Insight into the structure of black coatings of ancient Egyptian mummies by advanced electron magnetic resonance of vanadyl complexes

Abstract Ancient Egyptian mummies from the Late Period to the Greco–Roman Period were covered by a black coating consisting of complex and heterogeneous mixtures of conifer resins, wax, fat and oil with variable amounts of bitumen. Natural bitumen always contains traces of vanadyl porphyrin complexes that we used here as internal probes to explore the nanoscale environment of V 4+ ions in these black coatings by electron nuclear double resonance (ENDOR) and hyperfine sub-level correlation spectroscopy (HYSCORE). Four types of vanadyl porphyrin complexes were identified from the analysis of 14 N hyperfine interactions. Three types (referred to as VO-P1, VO-P2 and VO-P3) are present in natural bitumen from the Dead Sea, among which VO-P1 and VO-P2 are also present in black coatings of mummies. The absence of VO-P3 in mummies, which is replaced by another complex, VO-P4, may be due to its transformation during preparation of the black matter for embalming. Analysis of 1 H hyperfine interaction shows that bitumen and other natural substances are intimately mixed in these black coatings, with aggregate sizes of bitumen increasing with the bitumen content but not exceeding a few nanometres.


S4 Derivation of Equation 1
The 1 H ENDOR spectrum is the superposition of two independent signals: (i) one from the protons of the C-Hmeso bridges linking pyrole groups of porphyrin ligands, hereafeter referred to as VOP-1 H, and (ii) the other one from the matrix protons, hereafeter referred to as M-1 H, corresponding to protons of asphaltene, of the natural substances of the black matter, and of protons of alkyl substituent in porphyrin ligands.M-1 H protons are characterized by a pure dipolar hf interaction while VOP-1 H protons are characterized by an isotropic hf interaction in addition to the dipolar one.
Let  be the signal height at the frequency  ∥ corresponding to the parallel component of the VOP-1 H signal and  the signal height at the maximum of perpendicular component of the VOP-1 H at frequency  ⊥ (see Fig. 4a).Let also   ,   ,   and   be the respective contributions of a single VOP molecule and a single M-1 H to  and .
Then : where   and   are the total numbers of VOP molecules and matrix protons in the sample, respectively.
The VOP molecules are embedded in bitumen aggregates spread within a bioorganic matrix, which contains the M-1 H's.As the M-1 H's are detected upon saturating an EPR transition of the VOP molecules, they must have a residual dipolar hf interaction with the VOP's.We thus assume that the detected M-1 H's are in a layer of volume   surrounding a bitumen aggregate (Fig. S7), then   =     [𝐻] where   is the total number of bitumen aggregate in the sample and [] the concentration of M-1 H's in the matrix.We also have . Finally, we obtain:

S7 Estimation of second order contributions in 14 N parameters from dq-dq and sq-dq correlation peaks
The first order nuclear spin energy levels of a single ms state of VO 2+ interacting with the nuclear spin I = 1 of a 14 N nucleus is given by: where the energy E, the hf interaction A and the quadrupolar interaction Q are taken along the direction of the magnetic field.The corresponding energy level diagram is given in Fig. S9 for the two ms states.The frequencies of the single quantum ( ) nuclear spin transitions of 14 N are given by (Reijerse, et al., 1998;Dikanov, et al., 2004): The second order corrections    is not affected by 2 nd order correction: On the contrary, measurement of Q from expressions from Eqs.S5 is affected by second order corrections and necessitates the preliminary determination of , all transitions in the ms = -1/2 state are known without uncertainty due to 2 nd order corrections.Single-quantum transitions in the ms =+1/2 state were obtained to 1 st order by the equation and are thus affected by 2 nd order corrections.The resulting diagrams for VO-P complexes are given in Fig. S9.In the absence of unambiguous sq-dq correlations for VO-P3 and VO-P4, we could not obtain sq frequencies and quadrupolar parameter Q for these complexes.
The second order term in Eqs.S5, S6, S7 and S8 can be estimated as follows.Combining the two dq frequencies gives:

Figure S1 .
Figure S1.Binocular photographs of the samples studied in this work.© C2RMF.

Figure S6 .
Figure S6.Two examples of geoporphyrins commonly found in oil, with the corresponding parent biomolecules = [], with [] the concentration of VOP's in the sample and , the sample volume.As the experimental variable is  = []/[]  , where []  is the VOP concentration in the reference sample Ref 1,   is then rewritten as   = []  , yielding:

Figure S7 .
Figure S7.Schematic description of a bitumen aggregate in interaction with protons of bioorganic compounds.

Figure S9 .
Figure S9.Effect of values on simulated dq-dq correlation peaks for VO-P1 (in green) and VO-P2 (in red) complexes, showing the lack of blind spot effects.Field setting mI = +3/2┴ at 355.6 mT

Figure S10 .
Figure S10.Comparison of experimental and simulated HYSCORE spectra of VO-P1 and VO-P2 of sample Ref 1.The experimental spectrum is in grey, the simulated spectra are in green (VO-P1) and red (VO-P2).Field setting mI = +3/2┴ at 355.6 mT.The simulation parameters are given inTable 3 the hf interaction, n is the orientation of the magnetic field, and p and q are two orientations perpendicular to n and to each other.Determination of A from expressions of  dq

.
As only a part of the sq-dq correlations has been detected, only half of then sq frequencies could be determined precisely.The observed sq-dq correlations for VO-P1 and VO-P2 correlate the dq transition of the ms = +1/2 state with one of the sq transitions of the ms = -1 in Eq.S6 for VO-P complexes, which corresponds also to the uncertainty in the experimental measurement of dq frequencies in Fig.6.Concerning second order contributions in the determination of the quadrupolar interaction Q, expressions for sq frequencies give

Figure S11 .
Figure S11.Energy level diagram of an electron spin S = 1/2 interacting with a nuclear spin I = 1, showing single quantum (sq) transitions (in black) and double quantum (dq) transitions (in red), with the corresponding diagrams for the four VO-Ps detected in the black matter; the four experimental diagrams correspond to the observation of the EPR transition mI = +3/2┴.(for VO-P1, VO-P2 and VO-P4) and mI = -1/2 for VO-P3; the quadrupolar interaction can be measured from sq transitions only when sq-dq peaks are detectable (VO-P1 and VO-P2); aiso was deduced from dq-dq transitions obtained with the two EPR transitions mI = -1/2 and mI = +3/2┴..

Table S1 .
Description of samples