二维相关谱图专题培训课件

Discrete Hilbert transform
y(n)
1 m
m j1
yj
(n)
m
~ zj(n2) Njk ~ yk(n2)
k1
where
0
if jk
Njk 1/(kj) otherw ise
2D correlation spectra
F (n1,n2)m 1 1jm 1 ~ yj(n1)~ yj(n2) Y (n1,n2)m1 1jm 1 ~ yj(n1)~ zj(n2)
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Rapid and straightforward computation of 2D correlation spectra
Synchronous correlation spectrum: F(n1, n2)
▪ Autopeaks at diagonal positions represent the extent of perturbation-induced dynamic fluctuations of spectral signals
Perturbation
S(t)
Input
I(n)
System
Output
~y(n1,t)
~y(n2,t)
...
~y(nn,t)
Comparison of two signals
measured at different n along t
Cross-correlation function
nn n n (1 ,2 )~ y (1 ,t)~ y (2 ,t')
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
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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
• 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.
Fourier transform
Y ~ 1() ~ y(n1,t)eitdt
n Y ~ 2*( ) ~ y(2,t)eitdt
源自文库
2D correlation spectra
nn nn F (1 ,2 ) iY (1 ,2 )( T m a x 1 T m in )0 Y ~ 1 ()Y ~ 2 * ()d
▪ 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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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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Polystyrene/DOP Blend
Dioctyl phthalate (DOP)
Perdeuterated polystyrene
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Plasticized Polystyrene
• Motions of aromatic groups of PS and DOP are synchronized
Temperature, pressure, time, concentration, electromagnetic field ……
2D Correlation Spectra
Acquisition of 2D Correlation Spectra
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2D Correlation Analysis
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.
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Generalized 2D Correlation Formalism
Dynamic spectrum
~ y (n,t) y (n,t)0 y (n)
fo rT m in t T m a x o th e r w is e
where
n n 1
y( )
Tm ax y( ,t)dt.
T T m ax m in Tm in
• Band split of PVME methoxyl groups into 2815 cm-1 and 2824 cm-1 • Motion of PVME 2815 cm-1 is synchronized with PS phenyl
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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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d3PS/PVME (25:75) Blend
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Book
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Generalized Two-Dimensional Correlation Spectroscopy
Electromagnetic Probe IR, NIR, laser ……
Chemical System
Dynamic Spectra
External Perturbation
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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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
F(n1, n2) synchronous spectrum Y(n1, n2) asynchronous spectrum
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Practical Computational Method
Discrete spectral sampling
~ yj(n) yj(n)0y(n)
for1jm ot herwi se
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Generalized 2D Correlation Spectroscopy
Perturbation-based 2D correlation spectroscopy
I. Noda, Appl. Spectrosc., 47, 1329 (1993). 4
Reference Literature
= 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
▪ 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.
▪ 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.
二维相关谱图
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Two-Dimensional (2D) Spectroscopy
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Generalized 2D Correlation Spectroscopy
▪ 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
▪ Cross peaks represent simultaneous changes of spectral signals at two different wavenumbers, suggesting a coupled or related origin of intensity variations