Surface forces apparatus

A Surface Force Apparatus uses piezoelectric positioning elements (in addition to conventional motors for coarse adjustments), and senses the distance between the surfaces using optical interferometry.[6] Using these sensitive elements, the device can resolve distances to within 0.1 nanometer, and forces at the 10⁻⁸ N level. This extremely sensitive technique can be used to measure electrostatic forces, elusive van der Waals forces, and even hydration or solvation forces. SFA is in some ways similar to using an atomic force microscope to measure interaction between a tip (or molecule adsorbed onto the tip) and a surface. The SFA, however, is more ideally suited to measuring surface-surface interactions, can measure much longer-range forces more accurately, and is well-suited to situations where long relaxation times play a role (ordering, high-viscosity, corrosion). The SFA technique is quite demanding, nevertheless, labs worldwide have adopted the technique as part of their surface science research instrumentation.

In the SFA, method two smooth cylindrically curved surfaces whose cylindrical axes are positioned at 90° to each other are made to approach each other in a direction normal to the axes. The distance between the surfaces at the point of closest approach varies between a few micrometers to a few nanometers depending on the apparatus. When the two curved cylinders have the same radius of curvature, R, this so-called 'crossed cylinders' geometry is mathematically equivalent to the interaction between a flat surface and a sphere of radius R. Using the crossed cylinder geometry makes alignment much easier, enables testing of many different surface regions for better statistics, and also enables angle-dependent measurements to be taken. A typical setup involves R = 1 cm.

An example SFA setup showing the various layers, using a geometrically equivalent model.

Position measurements are typically made using multiple beam interferometry (MBI). The transparent surfaces of the perpendicular cylinders, usually mica, are backed with a highly reflective material usually silver before being mounted to the glass cylinders. When a white-light source is shined normal to the perpendicular cylinders the light will reflect back and forth until it is transmitted at where the surfaces are closest. These rays create an interference pattern, known as fringes of equal chromatic order (FECO), which can be observed by microscope. Distance between the two surfaces can be determined by analyzing these patterns. Mica is used because it is extremely flat, easy to work with, and optically transparent. Any other material or molecule of interest can be coated or adsorbed onto the mica layer.

The force measurements of the SFA are based primarily on Hooke's Law,

${\displaystyle F=kx}$

where F is the restoring force of a spring, k is the spring constant and x is the displacement of the spring.

Using a cantilevered spring, the lower surface is brought towards the top surface using a fine micrometer or piezotube. The force between the two surfaces is measured by

${\displaystyle \Delta F(x)=k(\Delta x_{applied}-\Delta x_{measured})}$

where ${\textstyle \Delta x_{applied}}$is the change in displacement applied by the micrometer and ${\displaystyle \Delta x_{measured}}$ is the change displacement measured by interferometry.

The spring constants can range anywhere from ${\displaystyle 30\times 10^{5}{\frac {N}{m}}}$ to ${\displaystyle 5\times 10^{5}{\frac {N}{m}}}$.[2] When measuring higher forces, a spring with a higher spring constant would be used.

• Atomic force microscope
• Colloidal probe technique

• Surface Science & Technology, Swiss Federal Institute of Technology
• Australian National University, Research School of Physical Sciences and Engineering
• "The X-ray Surface Forces Apparatus: Structure of a Thin Smectic Liquid Crystal Film Under Confinement" Science 24 June 1994: Vol. 264. no. 5167, pp. 1915 - 1918
• "The x-ray surface forces apparatus for simultaneous x-ray diffraction and direct normal and lateral force measurements". Review of Scientific Instruments, 73 (6):2486-2488 (2002).