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Application of Fourier transform infrared ellipsometry to assess the concentration of biological molecules

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Application of Fourier transform infrared ellipsometry to assess the concentration of biological molecules
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  See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/10995480 Application of Fourier Transform InfraredEllipsometry to Assess the Concentration of Biological Molecules  Article   in  Applied Optics · January 2003 DOI: 10.1364/AO.41.007339 · Source: PubMed CITATIONS 20 READS 61 4 authors , including: Some of the authors of this publication are also working on these related projects: Infrared polarimetry for double glazing research   View projectInfrared Spectroscopic Ellipsometry with Synchrotron Light   View projectEnric Garcia-CaurelÉcole Polytechnique 85   PUBLICATIONS   732   CITATIONS   SEE PROFILE Laurent SchwartzAssistance Publique – Hôpitaux de Paris 145   PUBLICATIONS   2,750   CITATIONS   SEE PROFILE All content following this page was uploaded by Enric Garcia-Caurel on 04 January 2017. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the srcinal documentand are linked to publications on ResearchGate, letting you access and read them immediately.   Application of Fourier transform infraredellipsometry to assess the concentration ofbiological molecules Enric Garcia-Caurel, Bernard Dre´villon, Antonello De Martino, and Laurent Schwartz Spectroscopic ellipsometry is a noninvasive optical characterization technique mainly used in the semi-conductor field to characterize bare substrates and thin films. In particular, it allows the gathering of information concerning the physical structure of the sample, such as roughness and film thickness, aswell as its optical response. In the mid-infrared   IR   range each molecule exhibits a characteristicabsorption fingerprint, which makes this technique chemically selective. Phase-modulated IR ellipsom-etry does not require a baseline correction procedure or suppression of atmospheric CO 2  and water-vaporabsorption bands, thus greatly reducing the subjectivity in data analysis. We have found that ellipso-metric measurements of thin films, such as the solid residuals left on a plane surface after evaporationof a liquid drop containing a given compound in solution, are particularly favorable for dosing purposesbecause the intensity of IR absorptions shows a linear behavior along a wide range of solution concen-trations of the given compound. Our aim is to illustrate with a concrete example and to justify theo-retically the linearity experimentally found between radiation absorption and molecule concentration.For the example, we prepared aqueous solutions of glycogen, a molecule of huge biological importancecurrentlytestedinbiochemicalanalyses,atconcentrationsrangingfrom1mg  lto1g  l,whichcorrespondto those found in physiological conditions. The results of this example are promising for the applicationof ellipsometry for dosing purposes in biochemistry and biomedicine. © 2002 Optical Society of America OCIS codes:  120.2130, 170.1420, 170.3890, 240.0310, 310.6870. 1. Introduction Standard spectroscopic ellipsometry 1 is a noninva-sive optical technique, generally performed in the visible and the near-ultraviolet range   270 to 800nm  , that was applied for several decades to charac-terize surfaces and thin films. In particular, thetechnique makes it possible to determine the opticalresponse of the sample as well as to gain informationaboutitsphysicalmicrostructuresuchasthepossiblepresence and thickness of surface coatings. Ellipso-metric measurements in the mid-infrared   IR   1 to12   m   have the additional advantage of probing themolecular vibrational modes of the sample com-pounds, thus giving the technique a chemical sensi-tivity because each molecule has a particular mid-IRradiation absorption pattern. Apart from ellipsom-etry, there are several vibrational spectroscopic tech-niques such as IR-absorption spectroscopy or Ramanspectroscopy that have demonstrated a remarkableperformance in material science for substance iden-tification or discrimination. 2–5 This chemical sensi-tivity also oriented the researchers to apply IRspectroscopic techniques to molecule characteriza-tion in analytical chemistry, biochemistry, and med-icine. 6,7 The requiredpropertiesof atechnique to besuccessfully applied in routine chemical or biochem-ical analytical tasks are quickness, precision, and ac-curacyontheabsoluteconcentrationquantificationof a given compound. The fast degradation of somemolecules, such as proteins or enzymes, when theyare placed out of their natural media for inspectionrequires quickness of application of the characteriza-tion technique. Further, the precise and accurateidentification of a given molecule and the measure-ment of its absolute concentration in a whole samplearedeterminants. Accordingtotheserequirements,IR ellipsometry appears to be an adequate technique E. Garcia-Caurel   garcia@poly.polytechnique.fr  , B. Dre´villon,and A. De Martino are with the Laboratoire des Interfaces etCouches Minces, Unite´ Mixte de Recherche 7647, E´cole Polytech-nique, 91128 Palaiseau, France. L. Schwartz is with Service deRadiothe´rapie, Hoˆpital Pitie´-Salpetrie`re, 75013 Paris, France.Received27May2002;revisedmanuscriptreceived4September2002.0003-6935  02  347339-07$15.00  0 © 2002 Optical Society of America 1 December 2002    Vol. 41, No. 34    APPLIED OPTICS 7339  because of its quickness   a typical spectrum can bemeasured in seconds   and, as is reported in this pa-per, because ellipsometry allows the identification of a given molecule by its characteristic IR-absorptionpattern and the determination of its absolute concen-tration. The dosing capability is supported by thefact that in ellipsometry, as well as in other vibra-tional spectroscopic techniques, the intensity of theabsorptions caused by a proven compound dependson its concentration in the sample. In this way, wehave found a favorable property of ellipsometry fordosing purposes. In particular, the intensity of IRabsorption of thin layers of solid residuals, left on thesurface of a plane substrate after evaporation of liq-uidsolutionsthatcontaintheprovenmolecule,showsa linear behavior along a wide range of concentra-tions of the given molecule in the srcinal solutions.The goal of this paper is to show empirically and to justify theoretically the existence of the above-mentioned linear relation between the intensity of absorbedradiationmeasuredbyellipsometryandthemolecule concentration in a given range. To do so,we performed the following experiment: we mea-sured the optical response, i.e., the absorption, of aglycogen layer left as a solid residual on a gold re-flecting plane surface after the evaporation of a dropofanaqueoussolutioncontainingthispolysaccharidein a known concentration, and then we correlated themeasured absorption with the concentration. In apreliminary study 8 we showed that the dependencebetween the intensity of absorbed IR radiation andthe glycogen concentration from 0.3 to 1 g  l was lin-ear. Inamoreaccurateexperiment,reportedinthispaper, we improved the sample preparation method,which allowed us to reduce the minimum detectableconcentration to as little as two orders of magnitudein comparison with the former attempt. In particu-lar, we show that linearity between IR absorptionand glycogen concentration is also found, and we pro- vide a theoretical argument to support this finding.The knowledge of this linearity allows, as a first step,the calibration of the measured optical responsegiven by samples with known concentrations of theproven molecule and, as a second step, the dosage of the concentration of this molecule from the opticalresponse of an unknown sample. Accordingly, the paper is organized as follows.First, a concise description of the Fourier transforminfrared   FTIR   ellipsometer is provided. Second,the principles of an ellipsometric measurement arereviewed to clarify the physical meaning of the mag-nitudes measured. Third, we present the descrip-tion of the results of an application exampleconsisting of the dosage of glycogen dissolved in wa-ter. Finally, there is a discussion that includes atheoretical justification of the results found. Glyco-gen has been selected as an example because it is amolecule that plays a major role in cell biology andthat has been characterized by different techniques,FTIR spectroscopy among them, 9,10 giving us the op-portunity to compare the results obtained with ourFTIR ellipsometer. 2. Experiment  A. Fourier Transform Infrared Ellipsometry Ellipsometrymeasuresthechangeinthepolarizationstate of a radiation beam after its reflection on thesurface or its transmission through the volume of agiven sample. An ellipsometric measurement is ex-pressed in terms of two angles,    and   , that arerelated to the complex reflectivity ratio   , defined as   r  p  r s  tan    exp   j  , (1)where  r  p  and  r s  are the Fresnel reflectivity coeffi-cients in polarization parallel and perpendicular, re-spectively, to the plane of incidence on the samplesurface. Working with    and    spectra has thedrawback that a baseline correction must be done forboth magnitudes. To overcome this problem, weworked with the optical density, defined 11 as  D  ln  tan      tan      j         (2)for a semi-infinite substrate coated with a singlelayer. The bars over    and    indicate that thesemagnitudes correspond to the bare substrate. Themain advantage of the optical density consists of eliminating the spectral features caused by the sub-strate, therefore enhancing those that are due to thecoating. In a common spectra, an absorption with aLorentzian-like shape appears in the real part of   D ,Re  D , as a Lorentzian peak and in the imaginarypart, Im  D , as an inflection. For practical reasons,we calculated the absolute value of the first deriva-tive of the imaginary part of   D ,   Im   D  , because itallowsananalysisoftheIR-absorptionfeaturesofthesample without the necessity to carry out the alwayssubjective baseline correction. Another advanta-geous characteristic of    Im   D   is that the signatureleft by an absorption appears in   Im   D   as a sharperand narrower peak than the corresponding one in Re  D . This last feature of    Im   D   implies an enhance-ment of a peak resolution with respect to that of Re  D because two near peaks are, in general, better re-solved in an   Im   D   spectrum, owing to their sharp-ness, than the corresponding ones appearing in a Re  D spectrum. Asanexample,Fig.1showsthreesim-ulated spectra, Re  D , Im  D , and   Im   D   that corre-spond to a semi-infinite substrate covered with a thin  0.1-  m   film characterized by two Lorentzian ab-sorptions centered at 2005 and 2060 cm  1 . In thefigure the spectra corresponding to Re  D  and   Im   D  arecomparedtoshowhowthesharpnessofthepeaksin   Im   D   allows a better resolution than those in Re  D . As we have previously stated, the two absorp-tions cause in the Im  D  spectrum two well-definedinflections.The basic optical elements common to all ellipsom-eters, apart from the radiation source and a detectionsystem, are the following: a linear polarizer placed just after the source; the sample, considered here asan optical element because it causes variations in the 7340 APPLIED OPTICS    Vol. 41, No. 34    1 December 2002  state of polarization of the radiation beam reflectedon it; and another polarizer called an analyzer be-cause it is used to analyze the polarization changescaused by the sample. Ideally, ellipsometric param-eters for a given wavelength are deduced from thecombination of the different beam intensities mea-sured after the optical polarizer is placed at a seriesof different orientations. A significant increase inthe acquisition rate is achieved by the placement of aphotoelasticmodulatorafterthepolarizertogenerateperiodically the needed ensemble of polarizationstates at a high frequency   50 kHz  . As an addi-tional advantage, the use of a photoelastic modulatordoes not require the movement of the polarizer, thuseliminating mechanical vibrations that could deteri-oratetheaccuracyandtheprecisionoftheapparatus.When dealing with IR radiation, it is common to useFourier transform sources that generate interfero-gramsbythechangingperiodicallyoftheopticalpathdifference between two interfering beams. Underideal conditions, the ensemble of measurements re-quired to determine the ellipsometric parametersshould be done at a fixed optical path difference. Inreal conditions the path difference is varied continu-ously owing to the mechanical constraints related tothe design of the interferometer. To minimize theerrors related to the fact of working under nonidealconditions, one must generate the ensemble of polar-ization states in a lapse of time during which thechange of the optical path difference can be consid-erednegligible. Thereforethefrequencyofthemod-ulator and those of the generation of interferogramsmust be as different as possible. In our case, theratio between those two frequencies is approximately100, thus giving an acceptable approximation to theideal conditions and allowing the acquisition of acomplete interferogram at 4 cm  1 of resolution in 4 s.Several interferogram accumulations are required toimprove the sensitivity of the ellipsometric measure-ments and hence the noise-to-signal ratio. All themeasurements presented in this paper were takenwith an accumulation of 300 interferograms. Thedescribed sequence of optical elements, which is notthe only one possible, is known as the polarizer–modulator–sample–analyzer configuration and is theone used by our ellipsometer. More accurate detailsconcerning the alignment of the optical elements andthe calibration procedure are given elsewhere. 12,13  After Fourier transform of the interferograms, spec-tra were obtained in the range between 900 and 3000cm  1 by use of a liquid nitrogen–cooled mercury ca-dium telluride detector. A common practice in ellip-sometry consists of setting the incidence angle asnear as possible to the Brewster angle of the mea-sured sample to maximize the contrast between theFresnel coefficients   see Eq.   1   and thus the sensi-tivity of the measurements. The angle of incidenceof the described ellipsometer is approximately 72°becauseitwasinitiallyconceivedformeasuringsemi-conductors such as silicon and thin semiconductingfilms deposited on metals. For the kinds of samplereported in this paper, that is, thin organic filmsdeposited on metallic surfaces, as will be detailed inSubsection 2.B, the mentioned angle of incidence isalso suitable, thus allowing the measurements tohave an acceptable accuracy. B. Sample Preparation Several glycogen solutions were prepared in ultra-pure water with concentrations varying from 3 mg  lto 1 g  l. The basic sample preparation consisted of depositing a drop of 40   l of each solution on the baresurface of a substrate and leaving it to dry at roomtemperature. The substrates were Corning glassescoatedwithathin  2000-Åthick  goldfilmtoincreasethe overall system reflectivity and therefore thesignal-to-noiseratio. Theshapeofthesolidresidualof glycogen was circular with an average surface of 49    3 mm 2 , large enough with respect to that of theIR beam spot   10 mm 2  . A major inconvenience of this kind of preparation is the inhomogeneity of thedeposit. However, we found two ways to avoid, or atleast to minimize, this drawback. First, duringevaporation, the substrates were left on vibratingtables that vibrated the solution drops at a frequencybetween 30 and 60 Hz. At these frequencies theamplitude of the mechanical vibrations of the dropsinduced by the table was resonant, thus optimizingthe mixing of glycogen in the evaporating water andthe homogenization of the thickness of the resultingdeposit. Second, we found empirically that the solidresidual layer resulting from the evaporation of suc-cessive drops was more homogeneous and, of course,thicker than those obtained from the evaporation of asingle drop. Because the IR-absorbed intensity in- Fig.1. SimulatedRe  D ,Im  D ,and  Im   D  spectrathatcorrespondto a gold substrate covered with a dielectric thin film showing twoabsorptions centered at 2005 and 2060 cm  1 . For clarity reasons,the spectral values corresponding to Re  D  has been shifted 0.2units upward. 1 December 2002    Vol. 41, No. 34    APPLIED OPTICS 7341  creases with the amount of proven material, workingwith thicker deposits was the key to enhance themeasured absorption intensity and therefore to beable to reduce the minimum detectable glycogen con-centration limit. In particular, the deposits corre-sponding to concentrations from 0.1 to 1 g  l weregrown from two drops, the deposits corresponding toconcentrations from 10 mg  l to 0.1 g  l were grownfrom six drops, and the rest of them, with concentra-tions between 2.5 mg  l and 10 mg  l, required 15drops. Because all of these solutions were far frombeing saturated, whenever a new drop was depositedon an existing solid residual, it was dissolved anduniformly distributed into the solution. Later, oncethe drop was evaporated, a new solid residual wasformed. 3. Results Three spectra were measured at different locations of each glycogen deposit and then averaged to enhancethe signal-to-noise ratio and to minimize the errorscaused by the remaining thickness inhomogeneitiesof the deposits. In all cases, the spot size was smallenough to avoid overlapping between different mea-surements.Figure 2 shows the measured Re  D  and   Im   D  spectra corresponding to three glycogen layers depos-ited on gold-coated substrates. Glycogen character-istic IR absorptions give rise to a strong and wideband between 950 and 1150 cm  1 . On the above-mentioned band there are four prominent absorp-tions at 1030, 1050, 1080, and 1150 cm  1 , which arecommonly used for glycogen identification. 14,15 These absorptions may be attributed to the C  O  Obond-stretching vibration mode. The fact that thesame vibration appears at different positions is ex-plained by coupling effects of this mode with those of the surrounding atoms. In this way, absorptions at1030, 1050, and 1080 cm  1 are induced by the  O  CH 2  O  OH group, and the one at 1150 cm  1 is in-duced by the  O  C T  2  O  OH group, where  T   is a substi-tutional group of hydrogen. The enhancedsensitivity and resolution of    Im   D   reveal not onlythe four absorption peaks at 1030, 1050, 1080, and1150 cm  1 seen previously but also three more peaksat 1130, 1180, and 1210 cm  1 . The peak at 1180cm  1 canbeattributedtowaggingmodevibrationsof the methylene group,  O   CH 2  n  , and the one at 1210cm  1 can be attributed to a deformation vibrationmode of the O  O  H bond. 16  As for the peak at 1130cm  1 , it has not been possible to assign it to a given vibration mode. In all cases, although the width of the peaks remains independent of glycogen concen-tration, their height varies in a linear fashion. Toillustrate this dependence, we calculated for eachsample the area under the peaks forming the char-acteristic absorption band between 1030 and 1150cm  1 and plotted it against the concentration. Thefact that not all the deposits were grown with thesame number of drops of solution was accounted forby normalizing the calculated area of each sample tothe corresponding number of drops used to create themeasured deposit. A linear regression was fitted,and the correlation coefficient,  r , measured. Figure3 represents the normalized area for all the samplesand the best-fitted linear regression. The resulting value for the correlation coefficient 0.984 indicatesthat in the investigated range of glycogen concentra-tions there exists an evident linear correlation be-tween this last magnitude and the intensity of themeasured IR-band absorption. Accordingly, theseresults show that FTIR ellipsometry can be used toidentify a given molecule from its characteristic IR-absorption fingerprint and to dose its total concen-tration in a solution. 4. Discussion The fact of finding a linear relation between the con-centration and the intensity of the measured absorp-tioncanbeexplainedoratleastjustifiedintwosteps.First,wearegoingtoprovethat,afteracceptingsomegeneral considerations, it is possible to find a linear Fig. 2. Measured Re  D  and   Im   D   spectra corresponding to thedry glycogen layers from three aqueous solutions prepared withdifferent glycogen concentrations.Fig. 3. Normalized area under the absorption band appearing in  Im   D   between 1030 and 1150 cm  1 for all the samples   circles  and the best-fitted linear regression   solid line  . 7342 APPLIED OPTICS    Vol. 41, No. 34    1 December 2002
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