By: Bahram Hemmateenejad

1. The Second Iranian Workshop of Chemometrics By:Bahram Hemmateenejad Multivariate Curve Resolution Analysis (MCR)

2. Complexity in Chemical Systems • Unknown Components • Unknown Numbers • Unknown Amounts

3. Modeling Methods • Hard modeling A predefined mathematical model is existed for the studied chemical system (i.e. the mechanism of the reaction is known) • Soft modeling The mechanism of the reaction is not known

4. Basic Goals of MCR • Determining the number of components coexisted in the chemical system • Extracting the pure spectra of the components (qualitative analysis) • Extracting the concentration profiles of the components (quantitative analysis)

5. Evolutionary processes • pH metric titration of acids or bases • Complexometric titration • Kinetic analysis • HPLC-DAD experiments • GC-MS experiments • The spectrum of the reaction mixture is recorded at each stage of the process

6. Nwav • Data matrix (D) Nsln

7. Bilinear Decomposition • If there are existed k chemical components in the system Nwav Nwav k S D = C k Nsln Nsln

8. + D = + + + …. + E

9. Mathematical bases of MCR • D = C S Real Decomposition • D = U V PCA Decomposition Target factor analysis • D = U (T T-1) V = (U T) (T-1 V) C = U T, S = T-1 V T is a square matrix called transformation matrix How to calculate Transformation matrix T?

10. Ambiguities existed in the resolved C and S • Rotational ambiguity • There is a differene between the calculated T and real T • Intensity ambiguity • D = C S = (k C) (1/kS)

11. How to break the ambiguities(at least partially) • Combination of Hard models with Soft models • Using of local rank informations • Implementation of some constraints • Non-negativity • Unimodality • Closure • Selectivity • Peak Shape

12. MCR methods • Non iterative methods (using local rank information) Evolving factor analysis (EFA) Windows factor analysis (WFA) Subwindows factor analysis (SWFA) • Iterative methods (using natural constrains) • Iterative target transformation factor analysis (ITTFA) • Multivariate curve resolution-alternative least squares (MCR-ALS)

13. Mathematical Bases of MCR-ALS • The ALS methods uses an initial estimates of concentration profiles (C) or pure spectra (S) • The more convenient method is to use concentration profiles as initial estimate (C) • D = CS • Scal = C+ D, C+ is the pseudo inverse of C • Ccal = D S+ • Dcal = Ccal Scal Dcal D

14. Lack of fit error (LOF) (LOF) =100 ((dij-dcalij)2/dij2)1/2 • LOF in PCA (dcalij is calculated from U*V) • LOF in ALS (dcalij is calculated from C*S)

15. Kinds of matrices that can by analyzed by MCR-ALS • Single matrix (obtained trough a single run) • Augmented data matrix Row-wise augmented data matrix: A single evolutionary run is monitored by different instrumental methods. D = [D1 D2 D3] Column-wise augmented data matrix: Different chemical systems containing common components are monitored by an instrumental method D = [D1;D2;D3]

16. Row-and column-wise augmented data matrix: chemical systems containing common components are monitored by different instrumental method D = [D1 D2 D3;D4 D5 D6]

17. Running the MCR-ALS Program • Building up the experimental data matrix • D (Nsoln, Nwave) • 2. Estimation of the number of components in the data matrix D • PCA, FA, EFA • 3. Local rank Analysis and initial estimates • EFA • 4. Alterative least squares optimization

18. Evolving Factor Analysis(EFA) Forward Analysis D FA FA 1f, 2f, 3f 1f, 2f

19. Backward Analysis D FA FA 1b, 2b, 3b 1b, 2b

21. MCR-ALS program written by Tauler • [copt,sopt,sdopt,ropt,areaopt,rtopt]=als(d,x0,nexp,nit,tolsigma,isp,csel,ssel,vclos1,vclos2); • Inputs: d: data matrix (r c) Single matrix d=D Row-wise augmented matrix d=[D1 D2 D3] Column-wise augmented matrix d=[D1;D2;D3] Row-and column-wise augmented matrix d=[D1 D2 D3;D4;D5;D6]

22.  • x0: Initial estimates of C or S matrices C (r k), S (k  c) • nexp: Number of matrices forming the data set • nit: Maximum number of iterations in the optimization step (default 50) • tolsigma: Convergence criterion based on relative change of lack of fit error (default 0.1)

23. isp: small binary matrix containing the information related to the correspondence of the components among the matrices present in data set. isp (nexp k) isp=[1 0;0 1;1 1] • csel: a matrix with the same dimension as C indicating the selective regions in the concentration profiles • ssel: a matrix with the same dimension as S indicating the selective regions in the spectral profiles

24. A B C 0 0 1 Nan Nan 1 Nan Nan Nan Nan Nan Nan 1 Nan Nan 1 Nan 0

25. vclos1 and vclos2: These input parameters are only used when we deal with certain cases of closed system (i.e. when mass balance equation can be hold for a reaction) • vclos1 is a vector whose elements indicate the value of the total concentration at each stage of the process (for each row of C matrix) • vclos2 is used when we have two independent mass balance equations

26. Outputs • copt: matrix of resolved pure concentration profiles • sopt: matrix of resolved pure spectra. • sdopt: optimal percent lack of fit • ropt: matrix of residuals obtained from the comparison of PCA reproduced data set (dpca) using the pure resolved concentration and spectra profiles. ropt = T P’ – CS’

27. areaopt: This matrix is sized as isp matrix and contains the area under the concentration profile of each component in each Di matrix. This is useful for augmented data matrices. • rtopt: matrix providing relative quantitative information. rtopt is a matrix of area ratios between components in different matrices. The first data matrix is always taken as a reference.

28. An example Protein denaturation Protein (intermediate) Protein (unfold) (denatured) denaturant denaturant

29. Metal Complexation • Complexation of Al3+ with Methyl thymol Blue (MTB)

30. Applications • Qualitative MCR-ALS • Quantitative MCR-ALS

31. The photo-degradation Kinetic of Nifedipine

32. Nifedipine 1,4-dihydro-2,6-dimethyl-4-(2-nitrophenyl)-3,5-pyridine dicarboxilic acid dimethyl ester selective arterial dilator hypertension angina pectoris other cardiovascular disorders

33. UV light 4-(2-nitrophenyl) pyridine daylight 4-(2-nitrosophenyl)-pyridine Nifedipine is a sensitive substance

35. 8 4 Log (EV) 0 -4 -8 1 3 5 7 9 11 13 15 No. of factors Data Analysis • Definition of the data matrix, D (nm) • n: No. of wavelengths • M: No. of samples • PCA of the data D = R C • R is related to spectra of the components • C is related to the concentration of the components • Number of chemical components

36. Score Plot

39. Linear segment CNIF = 1.181 ( 0.001)  10-4 – 4.96 (0.13)  10-9 t r2 = 0.995 • Exponential segment CNIF = 1.197 ( 0.003)  10-4 Exp (-6.22 ( 0.10) 10-5 t) r2 = 0.998 • Zero order 4.96 (0.13)  10-9 (mole l-1 s-1) • First-order 6.22 ( 0.10) 10-5 (s-1)

40. Behavior of iodine in the mixed solvents of cyclohexane with Dioxane and THF

41. When iodine dissolves in a binary mixture of donating (D) and non-donating (ND) solvents, preferential solvation indicates the shape of iodine spectrum • Nakanishi et al. (1987) studied the spectra of iodine in mixed binary solvents • Factor analysis was used to indicate the number of component existed • No extra works were reported

42. Iodine spectra in dioxane-cyclohexane

43. Iodine spectra in THF-cyclohexane

44. Eigen-values Plot

47. Behaviour of Cationid Dyse in SDS solutions Behaviour of Cationid Dyse in SDS solutions

48. Dye aggregates Dye monomer Dye-Surfactant ion-pairing Dye partitioned in the micelle phase Pre-micelle aggregate

49. Absorbance Spectra of MB