Charge Density in Nanorings from Scanning Force Microscopy

Several systems of nanometer or sub–nanometer dimensions are electrically charged rings. For example, molecular pumps use electrically charged rings to link amino acids into growing peptides, the efficiency depending on charge magnitude and location. Knowledge of charge content is necessary to apply these pumps to assemble other architectures. More generally, charge plays a key role in the structure attained by large molecules when they self-assemble. Also, charged rings are current candidates as physical support of information storage for qubits for quantum computing. In addition, for applications in biosensing and nano-optoelectronics, micrometer and nanometer rings of charge have been synthesized from a variety of materials. For example, carbon nanorings with radii of a few have been obtained by self-assembly of carbonized pluronic P123. The most common gold nanoring has been synthesized by a variety of methods, while whole silver nanorings of diameter have been produced by solvothermal methods.<br/>These examples underscore the relevance of understanding electrostatic measurements at the nanoscale with the <b>SFM </b>(scanning force microscope), and in particular, to understand those measurements on charged ring structures. While the <b>SFM</b> sensor mechanically responds to electrostatic inputs, it is not straightforward to connect this response to the electrostatic content of the sample under study. Specifically, <b>SFM</b> records a force trace which varies as the sensor explores different regions of the sample. In this study, we propose a method to convert this force curve into charge density content in the sample. We first solve the direct problem, whereby the SFM force is computed from the assumed know charge density. Afterward, we move to the realistic practical situation in microscopy and address the inverse problem. In the inverse problem, forces are measured in each voxel of a volume region above the sample and, using that information as input, the charge on the ring is produced.