Correlation Force Spectroscopy for Single Molecule Measurements

This thesis addresses development of a new force spectroscopy tool, correlation force spectroscopy (CFS), for the measurement of the mechanical properties of very small volumes of material (molecular to µm³) at kHz-MHz time-scales. CFS is based on atomic force microscopy (AFM) and the principles of CFS resemble those of dual-trap optical tweezers. CFS consists of two closely-spaced micro-cantilevers that undergo thermal fluctuations. Measurement of the correlation in thermal fluctuations of the two cantilevers can be used to determine the mechanical properties of the soft matter, e.g. a polymeric molecule, that connects the gap between the two cantilevers. Modeling of the correlations yields the effective stiffness and damping of the molecule. The resolution in stiffness is limited by the stiffness of the cantilever and the frequency by the natural frequency of the cantilevers, but, importantly, the damping resolution is not limited by the damping of the cantilever, which has enabled high-resolution measurements of the internal friction of a polymer. The concept of CFS was originally presented by Roukes' group in Caltech [Arlett et al., Lecture Notes in Physics, 2007]; I developed the first practical versions of CFS for experimentation, and have used it in two applications (1) microrheology of Newtonian fluids and (2) single molecule force spectroscopy. To understand the correlation in thermal fluctuations of two cantilevers I initially validated the theoretical approach for analyzing correlation in terms of deterministic model using the fluctuation-dissipation theorem [Paul and Cross, PRL, 2004]. I have shown that the main advantages of such correlation measurements are a large improvement in the ability to resolve stiffness and damping. Use of CFS as a rheometer was validated by comparison between experimental data and finite element modeling of the deterministic vibrations of the cantilevers using the known viscosity and density of fluids. Work in this thesis shows that the data can also be accurately fitted using a simple harmonic oscillator model, which can be used for rapid rheometric measurements, after calibration. The mechanical properties of biomolecules such as dextran and single stranded DNA (ssDNA) are also described. CFS measurements of single molecule properties of ssDNA reveal the internal friction of the molecule in solution.