Analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized single-chain model, such as the freely jointed chain model. To include bond stretching, the rigid links in the freely jointed chain model can be made extensible, but this almost always renders the model analytically intractable. Here, an asymptotically correct statistical thermodynamic theory is used to develop analytic approximations for the single-chain mechanical response of this model. The accuracy of these approximations is demonstrated using several link potential energy functions. This approach can be applied to other single-chain models, and to molecular stretching in general.

In this letter, we demonstrated stable nanoscale fracture in single-crystal silicon using an in-situ wedge-loaded double cantilever beam (DCB) specimen. The fracture toughness K_IC was calculated directly from instrumented measurement of force and displacement via finite element analysis with frictional corrections. Measurements on multiple test specimens were used to show K_IC= 0.72 ± 0.07 MPa m^1/2 on {111} planes and observe the crack-growth resistance curve in <500 nm increments. The exquisite stability of crack growth, instrumented measurement of material response, and direct visual access to observe nanoscale fracture processes in an ideally brittle material differentiate this approach from prior DCB methods. GRAPHICAL ABSTRACT IMPACT STATEMENT In-situ fracture toughness experiments on single-crystal silicon revealed stable nanoscale fracture and identified the shape of the crack-growth resistance curve, role of fabrication-induced artifacts, and origin of fracture surface features.

Analytic relations that describe crack growth are vital for modeling experiments and building a theoretical understanding of fracture. Upon constructing an idealized model system for the crack and applying the principles of statistical thermodynamics, it is possible to formulate the rate of thermally activated crack growth as a function of load, but the result is analytically intractable. Here, an asymptotically correct theory is used to obtain analytic approximations of the crack growth rate from the fundamental theoretical formulation. These crack growth rate relations are compared to those that exist in the literature and are validated with respect to Monte Carlo calculations and experiments. The success of this approach is encouraging for future modeling endeavors that might consider more complicated fracture mechanisms, such as inhomogeneity or a reactive environment.

A large array of elastically coupled micro cantilevers of variable length is studied experimentally and numerically. Full-scale finite element (FE) modal analysis is implemented to determine the spectral behavior of the array and to extract a global coupling matrix. A compact reduced-order (RO) model is used for numerical investigation of the array's dynamic response. Our model results show that at a given excitation frequency within a propagation band, only a finite number of beams respond. Spectral characteristics of individual cantilevers, inertially excited by an external piezoelectric actuator, were measured in vacuum using laser interferometry. The theoretical and experimental results collectively show that the resonant peaks corresponding to individual beams are clearly separated when operating in vacuum at the third harmonic. Distinct resonant peak separation, coupled with the spatially confined modal response, make higher harmonic operation of tailored, variable-length cantilever arrays well suited for a variety of resonant-based sensing applications.