Mixed surfactant system surface tension prediction method and system based on machine learning

Abstract

The invention discloses a mixed surfactant system surface tension prediction method and system based on machine learning. Measuring system surface tension data of the mixed surfactant at different temperatures through experiments; secondly, carrying out theoretical correction and data enhancement on the original data by utilizing a Szyszkowski equation; then constructing a multi-dimensional feature space; a nested K-fold cross validation strategy is adopted; the finally established XGB prediction model is excellent in performance on a test set of an enhanced data set, the determination coefficient R2 reaches 0.9994, and the mean square error MSE is 0.0713. The method is particularly suitable for a binary mixed system containing a nonionic polyether surfactant, and not only can accurately predict the surface tension value, but also can determine key parameters such as critical micelle concentration (CMC) and the like. An efficient and reliable technical means is provided for rapid screening and optimization of a surfactant formula, and the method has wide application prospects in the fields of daily chemicals, petroleum, pharmacy and the like.

Description

Technical Field

[0001] This invention relates to the field of colloid and interface chemistry, and in particular to a method and system for predicting the surface tension of a mixed surfactant system based on machine learning. Background Technology

[0002] Surfactants are a class of compounds with a unique amphiphilic structure. Their molecules consist of hydrophilic groups and hydrophobic chains, which can significantly reduce the surface tension of solvents and align themselves at the interface. This property makes surfactants irreplaceable in many industrial fields, including daily chemical products, oil extraction, pharmaceuticals, and environmental engineering.

[0003] In practical applications, single surfactants often fail to meet complex performance requirements, thus necessitating the use of mixed surfactant systems. By combining different types of surfactants, synergistic effects can be achieved, significantly enhancing interfacial activity, solubilization capacity, or stability. For example, anionic-nonionic mixed systems can overcome precipitation problems in high-salinity environments, while cationic-zwitterionic mixed systems perform exceptionally well in antibacterial applications. However, the surface tension behavior of mixed systems is far more complex than that of single-component systems, depending not only on the chemical structures of each component but also on factors such as concentration, ratio, and temperature.

[0004] Traditionally, the surface tension of mixed surfactant systems is mainly determined experimentally. While reliable, these methods are time-consuming and labor-intensive, making them unsuitable for high-throughput formulation screening. Theoretical models such as the Szyszkowski equation and Rubingh's rule solution theory can predict surface tension under specific conditions, but their application is limited by idealized assumptions, neglecting specific intermolecular interactions and making it difficult to extend to complex mixed systems.

[0005] In recent years, machine learning technology has demonstrated great potential in the fields of chemistry and materials science. By uncovering hidden patterns in data, machine learning models can establish complex nonlinear relationships between input features (such as molecular structure descriptors and environmental parameters) and target properties (such as surface tension). However, existing research has largely focused on predicting the properties of single surfactants, and the exploration of hybrid systems is still in its early stages. This is mainly due to two challenges: first, experimental data on hybrid systems is scarce and scattered, making it difficult to support data-driven modeling; second, the interactions between components in hybrid systems (such as electrostatic attraction and steric hindrance) increase the difficulty of feature engineering. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a method and system for predicting the surface tension of mixed surfactant systems based on machine learning, which not only helps to deepen the understanding of interfacial phenomena, but also provides an efficient and reliable tool for industrial formulation design.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a method for predicting the surface tension of a mixed surfactant system based on machine learning, comprising the following steps:

[0008] Step 1: Collect experimental data for the mixed surfactant system;

[0009] Step 2: Perform theoretical correction and data augmentation on the experimental data;

[0010] Step 3: Construct the feature set of the hybrid system and perform feature selection to obtain the filtered dataset;

[0011] Step 4: Divide the dataset, model using multiple machine learning algorithms, and optimize hyperparameters for model training;

[0012] Step 5: Evaluate the predictive performance of the model, select the best model, and perform generalization prediction.

[0013] In a preferred embodiment, step 1 specifically includes:

[0014] Step 101: Measure and record the surface tension values ​​of mixed surfactant solutions of different concentrations and proportions at 25°C using the Wilhelmy platinum plate method;

[0015] Step 102: Perform three repeatability tests on the original experimental data, take the average value and remove outliers to ensure data quality, and obtain a total of 1335 valid data points to construct the original dataset.

[0016] In a preferred embodiment, step 2 specifically includes:

[0017] Step 201: The Szyszkowski empirical formula captures the variation of surface tension of mixed surfactants with concentration at a fixed ratio, and its expression is as follows:

[0018]

[0019] Where γ0 is the surface tension of the solvent, which is water, and its surface tension at 25℃ is 71.92 mN / m; γ is the measured surface tension; c is the concentration; a = RTΓ m R is Avogadro's constant, T is temperature, and Γ is the constant. m denoted as saturated adsorption capacity, and b as an empirical constant; the parameters to be fitted are a and b; the surface tension-concentration curves of each mixing system are piecewise fitted using the Szyszkowski equation to obtain the surface tension curves.

[0020] Step 202: Sample more data points on the surface tension curves of each hybrid system to build an enhanced dataset, expanding it to 24,640 data points.

[0021] In a preferred embodiment, step 3 specifically includes:

[0022] Step 301: Calculate the feature parameters of the original dataset and the augmented dataset, including: the logarithm of concentration lgc, and the mole fraction of component A X. A Interface interaction parameter β δ micelle interaction parameter β m The molecular descriptors of surfactants were extracted using computational chemistry methods. First, the molecular structures were converted into the standard SMILES format using ChemDraw. Each molecular structure was then used by RDKit to calculate 210 molecular descriptors, covering multidimensional features including geometry, electronic, topological, and spatial configuration. Finally, each dataset contained 424 features.

[0023] Step 302: Then, a multi-stage feature selection strategy is adopted.

[0024] In a preferred embodiment, step 4 specifically includes:

[0025] Step 401: Divide the original dataset and the augmented dataset into training and test sets, and build models using different machine learning algorithms for each set;

[0026] Step 402: A nested K-fold cross-validation strategy is adopted. The outer loop evaluates the generalization ability of the model through data splitting, uses K-1 subsamples for training, and uses the remaining 1 subsample for validation. This is repeated K times to obtain the average evaluation result. The inner loop optimizes the hyperparameter space through grid search.

[0027] In a preferred embodiment, step 5 specifically includes:

[0028] Step 501: Use the coefficient of determination R 2 The model results are evaluated and visualized using mean squared error (MSE), and the model prediction mechanism is explained through feature importance analysis.

[0029] Step 502: Select the optimal model to predict the surface tension of the mixed surfactants at unknown concentrations and proportions;

[0030] Wherein, the determination coefficient R 2 The mean square error (MSE) is calculated as follows:

[0031]

[0032] yi represents the actual value, y'i represents the model's predicted value, and n represents the number of samples.

[0033] This invention also provides a machine learning-based surface tension prediction system for mixed surfactant systems. The system is applicable to binary mixed systems containing nonionic polyether surfactants and can simultaneously predict surface tension values ​​and critical micelle concentrations (CMC).

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] 1. This invention provides a method for predicting the surface tension of a mixed surfactant system based on machine learning algorithms. By integrating experimental measurement data, theoretical correction parameters, and molecular structure features as model inputs, and using multiple machine learning algorithms to construct a prediction model, a high-precision prediction of the surface tension of the mixed surfactant system is achieved. The prediction model for the enhanced dataset has an R² of 0.9994 and a mean square error of 0.0713 mN / m, which is significantly better than traditional experimental measurement methods and theoretical calculation methods.

[0036] 2. The theoretical correction and data augmentation strategy proposed in this invention expands the original data volume by more than 20 times through piecewise fitting of the Szyszkowski equation, solving the data scarcity problem in machine learning modeling. The construction of multi-dimensional feature engineering comprehensively considers the physicochemical properties of the mixed system, providing rich and accurate feature inputs for the model. Attached Figure Description

[0037] Figure 1 This is a flowchart of a preferred embodiment of the surface tension prediction method for a mixed surfactant system based on machine learning.

[0038] Figure 2 This is a diagram illustrating the construction of a database of polyether-type binary surfactant systems according to a preferred embodiment of the present invention.

[0039] Figure 3 This is a feature importance analysis diagram of surface tension prediction in a preferred embodiment of the present invention;

[0040] Figure 4 The graph shows a comparison of the predicted values ​​and experimental values ​​of the optimal model XGB, which is a preferred embodiment of the present invention, for the original dataset (left) and the augmented dataset (right). Detailed Implementation

[0041] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0042] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0043] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0044] A machine learning-based method for predicting the surface tension of mixed surfactant systems. (Reference) Figure 1-4 The specific technical process includes:

[0045] Step 1: Data Acquisition and Processing. The surface tension values ​​of mixed surfactant solutions with different concentrations and proportions at 25℃ were measured and recorded using the Wilhelmy platinum plate method. The original experimental data underwent three repeatability tests, and the average value was taken and outliers were removed to ensure data quality. A total of 1335 valid data points were obtained, and the original dataset was constructed.

[0046] Step 2: Theoretical Correction and Data Augmentation. The Szyszkowski empirical formula can capture the variation of surface tension of mixed surfactants with concentration at a fixed ratio, and its expression is as follows:

[0047]

[0048] Where γ0 is the surface tension of the solvent, which is water, and its surface tension at 25℃ is 71.92 mN / m; γ is the measured surface tension; c is the concentration; a = RTΓ m R is Avogadro's constant, T is temperature, and Γ is the constant. m Let be the saturated adsorption capacity, and b be an empirical constant. The parameters to be fitted are a and b.

[0049] The original data were theoretically corrected using the Szyszkowski equation. The surface tension curves were obtained by piecewise fitting of the surface tension-concentration curves of each mixing system. More data points were sampled from the surface tension curves of each mixing system to construct an enhanced dataset, which was expanded to 24,640 data points.

[0050] Step 3: Feature construction and selection to obtain the filtered dataset. Calculate the feature parameters of the original dataset and the augmented dataset, including: the logarithm of concentration (lgc), the mole fraction of component A (X). A), interface interaction parameter (β) δ ), micelle interaction parameter (β) m Molecular descriptors for surfactants were extracted using computational chemistry methods. First, ChemDraw was used to convert the molecular structures to the standard SMILES format. Each molecular structure was then used by RDKit to calculate 210 molecular descriptors, covering multidimensional features including geometry, electronic components, topological characteristics, and spatial configuration. Each dataset ultimately contained 424 features. A multi-stage feature selection strategy was then employed, using methods including, but not limited to, low-variance filtering, correlation analysis, and one or more combinations of PCA dimensionality reduction. Finally, 35 key features significantly correlated with surface tension were retained through screening.

[0051] Step 4: Split the dataset, use multiple machine learning algorithms for modeling, and optimize the hyperparameter model training. The original dataset and the augmented dataset are split into training (80%) and test (20%) sets. Different machine learning algorithms are used to build models for each set. This system constructs two linear regression models: L1-regularized Lasso regression and L2-regularized Ridge regression, and four decision tree-based ensemble models: Gradient Boosting Decision Tree (GBDT), Random Forest (RF), XGBoost (XGB), and LightGBM (LGBM). A nested K-fold cross-validation strategy is adopted. The outer loop evaluates the model's generalization ability through data splitting, using K-1 subsamples for training and the remaining subsample for validation. This process is repeated K times to obtain the average evaluation result. The inner loop optimizes the hyperparameter space through grid search. Optimized parameters include: learning rate; number of trees (n_estimators); and maximum tree depth (max_depth). The optimal parameter combination is determined through grid search, enabling the model to achieve R on the validation set. 2 >0.9.

[0052] Step 5: Evaluate the model, select the optimal model, and perform generalization prediction. This is done using the coefficient of determination R0. 2 The model results are evaluated and visualized using mean squared error (MSE). The model prediction mechanism is explained through feature importance analysis. The optimal model is selected to predict the surface tension of mixed surfactants at unknown concentrations and proportions.

[0053] Wherein, the determination coefficient R 2 The mean square error (MSE) is calculated as follows:

[0054]

[0055] Among them, y i Represents the actual value, y ’ iThis represents the model's predicted value, and n represents the number of samples.

[0056] The predictive model of this invention can predict the surface tension of mixed surfactants with different compositions, concentrations, and ratios with a high level of accuracy. This method can be widely applied to the design and optimization of surfactant formulations in the fields of daily chemicals, petroleum, and pharmaceuticals, significantly reducing experimental costs and shortening the research and development cycle.

[0057] The following are specific application examples:

[0058] Collecting experimental data from mixed surfactant systems: Constructing a database of polyether-type binary surfactant systems requires selecting two surfactants for mixing. For example... Figure 2 As shown, one type is a polyether-type nonionic surfactant, and four common types were selected: AEO9, TO8, TO10, and NP10, which are classified as Class A. Another type of surfactant selected one representative surfactant from each of the four types: SDS (anionic), CTAB (cationic), TX100 (nonionic), and BS12 (amphoteric), which are classified as Class B. The molar fraction (X) of the Class A surfactants was controlled. A A series of solutions were prepared in ultrapure water with values ​​of 0, 0.1, 0.3, 0.5, 0.7, 0.9, and 1. Surface tension was measured using the Wilhelmy platinum plate method, recording the surface tension values ​​of mixed surfactant solutions of different concentrations and proportions at 25°C. The original experimental data underwent three repeatability tests, with the average value taken and outliers removed to ensure data quality. A total of 1335 valid data points were obtained, which were used to construct the original dataset.

[0059] Explaining the model's prediction mechanism through feature importance analysis (e.g.) Figure 3 Using the coefficient of determination R 2 The model results are evaluated and visualized using the mean squared error (MSE) (e.g.) Figure 4 Combining Tables 1 and 2 below, it can be found that the original dataset in XGB (test set R) 2 The model XGB (test set R² = 0.9827, MSE = 1.9464) showed the best performance, while the augmented dataset showed the best overall performance on the XGB dataset (test set R² = 0.9994, MSE = 0.0713). The optimal model XGB can be used to predict the surface tension of mixed surfactants with unknown concentrations and proportions under the same conditions.

[0060] Table 1. Model Evaluation and Comparison of Original Datasets

[0061]

[0062] Table 2. Model Evaluation and Comparison on Augmented Datasets

[0063]

[0064] In summary, this invention provides a machine learning-based method for predicting the surface tension of mixed surfactant systems. By integrating experimental data from 16 typical surfactant combinations under different concentrations and ratios as input, and combining theoretical correction of the Szyszkowski equation with data augmentation techniques, a prediction model is constructed using various machine learning algorithms, establishing a high-precision and highly stable surface tension prediction model. The prediction model of this invention exhibits excellent performance on the augmented dataset test set, with a surface tension prediction determination coefficient R0. 2 The model achieves a mean square error of 0.0713 and a mean squared error of 0.9994. Through multidimensional feature engineering and nested K-fold cross-validation, the model can capture the physicochemical properties of the mixed system and achieve optimal hyperparameter configuration. This invention is particularly suitable for binary mixed systems containing nonionic polyether surfactants, accurately predicting surface tension values ​​and determining key parameters such as critical micelle concentration (CMC). This method overcomes the limitations of traditional experimental methods, providing an efficient technical means for the rapid screening and optimization of surfactant formulations, and has significant application value and industrialization prospects in the fields of daily chemicals, oil extraction, and pharmaceuticals.

[0065] This invention is not limited to the above-described examples and methods, and such modifications should not be construed as limiting the scope of protection of this invention. Any modifications made to the technical solutions based on the technical concepts proposed in this invention shall fall within the scope of protection of this invention.

Claims

1. A method for predicting the surface tension of a mixed surfactant system based on machine learning, characterized in that, Includes the following steps: Step 1: Collect experimental data for the mixed surfactant system; Step 2: Perform theoretical correction and data augmentation on the experimental data; Step 3: Construct the feature set of the hybrid system and perform feature selection to obtain the filtered dataset; Step 4: Divide the dataset, model using multiple machine learning algorithms, and optimize hyperparameters for model training; Step 5: Evaluate the predictive performance of the model, select the best model, and perform generalization prediction.

2. The method for predicting the surface tension of a mixed surfactant system based on machine learning according to claim 1, characterized in that, Step 1 specifically includes: Step 101: Measure and record the surface tension values ​​of mixed surfactant solutions of different concentrations and proportions at 25°C using the Wilhelmy platinum plate method; Step 102: Perform three repeatability tests on the original experimental data, take the average value and remove outliers to ensure data quality, and obtain a total of 1335 valid data points to construct the original dataset.

3. The method for predicting the surface tension of a hybrid surfactant system based on machine learning according to claim 1, characterized in that, Step 2 specifically includes: Step 201: The Szyszkowski empirical formula captures the variation of surface tension of mixed surfactants with concentration at a fixed ratio, and its expression is as follows: Where γ0 is the surface tension of the solvent, which is water, and its surface tension at 25℃ is 71.92 mN / m; γ is the measured surface tension; c is the concentration; a = RTΓ m R is Avogadro's constant, T is temperature, and Γ is the constant. m denoted as saturated adsorption capacity, and b as an empirical constant; the parameters to be fitted are a and b; the surface tension-concentration curves of each mixing system are piecewise fitted using the Szyszkowski equation to obtain the surface tension curves. Step 202: Sample more data points on the surface tension curves of each hybrid system to build an enhanced dataset, expanding it to 24,640 data points.

4. The method for predicting the surface tension of a hybrid surfactant system based on machine learning according to claim 1, characterized in that, Step 3 specifically includes: Step 301: Calculate the feature parameters of the original dataset and the augmented dataset, including: the logarithm of concentration lgc, and the mole fraction of component A X. A Interface interaction parameter β δ micelle interaction parameter β m The molecular descriptors of surfactants were extracted using computational chemistry methods. First, the molecular structures were converted into the standard SMILES format using ChemDraw. Each molecular structure was then used by RDKit to calculate 210 molecular descriptors, covering multidimensional features including geometry, electronic, topological, and spatial configuration. Finally, each dataset contained 424 features. Step 302: Then, a multi-stage feature selection strategy is adopted.

5. The method for predicting the surface tension of a mixed surfactant system based on machine learning according to claim 1, characterized in that, Step 4 specifically includes: Step 401: Divide the original dataset and the augmented dataset into training and test sets, and build models using different machine learning algorithms for each set; Step 402: A nested K-fold cross-validation strategy is adopted. The outer loop evaluates the generalization ability of the model through data splitting, uses K-1 subsamples for training, and uses the remaining 1 subsample for validation. This is repeated K times to obtain the average evaluation result. The inner loop optimizes the hyperparameter space through grid search.

6. The method for predicting the surface tension of a mixed surfactant system based on machine learning according to claim 1, characterized in that, Step 5 specifically includes: Step 501: Use the coefficient of determination R 2 The model results are evaluated and visualized using mean squared error (MSE), and the model prediction mechanism is explained through feature importance analysis. Step 502: Select the optimal model to predict the surface tension of the mixed surfactants at unknown concentrations and proportions; Wherein, the determination coefficient R 2 The mean square error (MSE) is calculated as follows: yi represents the actual value, y'i represents the model's predicted value, and n represents the number of samples.

7. A surface tension prediction system for a hybrid surfactant system based on machine learning, characterized in that... The surface tension prediction method for a mixed surfactant system based on machine learning, as described in any one of claims 1-6, is applicable to binary mixed systems containing nonionic polyether surfactants and can simultaneously predict surface tension values ​​and critical micelle concentration (CMC).

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