Prof. John A. Nairn
Oregon State University, Wood Science and Engineering Department
NAIRN Home Page > Computer Software > Copolymer Equation

Copolymer Equation

This JAVA applet plots the copolymer equation and lets you explore the effect of varying the parameters.

Using the Applet

  1. The theory of the copolymer equation is given below.
  2. Drag the sliders to set r1 and r2 or enter numbers for r1 and r2 in the text boxes. The plot will change for the new values.
  3. You can click the "Ideal" check box to calculate for ideal copolymerization (r2 = 1/r1). In this setting you can only change r1.
  4. If you click on any location and hold the mouse button, a red dot will appear and show the closest point on the current curve and the coordinates. When you release the mouse button, the dot will move in the direction that the copolymer composition will change as the reaction proceeds without addition of new monomer. As in real copolymerization, the dot will move faster when the copolymer curve is farther from the diagonal line.
  5. This applet requires a browser that supports Java 1.1.x or newer. If that applet does not automatically load and run, your browser may be lacking that support.

Theory

The copolymer equation lets you predict the composition of the polymer as a function of the current ratio of monomers and the relative reactivities for monomers reacting with themselves or with the comonomer. The equation is:

where capital F1 is the fraction of monomer 1 in the completed polymer and lower case f1 and f2 are the fractions of monomer in the reaction mix (f1 + f2 = 1). The terms r1 and r2 are monomer reactivity ratios defined by:

                                                 

These ratios give the relative probabilities that a monomer will react with itself vs. reacting with the other monomer. r1 and r2 can vary from zero (which means a monomer can only react with the other comonomer) to infinity (which means the monomers will not react and thus there will be no copolymerization).

A special case of the copolymer equation, known as "Ideal Copolymerization" occurs when r1 * r2 = 1. There is nothing actually "ideal" about ideal copolymerization, or "nonideal" about more general copolymerization. The name "Ideal Copolymerization" is derived from an analogy it has with vapor-liquid equilibria in binary systems. "Ideal Copolymerization" is analogous to vapor liquid equilibria if k11 and k21 are replaced my vapor pressure of component 1, k22 and k21 are replaced by vapor pressure of component 2 (and hence r1 * r2 = 1), and F1 and f1 are the mole fractions of component 1 in the vapor and liquid, respectively.

References

  1. Applet written by Dr. Dean C. Nairn using his Plot Applet.
  2. Copolymer theory can be found in various tests such as Paul J. Flory, "Principles of Polymer Chemistry." pages 178-203 (Cornell University Press, Ithaca and London, 1953). Paul J. Flory won the 1974 Nobel prize in chemistry.

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May 24, 2006