Surface potentials force-distance curves

In practice, the position where the motion of the probe complies with the piezo movement defines the point of zero distance. Force-distance curves recorded with AFM depend on the specific geometry of the probe and the surface. Usually, the interaction is displayed as the force divided by the radius of the colloid, R, in units N/m. The Derjaguin approximation relates this quantity to the interaction potential per unit area between equivalent flat surfaces at given separation distance, see (2.29). 

Figure 5. (a) Force—distance curves recorded upon compression of PLL(20)-g-PEG(2) polymer adlayers on niobiaby aSi02 microsphere in 10 mM HEPES buffer solution (pH 7.4), with PEG chain densities from 0 to 0.54 PEG nm". (b) Surface potential from DLVO fits (not shown) as a function of the grafting ratio, g, of the PLL-g-PEG polymer, highlighting charge reversal at g = 4. 

Total internal reflection microscopy enables the measurement of colloidal forces down to weak forces of 10 fNf under conditions of free Brownian motion that may better resemble true colloidal systems compared to other methods where force distance curves are recorded via enforced movement of surfaces. However, its application is limited to transparent surfaces and repulsive interaction potentials. Magnetic tweezers allow the measurement of forces down to 10 pN. Therefore, magnetic tweezers have mainly been applied to the measurement of molecular interactions. One advantage is the possibility to apply a defined torque, which has made them the most prominent tool to study twisting of molecules such as DNA. 

Protems can be physisorbed or covalently attached to mica. Another method is to innnobilise and orient them by specific binding to receptor-fiinctionalized planar lipid bilayers supported on the mica sheets [15]. These surfaces are then brought into contact in an aqueous electrolyte solution, while the pH and the ionic strength are varied. Corresponding variations in the force-versus-distance curve allow conclusions about protein confomiation and interaction to be drawn [99]. The local electrostatic potential of protein-covered surfaces can hence be detemiined with an accuracy of 5 mV. 

Consider a molecule above a surface with the distance from the surface being normal to the surface. There are two competitive types of influence occuring (a) repulsion between the cloud of electrons in the atoms that form the surface and those of the molecule and (b) van der Waals nuclear attraction force. The nuclear attraction has a much shorter radius of influence and as a result of the balance of these two forces, there is a well in the potential energy curve at a short distance from the surface, as shown in Figure 2.1. Molecules or atoms that reach this well are trapped or adsorbed by this potential energy well and cannot escape, unless they obtain enough kinetic energy to be desorbed. 

Figure 2.14 Measured electrostatic double-layer and van der Waals forces between two surfaces of curved mica of radius 1 cm in (a) water and (b) dilute KNO3 and Ca(N03)2 solutions. The lines are the predictions of the DLVO theory with a Hamaker constant of 2.2 x 10 J in the limits of constant surface charge and constant surface potential here xfrQ = -(j/s, the particle surface potential. (The lines for constant surface charge are slightly higher than those for constant surface potential at small D.) The inset in (b) is the measured force in 0.1 M KNO3, which shows a force minimum at a distance of around 7 nm. Since this minimum in force occurs away from the deep minimum at the surface, it is called a secondary minimum. (From Israelachvili and Adams 1978 and Israelachvili 1992, reprinted with permission from Academic Press.)...

The Derjaguin approximation can be applied to any type of force law, such as attraction, repulsion, or oscillation, if D is much less than the radii of the spheres. This has been verified experimentally and is very useful for interpreting experimental force data. The Derjaguin approximation shows that, even though the same pair-potential force is operating, the distance dependence of the force between two curved surfaces is guite different from that between two flat surfaces. 

The interaction energy potential is generally easier to derive for flat surfaces on the other hand, it is usually more accurate to measure the force-distance relation (F(Z))) between two curved surfaces, because the interaction area is precisely definable. The relationship between U D) per unit area for two flat surfaces and F D) between two curved surfaces is given by the Deijaguin approximation (Deijaguin 1934) which is derived for the close approach of two spheres of radii R and Ri ... 

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