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Consec_ABC_SVD_v7

# Consec_ABC_SVD_v7 - Irreversible Two-step Consecutive...

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Irreversible Two-step Consecutive Process: Analysis of Noisy UV-Vis Absorbance Data Dr. Kalju Kahn UC Santa Barbara, 2004-2010 This Notebook illustrates how to generate multiwavelength absorbance data containing random noise for the irreversible process A fi k1 B fi k2 C. The lack of isosbestic point in the three-component system is illustrated. First, we generate concentration profiles for A, B, and C for 40 time points with 0.2 second spacing. The concentrations follow consecutive first-order kinetics. In[1]:= Remove @ "Global` * " D twostep = DSolve @ 8 concA ¢ @ time D == - k1concA @ time D , concA @ 0 D == A0, concB ¢ @ time D == k1concA @ time D - k2concB @ time D , concB @ 0 D == 0, concC ¢ @ time D == k2concB @ time D , concC @ 0 D == 0 < , 8 concA @ time D , concB @ time D , concC @ time D< , time D Flatten; In[3]:= cA = concA @ time D . twostep Simplify cB = concB @ time D . twostep Simplify cC = concC @ time D . twostep Simplify Out[3]= A0 ª - k1time Out[4]= - A0 I ª - k1time - ª - k2time M k1 k1 - k2 Out[5]= A0 I k1 - ª - k2time k1 + I - 1 + ª - k1time M k2 M k1 - k2 Data Import and Setup We will use a previously generated noisy absorbance data matrix that describes multi-wavelength kinetics merasured from 200 to 700 nm over 8 seconds with 0.2 second time interval. The data was generated with k 1 = 0.5 and k 2 = 1.0. Our goal here is to obtain these rate coefficient values via analysis of the absorbance data. In[6]:= timeval = Table @ i, 8 i, 40 <D 5 N; wavelength = Table @ x, 8 x, 200, 700 <D ; matSignal = Import @ "dataABC.dat", "Table" D ; Dimensions @ matSignal D Out[9]= 8 501, 40 <

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In[10]:= ListPlot3D @ matSignal, DataRange fi 88 0, 8 < , 8 200, 700 < , 8 0, 1.2 << , AxesLabel fi 8 "Time, s", " Λ , nm", "A" < , Mesh fi False D Out[10]= Action Spectra In[11]:= wavelength = Table @ x, 8 x, 200, 700 <D ; signal1 = Transpose @ 8 wavelength, matSignal @@ All, 1 DD < D ; signal6 = Transpose @ 8 wavelength, matSignal @@ All, 6 DD < D ; signal12 = Transpose @ 8 wavelength, matSignal @@ All, 12 DD < D ; signal18 = Transpose @ 8 wavelength, matSignal @@ All, 18 DD < D ; signal24 = Transpose @ 8 wavelength, matSignal @@ All, 24 DD < D ; In[17]:= Needs @ "PlotLegends`" D ListPlot @8 signal1, signal6, signal12, signal18, signal24 < , PlotRange fi 88 200, 700 < , 8 0, 1.2 << , AxesLabel fi 8 " Λ , nm", "A" < , PlotLegend fi 8 "t = 1.2", "t = 2.4", "t = 3.6", "t = 4.8", "t = 6.0" < , 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[18]= 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 = 6.0 t = 4.8 t = 3.6 t = 2.4 t = 1.2 2 Consec_ABC_SVD_v7.nb
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 Singular Value Decomposition In[19]:= 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[19]= 8 51.39, 14.2257, 3.64231, 0.825702, 0.821802, 0.81015 < Out[20]= 1 2 3 4 5 6 Component 10 20 30 40 50 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_v7 - Irreversible Two-step Consecutive...

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