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Review
Developments on chemometric approaches to optimize and evaluatemicroextraction
Constantine Stalikas ∗, Yiannis Fiamegos, Vasilios Sakkas, Triantafyllos AlbanisDepartment of Chemistry, University of Ioannina, Ioannina 451 10, Greece
a r t i c l e i n f o
Article history:Received 19 September 2008Received in revised form20 November 2008Accepted 21 November 2008Available online 27 November 2008
Keywords:Microextraction
a b s t r a c t
Chemometric experimental design in microextraction plays a crucial role in sustaining the highest qual-ity of analytical data. Making use of the main significant points of chemometric experimental designand microextraction in analytical chemistry we formed the core of this review article. A step-by-stepchemometric approach is provided to optimize and validate microextraction-based analytical processes.Significant applications are reported with developments related to microextraction combined withchemometric optimization processes. As it appears from the numerous examples provided in this review,a great number of researchers give credit to the combination of microextraction and chemometrics recog-nizing that it significantly streamlines sample processing. Moreover, the combination of microextractionwith chemometrics addresses problems relating to improvement in detectability and method validation.
Chemometrics
Single-drop microextractionPCBs
A worked example on the microextraction of polychlorinated biphenyls is incorporated into the relevantsections of this article and comprehensively provides in a rational and integrated way guidance to people
Extraction methods share in common the same basic set of con-epts in order to separate the analytes from the matrix whereinhey exist, and concentrate the analytes selectively in one phase.
ore specifically, any analyte is distributed between two phasesccording to the distribution constant and the relative volumes ofhe phases. In this process, the extraction rates hinge on the migra-ion kinetics and hence are governed by the diffusion rates in thewo phases. Relevant parameters are essentially those which are
anipulated in chromatographic separations, and one can there-ore consider the extractions as a form of pre-assay chromatography1].
Classical liquid–liquid extraction (LLE) is among the most widelysed sample preparation methods. Because classical LLE employsignificant amounts of solvent that are often hazardous, thisime-tested technique has seen several modifications from itsoots, dated back at least a century. Over the last three decades,ewer miniaturized approaches to the classical liquid extractionave emerged, resulting in solvent and sample savings and lessime-consuming analysis. The new approaches have fostered thevolution into a family of different techniques that strain the abil-ty of the term “microextraction” to adequately describe almost allf them. By definition, “microextraction is an extraction techniquehere the volume of the extracting phase is very small in rela-
ion to the volume of the sample, and extraction of analytes is notxhaustive” [2]. This definition describes, in a holistic way, whatractically is the case when partitioning of analyte(s) between theample matrix and the extraction phase occurs, with one of thehases being in small scale.
Besides the scheme of data evaluation, any analytical methodinvolving equipment and procedure – is rarely as good as they
ould be. Assuming the equipment-configuration given, the proce-ure, the various factors and the data generated can be subjectedo a detailed investigation to generate sound results. This holdsqually true for any analytical method including those that relyn microextraction-related techniques. When trying to optimizemicroextractive analytical method we might need to define
he best extraction conditions in relation to the subsequentlysed detection method. The measurements depend upon a signalabsorbance, intensity of fluorescence but chiefly chromatographicesponse) which is itself influenced by several factors. In gen-ral, it is customary to seek overall conditions which can leado the maximum signal. If the factors involved in an analysis arendependent (which is rarely the situation), the most commonractice is to experiment with one-factor-at-a time (OFAT) whileolding all others fixed. However, the results are often mislead-
ng and fail to reproduce conclusions drawn from such an exercise.here is now increasing recognition that hereditary malpracticeught to be replaced by soundly based chemometric methods.more effective method for these situations is to study factors
ffects simultaneously by setting the design of experiments sta-istical technique. Statistical analyses are available to tease outhich factors really are significant in either mode of microextrac-
ion, and to determine what combination of levels produces theptimum.
It is, therefore, clear that the chemometric experimental designn miniaturized extraction plays a crucial role in sustaining theighest quality of analytical data for key applications, in relation tohe accompanied detection systems. Although individual steps orample microextraction methods have come under scrutiny, there
re no general monographs or reviews to emphasize the broadature of microextraction mated with chemometrics, the wideange of approaches that can be employed and the great impactn the data obtained. In this article, a step-by-step chemometricpproach is discussed to optimize and validate microextraction-
. A 1216 (2009) 175–189
based analytical processes. Moreover, significant applications arereported with developments related to microextraction com-bined with chemometric optimization processes, on the basisof the employment of separation and, to a lesser extent, ofnon-separation analytical techniques. In parallel, a worked exam-ple on the microextraction of polychlorinated biphenyls (PCBs),is woven into pertinent sections of the article, thus providinga guidance to people dealing with this subject, in a rationalway.
Over the past two decades there have been major breakthroughsin the area of sample preparation. In this vain, microextractioncould not lag behind. Earlier, in 1979, Murray developed a prototypeof a liquid microextraction technique for gas chromatography, rest-ing on the plausible argument that the methods of analyses whichavoid or minimize solvent consumption are most preferable for therecovery of trace organics from water. As high volumes as 10 l ofwater samples could conceivably be extracted, once, with organicsolvent in the range of microliters up to few milliliters. The methodfound followers even during the 1990s, when the needs in analyticalchemistry fuelled the boom in microextraction, in its contemporaryform [3].
The current trend in chemical analysis for “going small” has wit-nessed a really explosive growth during the past decade. Microscaleapproaches have burgeoned and microextraction has become abuzz word, in a quest for improved recoveries, higher samplethroughput and less organic-solvent consumption especially for‘heavy duty situations’ (e.g. complex matrixes). Depending on thekind of the extracting phase, microextraction techniques may bedivided into three broad groups [4]:
(I) microextraction based on sorbent enrichment,(II) miniaturized LLE and
(III) membrane microextraction.
Their theory and practice have been examined in considerabledetail in the recent years and numerous applications have beenreported and reviewed covering all the facets of microextraction.The extraction yield is highly dependent on the partitioning ormore strictly on the partitioning coefficient of analyte(s) betweenthe sample bulk phase and the extraction phase [5]. Partitioningis controlled by the physicochemical factors related to the analyte,the sample matrix and the extraction phase. Since partitioning isnot dependent on analyte concentration, quantification of sampleconcentration may be done from the absolute amount extracted.In many cases, the absolute amount extracted is insignificant rela-tive to the initial amount present (<1%). Thus, there is no significantchange in sample concentration during extraction. In this case, theamount extracted is independent of sample volume, allowing afurther simplification of the technique.
Introduced in 1990 by Arthur and Pawliszyn, solid-phasemicroextraction (SPME) initially gained wide acceptance for theanalysis of environmental samples [5]. Sensitivity and precision aregenerally as good as or better than standard methods, the methodsthemselves are simpler, and solvent use is eliminated.
A more recent technique, the stir-bar sorptive extraction, hascome into its own as a microextraction alternative and can be
deemed as a scaled-up version or “stirrer” variation of SPME [6].Analytes are concentrated using a magnetic stir bar coated with apolymeric material which is placed in the liquid sample. However, itis a procedure that unlike SPME more easily approaches exhaustiveextraction.
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The rapid developments in the areas of in-tube SPME applica-ions led to the sol–gel open-tubular microextraction technique orapillary microextraction, which typically uses a fused silica cap-llary internally coated with a sol–gel stationary phase. Extractionapillaries used in sol–gel capillary microextraction are disposable,hich gives flexibility to the technique [7].
Jinno et al. [8] in the so-called fiber-in-tube solid-phase extrac-ion approach managed to use a short capillary in which severalundred parallel filaments of synthetic polymers are packed longi-udinally which served as the extraction medium. Because of thearallel arrangement of the filaments a number of coaxial nar-ow channels are formed in the capillary, thus offering a reducedressure drop during the extraction and desorption, under flowonditions.
Microextraction in a packed syringe is a miniaturized, microolid-phase extraction mode that can be connected on-line to GC orC without any modifications [9,10]. In this microextraction mode,pproximately 1 mg of the solid packing material is inserted intosyringe (100–250 �l) as a plug. Sample preparation takes place
n the packed bed which may be coated to provide selective anduitable sampling conditions.
There have been several publications on miniaturizing of LLEn analytical chemistry. The major motivation behind this invari-bly was to facilitate automation and to effectively reduce theonsumption of organic solvents. Miniaturized LLE, or single-dropicroextraction (SDME), was introduced in 1996, and involved the
se of a droplet of organic-solvent hanging at the end of a micro-yringe needle. Drops can rapidly and reproducibly be formed andnteresting interfacial phenomenon can be employed, thus enhanc-ng the performance of a number of analytical techniques, as well asnabling the development of new ones [11,12]. Because of the unfa-orable geometry of the drop system–the spherical shape shows theowest surface-to-volume ratio—the techniques of dynamic sam-ling with the aspiration of sample have also been developed tomeliorate the relatively low extraction rate. An organic-solventlm formed in a microsyringe barrel was used as an extraction
nterface [13].Fattahi et al. devised the dispersive liquid–liquid microextrac-
ion which looks much like the classical LLE [14]. They managedo derivatize and extract chlorophenols into fine droplets ofhlorobenzene. After centrifugation, the fine droplets were sedi-ented at the bottom of the conical test tube and a small portionas injected into the GC.
There are many possibilities for building assemblies for mem-rane microextraction. Presently, a construction based on using
hollow fiber of the porous polymer, the so-called hollowber liquid-phase microextraction (HF-LPME), is most frequentlypplied [15–17]. In most cases, the driving force for the move-ent of the analyte across the membrane is a concentration
radient. This can be enhanced by effectively removing thenalyte from the receiving phase by ionization using buffers,omplexation, or derivatization, so that the free solution con-entration of the analyte species is reduced. Another simple andensitive mode of liquid-phase microextraction referred to asolvent-bar microextraction uses a small portion of organic sol-ent, which is held within a sealed hollow-fiber membrane andllows tumbling freely in the sample solution during extraction18].
Foremost among microextraction modes are the on-line alter-atives. An effective on-line coupling of microextraction andeparation enables to take advantageous features of the combined
ystem, such as high speed of analysis with high efficiency andelective analysis by developing tailor-made systems designed forarticular applications. Ramos et al. discussed the relationship ofiniaturized extraction procedures for integrated at-line or on-line
nalytical systems [19].
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3. Optimizing and assessing experimental conditions inanalytical microextraction by design of experiment: apractical example
One major challenge in the utilization of microextraction is theselection of experimental conditions that can provide acceptableresponse at low analyte concentration. The challenge facing exper-imentalists is to increase their understanding of microextractionmethods by obtaining an insight into the nature and dynamic char-acteristics of the microextraction process. The outcome enables theassessment of relevant variables and will also aid in discoveringways to optimize the method.
By their very nature, all modes of microextraction requirehandling small volumes under strictly defined extraction and/orreaction conditions. Therefore, the large number of variables andthe relationships between them rules out the possibility of OFATclassical optimization approach which fails to take into accountinteraction between or among variables. Chemometrics, a termoriginally coined by Wold in 1971 [20], is “a chemical disciplinethat uses mathematics, statistics, and formal logic (I) to design orselect optimal experimental procedures; (II) to provide maximumrelevant chemical information by analyzing chemical data; and (III)to obtain knowledge about chemical systems”. As is indicated ina leading textbook on the topic [21] there is hardly any quantita-tive analytical method that does not make use of or does not needchemometrics.
Recently, chemometrics has been employed for the optimizationof analytical methods, considering their advantages with regardto the requirement of less resources (time, reagents, experimen-tal work). Chemometrics offers a sound theoretical basis for theoptimization of chemical systems and processes. Moreover, chemo-metric tools through the development of mathematical models canassess the statistical significance of the independent variable effectsbeing investigated as well as to evaluate their interaction effects.If significant interaction effects between the examined variablesexist, the optimal conditions indicated by the univariate studieswill be much different from the correct results of the multivari-ate optimization. The larger the interaction effects the greater thedifference that will be found using univariate and multivariate opti-mization strategies and for this reason, multivariate optimizationemploys designs for which the levels of all the variables are changedsimultaneously [22]. Tools are based on the fit of a polynomial equa-tion to the experimental data, which must describe the behavior ofa data set with the objective of making statistical previsions. Onemay use experimental designs when addressing problems in whichthe influence of experimental variables on the response proper-ties is monitored and optimized. They can be well applied when aresponse or a set of responses of interest are influenced by severalvariables. The objective is to simultaneously optimize the levels ofthese variables to attain the best system performance.
The following points are considered essential in the conduct of astraightforward chemometric optimization of microextraction: (I)definition of the problem and selection of the appropriate variablesand response(s) through screening studies; (II) choice of design ofexperiment; (III) selection of levels of variables and codification;(IV) mathematical model fitting; (V) model adequacy checking;(VI) analysis of model and effect estimates; (VII) allocation of theoptima; (VIII) robustness checking.
In the sections below, an elaboration of the foregoing individualsteps of chemometric optimization in relation to microextrac-tion is made. Moreover, by way of a worked example, the SDME
of a PCBs mixture (Aroclor 1260) is detailed in order to figureout the importance of mating microextraction with chemometricsand to provide at least a flavor of the potential and the practicalaspects of the combined themes. Although PCBs are semivolatilecompounds and microextraction of these compounds has been per-
1 atogr. A 1216 (2009) 175–189
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Table 1Independent factors and levels used in Plackett–Burman design.
ormed using headspace sampling, in this case, the mode of directmmersion SDME was chosen for the following reasons: (I) direct-mmersion SDME represents a demanding and widely used modef microextraction but less frequently connected with chemometricevelopment approaches and (II) more variables could conceivablye comprised as operationally critical, in an integrated experimen-al design as compared to other microextraction techniques.
.1. Definition of the problem and the selection of the appropriateariables and response(s) through screening studies
Despite the simplicity in performing the microextraction tech-iques, some of them suffer from reduced repeatability, longxtraction time, low preconcentration by virtue of lack of infor-ation about variable interaction. For instance, a reasonable
ompromise for acceptable extraction time and drop depletionhould be selected in SDME along with the other determiningariables. Also, attention should be paid to consistent extractionperations to ensure uncompromised quantitative analysis. Theime spent on planning in the beginning of experiment is alwaysaid back with interest at the end.
In general, variables (and data) either represent measurementsn some continuous scale, the so-called continuous variables, orepresent information about some categorical or discrete char-cteristics, the so-called categorical or qualitative variables. Theistinction between continuous and categorical factors is impor-ant when one wants to add center points to the design. This allowshe latter to perform, for example, tests for the presence of curva-ure, and thus for the validity of the simple linear-effects model.epending on the mode of microextraction, the researcher mayxamine factors such as sample volume, extraction time, and whereppropriate agitation, salting out, extraction volume, sorbent mate-ial or solvent volume, sampling depth, adsorption temperature,dsorption time, headspace volume or less prominent parameters:onfiguration of stir bar, plunger movement pattern, and so on.
With regard to the criterion to assess the process, responsee.g. chromatographic peaks), recovery, extraction yield, and/ornrichment factor are usually selected for the microextractionethodology. Other response functions can be calculated or pure
ignals can be employed to monitor the process and bring out theignificance of factors depending on the intrinsic features of themployed measuring system. For the optimization of a developednalytical method, one or more responses could be selected toxamine if derivatives of the response(s) in respect of each individ-al variable are small. The analysis of a single response is a relativelyasy task. If more than one response should be considered, one canssociate to each response a desirability factor, which reconciles theesearcher’s priorities on building the optimization procedure. Itnvolves creating a factor for each individual response di which canake a value between 1 (desirable) and 0 (undesirable) and finallybtaining a global desirability D that should be maximized choosinghe best conditions of the designated variables.
When a list of variables to be investigated has been completed,n experimental design is chosen to estimate the influence of vari-bles. The need to screen a great number of variables in order todentify those that may affect significantly the response is suitedy the well-known Plackett–Burman design (two-level fractionalesign) or fractional factorial designs with particular resolution andliases are usually employed. Two levels using codification (upper+1) and lower (−1)) can be assigned to each variable correspondingo the levels of natural variables.
From the practical point of view, for the SDME system of PCBs,he following eight factors can initially be selected to define thexperimental conditions: stirring rate, drop volume, sample vol-me, extraction time, organic solvent, ionic strength, samplingepth, configuration of the stir bar. The factors were picked based
Configuration of the stir bar 8 Cylindrical Cross-shaped
a Refers to the distance of the end of the hanging drop from the top of the magneticbar.
on the literature information, the experience of the authors of thisreview article and the specific attributes of this microextractionmode. Another parameter that could be included in such a prelim-inary screening is the retracted drop volume, viz. the size of thedrop retracted after microextraction. Extraction temperature is notinvolved in the optimization as it may cause drop dissolution with-out affecting mass transfer of analytes. Likewise, pH cannot be adetermining parameter because of the molecular nature of Aroclorcomponents. Both the retracted drop volume and the temperaturecan be considered in detail, in a subsequent step of robustnessstudy. Finally, the elementary response function criterion of “totalresponse surface area” (TCPR) can be used as a straightforward prin-cipal response of microextraction comprising the total peak area.
Because of the large number of parameters to be tested in sucha practical example, reduced factorial designs are recommendedto be employed. A saturated Plackett–Burman matrix was usedwhich assumes that the interactions can be completely ignored;so, the main effects are calculated with a reduced number ofexperiments. The matrix consisted of eight real and three dummyfactors—variables, at two levels. The dummy factors are used for theestimation of the experimental error used in the statistical inter-pretation. The levels of variables (+1, −1) were selected on the basisof previous results and taking into account the limitations of theexperimental system. For instance, high stirring rate in connectionwith the cross-shaped configuration of stir bar can readily result indrop dislodgement. It is also worth noting that three of the studiedvariables are qualitative whereas organic solvent should, of neces-sity, be apolar and of low-water solubility. Also, it should be clearthat sampling depth refers to the distance of drop from the stir bar.
Table 1 gives the examined levels for each variable and matrixdesign. The 24 runs (12 runs in duplicate) are randomly carriedout in order to nullify the effect of extraneous or nuisance factors(Table 2). An analysis of variance test is used to evaluate the data andstatistically significant effects are determined using a t-test with95% probability, as will be detailed in Section 3.5. As mentionedabove, this screening step serves to screen out from the subsequentsteps parameters that do not have a significant effect on the TCPRor to predict, to some extent, the behavioral characteristics of therest of the parameters. This step reveals that extraction time is themost significant factor for the SDME of PCBs having positive effect,followed by stirring rate, sample volume and organic solvent withthe same sign. Negative significant effects were observed for sam-pling depth, drop volume and stir bar configuration. Ionic strengthshowed a positive, non-significant effect on TCPR. As this parame-ter constitutes an uncontrolled factor in different water matrixes,a sensible choice in a method development could be that all nextexperiments be carried out at the same ionic strength, under satura-
tion conditions. Being quantitative factors, organic solvent and stirbar can be excluded from the subsequent optimization after theyhave been fixed as toluene and cylindrical shape. In other cases,more solvents–solvent mixtures (or sorbent materials) could be
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Table 2Plackett–Burman design matrix of the screening experiment.
variables involved, their levels and the matrix of such a rotatableCCD are provided in Tables 3 and 4. Note that if any of the mainvariables considered are limited to two levels – and this holdsgood especially for quantitative variables – a mixed two- and three-
Table 3Independent factors and levels used in the rotatable CCD.
Variable Level Star points (˛ = 2)
Low (−1) Central (0) High (+1) −˛ +˛
7 1 −1 1 1 1 −11 2 −1 −1 −1 1 1
13 2 1 −1 1 −1 −114 2 1 1 −1 1 −1
nvolved with proper variable codification. However, this can causendesired increase to the number of experiments required in stepsubsequently undertaken.
.2. Choice of design of experiment
.2.1. Three-level full factorial designOne class of factorial design which has found favor in some
xperiments is the three-level full factorial design 3k, where k ishe number of factors. Such a design can provide information con-erning the interactions between variables at which main or linearnd quadratic or curvature effects can be separated. Nonetheless,his factorial design has limited application when the factor numbers higher than 2 since considerable number of experimental runs iseeded. For this reason, designs that present a smaller number ofxperimental points, such as the Box–Behnken, central compos-te, and Doehlert designs, are more frequently used [23]. Theseesigns are also easier to interpret and although they are not ableo examine a wide region of factors they are able to indicate majorrends.
.2.2. Doehlert designsIn Doehlert designs, the number of levels is not the same for
ll variables. For example, in a two-variable Doehlert design, oneariable is studied at five levels while the other is studied at onlyhree levels. This property allows a free choice of the factors to bessigned to a large or a small number of levels [24]. The number ofxperiments required (N) is given by N = k2 + k + C0, where k is theumber of variables and C0 is the number of center points.
.2.3. Box–Behnken designsIn several studies, researchers are inclined to require three
venly spaced levels. Box–Behnken design (BBD) is an efficientption (three-level factor quadratic design) at which the experi-ental points are located on the midpoints of the edges of a cube
nd at the center (central points). The special arrangement of the
BD levels allows the number of design points to increase at theame rate as the number of polynomial coefficients. The sphericalature of the BBD combined with the fact that the design is rotat-ble or nearly rotatable suggests that ample center runs should besed [23]. The number of experimental runs (N) is given by N = 2k
1 1 −1 1 −1 −11 −1 1 1 −1 1
−1 1 1 1 −1 1−1 −1 1 1 1 −1
(k − 1) + C0, where k is the number of variables and C0 is the numberof center points.
3.2.4. Central composite designThe central composite design (CCD) was presented by Box and
Wilson [23]. This design involves: (I) a two-level full factorial orfractional factorial design; (II) a star design in which experimentalpoints are at a distance � from its center; and (III) an experimentalpoint at the center. Center runs clearly provide information aboutthe existence of curvature in the system. By these means the designdisplays properties such as rotatability or orthogonality, in orderto fit quadratic polynomials. Usually, CCD consists of a 2k factorialruns with 2k axial runs and C0 center point runs. The total numberof experimental points needed (N) is determined: N = 2k + 2k + C0,where k is the number of variables and C0 is the number of centerpoints.
In Section 3.1 we decided on the final parameters to be includedas variables in the optimization experimental design of SDME ofPCBs. The popular CCD multi-level design can be one of the choicesto define the optimum settings of variable levels SDME of PCBs,i.e. the combination of values yielding the best results for theTCPR. A rotatable 2(5−1) fractional CCD (number of blocks: 1; designgenerator: 12345) is composed of a total of 29 randomized chro-matographic runs that includes 16 cube points in which 10 star and3 central points are included. Axial distance ˛ = 2 can be selectedin order to establish the rotatability conditions. The independent
evel factorial design can also express the multivariate optimizationxperiment.
.3. Selection of levels of variables
The selection of the domain of variables is another step thatdopts pivotal role in the experimental design. It defines the param-ter space within which the variable can range. The researchershould be on the lookout for the proper selection of space forontinuous and qualitative factors for a meaningful outcome. Ifhe variable range is too low, the variation of the response is toomall and the influence of the experimental error on the responses great. The consequence is that the calculated effects are smallnd not different from the error [25]. In any case, the limitationsf the experimental system under study should be allowed for.he above prerequisites are taken into consideration to form theariable ranges in the practical example, as given in Table 3.
Codification of the levels of the variable deals with the trans-ormation of each studied real value into coordinates inside a scaleith dimensionless values, which must be proportional at its local-
zation in the experimental space [26]. Selection of factors level forodification can be done on preliminary experiments, prior knowl-dge of the literature, and known instrumental limitations. Theariable levels Xi are coded as xi according to the following equa-ion:
i = Xi − X0
�Xi, i = 1, 2, 3, . . . , k,
here Xi and xi are the actual value and the dimensionless (codified)alue, respectively, X0 is the value of an independent variable atenter point, and �Xi is the step change.
.4. Mathematical model fitting
After the selection of the experimental design and codificationt is important to fit a mathematical model equation in order to
. A 1216 (2009) 175–189
describe the behavior of the response in the experimental domain.When there is no interaction between factors a simple linearfunction is proposed to establish whether they are statistically sig-nificant:
Y = ˇ0 + ˙ˇixi + ε
where Y is the response, ˇ0 is the constant term, ˇi represents thecoefficients of the linear parameters, xi represents the variables, andε is the residual associated to the experiments. This is the first-ordermodel, sometimes called a main effects model because it includesonly the main effects of the variables. The coefficient having thehighest absolute value corresponds to the most significant effect ofthe respective factor xi.
If the linear model is not sufficient to represent the experimentaldata adequately (significant lack of fit), more experiments can beperformed in addition to those of factorial design. When interac-tions between factors are suspected a central point in two-levelfactorial designs can be used for evaluating curvature. The nextlevel of the polynomial model should contain additional terms,which describe the interaction between the different experimentalvariables. This way, the first model with interaction presents thefollowing terms:
Y = ˇ0 + ˙ˇixi + ˙ˇijxixj + ε
where ˇij represents the coefficients of the interaction parametersxi and xj.
Center points cannot be added for qualitative factors; hence, tobalance the design, when center points are requested, usually fullfactorial designs for all qualitative factors at each center point areconstructed, for all continuous factors.
Often, the curvature in the response is strong enough that thefirst-order model (even with the interaction term included) is inad-equate. In order to determine a critical point (maximum, minimumor saddle), it is necessary for the polynomial function to containquadratic terms according to the following equation:
Y = ˇ0 + ˙ˇixi + ˙ˇiix2i + ˙ˇijxixj + ε
where ˇii represents the coefficients of the quadratic parameter. Toestimate the parameters in the above equation, the experimentaldesign has to assure that all studied variables are carried out in atleast three factor levels. For this case, response surface designs areavailable [26,27].
3.5. Model adequacy checking
It is always necessary to examine the fitted model to ensurethat it provides an adequate expectedness to the true system. Themodel is only validated when it shows a good predictability. Themodel adequacy can be assessed by the employment of differentstatistical tools.
3.5.1. Analysis of varianceThe most powerful numerical method for model validation is by
the application of analysis of variance (ANOVA), which is based on adecomposition of the total variability in the selected response (Y). Itchecks the adequacy of the regression model in terms of lack-of-fittest and whether the coefficients estimated are actually significant.ANOVA can compare the variation due to the treatment (change inthe combination of variable levels) with the variation due to ran-
dom errors inherent to the measurements of the responses. Fromthis comparison, it is possible to evaluate the significance of theregression used to foresee responses considering the sources ofexperimental variance [28]. This comparison is executed from F-value, which is the proportion between the mean-square of model
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nd remainder (residual) error. If the model is good herald of exper-mental results, F-value should be larger than tabulated value in aertain number of degrees of freedom and vice versa.
.5.2. Lack-of-fit testAnother way to evaluate model suitability is the lack-of-fit test.
he lack-of-fit test requires that true replicates are available on theesponse for at least one set of levels of the predictor variables [23].hus, the residual sum of squares can be further partitioned intoeaningful parts which are relevant for testing hypotheses. Specif-
cally, the residual sums of squares can be partitioned into lack of fitnd pure-error components. This involves determining the part ofhe residual sum of squares that can be predicted by including addi-ional terms for the predictor variables in the model (for example,igher-order polynomial or interaction terms), and the part of theesidual sum of squares that cannot be predicted by any additionalerms (i.e. the sum of squares for pure error). A test of lack of fit forhe model without the additional terms, then, can be performedsing the mean square pure error as the error term. This providesmore sensitive test of model fit, because the effects of the addi-
ional higher-order terms are removed from the error. A model wille well fitted to the experimental data if it presents a significantegression and a non-significant lack of fit.
.5.3. Properties of the least square estimatorsThe square of correlation coefficient (R2) quantitatively mea-
ures the correlation between the experimental data and theredicted responses. However, a large value of R2 is not always a solegent that the regression model is good, if it is not statistically signif-cant. An R2 of 1.0 indicates that the regression line perfectly fits theata. Adjusted R2 is a modification of R2 that adjusts for the numberf explanatory terms in a model. The adjusted R2 can be negative,nd will always be less than or equal to R2. When R2 and adjusted2 differ considerably, there is a good chance that non-significanterms have been included in the model.
.5.4. Residual analysisRaw residuals are the deviations of the actual values from the
redicted values and represent the difference that is not explainedy the model. The better the fit of the model, the smaller the valuesf residuals is; more to the point, residuals should be normally dis-ributed. The Shapiro–Wilk-W normality test or Anderson-darlingormality test of residuals provide the information regarding resid-al tests. From the graphical point of view, model predictabilityan also be determined by normal probability plot of residuals andistogram of residuals. Likewise, the plot of predicted and actualesponses can be used for model prediction; if the points of all pre-icted and actual responses fell in 45◦ line, a good response to theodel is indicated.
.6. Analysis of model and effect estimates
Student’s t-test is used to verify the significance of the regressionoefficients, whether the slope of a regression line differs signifi-antly from 0 or not. The ‘p’ values are used to check the significancef each interaction among the variables. Generally, the higher the talues, the smaller the p value is.
Graphical methods have an advantage over numerical methodsor model factors analysis because they readily illustrate a broadange of complex aspects of the relationship between model andata. The normal probability plot is a type of graph used to visualize
he ANOVA parameter estimates. In this plot, the normal probabil-ties of the rank-ordered parameters are plotted on the y-axis, andhe actual parameter estimates (optionally standardized) are plot-ed on the x-axis. If all estimates come from a population with a
ean parameter estimate of zero and a common variance, then the
Fig. 1. Standardized main effect Pareto chart for the Plackett–Burman design ofscreening experiment. Vertical line in the chart defines 95% confidence level.
points in this plot approximate a straight line. “Real” effects showup in this plot as outliers. Also, the Pareto chart is very popular anduseful for reviewing a large number of factors and for presentingthe results of an experiment to an audience that is not familiar withstandard statistical terminology. Using the main effects of a Paretochart, the bar length is proportional to the absolute value of theestimated main effect while a vertical reference line correspondingto a specified confidence interval (usually 95%) is included. Signif-icant is the effect that exceeds this reference line while positive ornegative sign reveals the cases when the response is enhanced orreduced, respectively, when passing from the lowest to the highestlevel of a specific variable.
The effects of the studied variables in the screening experi-ment of the worked example are portrayed in Fig. 1, in the formof a Pareto chart. Similar treatment of data can be done with CCDfor SDME of PCBs (Pareto chart is not shown). The variables stud-ied with the exception of drop volume and sampling depth havea significant effect on TCPR. Sampling depth and drop volume,exhibiting small negative and positive effects, respectively, werefixed at the central values, i.e. 2.1 cm and 1.5 �l. Besides, certainquadratic effects and second-order interactions influence TCPR toa significant degree. Based on the variables and interactions whichare statistically significant, the response could be fitted by a mul-tiple regression equation, including quadratic and second-orderinteraction terms, as given in Section 3.4.
3.7. Allocation of the optima
The optimum region to run a process is usually determinedafter a sequence of experiments has been conducted and a series ofempirical models obtained. In many applications, experiments areconducted and empirical models are developed with the objectiveof improving the responses of interest. From a mathematical pointof view, the objective is to find the operating conditions (or factorlevels) x1, x2, . . ., xi that maximize or minimize the system responsevariable Y. For this reason, response surface methodology is used[23].
In the cases of linear models, the surfaces (response graphs orcontour plots) generated can easily be used to indicate the optimal
conditions. For quadratic models, the critical optimization condi-tion (maximum, minimum, or saddle) could be calculated throughthe first derivate of the mathematical function, which describes theresponse surface and equates it to zero [28]. When two factors areused (x1, x2), the optimal conditions can be found by solving the
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rst grade system formed by the two equations and to calculate the1 and x2 values. The display of the predicted model equation can bebtained by the surface response plot. Usually, a two-dimensionalepresentation of a three-dimensional plot can be drawn. Thus, ifhere are three or more variables, the plot visualization is possiblenly if one or more variables are set to a constant value [28].
Other, less frequently used manners to reach optimal conditionsncompass artificial neural networks (ANNs). ANNs gather theirnowledge by detecting the patterns and relationships in data andearn (or are trained) through experience. They have the ability topproximate virtually any function in a stable and efficient way and,or this reason, they can be applied to quantify a nonlinear relation-hip between causal factors and responses by means of iterativeraining of data obtained from a designed experiment [29].
Finally, the simplex methods of optimization are intuitivelyppealing multifactor search strategies [30,31]. It is about hill-limbing algorithms that move a pattern of (n + 1) experimentaloints away from regions of worse response toward convergencen an optimum in the response surface, visualized in (n + 1)-imensional space for n factors. Various applications of the simplex
n methods development have demonstrated its general utility asn experimental approach to efficiently achieve optimal response.
Returning to the practical experiment of SDME of PCBs, we opted
or the graphical interpretation of the variation of response, viz. alot TCPR as a function of the independent variables which con-rol the process. Three-dimensional response surfaces show theffect of two independent variables on a given response at a con-tant value of the other three independent variables. Evidently,
ig. 2. Response surface plots for TCPR: (a) extraction time vs. stirring rate (sampling depolume (sampling depth: 2.1 cm; drop volume: 1.5 �l; extraction time: 24 min); (c) samplate: 225 rpm).
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high extraction time in conjunction with high agitation rate isable to achieve the highest response (Fig. 2a). In direct-immersionSDME, mass transfer into the drop is facilitated by both diffusionand convection phenomena, both augmented by the high agitation.Increasing the aqueous sample volume leads to increase in the totalamount of target analytes. Likewise, high sample volume requiresthat stirring rate be high enough (Fig. 2b). Definitely, high samplevolume calls for high extraction time (Fig. 2c).
3.8. Robustness checking
A usual requirement of an analytical method is robustness,which is typically defined as the ability of the method to provideaccurate and precise results despite variations in equipment andconditions. Robustness must be studied in terms of variations thatare equivalent to the greatest (or unusual) errors that may arisein establishing the nominal value of each variable, under routineexperimental situations. Recently, Goupy implied that finding andchecking robustness of analytical methods are two different prob-lems which must be treated with different tools [25]. “Findingrobustness is to discover an experimental region where nothinghappens, which means that the response of interest is not influ-enced by changing significantly the levels of the various operating
factors. Checking robustness is to verify the recommended settingsof the analytical method. This verification enables also to assessthe response variations near the operational point for each factor.”Plackett–Burman designs are often adequate for checking analyti-cal method; however, if the response surface presents an important
th: 2.1 cm; drop volume: 1.5 �l; sample volume: 8 ml); (b) stirring rate vs. samplee volume vs. extraction time (sampling depth: 2.1 cm; drop volume: 1.5 �l; stirring
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urvature, star designs, which are OFAT designs, seem be the bestay to verify the robustness of an analytical method. Again, robust-ess will be determined using six distinct steps in a process that
ooks much like chemometric optimization: (I) identification of theactors to be tested, (II) selection of the factor levels and level num-ers, (III) selection of the design of experiment, (IV) realization ofxperiments and measurement of response, where applicable, (V)alculation of the variable effects, and (VI) analysis and interpreta-ion of the results.
In the example of SDME of PCBs, seven factors were selected forhe examination of the robustness including temperature whichas not taken into account in the previously described optimiza-
ion step. The nominal values of the factors are stirring rate,00 rpm; sample volume, 10 ml; extraction time, 30 min; samplingepth, 2.1 cm; temperature, 25 ◦C; depressing drop volume, 1.5 �l;etracted drop volume, 1.5 �l. Recall that depressing and retractedrop volumes correspond to the volume of organic-solvent dropxposed to the aqueous sample and the volume retracted aftericroextraction has been completed. Drop volume during SDME
an either grow bigger due to solubility of water in the employedrganic solvent or diminish due to opposite reason.
In this example, two 27−4 saturated fractional factorial designsresolution R = III) can be selected, centered on the optimum, withpper and lower values corresponding to a modification of 5 and0% to the nominal value of the chosen variables. At least two repli-ates should be added to the design to estimate the experimentalrror, and all the experimental runs (total number: 16) are per-ormed in random order. The SDME process is proved to be robustt a variation of 5%, as none of the factors has a significant effectn the total response (data not shown). In contrast, at a variationnterval of 10%, total response is sensitive to sample volume and, tolesser extent, to the extraction time. Interestingly enough, TCPR
s insensitive to the rest of the operational factors.Again, the demonstration of the statistical significance of the
actor(s) can be displayed in the form of a Pareto chart ofig. 3. Seemingly, variations to the procedural values of agita-ion are not critical to the robustness, at high stirring rates.aradoxically, drop volume variation before and after microex-raction, a fact which is of concern for many SDME applicants,
pparently, has no bearing on the response. Three-dimensionalesponse plots, as described under the optimization of experimen-al conditions, can again be constructed to uncover the factors tohich chromatographic response is sensitive. Such plots should
ig. 3. Pareto chart of the main effects obtained from the fractional factorial designf robustness test.
. A 1216 (2009) 175–189 183
be linear with slopes that allow for making conclusions on therobustness.
As a conclusion drawn from the robustness study of practicalexample, maintaining the microextraction factors within appro-priate intervals, significant effects of them can be eliminated.Further development and validation of the microextraction methodis beyond the scope of this practical example.
4. Selected applications
A significant number of applications make use of the simul-taneous microextraction and chemometric aspects with SPMEalternatives to hold the largest share in this research area. Some ofthem include the step of derivatization in a pre- or post-extractionmode incorporating a reaction along with the microextraction[4]. Within the scope of this review article, the coverage shouldinevitably be representative rather than comprehensive. Havingin mind to give an overview of the most relevant applications, arepresentative number of them are described here.
Vidal et al. described a one-step and in situ sample preparationmethod used for quantifying chlorobenzene compounds in watersamples, through coupling microwave and headspace SDME [32].The chlorobenzenes were extracted directly onto an ionic liquidsingle-drop in headspace mode with the aid of microwave radiation.For optimization, a Plackett–Burman screening design was initiallyused, followed by a mixed-level factorial design. The factors consid-ered were drop volume, aqueous sample volume, stirring rate, ionicstrength, extraction time, ionic liquid type, microwave power andlength of the Y-shaped glass-tube. The results of this first screeningstudy revealed that five factors could be fixed (namely microwavepower, ionic liquid drop volume, Y-shaped glass-tube length, agi-tation and addition of NaCl) for the subsequent optimization step.Next, a factorial design was carried out to assess the influence ofthe three main factors on the microwave–microextraction processin order to obtain the optimal working conditions. Given that oneof the main factors considered was limited at two levels (i.e. twoionic liquids) and the other two were able to work at three lev-els, a mixed two- and three-level factorial design was used. Theoverall design, expressed as {21 × 32}, involved 36 runs (18 runs induplicate). Conclusive proof-of-application was produced by deter-mining chlorobenzenes in water samples.
The same authors developed a SDME for the determinationat ultratrace levels of benzophenone-3, in human urine [33]. APlackett–Burman design for screening and a circumscribed cen-tral composite design for optimizing the significant variables wereapplied. Ionic strength, extraction time, stirring rate, pH, ionic liquidtype, drop volume and sample volume were the variables stud-ied. The next step was concerned with optimizing the values ofthe significant variables in order to obtain the best extraction yieldof benzophenone-3. A circumscribed central composite design wasemployed, and the overall matrix of the design involved 23 experi-ments. The three variables considered were extraction time, stirringrate and sodium chloride concentration (ionic strength).
Headspace SDME was used for the extraction and preconcen-tration of 2,4,6-trichloroanisole and 2,4,6-tribromoanisole in winesamples, followed by analysis by GC–electron-capture detection(ECD) [34]. In order to obtain optimized conditions for extraction,a fractional factorial experimental design was used to evaluate thepreliminary significance of the variables, as well as the interactionsbetween them. The variables investigated were temperature andextraction time, sample pH, ionic strength (sodium chloride con-
centration) and sample matrix types (red wine or synthetic wine).All variables were evaluated at two levels. The significant variablesindicated by the Pareto chart, which was obtained after multiplelinear regression and analysis of variance, were optimized using aBox–Behnken design.
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Wu et al were the first to apply orthogonal array designs towardptimizing HF-LPME conditions for the analysis of three acidicnti-inflammatory drug residues in wastewater samples [35]. Sixelevant factors were investigated: type of organic solvent, compo-ition of donor phase and acceptor phase, stirring rate, extractionime and salt concentration. In the first stage, mixed-level orthogo-al array design was employed to study the effect of six factors, byhich the effect of each factor was estimated using individual con-
ributions, as response functions. Based on the results of the firsttage, 1-octanol was chosen as organic solvent for extraction. Thether five factors (i.e. concentration of HCl, concentration of NaOH,tirring rate, salt concentration added and duration of extraction)ere selected for further optimization using an orthogonal arrayatrix, using a four-level design. The corresponding enrich-ent factors used as responses for each experimental trial were
alculated.The recently developed dispersive liquid–liquid microextraction
echnique based on the dispersion of an extraction solvent intoqueous phase in the presence of a dispersive solvent was inves-igated for the preconcentration of Cu2+ [36]. 8-Hydroxyquinolineas used as a chelating agent prior to extraction. Flame atomic
bsorption spectrometry using an acetylene-air flame was used foruantitation of the analyte after preconcentration. Central com-osite design was used to optimize the preconcentration of Cu2+
y dispersive liquid–liquid microextraction. Five independent vari-bles, namely the volume of dispersion solvent, extracting solventHCl3, Cu2+ solution, pH and NaCl amount, were studied at five
evels with four repeats at the central point, using a circumscribedentral composite design. The significance and the magnitude ofhe estimated coefficients of each variable and all their possibleinear and quadratic interactions on the response variables wereetermined.
Speciation of organotin has been a very popular subject in therea of analytical chemistry for many years [37]. Lespes et al.eveloped a SPME method based on in situ ethylation and theimultaneous microextraction of the derivatives, followed by a gashromatographic analysis. The experimental design methodologysed was able to evaluate the influence of six analytical parametersn the peak area. Since a complete factorial design would lead to4 (i.e. 26) experiments, to reduce the number of experiments, aractional design 26−2 was finally used, leading to 16 experiments.igher-order interactions were studied to arrive at the optimal of
he factors involved. Adsorption time, sample volume and fiberoating were found to be the most critical factors.
Batlle et al. presented an optimized simultaneous extraction,reconcentration and derivatization of four gaseous diisocyanatestilizing a 2.3-�l water drop containing dibutylamine as aerivatization agent. In the first step, screening of the vari-bles was conducted based upon a resolution III design, followedubsequently by a Box–Behnken surface modeling and sim-lex optimization. Finally, the proposed method was tested inerms of robustness revealing a carryover effect between runs38].
Special attention should also be drawn to a combination ofxperimental design approach and artificial neural networks, whichllowed obtaining good extraction efficiencies in the SPME proce-ure for the determination of a group of eleven triazine herbicides
n groundwater samples [39]. A CCD was used as experimentalesign, with the quantitative variables: extraction time, sodiumhloride percentage, desorption time, and methanol percentage inhe desorption mixture. In this design, 26 runs plus 2 star points
ere randomly carried out, trying to nullify the effect of extraneous
ariables, and run in three blocks, after rotatability had been estab-ished. A three-layer feed forward back-propagation neural networkas developed in order to optimize the SPME procedure. The data
rom the experimental design were randomly reassigned in two
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sets: a training set consisting of 28 data and a verification set with5 data (ratio 5.6).
The optimization of a sample processing procedure comprisingcombined techniques, among them being microextraction, pre-dictably should take into account several continuous and qualitativefactors. Some of them are related to the practical feasibility of thecombination of both techniques while others correspond to theparticular optimization of each technique. An approach based onthe simultaneous supercritical fluid extraction (SFE) followed bySPME–GC/MS was developed as an analytical tool for the determi-nation of 15 organohalogenated compounds in aquaculture feed,at low levels [40]. The influence of several parameters in theefficiency of the SFE/SPME combination was systematically inves-tigated by a chemometric strategy in which several factors werestudied and optimized sequentially while maintaining the num-ber of experiments to a minimum. First, the variables that mayaffect technique compatibility were explored. Once the compat-ibility between techniques was granted, the particular variablesaffecting each technique were studied. In the case of SPME, theextraction time and temperature as well as the temperature inthe GC injector and desorption time were considered for opti-mization purposes using factorial and Doehlert designs. To finda compromise set of operational conditions in such a complexexperimental system, the authors have resorted to multicriteriadecision-making strategies using desirability function optimiza-tion. It should be noted that this strategy operates on the resultsproduced by the factorial or Doehlert designs, without requir-ing additional experiments. Optimum conditions were obtainedthat corresponded to the optimal compromise values adopted inthe supercritical fluid extraction stage of the SFE/SPME combina-tion.
A smart mode of headspace SPME for the determination ofmercury cannot go unnoticed [41]. More specifically, a gold wire,mounted in the headspace of a sample solution in a sealed bot-tle, was used for the collection of mercury vapor generated by theaddition of sodium tetrahydroborate. The gold wire was then sim-ply inserted in the sample introduction hole of a graphite furnace ofan electrothermal atomic absorption spectrometer. By applying anatomization temperature of 600 ◦C, mercury was rapidly desorbedfrom the wire and determined with high sensitivity. Factorial designand response surface analysis methods were also used for optimiza-tion of the effect of five different variables in order to maximizethe mercury signal. The parameters were the gold wire thickness,extraction time, sample volume, relative amount of sodium tetrahy-droborate, and stirring rate. A half-fraction factorial design with2(5+1)−1 = 32 experiments was selected. The response surfaces werecalculated by performing a central composite design including fourcenter points in cube and two center points in star with a total of20 runs.
Finally, a simultaneous multi-optimization strategy based on aneuro-genetic approach was applied to a headspace SPME methodfor GC–ECD determination of 12 PCBs in human milk [42]. Experi-ments according to a Doehlert design were carried out with variedextraction time and temperature, media ionic strength and concen-tration of the methanol (co-solvent). To find the best model thatsimultaneously correlate all PCB peak areas and SPME extractionconditions, a multivariate calibration method based on a BayesianNeural Network was applied. The net output from the neuralnetwork was used as input in a genetic algorithm optimizationoperation (neuro-genetic approach). The algorithm pointed out thatthe best values of the overall SPME operational conditions were
the saturation of the media with NaCl, extraction temperature of95 ◦C, extraction time of 60 min and addition of 5% (v/v) methanolto the media. These optimized parameters resulted in the decreaseof the detection limits and increase on the sensitivity for all testedanalytes. At the same time, it demonstrated that the use of neuro-
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Table 5Examples of simultaneous SPME and chemometric treatment.
HS-SPME: 24 full factorial design –incubation time, extraction time,sample temperature, waterCF–HS-SPME: 23 full factorialdesign – fiber temperature,extraction time, sampletemperature
Doehlert matrix – sampletemperature, extraction timeand fiber temperature in thecase of Cold Fiber HS-SPME
GC–MS [51]
Heterocyclic aromatic amines Commercial meat extracts SPME (CW/TPR) 23 factorial design – absorptiontime, soaking time, desorption time
Doehlert design – absorptiontime, soaking time
HPLC–UV/DAD [52]
Pyrethroids Water samples HS-SPME and SPME (PDMS,PDMS/DVB, PA, CW/DVB)
Water samples SPME (PDMS) MultiSimplex – extraction timeand temperature, desorptiontime and temperature, salt
GC–MS [55]
Volatiles Summer truffle aroma HS-SPME (DVB/CAR-PDMS) Rotatable CCD (23 factorialsign, plus 6 star points, plus 6replicates) for equilibriumtime, extraction temperatureand time
GC–FID,GC–MS
[56]
Organoselenium species Lupine, yeast, Indianmustard and garlic
SPME (CAR/PDMS) 23 Factorial design – extractiontemperature and time,temperature of injection port
MulticapillaryGC –microwaveICP-AES
[57]
Sterols Serum HS-SPME (PA, DVB/CAR/PDMS)with on fiber derivatization withBSTFA
25−2 Fractional factorial design– sorption time andtemperature, amount of salt,sample volume, desorptiontime
GC–FID [58]
Methyl tert-butyl ether Water samples HS-SPME (PDMS/DVB) 25−2 fractional factorial design –concentration of NaCl, extractiontemperature and time, agitation,headspace volume
CCD – extraction temperature,salt concentration
GC–FID [59]
Fluoxetine and norfluoxetine Plasma SPME (PDMS/DVB and CW/TPR) 24−1 fractional factorial design– time, temperature, ionicstrength and pH
HPLC–UV/Vis [60]
Pyrethroids andorganochlorine pesticides
Milk SPME and HS-SPME (PDMS, PA,PDMS/DVB, CAR/PDMS andCW/DVB)
Factorial design (25−1) – type offiber coating, sampling mode,agitation, extractiontemperature, salt
Glycol ethers Water samples HS-SPME (CW/DVB, PDMS andCAR/PDMS)
45 orthogonal array design –extraction time, temperature,salt concentration, two dummyfactors
GC–FID [63]
Volatiles Aniseed-flavored spiritdrinks
HS-SPME (PDMS, PDMS/DVB,CAR/PDMS, DVB/CAR/PDMS)
CCD – extraction temperatureand time, sample volume, saltconcentration
GC–MS [64]
Volatiles White wine HS-SPME (PDMS, PDMS/DVB,CAR/PDMS, DVB/CAR/PDMS,CW/DVB)
Two-level factorial design – samplevolume, agitation, volume of vial,amount of NaCl, extraction timeand temperature
CCD – sample volume,extraction time andtemperature
GC–FID,GC–MS
[65]
Residual solvents Drugs SPME and HS-SPME (PDMS,PDMS/DVB, CW/DVB, CAR/PDMS)
Repeated two-level,full-factorial design – sampletemperature, salt effect, water
GC–FID [66]
Volatiles Essential oil HS-SPME (PA, CW/DVB, PDMS) Plackett–Burman design – sorptiontime and temperature, desorptiontime and temperature, headspacevolume, headspace-to-samplevolume ratio
RSM design for sorption timeand temperature
GC–MS [67]
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Organochlorine pesticides andPCBs
Serum HS-SPME (PDMS, PDMS/DVB) 27−4 Plackett–Burman design –type of fiber, extractiontemperature and time, headspacevolume, pH, concentrations ofNa2SO4 and Triton X-100
enetic approach can be a promising way for optimization of SPMEethods.Other prominent examples of combining SPME and chemomet-
ics are tabulated properly in Table 5.
. Critical appraisal
To address problems such as large solvent consumption, labor-ntensive operations and cost, research activities in the past threeecades were oriented toward the development of convenient,fficient, economical, and miniaturized sample preparation tech-iques. It is widely accepted that it is a ‘research sin’ to perform anxperiment that is either too small or too large. Actually, experi-ents that are excessively large are obviously a waste of resources;
xperiments that are too small are perhaps even worse. Carryingut a thorough and dependable microextraction optimization maye tedious, but the consequences of not doing that right are surelyasted time, money and resources.
Since their inception for the purpose of chemical analysis, in con-emporary form in 1990, microextraction is still finding its niche inhe world of analytical sample preparation and several microextrac-ion alternatives have been explored for their ability to cover a wideange of analytes. Besides, chemometric techniques are increasinglyeing applied in many fields of analytical chemistry. Years ago, therimary users of chemometrics were the statisticians or a handfulf chemists focusing their efforts on the development of varioushemometric aspects of analytical chemistry. Therefore, today’seople that employ chemometrics start at a much higher levelf comprehension. As the science of analytical chemistry evolved,hese seminal works fostered the merging of chemometrics withnalytical mainstream and more and more analysts paid closerttention to this field assisted by the advent of the ease-of-useedicated software packages.
Microextraction and chemometric optimization are meant to beogether! Currently, more and more researchers have been realiz-ng the weakness of microextraction to meet the requirements of aeasonably applied method in the absence of chemometric methodsf approach. There are several reasons that keep research on, andse of, chemometrics alive in analytical laboratories dealing withicroextraction. These aspects, together with future needs, will
eep their coupling alive, not in a vegetative state, but in dynamiceal-life situations giving solutions to new needs and responses tohallenges in research laboratories, in an adequate manner. Theombination of microextraction with chemometrics permits notnly enhancement of recoveries of analytes, but also addressesroblems relating to improvement in detectability and methodalidation. The cases where microextraction and chemometricso together are unequivocally plentiful and consequential withreat impact on the implementation of the microextraction. Actualrogress in microextraction generates alternatives like nanoscale,hich are reasonably developed within the context of chemomet-
ics. This coexistence is advocated by the ready-to-use toolboxeshich are available to develop models using various techniques
ncluding experimental designs, neuronal networks and geneticlgorithms.
The step-by-step approach of optimization of SDME of PCBsnderpins the usefulness of chemometric methods to assess andighlight the intrinsic characteristics of the factors involved andheir interactions, by screening, optimizing and establishing theirritical conditions to ensure the absence of bias. Nonetheless, it is
he sense of the authors that the worked example, which unques-ionably is cumbersome and time consuming, is not meant to be
cut-and-dry procedure for future microextraction procedures.ctually, it is about a gradual approach of the theme which arrivest reasonable conclusions with respect to this simple mode of
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microextraction. In this manner, the dynamic mode of SDME wouldrequire a meticulous evaluation of other prominent factors in place,such as the volume of sampling, dwell time and number of sam-plings. As demonstrated under the section of selected applications,the specific consideration of any microextraction mode stronglyrests on the demands of the intended analytical method. The ana-lyst who is familiar with the system under scrutiny can choose theway he (she) desires to approach it based on the experience and thedegree of reliability of the method that should be developed.
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