(393l) Population Balance Modeling of Reverse Micelle Exchange Dynamics for the Controlled Release of Biologic Cargo

Reverse Micelles (RMs) are thermodynamically stable nanodroplets composed of a bulk organic solvent and an aqueous core stabilized by a surfactant layer. RMs are used in numerous applications ranging from biophysical studies of protein confinement and nanoparticle growth to large-scale industrial practices such as synthetic chemistry. Additionally, RMs can be effective delivery agents for the engineered release of biologic cargo such as proteins, nucleic acids, and peptides [1]. These applications rely on the ability of RMs to mix reactants within their aqueous cores, a process governed by the rate of coalescence and content exchange between droplets. This process is driven by Brownian motion, whereby RMs collide, coalesce to exchange contents, and decoalesce continuously in five main steps: micellar diffusion (K_diff,agg), surfactant layer opening (K_opening), molecular diffusion (K_diff,ions), reaction (K_reac), and decoalescence (K_decoal).

Since the distribution of molecules over the micelle population is not uniform, a Population Balance Model (PBM) was developed to determine the exchange rate constant (K_ex), assuming the solute distribution of newly formed micelles is decoalescence-dependent [2]. K_ex is expressed in terms of K_reac and K_decoal considering the kinetic inversion method [3] [4], in which, K_reac is determined using the experimental data from the reactions involved and the PBM, where the sum of squares of the error function between the experimental and model predicted values is minimized. To obtain the experimental data, the exchange process was monitored using a fluorescent chelate formed between terbium (III) chloride and dipicolinic acid within the aqueous cores of sodium bis(2-ethylhexyl) sulfosuccinate (AOT) RMs. Stopped-flow fluorescence was used to measure kinetics under varying conditions, including water loading (W₀), organic solvent, and surfactant headgroup pH. The influence that the tested conditions have on the elasticity of the surfactant layer was demonstrated, which is a key parameter that dictates the rate-limiting step in RM exchange, K_opening. The comparison of experimental exchange rates with model predictions highlights mechanistic insights and supports future efforts to develop predictive models for the controlled release of biologic cargo [5]. Furthermore, this will allow for the development of strategies for customized drug release for patient-specific care in the future.

References

[1] I. Dodevski et al., “Optimized Reverse Micelle Surfactant System for High-Resolution NMR Spectroscopy of Encapsulated Proteins and Nucleic Acids Dissolved in Low Viscosity Fluids,” J. Am. Chem. Soc., vol. 136, no. 9, pp. 3465–3474, Mar. 2014, doi: 10.1021/ja410716w.

[2] A. S. Bommarius, J. F. Holzwarth, D. I. C. Wang, and T. Alan. Hatton, “Coalescence and solubilizate exchange in a cationic four-component reversed micellar system,” J. Phys. Chem., vol. 94, no. 18, pp. 7232–7239, Sep. 1990, doi: 10.1021/j100381a051.

[3] W. Tang, L. Zhang, A. A. Linninger, R. S. Tranter, and K. Brezinsky, “Solving Kinetic Inversion Problems via a Physically Bounded Gauss−Newton (PGN) Method,” Ind. Eng. Chem. Res., vol. 44, no. 10, pp. 3626–3637, May 2005, doi: 10.1021/ie048872n.

[4] K. M. Yenkie and U. Diwekar, “The ‘No Sampling Parameter Estimation (NSPE)’ algorithm for stochastic differential equations,” Chemical Engineering Research and Design, vol. 129, pp. 376–383, Jan. 2018, doi: 10.1016/j.cherd.2017.11.018.

[5] K. M. Yenkie and U. M. Diwekar, “Comparison of different methods for predicting customized drug dosage in superovulation stage of in-vitro fertilization,” Computers & Chemical Engineering, vol. 71, pp. 708–714, Dec. 2014, doi: 10.1016/j.compchemeng.2014.07.021.