In order to determine the origin of image contrast in piezoresponse force microscopy (PFM), analytical descriptions of the complex interactions between a small tip and ferroelectric surface are derived for several sets of limiting conditions. Image charge calculations are used to determine potential and field distributions at the tip-surface junction between a spherical tip and an anisotropic dielectric half plane. Methods of Hertzian mechanics are used to calculate the response amplitude in the electrostatic regime. In the electromechanical regime, the limits of strong (classical) and weak (field-induced) indentation are established and the relative contributions of electroelastic constants are determined. These results are used to construct ''piezoresponse contrast mechanism maps'' that correlate the imaging conditions with the PFM contrast mechanisms. Conditions for quantitative PFM imaging are set forth. Variable-temperature PFM imaging of domain structures in BaTiO 3 and the temperature dependence of the piezoresponse are compared with GinzburgDevonshire theory. An approach to the simultaneous acquisition of piezoresponse and surface potential images is proposed. In order to determine the origin of image contrast in piezoresponse force microscopy ͑PFM͒, analytical descriptions of the complex interactions between a small tip and ferroelectric surface are derived for several sets of limiting conditions. Image charge calculations are used to determine potential and field distributions at the tip-surface junction between a spherical tip and an anisotropic dielectric half plane. Methods of Hertzian mechanics are used to calculate the response amplitude in the electrostatic regime. In the electromechanical regime, the limits of strong ͑classical͒ and weak ͑field-induced͒ indentation are established and the relative contributions of electroelastic constants are determined. These results are used to construct ''piezoresponse contrast mechanism maps'' that correlate the imaging conditions with the PFM contrast mechanisms. Conditions for quantitative PFM imaging are set forth. Variable-temperature PFM imaging of domain structures in BaTiO 3 and the temperature dependence of the piezoresponse are compared with Ginzburg-Devonshire theory. An approach to the simultaneous acquisition of piezoresponse and surface potential images is proposed.

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We have developed a controlled and highly reproducible method of making nanometer-spaced electrodes using electromigration in ambient lab conditions. This advance will make feasible single molecule measurements of macromolecules with tertiary and quaternary structures that do not survive the liquid-helium temperatures at which electromigration is typically performed. A second advance is that it yields gaps of desired tunnelling resistance, as opposed to the random formation at liquid-helium temperatures. Nanogap formation occurs through three regimes: First it evolves through a bulk-neck regime where electromigration is triggered at constant temperature, then to a few-atom regime characterized by conductance quantum plateaus and jumps, and finally to a tunnelling regime across the nanogap once the conductance falls below the conductance quantum.Electromigration has recently been successfully employed to make nanometer-spaced electrodes for single molecule devices [1,2,3,4]. The typical procedure entails an abrupt break at liquid-helium temperatures that yields a nanogap with a random tunnelling resistance [4,5,6,7,8]. However, this procedure makes gaps at room temperature which are typically too large for molecular measurements [6]. This hinders the application of the typical electromigration procedure to molecules which do not survive a sub-freezing environment, such as macromolecules that feature modest thermodynamic stability of their respective tertiary and quaternary structures.We have developed an electromigration procedure that is completely performed in ambient laboratory conditions and yields a controllable nanogap resistance to within a factor of about three of the target value in the 0.5 MΩ to 1 TΩ range. The electromigration procedure evolves through three regimes. At large conductance (G), local heating increases Au mobility and triggers electromigration in the metallic neck at a critical temperature. When the neck narrows to the few-atom regime it shows jumps and plateaus near multiples of the conductance quantum (G o = 2e 2 /h) and a sharp decrease in the critical temperature. A tunnelling regime is entered once G falls below G o accompanied by formation of a nanogap.We first fabricate two overlapping Au leads (each 8-30 nm thick) using electron-beam lithography and doubleangle evaporation of Au (Fig. 1a). An initial 3 nm thick Cr layer (deposited normal to surface) helps the contact * Electronic Address: drstrach@sas.upenn.edu † Electronic Address: cjohnson@physics.upenn.edu FIG. 1: (a) Field-emission SEM micrograph of electrodes before electromigration. (b) Nanogap after electromigration.pads adhere to the SiO 2 substrate while a final 40 nm thick layer of Au on the contacts reduces the resistance to between 100-200 Ω at room temperature. At room temperature and atmospheric pressure, we perform controlled electromigration with a succession of voltage (V ) ramps while monitoring the current (I) and conductance of the leads (Fig. 2). We make an initial measurement of G and compare this to later mea...

Amphiphilic, linear conjugated poly[p-{2,5-bis(3-propoxysulfonicacidsodiumsalt)}phenylene]ethynylene (PPES) efficiently disperses single-walled carbon nanotubes (SWNTs) under ultrasonication conditions into the aqueous phase. Vis-NIR absorption spectroscopy, atomic force microscopy (AFM), and transmission electron microscopy (TEM) demonstrate that these solubilized SWNTs are highly individualized. AFM and TEM data reveal that the interaction of PPES with SWNTs gives rise to a self-assembled superstructure in which a polymer monolayer helically wraps the nanotube surface; the observed PPES pitch length (13 +/- 2 nm) confirms structural predictions made via molecular dynamics simulations. This work underscores design elements important for engineering well-defined nanotube-semiconducting polymer hybrid structures.