Claims
- 1. A method for calculating thermodynamic and molecular properties of molecules of a substance dissolved in a solvent in the liquid state, which method comprises:
- (a) maintaining a sample portion of the substance at a concentration (C) in the solvent,
- (b) measuring apparent molar concentration (C.sub.M) at the actual concentration (C) to produce a data pair C vs. C.sub.M, the apparent molar concentration determined by a method in list consisting of:
- (1) measuring the deviation of vapor pressure and saturation temperature of the sample from that of the pure solvent,
- (2) measuring the deviation of the melting point of a sample portion from that of the pure solvent,
- (c) defining an average aggregate mass (M.sub.A) using the relation:
- M.sub.A =C/C.sub.M
- where the average aggregate mass (M.sub.A) is the average molecular mass of clusters of associated molecules and any unassociated molecules,
- (d) repeating steps (a) through (c) for m repetitions with a different concentration (C) for each repetition to produce a set of data points of concentration (C) vs. average aggregate mass (M.sub.A),
- (e) solving for a.sub.1, a.sub.2, . . . a.sub.j, and MW.sub.0 from the C and M.sub.A data points from the following set of equations:
- a subset of equations for n=2 to m defined by ##EQU16## an equation defined by ##EQU17## an equation defined by ##EQU18## and a subset of equations that are relations between k.sub.n and n, for n=2 to m
- k.sub.n =f(n,a.sub.1,a.sub.2, . . . ,a.sub.j)
- where:
- MW.sub.0 is the average molecular weight of the substance molecule,
- m is an integer greater than 2,
- k.sub.n for n=2 to m are equilibrium constants of association between monomers of the substance and clusters of monomers,
- a.sub.1, a.sub.2, . . . a.sub.j are constants,
- and j is an integer greater than 0,
- the number (m) of the apparent mass (M.sub.A) versus concentration (C) data points produced by the repetitions in step (e) being an integer greater than j.
- 2. The method of claim 1 wherein thermodynamic properties are determined from the values of k.sub.n.
- 3. The method of claim 1 additionally comprising repeating steps (a) through (e) at a different temperature of the sample portion to produce a plurality of subsets of equation sets k.sub.n.
- 4. The method of claim 3 wherein thermodynamic properties are determined from the values of k.sub.n.
- 5. A method for calculating thermodynamic and molecular properties in molecules of a substance dissolved in a solvent in the condensed state, which method comprises:
- (a) maintaining a sample portion of the substance at a concentration (C) in the solvent,
- (b) measuring apparent molar concentration (C.sub.M) at the actual concentration (C) to produce a data pair C vs. C.sub.M, the apparent molar concentration determined by measuring the deviation of vapor pressure and saturation temperature,
- (c) defining an average aggregate mass (M.sub.A) using the relation:
- M.sub.A =C/C.sub.M
- where the average aggregate mass (M.sub.A) is the average molecular mass of clusters of associated molecules and any unassociated molecules,
- (d) repeating steps (a) through (c) for m repetitions with a different concentration (C) for each repetition to produce a set of data points of concentration (C) vs. average aggregate mass (M.sub.A),
- (e) solving for a.sub.1, a.sub.2, . . . a.sub.j, and MW.sub.0 from the C and M.sub.A data points from the following set of equations:
- a subset of equations for n=2 to m defined by ##EQU19## an equation defined by ##EQU20## an equation defined by ##EQU21## and a subset of equations that are relations between k.sub.n and n, for n=2 to m
- k.sub.n =f(n,a.sub.1,a.sub.2, . . . ,a.sub.j)
- where:
- MW.sub.0 is the average molecular weight of the substance molecule,
- m is an integer greater than 2,
- k.sub.n for n=2 to m are equilibrium constants of association between monomers of the substance and clusters of monomers,
- a.sub.1, a.sub.2, . . . a.sub.j are constants,
- and j is an integer greater than 0,
- the number (m) of the average aggregate mass (M.sub.A) versus concentration (C) data points produced by the repetitions in step (e) being an integer greater than j.
- 6. The method of claim 5 wherein thermodynamic properties are determined from the values of k.sub.n.
- 7. The method of claim 5 additionally comprising repeating steps (a) through (e) at a difference temperature of the sample portion to produce a plurality of subsets of equation sets k.sub.n.
- 8. The method of claim 7 wherein thermodynamic properties are determined from the values of k.sub.n.
- 9. A method for calculating thermodynamic and molecular properties in molecules of a substance dissolved in a solvent in the condensed state, which method comprises:
- (a) maintaining a sample portion of the substance at a concentration (C) in the solvent,
- (b) measuring apparent molar concentration (C.sub.M) at the actual concentration (C) to produce a data pair C vs. C.sub.M, the apparent molar concentration determined by measuring the deviation of melting point,
- (c) defining an average aggregate mass (M.sub.A) using the relation:
- M.sub.A =C/C.sub.M
- where the average aggregate mass (M.sub.A) is the average molecular mass of clusters of associated molecules and any unassociated molecules,
- (d) repeating steps (a) through (c) for m repetitions with a different concentration (C) for each repetition to produce a set of data points of concentration (C) vs. average aggregate mass (M.sub.A),
- (e) solving for a.sub.1, a.sub.2, . . . a.sub.j, and MW.sub.0 from the C and M.sub.A data points from the following set of equations:
- a subset of equations for n=2 to m defined by ##EQU22## an equation defined by ##EQU23## an equation defined by ##EQU24## and a subset of equations that are relations between k.sub.n and n, for n=2 to m
- k.sub.n =f(n,a.sub.1,a.sub.2, . . . ,a.sub.j)
- where:
- MW.sub.0 is the average molecular weight of the substance molecule,
- m is an integer greater than 2,
- k.sub.n for n=2 to m are equilibrium constants of association between monomers of the substance and clusters of monomers,
- a.sub.1, a.sub.2, . . . a.sub.j are constants,
- and j is an integer greater than 0,
- the number (m) of the average aggregate mass (M.sub.A) versus concentration (C) data points produced by the repetitions in step (e) being an integer greater than j.
- 10. The method of claim 9 wherein thermodynamic properties are determined from the values of k.sub.n.
- 11. The method of claim 9 additionally comprising repeating steps (a) through (e) at a different temperature of the sample portion to produce a plurality of subsets of equations sets k.sub.n.
- 12. The method of claim 11 wherein thermodynamic properties are determined from the values of k.sub.n.
RELATED APPLICATIONS
This application a continuation of U.S. patent application Ser. No. 08/396,378, filed Feb. 28, 1995, now U.S. Pat. No. 5,574,215, issued Nov. 12, 1996 which is a is a continuation in part from U.S. patent application Ser. No. 08/204,553, filed Mar. 1, 1994, now abandoned.
STATEMENT OF GOVERNMENT INTEREST
This invention was made in part with United States Government support under contract No. #DE-AC21-93MC29240 awarded by the DOE. The government may have certain rights in this invention.
US Referenced Citations (2)
Number |
Name |
Date |
Kind |
5341672 |
Kawanami et al. |
Aug 1994 |
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5574215 |
Bunger et al. |
Nov 1996 |
|
Continuations (1)
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Number |
Date |
Country |
Parent |
396378 |
Feb 1995 |
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Continuation in Parts (1)
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Number |
Date |
Country |
Parent |
204553 |
Mar 1994 |
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