Exclusion Volume

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I've been trying to calculate the "height" of brush polymers on the surface of colloidal nanoparticles. The reference I'm using is "Polymer brushes" by Milner, Science, 1991, v.251, 905-914. The formula presented here (similar in many other cases I've looked at too) is h ~ N*(w*sigma*a^2)^(1/3).
h is the height [L], w is the excluded volume parameter, sigma is the coverage on the nanoparticle[1/L^2], a is the Kuhn's length [L].

First, can someone explain what the excluded volume parameter is? What are the units of this parameter? Based on this equation, the units are in volume. But when I looked at some other papers, this parameter is dimensionless. In addition, I can't seem to find a good explanation of the excluded volume, or a way of obtaining it theoretically. I need to find a way of finding this for DNA.

Hope someone can help me! Thanks!
 

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