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Consec_ABC_SVD_UnknownB_v7

# Consec_ABC_SVD_UnknownB_v7 - Irreversible Two-step...

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Irreversible Two-step Consecutive Process: Full Spectral and Kinetic Resolution without Pure Spectra Dr. Kalju Kahn UC Santa Barbara, 2010 This Notebook illustrates how to analyze multiwavelength absorbance data containing random noise. It illus- trates several powerful ideas: 1) Checking for the presence of intermediate(s) via the isosbestic point 2) Determination of the number of intermediates in the consecutive process via singular value decomposition 3) Estimation of values of the two rate coefficients from fitting double-exponential model to basis profiles 4) Reconstruction of the absorption matrix from significant basis spectra and basis profiles 5) Calculation of the spectra for reactant, product, and the intermediate from data in the absorbance matrix with the help of rate constants 6) Calculation of concentration profiles from reconstructed absorbance data and calculated spectra In[1]:= H * Spectra were collected for 10 seconds with 0.2 second spacing from 200 to 700 nm * L Remove @ "Global` * " D timeval = Table @ i, 8 i, 50 <D 5 N; wavelength = Table @ x, 8 x, 200, 700 <D ; matSignal = Import @ "dataABC.dat", "Table" D ; Dimensions @ matSignal D Remove::rmnsm : There are no symbols matching "Global` * ". Out[5]= 8 501, 50 < In[6]:= ListPlot3D @ matSignal, DataRange fi 88 0, 10 < , 8 200, 700 < , 8 0, 1.2 << , AxesLabel fi 8 "Time, s", " Λ , nm", "A" < , Mesh fi False D Out[6]=

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The 3D plot ob absorbance data shows a lot of noise but the disapperance of reactant at ca. 300 nm and apperance of product at ca. 500 nm is evident. Action Spectra In[7]:= wavelength = Table @ x, 8 x, 200, 700 <D ; signal02 = Transpose @ 8 wavelength, matSignal @@ All, 1 DD < D ; signal22 = Transpose @ 8 wavelength, matSignal @@ All, 11 DD < D ; signal42 = Transpose @ 8 wavelength, matSignal @@ All, 21 DD < D ; signal62 = Transpose @ 8 wavelength, matSignal @@ All, 31 DD < D ; In[12]:= Needs @ "PlotLegends`" D ListPlot @8 signal02, signal22, signal42, signal62 < , PlotRange fi 88 200, 700 < , 8 0, 1.2 << , AxesLabel fi 8 " Λ , nm", "A" < , PlotLegend fi 8 "t = 0.2", "t = 2.2", "t = 4.2", "t = 6.2" < , LegendPosition fi 8 0.4, 0.10 < , LegendSize fi 8 0.45, 0.45 < , PlotLabel fi "Action Spectra", LabelStyle fi 8 Medium, FontFamily fi "Helvetica" < , Background fi ColorData @ "Atoms", "He" DD Out[13]= 200 300 400 500 600 700 Λ , nm 0.0 0.2 0.4 0.6 0.8 1.0 1.2 A Action Spectra t = 6.2 t = 4.2 t = 2.2 t = 0.2 The action spectra do not show an isosbestic point, suggesting that the interconversion of the reactant to the product involves at least one intermediate. We can use singular value decomposition to find the number of species contributing to the observed signal. 2 Consec_ABC_SVD_UnknownB_v7.nb
Singular Value Decomposition In[14]:= sv = SingularValueList @ matSignal, 6 D ListPlot @ sv, Prolog fi PointSize @ 0.03 D , Background fi ColorData @ "Atoms", "He" D , PlotStyle fi 8 PointSize @ Medium D , Red < , PlotRange fi All, PlotLabel fi "SVD of Two - Component Kinetics", AxesLabel fi 8 "Component", "Singular Value" < , LabelStyle fi 8 FontFamily fi "Helvetica" <D Out[14]= 8 61.6816, 14.7608, 3.85562, 0.856113, 0.847488, 0.832194 < Out[15]= 1 2 3 4 5 6 Component 10 20 30 40 50 60 Singular Value SVD of Two - Component Kinetics It looks like three singular values are significantly different from zero.

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Consec_ABC_SVD_UnknownB_v7 - Irreversible Two-step...

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