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VISCAL07
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Viscosity of Pigmented Polymer Blends
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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.
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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.
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WLF equation Viscosity
(log)= C- A(T-Tg)/(B+T-Tg) 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.
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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.
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As input the viscosity, solids and temperature of the polymer solution is required. Hydroxyl numbers of the blend can also be calculated.
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The Mooney equation
logφ = logφe +
keVi/(2.303(1-Vi/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.
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Input
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Measured Data
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Polymers
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Solids
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Density
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VISC.
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OH number
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Temperature
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Solvent
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WLF EQUATION
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%
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g/ml
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CPS
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as supplied
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°C
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%
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Constants (Nielsen)
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Polymer
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1
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C=
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Polymer
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2
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A=
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Polymer
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3
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B=
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Polymer
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4
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Polymer Blend
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Amount
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Polymer
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Hydroxyl
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Solvent
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Polymer
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1
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Polymer
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2
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Polymer
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3
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Polymer
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4
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Total
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Nonvolatile, %
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Hydroxyl number
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Input Pigmentation
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VISCAL14
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Pigment
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Density
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MOONEY EQUATION
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amount
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g/ml
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Pigment
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logφ = logφe +
keVi/(2.303(1-Vi/φ)
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Pigment
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1
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Un-flocculated
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Flocculated
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Pigment
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2
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ke =
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Pigment
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3
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φ=
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Pigment
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4
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Total
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Resin absorbed
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Pigment to Binder ratio
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Temperature
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Pigment Density, average g/ml
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Resin g/ml
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Results
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Viscosity, Poise
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Resin blend
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Resin
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Pigmented Paint
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Pigment Paint Resin absorbed
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Volume fraction pigment,
Vi
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Tg
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Un-flocculated
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Flocculated
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Un-flocculated
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Flocculated
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Relative viscosity
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WLF equation
M.L.Williams, R.F.Landel and J.D.Ferry, J.Am.Chem.Soc.77,3701(1955)
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L.E.Nielsen, Polymer Rheology, Marcel Dekker, 1977,pp.33,74,133
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