# Monothetic Analysis and Response Surface Methodology Optimization of Calcium Alginate Microcapsules Characteristics

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## Abstract

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## 1. Introduction

^{2+}[13]. Calcium salts are used for crosslinking as they are economical, safe and easy to use. The alginate gelation occurs when the divalent cation binds itself to two carboxyl groups of an alginate molecule, as thoroughly documented and explained by the egg-box model [14]. The size, sphericity and shape of the capsules play a crucial role in the field of application of the polymer. Smaller-sized and spherical microcapsules are crucial as encapsulating materials for anti-corrosion materials in self-healing applications. The capsule’s resistance to shear and compressive pressures increases as its size decreases [15]. Excellent shear and compressive forces are essential to controlled release in self-healing for anti-corrosion. Smaller capsules can provide significant solid-liquid interface gaps in a given volume, facilitating substrate and product mass transfer [16,17] Alginate sphericity also has a direct correlation with chemical and mechanical stability. Spherical capsules have shown remarkable and more effective gel strength than non-spherical ones. Premature encapsulant burst and release are also due to tears, cracks and breakages of non-spherical capsules [18].

## 2. Materials and Methods

#### 2.1. Materials

_{6}H

_{9}NaO

_{7}) was purchased from Advent ChemBio PVT. Ltd, India. Calcium chloride 2-hydrate (CaCl

_{2}.2H

_{2}O) salt was purchased from AppliChem GmbH, Germany.

#### 2.2. Synthesis of Calcium Alginates Using Electrospray Technique

#### 2.3. Microcapsule Size Distribution Determination

#### 2.4. Sphericity Coefficient Determination

_{L}is the lateral diameter and D

_{F}is the mean frontal diameter of the capsule at varying positions. Sphericity of 1 indicates a perfect sphere, while sphericity approaching infinity indicates elongation, such as fibers.

#### 2.5. Experimental Size and Sphericity Optimization

_{a}and X

_{b}are the independent variables; β

_{o}is the overall average response constant/intercept; β

_{a}is the coefficient of the linear regression model on a linear level; β

_{aa}is the effect of squaring the linear coefficient; β

_{ab}is the effect of the interrelationship between the coefficients of the linear regression; and ε accounts for the error in the model.

#### 2.6. Model Validation

#### 2.7. Optimization

## 3. Results

#### 3.1. OFAT Analysis of Independent Parameters

#### 3.1.1. Effect of Sodium Alginate Concentration

#### 3.1.2. Effect of Voltage

#### 3.1.3. Effect of Flowrate

#### 3.1.4. Effect of Calcium Chloride Concentration

_{2}solution failed to harden, had weak walls and imploded, owing to inadequate crosslinker and hardening salt concentrations to produce stable microcapsules. From Figure 4, the 6% w/v calcium chloride microcapsules showed a smaller average particle size, with sporadic distribution indicating polydispersity and an overall poor average sphericity coefficient. The 2% w/v showed a larger average particle size fractionally, but with an impressive sphericity coefficient and a better-monodispersed range. Most of the 2% microcapsules were similar to the 4% w/v microcapsules, except for some outliers. The outliers of the 2% w/v microcapsules are few enough to be included in the margin of error. The sphericity coefficient also favored the 2% w/v concentration microcapsules. The effect of calcium chloride as an independent parameter had little significance on the overall bead diameter compared to other strong parameters, such as voltage, needle size and alginate concentration.

#### 3.1.5. Effect of Needle Size

#### 3.2. ANOVA and Model Generation

#### 3.2.1. Linear Variable Effect on Microcapsule Size and Sphericity

#### 3.2.2. Effect of Independent Variable Interaction on Microcapsule Particle Size and Sphericity

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Monothetic analysis, SEM and distribution of 25 randomly selected Calcium alginate Microcapsules with varying Sodium Alginate concentrations (

**a**) 2% w/v; (

**b**) 4% w/v; (

**c**) 6% w/v.

**Figure 3.**Microcapsule size distribution of calcium alginates electrosprayed at high (

**a**–

**c**) and low flowrates (

**d**–

**f**).

**Figure 4.**Box and Whiskers plot of the monothetic analysis of 25 randomly selected calcium alginate microcapsules crosslinked with varying concentrations of Calcium Chloride.

**Figure 5.**Monothetic Analysis of 25 random calcium alginate microcapsules electrosprayed through varying needle diameter.

**Figure 6.**Perturbation summary of independent parameters (A-Alginate concentration; B-Flowrate; C-Needle Size; D-Voltage; E-CaCl

_{2}concentration) on (

**a**) Microcapsule Diameter and (

**b**) Sphericity Coefficient.

**Figure 7.**3D Surface plots of varying independent parameter interactions. (

**a**) Alginate concentration and needle size; (

**b**) voltage and alginate concentration; (

**c**) needle size and flowrate; (

**d**) voltage and needle size; (

**e**) alginate concentration; (

**f**) voltage and flowrate and their effect on microcapsule diameter.

**Figure 8.**3D surface plot of independent variable interactions. (

**a**) Alginate concentration and flowrate; (

**b**) alginate concentration and needle size; (

**c**) alginate concentration and voltage; (

**d**) flowrate and needle size; (

**e**) alginate and CaCl

_{2}concentration; (

**f**) flowrate and voltage and their effect on sphericity.

Factor | Name | Units | Coded Low | Coded High |
---|---|---|---|---|

A(X1) | Sodium alginate concentration | % | 2.00 | 6.00 |

B(X2) | Flowrate | mL/h | 0.50 | 50.00 |

C(X3) | Needle size | G | 21.00 | 27.00 |

D(X4) | Voltage | kV | 13.00 | 21.00 |

E(X5) | Calcium chloride concentration | % | 2.00 | 6.00 |

Response | Name | Units | Observations | Minimum | Maximum | Mean | Std. Dev. | Ratio |
---|---|---|---|---|---|---|---|---|

R1 | Microcapsule diameter | µm | 50.00 | 75.253 | 1193.15 | 523.87 | 326.21 | 15.86 |

R2 | sphericity coefficient | N/A | 50.00 | 0.29632 | 0.9956 | 0.7731 | 0.1865 | 3.36 |

Source | Sum of Squares | df | Mean Square | F-Value | p-Value |
---|---|---|---|---|---|

Model | 5.212 × 10^{6} | 20 | 2.606 × 10^{5} | 3219.25 | <0.0001 |

A(X_{1})-sodium alginate concentration | 57,254.67 | 1 | 57,254.67 | 707.30 | <0.0001 |

B(X_{2})-Flowrate | 424.16 | 1 | 424.16 | 5.24 | 0.0295 |

C(X_{3})-Needle Size | 2.153 × 10^{6} | 1 | 2.153 × 10^{6} | 26,602.98 | <0.0001 |

D(X_{4})-Voltage | 9.512 × 10^{5} | 1 | 9.512 × 10^{5} | 11,751.21 | <0.0001 |

E(X_{5})-Calcium chloride concentration | 3.13 | 1 | 3.13 | 0.0386 | 0.8456 |

AB(X_{1}X_{2}) | 320.66 | 1 | 320.66 | 3.96 | 0.0561 |

AC(X_{1}X_{3}) | 4144.28 | 1 | 4144.28 | 51.20 | <0.0001 |

AD(X_{1}X_{4}) | 6493.40 | 1 | 6493.40 | 80.22 | <0.0001 |

AE(X_{1}X_{5}) | 4650.78 | 1 | 4650.78 | 57.45 | <0.0001 |

BC(X_{2}X_{3}) | 4288.83 | 1 | 4288.83 | 52.98 | <0.0001 |

BD(X_{2}X_{4}) | 3390.96 | 1 | 3390.96 | 41.89 | <0.0001 |

CD(X_{3}X_{4}) | 76,976.49 | 1 | 76,976.49 | 950.94 | <0.0001 |

CE(X_{3}X_{5}) | 1514.59 | 1 | 1514.59 | 18.71 | 0.0002 |

DE(X_{4}X_{5}) | 3414.89 | 1 | 3414.89 | 42.19 | <0.0001 |

${\mathrm{A}}^{2}({X}_{1}^{2})$ | 1566.25 | 1 | 1566.25 | 19.35 | 0.0001 |

${\mathrm{B}}^{2}({X}_{2}^{2})$ | 647.87 | 1 | 647.87 | 8.00 | 0.0084 |

${\mathrm{C}}^{2}\left({X}_{3}^{2}\right)$ | 1459.96 | 1 | 1459.96 | 18.04 | 0.0002 |

Residual | 2347.49 | 29 | 80.95 | ||

Lack of Fit | 1568.52 | 22 | 71.30 | 0.6407 | 0.8006 |

Pure Error | 778.96 | 7 | 111.28 | ||

Cor Total | 5.214 × 10^{6} | 49 |

Source | Sum of Squares | df | Mean Square | F-Value | p-Value |
---|---|---|---|---|---|

Model | 1.69 | 20 | 0.0847 | 253.24 | <0.0001 |

A(X_{1})-sodium alginate concentration | 0.4518 | 1 | 0.4518 | 1350.64 | <0.0001 |

B(X_{2})-Flowrate | 0.4692 | 1 | 0.4692 | 1402.38 | <0.0001 |

C(X_{3})-Needle Size | 0.0165 | 1 | 0.0165 | 49.20 | <0.0001 |

D(X_{4})-Voltage | 0.0222 | 1 | 0.0222 | 66.32 | <0.0001 |

E(X_{5})-Calcium chloride concentration | 0.0014 | 1 | 0.0014 | 4.28 | 0.0475 |

AB(X_{1}X_{2}) | 0.4440 | 1 | 0.4440 | 1327.09 | <0.0001 |

AC(X_{1}X_{3}) | 0.0070 | 1 | 0.0070 | 21.02 | <0.0001 |

AE(X_{1}X_{5}) | 0.0021 | 1 | 0.0021 | 6.36 | 0.0174 |

BC(X_{2}X_{3}) | 0.0041 | 1 | 0.0041 | 12.21 | 0.0015 |

BD(X_{2}X_{4}) | 0.0027 | 1 | 0.0027 | 8.15 | 0.0079 |

BE(X_{2}X_{5}) | 0.0080 | 1 | 0.0080 | 23.95 | <0.0001 |

CE(X_{3}X_{5}) | 0.0072 | 1 | 0.0072 | 21.54 | <0.0001 |

DE(X_{4}X_{5}) | 0.0040 | 1 | 0.0040 | 11.90 | 0.0017 |

A^{2}(X_{1}^{2}) | 0.0179 | 1 | 0.0179 | 53.42 | <0.0001 |

B^{2}(X_{2}^{2}) | 0.0089 | 1 | 0.0089 | 26.60 | <0.0001 |

D^{2}(X_{4}^{2}) | 0.0032 | 1 | 0.0032 | 9.57 | 0.0044 |

Residual | 0.0097 | 29 | 0.0003 | ||

Lack of Fit | 0.0083 | 22 | 0.0004 | 1.83 | 0.2093 |

Pure Error | 0.0014 | 7 | 0.0002 | ||

Cor Total | 1.70 | 49 |

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**MDPI and ACS Style**

Anani, J.; Noby, H.; Zkria, A.; Yoshitake, T.; ElKady, M.
Monothetic Analysis and Response Surface Methodology Optimization of Calcium Alginate Microcapsules Characteristics. *Polymers* **2022**, *14*, 709.
https://doi.org/10.3390/polym14040709

**AMA Style**

Anani J, Noby H, Zkria A, Yoshitake T, ElKady M.
Monothetic Analysis and Response Surface Methodology Optimization of Calcium Alginate Microcapsules Characteristics. *Polymers*. 2022; 14(4):709.
https://doi.org/10.3390/polym14040709

**Chicago/Turabian Style**

Anani, Joshua, Hussien Noby, Abdelrahman Zkria, Tsuyoshi Yoshitake, and Marwa ElKady.
2022. "Monothetic Analysis and Response Surface Methodology Optimization of Calcium Alginate Microcapsules Characteristics" *Polymers* 14, no. 4: 709.
https://doi.org/10.3390/polym14040709