## Critical Pigment Volume Concentration, CPVC

### Quick Start

For optimal printing we generally need as much pigment as possible - but not too much because print quality (especially gloss) goes down rapidly. So how do we find out the Critical Pigment Volume Concentration before things go wrong, because there's not enough binder to enclose the pigment?

The answer is that it's easy to calculate from the pigment supplier's density and Oil Absorption values. So that's two inputs and one output. Why all the other inputs/outputs? Because we need to know our actual Pigment Volume Concentration to see if we are close to the CPVC. For this we need our weights of pigment and other components.

The graph shows where your PVC is relative to CPVC, and what happens to a key property (coating density) if you exceed it.

### CPVC

We often need a lot of pigment in our coating or ink once all the solvent used to coat/print has disappeared. The problem is that pigment particles, when close packed, have lots of empty space between them. If we do not fill that space with binder then the properties are compromised: gloss, rub resistance, adhesion etc. will be lower than desired.

For each pigment there is a Critical Pigment Volume Concentration, CPVC, above which there is not enough binder present to fill all the voids (assuming that our binder is able to flow into and fill all available spaces). Pigment suppliers give us the density, ρ of the pigment and a value which tells us the amount of void space, expressed as the Oil Absorption, OA, which is the amount of a standard oil that the dry pigment can absorb. Because this oil has a density of 0.935 the CPVC is calculated as:

`CPVC = 1/(1+"ρOA"/93.5)`

Now that we know the CPVC, all we need to know is our actual pigment volume concentration, the PVC. Typically we have a weight of dry pigment, then one or two extra "components", C1 and C2 (binders, fillers etc.) which are typically supplied as solutions. To get the PVC we need to convert our weight of pigment into volume (that's easy, it's g/ρ), then we have to take our g of component solution, the density of the solution, the % solids of the solution and the density of the solvent, from which the volume of the component can be calculated. Once we know all the volumes, the PVC is easy to calculate. If it exceeds the CPVC then it is shown up with a red background.

The complication for the app is that with 3 possible components, you have to adjust them individually so that the Total is 100g. If you accidentally miss getting close to 100%, the Total is shown up with a red background.

Various properties change with PVC and you can determine the CPVC from seeing where there is a sudden change. In the app the coating density, ρ_{c}, is used to illustrate how you might go about this. As the CPVC is exceeded, the density decreases because of the air.

Where ρ_{f} is the density of the formulation matrix and ρ_{p} the particle density, the equations used at volume fraction x are:

Below CPVC `ρ_c = ρ_px+(1-x)ρ_f`

Above CPVC `ρ_c = CPVC(ρ_p+((1-x)ρ_f)/x)`