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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(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.
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 = 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.
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 = logφe + keVi/(2.303(1-Vi/φ)
Pigment 1   Un-flocculated 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   Un-flocculated Flocculated Un-flocculated     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  

Automatic recalculation