Mathematical Models as Tools to Predict the Release Kinetic of Fluorescein from Lyotropic Colloidal Liquid Crystals
Abstract
:1. Introduction
2. Materials and Methods
2.1. Materials
2.2. Lyotropic Colloidal Liquid Crystals
2.3. Physicochemical Characterization of Lyotropic Colloidal Liquid Crystals
2.4. Release Experiments
2.5. Statistical Criteria and Information on Selection of Mathematical Models
2.5.1. Akaike and Schwarz criteria
2.5.2. Imbimbo Criterion
2.5.3. Fisher (F) Test Criterion
2.6. Applied Mathematical Models
2.6.1. Zero Order Model
2.6.2. Noyes–Whitney Model
2.6.3. Weibull Model
2.6.4. Power Law Equation (Siepman–Peppas) Model
2.6.5. Construction of Diffusion Models by using Fick’s Second Law
2.6.6. Higuchi Square Root Law
2.6.7. Square Root Laws
2.7. Graphical Representation of Data
3. Results and Discussion
3.1. Analysis of the Physicochemical and Technological Properties of Lyotropic Colloidal Liquid Crystals
3.2. Description and Analysis of the Obtained Release Kinetics
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
(Brij® 92 or Brij O2) | Polyethylene glycol oleyl ether |
(Brij® 72) | Polyoxyethylene stearyl ether |
(Symperonic® PE/F127) | Polyoxyethylene-polyoxypropylene block copolymer 127 |
(Pluronic® PE 6800) | Polyethylene glycol-polypropylene glycol-polyethylene glycol block copolymer 6800 |
(Pluronic® PE 10500) | Polyethylene glycol block copolymer 10500 |
(Monomuls® 90-O18) | Glyceryl mono-oleate |
(NaCl 0.9 % w/v) | Isotonic sterile saline solution |
FL | (Fluorescein) |
PDI | (Polydispersity index) |
Z.P. | (Z-potential) |
E.M. | (Electrophoretic mobility) |
E.E. (%) | (Entrapment efficiency (%)). |
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Formulations | Monomuls | Brij 72 | Brij 92 | Pluronic 10500 | Pluronic F68 | Symperonic |
---|---|---|---|---|---|---|
1 | — | — | 90 mg | — | 50 mg | — |
2 | 90 mg | 50 mg | — | — | — | — |
3 | 90 mg | — | — | — | — | 50 mg |
4 | 90 mg | — | — | 50 mg | — | — |
5 | — | — | 90 mg | — | — | 50 mg |
Formulations | Size (nm) | PDI 2 | Z.P. (mV) 3 | E.M. (μm × cm/Vs) 4 | E.E (%) 5 |
---|---|---|---|---|---|
1 | 162.4 ± 1.3 | 0.16 ± 0.05 | −29.3 ± 1.5 | −2.1 ± 0.2 | − |
1 + FL 1 | 163.5 ± 2.1 | 0.18 ± 0.03 | −30.3 ± 0.5 | −2.1 ± 0.3 | 85.2 ± 3.1 |
2 | 548.2 ± 0.9 | 0.35 ± 0.09 | −15.4 ± 0.7 | −1.79 ± 0.1 | − |
2 + FL 1 | 550.4 ± 1.5 | 0.37 ± 0.06 | −16.3 ± 0.4 | −1.82 ± 0.1 | 87.1 ± 2.9 |
3 | 187.3 ± 1.5 | 0.24 ± 0.07 | −30.2 ± 1.4 | −2.39 ± 0.18 | − |
3 + FL 1 | 188.8 ± 1.7 | 0.26 ± 0.02 | −32.2 ± 0.9 | −2.42 ± 0.15 | 61.9 ± 4.1 |
4 | 183.4 ± 6.1 | 0.25 ± 0.09 | −33.1 ± 1.5 | −2.12 ± 0.21 | − |
4 + FL 1 | 185.2 ± 2.5 | 0.27 ± 0.1 | −34.9 ± 1.3 | −2.15 ± 0.18 | 75.1 ± 5.1 |
5 | 148.3 ± 1.6 | 0.14 ± 0.03 | −30.5 ± 1.4 | −2.3 ± 0.06 | − |
5 + FL 1 | 150.1 ± 1.6 | 0.16 ± 0.07 | −31.9 ± 1.7 | −2.5 ± 0.1 | 65.9 ± 5.7 |
Mathematical Model | Akaike | Schwarz | Imbimbo | F-test |
---|---|---|---|---|
Higuchi | 29.7 | 31.3 | 0.057 | 0.242 |
Weibul | 25.8 | 25.4 | 0.059 | — |
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Paolino, D.; Tudose, A.; Celia, C.; Di Marzio, L.; Cilurzo, F.; Mircioiu, C. Mathematical Models as Tools to Predict the Release Kinetic of Fluorescein from Lyotropic Colloidal Liquid Crystals. Materials 2019, 12, 693. https://doi.org/10.3390/ma12050693
Paolino D, Tudose A, Celia C, Di Marzio L, Cilurzo F, Mircioiu C. Mathematical Models as Tools to Predict the Release Kinetic of Fluorescein from Lyotropic Colloidal Liquid Crystals. Materials. 2019; 12(5):693. https://doi.org/10.3390/ma12050693
Chicago/Turabian StylePaolino, Donatella, Andra Tudose, Christian Celia, Luisa Di Marzio, Felisa Cilurzo, and Constantin Mircioiu. 2019. "Mathematical Models as Tools to Predict the Release Kinetic of Fluorescein from Lyotropic Colloidal Liquid Crystals" Materials 12, no. 5: 693. https://doi.org/10.3390/ma12050693