Indications exist that mobile phones may cause non-specific biological effects. They are classified as being of implausible non-thermal nature due to low quantum energy and low specific absorption rate levels, even if considering worst cases of "hot spots" of only millimeter size. The considerations of this paper demonstrate that classical theory of polarization offers a conventional interpretation for all three the existence of so far unclarified effects, their low reproducibility and their low intensity. The basis of this explanation is given by the assumption that hot spots contain even hotter “nano spots” on a molecular level according to well known mechanisms of γ-relaxation. In this paper, the concept is put for discussion assuming a heterogeneous system that consists of water molecules as well as larger-sized functional molecules. A consistent interpretation through temperature increase on the level of nanometer sized molecular compounds promises to favor interdisciplinary discussions with respect to safety regulations.
Mobile phones may cause eventual non-specific biological effects which usually are classified as being of implausible non-thermal nature. This is expressed by several review papers (e.g. [
In the early state of discussion, the biological risks through microwave radiation were estimated on the basis of total energy as being absorbed by the human body, not considering that a biological system―e.g. the human head―tends to show a very heterogeneous structure. However, practically all more recent work is focused on the specific absorption rate (local SAR in W/kg). Considering the dielectric properties of the different types of tissues (such as skin, skull and brain), numerical modeling―or also experimental phantom testing―of the multi-layered head is applied to identify “hot spots” of maximum SAR. As a problem, the results depend on the ratio of the wave length and the geometry of the different layers, due to reflection effects and specific absorption rates. In recent studies, this was met by parameter variation in order to identify the worst case [
SAR values were determined with spatial resolutions down to the order of 1 mm (e.g. [
In the following, we consider a sub-region within an a priori over-heated hot spot, considering this region as a heterogeneously built up cellular volume that contains portions of biologically functional molecules. The corresponding “thermal” effects are estimated by the well known classical theory of polarization. This offers a con- ventional explanation for all three the possible existence of single unexpected effects, their low reproducibility and their low intensity. The basis of this explanation is given by the assumption that hot spots contain even hotter “nano spots”, on a molecular level due to g-relaxation effects. At first time, the basic idea was presented in reference [
The fact that even “hot spots” tend to exhibit rather low levels of temperature increase θ results among others from the considerably large difference between the mobile phone (MP) frequency fMP (order 1 - 2 GHz) and the water molecule’s so-called g-relaxation frequency
with F a factor that considers deviations from spherical molecule shape, among others. This well known Debye formula considers polar molecules in the most approximate way. According to it, fR increases with increasing thermal energy kT which however can be assumed to be constant for the living system. It decreases with the viscosity h which results from the surrounding of the considered molecule and which can been interpreted as a source of inner friction of the medium. For the following considerations, a significant parameter is the molecule size d. For water molecules (WM) it is about 0.2 nm which yields fR,WM close to 10 GHz, with variations due to the varying content of bound water (clusters, hydration etc.) that yields increased effective h.
The water content of biological tissues is well reflected by the value of the permittivity
According to well known theory, microwave radiation acting on a quasi-homogeneous polar medium can be assumed to cause a dielectric energy loss density
with the energy loss P, the angular frequency ω = 2πf, the electric field E and the vacuum permittivity ε0. For a given frequency, the permittivity
Here Δε expresses the total decrease of
is the relaxation time constant
depending on the molecular shape. For water molecules surrounded again by water molecules, the already mentioned frequency value fR,WM = 10 GHz yields a value of τ close to 100 ps. According to (3), the frequency dependence of
As representative for a local region of the considered biological system, let us consider a volume
For a systematic discussion, we assume the following three types of molecular functions:
a) A predominant volume fraction cWM of polar (cellular) water molecules (WM),
b) A small fraction cFM of larger polar functional molecules (FM), or mobile polar molecular fragments, respectively, and
c) A small fraction cPM of large protein molecules (PM), or other macro-molecules, respectively, which may be polar as an option.
For a rough modelling of the heterogeneous case of water including a single type of polar particles FM, just two contributions to polarization are given. Neglecting intermolecular interactions, linear superposition yields
Interpreting continuum theory in a depictive way, irradiation of the above system can be expected to yield the following tendencies as a function of frequency:
A) Low frequency, e.g. f = 1 MHz, i.e. well below the MP frequency range
Both WM and FM are “operated” below fR. Due to their relatively small size d, they will follow the dynamic changes of the electric field vector E without significant delay, i.e. the polar moment will show some orientation. The extent of orientation will be equivalent to the high value
B) High frequency e.g. f = 10 GHz, i.e. above the MP frequency range
According to f = fR, WM, maximum
C) Medium frequency e.g. f = 1 GHz, i.e. corresponding to the mobile phone frequency range
Here, water molecules are operated below relaxation frequency, corresponding to strongly restricted power dissipation. As well, the latter is valid for the large molecule type PM which―if being polar―is operated above relaxation frequency. On the other hand, since f is close to fFM, optimum excitation results for the functional type of molecules. As a consequence of dynamic rotational vibration, changed interaction can be expected with neighbouring molecules, such as indicated in
Beyond the above qualitative discussion, a quantitative estimation can be based on the responses of
corresponding to portions of 59% and 41% to total losses. This means that FM contributes to the global energy increase of the volume ΔV in a predominant way, in spite of its small volume portion of only 20%. Neglecting active energy dissipation, the resulting values θFM and θWM of local temperature increase (on a molecular level) depend on the individual values of density ρFM , ρWM and specific heat κFM, κWM. Their relationship follows from the above ratio according to
Neglecting differences of ρ and also of κ would yield a temperature ratio
i.e. a 5-fold overheat of FM compared to WM. And finally with this proportion we find from the total energy
the ratio
It means that compared to the global temperature increase―as being detectable by measurement―, the protein portion within the considered volume is locally characterized by 3-fold temperature increase. This ratio quantity r3 expresses in an effective way the “excess rate” of temperature which can be expected to determine the chemical and biological behaviour of the considered functional type of molecule, thus representing a characteristic of the resulting hot nano spot.
The above estimation concerns 1 GHz. For higher fMP, e.g. close to 2 GHz, the energy uptake by WM would be higher due to reduced distance from fR,WM = 10 GHz. On the other hand, the uptake by FM will be slightly decreased since not operated any longer at relaxation frequency. As a consequence, all three ratio terms r1, r2 and r3 would be reduced. However, it should be stressed that all above data is based on the assumption that the rather high portion of 20% FM is given within the considered volume. Smaller concentrations―which are more likely to exist in practice―yield increased ratio terms r2 and r3. Roughly, a reciprocal dependence can be assumed corresponding to maximum values of temperature increase for singular functional molecules which happen to show relaxation at the frequency of mobile phones.
Let us now discuss the possible consequences of hot nano spots. The above model indicates that the functional behavior of the affected molecules will not correspond to the state of “hot spot” temperature increase―e.g. θHS = 1 K―, but to the state of a higher “hot nano spot” (HNS) temperature increase. For the example of data set for (9), this results in the value
In analogous ways, the above way of modelling is consistent with interpretations in [
a) Structural functions-molecular structures becoming less stable (see e.g. [
b) Enzymatic tasks-the molecular interaction becoming less stable thus reducing the probability of enzymatic effectiveness.
c) Controlling functions at membrane channels-affected polar molecules yielding increased or decreased permittivity, 1) to ions as a basis of neural effects as schematically outlined in
According to literature, it cannot be excluded that very specific effects are beyond the here proposed concept of nano spots. As a corresponding “archetype of (true) non-thermal microwave effects”, reference [
the recombination of radical pairs through magnetic field components. However, such effects need very high field intensities (exceeding 0.1 T [
Here it should be stressed that all above listed effects (a) to (c) can be assumed to be weak with respect to quantitative consequences. First of all, the probability is small that a given type of functional molecule happens to fulfill the condition fMP = fR,FM for full resonance. But even if it does, considering the role of h, an ensemble of a given type of molecule will not show a sharp resonance, but fR,FM of the individual molecules will be of distributed nature as depending on many parameters. Thus the maximum effects of a given value fMP will concern a restricted portion of individuals. And inside a hot spot, the concentration and temperature of hotter nano-spots will vary as well. Especially, an absolute energy maximum will be restricted to the center of an ensemble of identical molecules of type FM. The resulting statistical energy distribution can again serve as an explanation for the finding that mobile phone effects show weak intensity and low reproducibility, if occurring at all.
According to the above, the model presented in this paper indicates that a variety?if not the total-of apparently non-thermal effects can be interpreted as actually being of thermal nature. But it also indicates that such effects exhibit very low probability and are not likely to cause significant consequences on health, even for long-term activity.
Finally, it should be mentioned that the above concept promises to favor interdisciplinary discussions of health risks due to its consistent “thermal” nature. The concept distinguishes thermal effects on the following three levels:
a) The global level of total organism on the rough geometric scale of a meter.
b) The level of a cranial “hot spot” on the scale of millimeters, as taken as a basis for the determination of SAR values.
c) The level of molecular “nano hot spots” on the scale of nanometers.
At present, the SAR value according to level b) is indicated as a measure for risks in a global way, i.e. irrespective of frequency. On the other hand, it is evident, that molecular effects depend on the considered frequency band of radiation. Further studies should establish comparative assessments for the individual bands, in order to characterize the individual proneness to effects of molecular type c) through a second parameter. This does not necessarily need further experimental work, but can be based on systematic evaluations of the very high amount of already existing data.
Rather simple theoretical considerations that are based on conventional models of polarization yield the following main conclusions:
1) The usual SAR concept lacks from the fact that “hot spots” are defined as rather large regions with millimeter dimensions.
2) It is likely that such a region contains molecules which happen to show g-relaxation at mobile phone frequencies, thus representing considerably hotter “nano spots” which are not detected by the restricted resolution of SAR calculations or thermal measurements, respectively.
3) A given SAR-based microwave heating rate will affect such molecules more intensively than the same rate produced by non-microwave heating. The functional molecular behavior will correspond to the excess, “local” nano spot energy.
4) The hot nano spot will show thermal interaction with its cooler surrounding, analogous to the interaction of a hot spot with its even more cool surrounding, however, at a smaller (molecular) level.
5) The mechanism means that most so-called non-thermal effects―if not all―are of thermal nature in fact. The insignificant extent of effects is due to randomly distributed constellations that yield a hot nano spot.
6) A consistent interpretation of effects as thermal ones promises to favor interdisciplinary discussions of risks.
7) The estimation of risk through a mere, single SAR value is not satisfactory. A second parameter may express the proneness to possible molecular effects, depending on the given band of frequency.
The author thanks Prof. Eugenijus Kaniusas (TU Wien, Vienna, Austria) for valuable discussions and suggestions.
Helmut Pfützner, (2016) “Hot Nano Spots” as an Interpretation of So-Called Non-Thermal Biological Mobile Phone Effects. Journal of Electromagnetic Analysis and Applications,08,62-69. doi: 10.4236/jemaa.2016.83007