Journal of Chromatographic Science, Vol.

39, August 2001

A Simplex-Optimized Chromatographic Separation

of Fourteen Cosmetic Preservatives: Analysis of
Commercial Products
E. Marengo*, M.C. Gennaro, and V. Gianotti
Dipartimento di Scienze e Tecnologie Avanzate, Universit del Piemonte Orientale Amedeo Avogadro, Corso Borsalino, 54,
15100 Alessandria, Italy

Abstract
An ion-interaction high-performance liquid chromatography
(HPLC)diode-array detection method is developed and optimized
for the separation of typical antimicrobial agents used in cosmetics
and hygiene products. The most used preservatives contain
different molecular structures, different functionalities, and are
characterized by different chemical properties. Organic acids,
alkyl esters of benzoic acids, alkyl p-hydroxy benzoic acids
(parabens), phenol derivatives, and carbanilides represent the most
used preservatives, and are often present in multicomponent
mixtures. In order to develop a multicomponent method to be
used in quality control analysis, the ion-interaction reagent
reversed-phase HPLC technique seems to be particularly suitable,
because it allows for the simultaneous separation of acidic, basic,
and neutral species. The experimental conditions of the method
are developed by OVAT (one variable at a time) treatment and
further optimized by a multivariate approach based on a Simplex
algorithm that works on a desirability function targeted to
maximize the resolution in a multicomponent mixture. The new
method proposed that is able to simultaneously separate fourteen
preservatives is applied in the analysis of commercial products.

Introduction
The preservatives most commonly used as antimicrobial
agents in cosmetics and hygiene products that are permitted by
European Economic Community laws (1) belong to different
classes of compounds. Good preservatives are: (a) organic acids
(i.e., sorbic, salicylic, dehydroacetic, benzoic, and 4-hydroxybenzoic acid); (b) alkyl esters of benzoic acid (parabens); (c)
alkyl esters of alkyl-p-hydroxybenzoic acids; (d) phenol derivatives (i.e., o-phenylphenol and 4-chloro-m-cresol); and (e)
carbanilides (triclocarban). Because these preservatives are
often employed in multicomponent mixtures, multiresidue
methods are highly required.
* Email: gennaro@mfn.unipmn.it.

The determination of parabens is generally carried out by

reversed-phase (RP) high-performance liquid chromatographic
(HPLC) methods in isocratic (26) as well as gradient elution
(7,8), and sometimes coupled with solid-phase extraction (7).
High-performance thin-layer chromatography (911), capillary zone electrophoresis (12,13), and gas chromatography
(GC)mass spectrometry (MS) (14,15) methods are also used.
For bronopol determination an HPLC method with electrochemical detection is proposed (16). Triclocarban (17,18,6),
salicylic acid, and alkylbenzoates (5) are determined by HPLC
with UV detection. Flow injection analysis is employed for the
determination of 4-chloro-m-cresol in pharmaceutical preparations (19). Ion-pair HPLC is used for the determination of
benzoic and sorbic acids (20), which are also separated
(together with dehydroacetic acid) by GCMS after derivatization (15). Methods in literature mainly concern the separation
of preservatives characterized by a similar structure. For the
separation of multifunctionality mixtures only some examples
are reported that require the use of complex systems of detection (16) or gradient elution (19). Thus, for instance, only the
combined and alternative use of four different sets of conditions allowed the RP-HPLC separation of 47 preservatives (5).
In order to simultaneously separate compounds characterized by different hydrophilicity and chemical properties,
methods based on the ion-interaction reagent (IIR) RP-HPLC
technique seem to be very suitable, because they permit the
simultaneous separation of acidic, basic, and neutral species
(2124). In this study we propose a new IIR-HPLC method for
the simultaneous separation of as many components out of the
nineteen preservatives as possible, which would be representative of the most commonly used. The nineteen analytes considered in this study are characterized by different chemical
functionalities. They are benzoic acid, salicylic acid, 4-hydroxybenzoic acid, methyl-benzoate, ethyl-benzoate, propyl-benzoate, butyl-benzoate, benzyl-benzoate, methyl-paraben,
ethyl-paraben, propyl-paraben, butyl-paraben, benzyl-paraben,
o-phenyl-phenol, 4-chloro-m-cresol, triclocarban, sorbic acid,
bronopol, and dehydroacetic acid.

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339

Journal of Chromatographic Science, Vol. 39, August 2001

The optimization of the methods experimental conditions is

performed in a first step through the OVAT (one variable at a
time) treatment and then through the application of the Simplex algorithm. The Simplex explores the domain of the variables through a suitable desirability function that contains in
only one parameter all of the information we wish to optimize.
The Simplex method

The Simplex technique is a widely used multivariate optimization (2123) strategy. When p is considered as the number
of experimental factors to be optimized, the method starts
from a set of p + 1 initial experiments. The set of p + 1 experiments is called the Simplex. The optimization is based on the
set of successive projections of the experiment that gives the
worst response with respect to the centroid of the other ones.
The experiment that gives the worst response is in turn eliminated if the projection leads to a better response and is substituted by the new one. When the projection does not lead to
a better response, the second worst experiment is projected.
The classical Simplex method stops searching when no better
result can be obtained from the projection of all the experiments.
In the present research we used the modified Simplex

Desirability functions

The optimization for the simultaneous separation of the

nineteen preservatives considered in this study can be faced by
using a multicriterium selection method. The quality of the
separation is evaluated on the basis of the resolution (Rhj) of
every possible pair of peaks h and j, which is given by:
Rhj = 2

tR j tRh

Eq. 1

wj + wh

where tRh is the retention time of the h-th analyte and wh is the
width of the chromatographic peak of the same analyte. The
desirability of the separation of each couple of peaks is evaluated as:

di = R /1.5 if R < 1.5

di = 1
if R 1.5

0.50

D = ( i = 1,ndi)n

0.00
0.00

1.50

3.00

4.50

R
Figure 1. Plot of di as a function of R.

Table I. Simplex Optimization Procedure

Experiment

pH

1
2
3
4
5
6
7
8
9
10
11
12
13

5.50
5.96
5.61
5.61
5.61
5.20
5.51
5.35
5.23
5.23
5.24
5.26
5.59

340

Eq. 2

The optimization of the overall resolution is searched for

through the contemporary optimization of all the possible
resolutions by calculating an overall desirability function (D)
defined as:

1.00

di

version (22) in which during the search for the optimum the
Simplex changes its shape by performing a double projection
when the best result is found or by contracting on itself when
the projection leads to the worst result.

F
(mL/min) %ACN
0.90
0.94
1.08
0.94
0.94
0.99
1.08
0.89
0.79
1.01
0.88
0.90
1.06

50.00
50.54
50.54
52.31
50.54
51.15
52.27
52.59
53.62
53.62
54.84
52.49
52.91

pIIR

3.00
3.05
3.05
3.05
3.23
3.11
3.22
3.25
3.36
3.09
3.26
3.08
3.23

0.6786
0.6178
0.7793
0.7936
0.7521
0.7638
0.7814
0.8492
0.8136
0.8143
0.6901
0.7649
0.4393

Eq. 3

where the product ( i=1,n) of the di runs on the couples of

adjacent peaks or couples of peaks with a resolution less than
1.5. D, so defined, measures the overall resolution of the chromatogram. As summarized in the plot of di versus R (Figure 1),
di becomes null when at least a pair of peaks coelutes (identical
retention times) and it is equal to 1.0 when all the pairs of adjacent peaks show resolution equal to or greater than 1.5.
The Simplex optimization was performed
by evaluating all the experiments on the
basis of their D value, thus searching for
the maximum value of the overall desirable D.
initial Simplex
initial Simplex
initial Simplex
initial Simplex
initial Simplex
normal reflection of 2 on 1-3-4-5
normal reflection of 1 on 3-4-5-6
normal reflection of 5 on 3-4-6-7
double reflection of 5 on 3-4-6-7
normal reflection of 6 on 3-4-7-8
normal reflection of 3 on 4-7-8-10
contraction of 3 on 4-7-8-10
normal reflection of 12 on 4-7-8-10

Experimental
Apparatus

The analyses were carried out with a

Merck-Hitachi LaChrom-HPLC equipped
with a Pump Module D-7100 interfaced by
Module L-7000 with two detectors (the UV
detector Module L-7400 and the DiodeArray Detector Module L-7450). The data
were collected and elaborated by the D-7000
Multi HPLC system manager software program.

Journal of Chromatographic Science, Vol. 39, August 2001

A UVvis Unicam Spectrophotometer Series 8700 was used

for the spectrophotometric determinations, and a Crison
pH2001 pH meter equipped with a combined glasscalomel
electrode was employed for the pH measurements.
Reagents

Ultrapure water from Milli-Q (Millipore Corporation, Bedford, MA) was used.
Analytical-grade benzoic acid, 4-hydroxybenzoic acid, methyl

benzoate, ethyl benzoate, propyl benzoate, butyl benzoate,

benzyl benzoate, ethyl-paraben, propyl-paraben, butyl-paraben,
4-chloro-m-cresol, sorbic acid, dehydroacetic acid, butylamine,
hexylamine, octylamine, and o-phosphoric acid were obtained
from Fluka (Buchs, Switzerland). Salicylic acid, methylparaben, benzyl-paraben, o-phenylphenol, triclocarban, and
bronopol were purchased from Aldrich (Milano, Italy), and
HPLC-grade acetonitrile (ACN) and methanol were from Merck
(Darmstadt, Germany).

Intensity (mV)

Chromatographic conditions

Time (min)
Figure 2. Chromatogram recorded for the fourteen component mixtures under the optimized conditions:
benzoic acid, a; methyl benzoate, b; ethyl benzoate, c; propyl benzoate, d; butyl benzoate, e; benzyl
benzoate, f; 4-hydroxy-benzoic acid, g; methyl paraben, h; ethyl paraben, i; propyl paraben, l; butyl
paraben, m; benzyl paraben, n; salicylic acid, o; o-phenyl phenol, p; 4-chloro-m-cresol, q; bronopol,
r; sorbic acid, s; dehydroacetic acid, t; and triclocarban, u.

The stationary phase used was a Merck

Superspher 100 RP 18 endcapped column
(250.0 4.6 mm, 4 m) together with a
Chrompack C18 (3.0 5.0 mm, 5 m) guard
precolumn.
The mobile phases used in the experiments of the Simplex design were prepared
by adding to the required waterACN mixture the required amount of alkylamine and
o-phosphoric acid up to the required pH
value.
The chromatographic system was conditioned by passing (under isocratic conditions) the eluent through the column until
a stable baseline signal and reproducible
retention times for two subsequent injections were obtained (approximately 1 h at a
flow rate (F) of 1.0 mL/min was sufficient).
After use, the system was washed by flowing water (1.0 mL/min for 15 min), a 50:50
(v/v) waterACN mixture (1.0 mL/min for
15 min), and 100% ACN (1.0 mL/min for
5 min).

Real sample treatment

Table II. DLs and Correlation Coefficients

The samples were commercial cosmetic lotions from Nivea

Benzoic acid
4-Hydroxy benzoic acid
Salicylic acid
Methyl benzoate
Ethyl benzoate
Propyl benzoate
Butyl benzoate
Benzyl benzoate
Methyl paraben
Ethyl paraben
Propyl paraben
Butyl paraben
Sorbic acid
Bronopol
4-Chloro-m-cresol
o-Phenyl phenol
Dehydroacetic acid
Triclocarban
Benzyl paraben

DL
(g/L)

R2

70
50
120
60
70
70
40
80
9
60
70
70
80
3
820
105
730
90
70

0.9579
0.9994
0.9876
0.9696
0.9774
0.9802
0.9798
0.9815
1.0000
1.0000
0.9999
0.9994
0.9988
0.9402
0.9969
0.9909
0.9752
0.9916
0.9611

Table III. Analysis of Commercial Cosmetic Lotions

Retention time
(min)

Concentration
(mg/L)

Cosmetic lotion A
Propyl paraben
Ethyl benzoate
Butyl benzoate

6.82 0.04
10.64 0.06
27.41 0.03

0.89 0.04
179 9
11.2 0.6

Cosmetic lotion B
Propyl paraben
o-Phenylphenol
Butyl benzoate

6.60 0.03
10.59 0.04
26.45 0.07

0.76 0.05
16.7 0.8
10.2 0.5

Cosmetic lotion C
4-Chloro-m-chresol
Benzyl benzoate
Triclorocarban

6.99 0.02
23.41 0.04
35.36 0.06

5.7 0.3
74 4
3.7 0.2

Cosmetic lotion D
Benzyl benzoate
Triclorocarban

23.17 0.06
34.93 0.07

3.5 0.2
2.2 0.1

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Journal of Chromatographic Science, Vol. 39, August 2001

Bayersdof (Hamburg, Germany), Lancaster (New York, NY),

Wendell (Zurich, Switzerland), and LOreal (Paris, France) that
are internationally widespread diffused products that can easily be
found in worldwide stores.

The commercial samples were diluted 1:10 (v/v) with ultrapure water and filtered by a microfiltration system MFS-25
(25-mm i.d., 0.20-m pore size). The lotions in this study were
generically indicated (independently on the sequence order)
as lotion A, B, C, and D.

Results and Discussion

Intensity (mV)

The OVAT method

Intensity (mV)

Intensity (mV)

IIR liquid chromatography is a very

versatile technique that often allows the
development of methods that do not require
particular sample pretreatments. The
reason for the versatility and also its drawback is the dependence of the retention on
many experimental factors. In particular,
when using alkyl-ammonium o-phosphate
salts as the IIRs, the principal factors that
affect retention have been shown to be the
Time (min)
alkyl chain length, the IIR concentration,
the concentration of the organic modifier,
Figure 3. Chromatogram of lotion A (chromatographic conditions and peak identification are the
and the pH of the mobile phase (2427).
same as Figure 2).
Analytes characterized by different chemical functionalities can often be separated,
because the electrical double layer that forms onto the surface
of the stationary phase by the IIR allows for the simultaneous
separation of cationic and anionic species. Furthermore,
because not all the RP sites are modified, it is also possible to
achieve the simultaneous separation of neutral species, which
are retained through a conventional RP mode.
In order to find out the best experimental conditions for
the separation of the nineteen representative preservatives, a
first-optimization process based on the OVAT method was performed. A length of 240 nm was chosen as the average best
wavelength for the multicomponent analysis. On the basis of
previous results obtained in our lab (2427), ten experiments
were performed by employing mobile phases containing alkylammonium o-phosphate with an alkyl chain between 4 and 9,
a pH range between 4 and 8, and an ACN concentration
ranging between 30% and 70%. The results obtained in this
study confirmed the effects already observed in previous studies
(2427). Because of the more lipophilic properties assumed by
the modified surface, the increasing length of the alkyl chain
led to an increased retention of anions and a decreased retention of amines because of equilibria competing with alkylammonium already adsorbed onto the surface. The use of
hexylamine o-phosphate was shown to give the best separation.
Concerning the pH of the mobile phase, it must be stressed
that it exerts its effect not only on the analyte acidic dissociation equilibrium but also on the modification induced onto the
stationary phase. The experiments showed that a pH of 5.5
Time (min)
was the most suitable for the separation studied.
The increased concentration of the organic solvent in the
Figure 4. Chromatograms of lotion B recorded at (A) 230 nm and (B) 260
mobile
phase lead to a decrease in the retention of both the
nm (chromatographic conditions and peak identification are the same as
anionic
and cationic species, because the effect observed was
Figure 2).
the result of two contributions (one resulting from the

342

Journal of Chromatographic Science, Vol. 39, August 2001

increased eluotropic strength in the mobile phase and the

other from a decreased amount of the interaction reagent
adsorbed onto the stationary phase surface).
These preliminary experiments gave the conditions of the
mobile phase that were to be employed for the Simplex as
50% ACN, 1.0mM hexyl-ammonium phosphate, a pH of 5.5,
and a 0.9-mL/min F value.

exception of bronopol and dehydroacetic acid, which showed

smaller molar absorptivity values and for which a concentration range between 1.0 and 5.0 mg/L was explored. The calibration curves for all the analytes were linear with R2 values
> 0.94. In Table II are also reported the DLs evaluated for each
analyte by sensitivity (peak area for concentration unit) given
by the slope of the calibration plot and for a signal-to-noise
ratio of 3.

Simplex optimization

Intensity (mV)

Intensity (mV)

The experimental factors considered in the Simplex-based

Real samples analysis
Some widely diffused commercial cosmetic lotions from
optimization were the ACN concentration (%ACN), the pH
Nivea, Wendell, Lancaster, and LOreal were analyzed in order to
value of the mobile phase, and the hexyl-ammonium concencheck the capability and applicability of the method in routine
tration (IIR), expressed as pIIR (log [IIR]). Even if its effect is
analysis. All the samples were diluted 1:10 with ultrapure water
predictable, the F was also added as the fourth experimental
and then filtered and analyzed in the optimized conditions
factor in order to simultaneously optimize all of the chrousing the diode-array detector to confirm peak identification.
matographic conditions.
The quantitative data are given as an average between the
The aim was to obtain a set of conditions for the best sepadata obtained by the external calibration plots and the appliration of all the components of the mixture. The initial Simplex
cation of the standard addition method.
had five vertices (one more than the number of variables),
On the label of a cosmetic lotion (called A) the presence of
which corresponds to carrying out five experiments (experimethyl paraben was reported. This analyte was identified by the
ments 15 in Table I) whose conditions are obtained by applying
diode-array system but could not be quantitated because it
suitable changes to each factor of the starting experiment.
The results obtained in the optimization,
expressed as the desirability function D, are
reported in Table I. The first reflection of
the worst experiment (experiment 2) lead
to a better response. Because this was not
the absolute best, a new normal reflection
of the new worst experiment (experiment 1)
was performed. Again, a better result (but
not the absolute best) was obtained, thus a
new normal reflection of the worst experiment (experiment 5) was performed. The
new experiment was the very best, thus a
double reflection of experiment 5 was tried,
but the result did not lead to a better resoTime (min)
lution; therefore, this normal reflection was
retained. Because the following experiFigure 5. Chromatogram of lotion C (chromatographic conditions and peak identification are the
ments did not provide any better result, the
same as Figure 2).
optimization procedure was interrupted
and the experimental conditions were
found to be 52.59% ACN, 3.25mM hexylammonium phosphate, a pH of 5.35, and a
0.89-mL/min F value. A chromatographic
run
performed
with
these
experimental conditions provided the chromatogram of Figure 2 in which fourteen
analytes out of nineteen were separated. In
these conditions that were the best we
could obtained, the calibration plots were
built and the detection limits (DLs) evaluated.
Calibration curves and DLs

In the optimized conditions, the calibration curve for every analyte was built. The
concentration ranged between 0.125 and
2.500 g/L for all the analytes, with the

Time (min)
Figure 6. Chromatogram of cosmetic lotion D (chromatographic conditions and peak identification are
the same as Figure 2).

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Journal of Chromatographic Science, Vol. 39, August 2001

coelutes with other compounds. In addition, three other preservatives not declared by the manufacturer (namely propyl
paraben, ethyl benzoate, and butyl benzoate) were identified by
both retention times and UV spectra and then quantitated. A
fourth component was also found (possibly butyl paraben or
benzyl paraben, it was indistinguishable from the UV spectra
and the retention times). The chromatogram obtained is shown
in Figure 3, and the concentrations that were found are
reported in Table III.
Even if lotion B did not report on the label the presence of
any preservative, the analysis (retention time plus UV spectra)
showed the presence of three preservatives (namely propyl
paraben, o-phenylphenol, and butyl benzoate) and a fourth
compound that could have been butyl- or benzyl-paraben. Two
chromatograms that were recorded for this formulation at two
different wavelengths are reported in Figure 4, and the estimated concentrations are reported in Table III.
Lotion C reported on its label the presence of methyl
paraben, which was confirmed but not quantitated because
there was evidence of coelution. Three other preservatives not
declared were identified, namely 4-chloro-m-cresol, benzyl
benzoate, and triclocarban (the latter two were quantitated).
The results are reported in Figure 5 and Table III.
The label of lotion D reported the presence of sorbic acid as
a preservative. This analyte was identified by the diode-array
detector but could not be quantitated because it coelutes with
other compounds. The analysis also allowed for the identification and determination of benzyl benzoate and triclocarban,
which were not reported on the label. The chromatogram is
reported in Figure 6, and the concentrations of benzyl benzoate
and triclocarban are in Table III.

References
1. European Economic Community Directive No. 96/335/CE.
Reported in Gazzetta Ufficiale della Repubblica Italiana, No.
L132 01/06/1997.
2. E. Sottofattori, M. Anzaldi, A. Balbi, and G. Tonello. Simultaneous HPLC determination of multiple components in a commercial cosmetic cream. J. Pharm. Biomed. Anal. 18: 21317
(1998).
3. D. Kollmorgen and B. Kraut. Determination of methylparaben,
propylparaben and chlorpromazine in chlorpromazine
hydrochloride oral solution by high-performance liquid chromatography. J. Chromatogr. B 707: 18187 (1998).
4. Y. Maeda, M. Yamamoto, K. Owada, S. Sato, T. Masui,
H. Nakazawa, and M. Fujita. High-performance liquid chromatography determination of six p-hydroxybenzoic acid esters in
cosmetics using florisil cartridges for sample pre-treatment.
J. Chromatogr. 410: 41318 (1987).
5. N. De Kruijf, A. Schouten, M.A.H. Rijk, and L.A. PranotoSoetardhi. Determination of preservatives in cosmetic products II.
High-performance liquid chromatographic identification.
J. Chromatogr. 469: 31728 (1989).
6. L. Gagliardi, G. Cavazzutti, L. Turchetto, F. Manna, and D. Tonelli.
Determination of preservatives in cosmetic products by reversedphase high-performance liquid chromatography. IV. J. Chromatogr. 508: 25258 (1990).
7. S. Scalia and D.E. Games. Determination of parabens in cosmetic products by supercritical fluid extraction and high-performance liquid chromatography. Analyst 117: 83941 (1992).

344

8. M.A. Quarry, D.S. Sebastian, and R.C. Williams. Determination

of nalbuphine hydrochloride, methylparaben, and propylparaben
in nalbuphine hydrochloride injection by high performance liquid
chromatography. Chromatographia 47: 51522 (1998).
9. C. Burgi and T. Otz. Determination of preservatives in body
shampoos and bubble baths. Mitt. Geb. Lebensmittelunters Hyg.
83: 492508 (1992).
10. T. Imrag and A. Junker-Buchheit. Quantitative determination of
parabens. J. Planar Chromatogr. Mod TLC 9: 14648 (1996).
11. K. Lazaric, B. Cucek, and G. Faust. RPTLC method for determination of parabens in oral antacid suspension during stability
testing. J. Planar Chromatogr. Mod TLC 12: 8688 (1999).
12. R.J. Geise and N.I. Machnicki. A study of parabens as model
hydrophobic compounds by capillary electrophoresis and their
determination in cosmetic formulations. J. Capillary Electrophor.
2: 6975 (1995).
13. S.P. Wang and C.L. Chang. Determination of parabens in cosmetic
products by supercritical fluid extraction and capillary zone electrophoresis. Anal. Chim. Acta 377: 8593 (1998).
14. M. Kakemoto. Simultaneous determination of sorbic acid, dehydroacetic acid and benzoic acid by gas-chromatographymass
spectrometry. J. Chromatogr. 594: 25357 (1992).
15. C. De-Luca, S. Passi, and E. Quattrucci. Simultaneous determination of sorbic acid, benzoic acid, and parabens in food: a new gas
chromatographymass spectrometry technique adopted in a survey
on Italian food and beverages. Food Add. Contam. 12: 17 (1995).
16. J.W. Weyland, A. Stern, and J. Rooselaar. Determination of
bronopol, bronidox and methyldibromoglutaronitrile in cosmetics
by liquid chromatography with electrochemical detection.
J. AOAC Int. 77: 113236 (1994).
17. B. Wyhowski De Bukanski and M.O. Masse. Analysis of hexamidine, dibromohexamidine, dibromopropamidine and chlorexidine in cosmetics products by high-performance liquid
chromatography. Int. J. Cosmetic Sci. 6: 28392 (1984).
18. L. Gagliardi, A. Amato, A. Basili, G. Cavazzutti, E. Gattavecchia,
and D. Tonelli. Determination of preservatives in cosmetic products by reversed phase high-performance liquid chromatography.
II. J. Chromatogr. 325: 35358 (1985).
19. M.S. Bloomfield and K.A. Prebble. Determination of preservative
chlorocresol in a pharmaceutical formulation by flow injection
analysis. J. Pharm. Biomed. Anal. 10: 77578 (1992).
20. L. Gagliardi, A. Amato, A. Basili, G. Cavazzutti, E. Gattavecchia,
and D. Tonelli. Determination of preservatives in cosmetic products by reversed phase high-performance liquid chromatography.
I. J. Chromatogr. 315: 46569 (1984).
21. J.A. Nelder and R. Mead. Simplex optimisation. Computer J. 7:
308 (1964).
22. R. Carlson, L. Hansson, and T. Lundstedt. The modified Simplex
optimisation technique. Acta Chem. Scand b 40: 444 (1986).
23. R. Carlson. Design and Optimisation in Organic Synthesis. Elsevier, Amsterdam, The Netherlands, 1992.
24. E. Marengo, M.C. Gennaro, and C. Abrigo. Experimental design
and partial least squares for optimization of reversed-phase ioninteraction HPLC separation of nitrite, nitrate and phenylenediamine isomers. Anal. Chem. 64: 188593 (1992).
25. M.C. Gennaro, C. Abrigo, E. Pobozy, and E. Marengo. Retention
dependence on organic modifier and ion-interaction reagent concentration in ion-interaction HPLC. J. Liq. Chromatogr. 18:
31130 (1995).
26. E. Marengo, M.C. Gennaro, and S. Angelino. Neural network
and experimental design to investigate the effect of five factors in
ion-interaction high-performance liquid chromatography. J. Chromatogr. A 799: 4755 (1998).
27. E. Marengo, M.C. Gennaro, and C. Abrigo. Investigation by experimental design and regression models of the effect of five experimental factors on ion-interaction HPLC retention. Anal. Chim.
Acta 321: 22536 (1996).

Manuscript accepted April 11, 2001.