Near-infrared studies of glucose and sucrose in aqueous solutions: water displacement effect and red shift in water absorption from water-solute interaction
NNear-infrared studies of glucose and sucrose in aqueous solutions:water displacement effect and red shift in water absorption fromwater-solute interaction
Youngeui Jung and Jungseek Hwang , , ∗ Department of Physics, Pusan National University, Busan 609-735, Republic of Korea Department of Physics, Sungkyunkwan University,Gyeonggi-do, Suwon 440-746, Republic of Korea and ∗ Corresponding author: [email protected]
We use near infrared spectroscopy to obtain concentration dependent glucoseabsorption spectra in their aqueous solutions in the near-infrared range (3800 -7500 cm − ). We introduce a new method to obtain reliable glucose absorptionbands from aqueous glucose solutions without measuring the water displace-ment coefficients of glucose separately. Additionally, we are able to extractthe water displacement coefficients of glucose, and this may give a new gen-eral method using spectroscopy techniques applicable to other water solublematerials. We also observe red shifts in the absorption bands of water in thehydration shell around solute molecules, which comes from contribution of theinteracting water molecules around the glucose molecules in solutions. Theintensity of the red shift get larger as the concentration increases, which in-dicates that as the concentration increases more water molecules are involvedin the interaction. However, the red shift in frequency does not seem to de-pend significantly on the concentration up to our highest concentration. Wealso performed the same measurements and analysis with sucrose instead ofglucose as solute and compare.c (cid:13) OCIS codes: a r X i v : . [ c ond - m a t . m t r l - s c i ] O c t ndex Headings: Near infrared spectroscopy, Water displacement coefficient, Glucosesolution, Sucrose solution INTRODUCTION
The possibility of providing a direct, non-invasive approach to measuring glucose con-centrations in blood has inspired studies of the applications of infrared spectroscopy foranalyte detection in various solutions. It has been shown that glucose has many distinctinfrared (IR) absorption features in the far-infrared (FIR),[1–3] mid-infrared (MIR),[4–8]and near-infrared (NIR)[9–15] regions. However, water, the main component of blood, alsodisplays strong IR absorption features in these regions, with increased absorption as youmove further towards FIR. Water absorption modes in a wide spectral range can be foundin a literature.[16]In studies dealing with MIR analyte detection in blood,[4, 5] the experiments wereperformed on dry samples or using second derivative spectra to obtain concentrationdependence.[7] This causes a large inaccuracies due to an increase in noise because of deriva-tion. Water IR absorption in the MIR region as well as the FIR is overwhelming,[17] render-ing non-invasive glucose detection at physiological concentrations extremely difficult due tohigh water content in blood. In a recent work,[14] glucose absorption bands were extractedby using an independently measured water displacement coefficient of glucose. The waterdisplacement coefficient is a measure of the second order effect of the presence of glucoseon the spectrum of water. Since, at physiologically relevant concentration of glucose inblood, the water bands are orders of magnitude stronger than the glucose bands, incorrecttreatment can be a major source of error.In this study we introduce a new method to obtain reliable glucose absorption bandswithout measuring the water displacement coefficient separately. Because there is a strongwater absorption peak at 5200 cm − and almost no or negligible glucose absorption atthis frequency, we take advantage of this strong and isolated water absorption peak toremove water absorption from the measured transmission of aqueous glucose solutions. Byadjusting effective thicknesses of water in a liquid cell to match the amplitude of the waterpeak for six different glucose solutions in the same liquid cell we are able to remove waterabsorption bands accurately and to extract an accurate concentration dependent glucoseabsorption coefficient in solution. Additionally, we are able to obtain a water displacement2oefficients of glucose by using the concentration dependent effective thickness of waterin the cell. We also observe red shifts in the absorption bands of water in the solution.Similar there are red shifts from interacting water in macroscopic air-water and oil-waterinterfaces and in the hydration cell around nonpolar hydrocarbon solute groups.[18, 19]Water structure enhancement within hydration shells was reported.[20, 21] This indicatesthat water molecules around solute molecules are not free; they are interacting with solutemolecules. Our analysis shows that the number of interacting water molecules seems toincrease as the concentration of solute increases. We also apply the same method to anotherwater soluble material, sucrose, which has a higher molecular weight than glucose. Wecompare the results of sucrose with those of glucose. EXPERIMENTS
We prepared six different aqueous glucose and six sucrose solutions: the concentrationswere 1.00, 2.00, 4.00, 6.00, 8.00 and 10.00 g/dL. All solutions were prepared using anhy-drous D-(+)glucose (C H O ) purchased from Sigma-Aldrich (USA), sucrose (C H O )purchased from Junsei Chemical (Japan), and grade-3 deionized water. Aqueous sampleswere placed in a 250 ± µ m path-length liquid cell composed of glass. The cell was madeusing epoxy glue to attach 155 µ m thick pieces of microscope cover glass (Sargent-Welch,USA) to a 1-mm thick microscope slide (VWR Scientific, USA) forming a rectangular cham-ber ( ∼ × × ). By covering this with another microscope slide we created a250 ± µ m thick liquid cell appropriate for aqueous sample measurements. Reproducibilityand stability of the measurement system were tested before proceeding with the study. Wealso prepared a pure amorphous glucose pellet and a sucrose pellet melting the D-glucoseand sucrose powders, respectively. We measured those pellets to obtain the absorptioncoefficients of pure glucose and sucrose.A commercial Fourier transform infrared (FTIR) spectrometer, Bruker Vertex 80v wasused for collecting near infrared spectra. The optical setup consists of a 75 W tungstenlamp as a light source, a CaF beam splitter, and a room temperature deuterated triglycinesulfate (DTGS) detector. We measured transmittance spectra, T ( ω ), of samples on asample holder with a 5.0 mm diameter circular aperture and a resolution of 5 cm − over a range of 3800 - 7500 cm − . An empty glass cell was used as the reference for alltransmittance measurements except for the amorphous glucose and sucrose pellets. To3et transmittances of the two pellets an empty hole was used as the reference. We notethat for all transmittance measurements of liquid samples we used the same liquid cell.All transmittance spectra were taken at room temperature (23 o C). Absorption coefficientspectra, α ( ω ), were calculated from measured transmittances. MEASURED DATA AND ANALYSIS
We measured transmittance spectra of the six different glucose and six sucrose solutionsand pure water in the cell as well as pure amorphous glucose and sucrose pellets. Theabsorption coefficient can be extracted from a measured transmittance spectrum by usingthe well-known Beer-Lambert’s formula: α ( ω, C ) = − ln T ( ω, C ) d (1)where α ( ω ) is the absorption coefficient, T ( ω ) is the measured transmittance, C is theconcentration of the solution and d is the thickness of the sample. Figure 1 shows rawabsorption coefficients for the six glucose solutions, pure water, and a pure amorphousglucose pellet. For the solution samples (water and solutions) we used the same thickness d ∼ = 252 µ m since we used the same liquid cell. We also show a water absorption peakat 5200 cm − , which is a Lorentzian function. Since glucose absorption in the solution isvery weak compared with the water absorption at these concentrations, we can not see largedifferences among in solution spectra. In these solution spectra, we observe three strongwater absorption peaks in a spectral range between 3800 and 7500 cm − , which are near4000, 5200, and 6900 cm − . There are two physiologically relevant windows in the waterabsorption through this measured spectral range; one between 4000 cm − and 5200 cm − isthe combination region where four distinct glucose peaks are visible and the other between5200 cm − and 6900 cm − is the first overtone region where two broad glucose peaks whichare not as distinct or strongly absorbing as those in the combination region.To obtain the absolute magnitude of glucose absorption from a glucose solution, weinitially subtracted the measured water absorption coefficient from that of each solution. Asa first approximation, we assumed that the thicknesses of water are the same. Then we canformulate the subtraction procedure as follows: α sol ( ω, C ) − α w,d ( ω ) = − ln[ T sol ( ω, C )] d − (cid:104) − ln[ T w ( ω )] d (cid:105) (2)4
000 5000 6000 7000050100150 BA Frequency, ω (cm -1 ) α ( ω ) ( c m - ) pure water glucose 1 g/dL (0.056 M) glucose 2 g/dL (0.111 M) glucose 4 g/dL (0.222 M) glucose 6 g/dL (0.333 M) glucose 8 g/dL (0.444 M) glucose 10 g/dL (0.556 M) pure glucose water peak @ 5210 cm -1 A Fig. 1. (Color online) Absorption coefficients of a pure amorphous glucose (dotted dark blueline) a pure water (dash-dotted orange line), and six glucose aqueous solutions (from top tobottom; from low to high concentrations). We also show a water peak at 5210 cm − (greendashed line). In the inset A and B we show expanded views near 5150 cm − and 4750 cm − respectively.where d is the thickness of our liquid cell. α sol ( ω ) and α w,d ( ω ) are respectively the absorp-tion coefficients of a solution and pure water calculated using the cell thickness d = 252 µ m. T sol ( ω ) and T w ( ω ) are the measured transmittance spectra of the solution and purewater, respectively. Figure 2 (a) shows spectra resulting from this analysis procedure. Thereis only one clearly visible glucose peak at 4700 cm − , offset from the actual peak positionseen in figure 1 of 4740 cm − . Also, at 5200 cm − , there is a sharp downward peak, with thelarger peak for the higher concentrated solution. This concentration dependent downwardpeak appears in the difference spectra because we did not consider the water displacementeffect due to the glucose presence in the solution. When glucose is dissolved in water thevolume of the solution changes because each glucose molecule takes up a finite space. Wehave to take into account this (water displacement) effect to subtract an appropriate waterspectrum from the solution spectra.Our approach for solving the downward peak problem in the difference spectra shownin figure 2 (a) is as follows. There is absence or very weak absorption of glucose around5200 cm − , where water has a very strong absorption peak. It means that at that frequencyabsorption values of all solutions including pure water should be the same if we use a properthickness of water for each solution. We performed the following procedure to removean appropriate water absorption from the total absorption of each solution; by adjustingthe thickness of pure water so that its absorption value at 5200 cm − is the same as theabsorption value of each solution, we can then subtract a proper water spectrum from eachsolution spectrum to obtain pure glucose absorption due to glucose alone in each solution.We call the proper thickness of water for each solution the effective thickness of water. Theprocedure can be formulated as follows: α sol ( ω, C ) − α w,d eff ( ω ) = − ln[ T sol ( ω, C )] d − (cid:104) − ln[ T w ( ω )] d eff ( C ) (cid:105) (3)where d eff ( C ) is the effective thickness of pure water for each concentration and α w,d eff ( ω )is the absorption coefficient of water calculated using the effective thickness d eff ( C ), whichis dependent of the concentration. By performing the procedure, the concentration depen-dent negative peak, that was caused by subtracting too much water absorption, is removedalthough not completely. We will discuss this remaining downwards peak in the followingparagraphs. This uncovers new absorption peaks due to glucose that agree with the pureglucose absorption shown in figure 1, the dotted dark blue curve. The resulting absorptionspectra due to glucose in six solutions are shown in figure 2 (b). In contrast to the singlepeak evidence in figure 2 (a) at 4700 cm − , three others are obvious in the combinationregion and two in the first overtone region. Also, the peak centered at 4700 cm − in figure2 (a) has undergone a shift to the actual peak position of glucose at 4740 cm − . Glucoseabsorption bands in the first overtone region were also uncovered (see in the inset of figure2 (b)), displaying absorption at 5700 and 6360 cm − . We note that the relative intensitiesof the glucose peaks are revealed as well. The concentration dependent peak heights of thefour peaks in the combination region are displayed in figure 5 (a). They show an almost alinear dependence on concentration.In the inset of figure 2 (b) the peaks centered at 5700 and 6360 cm − have some visiblediscrepancies showing variation from the expected concentration dependence. In the firstovertone region it seems that the 4 g/dL solution (green curve) has a larger absorptionvalue than 6 g/dL (blue curve). However, looking at the 6 g/dL peak, it has a better-defined shape. Even though the 4 g/dL solution has a higher absorption value, the 6 g/dL6olution has a more well-defined absorption compared to its average height in the firstovertone region indicating a stronger real absorption. The same can be said for the 2 g/dLabsorption (red curve) due to glucose, which appears to have a lower absorption than the 1g/dL solution (black curve) in this region. Even though the area under the curves suggeststhat some weaker solutions have stronger absorption, the shape of the absorption peaksgives additional information about the concentration and a more accurate depiction of theconcentration dependence in the first overtone region. These results can be attributed tothe broader absorption peak of glucose in this region.[14] Due to a broader or worse definedpeak, it is more difficult to detect proper concentration levels through aqueous media. Asharper or narrower peak provides a greater chance to see the concentration dependence ofthe absorption peak at that frequency because it is a better defined peak.As we pointed out previously in figure 2 (b) we still have an extra feature near 5200 cm − ,which has both a peak (on lower frequency side) and a dip (on higher frequency side). Tounderstand this feature we simulate it with Lorentzian (reference) peaks. We found thatthere are three ways to produce such a feature. We show results of the three ways in figure3 (b), 3 (c) and 3 (d), respectively. In figure 3 (a) we show the reference Lorentzian peakalong with three peaks shifted the horizontal axis by ± − and one shifted peak by -100cm − . The Lorentzian peak can be described as follows: L peak ( ω ) = Aπ Γ / ω − ω c ) + (Γ / (4)where A is area under the peak, ω c is the center frequency of the peak, and Γ is the widthof the peak, which is the full width at half maximum (FWHM). In figure 3 (b) we showdifference between each shifted peak with various shifting amounts ( ω shift = -100, -5, -4, -3, -2, -1 and +5 cm − ) with a fixed width (Γ = 400 cm − ) and a fixed amplitude ( A = 200 cm − )and the reference peak; L shift ( ω ) − L ref ( ω ) = ( A/π )(Γ / { / [( ω − ω shift − ω c ) + (Γ / ] − / [( ω − ω c ) + (Γ / ] } . As we can see in the figure the more shifting produces the largerand better defined difference spectra. We note that the difference between the peak and dippositions do not change very much up to -100 cm − shift because of a large width 400cm − ofthe peak; 243 cm − for -100 case and 230 cm − for -5 case. But more shifting causes the largerinterval between the peak and the dip. The frequency at the zero crossing is shifted by a halfthe frequency shift amount; the difference for -100 cm − case the zero crossing frequency is1150 cm − . In figure 3 (c) we show difference between each peak at 5195 cm − (i.e. ω shift =7 cm − ) with various amplitudes ( A = 50, 100, 150 and 200 cm − ) and the reference peak; L amplitude ( ω ) − L ref ( ω ) = ( A/π )(Γ / { / [( ω − ω shift − ω c ) + (Γ / ] − / [( ω − ω c ) + (Γ / ] } ,where Γ = 400 cm − . Here we also change the amplitude of the reference peak accordingto each peak amplitude. The results are shown in the figure; the more intense peaks givethe larger differences. We note that the peak and dip positions are not at all dependentof the amplitude. In figure 3 (d) we show the difference between each broadened peak at5195 cm − (i.e. ω shift = 5 cm − ) with various widthes (Γ (cid:48) = 400, 450, 500, 550, 600, and650 cm − ) and the reference peak; L width ( ω ) − L ref ( ω ) = ( A/π ) { (Γ (cid:48) / / [( ω − ω shift − ω c ) +(Γ (cid:48) / ] − (Γ / / [( ω − ω c ) + (Γ / ] } , where A = 200 cm − and Γ = 400 cm − . As we cansee in the figure the sharpest peak gives the largest and most-defined difference. We alsonote that the peak (dip) position is red (blue) shifted as the width increases.From observation of these three cases we can conclude that the extra feature in figure 2(b) can be attributed to the second case i.e. amplitude changes with concentration. Theintensity of the sharp absorption band edge due to the interacting water around 5200 cm − isgetting larger as the amount of glucose increases, which is reasonable because more watermolecules get involved in the interaction with the glucose molecules as the concentrationincreases. We do not expect a concentration dependent change in the frequency of theinteracting water as long as we keep a relatively low glucose concentration in the solution.We fit the observed peak and dip feature near 5200 cm − in figure 2 (b) by using themodel of our second case. In figure 1 we show the reference water peak at 5210 cm − (greendashed line), here we only considered the sharp absorption edge part of the water absorptionband near 5200 cm − .[22] In figure 2 (b) we show an example fit (green dashed line) to thepeak and dip feature near 5200cm in the 10 g/dL spectrum. We note that the amplitude (orarea) of the reference peak is 3300 cm − and its width is 170 cm − . From the fit we find thatthe amount of red shift is quit small, (cid:39) − . However, the resolution of the frequencyshifting depends on the width of the reference peak considered. In our case the width (170cm − ) is quite large compared with the shift (2 cm − ) so it is not very resolvable. Still whatwe can tell clearly is that the water absorption peak experiences a red shift. Here one maywonder that the instrumental resolution used to collect the spectra is 5 cm − whereas theobserved shift in the water absorption band is around 2 cm − . However, we measure theresulting feature from the shift, which is much broader (about the width of the referencepeak) than the instrumental resolution shown in the figure. We also expect to observe red8hifts from other water peaks. To show this we display the absorption of pure glucose andthe extracted glucose absorption spectrum, α sol ( ω, C ) − α w,d eff ( ω ) for C = 10g/dL in a samepanel as shown in figure 4. In the figure we observe signatures of red shifts for other waterpeaks clearly. The signatures, which are strong dips, appear near sharp edges for waterabsorption namely, 3800 cm − , 5200 cm − , and 7000 cm − . So the red shifts seem to occurfor all water absorption peaks. Roughly, we can tell that the height of the peak or depth ofthe dip of the feature can be a measure of the intensity of the interaction (see figure 3 (c)).The resulting concentration dependent intensities of the red shift, height, and depth aredisplayed in figure 5 (b). As we expected, the extracted intensity is roughly proportional tothe glucose concentration. The deviation from the linearity may come from the uncertaintyin the water subtraction procedure.From the appropriate water subtraction procedure, which we described previously, we canobtain the effective thickness of water for each glucose solution. Figure 5 (c) displays theextracted effective thickness of water as a function of the glucose concentration. It shows astrong linear relationship between the effective thickness and the concentration from 1 g/dLthrough 10 g/dL. The water displacement coefficient is defined by the molar concentrationchange of water caused by the dissolution of a unit molar concentration of the solute. Themolar concentration is defined by the number of moles per a liter of solvent (in our case,water). More practically, the water displacement coefficient is the number of water moleculeswhich are replaced by a solute molecule in the solution. By using these definitions we canwrite down the effective thickness of water in the cell as a function of glucose concentration. d eff ( C ) = d (cid:104) C (cid:48) · w dis C (cid:48) · w dis (cid:105) and C (cid:48) ≡ M water · M solute C (5)where C is the concentration in g/dL, d eff ( C ) is the concentration dependent effectivethickness of water, M water is the molecular weight of water, M solute is the molecular weightof solute, d is the real thickness of the cell (in our case, 252 µ m) and w dis is the waterdisplacement coefficient. We see that C (cid:48) is a small quantity; 0.01 for 10 g/dL glucosesolution and 0.0053 for 10 g/dL sucrose solution, these are the maximum values for glucoseand sucrose solutions. The water displacement coefficient is roughly a single digit value. So C (cid:48) · w dis is small and we can rewrite the equation (5) approximately as follows: d eff ( C ) ∼ = d [1 + C (cid:48) · w dis · (1 − C (cid:48) · w dis )] or9 eff ( C ) (cid:39) d [1 + C (cid:48) · w dis ]= d + d · M water · w dis · M solute C (6)In the lower equation we made a further approximation assuming C (cid:48) w dis (cid:28)
1. This lastequation shows that d eff ( C ) is linear in the concentration C , which is what we obtain fromour analysis and the results shown in figure 5 (c). We fit the data points in figure 5 (c) to astraight line; d eff ( C ) = 251 . ± .
8) + 1 .
490 ( ± . C (in µ m). From the linear fitting weobtain the real thickness of the cell and the slope of the straight line. By using the fittingparameters we are able to estimate the water displacement coefficient of glucose. w dis = slope M solute · M water · d (7)where slope is the slope of the straight line. The water displacement coefficient of glucoseobtained is 5 . ± .
51 at 23 ◦ C. This means that one glucose molecule can take up thespace of 5.91 water molecules in the solution. This value seems to be rather large comparedto a value of 5.051 at 21 ◦ C reported in Ref [23]. We also note that the relative standarddeviation for the proposed method is 8.6 % (0.51/5.051) compared to a value of 0.056% (0.0035/6.245) from the direct density method reported in Ref [14]. The precision ofthis method for obtaining the water displacement coefficient is not as good as that of thedensity method. A new method introduced in the following paragraph allows us to obtain aconcentration dependent water displacement coefficient. The concentration dependent waterdisplacement coefficient of glucose (see lower figure 6) shows a better value for the coefficientat high concentrations; for 10 g/dL sample, the water displacement coefficient is 5.10, whichseems to be a more reliable value for the coefficient at 23 ◦ C.We also can obtain the water displacement coefficient from an another simpler methodas follows. By comparing intensities of an absorption peak of pure glucose (for example, at4000 cm − ) in figure 1 and the corresponding peak of glucose alone in solution in figure 2(b) we can estimate an effective thickness of glucose alone in solution compared to the totalthickness of the solution. If the total volume of the solution consists of glucose alone theabsorption coefficient of the solution sample would be identical to that of pure glucose. Sincethe absorption intensity of glucose is proportional to the effective thickness (or amount) ofglucose alone in solution the intensity ratio is the same as the effective thickness ratio as10he following equation, A solute.sol A solute.pure = C/M solute · w dis · N A [100 /M water + C/M solute · w dis ] · N A (8)where A solute.pure and A solute.sol are the peak heights of pure glucose and glucose in solution,respectively, C is the concentration in g/dL and N A is the Avogadro’s number. When wesolve for the water displacement coefficient, w dis , we get the following equation. w dis = A solute.sol · · M solute ( A solute.pure − A solute.sol ) · C · M water (9)This equation means that for a given concentration, if we know the water displacement of so-lute and its absolute absorption coefficient we can easily estimate the absorption coefficient ofsolute alone in solution. In other word if we can measure the absorption coefficient of solutealone in solution for a given concentration we are able to obtain the water displacement co-efficient of the solute. For example, we consider 10 g/dL glucose solution and the absorptionpeak at 4000 cm − . Then by using eq. (9) w dis = (3 . × × / [(72 . − . × × ∼ =5.10. Even though the value is slightly smaller than the previously extracted value (5.91) itis consistent with the previous one. The concentration dependent water displacement of glu-cose is shown in Fig. 6 along with the concentration dependent water coefficient of sucrose.It seems to be independent of concentration even though there are some noisy data pointsin the low concentration region due to the uncertainty in the water subtraction procedure.The water displacement coefficient of glucose shows a strong temperature dependence;5.051 at 21 ◦ C [23] and 6.245 at 37 ◦ C [14] and our extracted water displacement coefficientsof glucose seem to be consistent with other studies; at least our value is in between those twovalues obtained at two lower and higher temperatures. The temperature dependence in thewater displacement coefficient probably comes mostly from thermally induced morphologychange of glucose molecules in the water. More systematic studies should be performed ontemperature dependent water displacement of glucose. We note that, at very high concen-trations, the linear trend can not hold because interaction between nearest glucose moleculeswhich is an indirect repulsive interaction in water will become stronger as the concentrationincreases.We performed the same experiment and data analysis with a different solute, sucrose(C H O ), which has a larger molecular weight. The measured data and analysis resultsare displayed in figure 7, 8 and figure 9. Although there are some detailed qualitative11ifferences, the overall qualitative concentration dependent trends are very similar to thoseof glucose. There are four sucrose absorption peaks in the combination region and two peaksin the first overtone region as for glucose. One thing which we would like to note is thatthe relative intensities between the peaks are different. As we can see in the pure sucroseabsorption spectrum, the peak at 4390 cm − is relatively large. The recovered concentrationdependent peak height of sucrose absorption modes in the combination region are displayedin figure 9 (a). They show a linear dependence on the concentration as we expected. Weobserve an additional feature other than sucrose absorption peaks in figure 8 (b) as thosein figure 2 (b). We show an example fit to the feature for 10 g/dL only for the absorptionedge region. From this fitting we get that the red shift is very small around 2 cm − . Theconcentration dependent height and depth of the feature are shown in figure 9 (b). Thisindicates that water molecules around a sucrose molecule is not free; the absorption peaksdue to the water will be shifted to lower frequencies, i.e. red shifts, which is due to waterstructure enhancement within the hydration shells around solute molecules.[20, 21]We also display the concentration dependent effective thickness, d eff ( C ), ofwater in the liquid cell in figure 9 (c). We fit the data to a straight line; d eff ( C ) = 252 . ± .
4) + 1 .
427 ( ± . C (in µ m). By using eq. (7), and the ex-tracted slope of the line and d from the fit we can get the water displacement coefficientof sucrose, 10 . ± .
46 at 23 ◦ C. The water displacement coefficient tells us that a sucrosemolecule can take up space equivalent to 10.76 water molecules in the solution. We alsoused the other method (see eq. (9)) to obtain the water displacement coefficient of sucrose.For example, we consider the 10g/dL sucrose solution and the absorption peak at 4000cm − . Then by using eq. (9), w dis = (3 . × × / [(72 . − . × × ∼ = 9.35.Even though the value is slightly smaller than the previously extracted value (10.76) it isquite consistent with the previous one. The concentration dependent water displacementof sucrose is shown in Fig. 6. In low concentration region the data show more noise andseem to deviate from the concentration independent trend at high concentration due to theuncertainty in the water subtraction procedure in the low concentration region. The molec-ular weight of sucrose ( M sucrose = 342) is almost twice of glucose ( M glucose = 180) i.e. insolution a sucrose molecule also takes up almost twice the space of a glucose molecule. Thismay indicate that sucrose molecules in solution have elongated shapes instead of global ones.12 ONCLUSIONS
It is clear from our work as well as previous studies that water displacement is an impor-tant quantity that must be considered for a proper study of glucose concentration in aqueousmedia and blood. Our new method is fundamentally different from the study of Amerov,Chen, and Arnold, who realized the problem introduced by water displacement and com-pensated for it by using an independently measured water displacement coefficient basedon density measurements.[14] We introduce a new spectroscopic method which is simplewhere we remove water absorption bands accurately from measured glucose aqueous solu-tions without independent measurement of water displacement by the glucose. Using thelinear relationship on concentration found for the effective thickness of water in the liquidcell we can properly manipulate the spectra to remove water absorption and obtain reliableconcentration dependent glucose absorption bands. In the spectra obtained from the sub-traction procedure we observed signatures of interaction between water and solute moleculesin the solution. The red shift of the water absorption near 5200 cm − is around 2 cm − ,which is very small but clearly observable in the spectra. As we mentioned previously, theamount of shifting is not easily resolvable since the width of water absorption is quite broadcompared with the red shift. Additionally, we were able to extract the water displacementcoefficient of glucose, which is consistent with values reported in literatures.[14, 23] Theseresults may help to monitor non-invasively the glucose level in human body.This method has several advantages: first of all, by removing the need to measure thewater displacement coefficient independently, we can estimate a reliable water displace-ment coefficient from our concentration dependent spectrum, making it a self-consistentmethod which we can apply to other solutions. Actually, we also applied the samemethod to sucrose aqueous solution and got a reasonable water displacement coefficientof sucrose. The method of water displacement extraction in this paper can provide as anew general method using optical spectroscopy technique for other biological or organicmaterials. This method also allows us to observe red shifts in the difference spectra,which is not easy to detect with different experimental techniques. Similar red shifts wereobserved by other groups and other experimental techniques in different aqueous solutions,or water-oil and water-air interfaces. [18, 19] Our approach provides another useful toolto study water molecules in the hydration cell around a solute molecule in aqueous solutions.13 cknowledgement We thank T. Timusk and R. Peters for useful discussions. This workhas been supported by the special fund of Department of Physics at Pusan National Uni-versity, Busan, Republic of Korea. This work also was supported by the National ResearchFoundation of Korea Grant funded by the Korean Government (NRF-2010-371-B00008).14 glucose 1 g/dL (0.056 M) glucose 2 g/dL (0.111 M) glucose 4 g/dL (0.222 M) glucose 6 g/dL (0.333 M) glucose 8 g/dL (0.444 M) glucose 10 g/dL (0.556 M)
10 g/dL1 g/dL (a) α s o l ( ω , C ) - α w , d ( ω ) ( c m - ) pure glucose (x 1/22) fit (see figure 3 (b)) (b) α s o l ( ω , C ) - α w , d e ff ( ω ) ( c m - ) Frequency, ω (cm -1 ) Fig. 2. (Color online) (a) Glucose absorption bands in solutions obtained at six differentconcentrations by subtracting water spectrum from those of the glucose solutions. Waterdisplacement coefficient of glucose has not been considered on these spectra (see in the text).(b) Glucose absorption coefficients in six different solutions. Water displacement effects havebeen taken into account for the subtracting water absorption procedure (see in the text).The green dotted line is a fitted line to the feature near 5200 cm − with both peak and dipfrom a model calculation (see figure 3 (b) and corresponding text). The black dashed line inthe lower frame is the pure glucose absorption spectra with its intensity reduced by a factorof 22. In the inset we display an expanded view to show spectral features better in the firstovertone region. 15 .00.20.40.6 4000 5000 6000 7000-0.0050.0000.0050.010-0.0050.0000.0050.010 -0.0050.0000.0050.010 (a) reference with width 400 cm -1 ; L ref ( ω ) ctr freq. -100 ctr freq. -5 ctr freq. +5 L pea k ( ω ) Frequency, ω (cm -1 ) [ctr freq. = 5205 cm -1 ][amplitude = 200 cm -2 ] w650w400 (d) -5 (ctr freq.), w400 -5 (ctr freq.), w450 -5 (ctr freq.), w500 -5 (ctr freq.), w550 -5 (ctr freq.), w600 -5 (ctr freq.), w650 L w i d t h ( ω ) - L r e f ( ω ) -100 (x 0.1) [width = 400 cm -1 ][amplitude = 200 cm -2 ] -1-5 (b) -100 (ctr freq.) -5 (ctr freq.) -4 (ctr freq.) -3 (ctr freq.) -2 (ctr freq.) -1 (ctr freq.) +5 (ctr freq.) L s h i ft ( ω ) - L r e f ( ω ) amp50amp200 (c) [ctr freq. = 5205 cm -1 ][width = 400 cm -1 ] -5 (ctr. freq.), amp200 -5 (ctr. freq.), amp150 -5 (ctr. freq.), amp100 -5 (ctr. freq.), amp50 L a m p li t ude ( ω ) - L r e f ( ω ) Fig. 3. (Color online) (a) We show a reference peak which has its center at 5200 cm − andwidth 400 cm − . We also show two shifted peaks in horizontal direction by negative 5 cm − (dashed dotted red curve) and positive 5 cm − (dashed blue curve), respectively. In the insetwe expand the graphs near the peak region to show the shifts more clearly. (b) We also showresulting differences subtracted the reference peak at 5200 cm − from the shifted peaks byseven different amounts (see in the text). (c) We show resulting differences subtracted thereference peak at 5200 cm − from the peaks at 5205 cm − with four different amplitudes(see in the text). (d) (c) We show resulting differences subtracted the reference peak at 5200cm − from the peaks at 5205 cm − with six different widths (see in the text).16
000 5000 6000 7000-3-2-1012345 α sol ( ω ,C) - α w,d eff ( ω ), C=10g/dL pure glucose (x 1/22) water (x 1/40) α ( ω ) ( c m - ) Frequency, ω (cm -1 ) Fig. 4. (Color online) Comparison the pure glucose absorption and the extracted glucoseabsorption ( α sol ( ω, C ) − α w,d eff ( ω )) from 10g/dL solution. We note that we reduce theintensity of the pure glucose absorption by a factor of 22. We also show the water spectrumas well for comparison purpose and reduce its intensity by a factor of 40.17 .00.51.01.52.02.5 0 2 4 6 8 1025025526026527001234 (b) Depth Height he i gh t o r dep t h ( c m - ) (c) Effective Thickness linear fit: d eff ( C ) = 251.9 + 1.490 C ( µ m) d e ff ( C ) ( µ m ) Concentration, C (g/dL) d = 252 µ m w dis = 5.91 -1 -1 -1 -1 (a) pea k he i gh t ( c m - ) Fig. 5. (Color online) (a) The concentration dependent peak height of four absorption modesof glucose in the combination region. (b) The concentration dependent height and depth ofthe new feature in figure 2 (b). (c) Concentration dependent effective thickness of the cellextracted from the water subtraction procedure (see in the text). We observe a strong linearrelationship between the effective thickness of water and the glucose concentration.18 dis : sucrose w dis : glucose w d i s ( C ) Concentration, C (g/dL) Fig. 6. (Color online) We display the concentration dependent water displacement of glucoseand sucrose obtained by using eq. 9. BA Frequency, ω (cm -1 ) α ( ω ) ( c m - ) water sucrose 1 g/dL (0.029 M) sucrose 2 g/dL (0.058 M) sucrose 4 g/dL (0.117 M) sucrose 6 g/dL (0.175 M) sucrose 8 g/dL (0.234 M) sucrose 10 g/dL (0.292 M) pure sucrose water peak @ 5210 cm -1 Fig. 7. (Color online) Absorption coefficients of a pure amorphous sucrose (dotted darkblue) a pure water (dash-dotted orange), and six glucose aqueous solutions (from top tobottom; from low to high concentrations). We also show a water peak at 5200 cm − . In theinset A and B we show expanded views near 5150 cm − and 4750 cm − respectively.19 sucrose 1 g/dL (0.029 M) sucrose 2 g/dL (0.058 M) sucrose 4 g/dL (0.117 M) sucrose 6 g/dL (0.175 M) sucrose 8 g/dL (0.234 M) sucrose 10 g/dL (0.292 M)
10 g/dL1 g/dL (a) α s o l ( ω , C ) - α w , d ( ω ) ( c m - ) pure sucrose (x 1/20) fit (see figure 2 (b))
10 g/dL1 g/dL (b) α s o l ( ω , C ) - α w , d e ff ( ω ) ( c m - ) Frequency, ω (cm -1 ) Fig. 8. (Color online) (a) Sucrose absorption bands in solutions obtained at six differentconcentrations by subtracting water spectrum from those of the sucrose solutions. Waterdisplacement coefficient of sucrose has not been considered on these spectra (see in the text).(b) Sucrose absorption coefficients in six different solutions. Water displacement effects havebeen accounted for the subtracting procedure (see in the text). The black dashed line in thelower frame is the pure glucose absorption spectra with its intensity reduced by a factor of20. In the inset we display an expanded view to show spectral features better in the firstovertone region. 20 .00.51.01.52.02.5 0 2 4 6 8 1025025526026527001234 (b)
Depth Height he i gh t o r dep t h ( c m - ) (c) Effective Thickness linear fit: d eff ( C ) = 252.3 + 1.427 C ( µ m) d = 252 µ m w dis = 10.76 d e ff ( C ) ( µ m ) Concentration, C (g/dL) -1 -1 -1 -1 (a) pea k he i gh t ( c m - ) Fig. 9. (Color online) (a) The concentration dependent peak height of four absorption modesof sucrose in the combination region. (b) The concentration dependent height and depth ofthe new feature in figure 8 (b). (c) Concentration dependent effective thickness of water.We observe a strong linear relationship between the effective thickness of water and theconcentration. 21 eferences
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Essenpreis, and M. Cope. ”The influence of glucose concentration uponthe transport of light in tissue-simulating phantoms”. Phys. Med. Biol. , 1267–1287(1995). 23 ist of Figure Captions Fig. 1. Absorption coefficients of a pure amorphous glucose (dotted dark blue line) a purewater (dash-dotted orange line), and six glucose aqueous solutions (from top to bottom;from low to high concentrations). We also show a water peak at 5200 cm − . In the inset Aand B we show expanded views near 5150 cm − and 4750 cm − respectively.Fig. 2. (a) Glucose absorption bands in solutions obtained at six different concentrationsby subtracting water spectrum from those of the glucose solutions. Water displacementcoefficient of glucose has not been considered on these spectra (see in the text). (b) Glucoseabsorption coefficients in six different solutions. Water displacement effects have been takeninto account for the subtracting water absorption procedure (see in the text). The greendotted line is a fitted line to the feature near 5200 cm − with both peak and dip from amodel calculation (see figure 3 (b) and corresponding text). The black dashed line in thelower frame is the pure glucose absorption spectra with its intensity reduced by a factor of22. In the inset we display an expanded view to show spectral features better in the firstovertone region.Fig. 3. (a) We show a reference peak which has its center at 5200 cm − and width 400cm − . We also show two shifted peaks in horizontal direction by negative 5 cm − (dasheddotted red curve) and positive 5 cm − (dashed blue curve), respectively. In the inset weexpand the graphs near the peak region to show the shifts more clearly. (b) We also showresulting differences subtracted the reference peak at 5200 cm − from the shifted peaks byseven different amounts (see in the text). (c) We show resulting differences subtracted thereference peak at 5200 cm − from the peaks at 5205 cm − with four different amplitudes(see in the text). (d) (c) We show resulting differences subtracted the reference peak at5200 cm − from the peaks at 5205 cm − with six different widths (see in the text).Fig. 4. Comparison the pure glucose absorption and the extracted glucose absorption( α sol ( ω, C ) − α w,d eff ( ω )) from 10g/dL solution. We note that we reduce the intensity of thepure glucose absorption by a factor of 22. We also show the water spectrum as well forcomparison purpose and reduce its intensity by a factor of 40.24ig. 5. (a) The concentration dependent peak height of four absorption modes of glucosein the combination region. (b) The concentration dependent height and depth of thenew feature in figure 2 (b). (c) Concentration dependent effective thickness of the cellextracted from the water subtraction procedure (see in the text). We observe a stronglinear relationship between the effective thickness of water and the glucose concentration.Fig. 6. We display the concentration dependent water displacement of glucose and sucroseobtained by using eq. (9).Fig. 7. Absorption coefficients of a pure amorphous sucrose (dotted dark blue) a purewater (dash-dotted orange), and six glucose aqueous solutions (from top to bottom; fromlow to high concentrations). We also show a water peak at 5200 cm − . In the inset A andB we show expanded views near 5150 cm − and 4750 cm −1