Flory-Huggins theory - Revision history

88.8.154.104 at 10:34, 29 August 2012

2012-08-29T10:34:03Z

← Older revision		Revision as of 12:34, 29 August 2012
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	*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.		*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.
	*For polymer solutions (whose sites have the volume of a solvent molecule, <math>n_A</math>=1), the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system. Good solvent systems show significantly smaller positive values of <math>\chi</math>, e.g. 0.2.		*For polymer solutions (whose sites have the volume of a solvent molecule, <math>n_A</math>=1), the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system. Good solvent systems show significantly smaller positive values of <math>\chi</math>, e.g. 0.2.
	*For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site, e.g. 100 Angstroms. <math>\chi</math> values ~~and~~ can be positive or negative and they are usually very small in absolute value for compatible or near to compatible blends <ref>[ N. P. Balsara "Thermodynamics of Polymer Blends", in J. E. Mark, editor, “Physical Properties of Polymers Handbook” AIP Press, pp. 257-268, (1996) ISBN 1563962950] </ref>		*For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site, e.g. 100 Angstroms. <math>\chi</math> values can be positive or negative and they are usually very small in absolute value for compatible or near to compatible blends <ref>[ N. P. Balsara "Thermodynamics of Polymer Blends", in J. E. Mark, editor, “Physical Properties of Polymers Handbook” AIP Press, pp. 257-268, (1996) ISBN 1563962950] </ref>

	The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>		The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>

88.8.154.104 at 10:32, 29 August 2012

2012-08-29T10:32:02Z

← Older revision		Revision as of 12:32, 29 August 2012
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	*Positive values of <math>\chi</math> necessarily lead to immiscibility for polymer mixtures of high molecular weight.		*Positive values of <math>\chi</math> necessarily lead to immiscibility for polymer mixtures of high molecular weight.
	*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.		*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.
	*For polymer solutions (whose sites have the volume of a solvent molecule, <math>n_A</math>=1), the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system. Good solvent systems show significantly smaller positive values of <math>\chi</math>.		*For polymer solutions (whose sites have the volume of a solvent molecule, <math>n_A</math>=1), the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system. Good solvent systems show significantly smaller positive values of <math>\chi</math>, e.g. 0.2.
	*For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site, e.g. 100 Angstroms. <math>\chi</math> values and can be positive or negative and they are usually very small <ref>[ N. P. Balsara "Thermodynamics of Polymer Blends", in J. E. Mark, editor, “Physical Properties of Polymers Handbook” AIP Press, pp. 257-268, (1996) ISBN 1563962950] </ref>		*For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site, e.g. 100 Angstroms. <math>\chi</math> values and can be positive or negative and they are usually very small in absolute value for compatible or near to compatible blends <ref>[ N. P. Balsara "Thermodynamics of Polymer Blends", in J. E. Mark, editor, “Physical Properties of Polymers Handbook” AIP Press, pp. 257-268, (1996) ISBN 1563962950] </ref>

	The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>		The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>

Juan at 10:10, 29 August 2012

2012-08-29T10:10:58Z

← Older revision		Revision as of 12:10, 29 August 2012
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	*Positive values of <math>\chi</math> necessarily lead to immiscibility for polymer mixtures of high molecular weight.		*Positive values of <math>\chi</math> necessarily lead to immiscibility for polymer mixtures of high molecular weight.
	*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.		*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.
	*For polymer solutions (whose sites have the volume of a solvent molecule, <math>n_A</math>=1), the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system.		*For polymer solutions (whose sites have the volume of a solvent molecule, <math>n_A</math>=1), the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system. Good solvent systems show significantly smaller positive values of <math>\chi</math>.
	*For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site, e.g. 100 Angstroms. ~~Usual~~ <math>\chi</math> values are very small <ref>[ N. P. Balsara "Thermodynamics of Polymer Blends", in J. E. Mark, editor, “Physical Properties of Polymers Handbook” AIP Press, pp. 257-268, (1996) ISBN 1563962950] </ref>		*For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site, e.g. 100 Angstroms. <math>\chi</math> values and can be positive or negative and they are usually very small <ref>[ N. P. Balsara "Thermodynamics of Polymer Blends", in J. E. Mark, editor, “Physical Properties of Polymers Handbook” AIP Press, pp. 257-268, (1996) ISBN 1563962950] </ref>

	The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>		The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>

Juan at 10:00, 29 August 2012

2012-08-29T10:00:21Z

← Older revision		Revision as of 12:00, 29 August 2012
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	*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.		*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.
	*For polymer solutions (whose sites have the volume of a solvent molecule, <math>n_A</math>=1), the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system.		*For polymer solutions (whose sites have the volume of a solvent molecule, <math>n_A</math>=1), the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system.
	*For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site, e.g. 100 Angstroms. Usual values are ~~close to zero~~ <ref>[ N. P. Balsara "Thermodynamics of Polymer Blends", in J. E. Mark, editor, “Physical Properties of Polymers Handbook” AIP Press, pp. 257-268, (1996) ISBN 1563962950] </ref>		*For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site, e.g. 100 Angstroms. Usual <math>\chi</math> values are very small <ref>[ N. P. Balsara "Thermodynamics of Polymer Blends", in J. E. Mark, editor, “Physical Properties of Polymers Handbook” AIP Press, pp. 257-268, (1996) ISBN 1563962950] </ref>

	The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>		The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>

Juan at 09:57, 29 August 2012

2012-08-29T09:57:59Z

← Older revision		Revision as of 11:57, 29 August 2012
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	*Positive values of <math>\chi</math> necessarily lead to immiscibility for polymer mixtures of high molecular weight.		*Positive values of <math>\chi</math> necessarily lead to immiscibility for polymer mixtures of high molecular weight.
	*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.		*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.
	*For polymer solutions (whose sites have the volume of a solvent molecule, <math>n_A</math>=1), the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system. (For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site.)		*For polymer solutions (whose sites have the volume of a solvent molecule, <math>n_A</math>=1), the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system.
			*For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site, e.g. 100 Angstroms. Usual values are close to zero <ref>[ N. P. Balsara "Thermodynamics of Polymer Blends", in J. E. Mark, editor, “Physical Properties of Polymers Handbook” AIP Press, pp. 257-268, (1996) ISBN 1563962950] </ref>

	The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>		The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>

88.8.154.104 at 15:05, 28 August 2012

2012-08-28T15:05:52Z

← Older revision		Revision as of 17:05, 28 August 2012
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	*Positive values of <math>\chi</math> necessarily lead to immiscibility for polymer mixtures of high molecular weight.		*Positive values of <math>\chi</math> necessarily lead to immiscibility for polymer mixtures of high molecular weight.
	*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.		*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.
	*For polymer solutions (whose sites have the volume of a solvent molecule) <math>n_A</math>=1, the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system. (For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site.)		*For polymer solutions (whose sites have the volume of a solvent molecule, <math>n_A</math>=1), the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system. (For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site.)

	The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>		The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>

88.8.154.104: definition of site volume for polymer mixtures added by Juan

2012-08-28T15:04:51Z

definition of site volume for polymer mixtures added by Juan

← Older revision		Revision as of 17:04, 28 August 2012
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	*Positive values of <math>\chi</math> necessarily lead to immiscibility for polymer mixtures of high molecular weight.		*Positive values of <math>\chi</math> necessarily lead to immiscibility for polymer mixtures of high molecular weight.
	*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.		*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.
	*For polymer solutions(whose sites have the volume of a solvent molecule) <math>n_A</math>=1, the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system. (For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site.)		*For polymer solutions (whose sites have the volume of a solvent molecule) <math>n_A</math>=1, the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system. (For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site.)

	The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>		The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>

88.8.154.104 at 15:02, 28 August 2012

2012-08-28T15:02:30Z

← Older revision		Revision as of 17:02, 28 August 2012
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	*Positive values of <math>\chi</math> necessarily lead to immiscibility for polymer mixtures of high molecular weight.		*Positive values of <math>\chi</math> necessarily lead to immiscibility for polymer mixtures of high molecular weight.
	*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.		*Polymer mixing always take place if the <math>\chi</math> parameter is negative. Miscible polymer mixtures with negative <math>\chi</math> exist due to specific interactions between given polymer segments. Miscibility or compatibility can be induced by several methods. For instance, introducing opposite charges in the different polymers or adding a copolymer containing A and B segments.
	*For a ~~polymer solution,~~ <math>n_A</math>=1, the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system.		*For polymer solutions(whose sites have the volume of a solvent molecule) <math>n_A</math>=1, the critical Flory-Huggins parameter is close to <math>1/2</math>. The temperature corresponding to this value <math>\chi</math>=<math>1/2</math> would be the critical temperature if the polymer is infinitely long and defines the [[theta solvent \| theta temperature]] of the polymer-solvent system. (For polymer mixtures, <math>\chi</math> should be referred to the arbitrarily chosen microscopic volume defined as a site.)

	The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>		The <math>\chi</math> parameter is somewhat similar to a [[second virial coefficient]] expressing binary interactions between molecules and, therefore, it usually shows a linear dependence of <math>1/T</math>

Carl McBride: /* References */ Added a reference

2011-09-29T11:29:04Z

References: Added a reference

← Older revision		Revision as of 13:29, 29 September 2011
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	==References==		==References==
	<references/>		<references/>
			;Related reading
			*[http://dx.doi.org/10.1146/annurev.pc.02.100151.002123 P. J. Flory, and W. R. Krigbaum "Thermodynamics of High Polymer Solutions", Annual Review of Physical Chemistry '''2''' pp. 383-402 (1951)]
	[[Category: Polymers]]		[[Category: Polymers]]

Carl McBride: Added a paper

2011-09-28T13:40:06Z

Added a paper

← Older revision		Revision as of 15:40, 28 September 2011
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	The '''Flory-Huggins theory''' (~~perhaps~~ chronologically speaking it should be known as the Huggins-Flory theory) for [[solutions]] of [[polymers]] was developed by [[Maurice L. Huggins ]] <ref>[http://dx.doi.org/10.1063/1.1750930 Maurice L. Huggins "Solutions of Long Chain Compounds", Journal of Chemical Physics '''9''' p. 440 (1941)]</ref> and [[Paul J. Flory]] <ref>[http://dx.doi.org/10.1063/1.1750971 Paul J. Flory "Thermodynamics of High Polymer Solutions", Journal of Chemical Physics '''9''' pp. 660-661 (1941)]</ref><ref>[http://dx.doi.org/10.1063/1.1723621 Paul J. Flory "Thermodynamics of High Polymer Solutions", Journal of Chemical Physics '''10''' pp. 51-61 (1942)]</ref>, following the work by Kurt H. Meyer <ref>[http://dx.doi.org/10.1002/hlca.194002301130 Kurt H. Meyer "Propriétés de polymères en solution XVI. Interprétation statistique des propriétés thermodynamiques de systèmes binaires liquides", Helvetica Chimica Acta '''23''' pp. pp. 1063-1070 (1940)]</ref>. The description can be easily generalized to the case of polymer mixtures. The Flory-Huggins theory defines the volume of a [[polymers \|polymer system]] as a lattice which is divided into microscopic subspaces (called sites) of the same volume. In the case of polymer solutions, the solvent molecules are assumed to occupy single sites, while a polymer chain of a given type, <math>i</math>, occupies <math>n_i</math> sites. The repulsive forces in the system are modelled by requiring each lattice site to be occupied by only a single segment. Attractive interactions between non-bonded sites are included at the lattice neighbour level. Assuming random and ideal mixing, i.e. mixing volume <math>\Delta V_m = 0</math>, it is possible to obtain the well-known expression for the combinatorial [[entropy]] of mixing <math>\Delta S_m</math> per site of the Flory-Huggins theory for the general case of a mixture of two components, A (polymer or solvent) and polymer B (Eq. 10.1 of Ref. 3):		The '''Flory-Huggins theory''' (although chronologically speaking it should be known as the Huggins-Flory theory <ref>Paul J. Flory in [http://garfield.library.upenn.edu/classics1985/A1985AFW2600001.pdf Citation Classic '''18''' p. 18 May 6 (1985)]</ref>) for [[solutions]] of [[polymers]] was developed by [[Maurice L. Huggins ]] <ref>[http://dx.doi.org/10.1063/1.1750930 Maurice L. Huggins "Solutions of Long Chain Compounds", Journal of Chemical Physics '''9''' p. 440 (1941)]</ref> and [[Paul J. Flory]] <ref>[http://dx.doi.org/10.1063/1.1750971 Paul J. Flory "Thermodynamics of High Polymer Solutions", Journal of Chemical Physics '''9''' pp. 660-661 (1941)]</ref><ref>[http://dx.doi.org/10.1063/1.1723621 Paul J. Flory "Thermodynamics of High Polymer Solutions", Journal of Chemical Physics '''10''' pp. 51-61 (1942)]</ref>, following the work by Kurt H. Meyer <ref>[http://dx.doi.org/10.1002/hlca.194002301130 Kurt H. Meyer "Propriétés de polymères en solution XVI. Interprétation statistique des propriétés thermodynamiques de systèmes binaires liquides", Helvetica Chimica Acta '''23''' pp. pp. 1063-1070 (1940)]</ref>. The description can be easily generalized to the case of polymer mixtures. The Flory-Huggins theory defines the volume of a [[polymers \|polymer system]] as a lattice which is divided into microscopic subspaces (called sites) of the same volume. In the case of polymer solutions, the solvent molecules are assumed to occupy single sites, while a polymer chain of a given type, <math>i</math>, occupies <math>n_i</math> sites. The repulsive forces in the system are modelled by requiring each lattice site to be occupied by only a single segment. Attractive interactions between non-bonded sites are included at the lattice neighbour level. Assuming random and ideal mixing, i.e. mixing volume <math>\Delta V_m = 0</math>, it is possible to obtain the well-known expression for the combinatorial [[entropy]] of mixing <math>\Delta S_m</math> per site of the Flory-Huggins theory for the general case of a mixture of two components, A (polymer or solvent) and polymer B (Eq. 10.1 of Ref. 3):

	:<math>\Delta S_m = -R \left[ \frac{\phi_A}{n_A} \ln \phi_A + \frac{\phi_B}{n_B} \ln \phi_B \right]</math>		:<math>\Delta S_m = -R \left[ \frac{\phi_A}{n_A} \ln \phi_A + \frac{\phi_B}{n_B} \ln \phi_B \right]</math>