An evaluation method for aging characteristics of oil-impregnated paper based on micro-parameters

Abstract

This invention provides a method for evaluating the aging characteristics of oil-impregnated paper based on microscopic parameters. The method involves constructing oil-impregnated paper models of insulating paper and insulating oil, and performing molecular dynamics simulations to obtain physical parameters related to the aging life of oil-impregnated paper, such as self-diffusion coefficient, isobaric heat capacity, number of hydrogen bonds, and hydrogen bond lifetime. By evaluating the aging performance of oil-impregnated paper using these material physical parameters, the method achieves high accuracy and saves manpower and time, providing theoretical guidance for accurately, efficiently, and conveniently evaluating the aging performance of different insulating oils in delaying the aging of oil-impregnated paper.

Description

Technical Field

[0001] This invention belongs to the field of transformer insulation material technology, and particularly relates to an evaluation method for the aging characteristics of oil-impregnated paper based on microscopic parameters. Background Technology

[0002] To adapt to the green, environmentally friendly, and sustainable development of power equipment, insulation materials are shifting from traditional non-renewable resources to renewable resources. Oil-immersed transformers are an extremely important and critical part of the power grid, and the oil-paper insulation performance is the core of the transformer, requiring high standards for its insulation and heat dissipation properties. Ester-based insulating oils and other highly flame-retardant, environmentally friendly, renewable, and high-performance liquid dielectrics have developed rapidly in recent years and are expected to become a replacement for traditional fossil-based insulating oils. In the development of insulating oils, it is not only important to focus on the excellent performance of the insulating oil itself, but also on the compatibility characteristics of the insulating oil and insulating paper.

[0003] Transformers are susceptible to thermal stress during actual operation, leading to the aging and decomposition of the insulating paper and a gradual loss of its performance. In the development of new insulating oils, the aging characteristics of the new oil-impregnated paper are a crucial component in the lifespan assessment and prediction of new insulating oil transformers. Traditional methods for studying the aging of oil-impregnated paper primarily employ experimental approaches, conducting accelerated thermal aging tests on the paper in insulating oil at 110-130℃ for thousands of hours. The thermal aging characteristics of the oil-impregnated paper are evaluated based on changes in parameters such as the degree of polymerization during these accelerated thermal aging tests. Traditional methods for assessing the aging characteristics of oil-impregnated paper are extremely time-consuming, the testing methods for the degree of polymerization are complex, and the entire process requires significant manpower and resources, resulting in very high costs. Evaluation methods for the aging characteristics of oil-impregnated paper based on microscopic parameters are currently rarely reported. Summary of the Invention

[0004] The purpose of this invention is to provide an evaluation method for the aging characteristics of oil-impregnated paper based on microscopic parameters. The evaluation method in this invention can provide theoretical guidance for accurately, efficiently and conveniently evaluating the aging performance of different insulating oils in delaying the aging of oil-impregnated paper.

[0005] This invention provides a method for evaluating the aging characteristics of oil-impregnated paper based on microscopic parameters, comprising the following steps:

[0006] A) Obtain the oil impregnation rate of the insulating paper;

[0007] B) The monomer molecular structure model of cellulose, the main component of oil-impregnated paper, and the single molecular structure model of insulating oil were drawn using Gaussian View software. The periodic structure of oil-impregnated paper was constructed using Packmol software. The ratio of the cellulose monomer molecular structure model and the single molecular structure model of insulating oil in the oil-impregnated paper model was set according to the oil impregnation rate of the insulating paper.

[0008] C) The energy of the oil-impregnated paper model was minimized using Gromacs software, and then molecular dynamics simulation was performed under the NPT ensemble to obtain the simulated trajectory of the molecular dynamics of the oil-impregnated paper model.

[0009] D) Based on the simulated trajectory of molecular dynamics of the oil-impregnated paper model, calculate the self-diffusion coefficient, isobaric heat capacity, number of hydrogen bonds, and hydrogen bond lifetime of the oil-impregnated paper model, and evaluate the aging characteristics of the oil-impregnated paper based on the self-diffusion coefficient, isobaric heat capacity, number of hydrogen bonds, and hydrogen bond lifetime.

[0010] Preferably, the oil impregnation rate of the insulating paper is obtained by following these steps:

[0011] The insulating paper is dried and weighed to obtain its mass.

[0012] The insulating paper is immersed in insulating oil under vacuum conditions. After immersion, the oil-impregnated paper is removed, and the surface oil stains are removed before weighing to obtain the mass of the oil-impregnated paper.

[0013] The oil impregnation rate of the insulating paper is calculated based on the difference between the quality of the oil-impregnated paper and the quality of the insulating paper.

[0014] Preferably, the degree of polymerization n of the monomer molecular structure model of cellulose is ≥10, and -OH is added to the tail end of the monomer molecular structure model of cellulose for saturation treatment.

[0015] Preferably, based on density functional theory, the molecular structure models of cellulose monomers and insulating oil are geometrically optimized using Gaussian software B3LYP functionals and 6-311G(d,p) basis sets with D3 dispersion correction method, and then the oil-impregnated paper model is constructed.

[0016] Preferably, in the oil-impregnated paper model, the number of cellulose monomer molecular structure models is ≥30.

[0017] Preferably, after obtaining the oil-impregnated paper structure model, wavefunction files of the simulation results of the cellulose monomer molecular structure model and the insulating oil molecular structure model are obtained based on Gaussian geometric optimization. The Resp charge is calculated in Multiwfn software. The Ambertools tool is used in conjunction with the Accype script to generate the top and itp files required for the simulation of the cellulose monomer molecular structure model under the Glycam force field. The Sobtop software is used to obtain the top and itp files required for the simulation of the insulating oil monomolecular structure model under the GAFF force field. The top files of the cellulose monomer molecular structure model and the insulating oil monomolecular structure model are merged, and the calculated RESP charge is replaced in the corresponding itp file. Then, the energy minimization of the oil-impregnated paper model is performed.

[0018] Preferably, the steepest gradient method is used to minimize the energy of the oil-impregnated paper model.

[0019] Preferably, the self-diffusion coefficient of the oil-impregnated paper model is calculated according to formula (1):

[0020]

[0021] In equation (1), N is the total number of atoms, and i is the atom number. and Let represent the position vectors of the i-th atom at time t and time 0, respectively.

[0022] Preferably, the isobaric heat capacity of the oil-impregnated paper model is calculated according to formula (2):

[0023]

[0024] In equation (2), C P Here, H represents the isobaric heat capacity, H is the enthalpy of the model, T is the model temperature, and kJ / L is the kJ / L. B is the Boltzmann constant.

[0025] Preferably, the lifetime of the hydrogen bond is calculated according to formula (3):

[0026]

[0027] In equation (3), τ HB t0 represents the hydrogen bond lifetime, i is the hydrogen bond number, and t0 represents the initial time.

[0028] S i (t0) represents the existence of the i-th hydrogen bond at time t0. If the i-th hydrogen bond does not exist at time t0, then S i If (t0) is 0, then the i-th hydrogen bond exists at time t0, and S i (t0) is 1;

[0029] S i (t0+t) represents the existence of the i-th hydrogen bond at time t0+t. If the i-th hydrogen bond does not exist at time t0+t, then S i If (t0+t) is 0, and the i-th hydrogen bond exists at time t0+t, then S i (t0+t) is 1.

[0030] This invention provides a method for evaluating the aging characteristics of oil-impregnated paper based on microscopic parameters, comprising the following steps: A) obtaining the oil impregnation rate of the insulating paper; B) using Gaussian View software to draw monomer molecular structure models of cellulose, the main component of the oil-impregnated paper, and monomer molecular structure models of insulating oil, and using Packmol software to construct a periodic structure model of the oil-impregnated paper, and setting the ratio of the cellulose monomer molecular structure model and the insulating oil monomer molecular structure model in the oil-impregnated paper model according to the oil impregnation rate of the insulating paper; C) using Gromacs software to minimize the energy of the oil-impregnated paper model, and then performing molecular dynamics simulation under the NPT ensemble to obtain the simulation trajectory of the molecular dynamics of the oil-impregnated paper model; D) based on the simulation trajectory of the molecular dynamics of the oil-impregnated paper model, calculating the self-diffusion coefficient, isobaric heat capacity, number of hydrogen bonds, and hydrogen bond lifetime of the oil-impregnated paper model, and evaluating the aging characteristics of the oil-impregnated paper based on the self-diffusion coefficient, isobaric heat capacity, number of hydrogen bonds, and hydrogen bond lifetime. This invention constructs oil-impregnated paper models of insulating paper and insulating oil, and performs molecular dynamics simulations on them to obtain physical parameters related to the aging life of oil-impregnated paper, such as self-diffusion coefficient, isobaric heat capacity, number of hydrogen bonds, and hydrogen bond lifetime. The aging performance of oil-impregnated paper can be evaluated using these material physical parameters. This method is highly accurate and saves manpower and time, providing theoretical guidance for accurately, efficiently, and conveniently evaluating the aging performance of different insulating oils in delaying the aging of oil-impregnated paper. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0032] Figure 1 This is a schematic diagram of a mineral oil-impregnated paper model in an embodiment of the present invention;

[0033] Figure 2 This is a schematic diagram of a soybean-based natural ester oil-impregnated paper model in an embodiment of the present invention. Detailed Implementation

[0034] This invention provides a method for evaluating the aging characteristics of oil-impregnated paper based on microscopic parameters, mainly including the following steps:

[0035] Step 1: Test the oil impregnation rate of the insulating paper.

[0036] Prepare two or more untreated insulating papers with the same density and thickness. There are no specific requirements for size and shape. Place them in a vacuum drying oven at 80-100°C for 24-36 hours, preferably at 90°C for 24 hours. Test the moisture content of the oil-impregnated paper to ensure that it is below 0.5%.

[0037] Weigh each piece of insulating paper on an electronic balance and record its mass. Then, immerse each piece of insulating paper in insulating oil, ensuring the oil completely covers it. Vacuum impregnate the paper in a vacuum drying oven to obtain several different oil-impregnated papers.

[0038] In this invention, the insulating oil used for the different insulating papers can be the same or different; the vacuum impregnation temperature is preferably 50-80°C, more preferably 60-65°C, and the vacuum impregnation time is preferably 48-72 hours.

[0039] Remove the oil-impregnated paper, wipe off the surface oil stains, and weigh it on an electronic balance to obtain the mass of the oil-impregnated paper.

[0040] Based on the dried insulating paper, the oil impregnation rate of the oil-impregnated paper is calculated by the ratio of the mass difference of the insulating paper before and after oil impregnation to the mass of the insulating paper before oil impregnation.

[0041] Step 2: Molecular dynamics simulation of oil-impregnated paper.

[0042] The monomer molecular structure model of cellulose, the main component of oil-impregnated paper, was drawn using Gaussian View software. To ensure the accuracy of the simulation results, the degree of polymerization of the monomer model of polymer insulating material was not less than 10, and -OH was added to the tail end of cellulose for saturation treatment. Based on the composition of insulating oil, a single-molecule structure model of insulating oil was constructed.

[0043] Based on density functional theory, the geometric optimization of the constructed cellulose monomer model and insulating oil monomolecule model was carried out using Gaussian software B3LYP functional and 6-311G(d,p) basis set plus D3 dispersion correction method to make the model closer to the real structure.

[0044] Based on the geometrically optimized model and the oil impregnation rate of the insulating paper obtained in the previous step, two or more periodic structure oil-impregnated paper models are constructed using Packmol software. The number of cellulose molecules with a degree of polymerization of not less than 10 is not less than 30, and the number of insulating oil monomolecular structure models is calculated based on the oil impregnation rate.

[0045] Wavefunction files from simulations of cellulose and insulating oil molecular models were obtained using Gaussian geometry optimization. Resp charges were calculated in Multiwfn software. Ambertools, in conjunction with Accype scripts, was used to generate the top and itp files required for cellulose monomer simulations under the Glycam force field. Sobtop software was used to obtain the top and itp files required for insulating oil simulations under the GAFF force field. The top files for cellulose and insulating oil were merged, and the calculated RESP charges were replaced in the corresponding itp files. The energy of the oil-impregnated paper model was minimized using Gromacs software employing the steepest gradient method. Equilibrium was first achieved for 20–25 ns under the NPT ensemble, followed by a 10–15 ns simulation; the obtained trajectory was used for calculating various properties. The simulation temperature was set to the temperature at which the aging characteristics of the oil-impregnated paper were actually desired.

[0046] Step 3: Calculation of microscopic parameters of oil-impregnated paper.

[0047] Based on the molecular dynamics simulation trajectory of the oil-impregnated paper model obtained in the second step (10 ns), the self-diffusion coefficient, isobaric heat capacity, number of hydrogen bonds, and hydrogen bond lifetime of different oil-impregnated paper models were calculated.

[0048] The self-diffusion coefficient of the oil-impregnated paper model is calculated according to formula (1):

[0049]

[0050] In equation (1), N is the total number of atoms, and i is the atom number. and Let represent the position vectors of the i-th atom at time t and time 0, respectively.

[0051] The isobaric heat capacity of the oil-impregnated paper model is calculated according to formula (2):

[0052]

[0053] In equation (2), C P Here, H represents the isobaric heat capacity, H is the enthalpy of the model, T is the model temperature, and kJ / L is the kJ / L. B is the Boltzmann constant.

[0054] The lifetime of the hydrogen bond is calculated according to formula (3):

[0055]

[0056] In equation (3), τ HB t0 represents the hydrogen bond lifetime, i is the hydrogen bond number, and t0 represents the initial time.

[0057] S i(t0) represents the existence of the i-th hydrogen bond at time t0. If the i-th hydrogen bond does not exist at time t0, then S i If (t0) is 0, then the i-th hydrogen bond exists at time t0, and S i (t0) is 1;

[0058] S i (t0+t) represents the existence of the i-th hydrogen bond at time t0+t. If the i-th hydrogen bond does not exist at time t0+t, then S i If (t0+t) is 0, and the i-th hydrogen bond exists at time t0+t, then S i (t0+t) is 1.

[0059] Step 4: Evaluate the aging characteristics of different oil-impregnated papers based on the differences in microscopic parameters of the oil-impregnated paper.

[0060] Based on the calculation results of the self-diffusion coefficient, isobaric heat capacity, number of hydrogen bonds, and hydrogen bond lifetime of different oil-impregnated paper models obtained in the third step, the variation laws of the microscopic parameters of different old oil-impregnated paper models are summarized. The self-diffusion coefficient of oil-impregnated paper characterizes the strength of its thermal stability, and the isobaric heat capacity of oil-impregnated paper represents the heat required to raise its temperature by 1 degree Celsius. The larger the number and lifetime of hydrogen bonds in oil-impregnated paper, the stronger its intermolecular forces, and the less likely it is to decompose during thermal processes. The smaller the self-diffusion coefficient and the larger the isobaric heat capacity, the larger the number and lifetime of hydrogen bonds, the better its heat aging resistance. Therefore, by comparing the magnitudes of these four parameters—self-diffusion coefficient, isobaric heat capacity, number of hydrogen bonds, and hydrogen bond lifetime—of different oil-impregnated paper models, different oil-impregnated paper systems can be evaluated, and the desired oil-impregnated paper system can be obtained.

[0061] To further illustrate the present invention, the following describes in detail, with reference to embodiments, an evaluation method for the aging characteristics of oil-impregnated paper based on microscopic parameters, but this should not be construed as limiting the scope of protection of the present invention.

[0062] Example

[0063] The effectiveness of this patent is verified using mineral oil-impregnated paper and soybean-based natural ester oil-impregnated paper as examples.

[0064] Two insulating papers of the same size and density were dried in a vacuum drying oven at 90°C for 24 hours. The two insulating papers were then injected into two different insulating oils, ensuring that the insulating oils fully submerged the insulating papers. The papers were then vacuum-impregnated in a vacuum drying oven at 60°C for 48 hours to obtain two different types of oil-impregnated papers. The mass difference before and after impregnation was calculated, and the oil impregnation rate of both types of oil-impregnated papers was calculated to be approximately 20%.

[0065] A cellulose model with a degree of polymerization of 10 was constructed using Gaussian View software. Based on the composition of mineral oil and soybean-based natural esters, a monomolecular model of insulating oil was built. The constructed cellulose monomer model and the insulating oil monomolecular model were geometrically optimized using Gaussian software's B3LYP functional and 6-311G(d,p) basis set with D3 dispersion correction method to make the models closer to the actual structures.

[0066] Two oil-impregnated paper models were constructed using Packmol, with 30 cellulose fibers and mineral oil and soybean oil each comprising 20% ​​by mass. The two oil-impregnated paper models are shown below. Figures 1-2 As shown, where Figure 1 A paper model impregnated with mineral oil. Figure 2 A paper model made of soybean-based natural ester oil.

[0067] Wavefunction files from simulations of cellulose and insulating oil molecular models were obtained using Gaussian geometry optimization. Resp charges were calculated in Multiwfn software. Ambertools, in conjunction with Accype scripts, was used to generate the top and itp files required for cellulose monomer simulations under the Glycam force field. Sobtop software was used to obtain the top and itp files required for insulating oil simulations under the GAFF force field. The top files for cellulose and insulating oil were merged, and the calculated RESP charges were replaced in the corresponding itp files. The energy of the oil-impregnated paper model was minimized using Gromacs software employing the steepest gradient method. A 20 ns equilibrium period was first performed under the NPT ensemble, followed by a 10 ns simulation; the obtained trajectory was used to calculate various properties. The simulation temperature was set to the desired temperature for obtaining the aging characteristics of the oil-impregnated paper. The temperature was set to 393 K, and the simulation step size was 1 fs.

[0068] Based on the molecular dynamics simulation trajectory obtained from the 10 ns oil-impregnated paper model, the differences in self-diffusion coefficient, isobaric heat capacity, number of hydrogen bonds, and hydrogen bond lifetime of different oil-impregnated paper models were calculated, and the results are shown in Table 1.

[0069] Table 1 Calculation results of microscopic parameters of oil-impregnated paper

[0070]

[0071] Table 1 shows that soybean-based natural ester oil-impregnated paper has a lower self-diffusion coefficient, higher isobaric heat capacity, higher number of hydrogen bonds, and higher hydrogen bond lifetime, thus exhibiting excellent thermal aging performance. Verification Example

[0072] Two accelerated thermal aging tests were conducted on oil-impregnated paper to further verify the simulation results. The thermal aging test steps are as follows:

[0073] 1. Place mineral oil and soybean-based natural ester into a vacuum drying oven and dry at 90℃ / 50Pa for 48 hours. After drying, the moisture content of the insulating oil should be controlled below 50ppm.

[0074] 2. Thickness 0.5mm, density 1.5g / cm³ 3 The insulating paperboard was cut to a size of 6cm×6cm and dried at 90℃ / 50Pa for 24h. The moisture content of the insulating paper was tested to be less than 0.5%.

[0075] 3. Prepare several wide-mouth glass bottles, pour 1L of dried insulating oil into each bottle, and immerse the bottles in the oil at a ratio of 10:1 (insulating oil to insulating paper) for 48 hours at 60℃ / 50Pa.

[0076] 4. Conduct an accelerated thermal aging test at 120℃, take samples at different time periods, and test the degree of polymerization of the insulating paper according to IEC 60450.

[0077] The changes in the degree of polymerization of the two types of oil-impregnated paper at different aging days are shown in Table 2.

[0078] Table 2. Polymerization of two types of oil-impregnated paper at different aging days.

[0079] 0 days 12 days 85 days 166 days 221 days Mineral oil impregnated paper 1041.1 793.38 433.5 360.94 306.22 Soy-based natural ester oil-impregnated paper 1054.89 898.71 636.24 618.43 523.84

[0080] As shown in Table 2, the degree of polymerization of soybean-based natural ester oil-impregnated paper was higher than that of mineral oil-impregnated paper within 221 days of aging, thus proving the validity of the simulation results.

[0081] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for evaluating the aging characteristics of oil-impregnated paper based on microscopic parameters, comprising the following steps: A) Obtain the oil impregnation rate of the insulating paper; B) The monomer molecular structure model of cellulose, the main component of oil-impregnated paper, and the single molecular structure model of insulating oil were drawn using Gaussian View software. The periodic structure of oil-impregnated paper was constructed using Packmol software. The ratio of the cellulose monomer molecular structure model and the single molecular structure model of insulating oil in the oil-impregnated paper model was set according to the oil impregnation rate of the insulating paper. C) The energy of the oil-impregnated paper model was minimized using Gromacs software, and then molecular dynamics simulation was performed under the NPT ensemble to obtain the simulated trajectory of the molecular dynamics of the oil-impregnated paper model. D) Based on the simulated trajectory of molecular dynamics of the oil-impregnated paper model, calculate the self-diffusion coefficient, isobaric heat capacity, number of hydrogen bonds, and hydrogen bond lifetime of the oil-impregnated paper model, and evaluate the aging characteristics of the oil-impregnated paper based on the self-diffusion coefficient, isobaric heat capacity, number of hydrogen bonds, and hydrogen bond lifetime.

2. The method for evaluating the aging characteristics of oil-impregnated paper based on microscopic parameters according to claim 1, characterized in that, To obtain the oil impregnation rate of the insulating paper, follow these steps: The insulating paper is dried and weighed to obtain its mass. The insulating paper is immersed in insulating oil under vacuum conditions. After immersion, the oil-impregnated paper is removed, and the surface oil stains are removed before weighing to obtain the mass of the oil-impregnated paper. The oil impregnation rate of the insulating paper is calculated based on the difference between the quality of the oil-impregnated paper and the quality of the insulating paper.

3. The method for evaluating the aging characteristics of oil-impregnated paper based on microscopic parameters according to claim 1, characterized in that, The degree of polymerization n of the monomer molecular structure model of cellulose is ≥10, and -OH is added to the tail end of the monomer molecular structure model of cellulose for saturation treatment.

4. The method for evaluating the aging characteristics of oil-impregnated paper based on microscopic parameters according to claim 1, characterized in that, Based on density functional theory, the molecular structure models of cellulose monomers and insulating oil were geometrically optimized using Gaussian software B3LYP functionals and 6-311G(d,p) basis sets with D3 dispersion correction method, and then the oil-impregnated paper model was constructed.

5. The method for evaluating the aging characteristics of oil-impregnated paper based on microscopic parameters according to claim 1, characterized in that, In the oil-impregnated paper model, the number of cellulose monomer molecular structure models is ≥30.

6. The method for evaluating the aging characteristics of oil-impregnated paper based on microscopic parameters according to claim 1, characterized in that, After obtaining the oil-impregnated paper structure model, wavefunction files of the simulation results of the cellulose monomer molecular structure model and the insulating oil molecular structure model were obtained based on Gaussian geometry optimization. The Resp charge was calculated in Multiwfn software. The Ambertools tool and Accype script were used to generate the top and itp files required for the simulation of the cellulose monomer molecular structure model under the Glycam force field. The Sobtop software was used to obtain the top and itp files required for the simulation of the insulating oil monomolecular structure model under the GAFF force field. The top files of the cellulose monomer molecular structure model and the insulating oil monomolecular structure model were merged, and the calculated RESP charge was replaced in the corresponding itp file. Then, the energy minimization of the oil-impregnated paper model was performed.

7. The method for evaluating the aging characteristics of oil-impregnated paper based on microscopic parameters according to claim 1, characterized in that, The steepest gradient method is used to minimize the energy of the oil-impregnated paper model.

8. The method for evaluating the aging characteristics of oil-impregnated paper based on microscopic parameters according to claim 1, characterized in that, The self-diffusion coefficient of the oil-impregnated paper model is calculated according to formula (1): In equation (1), N is the total number of atoms, and i is the atom number. and Let represent the position vectors of the i-th atom at time t and time 0, respectively.

9. The method for evaluating the aging characteristics of oil-impregnated paper based on microscopic parameters according to claim 1, characterized in that, The isobaric heat capacity of the oil-impregnated paper model is calculated according to formula (2): In equation (2), C P Here, H represents the isobaric heat capacity, H is the enthalpy of the model, T is the model temperature, and kJ / L is the kJ / L. B is the Boltzmann constant.

10. The method for evaluating the aging characteristics of oil-impregnated paper based on microscopic parameters according to claim 1, characterized in that, The lifetime of the hydrogen bond is calculated according to formula (3): In equation (3), τ HB t0 represents the hydrogen bond lifetime, i is the hydrogen bond number, and t0 represents the initial time. S i (t0) represents the existence of the i-th hydrogen bond at time t0. If the i-th hydrogen bond does not exist at time t0, then S i If (t0) is 0, then the i-th hydrogen bond exists at time t0, and S i (t0) is 1; S i (t0+t) represents the existence of the i-th hydrogen bond at time t0+t. If the i-th hydrogen bond does not exist at time t0+t, then S i If (t0+t) is 0, and the i-th hydrogen bond exists at time t0+t, then S i (t0+t) is 1.

Images