Calculation Methods of Solution Chemical Potential and Application in Emulsion Microencapsulation

Abstract

Several new biased sampling methods were summarized for solution chemical potential calculation methods in the field of emulsion microencapsulation. The principles, features, and calculation 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 configuration according to the potential energy around the detection point, and hence, could be used for the oil-polymer mixtures of microencapsulation emulsion. For the macromolecule solutes in the oil or aqueous phase of the emulsion, the particle insertion bias could be applied to greatly increase the success rate of Widom insertions. Readers were expected to choose appropriate biased Widom methods to carry out their calculations on chemical potential, fugacity, and solubility of solutions based on the system molecular properties, inspired by this paper.

Widom insertion method in simulations with Ewald summation

“…The integral is easily calculate inside a canonical MC simulation by sampling the insertion probability exp(−βΔU) after the simulation with N particles has fully equilibrated. [28][29][30][31][32] Widom's method has been widely used for evaluating the excess chemical potential for different systems, such as supercritical fluid-solid equilibria, 33,34 mixture of Argon and 1-magne-4polybutadiene, 35 and binary phases. 36 The Widom insertion method was also used to calculate ionic solvation free energy in atomistic simulations.…”