Calculating Excluded Volume Parameter for Polymer Brushes

[xtrios]

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!

 

[eljose79]

I can provide some insight into the excluded volume parameter and how it is used in calculating the height of brush polymers on the surface of colloidal nanoparticles.

The excluded volume parameter, also known as the Flory parameter, is a measure of the interactions between polymer chains. It takes into account the steric hindrance and repulsion between polymer chains as they try to occupy the same space. In other words, it represents the volume that is not available for a polymer chain to occupy due to the presence of other polymer chains.

The units of the excluded volume parameter can vary depending on the context and the specific system being studied. In the equation you provided, the units are in volume because the excluded volume parameter is being multiplied by the square of the coverage on the nanoparticle (sigma) and the square of the Kuhn's length (a). However, in some cases, the excluded volume parameter may be reported as a dimensionless quantity.

There are several methods for determining the excluded volume parameter experimentally, such as light scattering, small-angle neutron scattering, and size exclusion chromatography. However, in order to calculate it theoretically, you would need to have information about the polymer chains, such as their size and shape, and the interactions between them. This information is usually obtained through computer simulations or theoretical models.

For DNA specifically, the excluded volume parameter has been extensively studied and its value has been determined for different lengths and conformations of DNA. It is also influenced by factors such as ionic strength and temperature. I would suggest looking at previous research on DNA brush polymers to see if the excluded volume parameter has already been calculated for your specific system.

I hope this helps clarify the concept of the excluded volume parameter and how it is used in calculating the height of brush polymers on colloidal nanoparticles. Good luck with your research!

 

[charng]

The excluded volume parameter is a measure of the steric hindrance or repulsive interactions between polymer chains in a brush configuration. It takes into account the fact that polymer chains cannot occupy the same space and therefore have limited space to extend in a brush-like structure. This parameter is important in understanding the overall height and density of polymer brushes on a surface, as it affects the conformation and packing of the chains.

The units of the excluded volume parameter can vary depending on the context and the specific equation used. In the equation you have provided, the units are in volume since it is multiplied by the square of the coverage on the nanoparticle and the Kuhn's length. However, in other cases, it may be dimensionless as it is a ratio of the volume of a polymer chain to the volume of its excluded space.

Obtaining the excluded volume parameter theoretically can be challenging, as it requires a detailed understanding of the polymer chain conformation and interactions. In general, it is obtained through simulations or experimental measurements. For DNA, it can be estimated using theoretical models or obtained experimentally through techniques such as atomic force microscopy.

I would suggest consulting with experts in the field or conducting further research to find a suitable method for determining the excluded volume parameter for DNA in your specific system. Additionally, you may find more information and explanations in other papers or textbooks on polymer brushes. Good luck!