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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.

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. The Fox equation is normally used to calculate the Tg of
acrylic copolymers.

For this program as input the viscosity, solids and temperature of the polymer
solution/melt 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

Viscosity

Temp.

OH number

Solvent


WLF EQUATION





%

cps

°C

as supplied

%


Constants (Nielsen)



Polymer

1







C=




Polymer

2







A=




Polymer

3







B=




Polymer

4











Polymer Blend



Polymer

Solvent

Hydroxyl







Polymer

1











Polymer

2











Polymer

3











Polymer

4











Total












Nonvolatile, %












Hydroxyl number












INPUT Pigmentation












VISCAL14




MOONEY EQUATION



Unflocculated

Flocculated


Resin g/ml








ke =




Pigment g/ml




logφ =
logφ_{e} +
keVi/(2.303(1Vi/φ)


φ =




Resin absorbed on pigment












Pigment to Binder ratio












Temperature






















Results



Viscosity, Poise





Resin blend

Resin


Pigmented Paint


Pigmented 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




Resin adsorbed on
pigment. Increase in volume fraction of pigment by factor, Factor1 =
no adsorption



