Review of the importance of CPVC (II)

By: Julián A. Restrepo*

In the previous edition the fundamental theoretical part related to the concept of PVC (pigment concentration in volume) and CPVC (critical concentration of pigment in volume) was discussed, with PVC being defined as the volumetric relationship between the pigment system and the solids of the dry coating, being expressed mathematically as:

PVC=V_P
V_P + V_R (1)

being
V_P: Volume of the pigment system of the coating
V_R: Volume of binder or resin solids

Where the pigmentary system is considered as the set of all the pigments present in the paint (active and inactive pigments).

To determine the value of the CPVC, in a boldly brief way, an equation is presented that can be used for its mathematical determination and other related expressions. The author has also considered a third part, in which he will try to explain in a practical way the usefulness of knowing the CPVC.

Deduction of a general expression for CPVC [2]
Bearing in mind the concepts discussed above, from the initial expression given for PVC (equation 1) CPVC can be defined as:

PVC= V_P       
V_P + V_R.C (2)

where,
V_P: Volume of the pigment system of the coating
V_R.C.: Volume of binder solids in the CPVC

The above expression can be rewritten as:

CPVC = (1 + V_R.C  )^-1 (3)
V_P         

and bearing in mind that: Volume = mass/density, one obtains:

CPVC = (1 + IA_m. _P  )^-1 (4)  
100 _m.h

where,
IA_m: It is the absorption rate (IA) of the pigment mixture determined in a moisturizing medium (m.h.), and expressed in units of (gr. of humectant medium)/(100 gr. of pigment).
_P: It is the specific gravity of the pigment mixture
_m.h.: It is the specific gravity of the wetting medium in which the MEASUREMENT of the AI was made.

It is necessary to bear in mind that the oil absorption index is commonly reported in mass units, but it can also be found in volumetric units, such as (mL of wetting medium / 100 gr. of pigment). Thus, the success of equation (4) will depend on the choice of the wetting medium and special care must be taken with the UNITS of the IA: In the deduction of this equation it has been established that the wetting medium must correspond to the polymer binder (100% solids) used as a resin in the analyzed coating, considering that the vast majority of resins conventionally used in solvent-based paints are supplied by the manufacturer in liquid form, containing these a fraction of volatile component.

In reality, measuring the AI with the liquid resin does not provide a realistic value of the AI of the pigment mixture, since when the resin is dissolved in the solvent, it does not have the same wetting characteristics that it would have 100% solids.

If we remember that the CPVC is defined as the value of pvc where there is just enough resin to moisten and completely fill the spaces between the particles of the pigment system, and bearing in mind that the test for the determination of the oil absorption index, where the end point of the test is established as the point where there is just enough of a moisturizing medium (linseed oil, whose quality is established according to the ASTM D-281 standard [3]), to completely moisturize a given amount of pigment, we warn that both definitions are equivalent. For this reason, it is accepted, in solvent-based coatings, that the measurement of AI is a parameter that allows to establish with a good degree of precision the measurement of the CPVC [2a].

On the other hand, for water-based coatings (those that use resins in aqueous dispersion), there is no "so successful" measurement of CPVC from AI (in this case, WAI is analyzed and not OAI since water, as a wetting medium, better represents the wetting characteristics of a resin in aqueous dispersion) [2b]. The fact that the "water-based resin" is in dispersion substantially modifies its wetting characteristics, presenting a lower binding capacity (defined by Berardi as Binder Power Index -BPI- [4]).

Because flaxseed oil is a 100% liquid binder of solids it is the "ideal binder" to be used as a moisturizing medium in the absorption test. But it is necessary to keep in mind how well flaxseed oil reproduces the wetting characteristics of the pigment system, just as the resins used in conventional solvent-based paints will.

Thus, examining more rigorously, we will realize that flaxseed oil will moisturize the pigment in a very similar way to how polymeric binders of the same chemical or close nature will do it, such as alkyd resins, a Body oil or a urethanic oil. While the greatest differences in wetting will have them with those resins with which it has greater physical-chemical differences, such as epoxy resins, amminic (either urea-formaldehyde, polyamine or polyamide) or unsaturated polyesters. Thus, flaxseed oil has spread as the moisturizing medium par excellence to determine the AI because it offers, among the different binders used in conventional paints, very similar characteristics of wetting to this type of resins.

Determination of CPVC in solvent-based systems [2]

UPVC = (1+ OIA_m. _P)^-1 (5)

93,5

where,
OAI_m: It is the absorption index of flaxseed oil of the pigmentary system
_P: It is the specific gravity of the pigment mixture

Recalling that the expression of the CPVC as a function of the UPVC is given by:

CPVC = UPVC - UPVC² ( d )³ (6)
                                               ^D
being
                _n
OAI_m = [ E ( X_i   ) ] ^-1 (7)
                 ^{i     OAI_i}

              _n
_P = [ E ( Xi ) ] ^-1 (8)
              ^{i       i}

The PVC/CPVC ratio
The mathematical relationship between PVC and CPVC was jointly defined by Bierwagen and Hay [5] as the reduced PVC or lambda parameter, being expressed by:

Λ = PVC (9)

CPVC

Currently this parameter is also called simply as PVC/CPVC ratio, using the Greek letter lambda (Λ) to denote it.

The level of pigmentation of the paint, which is given by PVC, depends on different requirements such as its viscosity, brightness, hardness, chemical resistance, cost, among others, and its relationship with the CPVC will define the porosity and permeability of the film. Thus, if the level of pigmentation is changed, the protective properties of the coating change, which makes the process of optimizing the formulation of a coating can be considered a complex process [6].

Final comments
The PVC/CPVC ratio is important considering that different types of systems have shown that their performance depends closely on this parameter, since the pigment system has an important role in the final performance of the coating.

Considering that the experimental determination of CPVC can involve an invaluable investment of time and money, the importance of mathematically establishing the CPVC of a coating is here, which will allow us to formulate coatings in a more versatile way.

We must bear in mind the importance of manufacturing paints that present an excellent dispersion: when you have the best dispersion of the system we have an "ideal dispersion" condition and the coating has the maximum CPVC that it can achieve, which allows the formulator to develop products that present an excellent cost/benefit ratio.
Finally, as an author I offer my excuses for presenting this topic in such a brief way, since its importance merits writings of a greater length, for this reason I have tried to divide it into various parts, always trying to preserve the technical rigor.

Dedication
This work is dedicated to the memory of D. Francisco Martínez (Q.E.P.D.), who had an important influence on my training in the world of paintings, especially in my beginnings and whom I have deeply admired.

References
[1] Restrepo, J.A. "A review of the importance of critical pigment concentration, p1. Fundamentals." Inpralatina, Vol. 14, No. 6, Nov./Dec. 2009.
[2] a) Restrepo, J.A. "A technical look at the theoretical determination of CPVC in solvent-based coatings". REC, No 11, Dec. 2006, pp. 7-14; b) Restrepo, J.A. "Predictive calculations of CPVC in water-based paints". Paper presented at Andina Paint: "Francisco Martínez", Medellín (Colombia), March 2005; c) Restrepo, J.A. "Practical Analysis of the PVC/CPVC relationship in anticorrosive paints". Paper presented at Eurocoat 2009, Barcelona (Spain), Sept. 29 to Oct. 1.
[3] ASTM D 281-84: "Standard Test Method for oil Absorption of pigments by Spatula Rub-out"
[4] Berardi, P. "Parameters affecting the CPVC of resins in aqueous dispersions". Paint technology, 27, 24, July (1963), p. 24.
[5] Bierwagen, G.P. and Hay, T.K. "The reduced pigment volume concentration as an important parameter in interpreting and predicting the properties of organic coatings". Prog. Org. Coat., 281, No. 3, (1975), pp. 281-303.
[6] Erich, S.J.F., Huinink, H.P., Adan, O.C.G., Laven, J. and Esteves, A.C. "The influence of the pigment volume concentration on the curing of alkyd coatings: A 1D MRI depth profiling study". Prog. Org. Coat., 63 (2008), pp. 399-404.

* Pinturas Sapolín - Invesa S.A.
[email protected]
Girardota, Colombia