Micro-Wilhelmy and Related Liquid Property Measurements Using Constant-Diameter Nanoneedle-Tipped Atomic Force Microscope Probes

Abstract

The micro-Wilhelmy method is a well-established method of determining surface tension by measuring the force of withdrawing a tens of microns to millimeters in diameter cylindrical wire or fiber from a liquid. A comparison of insertion force to retraction force can also be used to determine the contact angle with the fiber. Given the limited availability of atomic force microscope (AFM) probes that have long constant diameter tips, force-distance (F-D) curves using probes with standard tapered tips have been difficult to relate to surface tension. In this report, constant diameter metal alloy nanowires (referred to as "nanoneedles") between 7.2 and 67 microm in length and 108 and 1006 nm in diameter were grown on AFM probes. F-D and Q damping AFM measurements of wetting and drag forces made with the probes were compared against standard macroscopic models of these forces on slender cylinders to estimate surface tension, contact angle, meniscus height, evaporation rate, and viscosity. The surface tensions for several low molecular weight liquids that were measured with these probes were between -4.2% and +8.3% of standard reported values. Also, the F-D curves show well-defined stair-step events on insertion and retraction from partial wetting liquids, compared to the continuously growing attractive force of standard tapered AFM probe tips. In the AFM used, the stair-step feature in F-D curves was repeatably monitored for at least 0.5 h (depending on the volatility of the liquid), and this feature was then used to evaluate evaporation rates (as low as 0.30 nm/s) through changes in the surface height of the liquid. A nanoneedle with a step change in diameter at a known distance from its end produced two steps in the F-D curve from which the meniscus height was determined. The step features enable meniscus height to be determined from distance between the steps, as an alternative to calculating the height corresponding to the AFM measured values of surface tension and contact angle. All but one of the eight measurements agreed to within 13%. The constant diameter of the nanoneedle also is used to relate viscous damping of the vibrating cantilever to a macroscopic model of Stokes drag on a long cylinder. Expected increases in drag force with insertion depth and viscosity are observed for several glycerol-water solutions. However, an additional damping term (associated with drag of the meniscus on the sidewalls of the nanoneedle) limits the sensitivity of the measurement of drag force for low-viscosity solutions, while low values of Q limit the sensitivity for high-viscosity solutions. Overall, reasonable correspondence is found between the macroscopic models and the measurements with the nanoneedle-tipped probes. Tighter environmental control of the AFM and treatments of needles to give them more ideal surfaces are expected to improve repeatability and make more evident subtle features that currently appear to be present on the F-D and Q damping curves.

Damping behavior of bent fiber NSOM probes in water

“…Both measurements reveal the dramatic increase in damping followed by a progression to a steady-state value which is determined by the viscous damping of the probe oscillation. Similar overlap of the Q and rms curves is obtained when one raises the probe from the surface to break through the water-air interface at H ϳ500 m. However, in this case as more of the vertical part of the probe emerges from the water it effectively drags a progressively larger column of water which adheres to the flat end portion of the probe 21 ͑i.e., h max ϳ 2 times fiber diameter͒ creating the hysteresis effect shown in Fig. 3 for the high-k probe.…”

“…Ref. 21 has suggested that upon initial contact of their nanoneedle probe tip there appears a surface drag or squeeze damping force of the meniscus on the side walls of the probe caused by the large shear rates across the thin meniscus channel. In a separate experiment described in Sec.…”

“…3. The height h͑͒ of the meniscus surrounding a cylinder is given by 21 h͑͒ = R cos ln͓2.25/R͑1 + sin ͔͒, ͑2͒…”

“…The value for v is small ͑i.e., low-k probe v Ϸ 1. where "a" is a molecular cut-off length ͑chosen as 1 nm͒, which is used to avoid a singularity in the solution method. 21 The meniscus damping force is directly proportional to the product of the fiber radius and the viscosity and inversely proportional to the meniscus contact angle. It is only weakly dependent on the meniscus height through ln͑h/a͒.…”

“…Although the nature of this damping mechanism has not been investigated for bent fiber probes, one recent paper described the damping behavior of constant diameter nanoneedle probes ͑diametersϽ 400 nm͒ at an airliquid interface. 21 It was suggested that the damping at the interface was due to a surface drag or "squeeze damping" force of the meniscus on the side walls of the probe caused by the large shear rates across the thin meniscus channel. The authors constructed a model for meniscus damping based on capillary and wetting phenomena described in Ref.…”