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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.
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. 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 = 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 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 = logφe + keVi/(2.303(1-Vi/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      

Automatic recalculation