Appendix


The importance of van Deemter plots A van Deemter plot should be employed in chromatography to establish column performance and identify optimum velocity (minimum H, or maximum N) during method development. Final methods usually do not require optimum velocity. In a typical experiment, column efficiency (N) is measured for a given length (L) and converted to plate height (H) or reduced plate height (h). It is usually plotted against flow velocity (u) and broken into terms that have different velocity dependence, as shown in the following simple relationships.


H = L/N h = H/dP


H = A + B/u + Cu u = L/t0


(1) (2) (3) (4)


Time (t0) of an unretained peak may be used to estimate flow


velocity; however, useful results for columns of the same dimen- sions can be obtained by plotting H as a function of flow rate. For more complete discussions of flow velocity and the van Deemter equation, see Knox7,8


and Neue.16 As illustrated in Figures 1 and 2,


well-prepared columns with solid-core silica demonstrate much smaller h values and show narrower peaks with more plates/meter than porous silica with similar average particle size (dP


) but broader


PSD. Each term in Eq. (3) contributes to overall column performance but changes in relative importance with flow velocity. The A term is important to performance at all velocities, the B term dominates at low velocities and the C term dominates at high velocities.


The A term describes flow uniformity outside the particles and is smaller for solid-core particles because column beds apparently are more uniform. This was somewhat surprising when core-type columns were introduced, and was attributed to rougher surface, higher particle density and narrower PSD (D90/10


= 1.15). Since


the A term does not change significantly with velocity, it remains important at all flow velocities and establishes the overall level of column performance. Routine column operation at high pressure can create bed shifting, disruption of flow uniformity and loss of efficiency.


The B term describes longitudinal or axial diffusion that is primarily important while solutes are in the mobile phase and able to diffuse more freely; it decreases with velocity as solutes spend less time in the column. Surprisingly, this term is also smaller for core-type par- ticles because the presence of a solid core apparently restricts axial diffusion by reducing internal column volume and opportunities available for free diffusion. While early textbooks have suggested to ignore the B term in HPLC because of slow axial solute diffusion in


liquids, this approximation is unrealistic for modern, small-particle columns. The A term has become so small for new particles that the B term may be significant at all flow velocities; and its importance will increase at elevated column temperatures.


The C term increases with flow velocity and describes rate of mass transfer between flowing mobile phase and stagnant regions within and around particles. As expected, radial mass transfer is faster for solid-core particles because solutes must travel shorter distances inside the particle to interact and separate. While both porous and core-type particles deliver high performance for small molecules (<1000 MW) having large diffusion coefficients, advantages for solid-core particles with short diffusion paths begin to show when high mobile phase velocities drive high sample throughput. For large molecules (>10,000 MW), the C term becomes critically im- portant and speed-limiting under all flow and viscosity conditions, shifting the advantage further toward a core-type particle. It may be possible to reduce this performance gap between core-type and porous particles for large molecules by operating at elevated temperatures17


to decrease viscosity and increase diffusion rates.


The practical use of higher temperature in UHPLC experiments re- quires more study, however, because any performance gains from faster radial diffusion (smaller C term) may be offset by performance losses from faster axial diffusion (larger B term), especially in the UHPLC experiment where the B term has greater significance.18


Improvements in instrument design may be required before el- evated temperature operation becomes a precise tool in UHPLC. Complexity exists for HPLC systems because heater designs and instrument flow paths are not standardized, making results po- tentially difficult to reproduce between instruments compared to gas chromatography. Further complexity occurs for small particles when UHPLC columns are operated at high flows and pressures because frictional heating and poor thermal equilibra- tion can interfere with flow uniformity and cause performance loss in the important A term. Changes in selectivity may also occur. Frictional heating in UHPLC increases in importance with larger column diameters.


Kinetic studies are often employed in academic laboratories; how- ever, h-u plots should be used in industry during HPLC method development and optimization since solutes with different chemi- cal structures often behave differently with mobile phase velocity. When samples contain solutes that exhibit different curve shapes based upon experimental evidence as shown in Figure 2, a compro- mise in optimum velocity is required. In reversed-phase HPLC, polar solutes generally exhibit curves with smaller B terms and larger C terms, which shifts optimum velocity to lower values and can limit separation speed.


AMERICAN LABORATORY • 13 • AUGUST 2015


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