Year 2021,
Volume: 51 Issue: 1, 42 - 49, 30.04.2021
Murat Sami Berkman
,
Kadri Güleç
References
- • Abboud, E. (2010). Viviani’s theorem and its extension. The College Mathematics Journal, 41(3), 203-211.https://doi. org/10.4169/074683410X488683
- • Burguera, J. L., & Burguera, M. (2012). Analytical applications of emulsions and microemulsions. Talanta, 96, 11-20.https://doi. org/10.1016/j.talanta.2012.01.030
- • Das, S., Lee, S. H., Chia, V. D., Chow, P. S., Macbeath, C., Liu, Y., & Shliout, G. (2020). Development of microemulsion based topical ivermectin formulations: pre-formulation and formulation studies. Colloids and Surfaces B: Biointerfaces, 189, 1-8.https://doi. org/10.1016/j.colsurfb.2020.110823
- • Fanun, M., Papadimitriou, V., & Xenakis, A. (2011). Characterization of cephalexin loaded nonionic microemulsions. Journal of Colloid and Interface Science, 362(1), 115-121.https://doi.org/10.1016/j. jcis.2011.05.042
- • Green, G., & Thomson, W. (1828). An essay on the application of mathematical analysis to the theories of electricity and magnetism. Nottingham: T Wheelhouse.
- • Hathout, R. M., & Woodman, J. (2012). Applications of NMR in the characterization of pharmaceutical microemulsions. Journal of Controlled Release, 161(1), 62-72. https://doi.org/10.1016/j.jconrel.2012.04.032
- • Hickey, S., Hagan, S. A., Kudryashov, E., & Buckin, V. (2010). Analysis of phase diagram and microstructural transitions in an ethyl oleate/water/Tween 80/Span 20 microemulsion system using high-resolution ultrasonic spectroscopy. International Journal of Pharmaceutics, 388(1-2), 213-222.https://doi.org/10.1016/j. ijpharm.2009.12.003
- • Hoar, T. P., & Schulman, J. H. (1943). Transparent water in oil dispersions: oleopathic hydromicelle. Nature, 152, 102-103.https://doi. org/10.1038/152102a0
- • Kreilgaard, M. (2002). Influence of microemulsions on cutaneous drug delivery. Advanced Drug Delivery Reviews, 54(1), 77-98. https://doi.org/10.1016/S0169-409X(02)00116-3
- • Lawrence, M. J., & Rees, G. D. (2000). Microemulsion-based media as novel drug delivery systems. Advanced Drug Delivery Reviews, 45(1), 89-121.https://doi.org/10.1016/S0169-409X(00)00103-4
- • Lee, Y., & Lim, W. (2017). Shoelace formula: connecting the area of a polygon with vector cross product. The Mathematics Teacher, 110(8), 631-636.https://doi.org/10.5951/mathteacher.110.8.0631
- • Liengme, B. V. (2016). VBA user-defined functions. In B. V. Liengme (Ed.), A guide to Microsoft Excel 2013 for scientists and engineers (pp. 181-206). San Diego: Academic Press.https://doi.org/10.1016/ C2014-0-03421-1
- • Liu, D., Kobayashi, T., Russo, S., Li, F., Plevy, S. E., Gambling, T. M., Carson, J. L., & Mumper, R. J. (2013). In vitro and in vivo evaluation of a water-in-oil microemulsion system for enhanced peptide intestinal delivery. The AAPS Journal, 15(1), 288-298.https://doi. org/10.1208/s12248-012-9441-7
- • Sahoo, S., Pani, N. R., & Sahoo, S. K. (2014). Microemulsion based topical hydrogel of sertaconazole: Formulation, characterization and evaluation. Colloids and Surfaces B: Biointerfaces, 120, 193-199. https://doi.org/10.1016/j.colsurfb.2014.05.022
- • Schmidts, T., Nocker, P., Lavi, G., Khulman, J., Czermak, P., & Runkel, F. (2009). Development of an alternative, time and cost saving method of creating pseudoternary diagrams using the example of a microemulsion. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 340(1-3), 187-192. https://doi.org/10.1016/j. colsurfa.2009.03.029
- • Schulman, J. H., Stoeckenius, W., & Prince, L.M. (1959). Mechanism of formation and structure of microemulsions by electron microscopy. The Journal of Physical Chemistry, 63(10), 1677-1680. https:// doi.org/10.1021/j150580a027
- • Smith, M. J., Goodchild, M. F., & Longley, P. A. (2007). Building blocks of spatial analysis. In M. J. Smith, M. F. Goodchild & P. A. Longley (Eds.), Geospatial analysis: A comprehensive guide to principles, techniques and software tools (pp. 69-71). United Kingdom: Matador.
- • Soerjadi, R. (1968). On the computation of the moments of a polygon, with some applications. Heron, 16(5), 43-58.
- • Spernath, A., & Aserin, A. (2006). Microemulsions as carriers for drugs and nutraceuticals. Advances in Colloid and Interface Science, 128-130, 47-64.https://doi.org/10.1016/j.cis.2006.11.016
- • Yang, J. H., Kim, Y., & Kim, K. M. (2002). Preparation and evaluation of aceclofenac microemulsion for transdermal delivery system. Archives of Pharmacal Research, 25(4), 534-540.https://doi. org/10.1007/BF02976614
- • Zhang, H., Cui, Y., Zhu, S., Feng, F., & Zheng, X. (2010). Characterization and antimicrobial activity of a pharmaceutical microemulsion. International Journal of Pharmaceutics, 395(1-2), 154-160. https://doi.org/10.1016/j.ijpharm.2010.05.022
Pseudo ternary phase diagrams: a practical approach for the area and centroid calculation of stable microemulsion regions
Year 2021,
Volume: 51 Issue: 1, 42 - 49, 30.04.2021
Murat Sami Berkman
,
Kadri Güleç
Abstract
Background and Aims: This study aims to develop and evaluate a practical approach for the complicated area and centroid calculation of stable microemulsion regions. Pseudo ternary phase diagrams are used to determine the region of microemulsion existence. The effect of various surfactant/co-surfactant weight ratios on the extent of a stable microemulsion area can easily be observed with these diagrams. Furthermore, the optimum formulations are selected using the centroid of the microemulsion region. Methods: Microemulsion formulations were prepared by changing the weight ratios of the components. The titration method was used at a constant temperature. A pseudo ternary phase diagram was constructed using the spots of the stable microemulsion formulations. Results: The area and centroid of the stable microemulsion region were calculated by using the formulas manually and the macro edited for Microsoft® Excel. Both results were the same. The macro was user-friendly, easy to use, and worked well in Microsoft® Excel. Conclusion: Definitions, formulas, algorithms, and calculations used in this research will be constructive for everyone interested in this field and can be modified very easily in every different case.
References
- • Abboud, E. (2010). Viviani’s theorem and its extension. The College Mathematics Journal, 41(3), 203-211.https://doi. org/10.4169/074683410X488683
- • Burguera, J. L., & Burguera, M. (2012). Analytical applications of emulsions and microemulsions. Talanta, 96, 11-20.https://doi. org/10.1016/j.talanta.2012.01.030
- • Das, S., Lee, S. H., Chia, V. D., Chow, P. S., Macbeath, C., Liu, Y., & Shliout, G. (2020). Development of microemulsion based topical ivermectin formulations: pre-formulation and formulation studies. Colloids and Surfaces B: Biointerfaces, 189, 1-8.https://doi. org/10.1016/j.colsurfb.2020.110823
- • Fanun, M., Papadimitriou, V., & Xenakis, A. (2011). Characterization of cephalexin loaded nonionic microemulsions. Journal of Colloid and Interface Science, 362(1), 115-121.https://doi.org/10.1016/j. jcis.2011.05.042
- • Green, G., & Thomson, W. (1828). An essay on the application of mathematical analysis to the theories of electricity and magnetism. Nottingham: T Wheelhouse.
- • Hathout, R. M., & Woodman, J. (2012). Applications of NMR in the characterization of pharmaceutical microemulsions. Journal of Controlled Release, 161(1), 62-72. https://doi.org/10.1016/j.jconrel.2012.04.032
- • Hickey, S., Hagan, S. A., Kudryashov, E., & Buckin, V. (2010). Analysis of phase diagram and microstructural transitions in an ethyl oleate/water/Tween 80/Span 20 microemulsion system using high-resolution ultrasonic spectroscopy. International Journal of Pharmaceutics, 388(1-2), 213-222.https://doi.org/10.1016/j. ijpharm.2009.12.003
- • Hoar, T. P., & Schulman, J. H. (1943). Transparent water in oil dispersions: oleopathic hydromicelle. Nature, 152, 102-103.https://doi. org/10.1038/152102a0
- • Kreilgaard, M. (2002). Influence of microemulsions on cutaneous drug delivery. Advanced Drug Delivery Reviews, 54(1), 77-98. https://doi.org/10.1016/S0169-409X(02)00116-3
- • Lawrence, M. J., & Rees, G. D. (2000). Microemulsion-based media as novel drug delivery systems. Advanced Drug Delivery Reviews, 45(1), 89-121.https://doi.org/10.1016/S0169-409X(00)00103-4
- • Lee, Y., & Lim, W. (2017). Shoelace formula: connecting the area of a polygon with vector cross product. The Mathematics Teacher, 110(8), 631-636.https://doi.org/10.5951/mathteacher.110.8.0631
- • Liengme, B. V. (2016). VBA user-defined functions. In B. V. Liengme (Ed.), A guide to Microsoft Excel 2013 for scientists and engineers (pp. 181-206). San Diego: Academic Press.https://doi.org/10.1016/ C2014-0-03421-1
- • Liu, D., Kobayashi, T., Russo, S., Li, F., Plevy, S. E., Gambling, T. M., Carson, J. L., & Mumper, R. J. (2013). In vitro and in vivo evaluation of a water-in-oil microemulsion system for enhanced peptide intestinal delivery. The AAPS Journal, 15(1), 288-298.https://doi. org/10.1208/s12248-012-9441-7
- • Sahoo, S., Pani, N. R., & Sahoo, S. K. (2014). Microemulsion based topical hydrogel of sertaconazole: Formulation, characterization and evaluation. Colloids and Surfaces B: Biointerfaces, 120, 193-199. https://doi.org/10.1016/j.colsurfb.2014.05.022
- • Schmidts, T., Nocker, P., Lavi, G., Khulman, J., Czermak, P., & Runkel, F. (2009). Development of an alternative, time and cost saving method of creating pseudoternary diagrams using the example of a microemulsion. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 340(1-3), 187-192. https://doi.org/10.1016/j. colsurfa.2009.03.029
- • Schulman, J. H., Stoeckenius, W., & Prince, L.M. (1959). Mechanism of formation and structure of microemulsions by electron microscopy. The Journal of Physical Chemistry, 63(10), 1677-1680. https:// doi.org/10.1021/j150580a027
- • Smith, M. J., Goodchild, M. F., & Longley, P. A. (2007). Building blocks of spatial analysis. In M. J. Smith, M. F. Goodchild & P. A. Longley (Eds.), Geospatial analysis: A comprehensive guide to principles, techniques and software tools (pp. 69-71). United Kingdom: Matador.
- • Soerjadi, R. (1968). On the computation of the moments of a polygon, with some applications. Heron, 16(5), 43-58.
- • Spernath, A., & Aserin, A. (2006). Microemulsions as carriers for drugs and nutraceuticals. Advances in Colloid and Interface Science, 128-130, 47-64.https://doi.org/10.1016/j.cis.2006.11.016
- • Yang, J. H., Kim, Y., & Kim, K. M. (2002). Preparation and evaluation of aceclofenac microemulsion for transdermal delivery system. Archives of Pharmacal Research, 25(4), 534-540.https://doi. org/10.1007/BF02976614
- • Zhang, H., Cui, Y., Zhu, S., Feng, F., & Zheng, X. (2010). Characterization and antimicrobial activity of a pharmaceutical microemulsion. International Journal of Pharmaceutics, 395(1-2), 154-160. https://doi.org/10.1016/j.ijpharm.2010.05.022