Understanding Supported Reactions in Spherical Compartments:  A General Algorithm To Model and Determine Rate Constants, Diffusion Coefficients, and Spatial Product Distributions

Abstract

A general algorithm allowing the numerical modeling of the time and space dependence of product formation in spherical reaction volumes is described. The algorithm is described by the complete set of mass balance equations. On the basis of these equations, the effects of the diffusion coefficient, reaction rate, bead size, reagent excess, and packing density of the resin beads on the overall reaction rates are determined for second-order reactions. Experimental data of reaction progress are employed to calculate reaction rates and diffusion coefficients in polymer-supported reactions. In addition, the conditions for shell-like product formation are determined, and various strategies for the radial patterning of resin beads are compared. The effect of diffusion on polymer-supported enzyme-catalyzed reactions of the Michaelis-Menten type is treated, as well. Finally, the effects of typical nonideal solid-phase phenomena, namely, the inhomogeneity of rate constants and the concentration dependence of diffusion coefficients, on overall rates are discussed.

Development and Applications of Topologically Segregated Bilayer Beads in One-bead One-compound Combinatorial Libraries

“…Using fluorescent and infrared (IR) microscopy, Rademann et al studied the effects of bead size, diffusion and adsorption on the alkylation and acylation of resin beads [46]. Very recently, the same group reported a general algorithm that models the time and space dependence of chemical reactions on solid support such as beads [47]. Such studies may provide useful information that facilitates the development of better approaches for solid-phase reactions and for the construction of high-quality multilayer beads.…”

Transport phenomena in solid phase synthesis supported by cross-linked polymer beads

“…Egelhaaf and Rademann 21 proposed a dynamic model derived from Fick's second law for reactions in "spherical compartments". "Realistic modeling" is expected to be possible only when "simultaneous diffusion and reaction are considered".…”

“…Egelhaaf and Rademann 21 modified their model to fit experimental data of Knorr linker attachment on polystyrene…”

“…Limited research 13–20 indicates that mass transfer must be considered to get realistic modeling and to assess its contribution to the overall process. 20,21…”

Synthesis of Arrays Using Low Molecular Weight MPEG-Assisted Mitsunobu Reaction

“…Of course, a solid-supported phosphine can be combined with an azadicarboxylate removed by another method to avoid chromatography, , or vice versa, but this requires additional manipulation. The heterogeneous nature of reactions can also be an issue as intrinsic reactivity of the supported reagent , in a given solvent depends on the nature of the polymer, the size of its cavities, bead size/shape and loading, and there can be mixing problems and mechanical damage to resins. In a direct comparison between solid-supported TPP (2.1 mmol g −1 , 1% cross-linked diphenylphosphinopolystyrene) and TPP itself in the bromination of 2,4-dimethoxybenzyl alcohol using carbon tetrabromide, it was found that while the initial rate of reaction was similar, the overall conversion was lower for solid-supported TPP, presumably because not all the phosphine groups were accessible .…”