A method for evaluating surfactant complexing system based on molecular dynamics simulation

Abstract

The application provides a surfactant compound system evaluation method based on molecular dynamics simulation. The evaluation method constructs an oil / surfactant / water three-phase system model by means of molecular dynamics theory and simulation calculation software, so as to simulate and evaluate the interfacial behavior of different surfactant compound systems, including the interfacial structure and the interfacial property. The method is not only simple and time-saving, but also greatly shortens the experimental period. In addition, the method can study the microcosmic principle of different surfactant compound systems, provides theoretical guidance for the research of the surfactant compound system, is favorable for the rapid screening of the surfactant compound system in tertiary oil recovery, and has important value for improving the oil recovery rate.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of colloid interface science, and specifically comprises a surfactant complex system evaluation method based on molecular dynamics simulation. BACKGROUND

[0002] Crude oil is an important non-renewable energy source and plays an irreplaceable role in social development. Crude oil is complex in composition and diverse in distribution in the formation. A large amount of crude oil is distributed in the pores of reservoir rocks and is not easy to be produced, so it is necessary to conduct more in-depth research to improve oil recovery. In tertiary oil recovery, chemical flooding technology using surfactants, polymers and other chemicals has always been the main direction of improving oil recovery in China. The interfacial behavior of surfactants is derived from the special hydrophilic-lipophilic structure of the molecules, which can be adsorbed to the interface of the system, significantly reducing the interfacial tension of the oil / water interface, even to ultra-low interfacial tension; it can change the wettability of the rock surface, which is beneficial to the detachment of oil from the rock surface, thereby improving the recovery.

[0003] In practical applications, the effect of a single surfactant is often not ideal, and different types of surfactants are usually combined to provide better performance and achieve excellent synergistic effect. Some complex complex systems are difficult to directly and finely study their interfacial properties by laboratory means, so it is of great significance to study the interfacial structure and properties of complex systems and the micro-mechanism in the oil displacement process from the microscopic point of view for different types of surfactants. SUMMARY

[0004] In view of the above problems existing in the prior art, the purpose of the present application is to provide a surfactant complex system evaluation method based on molecular simulation. The evaluation method studies the interfacial behavior of the surfactant complex system from the molecular level, including the interfacial structure and the interfacial properties, which provides theoretical guidance for the research of the surfactant complex system, and has important value for improving oil recovery.

[0005] To achieve the above object, the technical scheme adopted by the present application comprises:

[0006] The present application discloses a surfactant complex system evaluation method based on molecular dynamics simulation, comprising the following steps:

[0007] (1) Constructing a molecular model of surfactants, water and oil of the complex system, using SPC model for water molecular model, optimizing the initial topological structure of the established surfactants and oil, and calculating the RESP charge of each atom in the molecule, and generating the corresponding force field parameters from the AMBER molecular force field;

[0008] (2) Constructing a surfactant box and stacking along the XY direction;

[0009] (3) performing preliminary processing on the accumulated surfactant box, restraining the position of the hydrophilic ion head of the surfactant, and ensuring that the relative position of the surfactant in the complex system does not change in the pre-processing process, then performing energy minimization processing and pre-equilibrium simulation to obtain a preliminarily balanced surfactant box, i.e., an.mdp file;

[0010] This position constraint fixes the position of each surfactant molecule, and on the other hand, in order to shorten the subsequent equilibrium time, the hydrophilic group of the surfactant is selectively close to the water molecule and the hydrophobic group of the surfactant is close to the oil molecule in the preliminary processing, so that the energy minimization processing and pre-equilibrium simulation are performed in a state closer to equilibrium.

[0011] (4) constructing a water box and an oil box, and then assembling the preliminarily balanced surfactant box into an oil / surfactant / water three-phase system model along the Z direction;

[0012] (5) performing energy minimization processing on the oil / surfactant / water three-phase system model to eliminate unreasonable contacts generated by model building, to obtain a minimized structure file; using the minimized structure file as an input file to perform molecular dynamics simulation to determine the oil / surfactant / water three-phase system model in a stable state, and to collect molecular trajectory files and three-dimensional coordinate files, and to export.xtc and.gro format files;

[0013] (6) analyzing the obtained molecular trajectory files and three-dimensional coordinate files to study the system density, interface arrangement and interaction, and obtaining the evaluation results of the interface behavior of the surfactant molecules in the complex system.

[0014] Further, the specific steps of step (1) are:

[0015] A molecular model of the surfactant and the oil is constructed using the simulation software Gaussian 09, and a coordinate file in.pdb format is exported. The initial topological structure of the surfactant and the oil is calculated at the B3LYP / 6-31+g(d) level for geometric optimization, the RESP charge of all molecules is calculated by B3LYP / 6-31+g(d,p) method using GAFF in AmberTools 19 program, and the van der Waals parameter and bonding parameter of each atom are directly obtained from the AMBER molecular force field;

[0016] The potential energy function used in the AMBER molecular force field is as follows:

[0017]

[0018] Wherein, E is the potential energy of the molecule, K r , K θand V n force constants for bond length, bond angle and dihedral angle, respectively; r eq and θ eq represent equilibrium bond length and bond angle, respectively; r, θ and γ represent bond length, bond angle and initial phase angle, respectively; n is a multiple, and φ is a phase angle; i, j are any two different atoms in the system, ε ij and σ ij are Lennard-Jones parameters between two atoms, ε0is vacuum permittivity, q i and q j represent net charge on two atoms, r ij represents the distance between two atoms.

[0019] Further, the specific steps of step (2) are:

[0020] The coordinate file of the surfactant molecule obtained in step (1) is introduced into the Packmol software, and the surfactant molecules in the complex system are uniformly arranged according to a certain proportion and periodically stacked in the XY direction. Exemplarily, when there are two different types of surfactants (A and B) in the complex system, if the proportion is 1:1, the uniform arrangement at this time means arranging in the AB cycle, and if the proportion is 1:2, the uniform arrangement at this time means periodically arranging in the BAB interpenetrating arrangement to avoid uncontrollable factors caused by the position of the surfactant. Those skilled in the art can also involve other regular arrangement forms according to the number and proportion of the surfactants, such as the random filling method used in the construction of the surfactant box in the traditional method, which is not suitable for two or more than two surfactant complex systems due to randomness and contingency.

[0021] Further, the energy minimization adopts the steepest descent method in the GROMACS software; the convergence criterion of the energy minimization processing is that the system energy converges to less than 100 kJ / mol; the pre-equilibrium simulation adopts the NVT ensemble simulation, and the pre-equilibrium simulation time is 50-100 ps.

[0022] Further, the step (5) of performing the molecular dynamics simulation further comprises: performing NVT ensemble simulation for 500 ps-1 ns to obtain an NVT structure file according to the size of the system; performing NPT ensemble simulation for 1 ns to obtain an NPT structure file by taking the NVT structure file as an input file; and performing NPT ensemble simulation for 5 ns to collect data of the balanced system and calculate after the model is balanced. The duration of the NVT ensemble simulation and the NPT ensemble simulation is not limited to the time disclosed above, as long as the system can reach stability. Since the time to reach stability is shorter in the present application, the duration of the NVT ensemble simulation and the NPT ensemble simulation is also shorter.

[0023] Further, the molecular dynamics simulation adopts a V-rescale temperature control method to control the system temperature, and the system temperature is selected to be 325 K, and the coupling time constant is set to be 0.1 ps.

[0024] Further, the step (5) of performing the molecular dynamics simulation further comprises:

[0025] The Berendsen pressure control method and the V-rescale temperature control method are adopted to control the pressure and the temperature of the 1 ns NPT ensemble simulation, respectively;

[0026] The Parrinello-Rahman pressure control method and the V-rescale temperature control method are adopted to control the pressure and the temperature of the 5 ns NPT ensemble simulation, respectively;

[0027] The system pressure is set to be 1.0 bar, the system temperature is selected to be 325 K, and the coupling time is set to be 1.0 ps.

[0028] Further, the parameters of interest for the interface arrangement include the tilt angle, the stretch degree and the chain segment rising height along the z-axis direction; and the parameters of interest for the interaction include the radial distribution function and the hydrogen bond.

[0029] Further, the.xtc and.gro format files in the step (5) can be viewed by using the VMD software, including the conformation file (gro file) and the trajectory file (trr file / xtc file) at each moment.

[0030] Further, the expression of the radial distribution function is:

[0031]

[0032] wherein N is the total number of oxygen atoms O in water within a distance r from the central atom of the polar head group of the surfactant, p is the number density of oxygen atoms in the water phase, and r is the distance from the central atom of the polar head group of the surfactant to the oxygen atom O in water. w w ​The distance to the central atom of the polar head group of the surfactant, g(r) is the radial distribution function of the oxygen atom and the polar head group of the surfactant.

[0033] Further, the geometric criterion of the hydrogen bond is defined as: the maximum distance between the hydrogen donor (D) and the hydrogen acceptor (A) is 0.35 nm, and the maximum angle of H-D…A is 30°.

[0034] Further, the surfactant includes an anionic surfactant, a cationic surfactant, a nonionic surfactant, or a combination of two or more of an amphoteric surfactant.

[0035] The present application has the following advantages:

[0036] The present application provides a method for evaluating a surfactant complex system based on molecular dynamics simulation, which studies the interfacial behavior of the surfactant complex system from the molecular level, including the interfacial structure and the interfacial properties. The method is not only simple and time-saving, but also greatly shortens the experimental period. It can also study the microcosmic principle of different surfactant complex systems, which provides theoretical guidance for the research of surfactant complex systems, and is conducive to the rapid screening of surfactant complex systems in tertiary oil recovery, which has important value for improving the recovery rate of crude oil. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 The structural schematic diagram of betaine (XSB / ASB / EDAS) and double alkyl chain anionic surfactant (AOT) in the embodiment is shown.

[0038] Figure 2 The simulation structural model of oil / surfactant / water interface in the embodiment is shown.

[0039] Figure 3 The schematic diagram of the density of each component of the AOT and ASB betaine complex system in the embodiment is shown.

[0040] Figure 4 The schematic diagram of AOT molecule and ASB betaine in the embodiment is shown.

[0041] Figure 5 The degree of extension of the C-C1 chain and the C-C2 chain of the AOT molecule in the embodiment is shown.

[0042] Figure 6 The height of the carbon atoms of the C-C1 chain and the C-C2 of the AOT molecule in the embodiment in the z-axis direction is shown.

[0043] Figure 7 The S-O obtained in the embodiment is shown. w The radial distribution function changes with simulation time.

[0044] Figure 8 SO3 in the embodiments - The number of hydrogen bonds with water as a function of simulation time. DETAILED DESCRIPTION

[0045] In order to more clearly illustrate the application, the application will be further described below in conjunction with preferred embodiments and the accompanying drawings. It should be clear that the described embodiments are only a part of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the application.

[0046] Embodiments

[0047] The V-rescale temperature control method was used to control the system temperature, and the system temperature was selected as 325 K, and the coupling time constant was set as 0.1 ps;

[0048] The Berendsen pressure control method was used to control the pressure of the 1 ns NPT ensemble simulation; the system pressure was set to 1.0 bar, and the coupling time was set to 1.0 ps;

[0049] The Parrinello-Rahman pressure control method was used to control the pressure of the 5 ns NPT ensemble simulation; the system pressure was set to 1.0 bar, and the coupling time was set to 1.0 ps.

[0050] The experimental example relates to the interfacial behavior research of betaine and AOT complex system. Specifically, the following steps are included:

[0051] (1) The Gaussian 09 software was used to establish the related molecular models of betaine, AOT and decane, and the coordinate files were saved in the.pdb format. The initial topological structure of the above molecules was calculated by the B3LYP / 6-31+g(d) method, and the molecular structures of betaine and AOT are as shown in Figure 1 The force field parameters used in the simulation process are from the general Amber force field (GAFF) of the AmberTools 19 program, and the restricted electrostatic potential (RESP) atomic charges are calculated by the B3LYP / 6-31+g(d,p) method. The AOT, betaine and n-decane molecular topology files are generated by the ACPYPE program, and the van der Waals parameters and bonding parameters of each atom are directly obtained from the AMBER molecular force field. The water molecules use a simple SPC model;

[0052] The potential energy function used in the AMBER molecular force field is as follows:

[0053]

[0054] where E is the potential energy of the molecule, K r , K θ and V n represent the force constants of bond length, bond angle and dihedral angle, respectively; r eq and θ eq represent the equilibrium bond length and bond angle, respectively; r, θ and γ represent the bond length, bond angle and initial phase angle, respectively; n is the multiple, and φ is the phase angle; i and j are any two different atoms in the system, ε ij and σ ij are the Lennard-Jones parameters between two atoms, ε0 is the vacuum permittivity, q i and q j represent the net charge on the two atoms, and r ij represents the distance between the two atoms.

[0055] (2) Using Packmol software, introduce the coordinate files of the two surfactant molecules and oil molecules obtained in step (1), arrange the betaine molecules and AOT molecules of the complex system according to a 1:1 ratio, and uniformly intercalate the arrangement of one betaine molecule and one AOT molecule. The size of the periodic box in the XY direction is 5nm x 5nm, and the surfactant box is obtained. The.gro file format is exported.

[0056] (3) Using Gromacs 2018.1 software, the surfactant box obtained in step (2) is subjected to preliminary processing, and the temperature of the simulation system is 325K. The S atoms on the hydrophilic ion head of betaine and AOT are positionally constrained to ensure that the relative positions of betaine and AOT molecules do not change during the pre-processing process, and the hydrophilic group of the surfactant is close to the water molecules, and the hydrophobic group of the surfactant is close to the oil molecules. The steepest descent method is used for energy minimization, and the system energy converges to less than 100kJ / mol. Then, 50ps NVT pre-equilibrium simulation is carried out to make the surfactant box reach preliminary equilibrium.

[0057] (4) Using Packmol software, calculate the number of water boxes and oil boxes under the temperature of the simulation condition, establish a water box with a size of 5nm x 5nm x 8nm (containing 6603 water molecules) and two oil boxes with a size of 5nm x 5nm x 4nm (containing 301 water molecules), and assemble the oil / surfactant / water three-phase system along the Z-axis direction as shown in Figure 2 , and export the.gro file format.

[0058] (5) Using the Gromacs 2018.1 software, the initial system obtained in step (4) is introduced to perform energy minimization to eliminate unreasonable contact generated by model building. The parameter file of the energy minimization process is the same as that in step (3), and after the system energy converges to less than 100 kJ / mol, 500 ps of NVT ensemble simulation is performed to obtain the NVT structure file; 1 ns of NPT ensemble simulation is performed using the NVT structure file as the input file to obtain the NPT structure file. On the basis of system equilibrium, 5 ns of NPT simulation is performed for data collection of the equilibrium system, and molecular dynamics calculation is performed on the system to obtain molecular trajectory files and three-dimensional coordinate files, and the.xtc and.gro format files are exported, and the data in the equilibrium state of the system in the last 5 ns are used for analysis.

[0059] The truncation method adopts the Verlet method; the Particle Mesh Ewald (PME) method is used to calculate the interatomic electrostatic interaction; the cutoff radius of non-bonding interaction is 1.4 nm. All covalent bond lengths are limited by the LINCS algorithm. The time step is set to 2.0 fs, and data is output every 500 steps, and periodic boundary conditions are applied in the xyz three dimensions.

[0060] (6) The molecular trajectory file and three-dimensional coordinate file obtained in step (5) are analyzed, and the main analysis steps are as follows:

[0061] 1) The density of the system is analyzed, and the gmx density command in GROMACS is used to analyze the density of each component. First, it is necessary to determine whether the density after simulation is consistent with the actual density of the system, to ensure that the simulated system can reflect the actual situation of the system. The system is uniformly divided into 100 layers along the Z-axis direction, and the mass density of each component is calculated. The main analysis of the density of each component is the density of the water phase, the oil phase, the surfactant phase and the ion, and the relative position relationship of the surfactant in the oil-water interface of the complex system is analyzed, as shown in Figure 3 When betaine is complexed with anionic surfactant AOT, betaine is closer to the water phase and AOT is closer to the oil phase.

[0062] 2) The tilt angle of betaine molecules and AOT molecules is analyzed, and the gmx gangle command in GROMACS is used to make ndx index file to extract S, N atoms of the polar part of betaine, C atoms of the non-polar part, central C atoms of AOT molecules, C1, C2 atoms at the tail of the alkyl hydrophobic chain, and the tilt angle of the polar part (S-N) and the non-polar part (S-C) of betaine with the Z-axis direction is analyzed, and the central angle (C1-C-C2) of AOT molecules is calculated, as shown in Figure 4 .

[0063] 3) The degree of extension of betaine and AOT molecules was analyzed. The degree of extension was defined as the ratio of the average distance of the vectors in the final 5 ns molecular dynamics simulation trajectory to the length of the corresponding vector of the fully extended surfactant in vacuum. The average distance of the vectors in the simulation trajectory was calculated using the `gmx distance` command in GROMACS, with the output file selected as `-oav` to obtain the average distance between atoms. The degree of extension of the C-C1 and C-C2 chains of the AOT molecule was calculated separately. Figure 5 As shown, the two alkyl chains of AOT always maintain a high degree of extension, and the extension of the two chains is approximately equal.

[0064] 4) Analyze the segmental ascent height of the AOT molecule along the z-axis, create an ndx index file to extract each carbon atom on the alkyl chain of the AOT molecule, set the central C atom of the AOT molecule as the reference point, calculate the change in perpendicular distance between the carbon atoms on the two alkyl chains and the reference point in the z-direction, and use the gmx distance command in GROMACS to calculate the height of the two atoms in the perpendicular direction. Select -oxyz as the output file to obtain the components of the distance between atoms in the xyz direction, and further analyze the interfacial arrangement of the AOT molecule in the complex system, such as... Figure 6 As shown, the C-C1 chain of the AOT molecule tends to be upright in the complex system, closer to the z-axis direction, compared to the C-C2 chain segment.

[0065] 5) The radial distribution functions of betaine and AOT molecules were analyzed. An ndx index file was created to extract the central S atom in the polar head of the AOT molecule and the Ow atom in water. Using the gmx rdf command in GROMACS, the radial distribution functions of the S atom in the polar head of the betaine and AOT molecules and the oxygen atom (Ow) in water were compared in various compound systems. Figure 7 As shown, when AOT is combined with EDAS betaine, which has a large number of interfacial vacancies, the number of water molecules around the polar head group of the AOT molecule is relatively large.

[0066] The radial distribution function is calculated using the following formula:

[0067]

[0068] Wherein, N refers to the oxygen atoms (O) in the water within the range of the central S atom (r) of the AOT polar head base. w The total number of oxygen atoms, ρ is the number density of oxygen atoms in the aqueous phase, and r represents the number of oxygen atoms (O2) in the water. w The distance from the oxygen atom to the central S atom of the AOT polar head group is given by g(r), which is the radial distribution function of the oxygen atom and the surfactant polar head group.

[0069] 6) Analysis of the average number of hydrogen bonds of betaine molecules and AOT molecules, the geometric criteria for judging the existence of hydrogen bond: r≤0.35 nm, α≤30° are the reference values for the existence of hydrogen bond, and the ndx index file is made to extract the polar head SO3 of betaine molecules and AOT molecules - , the gmx hbond command in GROMACS is used to analyze the change of the number of hydrogen bonds with simulation time, and the change of the average number of hydrogen bonds of the polar head of betaine molecules and AOT molecules in each complex system is compared, as shown in Figure 8 .

[0070] Obviously, the above embodiments of the present application are only examples for clearly illustrating the present application, and are not intended to limit the embodiments of the present application. For those skilled in the art, other different forms of changes or variations can be made on the basis of the above description, and it is impossible to enumerate all the embodiments here. Any obvious changes or variations derived from the technical solutions of the present application still fall within the protection scope of the present application.

Claims

1. A method for evaluating surfactant complexing system based on molecular dynamics simulation, characterized by, The method comprises the following steps: (1) constructing a molecular model of surfactants, water and oil in a complex system, using an SPC model for the water molecular model, and using an initial topological structure of the surfactants and oil as the molecular model of the surfactants and oil, performing structural optimization on the established initial topological structure of the surfactants and oil, and calculating the RESP charge of each atom in the molecule to generate corresponding force field parameters from an AMBER molecular force field; (2) constructing a surfactant box and stacking it in the XY direction; (3) performing preliminary processing on the stacked surfactant box, position-constraining the hydrophilic ion head of the surfactants, and ensuring that the relative position of the surfactants in the complex system remains unchanged during the pre-processing, then performing energy minimization processing and pre-equilibrium simulation to obtain a preliminarily equilibrated surfactant box; (4) constructing a water box and an oil box, and then assembling them into an oil / surfactant / water three-phase system model along the Z direction with the preliminarily equilibrated surfactant box; (5) performing energy minimization processing on the oil / surfactant / water three-phase system model to eliminate unreasonable contacts generated during model building, and obtaining a minimized structure file; using the minimized structure file as an input file to perform molecular dynamics simulation to determine the oil / surfactant / water three-phase system model in a stable state, and collecting molecular trajectory files and three-dimensional coordinate files to export.xtc and.gro format files; (6) analyzing the obtained molecular trajectory files and three-dimensional coordinate files to study the system density, interface arrangement and interaction, and obtaining evaluation results of the interface behavior of the surfactant molecules in the complex system.

2. The evaluation method according to claim 1, characterized by The specific steps of step (1) are: constructing a molecular model of surfactants and oil using simulation software Gaussian 09, exporting a.pdb format coordinate file, performing geometric optimization calculation on the initial topological structure of the surfactants and oil at the B3LYP / 6-31+g(d) level, using GAFF in the AmberTools 19 program, calculating the RESP charge of all molecules by the B3LYP / 6-31+g(d,p) method, and directly obtaining the van der Waals parameter and bonding parameter of each atom from the AMBER molecular force field; wherein the potential energy function used in the AMBER molecular force field is: where E is the potential energy of the molecule, K r , K θ , and V n represent the force constants of bond length, bond angle, and dihedral angle, respectively; r eq and θ eq represent the equilibrium bond length and bond angle, respectively; r, θ, and γ represent the bond length, bond angle, and initial phase angle, respectively; n is the multiple, and φ is the phase angle; i and j are any two different atoms in the system, ε ij and σ ij are the Lennard-Jones parameters between two atoms, ε0is the vacuum permittivity, q i and q j represent the net charge on the two atoms, and r ij represents the distance between the two atoms.

3. The evaluation method according to claim 2, characterized by, The specific steps of step (2) are: using Packmol software, introducing the coordinate file of the surfactant molecules obtained in step (1), uniformly arranging the surfactant molecules in the complex system according to a set proportion, and periodically stacking them in the XY direction.

4. The evaluation method according to claim 1, characterized by, The energy minimization uses the steepest descent method in the GROMACS software; the convergence standard for energy minimization processing is that the system energy converges to less than 100 kJ / mol; and the pre-equilibrium simulation uses NVT ensemble simulation, and the pre-equilibrium simulation time is 50-100 ps.

5. The evaluation method according to claim 1, characterized by, The process of performing the molecular dynamics simulation in step (5) further comprises: performing NVT ensemble simulation for 500 ps-1 ns to obtain an NVT structure file according to the size of the system; performing NPT ensemble simulation for 1 ns to obtain an NPT structure file by taking the NVT structure file as an input file; and performing NPT ensemble simulation for 5 ns to collect data of the balanced system and calculate after the model is balanced.

6. The evaluation method according to claim 1, characterized by The molecular dynamics simulation adopts a V-rescale temperature control method to control the system temperature, and the system temperature is selected as 325 K, and the coupling time constant is set as 0.1 ps.

7. The evaluation method according to claim 5, characterized by The process of performing the molecular dynamics simulation further comprises: The pressure and temperature of the 1 ns NPT ensemble simulation are controlled by adopting a Berendsen pressure control method and a V-rescale temperature control method respectively; The pressure and temperature of the 5 ns NPT ensemble simulation are controlled by adopting a Parrinello-Rahman pressure control method and a V-rescale temperature control method respectively; The system pressure is set as 1.0 bar, the system temperature is selected as 325 K, and the coupling time is set as 1.0 ps.

8. The evaluation method according to claim 1, characterized by, The parameters of interest for the interface arrangement include the tilt angle, the stretch degree and the chain segment rising height along the z-axis direction; the parameters of interest for the interaction include the radial distribution function and the hydrogen bond.

9. The evaluation method according to claim 8, characterized by, The expression of the radial distribution function is: where N is the total number of oxygen atoms O in water within a distance r from the center atom of the polar head group of the surfactant, p is the number density of oxygen atoms in the aqueous phase, r is the distance from the center atom of the polar head group of the surfactant to the oxygen atom O in water, and g(r) is the radial distribution function of the oxygen atom and the polar head group of the surfactant. w w where N is the total number of oxygen atoms O in water within a distance r from the center atom of the polar head group of the surfactant, p is the number density of oxygen atoms in the aqueous phase, r is the distance from the center atom of the polar head group of the surfactant to the oxygen atom O in water, and g(r) is the radial distribution function of the oxygen atom and the polar head group of the surfactant.​ 10. The evaluation method according to claim 1, characterized by, The surfactant includes two or two or more combinations of anionic surfactant, cationic surfactant, nonionic surfactant or amphoteric surfactant.

Images