# Modeling Xanthan Gum Foam’s Material Properties Using Machine Learning Methods

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}to 172.2 kg/m

^{3}. In addition, the compressive and flexural moduli were found to vary between 235.25 KPa and 1257.52 KPa and between 1939.76 KPa and 12,736.39 KPa, respectively. Five machine-learning-based methods (multiple linear regression, support vector machines, artificial neural networks, least squares methods, and generalized regression neural networks) were utilized to analyze the effects of the components used in the foam formulation. These models yielded accurate results without time, material, or cost losses, making the process more efficient. The models predicted the best results for density, compression modulus, and flexural modulus achieved in the experimental tests. The generalized regression neural network model yielded impressive results, with R

^{2}values above 0.97, enabling the acquisition of more quantitative data with fewer experimental results.

## 1. Introduction

## 2. Material and Methods

#### 2.1. Materials

^{3}. Citric acid with a density of 1.65 g/cm

^{3}was purchased from Kimetsan Chemical in Ankara, Turkey. Xanthan gum, which has a density of 1.48 g/cm

^{3}, and sodium dodecyl sulphate (SDS) were obtained from Aromel Chemical in Konya, Turkey.

#### 2.2. Production Process of Foams

#### 2.3. Characterization of Foams

#### 2.4. Machine-Learning-Based Prediction Methods of Foam Properties

#### 2.4.1. Multiple Linear Regression (MLR)

_{1}, x

_{2}, …, x

_{n}. The relationship between these independent and dependent variables can be linear or curvilinear. Independent variables are selected, and a mathematical model is developed based on the data that explain their connection with the dependent variable. This model is used to find the estimated value of the dependent variable [39,40]. When a model is used that includes multiple independent variables, its formulation is as follows:

_{1}x

_{1}+ β

_{2}x

_{2}+ β

_{3}x

_{3}+ ε

_{1}, x

_{2}, and x

_{3}represent the independent variables; β values represent the beta values corresponding to these x values; and ε is the error in the observed value.

#### 2.4.2. Least Squares Method (LSM)

#### 2.4.3. Support Vector Machine (SVM)

_{n}by a value no greater than ε and is as flat as possible.

_{i}and ${\xi}_{i}^{*}$ are measures of positive errors, and C is a constraining constant.

#### 2.4.4. Artificial Neural Networks (ANNs)

_{i}is the input value, w

_{i}is the weight, m is the number of data samples, b is the bias, and φ is the activation function.

#### 2.4.5. Generalized Regression Neural Networks (GRNNs)

## 3. Results and Discussion

#### 3.1. Effect of Components on the Physical and Mechanical Properties of Foams

^{3}and 172.71 kg/m

^{3}, depending on the concentration of the materials used. The porous structure of the produced foams allows them to dry without any structural collapse and enables the production of lightweight materials. The clustering of cellulose fibers occurs due to attractive forces. Removing the solvent in the suspension also causes the xanthan gum and cellulose fibers to intertwine. It is known that this has a significant effect on the density increase of the produced foam material [51]. Xanthan gum has the most significant effect on the density value of the produced foam material. The density values of produced foam materials vary over a wide range. Because the amount of polymers used increases, the solid content within the final foam material also increases. As a result, the densities of foam materials increase, leading to different values. Furthermore, xanthan gum has the greatest impact on density. This is due to xanthan gum having a density of 1.48 g/cm

^{3}, while cellulose has a density of 0.55 g/cm

^{3}. Therefore, even if these polymers are present in the foam material in equal proportions, xanthan gum increases the density of the produced foam material to a greater extent. It has been stated that foam materials produced with similar biopolymers also exhibit a wide range of density values [4,11,51]. This situation explains the reason behind the wide range of density values in foam materials. The produced foams are of a density that can be evaluated in areas such as insulation, cushioning, and packaging. The density of biodegradable and synthetic foams for different purposes ranges from 5 kg/m

^{3}to 930 kg/m

^{3}[52,53,54]. The density of aerogels produced from xanthan gum, clay, and agar via the freeze-drying technique ranges from 44 kg/m

^{3}to 101 kg/m

^{3}[55]. Surfactants such as SDS are added to reduce the density value in biopolymer-based foam production [56].

_{6}position, and the glucuronic acid groups of xanthan gum [66]. Also, xanthan gum has the greatest impact on mechanical properties due to its role as the matrix in the produced foam material. This is because the thicker the cell walls of the foam material, the more resistance it can provide against mechanical effects. Therefore, as the amount of each component increases, the density also increases, resulting in better mechanical properties of foams due to a decrease in the load per unit area [67]. In cellulose-based materials, such as foam and paper, the primary source of resistance to mechanical stress occurs predominantly from the points of contact between individual fibers [68]. Cellulose fibers improve the mechanical resistance of these contact points through polymer entanglements and increase the interfacial contact area [60]. The hydroxyl groups present in cellulose allow for polar–polar and hydrogen bond interactions, improving the mechanical properties of the produced foams [69]. Additionally, it has been reported that an increase in the concentration of citric acid by up to 5% can increase the crosslinking degree between cellulose macromolecular chains and allow for the formation of additional hydrogen bonds, resulting in a highly linear structure that enhances the mechanical properties of foam materials [70]. Previous studies have shown that foam materials produced with the addition of 5% citric acid exhibited an increase in their mechanical properties ranging from 30% to 37% [71,72]. Hence, there is a close relationship between the density of foam materials and the compression and flexural moduli in this study. This is stated as one of the reasons for the wide range of mechanical properties exhibited by foam materials.

#### 3.2. Machine-Learning-Based Prediction of Foam Properties

## 4. Conclusions

^{2}values above 0.97 and MAPE values below 16.4%. Considering the cost and time spent on experiments, using ML learning methods for predicting these values is important due to the demonstrated contribution to reducing the number of experiments. Xanthan gum foams can be utilized for indoor insulation purposes, cushioning, and packaging. The solubility of xanthan gum in external environments limits its usage. To enhance its water resistance and mechanical properties for application in external environments and the construction industry, cross-linking agents or hydrophobic polymers should be added during foam production. Additionally, for the produced foam to be applicable in biomedical fields, it could be used in combination with biopolymers such as chitosan, which possesses antibacterial properties. Numerous parameters influence the mechanical properties of foam materials. In future studies, new models can be developed by utilizing different parameters, such as varying mixture ratios and different types and quantities of polymers. Predicting the various technological and mechanical characteristics of foam materials can contribute to reducing costs in industry.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**(

**a**) The flexural modulus values of cellulose-reinforced xanthan-gum-based foams. SEM images of (

**b**) XCF-1, (

**c**) XCF-3, and (

**d**) XCF-5 at ×250 magnification.

**Figure 6.**MAPE and R-squared test data values for five-fold cross-validation of the GRNN model. (

**a**) Density, (

**b**) compression modulus, (

**c**) flexural modulus.

Codes | Xanthan Gum (%) | Citric Acid (%) | Cellulose (%) | SDS (%) |
---|---|---|---|---|

XCF-1 | 2 | 5 | 5 | 0.1 |

XCF-2 | 5 | 5 | 5 | 0.1 |

XCF-3 | 8 | 5 | 5 | 0.1 |

XCF-4 | 5 | 5 | 2 | 0.1 |

XCF-5 | 5 | 5 | 8 | 0.1 |

Codes | Density (kg/m^{3}) | Compression Modulus (KPa) | Flexural Modulus (KPa) |
---|---|---|---|

XCF-1 | 49.42 | 235.25 | 1939.76 |

XCF-2 | 112.12 | 747.39 | 5436.99 |

XCF-3 | 172.71 | 1257.52 | 12,736.39 |

XCF-4 | 76.90 | 436.85 | 3408.63 |

XCF-5 | 137.52 | 1002.69 | 8869.27 |

**Table 3.**R

^{2}and MSE values of the methods for predicting density, compression modulus, and flexural modulus parameters.

Density | Compression Modulus | Flexural Modulus | ||||
---|---|---|---|---|---|---|

MSE | R^{2} | MSE | R^{2} | MSE | R^{2} | |

Neural Network | 69,195 | 0.9642 | 7031.36 | 0.9505 | 791,205 | 0.9501 |

Linear Regression | 74,763 | 0.9613 | 7271.33 | 0.9489 | 1,373,913 | 0.9473 |

SVM | 75,326 | 0.9478 | 7624.01 | 0.9463 | 834,695 | 0.9135 |

Least Squares Method | 14,217 | 0.9398 | 12,971.6 | 0.9094 | 1,467,168 | 0.9074 |

GRNN | 68,582 | 0.9820 | 7100.18 | 0.9749 | 796,872 | 0.9747 |

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**MDPI and ACS Style**

Ergün, H.; Ergün, M.E.
Modeling Xanthan Gum Foam’s Material Properties Using Machine Learning Methods. *Polymers* **2024**, *16*, 740.
https://doi.org/10.3390/polym16060740

**AMA Style**

Ergün H, Ergün ME.
Modeling Xanthan Gum Foam’s Material Properties Using Machine Learning Methods. *Polymers*. 2024; 16(6):740.
https://doi.org/10.3390/polym16060740

**Chicago/Turabian Style**

Ergün, Halime, and Mehmet Emin Ergün.
2024. "Modeling Xanthan Gum Foam’s Material Properties Using Machine Learning Methods" *Polymers* 16, no. 6: 740.
https://doi.org/10.3390/polym16060740