CN112802559A - Method for rapidly debugging graphene-ion average force potential field in aqueous solution based on thermodynamic cycle principle - Google Patents
Method for rapidly debugging graphene-ion average force potential field in aqueous solution based on thermodynamic cycle principle Download PDFInfo
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Abstract
The invention discloses a method for quickly debugging a graphene-ion average force potential field in an aqueous solution based on a thermodynamic cycle principle. The method comprises the following steps: firstly, calculating an ion reference PMF, then calculating an ion and graphene vacuum PMF, and then superposing the ion reference PMF and the graphene vacuum PMF to obtain an ion-graphene PMF in an aqueous solution system, so as to obtain the graphene-ion average force potential field. The method is based on the principle of thermodynamic cycle, takes PMF of ions shielding graphene-ion action field parameters in aqueous solution as a reference, and superposes the graphene-ion PMF of the ions in vacuum to obtain PMF of any new graphene-ion action field parameters. The method can be used for debugging the graphene-ion PMF in the aqueous solution, has the advantages of rapidness, accuracy and the like, and can reduce the consumption of computing resources to hundreds of ten or even less than the original consumption.
Description
Technical Field
The invention belongs to the field of force field parameter debugging of computational chemistry molecular dynamics simulation, and particularly relates to a method for quickly debugging a graphene-ion average force potential field in an aqueous solution based on a thermodynamic cycle principle.
Background
The graphene-graphene interaction in the aqueous solution is the core of the fields of low-energy consumption and large-scale seawater desalination, low-cost sewage treatment and the like, and the ion-graphene interaction in the aqueous solution plays a significant role in promoting the development of the fields. To better explore the ion-graphene interaction in aqueous solutions, it is necessary to accurately test the PMF of graphene to ions. On the basis, various graphene-salt solution devices can be designed and the actual using effect of the devices can be estimated. PMFs of graphene-ions in aqueous solutions are difficult to determine experimentally and are therefore generally calculated using Umbrella Sampling (US) in the Molecular Dynamics (MD) method. However, in an aqueous environment, the ion-pi polarization between graphene and ions makes conventional force fields unable to accurately describe graphene-ion interactions.
Recently, williams.c.d., dix.j. et al, have proposed a new idea to solve this problem: the effect of simulating ion-pi polarization between ions and graphene is achieved by correcting the epsilon parameter of ion-graphene carbon atom interaction, so that an accurate PMF curve is obtained. However, the method needs to test a large number of different graphene-ion force field epsilon parameters, and the parameters are compared with standard adsorption energy, so that correct and available force field parameters are screened out. However, the US method calculates PMF of graphene-ions in aqueous solution in large amount, and is difficult to converge, requiring a large amount of calculation resources to be consumed. Also today there are many water models and ion models (force field parameters) and as the actual production progresses, more new water models and ion models will emerge. To calculate the PMFs of all the graphene-ions of the water model and the ion model in the aqueous solution, a large amount of computing resources are required, which is difficult to complete.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a method for quickly debugging the average force-potential field of graphene-ions in an aqueous solution based on the thermodynamic cycle principle.
The invention provides a method for quickly debugging a graphene-ion average force field in an aqueous solution based on a thermodynamic cycle principle, which is a method for improving the debugging efficiency of graphene and ion action force field parameters based on thermodynamic cycle.
The invention aims to provide a vacuum PMF superposition algorithm for accurately and quickly calculating graphene-ion PMF in an aqueous solution aiming at the problem that huge calculation resources are needed for calculating the graphene-ion PMF in the aqueous solution at present.
The purpose of the invention is realized by at least one of the following technical solutions.
The method for rapidly debugging the graphene-ion average force potential field (PMF) in the aqueous solution based on the thermodynamic cycle principle comprises the steps of firstly calculating an ion reference PMF, then calculating an ion and graphene vacuum PMF, and then superposing the ion reference PMF and the graphene vacuum PMF to obtain the ion-graphene PMF in the aqueous solution system, so as to obtain the graphene-ion average force potential field.
The process of calculating an ion reference, comprising: firstly, constructing an initial simulation system; and then setting the ion-graphene force field to be 0, performing pre-equilibrium simulation by using a molecular dynamics method, constructing an umbrella-shaped sampling simulation system by using the molecular dynamics method, simulating by using the umbrella-shaped sampling method by using the molecular dynamics method, and calculating the reference PMF by using a weighted histogram analysis method.
The process for calculating the ion and graphene vacuum PMF comprises: and (3) constructing a vacuum simulation system, simulating by using a molecular dynamics method umbrella-shaped sampling method and calculating the vacuum PMF by using a weighted histogram analysis method.
The invention provides a method for quickly debugging a graphene-ion average force potential field in an aqueous solution based on a thermodynamic cycle principle, which specifically comprises the following steps:
(1) establishing a simulation box in Gromacs software, placing a graphene sheet in the bottom of the simulation box, inserting an ion into a position of an initial reaction coordinate right above the graphene sheet, then inserting water molecules into the simulation box (performing box solvation), setting a non-bond action parameter of the graphene sheet and the ion to be 0 in a top file (so as to realize an effect of shielding ion-graphene interaction), then performing NPT pre-equilibrium simulation under a fixed graphene and ion coordinate state, then performing traction simulation, selecting a series of windows above the center of the graphene in an intermediate configuration of the traction simulation as a US (Umbrella sampling) initial configuration, performing US simulation on the US initial configuration, and calculating through a WHAM (weighted high gradient Analysis method) to obtain a reference PMF (potential Mean force);
(2) taking the US initial configuration of the reference PMF in the step (1), removing water molecules, taking the US initial configuration as the US configuration of the vacuum PMF, then carrying out US simulation, and obtaining the vacuum PMF through WHAM calculation;
(3) and (3) superposing the reference PMF in the step (1) and the vacuum PFM in the step (2) to obtain the graphene-ion average force potential field parameters in the aqueous solution.
Further, the dimensions of the simulated box of step (1) are 3.5nm × 3.5nm × 3.5nm to 5.0nm × 5.0nm × 5.0 nm; the graphene sheet of step (1) comprises 24 to 96 carbon atoms and 12 to 24 hydrogen atoms.
Preferably, the graphene sheet of step (1) comprises 54 carbon atoms and 14 hydrogen atoms.
Further, the ion in the step (1) is Li+、Na+、K+、Ca2+、Mg2+、Cl-One kind of (1).
Further, in the step (1), after the ions are inserted into the simulation box, the distance between the initial position and the upper part of the graphene sheet is 0.05nm to 0.15 nm; the number ratio of the ions to the water molecules is 1351:1 to 4040: 1.
Further, in the NPT pre-equilibrium simulation of step (1), the simulation step size is 0.5fs to 2fs, and the time of the NPT pre-equilibrium simulation is 5ns to 10 ns.
Further, in the traction simulation in the step (1), the simulation step length is 0.5fs to 2fs, the moving speed of ions is 0.001nm/ps to 0.01nm/ps, the traction simulation time is 5ns to 10ns, and the traction potential energy is 1000mol nm2To 3000mol nm2。
Further, the distance between a window above the positive center of the graphene in the step (1) and the initial reaction coordinate is 0.05nm to 3 nm; the number of the windows is 15-30, and the interval between every two windows is 0.05 nm-0.1 nm.
Further, in the US simulation of the step (1), the simulation step length is 0.5fs to 2fs, the US simulation time is 5ns to 10ns, and the traction potential energy is 1000mol nm2To 3000mol nm2。
The reference PMF in the step (1) is obtained by performing US simulation on each configuration by using a force field parameter of shielding ion-graphene interaction and calculating through a Weighted Histogram Analysis (WHAM) method after the simulation is completed.
Further, in the US simulation of the step (2), the parameters of the series of graphene-ion force fields epsilon are set to be from 0.5kJ/mol to 15.0kJ/mol, and the intervals are from 0.01kJ/mol to 0.5 kJ/mol.
In the step (2), because the vacuum environment is adopted, the balance of solvent molecules does not need to be considered, and therefore a series of US initial configurations along the reaction coordinate can be directly constructed.
Further, in the step (3), the superimposing of the reference PMF and the vacuum PMF includes: aligning x-axis coordinates of the reference PMF and the vacuum PMF, and superposing the two to obtain the graphene-ion PMF in the solution system, namely the graphene-ion average force potential field parameters in the aqueous solution.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the invention provides a vacuum PMF superposition algorithm based on thermodynamic cycle, which can solve the problems of time consumption and massive consumption of computing resources in the prior art; according to the method provided by the invention, the accurate calculated convergence value can be easily obtained through the ion-graphene PMF in vacuum, and meanwhile, the required calculation resource is very little compared with the method for directly calculating the graphene-ion PMF in the aqueous solution; the method is feasible and accurate from the thermodynamic aspect by superposing the ion-graphene PMF with the reference PMF in the vacuum environment, and the accuracy of the method is also verified in the following calculation examples.
Drawings
FIG. 1 is a baseline PMF profile, a vacuum PMF profile and a PMF profile in a synthetic aqueous solution obtained by the method of example 1;
FIG. 2 is a PMF curve in a synthetic aqueous solution obtained by the method of example 1 and a PMF curve obtained by conventional US;
FIG. 3 is a graph of the results of the calculation resource consumption obtained by the method of example 1 and the calculation resource consumption estimated by the conventional US method;
FIG. 4 is a baseline PMF profile, a vacuum PMF profile and a PMF profile in a synthetic aqueous solution obtained by the method of example 2;
FIG. 5 is a PMF curve in a synthetic aqueous solution obtained by the method of example 2 and a PMF curve obtained by conventional US;
FIG. 6 is a baseline PMF profile, a vacuum PMF profile and a PMF profile in a synthetic aqueous solution obtained by the method of example 3;
FIG. 7 is a PMF curve in synthetic aqueous solution obtained by the method of example 3 and a PMF curve obtained by conventional US.
Detailed Description
The following examples are presented to further illustrate the practice of the invention, but the practice and protection of the invention is not limited thereto. It is noted that the processes described below, if not specifically described in detail, are all realizable or understandable by those skilled in the art with reference to the prior art. The reagents or apparatus used are not indicated to the manufacturer, and are considered to be conventional products available by commercial purchase.
Example 1
Calculating graphene-Na in aqueous solution by adopting vacuum PMF superposition method+PMF curve of the ion: in the present example, Gromacs software was used to perform MD simulation, and the water molecule model was SPC-E.
(1) Calculating a reference PMF: firstly, constructing a simulation box with the size of 3.5 multiplied by 3.5nm, placing a graphene sheet containing 54 carbon atoms and 14 hydrogen atoms at the bottom of the simulation box, and inserting Na+Ions were taken as initial reaction coordinates 0.05nm above the very center of the graphene sheet, 1351 water molecules were subsequently inserted into the simulated system, while graphene-Na was inserted in the top file+Setting the non-bonding action parameter of the ions to be 0, and carrying out NPT (neutral point test) pre-balance simulation of 10ns in a step length of 2fs, wherein the coordinate of the graphene is fixed in the simulation process, and the subsequent simulation is the same; then, traction simulation is carried out for 10ns at a constant speed of 0.001nm/ps and step length of 0.5fs, and the magnitude of the traction force is 1000mol nm2Selecting the graphene above the positive center in the middle configuration of the traction simulationTaking 15 windows as US initial configurations, wherein the interval between two adjacent windows is 0.1nm, the distance between the window above the positive center of the graphene and an initial reaction coordinate is 0.1nm-1.5nm, and then carrying out US simulation of 10ns on each configuration by using 2fs, wherein NVT ensemble is adopted in the US simulation; the simulation results were calculated by WHAM to obtain the reference PMF (the curve is shown in FIG. 1).
(2) Calculation of vacuum PMF: and (3) taking the US configuration of the reference PMF, removing water molecules to obtain the US configuration of the vacuum PMF, setting the epsilon parameter of a series of graphene-Na + force fields to be 0.5kJ/mol to 5.0kJ/mol, setting the interval to be 0.05kJ/mol, then respectively carrying out US simulation, and respectively calculating the vacuum PMF through WHAM to obtain a series of vacuum PMFs.
(3) PMF in superimposed aqueous solution: superposing the reference PMF obtained in the step (1) with a series of vacuum PMFs to obtain a series of PMFs in the aqueous solution, wherein the steps are as follows: respectively aligning the x-axis coordinates of the reference PMF and a series of vacuum PMFs, and superposing the reference PMF and the series of vacuum PMFs to obtain the graphene-ion PMF in a series of aqueous solution systems.
FIG. 1 is a baseline PMF profile, a vacuum PMF profile and a PMF profile in a synthetic aqueous solution obtained by the method of example 1; FIG. 2 is a PMF curve in a synthetic aqueous solution obtained by the method of example 1 and a PMF curve obtained by conventional US; FIG. 3 is a graph of the results of the calculation resource consumption obtained by the method of example 1 and the calculation resource consumption estimated by the conventional US method.
By comparing standard adsorption energy, the correct epsilon i-pi parameter is 1.95kJ/mol (i represents ion, pi represents pi bond of graphene, and i-pi is polarization generated between the ion and the graphene pi bond, the same is applied below). Fig. 2 shows the results of the present embodiment using the novel algorithm and the results of the conventional US method, and it can be seen that the accuracy of the novel algorithm is not different from the conventional method. In this example, the calculation of the reference PMF (using 15 windows) takes 15.43CPU hours, and the calculation of the vacuum PMF (using 15 windows) takes 1.12CPU hours. Fig. 3 shows a calculation resource consumption curve of the present embodiment, and it can be seen that as the number of times of calculation increases, the new algorithm saves more and more calculation resources than the conventional US method.
As can be seen from fig. 1, 2, and 3, embodiment 1 of the present invention provides a vacuum PMF stacking algorithm based on thermodynamic cycle, which can solve the problem of time consuming and massive computing resource consumption in the prior art; according to the method provided by the embodiment 1 of the invention, the accurate calculated convergence value can be easily obtained through the ion-graphene PMF in vacuum, and meanwhile, the required calculation resources are much less than that of a method for directly calculating the graphene-ion PMF in the aqueous solution.
Example 2
Calculating graphene-Mg in aqueous solution by adopting vacuum PMF superposition method2+PMF curve of the ion: in the present example, Gromacs software was used to perform MD simulation, and the water molecule model was SPC-E.
(1) Calculating a reference PMF: firstly, constructing a simulation box with the size of 4.0 multiplied by 4.0nm, placing a graphene sheet containing 54 carbon atoms and 14 hydrogen atoms at the bottom of the simulation box, and inserting Mg2+Ions are taken as initial reaction coordinates 0.075nm above the exact center of the graphene sheet, 2108 water molecules are then inserted into the simulated system, and graphene-Mg is added in the top file2+Setting the non-bonding action parameter of the ions to be 0, and carrying out 8ns NPT pre-balance simulation with the step length of 1fs, wherein the coordinate of the graphene is fixed in the simulation process, and the subsequent simulation is the same; carrying out 8ns traction simulation at a constant speed of 0.005nm/ps and a step length of 1fs, selecting 15 windows above the positive center of graphene in an intermediate configuration of the traction simulation as an US initial configuration, wherein the interval between two adjacent windows is 0.075nm, the distance between the window above the positive center of the graphene and an initial reaction coordinate is 0.075nm-1.125nm, and then carrying out 8ns US simulation on each configuration with 1fs, wherein the US simulation adopts an NVT (noise, vibration and harshness) ensemble; and obtaining a reference PMF through WHAM calculation according to the simulation result.
(2) Calculation of vacuum PMF: taking the US configuration of a reference PMF, removing water molecules to be used as the US configuration of a vacuum PMF, and arranging a series of graphene-Mg2+The parameter of the force field epsilon is 4.0kJ/mol to 15.0kJ/mol, the interval is 0.5kJ/mol, then US simulation is respectively carried out, and then the vacuum PMF is respectively calculated by WHAM, so as to obtain a series of vacuum PMFs.
(3) PMF in superimposed aqueous solution: superposing the reference PMF obtained in the step (1) with a series of vacuum PMFs to obtain a series of PMFs in the aqueous solution, wherein the steps are as follows: respectively aligning the x-axis coordinates of the reference PMF and a series of vacuum PMFs, and superposing the reference PMF and the series of vacuum PMFs to obtain the graphene-ion PMF in a series of aqueous solution systems.
FIG. 4 is a baseline PMF profile, a vacuum PMF profile and a PMF profile in a synthetic aqueous solution obtained by the method of example 2; FIG. 5 is a PMF curve in a synthetic aqueous solution obtained by the method of example 2 and a PMF curve obtained by conventional US.
By comparison with the standard adsorption energy, the correct ε i- π parameter was found to be 5.5 kJ/mol. In this example, the calculation of the baseline PMF (using 15 windows) takes 13.35CPU hours, and the calculation of the vacuum PMF (using 15 windows) takes 1.14CPU hours.
As can be seen from fig. 4 and 5, embodiment 2 of the present invention proposes a vacuum PMF stacking algorithm based on thermodynamic cycle, which can solve the problem of time consuming and massive computing resource consumption in the prior art; according to the method provided by the embodiment 2 of the invention, the accurate calculated convergence value can be easily obtained through the ion-graphene PMF in vacuum, and meanwhile, the required calculation resources are much less than that of a method for directly calculating the graphene-ion PMF in the aqueous solution.
Example 3
graphene-Cl in aqueous solution is calculated by adopting vacuum PMF superposition method-PMF curve of the ion: in the present example, Gromacs software was used to perform MD simulation, and the water molecule model was SPC-E.
(1) Calculating a reference PMF: firstly, constructing a simulation box with the size of 5.0 multiplied by 5.0nm, placing a graphene sheet containing 54 carbon atoms and 14 hydrogen atoms at the bottom of the simulation box, and inserting Cl-Ions are taken as initial reaction coordinates 0.1nm above the positive center of a graphene sheet, 4040 water molecules are inserted into a simulation system, and graphene-Cl is added into a top file-Setting the non-bonding action parameter of the ions to be 0, and carrying out 5ns of NPT pre-balance simulation in a step length of 0.5fs, wherein the coordinate of the graphene is fixed in the simulation process, and the subsequent simulation is the same; carrying out 5ns traction simulation at a constant speed of 0.01nm/ps and a step length of 0.5fs, selecting 15 windows above the positive center of the graphene from the middle configuration of the traction simulation as an US initial configuration, wherein the interval between two adjacent windows is 0.05nm, and the distance between the window above the positive center of the graphene and an initial reaction coordinate is 0.05nm-0.75nm, and then carrying out 5ns US simulation on each configuration at 0.5fs, wherein the US simulation adopts NVT ensemble; and obtaining a reference PMF through WHAM calculation according to the simulation result.
(2) Calculation of vacuum PMF: taking the US configuration of a reference PMF, removing water molecules to serve as the US configuration of a vacuum PMF, and arranging a series of graphene-Cl-The parameter of the force field epsilon is 0.5kJ/mol to 1.5kJ/mol, the interval is 0.01kJ/mol, then US simulation is respectively carried out, and then the vacuum PMF is respectively calculated by WHAM, so as to obtain a series of vacuum PMFs.
(3) PMF in superimposed aqueous solution: superposing the reference PMF obtained in the step (1) with a series of vacuum PMFs to obtain a series of PMFs in the aqueous solution, wherein the steps are as follows: respectively aligning the x-axis coordinates of the reference PMF and a series of vacuum PMFs, and superposing the reference PMF and the series of vacuum PMFs to obtain the graphene-ion PMF in a series of aqueous solution systems.
FIG. 6 is a baseline PMF profile, a vacuum PMF profile and a PMF profile in a synthetic aqueous solution obtained by the method of example 3; FIG. 7 is a PMF curve in synthetic aqueous solution obtained by the method of example 3 and a PMF curve obtained by conventional US.
By comparison with the standard adsorption energy, the correct ε i- π parameter was found to be 1.48 kJ/mol.
In this example, the calculation of the baseline PMF (using 15 windows) takes 13.07CPU hours, and the calculation of the vacuum PMF (using 15 windows) takes 1.13CPU hours.
As can be seen from fig. 6 and 7, embodiment 3 of the present invention proposes a vacuum PMF stacking algorithm based on thermodynamic cycle, which can solve the problem of time consuming and massive computing resource consumption in the prior art; according to the method provided by the embodiment 3 of the invention, the accurate calculated convergence value can be easily obtained through the ion-graphene PMF in vacuum, and meanwhile, the required calculation resources are much less than that of a method for directly calculating the graphene-ion PMF in the aqueous solution.
The above examples are only preferred embodiments of the present invention, which are intended to be illustrative and not limiting, and those skilled in the art should understand that they can make various changes, substitutions and alterations without departing from the spirit and scope of the invention.
Claims (10)
1. A method for rapidly debugging a graphene-ion average force potential field in an aqueous solution based on a thermodynamic cycle principle is characterized by comprising the following steps:
(1) establishing a simulation box in Gromacs software, placing a graphene sheet in the bottom of the simulation box, inserting an ion into a position located at an initial reaction coordinate right above the graphene sheet, then inserting a water molecule into the simulation box, simultaneously setting a non-bond action parameter of the graphene sheet and the ion to be 0 in a top file, then performing NPT pre-equilibrium simulation under the condition of fixing the coordinates of the graphene and the ion, then performing traction simulation, selecting a window above the right center of the graphene in the middle configuration of the traction simulation as an US initial configuration, performing US simulation on the US initial configuration, and obtaining a reference PMF through WHAM calculation;
(2) taking the US initial configuration of the reference PMF in the step (1), removing water molecules, taking the US initial configuration as the US configuration of the vacuum PMF, then carrying out US simulation, and obtaining the vacuum PMF through WHAM calculation;
(3) and (3) superposing the reference PMF in the step (1) and the vacuum PFM in the step (2) to obtain the graphene-ion average force potential field parameters in the aqueous solution.
2. The method for rapidly debugging graphene-ion average force potential field in aqueous solution based on thermodynamic cycle principle of claim 1, wherein the dimensions of the simulated box of step (1) are 3.5nm x 3.5nm to 5.0nm x 5.0 nm; the graphene sheet of step (1) comprises 24 to 96 carbon atoms and 12 to 24 hydrogen atoms.
3. The method for rapidly debugging graphene-ion average force potential field in aqueous solution based on thermodynamic cycle principle of claim 1, wherein the ion in step (1) is Li+、Na+、K+、Ca2+、Mg2+、Cl-One kind of (1).
4. The method for rapidly debugging the graphene-ion average force potential field in the aqueous solution based on the thermodynamic cycle principle as claimed in claim 1, wherein in the step (1), after the ions are inserted into the simulation box, the distance between the initial position and the upper part of the graphene sheet is 0.05nm to 0.15 nm; the number ratio of the ions to the water molecules is 1351:1 to 4040: 1.
5. The method for rapidly debugging the graphene-ion average force potential field in the aqueous solution based on the thermodynamic cycle principle as claimed in claim 1, wherein in the NPT pre-equilibrium simulation of step (1), the simulation step size is 0.5fs to 2fs, and the NPT pre-equilibrium simulation time is 5ns to 10 ns.
6. The method for rapidly debugging graphene-ion average force potential field in aqueous solution based on thermodynamic cycle principle as claimed in claim 1, wherein in the traction simulation of step (1), the simulation step size is 0.5fs to 2fs, the moving speed of ions is 0.001nm/ps to 0.01nm/ps, the traction simulation time is 5ns to 10ns, and the traction potential energy is 1000 mol-nm2To 3000mol nm2。
7. The method for rapidly debugging the graphene-ion average force potential field in the aqueous solution based on the thermodynamic cycle principle as claimed in claim 1, wherein the distance between the window just above the center of the graphene in the step (1) and the initial reaction coordinate is 0.05nm to 3 nm; the number of the windows is 15-30, and the interval between two adjacent windows is 0.05 nm-0.1 nm.
8. The method for rapidly debugging graphene-ion average force potential field in aqueous solution based on thermodynamic cycle principle as claimed in claim 1, wherein in the US simulation of step (1), the simulation step size is 0.5fs to 2fs, the US simulation time is 5ns to 10ns, and the tractive force potential energy is 1000 mol-nm2To 3000mol nm2。
9. The method for rapidly debugging graphene-ion average force potential field in aqueous solution based on thermodynamic cycle principle as claimed in claim 1, wherein in the US simulation of step (2), the parameter epsilon of the series of graphene-ion force fields is set to be from 0.5kJ/mol to 15.0kJ/mol at intervals of from 0.01kJ/mol to 0.5 kJ/mol.
10. The method for rapidly debugging graphene-ion average force potential field in aqueous solution based on thermodynamic cycle principle according to any one of claims 1-9, wherein the superposition of the reference PMF and the vacuum PMF in step (3) comprises: aligning x-axis coordinates of the reference PMF and the vacuum PMF, and superposing the two to obtain the graphene-ion PMF in the solution system, namely the graphene-ion average force potential field parameters in the aqueous solution.
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