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This program utilizes the WLF
equation 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 Visc(log)= C- A(T-Tg)/(B+T-Tg)
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This
progam 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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The Fox equation is normally used to
calculate the Tg of acrylic polymers from the Tg of the individual
monomers, but it can also be modified to be used calculating the Tg
of polymer or oligomer blends.. No unusual interaction between the
polymers is assumed.
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1/Tgco=Wf1/Tg1+Wf2/Tg2+Wfx/Tgx
Tgco= Tg polymer blend, Wfx=weight fraction
polymer x, Tgx=Tg polymer x
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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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INPUT
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MEASURED DATA
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Solids
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Viscosity
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Temperature
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OH number
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Solvent.
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WLF EQUATION
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%
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CPS
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°C
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as supplied
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%
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Constants (Nielsen)
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Polymer composition
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1
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C=
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Polymer composition
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2
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A=
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Polymer composition
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3
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B=
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Polymer composition
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4
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Input Polymer Blend
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Polymer
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Solvent
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Hydroxyl
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Polymer composition
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1
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Polymer composition
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2
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Polymer composition
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3
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Polymer composition
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4
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Total
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Calculate Viscosity Polymer Blend
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Temperature,
°C
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Delta
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Nonvolatile, %
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Hydroxyl number
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Temperature, °C
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Viscosity, Poise
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Viscosity, cps
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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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