Editing MOZ

Jump to navigation Jump to search
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.

The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.

Latest revision Your text
Line 1: Line 1:
The [[Ornstein-Zernike relation | Ornstein-Zernike]]  equations for mixtures (MOZ) of monomers with coincident oligomers
The [[Ornstein-Zernike relation | Ornstein-Zernike]]  equations for mixtures of monomers with coincident oligomers
(coincident dimers, trimers,...,''n''-mers).
(coincident dimers, trimers,...,''n''-mers).


:<math>h_{an}({\mathbf r}) - c_{an}({\mathbf r}) =  \int  h_{aa} ({\mathbf r'})~\rho_a ~c_{an}(|{\mathbf r} - {\mathbf r'}|) {\rm d}{\mathbf r'}~~~~~n=a,2,3,...</math>
:<math>h_{an}(r) - c_{an}(r) =  \int  h_{aa} (r')~\rho_a ~c_{an}(|r - r'|) dr'~~~~~n=a,2,3,...</math>


Since all oligomers are at infinite dilution, the OZ's for all <math>n>1</math> are decoupled. The first member is for the bulk monomer fluid ''a'' (with size <math>\sigma</math> and
Since all oligomers are at infinite dilution, the OZ's for all <math>n>1</math> are decoupled. The first member is for the bulk monomer fluid ''a'' (with size <math>\sigma</math> and
energy <math>\epsilon</math>)
energy <math>\epsilon</math>)


:<math>h_{aa}({\mathbf r}) - c_{aa}({\mathbf r}) =  \int  h_{aa} ({\mathbf r'})~\rho_a ~c_{aa}(|{\mathbf r} - {\mathbf r'}|) {\rm d}{\mathbf r'}</math>
:<math>h_{aa}(r) - c_{aa}(r) =  \int  h_{aa} (r')~\rho_a ~c_{aa}(|r - r'|) dr'</math>


For a coincident dimer (<math>n=2</math>) of size <math>\sigma</math> and
For a coincident dimer (<math>n=2</math>) of size <math>\sigma</math> and
energy <math>2\epsilon</math> at infinite dilution in the bulk ''a''-monomers:
energy <math>2\epsilon</math> at infinite dilution in the bulk ''a''-monomers:


:<math>h_{a2}({\mathbf r}) - c_{a2}({\mathbf r}) =  \int  h_{aa} ({\mathbf r'})~\rho_a ~c_{a2}(|{\mathbf r} - {\mathbf r'}|) {\rm d}{\mathbf r'}</math>
:<math>h_{a2}(r) - c_{a2}(r) =  \int  h_{aa} (r')~\rho_a ~c_{a2}(|r - r'|) dr'</math>


For a coincident trimer (<math>n=3</math>) of size <math>\sigma</math> and
For a coincident trimer (<math>n=3</math>) of size <math>\sigma</math> and
energy <math>3\epsilon</math> at infinite dilution in the bulk ''a''-monomers:
energy <math>3\epsilon</math> at infinite dilution in the bulk ''a''-monomers:


:<math>h_{a3}({\mathbf r}) - c_{a3}({\mathbf r}) =  \int  h_{aa} ({\mathbf r'})~\rho_a ~c_{a3}(|{\mathbf r} - {\mathbf r'}|) {\rm d}{\mathbf r'}</math>
:<math>h_{a3}(r) - c_{a3}(r) =  \int  h_{aa} (r')~\rho_a ~c_{a3}(|r - r'|) dr'</math>
==References==
[[Category: Integral equations]]
[[Category: Integral equations]]
Please note that all contributions to SklogWiki are considered to be released under the Creative Commons Attribution Non-Commercial Share Alike (see SklogWiki:Copyrights for details). If you do not want your writing to be edited mercilessly and redistributed at will, then do not submit it here.
You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource. Do not submit copyrighted work without permission!

To edit this page, please answer the question that appears below (more info):

Cancel Editing help (opens in new window)
Retrieved from "http://www.sklogwiki.org/SklogWiki/index.php/MOZ"