstein J. Nanotech. 2014, 5, 2149; Beilstein J. Nanotech. 2016, 7, 554), and (iii) experimental validation on systems of interest such as polymers (Beilstein J. Nanotech. 2020, 11, 922; J. Appl. Phys. 2022, 131, 165101; Soft Matter, 2023, 19, 451-467) and biological systems (Nanoscale 2019, 11, 8918; Comm. Biol. 2022, 5, 17).
4. Application of quantum computing to study electronic structure
This project is led by Prof. Daniel Sierra-Sosa in collaboration with Prof. Gregorio Toscano, both from our Computer Science Department. In quantum computing (QC), a physical quantum system is used as a quantum simulator, whose time evolution mimics that of the system under study. In our project we seek to calculate the electronic structure of large, template-based molecular systems, such as polymers, which have repeating units. The approach follows the principles of the Fragment Molecular Orbital (FMO) method introduced by Kitaura and coworkers (Chem. Phys. Lett. 1999, 312, 319), which enables rapid calculations of the energy of large molecular clusters using molecular orbital methods (MO). In this method, one performs MO calculations on the molecules and the molecular pairs in the system, without explicitly performing a calculation on the whole system, thus significantly reducing the computation time. We intend to build on existing implementations of FMO in QC, such as the hybrid quantum-classical Variational Quantum Eigensolver (VQE) calculations performed on hydrogen clusters by No and coworkers (Sci. Rep. 2024, 14, 2422).