Home                      Measurement of Crosslink Density by Swelling

Polymers depending on the solubility parameter of the solvent can be dissolved or swollen in a solvent or solvent mix. Crosslinked polymers because of the restriction in the mobility of the polymer chains can only be swollen in a solvent. This restriction in polymer swelling provides an indication of the crosslink density of the coating. 
The Flory-Rehner equation permits the calculation of the crosslink density from swelling experiments
-[ln(1 -u2) + u2 + c1(u2)2] = V1n[(u2)1/3 - u2/2]
The value u2 is the volume fraction of polymer in the swollen mass, V1 is the molar volume of the swelling solvent, c1 is the Flory-Huggins polymer-solvent dimensionless interaction term, and n is the number of active chain segments per unit volume.  The quantity n equals r/Mc, where r is the density and Mc is the molecular weight between crosslinks.  Published data for the interaction term (or parameter) in chlorinated solvents indicates a value in the range of 0.4 - 0.5.
The measurement was conducted by placing a small slice of the polymer film on a glass slide and covering it with a cover glass and placing it on a microscope with a graduated viewfinder. The solvent was then wicked from a eye dropper under the cover glass. The size of the  film was measured before and after solvent exposure. Different solvents required different time to achieve equilibrium swelling. For dichloromethane (methylene chloride)  is achieved almost instantaneously. Linear swelling = L1/LO.  LO length of film before swelling, L1 length after swelling.
Solvent Data to be entered    
Molar Volume, V1  

Flory Huggins Interaction parameter, c1  
Swelling Results    
Swelling linear  
Results Crosslinked Polymer    
Elastic Chains, n  per/g  
Elastic Chains, n  per 1000g  
Average Molecular Weight between X-link, Mc   
FLORY -REHNER EQUATION, Introduction to polymer Science L.H. Sperling. J. H. Wiley and Sons. Inc. pg 428
Crosslink Density of High Solids Coatings. L.W. Hill., K. Kozlowski, and R.L. Sholes., J. Coat. Tech., 54.,No. 692. (1982) 67
B.A. Wolf in Polymer Handbook, J. Brandup and E.H. Immergut, 2nd Ed.,Wiley -  Interscience, New York, 1975

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Last edited on:

October 20, 2010

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