The fundamentals and applications of polymer brush-modified membranes are reviewed. This new class of synthetic membranes is explored with an emphasis on tuning the membrane performance through polymer brush grafting. This work highlights the intriguing performance characteristics of polymer brush-modified membranes in a variety of separations. Polymer brushes are a versatile and effective means in designing membranes for applications in protein adsorption and purification, colloid stabilization, sensors, water purification, pervaporation of organic compounds, gas separations, and as stimuli responsive materials.

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Due to a significant drop in the energy needed for RO desalination from 12 kWh/m 3 to ~2 kWh/m 3 over the past 20 years, which is close to 1 kWh/m 3 , the theoretical minimum for recovering salt-free water from seawater, the focus here is on the critical aspects that offer opportunities to further reduce costs. These include pre-and post-treatment; and analysis and optimization of the performance of RO systems, such as selectivity, capacity, and flux decline. Flux decline includes concentration polarization and fouling from inorganic, organic, biological constituents. We call these the "three legs' that undergird all membrane processes. The approach here is quantitative and includes detailed fluid mechanics and associated mass transfer of RO systems for optimizing performance.

Mean radical lifetimes and fluctuations in lifetime are shown to decrease with conversion and polydispersity index for atom transfer radical polymerization (ATRP) of both methyl methacrylate and styrene. In the first study of its kind, a comprehensive investigation of radical lifetimes in both ATRP and conventional free-radical polymerizations is reported using a kinetic Monte Carlo model. Quantile−quantile plots show the radical lifetimes to be exponentially distributed with equal mean and standard deviation. Radical lifetimes are shown to be thousands of times longer in conventional free-radical polymerization compared with ATRP. Reduced mean radical lifetimes and fluctuations offer a new perspective on the ATRP mechanism. Reduction in radical lifetime fluctuations ensures less variability in the number of monomer units added during the propagation steps and keeps the polydispersity index low. Deterministic models are used along with the kinetic Monte Carlo model to investigate several facets of these polymerization systems and are validated against experimental data.

Solving a comprehensive, yet simple, reaction model for describing the activators regenerated by electron transfer (ARGET)–atom transfer radical polymerization (ATRP) reaction cascade, we show that the molar ratios of transition metal catalyst to initiator and reducing agent to catalyst are critical parameters in the ARGET ATRP mechanism, with optimal values on the order of 0.1:1 and 10:1, respectively. The model also predicts an optimal molar ratio of reducing agent to initiator of 1:1. The ARGET ATRP reaction cascade is extremely complex with many adjustable species concentrations and reaction parameters. The effect of varying any of these parameters on the resulting temporal conversion trajectory of the polymerization is not straightforward. This analysis greatly simplifies the process allowing one to select the proper conditions to optimize the reaction and could save much effort, time and money. These results have severe implications when grafting polymer chains from surfaces, since the amount of surface-bound initiator is very low relative to the amount of catalyst. This suggests adding a sacrificial initiator to the reaction solution when grafting from surfaces is necessary to prevent loss of control on the polymerization. The most viable parameter for both increasing the polymerization rate and maintaining maximum attainable conversion for the ARGET ATRP system is to increase the reaction temperature. For broad use, the model was developed in MATLAB to predict conversion versus time behavior in the ARGET ATRP reaction cascade using an inexpensive ligand. Utilizing known rate constants and pre-exponential factors to the Arrhenius equations from the literature, the model was able to predict published experimental data for the methyl methacrylate (MMA), styrene (St), and glycidyl methacrylate (GMA) monomers at various temperatures. The main assumptions of the model are that termination reactions occur through radical coupling only and the propagation and termination reaction rates are chain length independent. The resulting model is shown to be very accurate, especially at conversions of 0.4 and lower. Sensitivity analyses were performed on the ARGET ATRP mechanism using MMA as a model monomer to identify key reaction parameters to ensure successful controlled polymerization.