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Calculation Methods of Solution Chemical Potential and Application in Emulsion Microencapsulation

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Calculation Methods of Solution Chemical Potential and Application in Emulsion Microencapsulation molecules Review Calculation Methods of Solution Chemical Potential and Application in Emulsion Microencapsulation Binkai Xu 1, Xiangdong Liu 2 and Bo Zhou 1,* 1 Jiangsu Key Laboratory of Micro and Nano Heat Fluid Flow Technology and Energy Application, School of Environmental Science and Engineering, Suzhou University of Science and Technology, Suzhou 215009, China; [email protected] 2 College of Electrical, Energy and Power Engineering, Yangzhou University, Yangzhou 225127, China; [email protected] * Correspondence: [email protected] Abstract: Several new biased sampling methods were summarized for solution chemical potential calculation methods in the field of emulsion microencapsulation. The principles, features, and calcu- lation efficiencies of various biased Widom insertion sampling methods were introduced, including volume detection bias, simulation ensemble bias, and particle insertion bias. The proper matches between various types of solution in emulsion and biased Widom methods were suggested, following detailed analyses on the biased insertion techniques. The volume detection bias methods effectively improved the accuracy of the data and the calculation efficiency by inserting detection particles and were suggested to be used for the calculation of solvent chemical potential for the homogeneous aqueous phase of the emulsion. The chemical potential of water, argon, and fluorobenzene (a typical solvent of the oil phase in double emulsion) was calculated by a new, optimized volume detection bias proposed by this work. The recently developed Well-Tempered(WT)-Metadynamics method skillfully constructed low-density regions for particle insertion and dynamically adjusted the system Citation: Xu, B.; Liu, X.; Zhou, B. configuration according to the potential energy around the detection point, and hence, could be used Calculation Methods of Solution for the oil-polymer mixtures of microencapsulation emulsion. For the macromolecule solutes in the Chemical Potential and Application oil or aqueous phase of the emulsion, the particle insertion bias could be applied to greatly increase in Emulsion Microencapsulation. the success rate of Widom insertions. Readers were expected to choose appropriate biased Widom Molecules 2021, 26, 2991. https:// methods to carry out their calculations on chemical potential, fugacity, and solubility of solutions doi.org/10.3390/molecules26102991 based on the system molecular properties, inspired by this paper. Academic Editor: Erich A. Müller Keywords: emulsion microencapsulation; molecular simulation; chemical potential; Widom inser- tion; Metadynamics Received: 22 March 2021 Accepted: 12 May 2021 Published: 18 May 2021 1. Introduction Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in Emulsion microencapsulation is a technique to prepare hollow polymer microspheres published maps and institutional affil- with W1/O/W2 double emulsion. The emulsion is generated by dispersing the oil phase iations. (O phase), which contains polymer macromolecules, and wraps the inner water phase (W1 phase) over the outer water phase (W2 phase). Hollow polymer microspheres can be obtained by curing the emulsion and removing the O phase solvent and the W1 phase. Hollow polymer microspheres are important polymer materials with an internal cavity, Copyright: © 2021 by the authors. which can encapsulate various types of matter. An illustration of the W/O/W structure Licensee MDPI, Basel, Switzerland. and the hollow sphere preparation process is shown in Figure1a. In the fields of medicine This article is an open access article and biology, Hollow polymer microspheres are widely used to encapsulate drugs to distributed under the terms and achieve long-distance macromolecule delivery and controlled release [1,2]. Due to the high conditions of the Creative Commons refractive index difference between the spherical shell of hollow polymer microspheres Attribution (CC BY) license (https:// and air, the spheres have a strong light-shielding ability and can be used in paint coatings creativecommons.org/licenses/by/ in construction and leather, as well as in the cosmetics and paper industry [1,3,4]. In the 4.0/). Molecules 2021, 26, 2991. https://doi.org/10.3390/molecules26102991 https://www.mdpi.com/journal/molecules Molecules 2021, 26, x FOR PEER REVIEW 2 of 19 Molecules 2021, 26, 2991 2 of 19 energy[1,3,4]. field, In the hollow energy polymer field, microspheres hollow polymer can wrap microspheres phase change materialscan wrap to phase prepare change materials phaseto prepare change microcapsulesphase change [5]. microcapsules [5]. FigureFigure 1. Illustration1. Illustration of (a) of the (a emulsion) the emulsion curing process, curing and process, (b) the typicaland (b O-phase) the typical (polystyrene- O-phase (polystyrene- octaneoctane in fluorobenzene),in fluorobenzene), and W2-phase and W2-phase (NaCl-polyvinyl (NaCl-poly alcoholvinyl in water) alcohol in double in water) emulsion in double for emulsion for microencapsulation.microencapsulation. Our group carried out some research in the field of efficient preparation of double emulsionsOur [6 group–10]. In carried the field out of microfluidics, some research an effective in the microfluidicfield of efficient method preparation based of double onemulsions a simple glass [6–10]. capillary In the assembly field of was microfluidics, proposed to encapsulatean effective solids microfluidic and prepare method based on doublea simple emulsions, glass andcapillary visual experimentsassembly was were performedproposed to to verify encapsulate the effectiveness solids of and the prepare double proposedemulsions, microfluidic and visual device. experiments The results showed were that perfor the devicemed controllablyto verify the encapsulated effectiveness of the pro- solidsposed in eachmicrofluidic double emulsion device. droplet The results produced, showed and the that number the of device encapsulated controllably solid encapsulated cores could be well controlled by adjusting the flow rates of different phases. In order tosolids improve in theeach quality double of theemulsion prepared droplet microspheres, produced, our research and the group number studied of theencapsulated solid solidificationcores could and be evaporation well controlled process by of theadjusting double emulsionthe flow from rates a microscopicof different point. phases. In order to Theimprove dissolution the andquality diffusion of the processes prepared of water microsph moleculeseres, on our the W/Oresearch interface group of thestudied the solidi- doublefication emulsion and evaporation were studied throughprocess molecular of the double dynamics emulsion simulation. from The dissolutiona microscopic point. The and diffusion of droplets were closely related to the chemical potentials in the three dense anddissolution complex phases and diffusion of a double processes emulsion. of As water shown mo in Figurelecules1b, on typical the W/O emulsion interface for of the double microencapsulationemulsion were studied involved through various molecules, molecular where dynamics the O-phase simulation. contained The polymer dissolution and dif- macromoleculesfusion of droplets as solidification were closel materialy related (i.e., polystyrene to the chemical and poly- potentialsα-methyl-styrene), in the three dense and short-chaincomplex alkanesphases as of regulating a double additives, emulsion. and As aromatics shown as in solvent. Figure The 1b, W2-phase typical acted emulsion for micro- asencapsulation the curing environment, involved in whichvarious polyalcohol molecules, molecules where were the surfactant,O-phase andcontained salt ions polymer macro- helped to inhibit the self-diffusion of water. The W1-phase was usually pure water or other fillermolecules that did notas participatesolidification in the material mass transfer (i.e., process polystyrene during emulsion and poly- curing.α-methyl-styrene), short- chainSolution alkanes thermodynamics as regulating theory additives, indicated and that aromatics the chemical as potentials, solvent. mThe, of W2-phase the acted as threethe phasescuring in environment, a double emulsion in werewhich closely polyalcohol related to theirmolecules Henry coefficients, were surfactant, vapor and salt ions pressures,helped fugacities,to inhibit free the energies, self-diffusion and other of parameters, water. The which W1-phase significantly was affected usually the pure water or evaporation and curing processes of the double emulsion and the quality of the final shell other filler that did not participate in the mass transfer process during emulsion curing. Solution thermodynamics theory indicated that the chemical potentials, μ, of the three phases in a double emulsion were closely related to their Henry coefficients, vapor pressures, fugacities, free energies, and other parameters, which significantly affected the evaporation and curing processes of the double emulsion and the quality of the final shell products. The fugacity, f, of a fluid relates with the chemical potential in the form μ = kBT ln f + C, when T is the temperature, kB is the Boltzmann’s constant, and C is a constant related to the reference state of the fluid. The fugacity of a pure substance system is equal to the product of its pressure and fugacity coefficient, while the fugacity of a component Molecules 2021, 26, 2991 3 of 19 products. The fugacity, f, of a fluid relates with the chemical potential in the form m = kBT ln f + C, when T is the temperature, kB is the Boltzmann’s
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