Ultra-High Pressure Liquid Chromatography (UHPLC)

with εt being the total column porosity1:





pp i

t   

   1 (1-31)

u represents an interchangeable term in the following chapters, but unless otherwise indicated should be assumed to mean ui when used in theoretical descriptions (and equations). εt and εi can be difficult and time-consuming to determine experimentally when using common methods inverse size exclusion chromatography (ISEC)22 or total pore-blocking methods23. Since finding

εt and εi for the many different columns tested and characterized throughout this dissertation would be very challenging, umeas (based on measured t0 values) is utilized for experimental results and figures.

1.3 Ultra-High Pressure Liquid Chromatography (UHPLC) 1.3.1 Comparison of HPLC and UHPLC

pressure limit remained stagnant at 400 bar (6,000 psi). The relationship between u and the pressure drop along the column (ΔP) is given by the Kozeny-Carman equation1:





with η equal to the mobile phase viscosity. Based on this equation, when the particle size

decreases the pressure required to maintain the same linear velocity grows with the inverse of the square of the particle diameter. As particles got smaller and pressure limits were reached, the only option was to decrease the length of the column, which limited the maximum efficiency that could be achieved.

This trend of decreasing column length ended with the introduction of UHPLC by the Jorgenson lab in 1997.24 Their early work24-27 and that of other early researchers of UHPLC28-33 found that particles in the 1-2 μm range could give exceptional performance if column lengths in the 10-50 cm range were used.34 A comparison of the expected H values (based on Equation 1- 17) for particle sizes typical of HPLC and UHPLC columns is shown in Figure 1-3. The improved column efficiency that can be achieved with these smaller particles is significant, but requires a much higher inlet pressure to be applied in order to maintain reasonable analysis times. Problems related to the use of sub-2 μm particles and the consequent pressure increase that had not been encountered in HPLC emerged and are described in the following sections.

1.3.2 Pressure, Flow, and Frictional Heating

If vopt is assumed to be 3, then Equation 1-19 can be arranged to show that uopt is

proportional to the inverse of dp. When combined with Equation 1-30, the true proportionality of pressure drop with particle size when trying to maintain the optimum linear mobile phase

3 1 p d P  (1-33)

This means that a drop in dp from 5 μm to 1 μm requires a 125-fold increase in pressure to preserve uopt. While most of the discussion so far has related to u, the movement of mobile phase through the column bed can also be described by the column flow rate (F)1:

2 c t meas r u F     (1-34)

where rc is the column radius. As mobile phase flows past particles, frictional heating occurs as power is dissipated according the following equation34,35:

P F

Power   (1-35)

When heat is generated in the column, it leads to axial and radial temperature gradients that can reduce chromatographic efficiency. This was one of the key reasons for the 400 bar pressure limit in HPLC as well as the rationale for early UHPLC columns being packed in capillaries (which require significantly lower flow rates and have improved heat dissipation).34 As most standard-bore columns available in HPLC are 4.6 mm in diameter and require much higher flow rates than capillary columns, viscous heating presents a major concern when higher pressures are applied. When UHPLC was first commercialized as UPLC by Waters Corporation in 2004 (with 1.7 μm particles), certain compromises were made to try and reduce the impact of frictional heating including setting a 1,000 bar (15,000 psi) pressure limit and decreasing the standard column diameter from 4.6 mm to 2.1 mm.36 The focus of Chapter 5 is related to frictional heating in UPLC columns and the determination of ways to reduce its impact on column performance.

1.3.3 Extra-Column Band Broadening

In an LC instrument, volumetric contributions from the injector, detector, connecting tubing, and unions add extra-column variances to an analyte band that can reduce the H

achievable by a column.37 This was of little consequence in 25 cm x 4.6 mm columns packed with 5 μm particles common to HPLC1

because of their large mobile phase volumes. UPLC columns have smaller on-column volumes (dimensions of 5-15 cm x 2.1 mm with 1.7 μm packing material) and are thus much more vulnerable to efficiency loss due to extra-column effects (making them essentially unusable on standard HPLC instruments). In addition to

increasing the instrument pressure, efforts have been made to reduce the extra-column volume of the UPLC instrument in order to maintain the high efficiency expected out of columns packed with sub-2 μm particles.36,37 Investigations of extra-column band broadening (specifically in the injectors and connecting tubing) for a small-volume UHPLC system are detailed in Chapter 6.