Summary
In chromatography the peak shape is often described by the method of statistical moments and therefore the second central moment is considered as the correct measure of peak width. Using the exponentially modified Gaussian peak model as an example and a criterion more related to chromatography, the extent of separation, it is shown that for nearly Gaussian peaks the width measured at 1/8 of the peak height is a more meaningful width parameter to evaluate the efficiency of chromatography and the resolution. The second central moment gives too much weight to the remote parts of the tail of the usual, somewhat skewed, peak.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- E:
-
efficiency of chromatography [34]
- hG :
-
peak height of the Gaussian constituent before it is exponentially modified
- M1 :
-
mean of the peak profile (first order normal statistical moment, centre of gravity)
- r:
-
fraction of the total peak height at which a distance measurement is made
- Rs :
-
resolution of two peaks [34]
- Sτ :
-
ratio of σ G and τ, eq. (6)
- t:
-
usual time in seconds or minutes
- tG :
-
time at which the maximum of the Gaussian constituent would elute
- T:
-
normalized dimensionless time, defined by eq. (1)
- wb :
-
peak width at base, defined by IUPAC [12]
- wr :
-
peak width from distance between the edges at fractional height r=2, 4, 8 ...
- Warea :
-
peak width deduced from area and peak height at maximum
- x:
-
argument in the function Z(x), defined by eq. (8)
- Y(T):
-
concentration profile (detector signal) as function of normalized time
- Z(x):
-
function of the argument x, defined in the appendix by eq. (24)
- δ:
-
retention difference of two more or less overlapping peaks with the same Sτ (interpeak separation distance between the maxima of the uncombined shapes)
- ξ:
-
extent of separation as defined by Rony [16] and eq. (17)
- μ2 :
-
second order central moment of the peak profile
- μ3 :
-
third order central moment of the peak profile
- σ G :
-
standard deviation of the Gaussian constituent before being exponentially modified
- τ:
-
time constant of the exponential decay
References
J. C. Giddings, Dynamics of Chromatography, Part I, Dekker, New York 1965.
T. S. Sørensen, J. Chromatogr.88, 197 (1974).
J. J. Kirkland, W. W. Yau, H. J. Stoklosa, C. H. Dilks, J. Chromatogr. Sci.15, 303 (1977).
H. Colin, M. Martin, G. Guiochon, J. Chromatogr.185, 79 (1979).
J. C. Sternberg, Advances in Chromatography, Vol. 2, 205 (1966).
A. H. Anderson, T. C. Gibb, A. B. Littlewood, J. Chromatogr. Sci.8, 640 (1970).
W. E. Barber, P. W. Carr, Anal. Chem.53, 1939 (1981).
W. W. Yau, Anal. Chem.49, 395 (1977).
O. Grubner, Anal. Chem.43, 1934 (1971).
E. Grushka, Anal. Chem.44, 1733 (1972).
R. E. Pauls, L. B. Rogers, Anal. Chem.49, 625 (1977).
International Union of Pure and Applied Chemistry, Pure Appl. Chem.37, 447 (1974).
I. G. McWilliam, H. C. Bolton, Anal. Chem.43, 883 (1971).
J. Å. Jönsson, Chromatographia13, 729 (1980).
J. Å. Jönsson, Chromatographia14, 653 (1981).
P. R. Rony, Separation Science3, 239 (1968).
P. R. Rony, Separation Science3, 357 (1968).
P. R. Rony, Separation Science5, 121 (1970).
P. R. Rony, J. Chromatogr. Sci.9, 350 (1971).
K. De Clerk, C. E. Cloete, Separation Science6, 627 (1971).
J. L. Glajch, D. C. Warren, M. A. Kaiser, L. B. Rogers, Anal. Chem.50, 1962 (1978).
H. M. Gladney, B. F. Dowden, J. D. Swalen, Anal. Chem.41 883 (1969).
R. E. Kaiser, J. High Res. Chromatogr. and C. C.2, 91 (1979).
F. Dondi, A. Betti, G. Blo, C. Bighi, Anal. Chem.53, 496 (1981).
S. N. Chesler, S. P. Cram, Anal. Chem.45, 1354 (1973).
S. D. Mott, E. Grushka, J. Chromatogr.148, 305 (1978).
I. G. McWilliam, H. C. Bolton, Anal. Chem.41, 1755 (1969).
J. J. van Deemter, F. J. Zuiderweg, A. Klinkenberg, Chem Eng. Sci.5, 271 (1956).
O. Nilsson, J. High Res. Chromatogr. and C. C.2, 605 (1979).
J. C. Giddings, P. D. Schettler, J. Phys. Chem.73, 257 (1969).
J. T. Lundeen, R. S. Juvet, Anal. Chem.53, 1369 (1981).
J.-C. Huang, R. Madey, Anal. Chem.54, 326 (1981).
F. Riedo, E. sz. Kováts, J. Chromatogr.239, 1 (1982).
R. Delley, Chromatographia15, 167 (1982).
J. E. Knoll, M. R. Midgett, J. Chromatogr. Sci.,20, 221 (1982).
C. H. Lochmüller, M. Sumner, J. Chromatogr. Sci.,18, 159 (1980).
S. M. Roberts, D. H. Wilkinson, L. R. Walker, Anal. Chem.42, 886 (1970).
M. Abramowitz, I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables Dover, New York 1965.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Delley, R. The peak width of nearly Gaussian peaks. Chromatographia 18, 374–382 (1984). https://doi.org/10.1007/BF02262484
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02262484