Kinetics of solid-phase extraction and solid-phase microextr, Artykuły naukowe, SPME i HS-SPME

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//-->Journal of Chromatography A, 873 (2000) 39–51www.elsevier.com / locate / chromaKinetics of solid-phase extraction and solid-phase microextractionin thin adsorbent layer with saturation sorption isotherm,1,2Semen N. Semenov* , Jacek A. Koziel, Janusz Pawliszyn*Department of Chemistry,University of Waterloo,Waterloo,Ontario,N2L3G1CanadaReceived 28 August 1999; received in revised form 24 December 1999; accepted 27 December 1999AbstractThe effects of sorbent saturation in thin adsorbent layers have been much overlooked in earlier research and should betaken into account in both the theory and practice of solid-phase extraction (SPE) and solid-phase microextraction (SPME).The adsorption kinetics of a single analyte into a thin adsorptive layer was modeled for several cases of agitation conditionsin the analyzed volume. The extraction process in the adsorbent layer was modeled using a Langmuir isotherm approximatedby the linear isotherm at low concentrations and by a saturation plateau at concentrations exceeding the critical saturationconcentration. Laplace transformations were used to estimate the equilibration time and adsorbed analyte concentrationprofile for no agitation, practical and perfect agitation in the analyzed volume. The equilibration time may be significantlyreduced at high degrees of oversaturation and / or agitation in the analyzed volume. The resulting models indicated that theadsorbent layer becomes saturated at some critical value of the oversaturation degree parameter. The critical value of theoversaturation parameter is affected by both the concentration of the analyte in the analyzed volume and the sorbentcharacteristics. It was also shown that the adsorption process is carried out via the propagation of the saturation adsorptionboundary toward the inner boundary of the adsorbent layer. These new adsorption models should serve as ‘‘stepping stones’’for the development of competitive adsorption kinetic models for both SPE and SPME, particularly in cases where fastsampling is used.©2000 Elsevier Science B.V. All rights reserved.Keywords:Adsorption isotherms; Mathematical modeling; Solid-phase microextraction; Solid-phase extraction; Kineticstudies; Sorbent saturation1. IntroductionSolute partitioning between a liquid or gas and a*Corresponding authors.E-mail addresses:sem@fly.triniti.troitsk.ru (S.N. Semenov),janusz@uwaterloo.ca (J. Pawliszyn)1On leave from the Institute of Biochemical Physics, RussianAcademy of Science, Kosygin Street 4, 117977 Moscow, Russia.Fax:17-095-137-4101.2Tel.:11-519-888-4641;fax:11-519-746-0435thin, solid or liquid sorbent layer is widely used inmany scientific and technological applications, in-cluding analyte extraction / sample preparation insolid-phase extraction (SPE) and solid-phase mi-croextraction (SPME). For SPE, a high-affinitysorbent retains and concentrates organic compoundsfrom a dilute liquid or gaseous phase. These com-pounds are later desorbed and introduced into achromatograph or other analytical device. Limita-tions to SPE (mainly due to its large adsorbent layer)have been addressed by SPME [1], which since its0021-9673 / 00 / $ – see front matter©2000 Elsevier Science B.V. All rights reserved.PII: S0021-9673( 99 )01338-240S.N.Semenov et al./J.Chromatogr.A873 (2000) 39–51introduction in the early nineties has found manyapplications [2]. For SPME, a thin layer of high-affinity solid (or liquid for absorptive extraction / pre-concentration) sorbent is coated on the surface of afused-silica fiber. Analytes partition to the sorbentand are later transferred to an analytical instrument,e.g. gas chromatograph, for sample desorption, sepa-ration and quantification. This method minimizes theextraction / sample preparation time and allows forthe same sorbent coating to be reused after eachsample extraction / injection / desorption cycle.In a typical adsorptive SPME extraction analytesdiffuse from the analyzed volume onto the sorbentlayer. To enhance analyte uptake, partition constantvalues for the sorbents used in commercially avail-able SPME typically range from 103to 105[1].However, sorbents with high partition constants maybe quickly saturated even at relatively low analyteconcentrations, due to the limited number of avail-able adsorption sites. Typical specific surface areasfor the solid adsorbents range between 102and 103m2g21[3]. The molecule size and the adsorption sitearea may be as low as approximately 1029m and10218m2, respectively. Thus, the maximum con-centration of adsorption sites available in thesesorbents cannot exceed 1020–1021g21. Consideringan average partition constant of approximately 104,these sorbents may be saturated at analyte con-centrations of 1016–1017g21, i.e., from 0.1 to 1 ppm.Larger molecules, e.g. greater than five characteristicatomic sizes, have an even smaller number ofavailable adsorption sites, and the critical concen-tration for sorbent saturation may be lower, rangingfrom 10 to 100 ppb. As such, sorbent saturation canbe reached for typical SPME applications, and itskinetics has not been fully addressed in the existingliterature.A comprehensive theory of extraction by absorp-tion-type SPME coatings was presented by Paw-liszyn [1]. Recently, Ai developed a theoreticaldescription of non-equilibrium absorption into SPMEcoatings [2,4–6]. These models can be used toestimate mass of analytes absorbed with SPME,when achieving equilibrium extraction for quantifica-tion purposes requires an inconveniently long time.Gorecki et al. developed a steady-state theory foranalyte extraction via adsorption by selected porouspolymer fibers [7]. To date, there is no comprehen-sive SPME theory for including competitive dynamicadsorption processes. Such processes are very im-portant in cases where very short sampling times areused, e.g. less than 10 s, and where the quantificationis based on molecular gas-phase mass transfer co-efficients [8]. Adsorption kinetics including displace-ment effects are well understood in processes involv-ing protein sorption [9,10]. However, the time scalefor protein adsorption is often an order of magnitudegreater than those used in fast sampling with SPME[11].Sorbent saturation is much different from the‘‘linear’’ extraction regime. First, the time necessaryfor establishing equilibrium between the adsorbedand free analytes should depend on the analyteconcentration in the analyzed volume, since only apart of the total amount of analyte can be adsorbed inthe saturation regime. For the same reason, the finalconcentration distribution and the amount of theanalyte adsorbed should not depend on its con-centration in the analyzed volume, and should becontrolled by the adsorbent capacity only. Secondly,analyte ‘‘outflow’’ from the free to the bound(adsorbed) form, where it could not move across theadsorbent layer, should lead to slower observablediffusion. Thirdly, mass transfer conditions shouldaffect the equilibration process, e.g. the degree ofagitation in the analyzed gas or liquid may controlthe boundary layer thickness in a sample volume.Finally, there is a potential for reversible binding andthe ‘‘displacement’’ of lower-molecular-mass ana-lytes by higher-molecular-mass compounds.In addition, competitive adsorption has been ob-served in SPME practice (Fig. 1). The effects ofsaturation and competitive adsorption in thin ad-sorbent layers were not fully taken into account inprevious theoretical developments of SPE / SPME[1,2]. A full understanding of this process is crucialfor expanding SPE / SPME applications to very com-plex analyte sample matrices. Thus, there is agrowing need for models describing saturation ef-fects and competitive adsorption in thin adsorbentlayers for commercially available SPME fibers.In this research, the kinetics of single analyteadsorption into a thin layer during SPE and SPMEwas modeled. Several limiting cases of extraction /mass transfer were considered. Laplace transforma-tions were used to estimate the analyte concentrationS.N.Semenov et al./J.Chromatogr.A873 (2000) 39–5141Fig. 1. Competitive adsorption for gas phasen-alkaneson a polydimethylsiloxane–divinylbenzene fiber.time profiles for no agitation, typical and perfectagitation conditions in a sample volume. The ex-traction kinetics were modeled in an adsorbent layerwith the saturation sorption isotherm approximatedby the linear isotherm at low concentrations and by asaturation plateau at concentrations exceeding thecritical saturation concentration. The resultingmodels are based on several physicochemical andextraction parameters, and should serve as a basis forthe development of new models for competitiveadsorption in thin, solid or semi-solid-phases.volume,Deis the diffusion coefficient of the analytein the analyzed volume,tis the time, andxis thetransverse coordinate in the adsorption layer. Theinitial condition to Eq. (1) has the formce(t50)5catx#(2)2. Theoretical development2.1.Formulation of the mathematical problemThe concentration distribution of an analyte in agiven volume (outside of sorbent layer) is commonlydescribed using a diffusion equation based on Fick’ssecond law. This relationship can be reduced to onedimension assuming that for a thin adsorbent layer,e.g. SPME, adsorptive coating curvature can beneglected:≠ce≠2ce] 5De? ]]≠t≠x2(1)whereceis the analyte concentration in the analyzedThe boundary condition to Eq. (1) depends on theagitation regime. Several analyte concentration dis-tributions in the analyzed volume near the adsorbentlayer for several limiting cases of agitation arepresented in Fig. 2. Eq. (1) describes the analyteconcentration with no agitation conditions, where nomeans are employed to agitate gas or liquid in theanalyzed volume (the no agitation regime in Fig. 2).The opposite case is represented by conditions ofperfect agitation, where the concentration distribu-tion is always uniform and does not depend on theanalyte outflow onto the adsorbent layer (the perfectagitation regime in Fig. 2). In typical SPME applica-tions, some means for agitation are used, and uni-form analyte concentration exists in the analyzedvolume outside a thin boundary layer with constantthicknessddetermined by the agitation conditions(the practical agitation regime in Fig. 2). The analyteconcentration inside the boundary layer changeslinearly with the distance, i.e. decreasing toward theboundary with the adsorbent layer [1].Inside the sorbent layer, i.e. between the outside42S.N.Semenov et al./J.Chromatogr.A873 (2000) 39–51Fig. 2. Concentration distribution of the analyte in the vicinity of the adsorbent layer boundary.and inside boundary of a sorbent, the analyte con-centration distribution is described by the followingequation [3]≠ci≠q≠ci] 1 ] 5Di? ]]≠t≠t≠x22(3)whereciis the concentration of the free analyte inthe adsorption layer,qis the concentration of thebound (adsorbed) solute, andDiis the diffusioncoefficient of the free analyte in the adsorption layer.The initial boundary conditions may be described byinitial extraction into pure adsorbent layer and thecondition of the wall impermeability at the innerboundary of the adsorbent layerce(t50)50 atx.and≠ci] 50 atx5h≠x(4)layer. However, the initial saturated layer is extreme-ly thin compared to the adsorption layer width, and itis established almost instantaneously (see AppendixA).The diffusion and sorption of an analyte in Eq. (3)can be solved ifqscd, also identified as the adsorptionisotherm, is known. The simplest form of thisadsorption isotherm can be described by the Lang-muir isotherm [3]qskcq(c)5 ]]qs1kc(6)whereqsis the maximum concentration of theadsorbed solute at saturation andkis the sorbentpartition constant. The adsorption isotherm wasassumed to be the sum of two partsq(c)5kcandqscd5qsqsatc. ]k(8)qsatc# ]k(7)(5)wherehis the adsorbent layer thickness. It wasassumed that a very thin saturation layer is alreadypresent at the external boundary of the adsorbentS.N.Semenov et al./J.Chromatogr.A873 (2000) 39–5143This approach allows for the consideration of twoseparate regions in the adsorbent layer, i.e. saturationregion, and non-saturation region, respectively (Fig.3). A transition between these two regions occurs,when the free analyte concentration in the adsorbentlayer reaches its critical valuecs5qs/k. Further-more, this approach simplifies the adsorption modelto the class of problems with moving boundaries[12]. The time dependence of the moving boundarycoordinatex(t) between the aforementioned regionscan be described by the equationqscisx,td5 ]k(9)approach should be coupled with the examination ofthe displacement process kinetics.For analyte concentrations low enough to considerthe linear adsorption isotherm, Eq. (3) reduces to≠ciDi≠2ci] 5 ]] ? ]]≠t11k≠x2(11)The adsorption layer becomes completely saturatedforx(teq)5h(10)i.e., the saturation boundary approaches the innerboundary of the adsorption layer. The adsorptionlayer saturation time (teq), also known as theequilibration time, can be estimated by solving Eq.(10). Similarly, the approximation of the adsorptionisotherm by Eqs. (7) and (8) reduces the mathemati-cal problem to solving Eq. (3) in the saturatedregion.In addition, this approach allows one to modelcases where a single analyte or several analytes areextracted and adsorbed to different adsorption sites.In the case where several analytes are extracted andcompete for the same adsorption sites, a similarwhere the parameterDi/(11k)represents the effec-tive analyte diffusion coefficient which accounts forthe analyte adsorption / desorption in the sorbentlayer. This effective diffusion coefficient should berelatively small for a strong adsorbent, i.e. fork41. Lower effective diffusion is common in chroma-tography [12], where peak broadening may occurdue to diffusion combined with the adsorption / de-sorption in a column coating.The diffusion equation for the free analyte in thesaturation region has the form≠ci≠2ci] 5Di? ]]≠t≠x2(12)The typical distribution of both free and boundanalyte in the adsorbent layer is presented in Fig. 4.The boundary conditions at the sorbent layer / ana-lyzed volume boundary should describe the continui-ty of the analyte concentration and the analyte flow-rate in the direction perpendicular to the boundary.Thus, the first boundary condition can be writtensimply ascesx5d5cisx5d(13)Fig. 3. Langmuir isotherm (solid line) and its approximation in this article (dashed line). [ Pobierz całość w formacie PDF ]
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