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Dendrimer SynthesisGeneration 4 EDA core PAMAM dendrimer was purchased from Dendritech (Midland, MI) as methanol solution (26 wt%). Acetic anhydride, pyridine, succinic anhydride, glycidol and all the remaining chemicals/solvents were purchased from Aldrich. Milli-Q deionized water (with resistivity >18 MΩcm) was used in all of the experiments. Regenerated cellulose dialysis membranes were purchased from Fisher Scientific. 4.1 mL of pyridine was added to 11.56 g of a solution of EDA core G4-NH 2 PAMAM dendrimer (3.0056 g) in methanol. The resulting solution was diluted to 40 mL by addition of methanol in a 250-ml round-bottom flask. A solution of 2.6 g acetic anhydride in methanol was then added drop wise to the dendrimer/pyridine mixture under continuous stirring. The resulting solution was equlibrated for 24 hours. The methanol was then removed from the reaction mixture on a rotary evaporator. The oily crude product was diluted and dialyzed with deionized water (6 X 4 liters) for three days to remove the excess reactants and byproducts. The final product was removed from the aqueous retentate, dissolved in deionized water and lyophilized. The yield (3.15g) was estimated at 88.2%. G4 EDA core PAMAM Dendrimer with Acetamide (NHCOCH 3 ) Terminal Groups (G4-Ac)

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[1] Particle-based models and continuum models have been developed to quantify mixinglimited bimolecular reactions for decades. Effective model parameters control reaction kinetics, but the relationship between the particle-based model parameter (such as the interaction radius R) and the continuum model parameter (i.e., the effective rate coefficient K f ) remains obscure. This study attempts to evaluate and link R and K f for the second-order bimolecular reaction in both the bulk and the sharp-concentration-gradient (SCG) systems. First, in the bulk system, the agent-based method reveals that R remains constant for irreversible reactions and decreases nonlinearly in time for a reversible reaction, while mathematical analysis shows that K f transitions from an exponential to a power-law function. Qualitative link between R and K f can then be built for the irreversible reaction with equal initial reactant concentrations. Second, in the SCG system with a reaction interface, numerical experiments show that when R and K f decline as t À1/2 (for example, to account for the reactant front expansion), the two models capture the transient power-law growth of product mass, and their effective parameters have the same functional form. Finally, revisiting of laboratory experiments further shows that the best fit factor in R and K f is on the same order, and both models can efficiently describe chemical kinetics observed in the SCG system. Effective model parameters used to describe reaction kinetics therefore may be linked directly, where the exact linkage may depend on the chemical and physical properties of the system. Citation: Zhang, Y., C. Papelis, P. Sun, and Z. Yu (2013), Evaluation and linking of effective parameters in particle-based models and continuum models for mixing-limited bimolecular reactions, Water Resour. Res., 49,

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