A mathematical model for cluster migration during the development of the particle morphology in emulsion polymerization has been developed. The motion of the clusters is due to the balance between the van der Waals forces and the viscous forces. Several illustrative calculations are presented including systems for which the final equilibrium morphologies were (i) core-shell, (ii) inverted core-shell, and (iii) occluded morphology.

A mathematical model for the development of particle morphology in emulsion polymerization has been developed. The polymer particles are considered to be a biphasic system comprising clusters of polymer 1 dispersed in a matrix of polymer 2. The model accounts for both polymerization and cluster migration. Polymerization of monomer 1 occurs both in the polymer matrix and in the clusters. The polymer 1 formed in the matrix diffuses instantaneously into the clusters. The clusters migrate toward the equilibrium morphology to minimize the free energy of the system. The driving forces for the motion of the clusters are the van der Waals interaction forces between the clusters and the aqueous phase and those between the clusters themselves. The effect of polymer matrix viscosity on the cluster motion is included. Illustrative simulations and comparisons with experimental data are presented.

A mathematical model for the development of the particle morphology in emulsion polymerization has been developed. The model accounts for phase separation leading to cluster nucleation, polymerization, polymer diffusion, and cluster migration. The model has been used to simulate batch emulsion polymerizations of methyl methacrylate on a polystyrene seed for which experimentally determined particle morphologies have been reported. A good agreement between experimental results and model predictions was achieved. On the other hand, sensitivity analysis showed that the final particle morphology was not significantly affected by either the initial cluster volume or the cluster nucleation rate constant.

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Population-wide vaccination is the most promising long-term COVID-19 disease management strategy. However, the protection offered by the currently available COVID-19 vaccines wanes over time, requiring boosters to be periodically given, which represents an unattainable challenge, especially if it is necessary to apply several doses per year. Therefore, it is essential to design strategies that contribute to maximizing the control of the pandemic with the available vaccines. Achieving this objective requires knowing, as precisely and accurately as possible, the changes in vaccine effectiveness over time in each population group, considering the eventual dependence on age, sex, etc. Thus, the present work proposes a novel approach to calculating realistic effectiveness profiles against symptomatic disease. In addition, this strategy can be adapted to estimate realistic effectiveness profiles against hospitalizations or deaths. All such time-dependent profiles allow the design of improved vaccination schedules, where each dose can be administrated to the population groups so that the fulfillment of the containment objectives is maximized. As a practical example for this analysis, vaccination against COVID-19 in Mexico was considered. However, this methodology can be applied to other countries’ data or to characterize future vaccines with time-dependent effectiveness values. Since this strategy uses aggregated observational data collected from massive databases, assumptions about the data validity and the course of the studied epidemic could eventually be necessary.

The current values for metabolizable energy of macronutrients were proposed in 1910. Since then, however, efforts to revise these values have been practically absent, creating a crucial need to carry out a critical analysis of the experimental methodology and results that form the basis of these values. Presented here is an exhaustive analysis of Atwater's work on this topic, showing evidence of considerable weaknesses that compromise the validity of his results. These weaknesses include the following: (1) the doubtful representativeness of Atwater's subjects, their activity patterns, and their diets; (2) the extremely short duration of the experiments; (3) the uncertainty about which fecal and urinary excretions contain the residues of each ingested food; (4) the uncertainty about whether or not the required nitrogen balance in individuals was reached during experiments; (5) the numerous experiments carried out without valid preliminary experiments; (6) the imprecision affecting Atwater's experimental measurements; and (7) the numerous assumptions and approximations, along with the lack of information, characterizing Atwater's studies. This review presents specific guidelines for establishing new experimental procedures to estimate more precise and/or more accurate values for the metabolizable energy of macronutrients. The importance of estimating these values in light of their possible dependence on certain nutritional parameters and/or physical activity patterns of individuals is emphasized. The use of more precise values would allow better management of the current overweight and obesity epidemic.

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