二维相关谱图

▪ The sign of a cross peak is positive if the intensity change at n1 occurs before n2.
▪ The sign of a cross peak is negative if the intensity change at n1 occurs after n2.
Applied Spectroscopy, vol. 54, no. 7, July, 2000. (Special issue on generalized 2D correlation spectroscopy)
Y. Ozaki and I. Noda, Eds. Two-Dimensional Correlation Spectroscopy, AIP Conference proceedings 503, AIP: Melville, 2000.
B. Alpha methyl A. Ester methyl
C. Methylene
S.K. Dirlikov and J.L. Koenig Appl. Spectrosc. 33, 555 (1979).
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Atactic PMMA
• Ester methyl peaks are in the synchronous spectrum almost exclusively • Alpha methyl and methylene found in the asynchronous spectrum
readily observable in conventional 1D spectra ▪ Sign of cross peaks to determine relative direction of intensity changes and
sequential order of events ▪ Comparison of different spectral data via hetero-correlation
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Generalized 2D Correlation Formalism
Dynamic spectrum
~y (n,
t)
y(n
,
t
) 0
y(n
)
for Tmin t Tmax otherwise
where
y(n) 1
Tmax y(n , t) dt.
T T max
min Tmin
Fourier transform
▪ Generally applicable to a broad range of spectroscopic techniques ▪ Based on a set of spectral data from a system under some perturbation ▪ Either time-dependent or static spectra may be used ▪ Enhance spectral resolution by spreading peaks along the second dimension ▪ Selective development of 2D peaks provides better access to information not
5
Book
6
Generalized Two-Dimensional Correlation Spectroscopy
Electromagnetic Probe IR, NIR, laser ……
Chemical System
Dynamic Spectra
External Perturbation
(n1,n2) ~y(n1,t) ~y(n2,t')
= F(n1,n2) + i Y(n1,n2)
Synchronous spectrum F(n1,n2) = Similarity of signal dependence on t
Asynchronous spectrum Y(n1,n2) = Dissimilarity of signal dependence on t
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Practical Computational Method
Discrete spectral sampling
~y j
(n
)
y
j
(n
) 0
y(n
)
for 1 j m otherwise
Discrete Hilbert transform
y(n ) 1
m
m
y j (n )
j 1
m
~z j (n2 ) N jk ~yk (n2 )
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Asynchronous correlation spectrum: Y(n1, n2)
▪ Cross peaks develop only if the intensity varies out of phase with each other for some Fourier frequency components of signal fluctuations
2008年中国科大
Two-Dimensional (2D) Correlation Spectroscopy
武培怡
复旦大学高分子科学系
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Two-Dimensional (2D) Spectroscopy
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Generalized 2D Correlation Spectroscopy
▪ Cross peaks represent simultaneous changes of spectral signals at two different wavenumbers, suggesting a coupled or related origin of intensity variations
Y~1( )
~y (n 1 , t )
e i t dt
Y~2*( )
~y(n 2 , t)
eit dt
2D correlation spectra
1
F(n1,n2 ) i Y(n1,n2 ) (Tmax Tmin )
0
wenku.baidu.com
Y~1( ) Y~2*( )
d
F(n1, n2) synchronous spectrum Y(n1, n2) asynchronous spectrum
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Polystyrene/Polyethylene Blend
• Separate synchronous correlations for PS and PE bands
• Asynchronous correlation between PS and PPE bands
•
Asynchronicity within PS bands (backbone vs. side group)
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PS/PVME Blends
Polystyrene (chain-deuterated)
Poly(vinyl methyl ether)
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d3PS/PVME (25:75) Blend
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Polystyrene/DOP Blend
Dioctyl phthalate (DOP)
Perdeuterated polystyrene
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Plasticized Polystyrene
• Motions of aromatic groups of PS and DOP are synchronized
k 1
where
0
N jk
1
/
(k
j)
if j k otherwise
2D correlation spectra
1
F(n1,n2 ) m 1
m j 1
~y j (n1) ~y j (n2 )
1
Y(n1,n2 ) m 1
m j 1
~y j (n1) ~z j (n2 )
Rapid and straightforward computation of 2D correlation spectra
3
Generalized 2D Correlation Spectroscopy
Perturbation-based 2D correlation spectroscopy
I. Noda, Appl. Spectrosc., 47, 1329 (1993). 4
Reference Literature
▪ If the sign of a cross peak is positive, the intensities at corresponding wavenumbers are increasing (or decreasing) together. If the sign is negative, one is increasing, while the other is decreasing.
Temperature, pressure, time, concentration, electromagnetic field ……
2D Correlation Spectra
Acquisition of 2D Correlation Spectra
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2D Correlation Analysis
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Synchronous correlation spectrum: F(n1, n2)
▪ Autopeaks at diagonal positions represent the extent of perturbation-induced dynamic fluctuations of spectral signals
• DOP aliphatic chains move asynchronously (independently)
with respect to PS phenyl rings
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Remola Model of Plasticization
rem’o-ra, n. [L., hinderance.] 1. Any of several fishes (gerera Echenecis, Remora, family Echneididae), with a suctional disk on the head by which they cling to other fishes or to ships. 2. A clog; drags; hinderence.
▪ The above sign rules are reversed if F(n1, n2)<0.
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Polystyrene/Polyethylene Blend
Polystyrene
–(CH2CH)n–
Polyethylene
–(CH2CH2)n–
• PS and PE are immiscible (phase separated) • No molecular level interactions
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Human Hair Keratin
Assignments (cm-1) a-helix 1661, 1649
b-like extended chains and turns 1679, 1669, 1645 1641, 1620
Disordered structures 1656
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Selectively Deuterated Polystyrene
–(CH2CH)n–
–(CD2CD)n–
vs.
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Atactic Poly(methyl methacrylate)
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Pure Group Frequency Spectra of PMMA
Perturbation
S(t)
Input
I(n)
System
Output
~y (n1,t)
~y(n 2,t) ...
~y (n n ,t)
Comparison of two signals
measured at different n along t
Cross-correlation function