# High Performance Liquid Chromatography - Lough W.J.

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1 M

i2

C = =—f-e-Jl—J (2.4)

Fvct V27T

where Fv is the volumetric flow rate, a is the standard deviation of the distribution, M is the mass injected and tT is the retention time or the time from the point of injection to the peak maximum. Equation (2.4) can be

rewritten in terms of ct (equation (2.5)) to show the relationships between

the peak width and the standard deviation of the peak,

r (f2)

- = åÓ2> (2.5)

Ñ,

max

Figure 2.1 shows that the width of the peak at its base (í>ü) is equal to 4ct, which may be obtained by drawing lines at tangents to the points of inflection intersecting the baseline. The points of inflection occur where the width of the peak equals 2ct and C/Cmax = 0.607. The peak width at half height (i.e. C/Cmax = 0.5) is given by

w0.5 = 2.354 ct (2.6)

2.3.2 Peak area and peak height

Most analytical determinations employing liquid chromatography are based on the measurement of peak area (A) or peak height (ht). The peak area is equal to the zeroeth moment of the Gaussian distribution (M0),

M0 = A =

Cdt (2.7)

In practice the peak area (A) is measured by electronic integration of the signal from an on-line detector, in which the response is proportional to the concentration of the solute in the flow cell, according to the relationship

^end

A=F^Qt, (2.8)

1“ tstart

where F is the proportionality factor relating concentration to response. Quantitative determinations may also be based on peak height because the ratio of the peak area to its height is constant (equation (2.9)). Peak heights can be measured electronically or manually from the chart paper.

Figure 2.1 Relationships between the widths of a gaussian distribution and the value of a at various fractions of the peak maximum (C/Croax).

2.3.3 Peak asymmetry

Although theory predicts that chromatographic peaks will be symmetrical, peak asymmetry is common, even in the most carefully controlled analytical and preparative separations. The most rigorous definition of peak asymmetry is given by the peak skew (y), which is related to the second (M2) and third moments (M3) of the Gaussian distribution:

ÖÑÎ

M2 = ct2 = - Ct2dt-tT2 (2.10)

^Jo

Time

Figure 2.2 Calculation of the front (a) and the tail (b) of an asymmetric peak at 5% and 10% of the peak maximum (equation (2.13)).

Mi = -

Qf2 - tT2) dr

(2.11)

Y =

M3

(M2)'

0.67

(2.12)

More practical measures of peak asymmetry (As) involve the comparison of the width of the tail, bf, of the peak to its front, af (Figure 2.2)

ë -bf

(2.13)

Recommendations for the position at which As>{ should be measured vary. One of the most rigorous treatments of peak asymmetry is that of Foley and Dorsey (1983) who have described tailing in terms of an exponentially

modified Gaussian peak. This group recommend that ASyf be measured at 10% of the peak height, whereas others (including the United States Pharmacopoeia (1990)) recommend that ASfr be measured at 5% of the peal height (see section 2.6.3).

In analytical applications of liquid chromatography the most common causes of peak asymmetry are mixed mechanisms of retention, incompatibility of the sample with the chromatographic mobile phase, or development of excessive void volume at the head of the column. In preparative applications of liquid chromatography and related techniques, column overload can also contribute to peak asymmetry. The causes of severe peak asymmetry in analytical applications should be identified and corrected because they are frequently accompanied by concentration-dependent retention, non-linear calibration curves and poor precision. In addition, peak asymmetry can significantly compromise column efficiency leading, in turn, to reduced resolution and lower peak capacity (see sections 2.5 and 2.6).

2.4 Retention relationships

2.4.1 Retention time (tj

The retention time of a chromatographic peak is defined by the first moment of the Gaussian distribution (M\, equation (2.14)) and is measured from the point of injection to the peak maximum.

Ml tr A

Ctdt (2.14)

Jo

However, most analytical applications require a definition of retention that is independent of system variables such as column dimensions and flow rate.

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