. 2023 May 25;71(22):8602–8612. doi: 10.1021/acs.jafc.2c07339

Table 2. ³¹P MAS NMR Isotropic Chemical Shift, Chemical Shift Anisotropy, Asymmetry Parameter, Composition, Fitting Quality, T₁ Relaxation Times, and Back-Calculation Factors of Phosphate Standards.

sample	formula	δ(iso)^a	δ(CSA)^b	η(CSA)^c	fraction^d	best overlap (%)^e	T₁ (s)^f	T₁ back-calculation factor^g
MCP	Ca[H₂PO₄]₂	0.69	–84.8	0.05	0.49	69.2%	877	2.57
		–3.77	–96.9	0.14	0.51		1099	2.99
MSP	Na[H₂PO₄]	3.37	–93.7	0.46	0.46	93.1%	1388	3.55
		2.11	–64.7	0.00	0.54		1492	3.75
MKP	K[H₂PO₄]	4.93	–46.4	0.07	1.00	88.0%	546	1.94
STPP	Na₅[P₃O₁₀]	5.85	109.8	0.08	0.38	90.0%	1031	2.86
		2.21	97.7	0.10	0.30		631	2.10
		–4.93	–123.1	0.11	0.18		1408	3.59
		–6.54	–127.8	0.10	0.14		1036	2.87
KTPP	K₅[P₃O₁₀]	0.11	101.3	0.06	0.36	89.9%	801	2.43
		–2.83	104.8	0.06	0.31		1009	2.82
		–15.68	–117.0	0.08	0.029		271	1.44
		–18.0	–134.9	0.08	0.30		1543	3.84
TSPP	Na₄[P₂O₇]	3.95	107.4	0.11	0.15	73.9%	753	2.33
		3.47	83.1	0.02	0.44
		3.04	83.3	0.03	0.28
		2.65	98.1	0.02	0.13
TKPP	K₄[P₂O₇]	2.04	94.0	0.10	0.15	93.2%	523	1.90
		1.61	91.8	0.10	0.072		605	2.05
		1.24	88.3	0.08	0.15		536	1.92
		0.58	79.8	0.09	0.093		612	2.07
		–0.07	86.1	0.10	0.24		408	1.69
		–1.85	83.9	0.11	0.082		644	2.13
		–3.11	86.4	0.12	0.19		608	2.06
		–3.67	89.0	0.11	0.027		537	1.93
bone meal	unknown	3.56	–60.5	0.06	0.03	95.1%	23	1.15
		1.68	–62.2	0.01	0.12		25	1.15
		0.16	–52.2	0.00	0.28		27	1.15
		–1.08	–64.3	0.00	0.57		27	1.15

Isotropic chemical shift in ppm.

Chemical shift anisotropy in ppm.

Asymmetry parameter.

Fraction = (integral of one component)/(total integral from all components). The relative uncertainties (standard deviation/mean) from repeated iterations of deconvolution are less than 0.3%.

Best overlap (%): the simplex iteration minimizes the least squares difference between the experimental spectrum and the superimposed simulated spectra. overlap (%) > 70–90, good agreement. A single Lorentzian–Gaussian line width was used for all the peaks.

T₁ relaxation time (fitted with eq 1) for each individual isotropic peak. The components for TSPP are overlapped; therefore, a bulk T₁ relaxation time is measured from the entire isotropic chemical shift region (5.2–1.7 ppm). The relative uncertainties (standard deviation/mean) from multiple measurements of T₁ for each signal are less than 0.8%.

T₁ relaxation back-calculation factor is defined in eq 3 in the Discussion session (vide infra, Discussion, eq 3).

Table 2. 31P MAS NMR Isotropic Chemical Shift, Chemical Shift Anisotropy, Asymmetry Parameter, Composition, Fitting Quality, T1 Relaxation Times, and Back-Calculation Factors of Phosphate Standards.

Table 2. ³¹P MAS NMR Isotropic Chemical Shift, Chemical Shift Anisotropy, Asymmetry Parameter, Composition, Fitting Quality, T₁ Relaxation Times, and Back-Calculation Factors of Phosphate Standards.