Very Dilute Aqueous Solutions — Structural and Electromagnetic Phenomena

The customary models of water and their solutions predict that serial dilutions, combined with vigorous shaking and exposure to ambient EM radiation, do not affect their characteristics (Horne, 1972; Robinson and Stokes, 2002). In addition, these models predict that H₂O molecules move randomly, with the exception of solvation shells’ H₂O. Moreover, these models predict that solvated solutes distribute homogenously, move independently and randomly. These customary models explicitly describe electro-static forces and assume that electro-dynamic ones can be treated perturbatively or often even may be ignored. However, QED models explicitly (non-perturbatively) describing electro-dynamic forces show that these forces may lead to association of H₂O and solute molecules (Del Giudice et al., 1988, 1998, 2000, 2002, 2006; Preparata, 1995 chapters 2, 5, 10; Arani et al., 1995; Bono et al., 2012; Yinnon and Yinnon, 2012). Interactions between EM radiation and electrolytic solutes, polar solute molecules, the dipole moments of H₂O or the electrons of H₂O may lead to formation of various domain types. Here such domains are denoted QED domains. Formation of these domains occurs only in specific concentration ranges, which depend on solute type. These domains may agglomerate into supra-domains. These supra-domains are not ensembles of molecules but agglomerates of domains, like domains in liquid crystals.

A concise review of the QED theory of water and their solutions has been presented by Yinnon and Liu (2015a). The various hitherto identified QED domains present in these liquids, their schematic pictures, their properties and the physics underlying the dependence of the domains’ formation on concentration are all summarized in Yinnon and Liu (2015a). In their review, Yinnon and Liu (2015a) emphasized that the QED theory of water is based on an explicit non-perturbative description of the van der Waals’ dispersion forces. The imperative for adequately describing van der Waals’ dispersion interactions and other electro-dynamic interactions in various condensed matter systems has also recently been pointed out by Ferri et al. (2015), Fiorini (2016) and Ambrosetti et al. (2016).

Investigations of the dielectric permittivity and electrical conductivity of SDVSAS of membranotropic amphiphilic calix[4] resorcinarene with tris (hydroxymethyl) methylamide groups (MAC4RWTHMG) at concentrations in the range of 10^-11-10^-3 M have shown that its molecular associates have fractal structures (Lunev et al., 2014). Analyses by Yinnon and Liu (2015c) have shown that this SDVSAS has the characteristics specified in paragraphs I-V — the analyses pertain to the experimental data on the physicochemical properties of these liquids and on the sizes and electrokinetic potential of their molecular associates measured by Ryzhkina et al. (2012b).

Self similarity is a property of the QED domains (Vitiello, 2012, 2014), e.g., of supra-CD_rot, supra-, supra-CD_plasma and supra-IPD_plasma. According to the above presented QED model, for C < , SDVSAS contain one or more of these domain types. Therefore, the molecular associates in SDVSAS, which are mediated by EM radiation, indeed should have fractal orderings. To the best of my knowledge, the analyses of the experimental data of the SDVSAS of MAC4RWTHMG, carried out by Lunev et al. (2014), provide the first confirmation of the self similarity aspect of the SDVSAS model. It should be noted, however, that the self similarity of the H₂O orderings in water perturbed with a Nafion membrane (iterative Nafionized water) or in water perturbed by iterative filtrations was recently proven by Capolupo et al. (2014). These researchers showed that the linear correlations between the logarithm of various physicochemical properties (e.g., χ, Q or density) and the pH of these perturbed waters [measured by the group of Elia et al. (2013a,b, 2014a,b, 2015)] reflect the self similarity of their H₂O orderings. These orderings have been identified as and CD_rot by Yinnon and Elia (2013), Yinnon et al. (2016) and Elia et al. (2017). Linear correlations between the logarithm of χ, the logarithm of Q and pH have also been observed for SDVSAS (Elia et al., 2004b; Belon et al., 2008; Elia et al., 2015). Thus, from the analyses of Capolupo et al. (2014), Elia et al. (2004b), Belon et al.(2008) and Elia et al. (2015), one could infer that the H₂O orderings observed in SDVSAS should have a fractal structure. The study by Lunev et al. (2014) confirmed this inference.

Emission of ULF radiation by SDVSAS

Data on SDVSAS emitting ULF radiation reported in the literature — Montagnier et al. (2009, 2011, 2015) demonstrated that SDVSAS of some types of deoxyribonucleic acid (DNA) emit ULF (500-3000 Hz) EM radiation.^d The SDVSAS were prepared in plastic 1.5 mL Eppendorf tubes. Specifically, they demonstrated the following:

• The number of dilution steps required for the SDVSAS to emit the radiation depends on the type of the DNA (e.g., DNA extracted from bacteria or viruses). Typically, at least six decimal dilutions of a few nano gram (ng) of DNA are required for the emission of ULF radiation to be detectable. After applying more than about 10 to 17 decimal dilutions, the emission is no longer observable. Expressed differently, the emission of ULF radiation is typically observed for SDVSAS of DNA with concentrations in the 10^-5 M to 10^-18 M range. The intensity of the emitted radiation non-monotonically depends on the concentration. The fact that no emission was detectable for SDVSAS of DNA with C<10^-18 M might be due to limitations of the experimental set up. The emission might be too weak to be observable with the simple apparatus employed by Montagnier et al. (2009, 2011, 2015).^d No emission of ULF radiation was detectable for serially diluted DNA solutions which were not vigorously shaken after each dilution step.
• The SDVSAS of DNA only emit ULF radiation when these are stimulated by background extremely low frequency (ELF) radiation. The sources of the ELF radiation may be the natural Schumann resonances of the geomagnetic field or artificial ones. The frequency of the Schumann resonance, which has the lowest frequency, is 7.83 Hz (Nickolaenko and Hayakawa, 2002). Storing the SDVSAS in Permalloy containers, which screens the background EM radiation, affects their emission of the ULF radiation. For some samples, after several hours of such storage, no emission was detectable anymore. For other samples, after having been stored for 48 h under equivalent conditions, emission of ULF was still detectable.
• The radiation emitted by the SDVSAS of DNA is absorbable by neighboring pure water samples. The absorbed radiation alters the physicochemical properties of the neighboring pure water samples. These samples acquire properties reminiscent of those of the SDVSAS of DNA.

Elia et al. (2012) demonstrated that also SDVSAS of other solutes (e.g., fullerene), which were 5, 7, 9, 12 or 30 times centesimally diluted, emit radiation which alter the physicochemical properties of neighboring water samples.

Explanations for the emission of ULF radiation by SDVSAS — Montagnier et al. (2011, 2015) provided explanations for some of their experimental results. Their explanations, which are based on the processes detailed in paragraphs (v) and (vii), are as follows.

a) DNA are poly-electrolytes surrounded by a cloud of positive counter-ions. These ions may orbit around  (Del Giudice et al., 2002). The circular speed of the orbiting ions is proportional to the ion cyclotron frequency (v_c). Typically, v_c falls in the 1-100 Hz range. Ions orbiting around  get extracted from their loops by background alternating magnetic fields (Schumann resonances or artificial fields). Extraction of the ions from their orbits (because of conservation of angular momentum) causes a rotation of the plasma of the quasi-free electrons (QFE) present in the  (i.e., the extraction excites the domain and induces vortices). Since the mass of electrons is much smaller than that of the ions, the rotating plasma has a frequency v_p that is much higher than v_c. Typically, the lowest v_p value is of the order of 1000 Hz and the spacing between the rotating plasma frequencies is of the same order, e.g., in the ULF range.

b) The rotation of the QFE produces the magnetic component of the ULF radiation.

c) The frequency and intensity of the emitted ULF radiation depend on the concentration of the counter-ions, i.e., the degree of dilution of the SDVSAS of DNA. The following causes underlie this dependency: Firstly, v_p depends on the number of counter-ions participating in the orbiting and extraction processes. This number is a function of their concentration. v_p is also determined by the quantization of angular momentum. Secondly, the co-resonating fields appearing in the surroundings of the rotating depend on the concentration of the counter-ions. These fields may produce coherence among the individual and thus affect the frequency and intensity of the emitted ULF radiation.

Montagnier et al. (2011, 2015) emphasized that their conjecture — that the emission of ULF radiation is due to magnetic activity — is supported by the absence of such emission after the SDVSAS samples were stored in Permalloy containers.^e

As to the solute reminiscent alterations of pure water samples neighboring on SDVSAS of DNA, Montagnier et al. (2011, 2015) conjectured that it is due to the SDVSAS samples emitting ULF radiation which triggers coherence among the of the pure water samples. They noted that the physics underlying the copying of properties of SDVSAS to neighboring pure water samples is  similar to that of: “the proximity effect observed in two superconducting samples or in the arrays of Josephson junctions, by which the samples or the junctions fall into a phase-locking regime.”

^e EM radiation at frequencies of kHz – Tera Hz can also be attributed to vibrations of electrically polar structures (Cifra, 2015), e.g., proteins, EDA^CDrot or EDA^IPDplasma.

Unexplained phenomena pertaining to emission of ULF radiation by SDVSAS — To the best of my knowledge, no explanations have yet been forwarded for several of the observations made by Montagnier et al.’s (2009) and Elia et al. (2012).  In the following, I attempt to clarify them with the QED model of SDVSAS:

♦ Why was emission of ULF radiation not detectable for serially diluted aqueous solutions of DNA, when these solutions were not vigorously shaken after each dilution step?

According to the QED model’s aspects summarized in paragraph I: For < C < , part of the solvated solutes aggregates in CD_plasma. Organization of DNA molecules (or their counter-ions) in domains with characteristics of CD_plasma has been observed by Samal and Geckeler (2001), as discussed by Yinnon and Yinnon (2009).

According to paragraph II: for C < , CD_plasma transform into IPD_plasma. Typically 10^-6 M < <10^-4 M. According to paragraph III, vigorous shaking of solutions containing IPD_plasma excites or break up these domains and creates EDA^IPDplasma.

According to paragraph V: Firstly, for C < , EDA^IPDplasma stabilize CD_rot. Secondly, vigorous shaking of the liquid excites or breaks up the CD_rot and thus creates EDA^CDrot. Thirdly, the CD_rot and EDA^CDrot may agglomerate into supra-CD_rot with their electric dipole moments ordered more or less parallel or anti-parallel. The orientation of the electric dipole moments of the CD_rot affects the physicochemical properties of the SDVSAS.

As noted in paragraphs I-V, may get stabilized by all the domains mentioned in the last three paragraphs, i.e., by CD_plasma, IPD_plasma, EDA^IPDplasma, EDA^CDrot or CD_rot. For C above the Avogadro limit, all these domains contain coherently oscillating ions, which can orbit around . Vigorous shaking may excite the , i.e., its plasma of QFE.

In regards to the information presented in the last four paragraphs and in paragraphs (a) – (c), the observation that only serially diluted solutions of DNA which were vigorously shaken after each dilution step emitted ULF radiation, alludes to the following: Only the micron sized CD_rot, EDA^CDrot, EDA^IPDplasma or their agglomerates (creation of which requires serial dilutions and vigorous shaking after each dilutions step, and which all contain ferroelectric ordered H₂O) can induce coherence among many of the 10^-7 m sized . The coherence assures that the intensity of the ULF emitted by the excited plasma of QFE of the is strong enough to be detected with a solenoid.

The abovementioned shows that the observed emission of ULF radiation by SDVSAS provides additional support for the main aspect of its model.  In other words, CD_rot, EDA^CDrot, and EDA^IPDplasma are the entities underlying these liquids’ extraordinary properties. It also substantiates the conjecture of Montagnier et al. (2015) that the emission of ULF radiation by SDVSAS of DNA is the outcome of symmetry breaking. As they formulate it: “the symmetry which gets broken is the rotational symmetry of the electrical dipoles of the H₂O and correlation modes are the ones associated to the dipole waves (similar to spin waves in ferromagnets).”

♦ Which ions orbit around  in SDVSAS diluted below the Avogadro limit?

Elia et al. (2012) demonstrated that SDVSAS diluted below the Avogadro limit emit EM radiation. Their experiments, however, did not reveal the wavelengths of the radiation. In case the radiation includes ULF radiation, the question arises: Which ions orbit around in these extremely diluted liquids? Elia et al. (2012) prepared these SDVSAS in glass vessels. Therefore, these liquids contained dissolved components of the glassware containers at impurity level concentrations. However, in the absence of such impurities, such as when SDVSAS are prepared in plastic containers, H₃O⁺ or OH^– ions are present. The pH of SDVSAS is affected by their molecular associates (Elia et al., 2004a; Ryzhkina et al., 2010, 2012b, 2013). [The effect of the associates on the pH has been explained in paragraph vi of the discussion section in Yinnon and Liu (2015c).] Hence, H₃O⁺, OH^– or impurity ions may all orbit around in SDVSAS.

♦ Why is emission of ULF radiation no longer detectable for some samples, after their storage for a few hours in Permalloy containers, while other samples stored for 48 hours under equivalent conditions still emitted ULF radiation?

For clarification of these phenomena, it should be emphasized that experiments have shown that the dynamics of SDVSAS are that of far-out-of equilibrium dissipative systems (Elia et al., 2008a,b, 2010). The dissipative dynamics of their molecular associates occur over macroscopic time scales, i.e., the dynamics may continue for months and even many years when the SDVSAS are kept at room temperatures and pressures.

The dissipative dynamics of SDVSAS, according to the QED model of SDVSAS, are due to a constant reorganization of the CD_rot and EDA^CDrot constituting the supra-CD_rot (Yinnon and Elia, 2013). It is also due to the stabilization and disintegration of and reorganization of supra-. Agitating SDVSAS by vigorously shaking accelerates reorganization of its domains. It also enhances excitation of the QFE of its . The dynamics of CD_rot (which is related to the rotational excitation of H₂O) is much slower than that of (which is related to the electronic excitation of H₂O).

The continuous reorganization of the domains in SDVSAS affects the radiation emitted and absorbed by these liquids. On disintegration of , the EM radiation condensed within these domains is released (see paragraph i). The released radiation may enhance stabilization of new ,  it may escape to the environment or it may transform to heat. The same holds for the EM radiation condensed within CD_rot. Reorganization of the domains in SDVSAS also affects the vortices of the QFE of , as it affects the emission of ULF radiation. Part of the emitted ULF radiation may get absorbed by QFE of neighboring .

Placing SDVSAS in Permalloy containers screens its CD_rot and  from ambient IR and UV radiation. These are the sources of the radiation mediating the interaction between the molecules constituting these domains (see paragraphs I and V). However, the EM radiation released by the reorganization and disintegration of CD_rot and  cannot escape through the walls of the Permalloy container to the environment. Thus, on placing SDVSAS samples in Permalloy containers, the non-linear dissipative processes taking place in these liquids imply that in some samples the CD_rot and persist for a long time and continue to emit ULF radiation.  Conversely, in other samples most of these domains quickly disintegrate.

♦ Why does the intensity of the ULF radiation emitted by the SDVSAS of DNA depend non-monotonically on their concentration?

The non-monotonic dependence on concentration of the intensity of the ULF radiation emitted by SDVSAS [as with similar dependencies of other physicochemical properties of SDVSAS, noted in paragraph (7)] result from the reorganization of their associates. More specifically, according to the model of SDVSAS, every perturbation like a dilution or shaking alters the ordering of the electric dipole moments of the supra-CD_rot. These alterations affect the prevalence of the  and supra- . As such, the alterations also affect the ULF radiation emitted by the pool of quasi free electrons of .

Hitherto, to the best of my knowledge, emission of ULF radiation has been reported only for SDVSAS of some types of DNA. This calls for research aimed at searching for SDVSAS of other solutes which emit ULF radiation. Such research might verify the various explanations presented in this section.

Impact of EM radiation on the formation of associates in SDVSAS

This section shows that recent experimental data, obtained by A.I. Konovalov’s group (D.A. Konovalov et al., 2015), support some aspects of the explanations of Montagnier et al. (2011, 2015) discussed in the previous section. The data supports the hypothesis that the  present in an aqueous SDVSAS with concentration less than C_thr but above the Avogadro limit are affected by 7.85 Hz EM fields.

A.I. Konovalov’s group was the first to demonstrate that only when SDVSAS with C less than C_thr but above the Avogadro limit were stored under ambient EM fields, the presence of molecular associates in these liquids were observable with dynamic light scattering (DLS) (Ryzhkina et al., 2011a; Konovalov and Ryzhkina, 2014). After storage of these SDVSAS for 24 hours in Permalloy containers, DLS could not distinguish associates in these liquids. Moreover, after such storage, these liquids’ characteristic physicochemical and bioactive properties disappeared. Analyses of the associates and their impact on the physicochemical properties of SDVSAS indicate that these associates include , CD_rot and EDA^CDrot (Yinnon and Liu, 2015b&c).

Recently, A.I. Konovalov’s group built a hardware complex, which enabled controlling the amplitude and frequency of the magnetic field in a Permalloy container (D.A. Konovalov et al., 2015). The group prepared samples of SDVSAS of biologically active p-sulfonato-calix[6]arene with C=1×10^-9 M. The C_thr of this SDVSAS is about 10^-7 M, significantly larger than C. One series of the samples was kept for 24 hours on the laboratory bench. In this paper, these samples are denoted as SDVSAS_LB. A second series was kept for 24 hours under hypo electromagnetic conditions, in the Permalloy container. Here these samples are denoted as SDVSAS_P. A third series was placed for 24 hours in the hardware complex, with the frequency of its magnetic field tuned to 7.85 Hz. These samples are denoted as SDVSAS_MF-7.85. This third series was subdivided into four sub-series, each of which was subjected to magnetic fields with different amplitudes, respectively, 48, 24, 12 and 6.4 A/m. These samples are denoted as SDVSAS₄₈, SDVSAS₂₄, SDVSAS₁₂ and SDVSASL_6.4, respectively.

D.A. Konovalov et al. (2015) showed that molecular associates were detectable with DLS in their SDVSAS_LB, but were not detectable in their SDVSAS_P. The average hydrodynamic diameter of the associates present in the SDVSAS_LB samples was 230 nm. These results conform to those of many previously studied SDVSAS (Konovalov and Ryzhkina, 2014). The 230nm average hydrodynamic diameter is typical for the supra- present in SDVSAS for C<C_thr (Yinnon and Liu, 2015c). DLS also evidenced associates in SDVSAS₄₈, SDVSAS₂₄ and SDVSAS₁₂, but did not uncover any associates in SDVSAS_6.4. The size distributions of the associates in SDVSAS₄₈ and SDVSAS₂₄ were mono-modal. These distributions were the same as those of SDVSAS_LB. However, decreasing the magnetic field’s amplitude from 24 to 12A/m led to poorly reproducible results, as the SDVSAS₁₂ samples had poorly reproducible bimodal associate size distributions.

In the following, two complementary possible explanations for the findings of D.A. Konovalov et al. (2015) are offered:

♣ As noted in paragraphs I and V, interactions between UV EM fields and H₂O underlie formation of , while interactions between IR EM fields and H₂O underlie formation of CD_rot. Despite Permalloy screening ambient UV and IR EM fields, the analyses of the experimental data obtained by Montagnier et al. (2009) have indicated that placing SDVSAS samples in Permalloy containers does not lead to immediate disintegration of all its molecular associates. In some samples, the associates seem to persist for at least 48 hours. Thus, D.A. Konovalov et al. (2015)’s finding that DLS measurements did not reveal associates in SDVSAS_P, likely does not mean that no associates were any longer present in samples after these were screened from ambient EM fields for 24 hours. It is conceivable that the screening considerably diminished the number of associates,  so that their prevalence was below the detection limit of DLS. According to QED, on disintegration of part of the supra-CD_rot and supra-, the remaining domains are less stable. For , their destabilization implies that the continuing adsorption and desorption of their H₂O (described in paragraph iii) take place on shorter timescales,  so that it becomes more difficult to observe these domains.

The difference between SDVSAS_P and SDVSAS_MF-7.85 is that the latter were exposed to 7.85 Hz EM fields. Since DLS showed that the size distribution of the domains in SDVSAS₄₈ and SDVSAS₂₄ was similar to that of SDVSAS_LB, i.e., these liquids contained nano-associates with a 230 nm average hydrodynamic diameter, the presence of the 7.85 EM field seemingly enhanced stabilization of . The stabilization is likely attributable to processes involving the vortices of the plasma of the QFE of . These vortices are created by the 7.85 Hz EM field (see paragraph vii). For example, one possible stabilization process is that of the vortices of different  interacting with each other. Another process is that these vortices interact with the terrestrial magnetic field. This explanation implies that the intensity of the alternating 7.85 Hz EM field must be sufficiently strong to extract ions cycling around  from their orbit, because such extraction creates vortices (see paragraph vii). In other words, on lowering of the intensities of the applied 7.85 Hz field, fewer or no vortices are created in the plasma of QFE of . It is to be expected that few vortices cannot considerably stabilize , and that these cannot significantly reduce the rate of the continuous adsorption and desorption of the H₂O of these domains. This explanation is compatible with the difficulties D.A. Konovalov et al. (2015) faced in observing molecular associates in SDVSAS₁₂ . It is also compatible with them  not being able to discern associates in SDVSAS_6.4.

In paragraph V it was emphasized thatn may get stabilized by CD_rot. In other words, that the , which are meta-stable in bulk water at ambient conditions (see paragraph iii), get stabilized by CD_rot. The stabilization of  in SDVSAS occurs when these liquids are diluted below and CD_rot domains are stabilized by EDA^IPDplasma or polar macromolecules. The findings of D.A. Konovalov et al. (2015) imply that SDVSAS stabilization of requires the presence of CD_rot as well as the presence of 7.85 Hz magnetic fields. Indeed, the recent experiments by D’Emilia et al. (2015, 2016) hint that in bulk water, such fields reduce the continuously changing space distribution of the H₂O constituting its meta-stable and its non-coherent H₂O. Their findings suggest that exposing pure water to sufficiently strong magnetic fields with a frequency equaling that of one of the ion cyclotron frequencies of H₃O⁺, e.g., v_c=7.83 Hz, reduces the flickering of its landscape. In other words, it reduces the frequency of the adsorption and desorption of these domains’ H₂O.

♣ Non-linear optical processes, induced by 7.85 Hz magnetic fields, are also possible sources for stabilizing the in SDVSAS₄₈ and SDVSAS₂₄. In other words, the 7.85 Hz EM field, the ULF radiation emitted from the QFE of , the UV radiation emitted from disintegrating , and the IR radiation emitted from disintegrating CD_rot all may non-linearly interact with the molecules constituting these domains. These non-linear interactions may re-stabilize disintegrating and CD_rot.  Since the H₂O organized in the supra- oscillate coherently in phase with a coherently condensed EM field, and the same holds for the H₂O constituting the supra-CD_rot, non-linear optical processes may play significant roles. Coherence of photons is known to enhance non-linear optical effects (Zheltikov et al., 2007).

As to the likelihood of non-linear optical processes playing a role in stabilization of CD_rot and , phenomena pertaining to the exclusion zone (EZ) water forming in water adjacent to a hydrophilic membrane should be mentioned. The analyses by Del Giudice et al. (2013) and Yinnon et al. (2016) have indicated that EZ water is composed of  and CD_rot. The width of the EZ zone has been observed to expand on its irradiation with UV-visible and IR radiation, such as 270 – 700 nm and 1750 – 4200 nm radiation (Chai et al., 2009). On irradiation, up to 300 percent widening of the EZ has been observed. The degree of widening increased with wavelength, except for a few local maxima. These maxima appeared at wavelengths for which the absorption of radiation by the EZ is maximal, e.g., at 270 nm and 3.1 µm. The widening of the EZ was observed to be a function also of the irradiation time and intensity. These phenomena allude that non-linear optical processes affect the expansion of the EZ (i.e., affect the stabilization of and CD_rot).

To investigate the role of non-linear optical processes in stabilization of and CD_rot in SDVSAS, research is called for that focuses on excitation of these liquids not just by 7.85 Hz radiation but also with EM radiation at a large variety of frequencies.

Structural Aspects of SDVSAS Diluted Below the Avogadro Limit 

Recently, the group of A.I. Konovalov extended its DLS measurements to SDVSAS diluted below the Avogadro limit (Ryzhkina et al., 2015b). The group measured the DLS of SDVSAS of polyclonal antibodies to the protein interferon gamma. The SDVSAS were prepared with freshly double distilled water. Glass vials (Wiegand 120011543) were used. The stock solution was centesimally diluted. The concentration of the stock solution was 0.1 mg/ml. The SDVSAS samples were labeled as C2-C15, C30 and C50. The C indicates that the SDVSAS were centesimally diluted. The number denoted the number of dilutions steps (NDS). For the C7 samples, the molarity was calculated. It was of the order of 10^-18 M. The properties of all the samples were measured after they were kept for 18 – 20 h on the laboratory bench or in Permalloy containers. The former are denoted as  (i.e., SDVSAS of anti-bodies kept at the laboratory bench). The latter are denoted as  ( i.e., SDVSAS of anti-bodies kept in Permalloy containers).

Ryzhkina et al.(2015b) also measured the electrical conductivity (χ), the surface tension (σ) and the ∆pH of   and . ∆pH is the difference between the pH of the SDVSAS and the pH of the double distilled water with which the SDVSAS were prepared, (the pH of the distilled water on the day the SDVSAS were prepared).

For controls, Ryzhkina et al.(2015b) prepared samples of serially diluted, vigorously shaken water (SDVSW), (double distilled water which was serially diluted with double distilled water and vigorously shaken after each dilution step).

A concise summary of the findings of Ryzhkina et al. (2015b) is presented in the next three paragraphs. Following the summary, these findings are analyzed within the context of the QED model of SDVSAS.

For  with concentrations above the Avogadro limit, just as Konovalov and Ryzhkina (2014) had observed for SDVSAS of many other solutes, Ryzhkina et al. (2015b) found that their χ, σ and ∆pH values vary non-monotonically with NDS. For  diluted below the Avogadro limit, they observed that these values also vary non-monotonically with NDS. Moreover, for SDVSW, they observed that the values of these variables vary non-monotonically with NDS and differ from those of  . In addition, they measured significant differences between the values of these variables for  or SDVSW versus those of double distilled water. [Elia and Niccoli (1999, 2000, 2004a) and Elia et al. (2005, 2015) did also report non-monotonic dependencies of χ, pH and other physicochemical properties of SDVSAS and SDVSW on NDS. They observed such non-monotonicity for SDVSAS of many different solutes. These SDVSAS had concentrations above the Avogadro limit or were diluted below this limit.]

For , Ryzhkina et al. (2015b) found that their χ and ∆pH variables only significantly vary non-monotonically with NDS when these liquids were less than 13 times centesimally diluted. When  and  were 13 times or more centesimally diluted, the χ and ∆pH of the former are higher or equal to those of the latter. As to σ, Ryzhkina et al. (2015b) observed an analogous behavior when  and  were more than 12 times centesimally diluted.

As to the DLS measurements of  and , the main results of Ryzhkina et al. (2015b) are:

A. For  with C2-C6, C8, C10-C12, C14 and C15, DLS does not indicate presence of associates.

B. For  with C7 or C9, DLS revealed presence of nano-associates with a monomodal size distribution. The average diameters of the associates are respectively, ~170 nm and ~140 nm.

C. The associates in C7  are absent in C7 .

D. For C9  and C9 , their associates have nearly the same dimensions. The monomodal size distribution of is a bit narrower than that of  .

E. In C13, C30 or C50 , as well as in C13, C30 or C50  , DLS revealed particles with a trimodal size distribution. For such a distribution, the DLS method is inadequate for accurately measuring the average sizes of the particles. Yet the DLS measurements hint that particles with sizes of the order of 10^-9 m, 10^-8 m and 10^-7 – 10^-6 m are present in these liquids.

For analyzing the above cited findings of Ryzhkina et al. (2015b), foremost, the following should be emphasized: although DLS does not indicate presence of associates in C2 -C7, C8, C10-C12, C14 and C15 of  (see paragraph A), these liquids’ physicochemical variables and the non-monotonic variance of these variables with NDS reflect that these liquids’ properties differ from those of double distilled water. Analyses of experimental data reported in earlier publications, pertaining to measured physicochemical variables of SDVSAS of other solutes with concentrations above the Avogadro limit or which were diluted below this limit (Elia and Niccoli, 1999, 2000, 2004a; Elia et al., 2005, 2015, 2008a&b; Belon et al.2008), as well as those pertaining to SDVSW, suggest that for  C < = C_thr, in these liquids, CD_rot underlie the non-monotonic variance of their physicochemical variables (Yinnon and Yinnon, 2011; Yinnon and Elia, 2013; Yinnon and Liu, 2015b&c). The analyses indicate that the impact of CD_rot on the physicochemical properties of SDVSAS or SDVSW slowly increases with the age (months, years) of these liquids. Since the data show that the physicochemical variables greatly vary with the age of those SDVSAS which were only a few times diluted, shortly shaken and stored for less than a year, it suggests the following: the sizes of the CD_rot in such “young” SDVSAS are still small and the ordering of these domains in supra-CD_rot vary greatly with time. Based on these analyses, the findings presented in paragraph A hint that DLS is insensitive to the presence of young CD_rot. This insensitivity will be discussed further on.

As to the findings presented in paragraphs B and C, monomodal distributions of molecular associates with average diameters of the order of 10^-7 m, which disappeared on screening of the liquid by Permalloy, (like the one observed for C7 ) have been detected in SDVSAS of many solutes (Konovalov and Ryzhkina, 2014). The associates underlying such distributions were shown to have the typical characteristics of  and supra- (Yinnon and Liu, 2015b&c). As noted in previous sections, for C < = C_thr, these domains are stabilized by CD_rot and low frequency magnetic fields. It is thus most likely that the 170 nm sized associates observed in C7  are supra-. Measurements of their electrokinetic potential are called for. Such measurements could provide additional evidence for this conclusion.

A question arising from the above presented data is: “Why did not DLS detect a monomodal distribution of associates with sizes of the order of 10^-7 m in  which were less than 7 times centesimally diluted (see paragraph A)?” The concentrations of the antibodies in C2 – C7  are in the range of 10^-8 – 10^-18 M. A value as low as about 10^-18 M has not been reported for  = C_thr of SDVSAS of other solutes. Typically, ~10^-10 M <  = C_thr< ~10^-6 M.

A possible answer is that in  which were less than 7 times centesimally diluted, the alignment of CD_rot in supra-CD_rot and the incorporation of the solutes in these domains are detrimental to stabilization of  in numbers sufficient for these domains to be observable with DLS. Such an answer might also be applicable to C8, C10-C12, C14 and C15 , in which as noted in paragraph A, DLS did not detect associates with diameters of the order of 10^-7 m. A similar explanation has been given for the relation between the prevalence of molecular associates with sizes of the order of 10^-7 m observed in SDVSAS of many solutes and the dielectric permittivity of these liquids (Konovalov and Ryzhkina, 2014; Yinnon and Liu, 2015c). (The dielectric permittivity reflects the alignment of the electric dipoles of CD_rot in supra-CD_rot.)

The above analyses raise the issue: “How is information on CD_rot and supra-CD_rot reflected in DLS data?” At least theoretically, these domains may grow to sizes of 10^-5 – 10^-4 m. The issue has not been clarified in the earlier published analyses of SDVSAS. Some clues are provided by atomic force measurements (AFM) of the residues left over after evaporating drops of SDVSAS. AFM data revealed that in addition to more or less spherical 10^-7 m sized chunks, micron sized elongated molecular associates were present in these residues [see Fig. 3f in Ryzhkina et al. (2012b); Fig. 1 in Ho (2014); Fig. 5 in Elia et al. (2015)]. The widths of these elongated associates were of the order of 10^-9 – 10^-7 m. Their lengths were of the order of 10^-6 – 10^-5 m. These elongated associates were more or less linear or curled up. The diameters of the ball-shaped curled up ones were of the order of 10^-7 – 10^-6 m. Earlier published analyses of the various physicochemical properties of these SDVSAS evoked that the elongated associates are CD_rot, or supra-CD_rot organized in chains with their electric dipole moments parallel oriented (Yinnon and Liu, 2015c). The analyses also indicated that the chunks are supra-. Therefore, in relation to the abovementioned issue, it is my conjecture that DLS cannot clearly distinguish between the presence of supra- and the presence of the supra-CD_rot when these elongated associates are curled up in balls. Moreover, it is likely that DLS is insensitive to very thin linear molecular associates, such as the more or less linearly micron sized CD_rot or supra-CD_rot with width of the order of 10^-9 m.

In regard of this conjecture, the data reported in paragraphs B and D possibly can be understood as follows: The monomodal distribution of associates with sizes of the order of 10^-7 m which were present in C9  mainly reflect the presence of curled up supra-CD_rot and few . On screening of this  by Permalloy for 18 – 20 h, most of these few  disintegrated. However, as noted above, CD_rot have much slower dynamics than . Therefore, CD_rot disintegrate slower than . So many supra-CD_rot could persist in the samples after their storage for 18 – 20 hours in Permalloy containers. Moreover, since CD_rot formation is mediated by far IR radiation, while  formation is mediated by UV radiation, it is possible that screening by Permalloy affects the former less than the latter. These explanations potentially clarify why the difference between the observed DLS results for C9 and C9 is small.

As to the findings presented in paragraph E, my conjecture also enables explanation of the characteristics of the associates in C13, C30 or C50 of  and . The associates with diameters of the order of 10^-7 – 10^-6 m, which were revealed in these  by DLS, likely mainly are curled up CD_rot and supra-CD_rot. These CD_rot may have stabilized few 10^-7 m sized . On screening these  with Permalloy for 18 – 20 hours, many of the CD_rot prevailed, while the mostly disintegrated. The persistence of CD_rot explains that the χ, σ and ∆pH values of these significantly differed from those of double distilled water.

As to the 10^-9 m and 10^-8 m sized particles which were observed in C13, C30 or C50 of  and in , these may include broken CD_rot pieces (i.e., EDA^CDrot) created by the vigorous shaking of these liquids. The slow dynamics of CD_rot implies that their size distribution is wide. The 10^-9 m sized particles also may be (hydrated) compounds released by the containers or other impurities. Such particles were not discerned with DLS in or in diluted less than 13 times. Likely, in these solutions, their concentrations were very low, i.e., too low to be detectable with DLS. The concentration of compounds released by the glass container slowly increases with the number of dilution steps, because after each dilution step the liquid is vigorously shaken and a percentage of the liquid is transferred to a new vial containing double distilled water.

The upshot of the above analyses is that in the , which were diluted below the Avogadro limit, CD_rot and supra-CD_rot are apparently present. Also analyses reported in earlier publications pertaining to SDVSAS of other solutes which were diluted below this limit, as well as those pertaining to SDVSW, suggested presence of such domains in these liquids (Yinnon and Elia, 2013). However, the analyses presented in the previous paragraphs hint that the capability of DLS to detect these domains depends on their shape. Since experimental data hint that on aging of SDVSAS, CD_rot grow and organize in supra-CD_rot (Yinnon and Elia, 2013), DLS measurements of aged SDVSAS are called for. In addition to DLS, it seems desirable to employ other techniques for revealing typifying fingerprints of CD_rot and supra-CD_rot in SDVSAS diluted below the Avogadro limit (e.g., their ferroelectric orderings and the electric dipole rotations of their H₂O.) Their ferroelectric orderings may be revealed by dielcometric titrations, as the experimental data obtained by Ryzhkina et al. (2012b, 2013) and their analyses by Yinnon and Liu (2015c) have indicated. Moreover, as the recent results obtained by Mahata (2013) suggest, such orderings and rotations of the electric dipoles of their molecules may possibly be revealed by dielectric dispersion measurements.

Dielectric dispersion measurements have provided evidence for the presence of about 3×10^-5 m sized molecular structures in water samples to which a few drops of one of the following liquids were added: 6 or 30 times serially diluted solutions of Graphites or Copper, vigorously shaken after each dilution step (Mahata, 2013). The solvent of these serially diluted solutions was ethanol. After addition of the drops to the water samples, the samples contained about 3 percent ethanol. The 3×10^-5 m sized structures affected the polarization of the samples. The effect became distinguishable about 24 – 48 hours after the drops were added to the water samples. The detailed experimental results indicate that formation of the structures involves electric dipole rotations of the liquids’ molecules. More accurately, it involves rotations of the solvent molecules, but does not involve rotations of Copper or Graphite molecules. The QED model of serially diluted, vigorously shaken polar liquids indicates that such liquids should contain CD_rot (Yinnon and Yinnon, 2011). Analyses of experimental data pertaining to such liquids revealed fingerprints of such domains (Yinnon and Liu, 2015c). So the drops which Mahata (2013) added to the water samples probably contained CD_rot composed of the polar ethanol molecules. Since such CD_rot are aggregates with an electric dipole moment, QED predicts that these may stabilize CD_rot composed of H₂O in the water samples (Del Giudice et al., 1988). So it is likely that the 3×10^-5 m sized molecular structures are CD_rot. This is likely because according to QED, electric dipole rotations underlie the CD_rot composed of ethanol or water. However, it should be emphasized that Mahata (2013) observed the structures in water containing about 3 percent ethanol. In such aqueous solutions, as when neither the water nor the ethanol are serially diluted and vigorously shaken, domains are present (Sedlak, 2006; Sedlak and Rak, 2013). These domains have characteristics of QED coherent domains (Yinnon and Yinnon, 2009). Recent analyses indicated that in water containing a few percentage of ethanol, fractal structured molecular associates are present (Ghosh and Bagchi, 2016). As noted above, fractality is a property of supra-QED coherent domains^f. So repeating the experiments of Mahata (2013) for controls is called for. For example, the controls may be water samples to which drops of SDVSAS of Copper or Graphite were added — according to the above and previous published analyses, these drops should contain CD_rot.  Also, water samples to which drops of non-serially diluted non-vigorously shaken ethanol solutions of Copper or Graphite are added may serve as controls — these liquids should not contain CD_rot. Yet, even in the absence of data for controls, the findings of Mahata (2013) are significant. They suggest that dielectric dispersion measurements for SDVSAS diluted below the Avogadro limit seem to be capable of providing more direct evidence of CD_rot in these liquids.

Discussion

The above analyses show that the QED model of SDVSAS explains the recently observed self-similarity topology of these liquids. This self-similarity, together with the dissipative properties of SDVSAS identified in previous studies (Elia et al., 2000, 2008a&b; Belon et al., 2008; Elia et al., 2015), in combination with the analyses by Vitiello (2012, 2014), corroborates that QED coherence plays a significant role in these liquids.^f In other words, the above analyses substantiate the model’s assumption that QED coherence domains (e.g., CD_rot, and IPD_plasma), underlie the structural properties of SDVSAS.

Furthermore, the above analyses show that the QED model of SDVSAS clarifies the EM phenomena of these liquids. The model elucidates some missing links in the explanations of Montagnier et al. (2011, 2015) pertaining to the emission of ULF radiation by SDVSAS of DNA.

The above analyses also complement previous ones, which showed that the QED model of SDVSAS consistently explains many structural and physicochemical properties of these liquids (Yinnon and Yinnon, 2011; Yinnon and Elia, 2013; Yinnon and Liu, 2015a-c). The above analyses of the recent DLS, electrical conductivity, pH and surface tension measurements carried out by Ryzhkina et al. (2015b) support the model. These recent measurements, which pertain to SDVSAS diluted beyond the Avogadro limit, complement the many earlier measurements for SDVSAS diluted up to this limit. The analyses indicate that the nano-associates observed in SDVSAS diluted below the Avogadro limit are also QED coherence domains, i.e., CD_rot and .
The analyses presented above, together with those presented in earlier publications and schematically portrayed in the lecture by Konovalov et al. (2014)^g and the poster by Yinnon and Konovalov (2014)^h, accentuate that an appropriate description for the molecular associates in SDVSAS is the term recently coined by Konovalov and Ryzhkina (2016): “nano-sized self-organized substrate-induced molecular ensembles.” The term “substrate” here refers to the solute with which the SDVSAS is prepared. At concentrations slightly lower than the transition concentrations or , the solute molecules serve as substrates which may stabilize respectively, IPD_plasma or CD_rot. Vigorous shaking of the liquid excites the domains, i.e., creates electric dipole aggregates.  For C < , these aggregates stabilize additional CD_rot. Thus for C < , the creation of new electric dipole aggregates no longer depends on the solute molecules. The CD_rot may stabilize . At C ~ or at lower C, the solute properties become imprinted in the CD_rot and . On diluting the liquid, part of these domains get transferred to the dilute. Vigorous shaking of the dilute breaks up the CD_rot and thus creates new electric dipole aggregates. These aggregates stabilize new CD_rot and . At C above the Avogadro limit but below , the solutes locate within CD_rot and may orbit around . At such low concentrations, solutes still may affect physical, chemical or biological processes, e.g., through resonances (Del Giudice et al., 2010b). For SDVSAS diluted below the Avogadro limit, the current data hint that the physicochemical and biological properties of these liquids are attributable to CD_rot, and the imprint of the characteristics of the substrates (original solutes) in these domains.