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VISCAL07








Viscosity of Pigmented Polymer Blends

This program utilizes the FOX, WLF and Mooney equations to calculate the viscosity of pigmented blends.
As many as four polymers, polymer solutions or oligomers and as many
as four pigments can be used in this calculation. Because of the
potential for higher packing densities with pigments with a wide
particle size distribution, this program will give higher
estimated viscosities than actually measured.

The WLF equation is used to calculate the glass transition temperature (Tg) of a polymer, oligomer or an solution. This information is used in conjunction with the
FOX equation to obtain the Tg of a polymer blend and the resulting viscosity of the blend.

WLF equation Viscosity
(log)= C A(TTg)/(B+TTg) This program uses a modification of this equation, which uses universal constants according to
Nielsen. These universal constants are reasonable accurate for
most polymers. If a deviation is found for a series of polymers these constants can be readjusted.

Fox equation 1/Tgb = W1/Tg1 + W2/Tg2 +Wn/Tgn; W1, W2, Wn = weight fraction of polymer or polymer solutions;
Tg1, Tg2, Tgn = Tg of polymer or polymer solution.

As input the viscosity, solids and temperature of the polymer solution is required. Hydroxyl numbers of the blend can also be calculated.

The Mooney equation
logφ = logφ_{e} +
keVi/(2.303(1Vi/φ)
permits to calculate the viscosity of pigmented formulations.
ke
and
φ are constants for spherical particles. For flocculated systems different constants are used, these constants can be adjusted for different degrees of flocculation.
Vi
is the volume phase of the dispersed phase. Adsorbed resin increases the amount of dispersed phase, the amount of resin adsorbed can be adjusted in the equation.

Input


Measured Data





Polymers


Solids

Density

VISC.

OH number

Temperature

Solvent

WLF EQUATION



%

g/ml

CPS

as supplied

°C

%

Constants (Nielsen)

Polymer

1







C=


Polymer

2







A=


Polymer

3







B=


Polymer

4









Polymer Blend


Amount

Polymer

Hydroxyl

Solvent





Polymer

1









Polymer

2









Polymer

3









Polymer

4









Total










Nonvolatile, %










Hydroxyl number










Input Pigmentation










VISCAL14


Pigment

Density



MOONEY EQUATION




amount

g/ml

Pigment


logφ = logφ_{e} +
keVi/(2.303(1Vi/φ)

Pigment

1





Unflocculated

Flocculated


Pigment

2





ke =




Pigment

3





φ=




Pigment

4









Total










Resin absorbed










Pigment to Binder ratio










Temperature










Pigment Density, average g/ml










Resin g/ml










Results



Viscosity, Poise




Resin blend

Resin

Pigmented Paint

Pigment Paint Resin absorbed


Volume fraction pigment,
Vi


Tg


Unflocculated

Flocculated

Unflocculated

Flocculated












Relative viscosity




















WLF equation
M.L.Williams, R.F.Landel and J.D.Ferry, J.Am.Chem.Soc.77,3701(1955)


L.E.Nielsen, Polymer Rheology, Marcel Dekker, 1977,pp.33,74,133

