Structure-flammability relationship study of phosphoester dimers by MLR and PLS

Crisan, Luminita; Iliescu, Smaranda; Funar-Timofei, Simona

doi:10.1590/0104-1428.2306

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Seção Técnica • Polímeros 26 (2) • Apr-Jun 2016 • https://doi.org/10.1590/0104-1428.2306 copy

Structure-flammability relationship study of phosphoester dimers by MLR and PLS^a Dedicated to the 150th anniversary of the Romanian Academy.

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Polyphosphonates and polyphosphates having good flame retardancy represent an important class of organophosphorus based polymer additives. In this analysis the flammability of 28 previously synthesized polyphosphoesters, modelled as dimmers, was explored using the multiple linear regression (MLR) and Partial Least Square (PLS) methodology. The statistical quality of the final MLR and PLS models was estimated using the following parameters: the squared correlation coefficient ( $r_{t r a i n i n g}^{2}$ = 0.917 and 0.976), the training root-mean-square errors (RMSE_tr = 0.029 and 0.016) and the leave-seven-out cross-validation correlation coefficient ( $q_{L 7 O}^{2}$ = 0.748 and 0.881), respectively. External validation was checked for a test set of seven compounds using several criteria. The MLR models had somewhat inferior fitting results. The final MLR and PLS models can be used for the estimation of limiting oxygen index (LOI) values of new polyphosphoester structures. The presence of phosphonate groups and increasing molecular branching in an isomeric series favour the dimer flammability.

Keywords:
quantitative structure-property relationships; polyphosphonate; polyphosphate; limiting oxygen index; flame retardancy

No	Exp. LOI	Calc. LOI by MLR_RR	Calc. LOI by PLS_RR	MSD	EEig09d	R2m+	nP(=O)O2R
1	0.38^a a from reference [6] and b from reference [7].	0.38	0.36	0.218	2.266	0.022	2
2	0.35^a a from reference [6] and b from reference [7].	0.41	0.37	0.228	2	0.023	2
3	0.30^a a from reference [6] and b from reference [7].	0.33	0.33	0.235	2.245	0.026	2
4	0.48^a a from reference [6] and b from reference [7].	0.45	0.45	0.213	2.058	0.023	2
5	0.55^a a from reference [6] and b from reference [7].	0.55	0.55	0.191	2.652	0.187	2
6	0.28^a a from reference [6] and b from reference [7].	0.26	0.28	0.235	2.569	0.043	2
7	0.29^a a from reference [6] and b from reference [7].	0.32	0.29	0.218	2.576	0.044	2
8	0.42b	0.44	0.41	0.2	2.271	0.021	2
9	0.44^a a from reference [6] and b from reference [7].	0.42	0.44	0.182	2.744	0.062	2
10	0.50^a a from reference [6] and b from reference [7].	0.45	0.54	0.212	2.467	0.117	2
11	0.47b	0.52	0.54	0.169	2.361	0.022	2
12	0.32^a a from reference [6] and b from reference [7].	0.31	0.32	0.209	2.621	0.016	2
13	0.40^a a from reference [6] and b from reference [7].	0.45	0.44	0.191	2.361	0.021	2
14	0.33^a a from reference [6] and b from reference [7].	0.28	0.31	0.219	2.619	0.019	2
15	0.28^a a from reference [6] and b from reference [7].	0.29	0.25	0.216	2.434	0.018	0
16	0.25^a a from reference [6] and b from reference [7].	0.28	0.25	0.226	2.359	0.025	0
17	0.22^a a from reference [6] and b from reference [7].	0.24	0.27	0.232	2.431	0.026	0
18	0.36^a a from reference [6] and b from reference [7].	0.31	0.37	0.211	2.454	0.025	0
19	0.40^a a from reference [6] and b from reference [7].	0.37	0.47	0.19	2.722	0.082	0
20	0.18^a a from reference [6] and b from reference [7].	0.19	0.18	0.232	2.691	0.04	0
21	0.20^a a from reference [6] and b from reference [7].	0.23	0.19	0.216	2.695	0.032	0
22	0.31^a a from reference [6] and b from reference [7].	0.35	0.32	0.198	2.434	0.017	0
23	0.33^a a from reference [6] and b from reference [7].	0.37	0.35	0.181	2.749	0.063	0
24	0.50^a a from reference [6] and b from reference [7].	0.49	0.50	0.21	2.514	0.204	0
25	0.48^a a from reference [6] and b from reference [7].	0.45	0.47	0.168	2.445	0.017	0
26	0.23^a a from reference [6] and b from reference [7].	0.24	0.25	0.207	2.723	0.016	0
27	0.37^a a from reference [6] and b from reference [7].	0.38	0.37	0.189	2.441	0.019	0
28	0.24^a a from reference [6] and b from reference [7].	0.21	0.23	0.217	2.724	0.016	0

Model	N_training	R_X²	*$r_{t r a i n i n g}^{2}$*	*$q_{L 7 O}^{2}$*	RMSE_tr	MAE_tr	CCC_tr	*$r_{S c r}^{2}$*	*$q_{S c r}^{2}$*
MLR_RR	21	-	0.917	0.748	0.029	0.025	0.957	0.198	-0.453
MLR_RS	21	-	0.830	0.658	0.042	0.032	0.907	0.199	-0.422
MLR_SR	21	-	0.863	0.743	0.037	0.029	0.926	0.149	-0.309
MLR_SS	21	-	0.889	0.800	0.034	0.025	0.941	0.152	-0.340
PLS_RR	21	0.726	0.976 (4)^ Number of components is given in parenthesis.	0.881	0.016	0.012	0.988	0.635	-0.510
PLS_RS	21	0.701	0.965 (4)^ Number of components is given in parenthesis.	0.754	0.019	0.014	0.982	0.627	-0.557
PLS_SR	21	0.702	0.972 (4)^ Number of components is given in parenthesis.	0.792	0.017	0.013	0.986	0.556	-0.571
PLS_SS	20^* * Compound 5 was found as outlier and omitted from the final model;	0.461	0.885 (2)^ Number of components is given in parenthesis.	0.656	0.031	0.026	0.939	0.324	-0.398

Model	$Q_{F 1}^{2}$	$Q_{F 2}^{2}$	$Q_{F 3}^{2}$	RMSE_ext	MAE_ext	CCC_ext
MLR_RR	0.811	0.808	0.833	0.041	0.037	0.900
MLR_RS	0.814	0.811	0.836	0.041	0.033	0.901
MLR_SR	0.713	0.708	0.747	0.051	0.044	0.856
MLR_SS	0.787	0.783	0.812	0.044	0.039	0.896
PLS_RR	0.777	0.773	0.803	0.045	0.039	0.912
PLS_RS	0.727	0.723	0.759	0.050	0.040	0.902
PLS_SR	0.716	0.711	0.749	0.051	0.042	0.898
PLS_SS	0.554	0.529	0.514	0.050	0.056	0.799

Model	$r_{t e s t}^{2}$	$\frac{r^{2} - r_{0}^{2}}{r^{2}}$	$\frac{r^{2} - r_{0}^{' 2}}{r^{2}}$	k	k’	$\| r_{0}^{2} - r_{0}^{' 2} \|$
MLR_RR	0.832	0.000	0.039	0.963	1.028	0.032
MLR_RS	0.867	0.004	0.050	0.945	1.049	0.040
MLR_SR	0.732	0.032	0.022	0.994	0.987	0.008
MLR_SS	0.812	0.032	0.002	1.014	0.973	0.025
PLS_RR	0.941	0.022	0.006	0.912	1.091	0.015
PLS_RS	0.970	0.037	0.019	0.896	1.115	0.018
PLS_SR	0.940	0.050	0.018	0.903	1.100	0.030
PLS_SS	0.687	0.073	0.018	0.923	1.059	0.038

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Structure-flammability relationship study of phosphoester dimers by MLR and PLSa Dedicated to the 150th anniversary of the Romanian Academy.

Abstract

Structure-flammability relationship study of phosphoester dimers by MLR and PLS^a Dedicated to the 150th anniversary of the Romanian Academy.