# Long-Term Effect of Low-Frequency Electromagnetic Irradiation in Water and Isotonic Aqueous Solutions as Studied by Photoluminescence from Polymer Membrane

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

^{TM}in deionized water and isotonic NaCl and Ringer’s solutions was studied by photoluminescent spectroscopy. According to our previous studies, the surface of this membrane could be considered as a model for a cellular surface. Liquid samples, in which the membrane was soaked, were subjected to preliminary electromagnetic treatment, which consisted of irradiating these samples with electric rectangular pulses of 1 µs duration using platinum electrodes immersed in the liquid. We used a series of pulses with a repetition rate of 11–125 Hz; the pulse amplitudes were equal to 100 and 500 mV. It turned out that at certain pulse repetition rates and their amplitudes, the characteristic swelling time of the polymer membrane significantly differs from the swelling time in untreated (reference) samples. At the same time, there is no effect for certain frequencies/pulse amplitudes. The time interval between electromagnetic treatment and measurements was about 20 min. Thus, in our experiments the effects associated with the long-term relaxation of liquids on the electromagnetic processing are manifested. The effect of long-term relaxation could be associated with a slight change in the geometric characteristics of bubston clusters during electromagnetic treatment.

## 1. Introduction

^{TM}polymer membrane swells in water, polymer fibers “unwind” into the water bulk. It is important that these fibers do not completely tear off the membrane interface, i.e., a “brush”-like structure close to the interface is generated. Furthermore, when Nafion swells in water, a network of through channels in the membrane volume is formed (see the review [11] for more detail). The presence of such channels has been applied in a number of practical applications. For example, the processes of liquid transfer through the capillary network of such channels are widely studied with taking into account their fractal properties and the surface roughness of the membrane, see, for example, [12,13].

## 2. Materials and Methods

#### 2.1. Materials

_{7}HF

_{13}O

_{5}S × C

_{2}F

_{4}) is a sulfonated tetrafluoroethylene based fluoropolymer-copolymer. The polymer matrix consists of a tetrafluoroethylene backbone, where perfluorovinyl ether groups are terminated with sulfonate groupsHSO

_{3}.We investigated NafionN117 plates (Sigma Aldrich, St. Louis, MO, USA) with a thickness of L

_{0}= 175 μm. The Nafion plates were soaked in Milli-Q water with a resistivity of 4 MΩ⋅cm (measurement were made 1 h after the preparation) in isotonic NaCl (0.9%; Mosfarm, Russia) and Ringer’s (Medpolymer, Russia) solutions. In our particular case, the Ringer’s solution was composed of NaCl (8.6 g/L), KCl (0.3 g/L), and CaCl

_{2}× 6H

_{2}O (0.25 g/L), dissolved in water.

#### 2.2. Instrumentation

#### 2.2.1. Photoluminescence Study

_{3}serve as the centers of Nafion luminescence under UV irradiation.

_{Naf}

_{Naf}is the volume number density of the luminescence centers, i.e., terminal sulfonic groups. Since these groups are attached to polymeric chains, n

_{Naf}can be associated with the volume number density of Nafion particles. The dependence obtained can be represented as:

_{pump}σ

_{lum}n

_{Naf}V,

_{pump}is the pump intensity, A = −270 relative units corresponding to the spectral density of the mini-spectrometer noise and stray-light illumination, k is the transfer coefficient of the setup, V is the luminescence volume, and σ

_{lum}is the luminescence cross section (it is obvious that the spectral maximum of σ

_{lum}corresponds to λ = 460 nm). It follows from Figure 1 that σ

_{lum}= const.

#### 2.2.2. Processing of Liquid Samples

^{2}. We used pulses with durations of μs and amplitudes of 100 mV and 500 mV (the voltage data was taken after immersing the electrodes in a liquid sample). Liquid samples were exposed to electrical impulses for 20 min (the time of processing). Typical pulses used in our experiment are shown in Figure 3a—100 mV and Figure 3b—500 mV; the pulse repetition rate is indicated in the lower right corner. The electrochemical potential of platinum in accordance with the reaction Pt

^{2+}+ 2e

^{−}⇌ Pt (s) is φ

_{0}= +1.2 V, see Ref. [24]; it is obvious that the voltage of pulses supplied to the electrodes should not exceed the value of φ

_{0}just to avoid electrochemical reactions on the electrodes. To make sure that we did not have to deal with electrochemical reactions, we controlled the pH of the test liquids before and after electromagnetic processing. For that purpose, we used pH-meter HANNA HI 98108 PHep+ (USA), which was calibrated with standard acid and alkaline titers, having pH = 4.06 and 9.18 accordingly. It turned out that the electromagnetic processing did not result in the change of pH: before and after processing for deionized water the pH = 5.7 ± 0.1, for NaCl solution pH = 6.2 ± 0.1, for Ringer’s solution pH = 5.5 ± 0.1.

## 3. Experimental Results

_{0}= 14.3 min, and for Ringer’s solution (Figure 4b we have τ

_{0}= 12.3 min. The pre-exponential factors and free constants for the given exponentials also insignificantly differ. Thus, for untreated deionized water and isotonic salt solutions the time dependences of the luminescence intensity are well approximated by very close decaying exponential functions, i.e., the ionic additives would hardly influence on the dynamic of swelling Nafion.

_{0}, where τ

_{0}is the decay time of the reference dependence, τ is the decay time of the corresponding dependence after processing, on the pulse repetition rate for deionized water (Figure 8a), isotonic NaCl solution (Figure 8b), and Ringer’s solution (Figure 8c); black curves correspond to the pulse amplitude of 100 mV, and red curves correspond to 500 mV pulse amplitude. It is seen that the obtained dependences are qualitatively correlated to one another for all investigated liquids.

## 4. Discussion

_{Naf}(sulfonic groups in our case, see [10]), the luminescence cross section σ

_{lum}and the luminescence volume V. The volume number density of luminescence centers in volume V can be represented as n

_{Naf}= C/V, where C is the total amount of the polymer particles in the volume V. Obviously, this volume is determined by the cross section of the laser beam in the near-surface layer of the Nafion plate (recall that we irradiate the plate in grazing incidence geometry), and the plate height, i.e., the volume V is fixed. Since water molecules penetrate the surface layer of the membrane during swelling, the n

_{Naf}value inside this layer should decrease. Then, under the assumption that σ

_{lum}is constant (note that there is no reason to assume that σ

_{lum}changes at swelling), the only time-dependent parameter is the bulk density of luminescence centers n

_{Naf}. Introducing the characteristic decay time τ, which is about the swelling time, we obtain the differential equation:

_{Naf})

_{0}is the volume number density of luminescence centers at t = 0 (i.e., in dry Nafion). As follows from the above experimental plots, processing with electrical pulses leads to a change in the swelling time τ.

_{lum}does not change as a result of processing, that is, the dynamics of membrane swelling for treated and untreated samples is described by exponential Equation (4). It is very important that for the reference samples the exponential functions describing the swelling dynamics are practically the same, see Figure 4. At the same time, as is seen from the graphs in Figure 8, the characteristic swelling time τ changes after the treatment with electric pulses.

_{0}for different samples depends significantly on the repetition rate and amplitude of the pulses. For example, for isotonic NaCl solution (panel (b)), treatment at frequencies of 11 and 20 Hz for the pulse amplitude of 100 mV leads to a significant increase in the swelling rate of the polymer membrane, while for the pulse amplitude of 500 mV, the swelling rate very slightly changes compared to the reference sample. Note also that the most significant increase in the swelling rate is also observed for an isotonic NaCl solution at a repetition rate of 125 Hz for both pulse amplitudes. Interestingly, the pulse treatment of deionized water for both pulse amplitudes leads primarily to a slowdown, rather than an increase in the swelling rate (τ/τ

_{0}≤ 1); the exception is processing by pulses at frequency of 125 Hz with amplitude 500 mV. Note also that the frequency of 100 Hz looks special, since for this frequency the values of τ/τ

_{0}for 100 and 500 mV are very close for all investigated samples. In addition, for all investigated liquids, an increase in τ/τ

_{0}is observed in the range 100–125 Hz for both pulse amplitudes.

_{0}on the pulse repetition rate (these dependences are shown in Figure 8 must behave monotonously. In addition, it is very important for us that for untreated samples of deionized water and isotonic NaCl and Ringer solutions, the decay times τ

_{0}coincide to one another with a good accuracy. Finally, for all studied samples, the pH value does not change before and after treatment. Thus, in our opinion, the contamination mechanism can be excluded.

^{−11}–10

^{−12}s. This is, firstly, the lifetime of the hydrogen bond between water molecules; the breaking of the hydrogen bond occurs due to the rotational Brownian diffusion of molecules. Second, this is the decay time of local pressure/density fluctuation. Assuming that the characteristic size of this fluctuation is δ—10–100 nm, we obtain for the decay time of such fluctuation the estimate τ ~ δ/c, where c is the speed of sound in water, i.e., τ ~ 10

^{−11}–10

^{−10}s. Thus, it would seem that the processes with relaxation times of the order of several tens of minutes cannot arise in water and aqueous solutions of electrolytes.

_{3}

^{−}and CO

_{3}

^{2−}anions on the bubston surface, see our recent work [34]. These anions arise owing to the dissociation of carbonic acid, which, in turn, is the result of a hydrolysis of CO

_{2}in water. The nucleation of bubstons occurs due to the Coulomb instability of the so-called “droplets of an ionic condensate”. The nuclei for such droplets are the dimers “ion-gas molecule”, see our recent work [35]. In the same work, in particular, we estimated the bubston nucleation time, which is about 2.4 × 10

^{−8}s.

^{−17}C, i.e., about 100 elementary charges. Assuming further the distance d between the capacitor plates to be equal to 1 cm, we obtain for the electric field strength inside the capacitor E = U/(εd) ≈ 0.6 V/m. In case of a uniform moving of a bubston, having velocity v, we arrive at:

^{−3}Pa⋅s is dynamic viscosity of water at room temperature. Thus, we obtain that force F = 0.6 × 10

^{−17}N is applied to the bubston, and the bubston velocity is v = 0.3 × 10

^{−8}m/s, i.e., for a time τ′ = 1 µs, the bubston travels a distance Δl′ ~ 3 × 10

^{−15}m. Let us further estimate a random displacement of the bubston Δl″ as a result of Brownian diffusion within the intervals τ′; we obtain:

^{−6}M.

^{5}cm

^{−3}. The dependence of the volume number density of individual bubstons vs. the ionic concentration in NaCl solution was studied in [29]. It was found in this work that at ion concentration of 10

^{−6}M the volume number density of bubstons is 10

^{6}cm

^{−3}, while at a concentration of 10

^{−1}M (physiological solutions) we have 3 × 10

^{7}cm

^{−3}. Thus, the volume number densities of bubstons/bubston clusters differ significantly in deionized water and isotonic solutions. Furthermore, the clusters are not revealed in experiments with dynamic light scattering in deionized water. In addition, the clusters are fractal objects; their fractal dimensions and gyration radii in aqueous NaCl solutions were measured in [29,39,40,41]. Finally, the characteristic lifetime of the clusters was measured in [29]. In this experiment, we first measured the distribution of scatterers over size in 1 M NaCl solution, and then the liquid sample was settled for 6 months under stationary conditions in hermetically sealed (without an access of atmospheric air) cell of 2-cm height. It turned out that the micron-sized scatterers (bubston clusters) disappear after settling, while submicron-sized scatterers (individual bubstons) remain in the liquid (“survive”). The disappearance of the coarse scatterers is obviously associated with a cluster floating up following by its destruction at the liquid interface, whereas individual bubstons have a neutral buoyancy, i.e., do not float up. Thus, we can argue that bubstons are an equilibrium phase of an aqueous electrolyte solution under normal conditions, while bubston clusters are a long-lived phase.

_{0}of the gas core of radius R

_{0}and the cloud of counterions surrounding the gas core (the thickness of this cloud is equal to (r−R

_{0}), where the radius vector r is originated at the bubston center) in salt solutions with a low ionic concentration is a monotonic function: Q(r) → 0 for r → ∞ for all values of r. At the same time, at high ionic concentrations, the function Q(r) is not monotonic anymore: at a certain value r = r

_{0}, we have Q(r

_{0}) = 0 (isoelectric point), but the condition Q(r) → 0 at r → ∞ is still met. Thus, we can talk about the inversion of the sign for the function Q(r) in concentrated ionic solutions. This effect is described, for example, in Refs [43,44,45]; the physical nature of this effect is related to the gas-core charge Q

_{0}: at low ion concentrations, we have the condition:

^{3}hierarchical-type clusters obeying exponential distribution p(N)–exp(−αN) over the number N of bubstons in a cluster (N ≥ 1, α > 0). Here, α is a model parameter that takes into account the attraction of particles during the aggregation of a ballistic type. In such a hierarchical model of cluster-cluster aggregation, the average fractal dimension D of the ensembles of clusters monotonically depends on the parameter α. The parameter α can be considered as an additional “degree of freedom”, which allows one to describe the experimentally found angular dependence of the scattering indicatrix elements, see our study [39]. In this work we calculated a set of the scattering matrices as the averages over random cluster ensembles with the statistical parameters, taken on a uniform discrete grid. The solution to the inverse scattering problem was found by minimizing the divergence between the measured angular profiles of the scattering matrix and the same profiles. In Figure 9 we exhibit an example of such realizations for a physiological NaCl solution; α = −1.4, fractal dimension of the cluster D = 2.45, number of bubstons in the cluster N = 420, bubston radius R = 100 nm; this figure was taken from [39].

^{−17}C and the attractive center on the cluster surface. Let this center have charge q; the exact value of this charge is unknown to us. However, without loss of generality, we can put q ≈ −Q, assuming we deal with an attractive interaction. Thus for r ~ 1 µm (the characteristic radius of the cluster), we obtain F′ ~ 10

^{−14}N >> F, where F is the force applied to an individual bubston in the field of a flat capacitor, see the comments to Equation (6). It is clear, however, that the estimate for the force F′ is very approximate, since we do not know the effective charge q. Apparently, a more accurate theoretical analysis and new experiments are required. These experiments should involve the study of the angular dependences of the scattering matrix elements for processed/non-processed liquid samples. It is clear, however, that in the absence of an applied pulsed field, the aggregation of bubstons and the formation of clusters develop in a centrally symmetric field, while upon processing with electric pulses, aggregation of bubstons occurs in a combination of centrally symmetric field and a uniform field of a flat capacitor. Thus it can be argued that the modes of aggregation of bubstons and the fractal properties of bubston clusters will be slightly different for the processed/non-processed samples. In addition, since the volume number density of bubston clusters in deionized water and aqueous salt solutions are different, the effects of treatment with electric pulses for these liquids should also differ from one another. Of course, we still cannot comment on why a change in the geometrical properties of bubston clusters, whose volume number density in 0.1 M NaCl solution is not very high (~2 × 10

^{5}cm

^{−3}), leads to a change in the swelling rate of the polymer membrane. However, we believe that this model could shed light to the mechanisms of a long-term relaxation in water and aqueous salt solutions.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Schematic of the experimental setup for laser luminescence spectroscopy. (1) 369-nm pump beam, (2) optical fiber for pump radiation, (3) thermostat, (4) Nafion plate, (5) optical fiber for photoluminescence signal, (6) spectrometer, (7) personal computer, (8) micrometric-feed table.

**Figure 3.**Oscillograms of pulses used in the experiment; the repetition frequency f is indicated in the lower right corner (in this particular case f = 100 Hz). (

**a**)—100 mV and (

**b**)—500 mV.

**Figure 4.**Intensity of luminescence in the spectral maximum vs. the time of soaking of the polymer membrane for untreated solutions (reference samples); (

**a**)—deionized water; —NaCl solution; (

**b**)—Ringer’s solution.

**Figure 5.**The results of processing with pulses of amplitude 100 mV at a repetition rate of 20 Hz: for Ringer’s solution.

**Figure 6.**The results of processing with pulses of amplitude 125 mV at a repetition rate of 500 Hz: for Ringer’s solution.

**Figure 7.**The results of processing with pulses of amplitude 100 mV at a repetition rate of 100 Hz for Ringer’s solution.

**Figure 8.**Dependence of τ/τ

_{0}on the pulse repetition rate for pulse amplitudes of 100 mV (black curve) and 500 mV (red curve); (

**a**)—deionized water; (

**b**)—NaCl solution; (

**c**)—Ringer’ solution.

**Figure 9.**Mutually perpendicular projections of a stochastic realization of hierarchic bubston cluster with the parameters: the number of bubstons N = 400, the bubston radius R = 100 nm, fractal dimension D = 2.45, see [39].

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Bunkin, N.F.; Bolotskova, P.N.; Bondarchuk, E.V.; Gryaznov, V.G.; Gudkov, S.V.; Kozlov, V.A.; Okuneva, M.A.; Ovchinnikov, O.V.; Smoliy, O.P.; Turkanov, I.F. Long-Term Effect of Low-Frequency Electromagnetic Irradiation in Water and Isotonic Aqueous Solutions as Studied by Photoluminescence from Polymer Membrane. *Polymers* **2021**, *13*, 1443.
https://doi.org/10.3390/polym13091443

**AMA Style**

Bunkin NF, Bolotskova PN, Bondarchuk EV, Gryaznov VG, Gudkov SV, Kozlov VA, Okuneva MA, Ovchinnikov OV, Smoliy OP, Turkanov IF. Long-Term Effect of Low-Frequency Electromagnetic Irradiation in Water and Isotonic Aqueous Solutions as Studied by Photoluminescence from Polymer Membrane. *Polymers*. 2021; 13(9):1443.
https://doi.org/10.3390/polym13091443

**Chicago/Turabian Style**

Bunkin, Nikolai F., Polina N. Bolotskova, Elena V. Bondarchuk, Valery G. Gryaznov, Sergey V. Gudkov, Valeriy A. Kozlov, Maria A. Okuneva, Oleg V. Ovchinnikov, Oleg P. Smoliy, and Igor F. Turkanov. 2021. "Long-Term Effect of Low-Frequency Electromagnetic Irradiation in Water and Isotonic Aqueous Solutions as Studied by Photoluminescence from Polymer Membrane" *Polymers* 13, no. 9: 1443.
https://doi.org/10.3390/polym13091443