Patent Description:
The use of computer based liquid simulation, such as the functionality provided by the method COSMO-RS and the software COSMOTHERM®, is used to develop products, e.g., liquids, in numerous industries, such as pharmaceutical and chemical product industries. Moreover, the results of these liquid simulations are also used to modify or control product manufacturing processes and improve system, e.g., manufacturing, efficiency.

While the use of computer based liquid simulation has become widespread, such methods and systems can benefit from improvements to simulation accuracy.

Embodiments of the invention are defined in the appended claims and provide such improvements. In particular, embodiments improve quantitative simulations of mutual liquid solubility and solve problems in computer based simulation of thermodynamic equilibria of liquid systems. Embodiments accurately predict the mutual solubilities of two liquids close to a critical solution temperature.

One such embodiment, which may be referred to herein as CAFE (complete asymmetric fluctuation equation), constructs a partition function based on the total free energy curve g(x;T) of a liquid mixture of two components that covers all possible symmetric and asymmetric linear fluctuations of the mole fraction around the average mole fraction X at a temperature T. Such an embodiment calculates the renormalized free energy curve gren(x) as a negative logarithm of the constructed partition function multiplied by the thermal energy RT, where R is the universal gas constant. An example embodiment utilizes a scaling parameter λ for the temperature T, which is either a universal constant or a universal linear function of properties available from the unrenormalized g(x;T) curve. To continue, a renormalized liquid-liquid equilibrium (LLE) curve is then calculated from gren(x;T) using a standard tangent construction method that implements fundamental thermodynamics calculations. In turn, this renormalized LLE curve is used to simulate the liquid mixture.

The invention according to claim <NUM> is a computer-implemented method for simulating a liquid mixture. The method 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. Then, the behavior of the liquid mixture is simulated using the calculated renormalized free energy curve. Simulating the behavior of the liquid mixture using the calculated renormalized free energy curve includes predicting at least one of: critical solution temperature; lower critical solution temperature; upper critical solution temperature; and renormalized equilibrium compositions of the two components. Such simulation application of the calculated or resulting renormalized free energy curve provides advantages and efficiencies heretofore unachieved in simulation technologies.

An embodiment receives the free energy curve in the form of a mathematical representation. Moreover, because the method is computer-implemented, the free energy curve may be received from any point communicatively coupled to the computing device implementing the method. According to an embodiment, the constructed partition function covers symmetric and asymmetric fluctuations of the mole fractions of the two components around an average mole fraction. In an embodiment, the renormalized free energy curve is a negative logarithm of the constructed partition function multiplied by molar thermal energy, RT. In another example embodiment, the renormalized free energy curve is a function of a temperature scaling parameter. In such an embodiment, the temperature scaling parameter can be a constant or a function of properties determined based on the received free energy curve of the liquid mixture.

In an embodiment of the method, simulating behavior of the liquid mixture using the calculated renormalized free energy curve includes predicting liquid-liquid-equilibrium of the liquid mixture using a tangent construction method. The simulation performed using the calculated renormalized free energy curve may be used to predict a variety of different properties of the behavior of the liquid mixture. Embodiments of the invention predict critical solution temperature, e.g., lower critical solution temperature and upper critical solution temperature, and/or renormalized equilibrium compositions of the two components.

An example embodiment determines a more realistic shape of predicted liquid-liquid equilibrium curves for a liquid mixture at different temperatures. Embodiments can be implemented in existing simulation applications and programs, such as COSMOTHERM®, to improve the results, e.g., liquid-liquid equilibrium curves, determined by these existing applications. Embodiments can be employed for liquid processing and screening simulations. Embodiments can be used to determine optimal mixtures and conditions for creating mixtures. Such embodiments can be used across a variety of fields and applications, including chemical and pharmaceutical applications, and any applications where liquid mixture simulation is utilized.

Another embodiment is directed to a system that includes a processor and a memory with computer code instructions stored thereon. In such an embodiment, the processor and the memory, with the computer code instructions, are configured to cause the system to implement any embodiments or combination of embodiments described herein.

Yet another embodiment of the present invention is directed to a cloud computing implementation for simulating a liquid mixture. Such an embodiment is directed to a computer program product executed by a server in communication across a network with one or more clients, where the computer program product comprises instructions which, when executed by one or more processors, causes the one or more processors to implement any embodiments described herein.

As described above, embodiments of the present invention provide improved computer based simulation of liquid mixtures. Liquid mixtures of chemical compounds usually have temperature ranges, in which both compounds are miscible (form a homogenous solution) at any concentration, and other temperature regions, in which the compounds decompose into two or more sub-volumes (phases) with different compositions. The composition range between the equilibrium concentrations is called the miscibility gap. The coexistence of multiple phases at one temperature is called liquid-liquid-equilibrium (LLE). Usually, the liquids are miscible above an upper critical solution temperature (UCST) and immiscible below the UCST. However, it may also be possible for a liquid to be miscible below a lower critical solution temperature (LCST) and immiscible above the LCST. Herein, the term critical solution temperature (CST) is used to refer to both UCST and LCST.

For a liquid mixture, as long as the temperature is sufficiently far away from the CST, the phases are well separated by a maximum in the total free energy profile (TFEP) of the mixture, i.e. the total free energy of the system as a function of the concentration variables, and the composition of each phase is fixed to the resulting minimum. However, if the temperature of the liquid mixture approaches the CST, the barrier between the minima gets lower and lower and the system, i.e., liquid mixture, can fluctuate in a wide range of composition spaces. This phenomenon, which also appears at the gas-liquid transition of pure fluids, causes long-range composition fluctuations, also called critical density fluctuations. These fluctuations cause an effective smoothing of the free energy landscape and a lowering of the barrier and, thus, the appearance of the critical fluctuations is a self-supporting process, which causes the rapid disappearance of the LLE gap.

Existing analytical models for the calculation of the total free energy (TFE) of liquid mixtures do not include the effects of the critical fluctuations and, therefore, yield UCSTs that are too high and LCSTs that are too low. Moreover, existing methods overestimate the width of the miscibility gap for temperatures close to the CST. This limits the practical use of predictive models in the simulation, development, and optimization of solubilization and separation processes.

The plot <NUM> in <FIG> illustrates the critical fluctuations that cannot be simulated using existing methods. The plot <NUM> shows the free energy profile (g(x) curves) for the simple-cubic lattice fluid with nearest neighbor interaction energy GAB at four different temperatures (<NUM> curve <NUM>, <NUM> curve <NUM>, <NUM> curve <NUM>, <NUM> curve <NUM>), quantified in GAB energy units. The g(x) curves <NUM>, <NUM>, <NUM>, and <NUM> displayed in <FIG> are taken from COSMOSPACE and have the mathematical form: <MAT> with <MAT> being the surface fractions, A<NUM> and A<NUM> being the molecular surface areas, and ω being given by: <MAT> where E<NUM> is the interaction energy between segments of type <NUM> and <NUM>. The lines <NUM>, <NUM>, <NUM>, and <NUM> in the plot <NUM> indicate the energy level T/TcritΔcrit relative to the minimum, where Δcrit is the barrier height at the critical temperature, which roughly corresponds to RT/<NUM>.

At temperatures sufficiently below the critical temperature (curve <NUM>), the system is quite confined to the regions close to the minima of the total free energy (the minima of the curve <NUM>), which are well separated by a free energy barrier. At increasing temperatures, thermal energy increases, but more importantly the free energy barrier decreases and the minima get more and more shallow. By that, more and more states in composition space become thermally available, and the system fluctuates between these states. At some temperature, i.e. the true UCST, the barrier gets so small that the fluctuations are no longer confined to the individual minimum regions, and thus no separate regions of different composition, i.e. no separate phases, can be distinguished. At this point, the system (liquid mixture) is macroscopically homogeneous, although there is a small free energy barrier separating the original phases. This barrier only disappears at the UCST of the analytic free energy model, in this case the COSMOSPACE model [<NUM>]. When performing simulations of such a liquid, existing methods cannot accurately simulate the fluctuations and, thus, generally inaccurately predict the true UCST.

Methods have been developed in an attempt to correctly determine the simulation, e.g., the correct UCST. The procedures and algorithms for the conversion of LLE-curves from their wrong, analytical shape to the realistic shape resulting from the critical fluctuations, are referred to as renormalization methods. Existing renormalization methods require fitting of a number of adjustable parameters to experimental data of the specific system (liquid mixture) under consideration. Therefore, the existing renormalization methods cannot be used in a predictive manner, i.e., for the prediction of the LLE curves and CSTs of systems which have not been explored experimentally before.

The problem of the quantitative description of the mutual solubilities of liquids close to the upper (or lower) critical solution temperatures, UCST or LCST, respectively, is a longstanding problem known for more than a century [<NUM>-<NUM>]. All analytic free energy approaches, which often give a reasonable description of the solubility curves as a function of temperature, also called LLE (liquid-liquid equilibrium) curves, for temperatures below <NUM>% of the UCST, strongly fail above this limit. The closure of the predicted LLE curves is much too slow with a critical exponent of <NUM>, typically yielding a predicted UCST which is about <NUM>% high, which can easily be <NUM> - <NUM>. Meanwhile, the experimental LLE curves close very rapidly with a critical exponent of ~<NUM>. For practical application in chemical engineering, e.g. the development of separation processes for chemicals, such inaccurate predictions are often a hindrance for using prediction methods.

Many interpolative methods have been developed, partly based on complicated theories, such as Renormalization Group theory by Ginzburg and Landau [<NUM>]. However, these existing methods require many experiments of the same system in order to fit the numerous model parameters to the experimental data. Furthermore, even with many parameters, it is not trivial to describe the unusual behavior with the critical exponent of <NUM> adequately. Most approaches, which are accurate close to the UCST, fail in the cross-over region to the analytically well described region.

Molecular simulation in both variants, molecular dynamics simulations and Monte Carlo Simulations are able to describe the critical behavior if sufficiently large systems are simulated for a very long time. However, this requires dramatically long simulation times. Furthermore, the thermodynamic accuracy of such force-field-based simulation approaches is typically much lower than the accuracy of analytic free energy models. Therefore, such simulations are not at all of practical interest for industrial applications, i.e., simulation, development, and manufacturing of real-world liquid mixtures.

A predictive method, which can be efficiently applied to free energy curves resulting from a good predictive free energy model, in order to provide robust, improved, LLE predictions close to the UCST, without using any experimental data of the system, is still missing.

Embodiments of the present invention address the foregoing shortcomings in the art and provide such functionality. <FIG> is a flowchart of one such computer implemented method <NUM> for simulating a liquid mixture. The method <NUM> starts at step <NUM> by receiving a free energy curve of a liquid mixture comprising two components. Because the method <NUM> is computer-implemented, the free energy curve may be received at step <NUM> from any point communicatively coupled to the computing device implementing the method <NUM>. The curve received at step <NUM> may pertain to any binary liquid mixture known in the art and, likewise, the two components may be any components known in the art. For example, cylclooctane and pentafluorobutane, amongst other examples. In an embodiment of the method <NUM>, the free energy curve received at step <NUM> is in the form of a mathematical representation. For example, the free energy curve received at step <NUM> (an unrenormalized free energy curve) may be in the form: <MAT> where k is the Boltzmann constant, T is the temperature, x<NUM> and x<NUM> are the mole fractions, and γ<NUM> and γ<NUM> are the activity coefficients of the of the two components. The latter may be taken from any analytic activity coefficient model such as NRTL, UNIQUAC, Wilson, and van Laar, amongst others, or from the COSMOSPACE model. The logarithmic activity coefficient may be taken from the NRTL model (Non-Random-Two-Liquid-Model, <NPL>). If the logarithmic activity coefficient is taken from the NRTL model, the mathematical expression for the logarithmic activity coefficient is given by: <MAT> <MAT> where the τij and Gij are parameters adjusted to the system.

Returning to <FIG>, at step <NUM>, a partition function describing fluctuations of mole fractions of the two components in the liquid mixture is constructed based on the received free energy curve. In an embodiment of the method <NUM>, the partition function is constructed at step <NUM> using the functionality described hereinbelow in relation to equations (<NUM>)-(<NUM>). According to an embodiment of the method <NUM>, the partition function constructed at step <NUM> using equations (<NUM>)-(<NUM>) covers or takes into account symmetric and asymmetric fluctuations of the mole fractions of the two components around an average mole fraction.

To continue, at step <NUM>, a renormalized free energy curve of the liquid mixture is calculated using the constructed partition function resulting from or output by step <NUM>. An example of the renormalized free energy curve calculated at step <NUM> is given by the equation (<NUM>) below. According to an embodiment, the renormalized free energy curve calculated at step <NUM> is a negative logarithm of the constructed partition function multiplied by molar thermal energy RT. In yet another example embodiment, the renormalized free energy curve calculated at step <NUM> is a function of a temperature scaling parameter. In such an embodiment of the method <NUM>, the temperature scaling parameter can be a constant or a function of properties determined based on the free energy curve of the liquid mixture received at step <NUM>.

At step <NUM>, the behavior of the liquid mixture is simulated using the calculated renormalized free energy curve from step <NUM>. In an embodiment of the method <NUM>, simulating behavior of the liquid mixture at step <NUM> using the calculated renormalized free energy curve includes predicting liquid-liquid-equilibrium of the liquid mixture using a tangent construction method. Embodiments may use any implementation of the tangent construction method known in the art, such as the functionality described in [<NUM>] <NPL>. Performing the simulation at step <NUM> may predict a variety of different properties of the behavior of the liquid mixture. For example, embodiments of the method <NUM> may predict critical solution temperature, lower critical solution temperature, upper critical solution temperature, and/or renormalized equilibrium compositions, i.e., mutual solubilities, of the two components (compounds), amongst other examples.

In an embodiment of the present invention, e.g., the method <NUM>, renormalization of a free energy function g(x) is described by the following equations: <MAT> <MAT>.

Equation <NUM> indicates that the renormalized free energy of the system, including the free energy contributions resulting from the critical fluctuations, is calculated from a logarithm of a partition function. According to fundamental statistical thermodynamics, this is even the definition of the free energy. The art of statistical thermodynamics is to find the right way of enumerating the states of a system.

Equation <NUM> indicates that at a given total composition x, any fluctuation conserves this average concentration. Traditional renormalization theories only consider symmetric fluctuations consisting of two equal regions with compositions x+δ and x-δ. Since negative compositions are impossible, this definition restricts δ to the range <NUM> < δ < x, which means, that no fluctuation could reach a composition larger than 2δ. The other physically unrealistic aspect of the symmetric (x+δ, x-δ) fluctuations usually not taken into account, is the free energy of the cross-over region between the extremes. However, a fluctuation unavoidably has such cross-over regions. Embodiments overcome these problems for the first time in the art by using a two dimensional representation of the fluctuations, characterized by their extreme compositions y < x and z > x, where g(x, y, z) is the averaged free energy of the considered fluctuation, based on the underlying analytic free energy model.

For a given set of mole fractions x, y, and z, one of the possible assumptions for the shape of the fluctuation of the free energy g(x, y, z) is given by a linear weight function. The shape of the fluctuation of the free energy can also be given by an exponential weight function or a piecewise linear weight function, amongst other examples. In such an embodiment, the free energy is given by the integral of all intermediate mole fractions between y and z with a linear interpolation weight function: <MAT>.

The norm of the weight function is unity (<NUM>) and the average composition is x, resulting in equations <NUM> and <NUM>: <MAT>.

Equations (<NUM>) and (<NUM>) can be solved analytically, resulting in equations <NUM> and <NUM>: <MAT>.

These equations <NUM> - <NUM> thus describe a complete model for the calculation of the renormalized free energy. The equilibrium compositions can be derived from this model by thermodynamic standard methods, as the search for the two minimum of the the free energy for symmetric systems, or the tangent line search for asymmetric systems. The above equations have the scaling factor λ as the only empirical parameter. <NUM>/λ may be interpreted as the number of molecules which is required in order to define the composition of a volume region, since a single molecule does not define a composition.

For the examples described below in relation to <FIG>, λ = <NUM>. It can be interpreted that about <NUM> molecules build up a sufficient volume to define a composition in composition space. The results in <FIG> compare results determined using embodiments of the present invention with results determined using lattice-Monte-Carlo (LMC) techniques.

The plot <NUM> in <FIG> shows the results of simulation determining LLE curves for the four Ising-analogues for 3D-lattices diamond, simple-cubic, face-centered cubic (fcc), and body-centered cubic (bcc) with the correspnding coordination numbers, i.e. the number of nearest neighbor molecules, of <NUM>, <NUM>, <NUM>, and <NUM>, respectively. The lines 331a-d are the LMC results, which can be considered as essentially exact in these Ising cases. The lines 332a-d are the results of the corresponding COSMOSPACE calculations. The lines 333a-d are the results generated using an embodiment of the present invention, e.g., CAFE which may include the method <NUM>. The plot <NUM> shows that embodiments of the present invention provide a good fit of all <NUM> cases.

The plot <NUM> of <FIG> shows LLE curves and renormalized LLE curves (determined using embodiments) of a lattice fluid mixture of a polar pseudo-compound (pseudo-water) and a non-polar pseudo-compound (pseudo-methane). In <FIG>, the LMC results (lines <NUM> and <NUM>) were determined using Hahn & Klamt [<NUM>]. The unrenormalized free energy curve <NUM> and LLE curve <NUM> were produced with the COSMOSPACE method [<NUM>]. In the plot <NUM> the LLE curves <NUM>-<NUM> become asymmetric due to the different interactions. The lines <NUM> and <NUM> show the results generated using embodiments of the present invention, i.e., CAFE. Although the results <NUM> and <NUM> generated using embodiments of the present invention do not give a perfect match with the LMC results <NUM> and <NUM>, the results <NUM> and <NUM> generated using embodiments give a good quantification of the critical fluctuation effect. It is noted, that these LMC results <NUM> and <NUM> also have a substantial uncertainty.

The plot <NUM> in <FIG> illustrates LLE curves for size-asymmetric systems, where compound <NUM> consists of <NUM> cube, while compound two is built from <NUM>, <NUM>, <NUM>, and <NUM> linearly connected cubes, respectively (from left LLE to right LLE). The LMC (series <NUM>) calculations were performed by Max Hahn. Series <NUM> are the COSMOSPACE results, using the standard combinatorial free energy expression of COSMOTHERM®. Series <NUM> are the CAFE results, i.e., results generated using an embodiment of the present invention, based on the COSMOSPACE+COSMOcombi free energy curves. <FIG> shows that the CAFE results (<NUM>) are not in perfect agrement with LMC (<NUM>), but give a considerable improvement over the COSMOSPACE LLE curves (<NUM>) in all cases.

An embodiment corrects, i.e. renormalizes, the predicted critical fluctuation miscibility gap (LLE points) of a liquid mixture based on the total free energy profiles calculated with an accurate predictive pairwise surface segment fluid phase thermodynamics model, which has not been fitted to experimental or Monte-Carlo-Simulation data of the liquid mixture under consideration.

Embodiments can be used predictively without the need for system-specific adjustable parameters. Embodiments are computationally efficient and robust. Embodiments also provide a renormalized total free energy curve, which has numerous applications. For instance, the renormalized total free energy curve may be used to calculate renormalized activity coefficients, which may be used for LLE prediction in thermodynamic simulations, amongst other examples. No methods exist in the art to date for providing such renormalized free energy curves.

Embodiments of the present invention, e.g., the method <NUM>, are computer implemented. As such, embodiments may be implemented using any combination of processors and computer memory programmed in such a way so as to perform the functionality described herein. For instance, an embodiment that implements CAFE renormalization of a free energy function g(x) can be implemented by the following FORTRAN subroutine:
<IMG>
<IMG>.

Hereinbelow, an example application of an embodiment of the present invention is provided. In such an illustrative embodiment, a refrigeration machine producer plans to optimize a refrigeration medium by using mixtures of refrigerants. The process needs to operate in the homogeneous mixture region and, thus, it is crucial for him to forecast the miscibility range of mixtures. An example embodiment can be used to make such a forecast. It is noted that the example implementation described below is but one example use of embodiments and embodiments can be employed for any application where computer-based or computer-automated liquid simulation is desired.

This example embodiment simulates a mixture of alkane cyclooctane with a partially fluorinated compound <NUM>,<NUM>,<NUM>,<NUM>,<NUM>-pentafluorobutane (PFB). In such an embodiment, an existing simulation application, e.g., the predictive thermodynamic model COSMO-RS in its commercially available COSMOTHERM® implementation, is used to calculate the liquid-liquid equilibrium (LLE) curve of this binary mixture. Input requires the DFT/COSMO surface polarity information of both compounds, which is calculated with an existing application, such as the quantum-chemical program TURBOMOLE (or equivalent other quantum chemical programs). The results of these calculations are shown in <FIG> for both compounds, cyclooctane and PFB. <FIG> illustrates the surface polarity 660a, i.e., DFT/COSMO surface polarization charge density of cyclooctane. For PFB two relevant intramolecular geometries, so-called conformations, are taken into account. <FIG> depict the surface polarities 660b and 660c, respectively, for the two relevant geometries of PFB.

To continue this illustrative embodiment, a user can load these COSMO results into the COSMOTHERM® program (or other such program to calculate LLE) and select the LLE calculation panel. A start temperature for the LLE search is then set (in the example - <NUM>) and the COSMOTHERM® program automatically calculates the unrenormalized LLE points in predefined temperature steps. At each temperature the program calculates the total free energy curve. This free energy curve can then be processed as described herein, e.g., using the method <NUM>, to determine a renormalized LLE curve. In an example implementation, a local addition to the COSMOTHERM® program (or other such program used to determine LLE), is configured to apply an embodiment of the present invention (e.g., CAFE renormalization equations <NUM>-<NUM> or CAFE subroutine as given above) and searches for the LLE points using a tangent procedure.

The plot <NUM> in <FIG> shows the unrenormalized miscibility curve <NUM> with the typical parabolic behavior near the UCST which is approximately <NUM>. Applying embodiments of the present invention, e.g., CAFE renormalization procedures, upon the original free energy curves from COSMOTHERM®, yields the LLE curve <NUM> with the typical flat region close to the UCST, which now is <NUM>. As such, by applying the example embodiment of the present invention, it is determined that the correct homogeneous temperature range reaches down to about <NUM>, while unrenormalized COSMOTHERM® would have yielded about <NUM> as the lower limit of homogeneity. Based on this more precise prediction, a user can make better selections of promising refrigerants mixtures before tests are run in the lab.

<FIG> is a simplified block diagram of a computer-based system <NUM> that may be used to simulate a liquid mixture according to any variety of the embodiments of the invention described herein. The system <NUM> comprises a bus <NUM>. The bus <NUM> serves as an interconnect between the various components of the system <NUM>. Connected to the bus <NUM> is an input/output device interface <NUM> for connecting various input and output devices such as a keyboard, mouse, touch screen, display, speakers, etc. to the system <NUM>. A central processing unit (CPU) <NUM> is connected to the bus <NUM> and provides for the execution of computer instructions. Memory <NUM> provides volatile storage for data used for carrying out computer instructions. Storage <NUM> provides non-volatile storage for software instructions, such as an operating system (not shown). The system <NUM> also comprises a network interface <NUM> for connecting to any variety of networks known in the art, including wide area networks (WANs) and local area networks (LANs).

It should be understood that the example embodiments described herein may be implemented in many different ways. In some instances, the various methods and machines described herein may each be implemented by a physical, virtual, or hybrid general purpose computer, such as the computer system <NUM>, or a computer network environment such as the computer environment <NUM>, described herein below in relation to <FIG>. The computer system <NUM> may be transformed into the machines that execute the methods described herein, for example, by loading software instructions implementing method <NUM> into either memory <NUM> or non-volatile storage <NUM> for execution by the CPU <NUM>. One of ordinary skill in the art should further understand that the system <NUM> and its various components may be configured to carry out any embodiments or combination of embodiments of the present invention described herein. Further, the system <NUM> may implement the various embodiments described herein utilizing any combination of hardware, software, and firmware modules operatively coupled, internally, or externally, to the system <NUM>.

<FIG> illustrates a computer network environment <NUM> in which an embodiment of the present invention may be implemented. In the computer network environment <NUM>, the server <NUM> is linked through the communications network <NUM> to the clients 993a-n. The environment <NUM> may be used to allow the clients 993a-n, alone or in combination with the server <NUM>, to execute any of the embodiments described herein. For non-limiting example, computer network environment <NUM> provides cloud computing embodiments, software as a service (SAAS) embodiments, and the like.

Embodiments or aspects thereof may be implemented in the form of hardware, firmware, or software. If implemented in software, the software may be stored on any non-transient computer readable medium that is configured to enable a processor to load the software or subsets of instructions thereof. The processor then executes the instructions and is configured to operate or cause an apparatus to operate in a manner as described herein.

Further, firmware, software, routines, or instructions may be described herein as performing certain actions and/or functions of the data processors. However, it should be appreciated that such descriptions contained herein are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc..

It should be understood that the flow diagrams, block diagrams, and network diagrams may include more or fewer elements, be arranged differently, or be represented differently.

But it further should be understood that certain implementations may dictate the block and network diagrams and the number of block and network diagrams illustrating the execution of the embodiments be implemented in a particular way.

Accordingly, further embodiments may also be implemented in a variety of computer architectures, physical, virtual, cloud computers, and/or some combination thereof, and thus, the data processors described herein are intended for purposes of illustration only and not as a limitation of the embodiments.

Claim 1:
A computer implemented method for simulating a liquid mixture, the method comprising:
receiving 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;
calculating a renormalized free energy curve of the liquid mixture using the constructed partition function; and
simulating behavior of the liquid mixture using the calculated renormalized free energy curve;
wherein simulating behavior of the liquid mixture using the calculated renormalized free energy curve includes predicting at least one of:
critical solution temperature;
lower critical solution temperature;
upper critical solution temperature; and
renormalized equilibrium compositions of the two components.