Renormalization by complete asymmetric fluctuation equations (CAFE)
Embodiments simulate liquid mixtures. An embodiment begins by receiving a free energy curve of a liquid mixture comprising two components. Based on the received free energy curve, a partition function describing fluctuations of mole fractions of the two components in the liquid mixture is constructed. In turn, a renormalized free energy curve of the liquid mixture is calculated using the constructed partition function. The behavior of the liquid mixture is then simulated using, i.e., applying, the calculated renormalized free energy curve. Computer automated simulation systems and apparatus are example applications of the inventive method and disclosed techniques.
1 . A computer implemented method for screening liquid mixtures, the method comprising, by a processor:
receiving, in memory of the processor, a free energy curve of a liquid mixture comprising two components;
based on the received free energy curve, constructing a partition function describing fluctuations of mole fractions of the two components in the liquid mixture, wherein the partition function constructed covers symmetric and asymmetric fluctuations of the mole fractions of the two components around an average mole fraction;
using the constructed partition function, calculating a renormalized, with respect to the received free energy curve, free energy curve of the liquid mixture;
generating properties of the liquid mixture by performing a computer-based simulation of behavior of the liquid mixture using the calculated renormalized free energy curve, wherein the properties generated include at least one of: critical solution temperature, lower critical solution temperature, upper critical solution temperature, and renormalized equilibrium compositions of the two components of the liquid mixture; and
screening the liquid mixture based on the properties generated.
2 . The method of claim 1 wherein the renormalized free energy curve is a negative logarithm of the constructed partition function multiplied by molar thermal energy RT.
3 . The method of claim 1 wherein the renormalized free energy curve is a function of a temperature scaling parameter.
4 . The method of claim 3 wherein the temperature scaling parameter is a constant or a function of properties determined based on the received free energy curve of the liquid mixture.
5 . The method of claim 1 wherein performing the computer-based simulation of behavior of the liquid mixture using the calculated renormalized free energy curve includes:
generating liquid-liquid-equilibrium of the liquid mixture using a tangent construction method.
6 . A system for screening liquid mixtures, the system comprising:
a processor; and
a memory with computer code instructions stored thereon, the processor and the memory, with the computer code instructions, being configured to cause the system to:
receive a free energy curve of a liquid mixture comprising two components;
based on the received free energy curve, construct a partition function describing fluctuations of mole fractions of the two components in the liquid mixture, wherein the partition function constructed covers symmetric and asymmetric fluctuations of the mole fractions of the two components around an average mole fraction;
using the constructed partition function, calculate a renormalized, with respect to the received free energy curve, free energy curve of the liquid mixture;
generate properties of the liquid mixture by performing a computer-based simulation of behavior of the liquid mixture using the calculated renormalized free energy curve, wherein the properties generated include at least one of: critical solution temperature, lower critical solution temperature, upper critical solution temperature, and renormalized equilibrium compositions of the two components of the liquid mixture; and
screen the liquid mixture based on the properties generated.
7 . The system of claim 6 wherein the renormalized free energy curve is a negative logarithm of the constructed partition function multiplied by molar thermal energy RT.
8 . The system of claim 6 wherein the renormalized free energy curve is a function of a temperature scaling parameter.
9 . The system of claim 8 wherein the temperature scaling parameter is a constant or a function of properties determined based on the received free energy curve of the liquid mixture.
10 . The system of claim 6 wherein to perform the computer-based simulation of behavior of the liquid mixture using the calculated renormalized free energy curve, the processor and the memory, with computer code instructions, are further configured to cause the system to:
generate liquid-liquid-equilibrium of the liquid mixture using a tangent construction method.
11 . A computer program product for screening liquid mixtures, the computer program product executed by a server in communication across a network with one or more clients and comprising:
a non-transitory computer readable medium, the computer readable medium comprising program instructions, which, when executed by a processor, causes the processor to:
receive a free energy curve of a liquid mixture comprising two components;
based on the received free energy curve, construct a partition function describing fluctuations of mole fractions of the two components in the liquid mixture, wherein the partition function constructed covers symmetric and asymmetric fluctuations of the mole fractions of the two components around an average mole fraction;
using the constructed partition function, calculate a renormalized, with respect to the received free energy curve, free energy curve of the liquid mixture;
generate properties of the liquid mixture by performing a computer-based simulation of behavior of the liquid mixture using the calculated renormalized free energy curve, wherein the properties generated include at least one of: critical solution temperature, lower critical solution temperature, upper critical solution temperature, and renormalized equilibrium compositions of the two components of the liquid mixture; and
screen the liquid mixture based on the properties generated.
12 . The computer program product of claim 11 wherein the renormalized free energy curve is a negative logarithm of the constructed partition function multiplied by molar thermal energy RT.
13 . The computer program product of claim 11 wherein the renormalized free energy curve is a function of a temperature scaling parameter.
14 . The computer program product of claim 13 wherein the temperature scaling parameter is a constant or a function of properties determined based on the received free energy curve of the liquid mixture.
15 . The computer program product of claim 11 wherein to perform the computer-based simulation of behavior of the liquid mixture using the calculated renormalized free energy curve, the program instructions cause the processor to:
generate liquid-liquid-equilibrium of the liquid mixture using a tangent construction method.