for particle PDMS surface electrostatics interaction, there are a number of formula, some of them use constant charge, some of them potential, some of them uses charge regulation. how to correlate with AFM data?
For large distances (several Debye lengths) between the interacting particles, there's no difference.
For small distances, the first particle affects the electrostatic potential at the surface of the second, causing change of the adsorption of all ionic species there.
Constant charge means that the adsorbed charge does not change. This corresponds to the highest possible interaction (highest repulsion, in case of two equivalent surfaces).
In reality, when two positively charged particles are close to each other, the repulsion leads to the positive ions being desorbed (or similarly, negative ions being adsorbed). This leads to smaller interaction.
The largest decrease one can get is the one between metal particles of fixed potential (two grounded spheres). Theory says you cannot get a larger drop of the surface charge then this fixed surface potential case.
The reality is always between these two limiting cases. Instead of adsorption = const or potential = const, a condition for chemical equilibrium is valid, i.e. an adsorption isotherm, such as Davies isotherm (Gamma = Ka*C*exp(-e*phi/kT) + Gouy equation).
I might assume you are considering results from force-distance curves with AFM. The equations for force in a constant charge or a constant potential situation are different. The equations are also different in whether they are derived from a statistical charge distribution analysis or from a Gibb's energy analysis as well as where they make approximations in specific terms in the equations. At the end, you will have a number of different equations as you note. In all cases, the differences become apparent especially within and below the range of the Debye length. The physical meaning of each case is also different. In this set of options, the best approach is to know as much of the physics and chemistry of your system at the start and then apply what can be said to be the best model equation to the AFM data for the system. The sphere-plat system is a well-defined one to test the equations.
I hope this is the direction of answer that you seek.
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Modeling
- Analyses of Variance
- ANOVA