Intra-particle sorption rate and liquid chromatographic bandbroadening in porous polymer packings I. Methodology and validation of the model

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An approach is proposed by which an experimentally measured sorption-rate curve for a solute on a Chromatographic sorbent may be used to accurately predict the plate height and peak shape contributions of intra-particle sorption rate to the Chromatographic peak that will be obtained when the solute elutes from a liquid Chromatographic column of the sorbent. The sorption-rate curve is measured on a “shallow bed” of sorbent (e.g. ≈ 1 mm) under “infinite solution volume” conditions and is fit by an empirical tri-exponential equation. Intra-particle rate processes include the bandbroadening phenomena traditionally identified by the HS and HSM plate-height terms. The elution Chromatographic column is imagined to be composed of three “hypothetical columns” in series, and the hypothetical peak eluting from each is calculated from well-known equations. Numerical convolution of these hypothetical peaks in series yields the overall predicted elution peak contribution from intra-particle rate processes. The accuracy of this model is demonstrated by comparing predicted peaks with eluted peaks measured on a long column of very large diameter (0.36 mm) porous polymer sorbent. On this column, Chromatographic bandbroadening is due nearly exclusively to slow intra-particle processes. The proposed approach is not limited, either theoretically or in practice, to large particles or to porous polymers.