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INTRODUCTION

The absorbance detector, a.k.a. UV, detector has

become a ubiquitous part of the practice of

contemporary HPLC and UPLC. Its wide dynamic range with noise around 5 micro AU and an upper limit of 2 AU

permits the measurement of both very small and very

large peaks within the same chromatogram.

Absorbance detectors are commonly characterized by a linearity specification based on ASTM E685-79 which

defines a protocol to determine the absorbance at which

the deviation from linearity is five percent (5%). A typical linearity specification is between 2 and 2.5 AU

for the five percent deviation vis-à-vis E685-79. Figure

1 indicates that for absorbances greater than 1.5, the linearity errors sharply increase with increasing

absorbance.

One of the principal sources of deviations from linearity in absorbance measurements is the presence of

so-called stray light. Figure 2 shows a plot of the stray

light requirement as a function of the ASTM 5% deviation limit. The figure indicates that improving the

ASTM limit from 2 AU to 3 AU will require a reduction of

the apparent stray light from 0.26% to 0.04% and that a 4 AU limit would require less than 0.005% stray light.

Reducing stray light to such low values is likely to

require compromising the noise performance of the detectors. Consequently, extending the linearity of the

detectors by modeling the stray light behavior is an

attractive solution to extending the linear dynamic range of absorbance detectors.

EXTENDING THE LINEAR DYNAMIC RANGE OF ABSORBANCE DETECTORS

Richard W. Andrews and Peyton Beals

Waters Corp. , 34 Maple Street, Milford, MA 01757 USA

Figure 1. Linearity Plot for Absorbance Detector with ASTM

Limit of 2.2 AU.

Figure 2. Stray Light Requirements for ASTM Linearity.

METHODS

Chromatographic Conditions: Waters Acquity UPLC Systems including H-Class QSM Solvent Manger, FTN Sample Manager, CHA Column Heater, and Acquity PDA detector all controlled from an Empower workstation. Columns included 2.1x50 mm Acquity BEH (1.7 µm C18) and XBridge XP 4.6x150 mm (2.5 µm C18) with mobile phases containing water, acetonitrile and/or methanol. Column temperature set to 40 C unless otherwise noted. Flow rates were 0.6

mL/min for 2.1 mm ID columns and 1.4 mL/min for 4.6 mm ID columns. Data Analysis: Chromatograms were captured in Empower. Stray light was estimated by non-linear regression with Table Curve 2D® software (Systat Software Inc.). Transformation of raw chromatograms was performed in Microsoft Excel®.

Calculations: The apparent stray light from calibration data was estimated from the model equation (1) shown below.

Am = log10 {(1+s)/(10-A +s)} (1)

where s = stray light, A = true absorbance, and Am = measured absorbance . Equation (1) can be solved for the true absorbance as a function of Am and s to give Equation 2.

A = -log{(1-s(10Am -1))/10Am } (2)

It should be noted that s is assay specific, i.e., it depends upon the wavelength, the spectrum of the analyte, the mobile phase and the characteristics of the optics such as spectral bandpass and resolution.

RESULTS

Calibration curves were constructed using an Acquity

PDA with a standard analytical flow cell (10 mm path length) and a high sensitivity flow cell (25 mm path length) using a

series of caffeine standards appropriate for high performance HPLC (2.5 µm particle column). The results are shown in

Figure 3. The ASTM limits for the cells were 2.25 (10 mm) and 2.45 (25 mm) respectively. The slopes have a ratio of

2.47:1 which is in agreement with the path lengths.

Figure 3. Caffeine Calibration Curves for 10 mm and 25 mm path length flow cells.

The chromatograms for the high sensitivity cell are

shown in Figure 4. Note that the peak absorbance changes significantly for only the highest concentrations.

Figure 4. Transformed (dotted lines) and observed chromatograms for 25 mm cell .

The separation of a five component column test mixture

with peaks of various concentrations is shown in Figure 5 and

illustrates the effect of the transformation which is strongest on the largest peaks. The sample contains thiourea (void

marker), toluene, amyl benzene, heptanophenone, and decanophenone and is eluted in 30:70 water:acetonitrile at 0.6

mL/min. from an Acquity BEH C18 column (2.1 x 50 mm, 1.7 µm).

Figure 5. Column Test Mix Separation for Injection Volumes of 1, 2, 4, 6 and 8 µL. Data is not linearized. Note peak AU =

2.8.

Figure 6 shows the linearized results for the last peak

decanophenone. Note that the peak AU is now 4.1 AU.

Figure 6. Linearized Decanophenone Peak with 25 mm Flow

Cell.

CONCLUSIONS

Linear dynamic range is limited by the

presence of stray light in absorbance

detectors.

Increasing the linear dynamic range to 4 AU

requires a reduction of the stray light to less

than 0.005 % which is not a practical solution.

Apparent stray light can be estimated from

calibration data.

Measured absorbance can be corrected for the

presence of stray light.

Stray light corrected absorbance restores the

concentration dynamic range of high

sensitivity (long path length) flow cells.

*Patent Pending.

DISCUSSION

The use of Equation 2 to enhance the linearity of

absorbance data requires a robust estimate of the apparent

stray light. That estimate is specific to an assay and the instrument used. However, once measured it can be used to

create linearized absorbance data channels which can be treated as ordinary chromatograms with typical

chromatographic data systems*.

The use of so-called high sensitivity cells with extended path lengths has been limited by the reduced dynamic range in

concentration. The noise performance is not a strong function of path length (unless the mobile phase absorbs at the

monitoring wavelength) and without a correction for non-linearity from stray light, the upper concentration limit is

reduced by the increase in path length. The use of stray light correction restores the dynamic range of the extended path

length flow cells making them more useful for the detection

and quantitation of both very small and large peaks in the same chromatogram.

The dynamic range of a detector can be described as a

range of concentrations over which the uncertainty of the measurement is acceptable. In the case of an absorbance

detector, the relative uncertainty in absorbance can be plotted against the absorbance to create the so-called photometric

error curve which accounts for the principal noise sources in absorbance measurements — shot noise, source (flicker) noise

and fixed (read) noise — provides a visual model for dynamic range. Figure 7 shows a typical photometric error curve for a

photodiode array detector. With such a plot an error analysis can be performed in which a defined uncertainty, e.g. 1

percent, can be specified and the absorbances which have

uncertainties less than the specified values can be identified.

Figure 7. Photometric Error Curve Showing Dynamic Range as

a log-log Plot.

When the linearity errors limit the working range to 2 AU

the dynamic range is about 2200:1. When the stray light correction is applied the dynamic range increases to 4800:1 for

an improvement of 2.2x. A similar improvement would require a reduction of the instrument’s stray light by a factor of 50

which would compromise baseline noise performance.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

1.70 2.20 2.70 3.20 3.70 4.20

Stra

y Li

ght

(%)

ASTM 5% Limit (AU)

0.0

1.0

2.0

3.0

4.0

5.0

2.0 2.5 3.0 3.5 4.0 4.5 5.0

abso

rban

ce @

27

3 n

m

time (min.)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.00 0.05 0.10 0.15 0.20 0.25

Abso

rban

ce (

273

nm)

mg/mL caffeine

A 25mm lin 25 mm

A 10mm lin 10 mm

Dynamic Range = 4800:1 at 4.34 AU

Dynamic Range = 2200:1 at 2 AU