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1 MCR-ALS analysis using initial estimate of concentration profile by EFA
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10 Deducing Chemical Rank (Factor Analysis) Scree plot Indicator function Loading plot Eigen-value ratio …
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14 Calculating Initial estimate by EFA
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36 Source of differences? Rotational ambiguity PCA: D=TP Beer-Lambert: D=CS In MCR we want to reach from PCA to Beer-Lambert D= TP = TRR -1 P, R: rotation matrix D = (TR)(R -1 P) C=TR, S=R -1 P (R 2)(0.5 R -1 ) = RR -1
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37 How can we overcome this problem? More extra constraints: 1.Selectivity 2.Peak Shape 3.Matrix augmentation 4.Combined hard model
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38 Implementation of selectivity in pure spectra If we know the pure spectrum of the reactant
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44 Implementation of selectivity in concentration profile At the beginning of reaction only reactant is existed and the other species are absent
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49 Two other experiments
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50 Next step?
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51 Matrix augmentation 3 kinetic experiments run at three different experimental conditions D1 D2 D3
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52 Steps for column-wise data augmentation 1. calculate initial estimate of concentration for each data set [e1,ef1,ef2]=efa(d1); [e2,ef2,ef2]=efa(d2); [e3,ef3,ef3]=efa(d3); 2. produce a matrix of initial estimate e=[e1;e2;e3]; 3. collect all data matrices in a single matrix d=[d1;d2;d3];
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58 Analysis of a single data matrix Analysis of augmented data matrices
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71 Original Values: k 1 =0.2 k 2 =0.02 Original Calculated k 1 k 2 k 1 k 2 R1 0.20 0.02 0.22 0.017 R2 0.30 0.08 0.31 0.072 R3 0.45 0.32 0.45 0.29
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72 Row and column wise data augmentation If the experiments are also monitored by spectroflourimetric method Da1 Da2 Da3 Df1 Df2 Df3
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