# Stochastic Ultralow-Frequency Oscillations of the Luminescence Intensity from the Surface of a Polymer Membrane Swelling in Aqueous Salt Solutions

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

^{TM}(C

_{7}HF

_{13}O

_{5}S × C

_{2}F

_{4}) consists of perfluoro-vinyl ether groups terminated with sulfonic groups on a tetrafluoroethylene (Teflon) backbone. Teflon is very hydrophobic, while the sulfonic groups are essentially hydrophilic. While swelling in an aqueous media, a nanostructure consisting of cylindrical reverse micelles appears. Water-filled channels of 2–3 nm diameter form within the Nafion membrane; see [1] for more details. The polymer Nafion is widely studied in various fields, such as physics, chemistry, and hydrogen energetics (see, e.g., references [2,3,4,5,6], related to the articles issued in 2021). The majority of techniques, applied for Nafion studies, are focused on the study of the polymer bulk properties. At the same time, water adjacent to the swollen polymer surface has also been explored, see recent works [7,8,9,10], and the monograph [11] describes experiments, in which a Nafion membrane is immersed in an aqueous suspension of colloidal microspheres. It transpired that the microspheres are repelled from the membrane up to a distance of several hundreds of microns. The area, from which the colloidal microspheres are effectively pushed out, has been termed the “exclusion zone” (EZ). EZ phenomena may have important engineering applications in water filtration, reducing biofouling [12] and microfluidics [13]. EZ phenomena also have an obvious importance to understanding biological systems and resolving outstanding questions regarding “biological water” [14]. In accordance with the model developed in monograph [11], Nafion’s surface imparts a quasicrystalline structure on a macroscopic scale to adjacent water layers; in monograph [11] (see also numerous references therein), this effect was called the formation of the “fourth phase” of water.

_{17}H

_{19}NO

_{3}), which stimulates the conductivity of calcium [21] and potassium [22] ions in human cell channels, is of particular interest to study. Indeed, because the Nafion membrane contains negatively charged channels that are the conductors of protons, it is very important to study the interaction of piperine with Nafion.

## 2. Materials and Methods

#### 2.1. Materials

^{2}square area. The Nafion plates were soaked in Milli-Q water with a resistivity of 4 MΩ × cm (measurement were made 1 h after the preparation with a conductometer CON270043S Eutech, Thermo Fisher Scientific, Waltham, MA, USA), as well as in isotonic NaCl (0.9%; Mosfarm, Moscow region, Russia) and Ringer’s (Biosintez, Penza, Russia) solutions. In our 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. The deuterium content of these samples was 157 ± 1 ppm. In some cases, reagent-grade NaCl (Sigma-Aldrich, St. Louis, MO, USA) was used to prepare 0.9% NaCl solutions based on deuterium depleted water (DDW; deuterium content ≤ 1 ppm, purchased from Sigma-Aldrich, St. Louis, MO, USA). Piperine (C

_{17}H

_{19}NO

_{3}), 98%, was purchased from CheMondis GmbH, Cologne, Germany. Mixtures of piperine were prepared in Ringer’s solution with a concentration of 40 mg/L; this concentration corresponds to a saturated mixture.

#### 2.2. Instrumentation

#### 2.2.1. Processing of Liquid Samples

^{2}, and the distance between them was 5 cm, i.e., the capacitance was 1.77 pF. The results reported below are related to 100 mV amplitude of a pulse; see Figure 1b. Liquid samples were exposed to electric pulses for 20 min (the time of processing). After irradiation of a liquid sample, the processed liquid was poured into the cell shown in Figure 2 to study the photoluminescence signal from the Nafion plate. The interval between the end of electric pulses processing and the beginning of the luminescence experiment was ~20 min. It is generally accepted that the characteristic relaxation times in water and aqueous solutions are limited by the hydrogen bond lifetime, being approximately a picosecond; see, e.g., [32]. Thus, it would seem likely that all the effects associated with electromagnetic treatment should not reveal 20 min after this treatment.

#### 2.2.2. Photoluminescence Study

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

_{Naf}, and can be expressed as:

_{3}. Because these groups are attached to polymeric chains, n

_{Naf}can be associated with the volume number density of Nafion particles. Here I

_{pump}is the pump intensity, A = 20–270 arbitrary units correspond to the spectral density of the mini-spectrometer noise and stray-light illumination in relative units, k is the setup transfer coefficient, V is the luminescence volume, and σ

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

_{lum}corresponds to λ = 460 nm). The linear dependence of the luminescence intensity, I vs. n

_{Naf}, is realized, providing that σ

_{lum}= const.

## 3. Experimental Results

_{lum}, is constant. Indeed, assuming that the volume number density, n

_{Naf}, of the luminescence centers (sulfonic groups in our case) obeyed Equation (1), i.e., n

_{Naf}in the near-surface polymer layer decreases due to penetrating of water molecules into this layer, we can write:

_{Naf}(see Equation (1)), it should exponentially decay.

^{−4}Hz on all curves. It is also seen that at the frequency f → 0 the dependence A(f) diverges, which is related to the specifics of the wavelet transforms using the Morlet wavelet at ultralow frequencies (see [35]), i.e., the growth of the function A(f) at low frequencies can be ignored. In further analysis, a segment of A(f) with an isolated spectral maximum was allocated from the dependences A(f), and for this segment the spectral density, A

^{2}(f), was found, which, in turn, was approximated by Lorentzian:

_{0}is the central (resonant) frequency, and τ

_{corr}is the correlation time of random process with the Lorentzian spectral line; the Lorentzian contour width is Δf~(τ

_{corr})

^{−1}, see [36]. In Figure 8, we show the dependence, A

^{2}(f), for the curve, A(f), shown in Figure 7 for τ = 52.5 h. In Figure 9a,b, we exhibit the dependences of the Pearson rank correlation coefficient, R, vs. time, τ. A detailed description of the methods for calculating the Pearson rank correlation coefficient can be found in the hyperlink [37]. In our case, Pearson’s correlation coefficient, when applied to a sample, is described by the formula:

_{i}and y

_{i}are the individual sample points indexed with i, $\overline{x}=\frac{1}{n}{\displaystyle \sum _{i=1}^{n}{x}_{i}}$ (the sample mean; analogously for $\overline{y}$). In Formula (5), the set of values x

_{i}corresponds to the first measurement of I(t) in Figure 6 (indicated by the symbol (1) on the graphs), and the set of values y

_{i}corresponds to the measurement of I(t) after a time, τ. As follows from Equation (5), R(τ = 0) = 1.

## 4. Discussion

_{0}= 3.8 × 10

^{−4}Hz, and the spectral line width at the half-height level is Δf = 1.416 × 10

^{−4}Hz (see the inset in Figure 8). The value of Δf is consistent with the dependences of the correlation coefficient R(τ); see Figure 9a,b. As is seen in Figure 9a,b, the experimental points fit well the decaying exponential function R(τ) ~ exp(−τ/τ

_{corr}), where τ

_{corr}is the decay time (correlation time). As follows from the graphs in Figure 9, it does not matter from what moment of time we started the measurements of I(t). In addition, the results obtained are indifferent to the spatial position of the experimental setup. Thus, we are apparently dealing with stationary and spatially homogeneous external electromagnetic waves. As follows from the Wiener–Khinchin theorem [36], the dependence R(τ) ~ exp(−τ/τ

_{corr}) corresponds to the spectral density of a random process, described by Lorentzian contour of width Δf ~ (τ

_{corr})

^{−1}. In the case of pattern, exhibited in Figure 9a, we have τ

_{corr}= 25,740 s and Δf ≈ 0.4 × 10

^{−4}Hz. In the case of pattern in Figure 9b, we have τ

_{corr}= 21,780 s and Δf ≈ 0.5 × 10

^{−4}Hz. Thus, the values of Δf obtained on the basis of the data in the graphs of Figure 8 and Figure 9 are of the same order of magnitude. We still do not know why this stochastic behavior reveals only at certain frequencies of processing liquid samples.

^{−1}= 9 × 10

^{−4}Hz ≈ 2f

_{0}. Therefore, we cannot assert that the source of the radio waves leading to the stochastic behavior of I(t) corresponds to that described in [38]. It is very important for us that such sources really do exist. Therefore, without loss of generality, we will assume that we are dealing with pulses of a linearly polarized electromagnetic wave with a frequency of 100 MHz; the repetition rate of these pulses is f

_{0}= 3.8 × 10

^{−4}Hz.

_{S}is static permittivity (for water ε

_{S}= 81), ε

_{∞}is the dielectric permittivity in the optical range (for water ε

_{∞}= 1.77), r is molecular radius (for water r = 1.38 Å), and η is the dynamic viscosity (for water η = 8.9 × 10

^{−4}Pa·s). After the substitutions for water under normal conditions, we obtain τ ≈ 8.27 ps. This implies the estimate ωτ ≈ 8.3 × 10

^{−4}, that is, ε″ << ε′ ≈ ε

_{S}, and absorption at this frequency can be neglected.

^{−17}C, i.e., the bubston charge is approximately a hundred elementary charges. The other parameters in Equation (9) are the following: r is the bubston cluster radius (~1 μm) and q is the effective charge of the center, which attracts a bubston in the coagulation process. Thus, we obtain an estimate F′ $~{10}^{-14}\mathrm{N}$. Here we do not know the exact value of the charge, q; in Equation (9) we assume q~−Q. However, because the cluster is an aggregate of dimers consisting of particles, having the opposite sign, the charge, q, should be calculated as a sum of the terms of the alternating series. Thus, most likely, |q| << |Q|, i.e., F′ << 10

^{−14}N. It is clear that, due to the interaction (9) a spherically symmetric bubston cluster should form. Experimental studies of bubston clusters in aqueous solutions of NaCl are presented in [48]; transpired that the cluster phase is manifested in experiments at ion concentrations >0.1 M. It is obvious that isotonic NaCl and Ringer solutions meet this condition, while in deionized water the concentration of ions is less, and the cluster phase is absent. Indeed, in accordance with our measurements, the pH value in deionized water is 5.7, i.e., the ion content is 10

^{−6}M, which is not sufficient for the coagulation of bubstons, and the clusters are not manifested in experiments with dynamic light scattering in water.

^{−17}N arises in a flat capacitor, which is superimposed on the spherically symmetric Coulomb force (9). Assuming F′~10

^{−14}N, we have an F/F′~10

^{−3}, but this is apparently underestimated, see above. Assuming F′ ≈ F, we find that the force, F, generated inside a plane capacitor, can violate the bubston cluster’s spherical symmetry, and the cluster becomes slightly anisotropic. This was indirectly confirmed in the experiment with the NaCl solution treatment at a frequency of 417 Hz; in this case, one flat capacitor (see Figure 13a) or two flat capacitors, installed normally with each other (Figure 13b), were used. The dependence, I(t), is shown in Figure 13c. As follows from the graphs in Figure 13c, when using one flat capacitor, the luminescence intensity, I(t), behaves stochastically (red curve), while processing with two mutually perpendicular capacitors (blue curve), the run of I(t) is close to the reference dependence.

_{sca}, in this case will be very small, because σ

_{sca}~ 1/λ

^{4}[39] and λ ~ 1 m. Scattered radiation will interact with charged polymer fibers unwound into the bulk of the liquid. We do not know the mass and charge of these fibers, so we do not present formulas that describe the dynamics of these fibers in the field of the incident wave. However, in accordance with the literature data, radiation at frequencies of this range is used in medical practice (in particular, for the treatment of oncological diseases), and this radiation is related not only to electromagnetic waves, but also to acoustic waves; see [50,51]. Based on these indirect data, we can argue that the polymer fibers unwound into the liquid bulk will oscillate at frequency of 100 MHz. In the case of linearly polarized radiation, these oscillations will occur in one plane, but in the case of depolarized radiation, the oscillations will happen in different planes.

_{lum}, does not change upon swelling, then the luminescence intensity, I(t), decreases exponentially. Thus, the stochastic behavior can be explained by random oscillations of σ

_{lum}. To explain this effect on a qualitative level, it is necessary to use the model of non-radiative energy transfer from a donor of luminescence to an acceptor of luminescence; see monograph [52]. Let us imagine that there exists a luminescence center on the membrane surface, which we will call a donor of luminescence. Let us further imagine that at a certain distance, R, from the donor there exists another particle (acceptor of luminescence), whose absorption spectrum coincides with the absorption spectrum of the donor. Then, at a certain R the process of resonant energy transfer from the donor luminescent level to the acceptor level is possible. An electron from an acceptor level passes into the ground state of an acceptor, which can be accompanied by a photon (luminescence) emission, but a non-radiative transition is also possible. In this case, the luminescence from the donor is quenched. If we consider protein membranes, then donors and acceptors, as a rule, are the same groups of proteins, but in the case of acceptors these groups are slightly changed; see [52]. Because in our case the luminescence centers are sulfonic groups, we can assume that the acceptor is a slightly modified sulfonic group, which is not active with respect to the luminescence. The efficiency, S, of energy transfer from a donor to an acceptor is given as:

_{0}= 30–60 Å is the so-called Forster parameter; see [52]. Thus, the value of S varies as R

^{−6}, i.e., it is a very steep function. Note that if the donor and acceptor are rigidly fixed on the membrane surface, then the distance, R, between them is always fixed, i.e., the luminescence cross section, σ

_{lum}, does not change upon swelling. However, in our case, the donor and acceptor are located on the polymer fibers unwound in the liquid bulk, i.e., their spatial position can change due to some external electromagnetic forces (remember that sulfonic groups are charged). If these forces change the distance, R, then, according to Equation (10), the value of S can be either ~1, and the luminescence stops (the effect of quenching), or S << 1, and in this case there is no energy transfer, and the luminescence is quite intense. Thus, the only mechanism in our experiments, due to which the luminescence can disappear/reappear in NaCl solutions based upon natural water, is changing the distance, R, which leads to the oscillations of σ

_{lum}. It seems obvious that when the polymer fibers, unwound into the liquid bulk, are driven by linearly polarized radiation, these fibers will vibrate in the single plane. In this case the distance, R, between the donor and the acceptor does not change, that is, the value of σ

_{lum}remains constant. At the same time, if these fibers are swayed by depolarized radiation, that is, there exist polarizations in different planes, then the distance, R, will change randomly, and stochastic switching of luminescence quenching/excitation modes is possible. Within the framework of this model, the appearance of stochastic phenomena in our experiments is qualitatively explained. The question of why the addition of piperine also leads to the stochastization in the behavior of I(t) remains unclear.

_{sca}.

## 5. Conclusions

_{lum}. These changes occur due to the fact that liquid samples contain bubston clusters, which, as a result of treatment with electrical pulses, acquire anisotropic properties. Incident linearly polarized low-frequency radiation, being scattered in liquid samples, becomes depolarized. In this case, the polymer fibers unwound into the bulk of the liquid experience oscillations in the field of an external wave in different planes, which leads to a change in the average distance between these fibers. It is assumed that, in our case, the effects of resonant luminescence energy transfer between the donor and acceptor are possible, and the distance, R, between the donor and acceptor, which are localized on unwound fibers, changes randomly. Within the framework of this qualitative model, it is possible to explain the effects of stochastization arising in our experiments.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Panel (

**a**) irradiation of a test liquid in a flat capacitor. Panel (

**b**) the shape of an electric pulse applied to the plates of the capacitor.

**Figure 2.**Schematic of the experimental setup for laser luminescence spectroscopy. (1) laser diode; (2) optical fiber; (3) cylindrical cell; (4) Nafion plate; (5) quartz fiber; (6) minispectrometer; (7) computer; (8) stepping motor; T–thermostat.

**Figure 3.**Intensity, I, of luminescence in the spectral maximum vs. the polymer membrane soaking time, t, for liquid samples, processed with 100 mV amplitude electric pulses at a repetition rate of 60 Hz; unprocessed (reference) samples are highlighted with a dashed line; (

**a**)—Milli-Q water; (

**b**)—NaCl solution; (

**c**)—Ringer’s solution.

**Figure 4.**Dependence of I(t) for isotonic Ringer solution containing piperine with the concentration 40 mg/L (saturated mixture). The red curve is related to the measurements immediately after the piperine diluting, while the blue curve is related to the same measurements, performed 24 hr after.

**Figure 5.**The dependence of I(t) for NaCl solutions, processed with 100 mV amplitude electric pulses at a 400 and 440 Hz repetition rate.

**Figure 6.**The intensity I(t) for isotonic NaCl solution after processing at the 417 Hz pulse repetition rate. The difference between the graphs in panels (

**a**,

**b**) is that the measurements were made in different laboratories; the distance between the laboratories is 20 km. Here, τ is the time interval between the beginnings of the corresponding measurements. Pearson rank correlation coefficient was calculated for all values of τ.

**Figure 7.**Results of the Fourier transform of I(t) dependences shown in Figure 6b. The frequency dependences of the spectral amplitude, A(f), were obtained using the Morlet wavelet transform. The dashed line marks the central frequency of the spectral maximum.

**Figure 8.**Spectral density, A

^{2}(f), for the dependence A(f) at τ = 52.5 h in Figure 7. This dependence is approximated by Lorentzian; see Equation (4).

**Figure 10.**The dependence of I(t) after processing at a 417 Hz pulse repetition rate for NaCl solution; the liquid sample was wrapped with 10 µm-thick aluminum foil during treatment.

**Figure 11.**The dependence of I(t) after processing at a 417 Hz pulse repetition rate for NaCl solution; the photoluminescence setup was covered with a 10 µm-thick aluminum foil screen (blue curve), or non-covered with the screen (red curve). The stochastic behavior is restored immediately after removing the screen.

**Figure 12.**Dependence of I(t) in DDW-based NaCl solution, processed with the electric pulses at 417 Hz repetition rate.

**Figure 13.**Panel (

**a**)—the schematic of processing with one capacitor. Panel (

**b**)—the schematic of processing with two capacitors. Panel (

**c**)—dependence of I(t); the NaCl solution was processed beforehand with 417 Hz frequency electric pulses using one/two mutually perpendicular flat capacitors. Red curve is related to one capacitor, whereas blue curve is related to two capacitors.

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**MDPI and ACS Style**

Bunkin, N.F.; Bolotskova, P.N.; Bondarchuk, E.V.; Gryaznov, V.G.; Kozlov, V.A.; Okuneva, M.A.; Ovchinnikov, O.V.; Smoliy, O.P.; Turkanov, I.F.; Galkina, C.A.;
et al. Stochastic Ultralow-Frequency Oscillations of the Luminescence Intensity from the Surface of a Polymer Membrane Swelling in Aqueous Salt Solutions. *Polymers* **2022**, *14*, 688.
https://doi.org/10.3390/polym14040688

**AMA Style**

Bunkin NF, Bolotskova PN, Bondarchuk EV, Gryaznov VG, Kozlov VA, Okuneva MA, Ovchinnikov OV, Smoliy OP, Turkanov IF, Galkina CA,
et al. Stochastic Ultralow-Frequency Oscillations of the Luminescence Intensity from the Surface of a Polymer Membrane Swelling in Aqueous Salt Solutions. *Polymers*. 2022; 14(4):688.
https://doi.org/10.3390/polym14040688

**Chicago/Turabian Style**

Bunkin, Nikolai F., Polina N. Bolotskova, Elena V. Bondarchuk, Valery G. Gryaznov, Valeriy A. Kozlov, Maria A. Okuneva, Oleg V. Ovchinnikov, Oleg P. Smoliy, Igor F. Turkanov, Catherine A. Galkina,
and et al. 2022. "Stochastic Ultralow-Frequency Oscillations of the Luminescence Intensity from the Surface of a Polymer Membrane Swelling in Aqueous Salt Solutions" *Polymers* 14, no. 4: 688.
https://doi.org/10.3390/polym14040688