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MCR-ALS analysis using initial estimate of concentration profile by

EFA

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Deducing Chemical Rank(Factor Analysis)

• Scree plot

• Indicator function

• Loading plot

• Eigen-value ratio

• …

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Calculating Initial estimate by EFA

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1.2

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1.2

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1.2

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1.2

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Source of differences?

Rotational ambiguityPCA: D=TPBeer-Lambert: D=CSIn MCR we want to reach from PCA to Beer-Lambert

• D= TP = TRR-1P, R: rotation matrix• D = (TR)(R-1P)• C=TR, S=R-1P• (R2)(0.5R-1) = RR-1

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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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Implementation of selectivity in pure spectra

• If we know the pure spectrum of the reactant

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1.2

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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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1.2

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Two other experiments

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Next step?

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Matrix augmentation

• 3 kinetic experiments

• run at three different experimental conditions

• D1

• D2

• D3

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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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Analysis of a single data matrix Analysis of augmented data matrices

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Original Values: k1=0.2 k2=0.02

Original Calculated

k1 k2 k1 k2

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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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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