Article pubs.acs.org/ac
2D Correlation Analysis: Sequential Order Judging He Huang,*,† Xiaomin Ding,†,⊥ Chunlei Zhu,§,⊥ Zhipeng He,† and Yibiao Yu*,§ †
Jiangsu Key Laboratory for the Design and Applications of Advanced Functional Polymeric Materials, College of Chemistry, Chemical Engineering & Materials Science, Soochow University, Suzhou 215123, China § Electronic Information School of Soochow University, Suzhou 215123, China S Supporting Information *
ABSTRACT: Using a two-dimensional (2D) correlation analysis technique to determine the sequential order of physical or chemical events has received keen interests in the past ten years. However, our continuous work demonstrates that the sequential order of events determined by the “sequential order” rules of this technique may lead to ambiguous or even wrong conclusions, because the physical significance of the sequential order in generalized 2D correlation analysis is neither well-defined nor meaningful in general situations, and the word “occur” used in the “sequential order” rules may easily give rise to ambiguity. In contrast to the integrated sequential order derived from periodic changes as in mechanical perturbation based 2D correlation infrared spectroscopy, there is a local/chronological sequential order for nonperiodic changes in general situations. The current work shows that the integrated sequential order in 2D correlation analysis is a reflection of the sequential order of the phases, i.e., phase sequence/difference. The integrated sequential order may indicate the relative state of two events (one event occurs/exists before or after the other one) according to a specific reference, only if both are obtained under the same frequency for periodic changes or even speeds for nonperiodic changes in general situations. The integrated sequential order may not always be able to reveal whether one event occurs/happens before or after another one for nonperiodic changes in terms of timings of happenings. For nonperiodic changes, the integrated sequential order is not so meaningful and must be replaced by the local/chronological sequential order. To judge whether one event occurs/happens before or after another one for two nonperiodic changes in general situations, the original spectral intensity changes must be verified to determine if a chronological/local sequential order exists between two events.
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published in the past ten years or so. However, our continuous work16−19 and that of other’s20 demonstrate that sequential order of events determined by the “sequential order” rules of generalized 2D correlation spectroscopy may lead to ambiguous or even wrong conclusions. In a previous publication,16 we addressed the issue of “sequential order” rules which are the bases of the second advantage of this technique. It was noted that, in generalized 2D correlation spectroscopy, the dynamic spectral intensity variations are generally nonperiodic, i.e., spectral intensity changes are largely instantaneous and monotonic, rather than a simple sinusoid as in mechanical perturbation-based 2D infrared (IR) spectroscopy. The sequential order of events in general situations, such as under temperature or pressure perturbations, would be localized, instead of taking an integrated or overall form as in the latter. So, we tested whether or not the “sequential order” rules, which are derived from periodic data, are applicable to such nonperiodic changes. It was found that the “sequential order” rules may correctly identify the local sequential order of two events in some cases but fail in some other cases. In addition, 2D
ince its appearance in early 1990s, generalized twodimensional (2D) correlation spectroscopy, originated from the mechanical perturbation-based 2D infrared (IR) technique, has been extended to various areas of spectroscopy, e.g., UV, near-infrared, Raman, fluorescence and dielectric relaxation spectroscopy, etc., or even to any form of analytical technique, e.g., chromatography, differential scanning calorimetry, microscopy, and so on. It has been widely used in many areas, from simple inorganic and organic compounds to polymers and complex biological systems. This has been attributed to its two major advantages: spectral resolution enhancement and determination of the sequential order of events via the so-called “sequential order” rules.1,2 Quite a number of studies,3−15 including our systematic studies in polymers,8−12 on the first advantage of this technique, spectral resolution enhancement, have found that variables such as band overlapping, bandwidth change, peak shift, and experimental data set may have a big influence on the final 2D plots. In other words, there is a large uncertainty on the new features revealed in the 2D plots which do not necessarily correspond to real infrared absorption bands. Using the second advantage of this technique to determine the sequential order of physical or chemical events has become more popular, and numerous papers in this field have been © 2013 American Chemical Society
Received: October 2, 2012 Accepted: January 27, 2013 Published: January 28, 2013 2161
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correlation analysis is not able to distinguish the local sequential order from the rate difference of events. Our conclusion was that synchronous and asynchronous spectra in the generalized 2D correlation spectroscopy do not necessarily provide the information on the local sequential order or rate difference of events.16 Our recent experimental results17−19 also supported the above conclusion on 2D correlation analysis. Since the publication of this work, we received supports,20−24 including oral and private communications,25 as well as several criticisms26−28 which are unfortunately not convincing. The latter is the driving force for us to shed further light on the “sequential order” issue of 2D correlation spectroscopy. So, in this report, the physical significance that the sequential order represents in 2D correlation spectroscopy was first elaborated and emphasized, then the various understanding or interpretation that may occur on the sequential order were discussed. Finally, an experimental example was used to demonstrate how problems regarding sequential order results may arise using 2D correlation analysis and how to judge the sequential order of events in general situations.
though it is easy to do so (our simulation study was also included in the supporting materials). These sequential order rules have been used since the early 1990s to determine if one dipole-transition moment associated with the band at wavenumber ν1 reorients before or after the transition moment at ν2. However, no one has asked the following question so far: can the sequential order (in terms of phase relationship) of two sinusoidal changes represent the sequential order that two nonperiodic changes occur in terms of timings of happening? To answer this question, one needs to understand what the sequential order really represents in mechanical perturbationbased 2D infrared spectroscopy. From the demonstrations using simulation data (see supporting materials), as well as the theory of the mechanical-perturbation based 2D IR spectroscopy, it is very clear that the sequential order of two band intensity changes derived from the mechanical-perturbation based 2D IR spectroscopy is determined by the phase dif ference of two sinusoidal functions; one event with a larger/earlier phase occurs before another one with a smaller/later phase, and vice versa. In addition, the two sinusoidal functions have the same frequency, which is actually the prerequisite for the comparison on the sequential order of two events with sinusoidal functions. Technically, phase difference between two entities at various frequencies is undefined and does not exist. Because the sequential order is determined by the phase dif ference of two events with sinusoidal functions having the same frequency, apparently, the sequential order in mechanical perturbation-based 2D infrared correlation spectroscopy indicates the sequential order of the phases, or phase sequence of two events, i.e., the order of sinusoid passing through a certain value, see, the maximum. Naturally, such a sequential order (larger or smaller, earlier or later phase) is in the frequency domain. Phase refers to state. In other words, “sequential order” rules in mechanical perturbation-based 2D infrared correlation spectroscopy reveals the state of event changes, i.e., the state of one event is/is present/exists before/ after that of another one. It does not give any information on the occurring sequential order of event changes, i.e., timings of the event happenings. This phenomenon is analogous to two moving sea waves. What we see is one sea wave is present/exists or moves before or after the other, using the sea shore or something else as a reference, no matter which one occurs (happens or is created) first. The phase sequence (dif ference) in mechanical-perturbation based 2D IR correlation spectroscopy is also analogous to two athletes running around a race track at the same speed and direction but starting to run at different positions on the track at the same time. They pass a point at different instants in time. But the time (phase) difference (here time zone is also analogous to phase difference) between them is a constant same for every pass since they are at the same speed and in the same direction. If they were at different speeds (different frequencies), the phase sequence (dif ference) is undefined. However, when we are talking about the sequential order of event changes (nonperiodic band intensity changes) in spectroscopy, i.e., one event occurs before or after another, the integrated/overall sequential order in the frequency domain is meaningless16 (more on this later), and the sequential order should refer to time domain, i.e., timings of the event happenings. In this case, another concept, chronological order is usually used. Chronological order refers to the arrangement of events progressively on the basis of a timeline. If things are
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EXPERIMENTAL SECTION IR Study on the Evaporation of a Mixture of Solvents. The solvent mixture consisting of dimethyl sulfoxide (DMSO) and carbon tetrachloride (CCl4) was sandwiched between two KBr windows. IR spectra were collected at room temperature by coadding 32 scans with a resolution of 2 cm−1 on a Nicolet 6700 spectrometer equipped with a mercury cadmium telluride (MCT) detector. Simulations. At least two bands must be considered while comparing the sequential order of their intensity changes. Spectra were simulated using two Gaussian bands centered at 1720 and 1650 cm−1 with no peak shift or bandwidth change. Two-Dimensional Correlation Analysis. A standard twodimensional correlation analysis was carried out; that is, the average (or mean) spectrum of the spectra in the chosen set is subtracted from each of the spectra to obtain a set of “dynamic” spectra. Synchronous and asynchronous correlation spectra are then calculated from these dynamic spectra using the Hilbert transform suggested by Noda.1,2 In the 2D correlation plots, shaded regions indicate negative correlation intensities, while unshaded ones positive. The calculation was performed by using the 2Dshige software, written at Kwansei Gakuin University. The contour level is 8 when not specified.
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RESULTS AND DISCUSSION
To further tackle the “sequential order” issue in generalized 2D correlation spectroscopy, it is necessary to revisit the “sequential order” rules in mechanical perturbation-based 2D infrared spectroscopy, because the former is an extension of the latter. Revisiting the “Sequential Order” Rules in Mechanical Perturbation-Based 2D Infrared Spectroscopy. It may be superfluous to repeat the “sequential order” rules in mechanical perturbation-based 2D infrared spectroscopy. For the completeness of discussion, however, the rules and the development of the rules29 are cited in the supporting materials. The “sequential order” rules were all derived from the phase relationships of dynamic signals with a simple sinusoid waveform. The rules are straightforward in terms of phase relationship of dynamic signals with sinusoid waveform and, therefore, were not substantiated even with simulation data, 2162
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Figure 1. Peak intensities of two bands centered at 1720 and 1650 cm−1 decrease simultaneously, taking the exponential form of y = e−0.2x and y = e−0.1x, respectively.
described or shown in chronological order, they are described or shown in the order in which they happened. This chronological order is equivalent to the local sequential order (in contrast to the integrated/overall sequential order) we proposed a couple of years ago.16 More specifically, the sequence that two events occur (happen) is determined by the starting time of each event, which has nothing to do with the overall process each event experiences. Assume two events A and B take the function of f(t) and g(t) respectively. If Δf(t) = 0 when t < t1, and Δf(t) ≠ 0 when t = t1, A starts to change at t1. Similarly, t2 is the time that B starts to change. If t1 < t2, the change of A occurs/happens before that of B. If t1 > t2, A’s change occurs/ happens after that of B. If t1 = t2, A’s and B’s changes occur/ happen at the same time, i.e., no sequential order. This may be demonstrated by two athletes running along the 100 m race track. Assuming athlete 1 starts to run at time t1, and athlete 2 starts running at time t2, after the starting gun has been fired. If t1 < t2, athlete 1 starts to run before athlete 2. If t1 > t2, athlete 1 starts to run after athlete 2. If t1 = t2, two athletes start running at the same time. Of course, any time-domain function can be projected onto the frequency-domain through the Fourier transform. Although one time-domain signal occurs before a second time-domain signal in time, the phase of the frequency-component of the earlier signal is usually larger or earlier than that of the retarded signal, the reverse may not be true always. The latter is selfevident for the two events in cases 1 and 3 in the simulation study (see the Supporting Information), where the band intensities at 1650 and 1720 cm−1 start to change at t = 0; that is, they change simultaneously in the time-domain, but with a phase difference in the frequency domain. Obviously, “sequential order” rules in mechanical perturbation-based 2D infrared may not be able to tell the order of two
events in terms of timings of the happenings, i.e., the chronological/local sequential order. In summary, the sequential order in mechanical perturbationbased 2D infrared correlation spectroscopy indicates the sequential order of the phases, or phase sequence of two events in the frequency domain. It reveals the state of event changes, i.e., which one is present/exists before/after another one. It may not be able to tell the chronological/local sequential order of two events in terms of timings of the happenings. “Sequential Order” in Generalized 2D Correlation Spectroscopy. In contrast to the mechanical perturbationbased 2D infrared (IR) spectroscopy, the dynamic spectral intensity variations in generalized situations are generally nonperiodic; that is, spectral intensity changes are largely instantaneous and monotonic. The synchronous and asynchronous 2D correlation intensities of two dynamic spectra ỹj(v1),ỹj(v2) are therefore calculated in a different way (see ref 1 and the Supporting Information). However, the “sequential order” rules of the mechanical perturbation-based 2D IR spectroscopy were adopted and automatically transferred to the generalized methodology with a simplified statement, as cited below: “The sign of an asynchronous cross peak becomes positive if the intensity change at ν1 occurs predominantly before ν2. On the other hand, the peak sign becomes negative if the change at ν1 occurs predominantly af ter ν2. However, this sign rule is reversed if the synchronous correlation intensity at the same coordinate becomes negative, i.e., Φ(ν1, ν2) < 0. Furthermore, if the intensity of the synchronous cross peak is zero, the sequential order cannot be determined.” The problem of such a transfer created has been elucidated in our previous publication.16 To reiterate, one example is given below (Figure 1) and enough to demonstrate how the problem associated with sequential order judgment could be created 2163
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the sequential order rules, “one event occurs before/after another one”, can be ambiguous, because the wording “occur” is likely to lead to ambiguity. In addition to the many other meanings, “occur” may have the meaning of “happen” or “exist (is present)”. When something occurs, it happens. When something occurs in a particular place, it exists or is present there. It should be very clear now that the integrated sequential order derived from 2D correlation analysis is a reflection of the sequential order of the phases, or simply speaking, phase sequence/difference. It may indicate the relative state of two events (one event occurs/is present/exists before/after the other one), according to a specific reference, only if both under same frequency for periodic changes or even speeds for nonperiodic changes in general situations. Therefore, the integrated sequential order may not be able to reveal whether one event occurs/happens before/after another one for nonperiodic changes in terms of timings of happenings. In general situations, two spectral band intensity changes are not always under even speeds, the integrated sequential order of these two band intensity changes is therefore not a fixed one under the period of experimental observation. This explains perfectly why different integrated sequential orders could be obtained by selection of different sampling intervals from a certain set of experimental data.17,20 Such a varying integrated sequential order is obviously not so meaningful and must be replaced by the local/chronological sequential order. To judge whether one event occurs/happens before/after another one in general situations, the original spectral band intensity changes must be verified to determine if a chronological/local sequential order exists between two events. Below, we will demonstrate how problem may arise from 2D correlation analysis regarding the integrated sequential order (when not specified, sequential order refers to the integrated sequential order) and how to judge the real chronological/local sequential order of events (if exists) by using the evaporation of an organic solvent mixture as a convincing example. Sequential Order Judging: an Experimental Example. This solvent mixture consists of dimethyl sulfoxide (DMSO) and carbon tetrachloride (CCl4), with a small amount of water in DMSO due to its easy absorption of water. Figure 2A shows the IR spectra of DMSO and CCl4. CCl4 has negligible absorptions above 1000 cm−1, which facilitates the analysis on the band intensity changes of DMSO functional groups with evaporation time. The solvent mixture was sandwiched inbetween two KBr windows so that a confined environment was created and the evaporation rate is relatively slow (Figure 2B). The spectra in the first 6 min of evaporation were recorded (Figure 2B). Except for the region of above 3100 cm−1, no significant spectral changes can be observed, confirming the relatively slow evaporation rate. To simplify the discussion, we are focused on the major absorption bands of DMSO that are not overlapped with those of CCl4, i.e., 3422, 3002, 2912, 1653, 1437, 1406, and 1315 cm−1. The 3422 and 1653 cm−1 bands are from water in DMSO. The band assignments are given in Table 1. Figure 3 is the 2D plots for DMSO evaporation in the region of 2850−3050 cm−1, where one can find the symmetric (2908 cm−1) and asymmetric (2992 cm−1) C−H stretching vibrations from the CH3 groups of DMSO. From the signs of the cross peaks (Φ (2908, 2992) > 0, and Ψ (2908, 2992) < 0), it is easy to conclude that the intensity change of the symmetric C−H stretching band (2908 cm−1) occurs after that of the asymmetric C−H stretching band (2992 cm−1). Note that
using 2D correlation analysis. As shown in Figure 1, the cross peaks at (1720, 1650) is positive in the synchronous and asynchronous plots (Figure 1c,d), suggesting that the intensity change at 1720 cm−1 occurs before that at 1650 cm−1, according to the “sequential order” rules. This integrated sequential order is obviously meaningless and contradictory to the real situation simulated that the intensity at 1720 cm−1 decreases simultaneously with but faster than that at 1650 cm−1. In the above example, the intensity changes of two bands are nonperiodic with no chronological/local sequential order. What one can see is the instantaneous changes of the two band intensities with time. Nevertheless, 2D correlation analysis produces sequential order result of the two band intensity changes. This sequential order, of course, reveals the phase sequence/state of the two band intensity changes as a whole, as in mechanical-perturbation based 2D IR spectroscopy. However, such a phase sequence/state in general situations is not so meaningful. The above phase sequence/state in Figure 1 is analogous to two athletes running around part of a race track at the same direction and starting at the same position on the track at the same time but with different speeds. They pass a point at different instants in time. The time (phase) difference between them is not a constant, not the same for every pass if they are not at even speeds though in the same direction. Therefore the phase sequence (dif ference)/state is undefined if they are not at even speeds. The time (phase) difference between them is a constant only if they are at even speeds. If athlete 1 runs faster than athlete 2 (both under even speeds), athlete 1 will pass by the middle point or arrive at the end point earlier than (before) athlete 2. Otherwise, athlete 1 will be later than (after) athlete 2. Apparently, such sequential order is only indicative of the (before/after) positions/states they are with the middle or end point as a reference; one athlete will be arriving at the end point before/after another one if runs faster/slower (both under even speeds) than the other one. Such a sequential order has nothing to do with the fact that who starts running first. Only if the two athletes started running around part of a race track at the same direction but at different time, no matter starting at the same position or not, can we judge who started running first. From this point of view, the sequential order may reflect the rate difference of two events in general cases, but with too many exceptions.16,20,28 The reason behind this problem is that two spectral band intensity changes are not always under even speeds, thereby creating varying and meaningless sequential orders for two events. In summary, the sequential order derived from 2D correlation analysis in generalized 2D correlation spectroscopy is also of an integrated nature. But such an integrated/overall sequential order is not so meaningful for nonperiodic changes in general situations where the chronological/local sequential order should apply. Some Further Comments on the Concept of Sequential Order. It is apparent from the above discussions that various understanding or interpretation on the sequential order may occur. (While finalizing this manuscript, we noticed a new publication criticizing our misunderstanding and misinterpretation on the sequential order of generalized 2D correlation spectroscopy,30 though the same author strongly supported our idea a couple of years ago.25 This work will therefore serve as a partial response to such a criticism.) In contrast to the integrated sequential order, there is a local/ chronological sequential order. In fact, the statement itself in 2164
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problem resulting from the calculation procedure used in generalized 2D correlation analysis as we discussed almost 9 years ago.8,12 For the sake of clarity, the two apparently inconsistent wavenumbers will be placed side by side in the text below. The above sequential order conclusion is right in terms of phase relationship between the two band intensity changes, i.e., the intensity change of the symmetric C−H stretching band (2908/2912 cm−1) occurs/is present/exists after that of the asymmetric C−H stretching band (2992/3002 cm−1) . This conclusion, however, is neither meaningful nor reasonable in practice. Because the symmetric (2908/2912 cm−1) and asymmetric (2992/3002 cm−1) C−H stretching bands are from the same CH3 groups of DMSO, simultaneous intensity change of the two bands is expected to occur/happen theoretically with the evaporation of DMSO. However, sequential order was found from the 2D plots, based on the “sequential order” rules, between the two band intensity changes. This indicates, with no doubt, that sequential order conclusion derived from the “sequential order” rules may be wrong.16,20 This judgment may be easily verified by the real band intensity changes with evaporation time as shown in figure 4, where simultaneous intensity changes between the symmetric (2908/2912 cm−1) and asymmetric (2992/3002 cm−1) C−H stretching bands occurred, with no chronological/ local sequential order existing. From this experimental result, it should be very clear how problem associated with sequential order conclusions could arise from 2D correlation analysis. The same problem was found for the 2D correlation analysis result in the region of 1460−1260 cm−1 (Figure 5). The cross peak signs of the three major bands in this region are presented in table 2. From Table 2, it is easy to find the sequential order of intensity changes among the three bands: 1437 cm−1 (asym. C−H def) < 1406 cm−1 (asym. C−H def) < 1315 cm−1 (sym. C−H def). This suggests that the intensity change of the symmetric C−H deformation band (1315 cm−1) occurs (is present/exists) before that of the asymmetric C−H deformation bands (1406 and 1437 cm−1), and the intensity change of the asymmetric C−H deformation band around 1406 cm−1 occurs (is present/exists) before that around 1437 cm−1. The above conclusion, however, is apparently not meaningful and contradictory to the experimental results shown in Figure 6, where no chronological/local sequential order was observed, an indication of simultaneous intensity changes between the asymmetric (1437 cm−1, 1406 cm−1) and symmetric (1315 cm−1) C−H deformation bands. Theoretically, the band intensity changes of different C−H deformation modes are supposed to occur/happen at the same time, because they are from the same CH3 group. Different C−H vibrational modes from the same CH3 groups of DMSO are compared above. Now let us turn to compare the different vibrational modes from DMSO and water. Figure 7 (A and B) shows the 2D correlation plots between the O−H stretching band centered around 3447 cm−1 and the asymmetric C−H stretching band around 2996 cm−1. Note again, the O−H and asymmetric C−H stretching band positions obtained from 2D polts in Figure 7 are different from those (3422 and 3002 cm−1 respectively) in the 1D IR spectra in Figure 2 and listed in Table 1). The cross peak at (2996, 3447) is negative in the synchronous plot, but the asynchronous plot (Figure 7B) seems to be full of noise. This implies that the intensity changes of the O−H stretching band
Figure 2. IR spectra of DMSO and CCl4 (A) and the mixture of DMSO and CCl4 with evaporation time (B).
Table 1. Band Assignments for DMSO (and Water) band
assignments
source
3422 3002 2912 1653 1437 1406 1315
O−H str. asym. C−H str. sym. C−H str. O−H bend asym. C−H def asym. C−H def sym. C−H def
H2O DMSO DMSO H2O DMSO DMSO DMSO
Figure 3. 2D (A, synchronous; B, asynchronous) plots for DMSO evaporation in the region of 2850−3050 cm−1.
the asymmetric/symmetric C−H stretching band positions obtained from the 2D plots (2992/2908 cm−1) are quite different from that in the 1D IR spectrum (3002/2912 cm−1), as found in many other literatures. This is in fact a common 2165
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Figure 4. Instantaneous intensity changes of the symmetric (A, 2908/2912 cm−1) and asymmetric (B, 2992/3002 cm−1) C−H stretching bands.
(3447/3422 cm−1) and the asymmetric C−H stretching band (2996/3002 cm−1) occurs simultaneously, according to the sequential order rules. If careful enough, however, it can be found that the cross peak at (2996, 3447) is also negative in the asynchronous plot, which is more apparent when reducing the contour level to 4, as shown in Figure 7D. This suggests that the intensity change of the O−H stretching band (3448/3422 cm−1) occurs after that of the asymmetric C−H stretching band (2996/3002 cm−1), based on the sequential order rules. Therefore, the choice of contour level may be another problem in 2D correlation analysis sometimes, as we mentioned previously.17 To find the real picture, it is necessary to check the instantaneous intensity changes of the two bands at 2996/3002 cm−1 and 3447/3422 cm−1 with evaporation time. The former was shown in Figure 4B, and the latter is given in Figure 8A, where the 3447/3422 cm−1band intensity did not change until 50 s (Figure 8A) later. There is an obvious chronological/local sequential order between the intensity changes of the two bands. The intensity change of the O−H stretching band (3447/3422 cm−1) occurs 50 s later than that of the asymmetric C−H stretching band (2996/3002 cm −1 ).
Figure 5. 2D (A, synchronous; B, asynchronous) plots for DMSO evaporation in the region of 1460−1260 cm−1.
Table 2. Cross Peak Signs of the Three Major Bands in the Region of 1460−1260 cm−1 and the Sequential Orders among the Three Band Intensity Changes Φ (ν1,ν2)
Ψ (ν1,ν2)
sequential order
Φ(1437,1406) > 0 Φ(1437,1315) > 0 Φ(1406,1315) > 0
Ψ(1437, 1406) < 0 Ψ(1437, 1315) < 0 Ψ(1406, 1315) < 0
1437 < 1406 1437 < 1315 1406 < 1315
Figure 6. Instantaneous intensity changes of the asymmetric (A, 1437 cm−1; B, 1406 cm−1) and symmetric (C, 1315 cm−1) C−H deformation bands. 2166
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Figure 9. 2D (A, synchronous; B, asynchronous) plots for DMSO evaporation in the region of 1740−1360 cm−1.
Table 3. Sequential Order between Different Vibrational Modes from DMSO and Water Φ (ν1,ν2)
Ψ (ν1,ν2)
(2996, 3448) < 0 (1437, 1658) < 0
(2996, 3448) < 0 (1437, 1658) < 0
sequential order 2996 > 3448 1437 > 1658
In summary, one may probably always obtain the sequential order of two band intensity changes with 2D correlation analysis, even though such a sequential order is meaningless. To find out whether one band intensity change occurs prior/after another one, the instantaneous spectral intensity changes must be verified to determine if a chronological/local sequential order does exist between two band intensity changes.
Figure 7. 2D (A, synchronous; B, asynchronous) plots for DMSO evaporation in the region of 3630−2960 cm−1. Also shown in C and D are the 2D plots when the contour level is 4.
Apparently, this experimental observation is the arbiter of the above two possible conclusions. Once again, problem regarding sequential order conclusions may arise from appearance-based 2D correlation analysis result. A similar phenomenon was found for the O−H bending band (1658 cm−1) of the OH group of water and the asymmetric C−H deformation band (1437 cm−1) of the CH3 group of DMSO (Figures 6A, 8B, and 9 and Table 3). It was a surprise at first sight to notice that the intensities of the O−H stretching band (3447/3422 cm−1) and the O−H bending band (1658 cm−1) increase with the evaporation of DMSO under the experimental condition (Figure 8). This is actually reasonable and is the result of easy water absorption of DMSO molecules. The evaporation of DMSO molecules will take away some water molecules. The easy absorption of water of DMSO molecules, on the other hand, will absorb some water in the air. The dual tendency results in the appearance of a clear platform at the first 50 s in the evaporation plot of the O−H stretching band (3447/3422 cm−1) and the O−H bending band (1658 cm−1), respectively. After 50 s, a monotonic intensity increase was observed for both the O−H stretching band (3447/3422 cm−1) and the O−H bending band (1658 cm−1).
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CONCLUSIONS The sequential order of two events obtained from mechanicalperturbation based 2D correlation infrared spectroscopy was first revisited and it indicates the sequential order of the phases, or phase sequence/difference of two events, i.e., the state of one event is/is present/exists before/after that of the other one in the frequency domain. It may not be able to tell the chronological/ local sequential order of two events in terms of timings of the happenings. The sequential order of two events obtained from generalized two-dimensional correlation spectroscopy is also of an integrated/overall characteristic and reveals the phase sequence/state of the two band intensity changes as a whole, as in mechanical-perturbation based 2D correlation infrared spectroscopy. However, the phase sequence/state in generalized situations is not so meaningful. It may also indicate that the state of one event is before/after that of the other one in empirical cases, but with many exceptions. To judge whether one event occurs/happens prior/after another one, the original spectral intensity changes must be
Figure 8. Instantaneous intensity changes of the O−H stretching band (A, 3447/3422 cm−1) and the O−H bending band (B, 1658 cm−1). 2167
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(27) (28) (29) (30)
verified to determine if a chronological/local sequential order exists between two events.
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ASSOCIATED CONTENT
Noda, I. J. Mol. Struct. 2010, 974, 3. Czarnecki, M. A. Anal. Chim. Acta 2011, 702, 72. Noda, I. Appl. Spectrosc. 1990, 44, 550. Noda, I. Vib. Spectrosc. 2012, 60, 146.
S Supporting Information *
Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions ⊥
These authors contributed equally to this work.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work (a PAPD project) was supported by the National Natural Science Foundation of China under Grants 20774024 and 21074087 and by The Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant 20113201110004.
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dx.doi.org/10.1021/ac3027355 | Anal. Chem. 2013, 85, 2161−2168
