MOZ - Revision history

Nice and Tidy at 15:17, 10 July 2007

2007-07-10T15:17:13Z

← Older revision		Revision as of 17:17, 10 July 2007
Line 1:		Line 1:
	The [[Ornstein-Zernike relation \| Ornstein-Zernike]] equations for mixtures of monomers with coincident oligomers		The [[Ornstein-Zernike relation \| Ornstein-Zernike]] equations for mixtures (MOZ) of monomers with coincident oligomers
	(coincident dimers, trimers,...,''n''-mers).		(coincident dimers, trimers,...,''n''-mers).

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

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

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

	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}(r) - c_{a3}(r) = \int h_{aa} (r')~\rho_a ~c_{a3}(\|r - r'\|) dr'</math>		:<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>
			==References==
	[[Category: Integral equations]]		[[Category: Integral equations]]

Nice and Tidy at 12:10, 27 February 2007

2007-02-27T12:10:55Z

← Older revision		Revision as of 14:10, 27 February 2007
Line 18:		Line 18:

	:<math>h_{a3}(r) - c_{a3}(r) = \int h_{aa} (r')~\rho_a ~c_{a3}(\|r - r'\|) dr'</math>		:<math>h_{a3}(r) - c_{a3}(r) = \int h_{aa} (r')~\rho_a ~c_{a3}(\|r - r'\|) dr'</math>
			[[Category: Integral equations]]

Carl McBride at 14:57, 21 February 2007

2007-02-21T14:57:32Z

← Older revision		Revision as of 16:57, 21 February 2007
Line 4:		Line 4:
	:<math>h_{an}(r) - c_{an}(r) = \int h_{aa} (r')~\rho_a ~c_{an}(\|r - r'\|) dr'~~~~~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 $n>1$ 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>)

Carl McBride: New page: The Ornstein-Zernike equations for mixtures of monomers with coincident oligomers (coincident dimers, trimers,...,''n''-mers). : $h_{an}(r) - c_{an}(r...$

2007-02-21T14:55:46Z

New page: The Ornstein-Zernike equations for mixtures of monomers with coincident oligomers (coincident dimers, trimers,...,''n''-mers). :<math>h_{an}(r) - c_{an}(r...

New page

The [[Ornstein-Zernike relation | Ornstein-Zernike]] equations for mixtures of monomers with coincident oligomers
(coincident dimers, trimers,...,''n''-mers).

:<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 $n>1$ are decoupled. The first member is for the bulk monomer fluid ''a'' (with size <math>\sigma</math> and
energy <math>\epsilon</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
energy <math>2\epsilon</math> at infinite dilution in the bulk ''a''-monomers:

:<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
energy <math>3\epsilon</math> at infinite dilution in the bulk ''a''-monomers:

:<math>h_{a3}(r) - c_{a3}(r) = \int h_{aa} (r')~\rho_a ~c_{a3}(|r - r'|) dr'</math>

MOZ - Revision history

Nice and Tidy at 15:17, 10 July 2007

Nice and Tidy at 12:10, 27 February 2007

Carl McBride at 14:57, 21 February 2007

Carl McBride: New page: The Ornstein-Zernike equations for mixtures of monomers with coincident oligomers (coincident dimers, trimers,...,''n''-mers). :h_{an}(r) - c_{an}(r...

Carl McBride: New page: The Ornstein-Zernike equations for mixtures of monomers with coincident oligomers (coincident dimers, trimers,...,''n''-mers). : $h_{an}(r) - c_{an}(r...$