In 2004, Knothe and Kenar [1] published a research paper regarding the determination of the fatty acid profile by ^{1}H NMR spectroscopy in this journal. The procedure was deduced in detail, by using the integration values of the signals of protons specific for different common fatty acids in many vegetable oils. It offered a novel alternative to analyze fatty acid profile as compared with the traditional GC method. However, at the end of Section 3.2 which quantifies saturated fatty acids, there are three typeset errors maybe caused by reediting. We have not yet detected it until we applied the integration values of my ^{1}H NMR spectrum of a palm oil sample to this calculation process and encountered abnormal results contradicting those obtained from GC-mass spectroscopy (GC-MS). Although they have little interference with the general principle of the determination method for fatty acid profile, it becomes confusing that we should reconsider them before referring to it and applying the calculation process to our recent research on glycidyl fatty acid esters. And faithfully, this useful determination scheme has made great contribution to the improvement of our research. Thus here we do some analysis by comparing the result with that of GC-MS determination, and correct them through chemical and mathematical approaches. We believe that the modified version will not have a negative impact to its original principle but make it much more versatile in its popularization.

The typeset errors begin with Eq. (24), in which *I*_{C18:0–C16:0} should equal the sum of *I*_{diff,CH2,C18:0} and *I*_{diff,CH2,C16:0} rather than their difference. This is clear when relating Eq. (22) to (23). The remaining two appear in the subsequent Eq. (25), where the dividend *I*_{diff,CH2,C16:0} in the bracket should be replaced by *I*_{diff,CH2,C18:0}, and the following multiplier *A*_{unsat} should be rectified to its counterpart *A*_{sat}. The above typeset errors and corrections seem abstract, but the theories behind them, in fact, are easy to understand.

As is described in the paper, the amount of C16:0 is obtained by determining its actual contribution to the integration value of the CH_{2} proton signal and multiplying this proportion by the amount of saturates *A*_{sat}. However, the actual contribution to the integration value of the CH_{2} proton signal by C16:0 is not the difference between the theoretical (for pure C16:0) and actual integration value (*I*_{CH2, sat}), but the difference between the theoretical (for pure C18:0) and actual integration value (*I*_{CH2, sat}). It is the portion of C16:0 in the saturated mixture that causes the difference between the theoretical (for pure C18:0) and actual integration value (*I*_{CH2, sat}). In this sense, the proportion of C16:0 can be determined from this difference, i.e., *I*_{diff,CH2,C18:0}, which is the corrected equation below:

Similarly, the proportion of C18:0 can be determined from the difference between the theoretical (for pure C16:0) and actual integration value (*I*_{CH2, sat}), i.e., *I*_{diff,CH2,C16:0}, as shown in the corrected equation below:

On the other hand, a system of linear equations with two variables can be an alternative to explain the difference method in a mathematical way. Let the proportions of C16:0 and C18:0 in the saturated mixture (assuming completely compose of C16:0 and C18:0) be *x* and *y*, respectively. Thus

Finally, multiplication of *x* and *y* with the amount of saturates *A*_{sat} yields the proportion of C16:0 and C18:0 in the oil sample.

The modified scheme was validated by chromatographic analysis. The fatty acid profile of a palm oil sample was determined by GC-MS (Agilent 7890A GC-5975C MS), equipped with a capillary column (J&W DB-WAX, 10 m × 0.1 mm i.d., 0.25 µm in film thickness). Palm oil was transesterified into FAMEs, and the FAMEs were analyzed according to the method in our previously published work [2]. The fatty acid composition was based on peak area response, which indicated the mass ratios of different FAMEs. The data of the sample analyzed in triplicate were recorded as means ± SD. As the chromatographic signals are based on mass, it is necessary to transform the mass ratios into molar ratios via the molecular weights of different FAMEs in order to compare the chromatographic results with the ^{1}H NMR ones on the same metric unit. The molar ratios are listed in the last column of Table 1.

Composition of FAMEs | Percentage (%) in mass | Molecular weight of FAMEs | Percentage (%) in mole |
---|---|---|---|

- a)The percentages in mass and mole are expressed as means ± SD (
*n*= 3).
| |||

Palmitic acid methyl ester (C16:0) | 44.70 ± 0.17 | 270.46 | 46.97 ± 0.17 |

Stearic acid methyl ester (C18:0) | 4.71 ± 0.01 | 298.52 | 4.48 ± 0.01 |

Oleic acid methyl ester (C18:1) | 41.28 ± 0.24 | 296.51 | 39.56 ± 0.23 |

Linoleic acid methyl ester (C18:2) | 9.32 ± 0.06 | 294.48 | 8.99 ± 0.06 |

^{1}H NMR spectrum (500 MHz) of palm oil was obtained under ambient conditions on a Bruker (Billerica, MA, USA) BioSpin GmbH spectrometer using *d*-chloroform as solvent. The assignment to the chemical shifts of the signals of components in TAGs and different fatty acids has been well known in the literature [3]. Figure 1 demonstrates the assignment to protons of different functional groups and their intensities relative to the reference signal of glyceryl protons A whose intensity is defined as 2.00. The integration value for each signal is annotated underneath the baseline.

By following the originally reported procedure to quantify the unsaturated fatty acids, the total amount of unsaturates in the palm oil sample is 47.25%, containing 0% linolenic acid (C18:3), 7.50% linoleic acid (C18:2), and 39.75% oleic acid (C18:1). Thus the total amount of saturates is:

With the unsaturates quantified, the experimental CH_{2} integration value contributing to those of the saturates can be determined:

where *I*_{exper,sat,total} was adjusted to its 1/3 because the number of protons in the fatty acid chains per molecule TAG is three times that of MAG and FAMEs. And only TAGs were detected in the palm oil sample due to the observation that the glyceryl protons fall in the chemical shift 4.0–4.3, which is a typical characteristic to distinguish TAGs from other acylglycerols.

According to the modified scheme, the remaining part of the CH_{2} integration value is theoretically contributed by either C16:0 or C18:0:

The differences between theoretical (for pure C16:0 and C18:0) and actual integration values are:

The difference between the theoretical integration values for contribution by either only C16:0 or C18:0 is determined by:

The amounts of C16:0 and C18:0 are derived from Eqs. (1) and (2):

The above results obtained from ^{1}H NMR and the modified quantification scheme are very close to those from GC-MS method in Table 1. Note that if calculated by following the original quantification scheme, the molar percentages of C16:0 and C18:0 are 4.04 and 48.71%, respectively, which is obviously reversed. In conclusion, with the minor typeset errors revised, in this work, the authors have successfully applied the novel method built by Knothe and Kenar to determine the fatty acid profile by ^{1}H NMR spectroscopy.