TEM investigation
Transmission electron microscopy is a valuable tool that provides fundamental data about the nanomaterials’ organization; this knowledge is very important for the materials science understanding and development, and in the same way, for the field of the highly diluted solutions which are also constituted from nanostructures.
Aurum metallicum 6C
Figure 1 contains several TEM images obtained with two different instruments (see Materials and methods section) for the 6C potency of AUR. Two different media have been employed for its preparation – the first one is a 50% v/v ethanol solution and it has been used for the AUR samples analyzed in Romania (E-AUR 6C). The second one is purified water and has been employed for the samples investigated in Turkey (W-AUR 6C). Despite the underlying differences in solvents, the obtained TEM images are quite similar regarding the shape of the nanoparticles. However, the nanoparticle size depends on the solvent type. This is revealed in the histograms of the two samples, indicating smaller nanoparticles for the E-AUR 6C than for the W-AUR 6C (Fig. 1C, G), most likely because ethanol is more effective as a stabilizing agent than water. The EDX data (insets from Fig. 1 and Supplementary Fig. S1 and S2) show a comparable percentage for gold – Au in both samples and the presence of silicon - Si and oxygen - O (the copper – Cu is from grid).
Aurum metallicum 30C
Furthermore, the 30C potency of AUR was investigated; Fig. 2 and Supplementary Fig. S3–S6 show the TEM images, EDX data and TEM-EDX mapping acquired for this potency. Here, it is worth mentioning the similarities between the two samples, E-AUR 30C and W-AUR 30C, in terms of the nanostructure shape and impurities visibility. As in the previous case, potency 6C, the size of the nanoparticles/nanostructures tends to be smaller for the E-AUR sample compared to W-AUR, Fig. 2C, G; this behavior is explained by the capacity of ethanol to act as an efficient stabilizing agent. Moreover, the histograms from Figs. 1 and 2 depict smaller nanostructures in the E-AUR 30C sample compared to E-AUR 6C, and a significant decrease of that larger than 150 nm from the water-based samples; these large structures are clearly seen in W-AUR 6C, but only in traces in the W-AUR 30C sample. This significant change in the profile of the two potencies, 6C and 30C, appears after the potentization process, which involves several successive dilutions and succussions.
As a general observation, silicon (Si) and oxygen (O) are the two elements omnipresent in the potency of 30C, while isolated nanoparticles containing impurities such as iron (Fe), titanium (Ti), calcium (Ca), magnesium (Mg), and aluminum (Al) are visible in the E-AUR 30C sample, where the constituents seem to possess smaller sizes (Fig. 2 and Supplementary Fig. S3–S5). These impurities originate either from the solvent used or could be formed in the potentization treatment by dissolution from the glass vials (e.g., Si or Ti). The reason that these impurities appear so evident in potency 30C can be attributed to the size of the remedies’ constituents, which is smaller than the size of the other two potencies 6C and 200C, as depicted in the histograms of Fig. 1C, G, Fig. 2C, G. and Fig. 3C, G.
In addition, the filiform profile observed in the W-AUR 30C sampling, Fig. 2D, the occurrence of some arrangements based on carbon (C) in the E-AUR 30C case, Supplementary Fig. S5B, and the presence of gold in the two 30C potency samples, Fig. 2 inset and Supplementary Fig. S3 and S6B, must also be highlighted.
All these observations suggest a different organization for the 6C and 30C potencies of AUR and prove the presence of both nanoparticles and cluster assemblies in the 30C samples. Thus, the clear nanoparticle shape of impurities and the filiform/cluster assembly profile formed from small structures promote the idea that at least for AUR 30C, the observed organization is not so much related to the nanoparticulate systems but more to a large assembly (large clusters) of small structures. Most likely, these clusters also contain ethanol and water (in E-AUR) or water (in W-AUR) molecules, while impurities, either isolated or linked to these large assemblies, appear as nanoparticles (clear round shape and different sizes). Although the presence of gold has been identified in all the investigated samples, it appears scattered on the grid surface in the TEM-EDX mapping images.
Aurum metallicum 200C
The characteristics of the 200C potency are illustrated in Fig. 3 and Supplementary Fig. S7–S9 by analyzing two samples (E-AUR 200C – prepared using an aqueous 50% v/v ethanol solution and W-AUR 200C – obtained only with purified water). The general tendency, already observed for the 6C and 30C potencies, is also present here; more precisely, the size of the nanostructures from the E-AUR 200C sample is smaller than those of the W-AUR 200C, as revealed in the histograms from Fig. 3. Moreover, for both 200C samples, the nanoparticles are larger in size than the nanoparticles observed at 30C potency and very different in size and shape from the nanoparticles at 6C potency (Figs. 1–3).
A distinct organization and the total lack of impurities inside some AUR 200C cluster associations are incontestably displayed in Fig. 3B. Moreover, the preference for the branched assembly of AUR 200C seems to be clear for both samples, Fig. 3A, D, while the presence of some small amounts of impurities such as silicon (Si) and iron (Fe) in these clusters is demonstrated by the EDX data presented in the inset of Fig. 3 and Supplementary Figs. S7, S9B. These results suggest an extended organization of AUR 200C molecules, also indicating the existence of stable and organized structures over a larger area. In the case of 200C potency of AUR, the impurities are also identified as a large assembly presented in Supplementary Fig. S8B. Thus, the TEM-EDX mapping shows the presence of large impurities (micrometer scale) such as silicon (Si), aluminum (Al), iron (Fe) and oxygen (O) linked together.
Some of these results are sustained by the literature data; thus, the presence of gold, even at
high potencies, 30C and 200C, of Aurum metallicum, which are beyond the Avogadro number, have also been shown in the papers of Chikramane et al.9 and Rajendran32. In the Chikramane work, the elemental composition of TEM particles was identified by selected area electron diffraction (SAED) investigation and sustained by inductively coupled plasma-atomic emission spectroscopy (ICP-AES) analysis9.
The study of Rajendran highlights the idea that nanoparticles are found mostly on the quantum dots scale in all solutions; their particle sizes are more or less similar to our data32. This nanoparticulate perspective is also supported by our findings, but in addition, our results demonstrate that AUR’s structure combines a mixture of nanoparticles and cluster arrangements, which are formed by smaller or larger nanostructures. The latter are more evident for the high dilutions that are beyond the Avogadro number and are influenced by the solvent nature and by the level of potentization; the higher the potency, the more branched and larger structures are formed. This organization extended over a large area should lead to structures that are more stable and could be detected by various investigations. To verify this hypothesis, Raman spectroscopic measurements were additionally employed.
Raman Spectroscopy And Machine Learning Investigations
For all the aforementioned reasons, and due to larger assemblies observed in TEM for the water-based samples, Raman spectroscopy was applied to water-based solutions only. The objective was to investigate the transformations that appear in three classes: purified water (PW), unpurified water (UW), and AUR. PW is the water generally employed for the homeopathic remedies’ preparation, while UW is a partially purified water; these types of water possess different characteristics. Here, we retain the low conductivity of PW samples (0.7–0.88 µS/cm) and their low levels of ions (NO3− <0.2 ppm, Al < 3–5 ppb, total heavy metals 0.00682 ppm), and note, for the UW samples, the higher values of the conductivity (196 µS/cm) as well as the higher concentration of different ions (nitrate, carbonate, sodium, etc. ), see Materials section for more details.
Potentization was applied to the PW, UW, and AUR samples prepared at three different days to obtain three batches of potentized samples at 6C, 30C and 200C potencies. The PW and UW are not generally potentized for commercialization; the potentization procedure was applied to them only for this study, and thus, 33 samples were analyzed by Raman spectroscopy. Each sample was analyzed at 5 points to obtain representative data of the investigated solutions. A total of 165 Raman spectra (domain 72-4020 cm− 1) were subjected to the classification study.
In effect, we attempt to investigate if this methodology (based on Raman spectroscopy and machine learning algorithms) is able to classify solutions not significantly different in structure, such as i) purified versus unpurified water solutions, where the differences between them are subtle, since the unpurified water used in these experiments is essentially purified water used in cosmetics, and ii) purified water versus Aurum metallicum solutions, where the differences are due to the presence of very low concentrations of gold in the Aurum metallicum samples. Note that the complexity and dynamics of water-based structures have a response in the investigated Raman region (especially OH stretching range), as demonstrated by Q. Sun24 and several other authors20–23.
Average Raman spectra are shown in Fig. 4 (left), obtained for different levels of potentization (6C, 30C, 200C) of the investigated classes (PW, UW and AUR) plotted together with spectra of non-potentized PW and UW samples. More details containing the Raman spectra of each of the 5 points registered for each sample are presented in Supplementary Figs. S10-S12. The PW spectra showed the characteristic H-O-H bending vibrations of water at approximately 1646 cm− 1 and the O-H stretching signals in the 3000–3700 cm− 1 region33. The variations observed in both regions (bending and stretching vibrations of water) of the three investigated classes could be the result of different intra- or intermolecular interactions that depend on the local molecular environments of each sample34. These differences are obvious by simple inspection and are further analyzed by ML algorithms in an attempt to examine the capacity of AI tools to differentiate Raman spectra obtained from potentized and non-potentized solutions.
Some AI tools commonly adopt ML methods that have proven efficient in discriminating various complex materials’ Raman spectra (i.e. minerals) or classifying of high-dimensional spectroscopic data27,28. For the classification study, several ML algorithms have been employed to differentiate these spectra by making use of various classification models, such as decision trees, discriminant analysis, support vector machines, nearest neighbor, ensemble classifiers, deep learning, and optimized algorithms with respect to the parameter choice for all these classes of classification methods available in MATLAB R2021b (MathWorks, USA). The best parameters for all optimized models are listed in Tables 1 and 2. The default choice of k-fold cross-validation, with k = 5, was used throughout, which is one of the most popular resampling techniques for protection against overfitting, and it generally delivers a less biased estimate of the model skill than other methods, such as simple train/test splits35.
Confusion matrices are commonly employed when solving binary classification as well as multiclass classification problems. A confusion matrix summarizes the classification performance of a classifier with respect to some test data. It is a two-dimensional non-symmetric matrix, indexed in one dimension by the true class of an object and in the other by the class that the classifier assigns36. Their entries represent counts from predicted and actual values. Each entry in a confusion matrix denotes the number of predictions made by the model where it assigned classes correctly or incorrectly. The diagonal entries of a confusion matrix represent the number of instances that the classifier has correctly assigned. The classes are listed in the same order in the rows as in the columns; therefore, the correctly classified elements are located on the main diagonal from top left to bottom right, and they correspond to the number of times the two raters agree. The columns represent the predicted classification, whereas the rows display the true classification.
Classifying classes
First, we investigated the capacity of the ML algorithm to recognize spectra that belong to the same class and group them together. From all the ML algorithms and their optimized versions with respect to the choice of parameters, the optimized KNN model, using the parameters shown in Table 1, demonstrated the ability to classify between different classes AUR, PW, and UW, with only 3 out of 165 misclassified spectra. More precisely, only a single spectrum of AUR 6C was classified as UW 30C, one spectrum of PW 200C was misclassified as UW 30C, and finally, one spectrum of UW 30C was classified as AUR 6C. The classification result is summarized in the confusion matrix of Fig. 4 (right) and indicates a different organization of the three investigated classes. It seems that the potentization results are strongly influenced by the type of substrate submitted to the process; they can be seen as a certain type of organization of the initial structures. In other words, the potentization process can be realized on purified water, on purified water containing a substance or on water containing different impurities/ions, and for each case, it leads to the formation of some specific, organized structures. Note that these results have been obtained on three batches, prepared in three different days, so possessing some variations of the starting solutions’ characteristics. Even in these circumstances, the model is able to find structures that are specific to each class; these considerations allow us to assume that the potentization process imprints on each class a specific organization that is not affected by the minor variations of the initial solutions’ properties.
Table 1. Optimal parameters for the KNN model used for classifying among different classes
Table 2. Optimal parameters for classifying potencies within each solution class (PW, UW, AUR) and within solutions of the same potency (6C, 30C, and 200C)
Despite the success of KNN for discriminating among the AUR, PW and UW classes, the classification score achieved was only 61.2%. A careful inspection of Fig. 4 (right) reveals that within each class, there are several misclassified spectra. We therefore attempt a further refinement of these results within each class.
Classifying potencies within each class
All possible ML algorithms with their associated optimal versions were applied to 3 different datasets, one dataset for each class group, more precisely (PW, PW 6C, PW 30C, PW 200C), (UW, UW 6C, UW 30C, UW 200C), (AUR 6C, AUR 30C, AUR 200C, PW). The potency levels of the AUR class were classified against the spectra obtained from the non-potentized PW class to investigate whether the ML algorithm can distinguish AUR spectra at any potency level from non-potentized purified water spectra. The optimal hyperparameters are listed in Table 2.
In Fig. 5 (left), we observe that for the PW class, non-potentized PW spectra (first row) were successfully recognized. Spectra from PW 30C and PW 200C samples were also classified with satisfying accuracy, 14 out of 15 for PW 30C and 13 out 15 correspondingly. For UW and UW 6C, 14 out of 15 spectra were also correctly classified (Fig. 5, middle). From the AUR class, all spectra were successfully discriminated from spectra of the PW class, and there were no misclassifications of PW as AUR at any potency or vice versa, but a good similarity of the spectra was found only for AUR 200C, where 12 out the 15 spectra were correctly assigned (Fig. 5, right).
The ability of ML to differentiate spectra obtained by these classes can be attributed to the nanostructures formed inside each class during the potentization process and each different level of potentization. Nevertheless, dynamics between different H-bonding structures have been reported even inside liquid water24. Therefore, the ML results reveal a strong relation between the H-bonding structures formed during the potentization process and the potentization level. However, further studies are necessary to verify, understand the physical process, and explain how the potentization level can be derived from Raman profiles.
Classifying within the same levels of potentization
Finally, we investigated the ability of ML algorithms to classify potentized PW, UW, and AUR samples at a particular potency from the non-potentized PW and UW. More precisely, we formed the following groups: (AUR 6C, PW, PW 6C, UW, UW 6C), (AUR 30C, PW, PW 30C, UW, UW 30C), and (AUR 200C, PW, PW 200C, UW, UW 200C). From all the available classification algorithms, SVM achieved the highest classification scores, more precisely 90.7% for the 6C group and 88% for the 30C and 200C groups. The optimal hyperparameters are listed in Table 2. The classification results summarized in the confusion matrices presented in Fig. 6 demonstrate that such a classification is possible and fairly accurate since, at each potency, very few spectra were misclassified. More precisely, at potency 6C, only one AUR 6C spectrum out of 15 was misclassified as UW 6C and vice versa, while for UW, all 15 spectra were correctly classified. At potency 30C, 2 out of 15 AUR 30C spectra were misclassified as PW 30C and UW 30C, all 15 PW spectra were correctly classified, and only 3 out of 15 UW spectra were misclassified as AUR 30C and UW. At potency 200C, only 1 out of 15 AUR 200C spectra was misclassified as UW, and only 1 of the 15 UW spectra was misclassified as UW 200C, while all UW 200C spectra were correctly classified.
These results are sustained very well by the TEM data presented in Figs. 1, 2, and 3, which indicate a different organization of the three types of potentized samples. Thus, the TEM images of the 30C sample of AUR showed more impurities visible in the collected images, while the investigation of the Raman data indicated some similarities with the 30C potentized samples of PW and UW solutions. The authors assumed that the impurities are more easily visible in the 30C potency due to the smaller size of the organized therein cluster constituents, and consequently, these observations highlight the final solution dependence of the eluent purity, as well as the fact that various structures could be part of the initial solution. Thus, the ML analysis of the AUR 30C solution indicates exactly the same 30C potency dependence of the eluent composition, and for this reason, the Raman data of some samples appeared to possess similarities with the spectra of the 30C potentized PW or even UW solutions.
Considering the PW and UW probes, it is evident that the potentization process also applied to these samples. It seems that more similarities between the batches are found inside the potentized UW samples, PW spectra showing fewer similarities during the ML analysis. The classification results obtained in this study involve a relatively low number of samples, which is why the SVM family of algorithms seems to perform better than the rest. Further investigations are therefore required, and sufficiently more measurements are required to unequivocally determine the reproducibility of these results.