# Adsorption of Methylene Blue on the Surface of Polymer Membrane; Dependence on the Isotopic Composition of Liquid Matrix

^{*}

## Abstract

**:**

## 1. Introduction

_{7}HF

_{13}O

_{5}S × C

_{2}F

_{4}) is manufactured via the copolymerization of a perfluorinated vinyl ether comonomer with tetrafluoroethylene, resulting in the chemical structure given below:

_{3}H + H

_{2}O ⇔ R—SO

_{3}

^{−}+ H

_{3}O

^{+}. In addition, it is necessary to take into account the formation of through channels with a diameter of 2–3 nm in the bulk of the polymer matrix (see [1] for more details). Negatively charged areas at the inner surface of these channels provide a possibility for cations to transit through the membrane bulk. Furthermore, the nanometer-sized structure of these channels allows for the separation of H

^{+}and OH

^{−}ions from both sides of the membrane, which is used in low-temperature hydrogen fuel cells. The physical mechanism of such a separation has been comprehensively studied; see, for example, the review [2]. Note also that, currently, the anion-exchange membranes are also widely explored; see a recent review [3].

_{16}H

_{18}ClN

_{3}S, is a tricyclic phenothiazine dye that is deep blue in color; antioxidant properties of MB were described in detail in a recent work [11]. MB undergoes reduction by nicotinamide adenine dinucleotide phosphate to produce leucomethylene blue (leucoMB), which is a colorless compound. The choice of this particular antioxidant is due to the following. As is known [12], MB in aqueous solutions is a Zn

^{+2}ionophore, i.e., it is able to transfer this ion across a lipid membrane in a living cell. At the same time, Nafion is also capable of passing cations of certain sizes through the pores formed during swelling in water (see Ref. [1]), i.e., the properties of Nafion and MB in water appear to be close to one another.

^{2+}ions inhibit the elongation of ribonucleic acid (RNA) polymerase, a component of the RNA viruses that are not found in the human body. In fact, MB has the ability to transport Zn

^{2+}across the viral envelope by endo-lysosomes. Therefore, MB is widely used to treat patients with SARS-CoV-2; see [13,14,15,16,17].

## 2. Materials and Methods

^{2}were investigated. The test liquids were deionized (natural) water (deuterium content is 157 ± 1 ppm) with a resistivity of 18 MΩ × cm at 25 °C, refined by a Milli-Q apparatus (Merck KGaA, Darmstadt, Germany), and deuterium-depleted water (DDW, deuterium content is 1 ppm), purchased from Sigma Aldrich, St. Louis, MO, USA. For the preparation of MB solutions with different weight concentrations, ultrahigh-purity methylene blue (MB) powder was purchased from the manufacturer Macsen Labs (N.K. Agrawal Group, Udaipur, Rajasthan, India).

## 3. Experimental Results

## 4. Discussion

_{b}is the concentration of adsorbed substance in the bulk of the solution, C

_{S0}is the number of free adsorption sites per the surface unit before the beginning of the adsorption process (C

_{S0}is a constant value), σ is the area of adsorbed molecules, and k

_{a}and k

_{d}are two proportionality constants. Obviously, C

_{b}= C

_{b}(t) is decreasing as a function of time. The solution to Equation (1) at the initial condition n = 0 for t = 0 has the following form (see [34]):

_{b}(t) obeys the diffusion equation with the initial condition C

_{b}= C

_{0}at t = 0:

_{01}(%) and relaxation times τ

_{1}(min) for MB concentrations C

_{0}= 0.015, 0.02, and 0.025 mg/mL for the solutions based on natural water, and Table 2 shows the same values Y

_{02}and τ

_{2}for the solutions based on DDW.

_{1}or 1/τ

_{2}, i.e., this rate is higher for the solutions based on DDW. This was to be expected: when Nafion is soaked in the solution based on natural water, the polymer fibers are unwound, i.e., the surface area of the membrane, containing adsorption centers, increases substantially compared to the case of swelling in DDW (no unwinding effect). Within the framework of the model that the adsorption is controlled by diffusion (see Equations (3) and (4)), it can be argued that the diffusion coefficient D inside the layer of unwound polymer fibers is significantly less than the diffusion coefficient D in a free liquid. Unfortunately, we cannot perform a more detailed quantitative analysis of adsorption dynamics based only on the data in Table 1 and Table 2. Still, some numerical estimates can be made. Namely, for MB concentrations of 0.015, 0.02, and 0.025 mg/mL, the time ratios τ

_{1}/τ

_{2}for solutions based on natural water and DDW are equal, respectively, to 2.67, 2.63, and 2.4, i.e., diffusion in a free liquid is accelerated by ~3 times compared with a layer containing unwound fibers.

^{−30}Q × m. Thus, it can be assumed that the “MB + water” particles form polar complexes with a dipole moment

**d**′. The energy of the dipole interaction with the charged membrane can be presented as a scalar product—

**d′E**, where

**E**is the electric field strength vector near the Nafion surface.

_{0}(t) = σ′(t)/(εε

_{0}), where σ′(t) is the surface charge density on the Nafion membrane, ε = 81 is the static permittivity of water, and ε

_{0}= 0.9 × 10

^{−11}F/m is the electrical constant; see [39]. Here, we assume that after removal of the Nafion plate from the solution, the polymer surface eventually becomes electrically neutral, i.e., the charge density σ′(t) → 0. Taking into account the effects of screening due to the presence of ions in liquid, the electric field strength has the form E(x,t) = E

_{0}(t)exp(−x/R

_{D}), i.e., this value decreases on the scale of the Debye screening radius R

_{D}; for a symmetrical monovalent electrolyte, we have for R

_{D}:

_{i}

_{0}is the equilibrium volume number density of ions, x is the coordinate perpendicular to the membrane surface (x = 0 corresponds to the position of the surface), k is the Boltzmann constant, and e is the elementary charge; see [40]. According to the results of measurements of the pH value close to the Nafion surface [41], this value at the distance x = 1–10 mm eventually reaches a stationary level: pH = 5.5. Apparently, it is precisely this pH value that corresponds to the equilibrium value n

_{i}

_{0}in Equation (5). After finding n

_{i}

_{0}and substituting it into Equation (5), we obtain that R

_{D}≈ 100 nm. In addition, short-range dispersion forces act on the “MB + water” complexes from the polymer membrane. The potential of dispersion forces is −A/x

^{6}, where A is a dimensional constant, and the radius of dispersion forces is ~1 nm; see monograph [42]. Finally, the exchange repulsion potential B/x

^{12}acts from the membrane surface, where B is another dimensional constant; see [42]. Thus, the “MB + water” complexes are located in the potential well

_{1}acquires a well-known form, which is called the Lennard–Jones, L–J, or “6–12” potential

_{0}′ and x

_{0}of the minima of functions W

_{1}(x,0) and W

_{2}(x). In the latter case, after differentiating of Equation (7), we obtain

_{0}(the minimum of the potential W

_{2}(x)) is related to the shortest distance between the centers of two interacting particles; these particles are assumed to be spherical, and these spheres are in contact with one another. In our case, these particles are the “MB + water” complex and the Nafion macromolecule, i.e., the coordinate x

_{0}is about 1 nm. Let us now find the coordinate x

_{0}′, which corresponds to the minimum of W

_{1}(x,0). After differentiation in (8), we obtain the algebraic equation:

_{0}′ as compared to x

_{0}. Thus, the condition x

_{0}′ << R

_{D}= 100 nm must be satisfied, that is, [C(0)/R

_{D}]exp(−x

_{0}′/R

_{D}) ≈ C(0)/R

_{D}. In addition, we assume that at x = x

_{0}′, the Coulomb interaction of a polar particle with a charged surface, which is described in (10) by the term C(0)/R

_{D}, exceeds essentially the dispersion interaction, which, as is known [42], is due to the fluctuations of dipole moments of particles. Therefore, we can put in (10) A = 0. After these simplifications, we arrive at

_{0}and x

_{0}′ must coincide. The curves W

_{2}(x) and W

_{1}(x,0) are qualitatively shown in Figure 10a,b, respectively. It is seen that the depth of the potential well decreases with time, cf., panels (a) and (b).

_{2}(x) and W

_{1}(x,0) are immobile, while water molecules should oscillate relative to the position of the MB particle; the area of these oscillations is marked with a double-arrowed horizontal straight line. The points of intersection of this line with the curves W

_{2}(x) and W

_{1}(x,0) set the height of the desorption thresholds ΔW

_{1}and ΔW

_{2}along the ordinate axis. It is seen that |ΔW

_{1}| > |ΔW

_{2}|, where |ΔW

_{1}| is related to panel (b) (t = 0, the membrane surface is charged), while |ΔW

_{2}|is related to panel (a) (the membrane surface is neutral). Following the general concepts of kinetic processes—see, for example, [43]—the desorption flux is proportional to the value exp(−ΔW/kT), i.e., at t = 0, the desorption of water is hindered. As |ΔW(t)| is a time-decreasing function, |ΔW(t)|→|ΔW

_{2}|, i.e., the water desorption flux must increase with time.

_{D}. In this case, the problem of the distribution of the electric field strength E becomes very difficult, especially bearing in mind the nonstationary character of this problem. At present, we are developing an adequate theoretical model for describing adsorption and desorption with accounting for the unwinding of polymer fibers.

_{1}| up to the level of |ΔW

_{2}|) leads to the redshift in the line at wavelength λ = 646 nm to the line at wavelength λ = 666 nm (see the triplet in Figure 8a,b). Indeed, as the water molecule has a dipole moment, it is captured on a charged polymer surface due to Coulomb forces; in this case, the potential well W(x), inside which the water molecule performs a finite motion (oscillations), is deep enough; see Figure 10b. However, as the zero charge on the membrane is being restored, the Coulomb interaction between the water molecule and the Nafion surface disappears, and the potential well holding water molecules is only due to dispersion forces, which result from the fluctuations in the dipole moments of the interacting particles. Obviously, in this case, the depth of the potential well is much smaller than in the case of the Coulomb interaction, cf., Figure 10a,b. As the frequency of the oscillator is $\omega =\sqrt{\frac{k}{m}},$ where m is the effective mass and k is the elasticity constant, and the potential well for the oscillator (the potential energy for a quasi-elastic force) has the form W(x) = kx

^{2}/2, the value of k decreases upon reducing W(x); that is, when passing from the Coulomb to the dispersion interaction, the oscillator frequency ω should also decrease. Apparently, the triplet structure corresponds to the situation when the potential energies of the Coulomb and dispersion interactions are approximately the same.

_{1}′ ≈ 12 min, and in the case of the MB solution based on DDW, this transition is completed at τ

_{2}′ ≈ 4 min. Obviously, when calculating the rates of water desorption, we can ignore the difference in molar masses for natural water and DDW, as the deuterium content in natural water is 157 ppm, while in DDW, the deuterium content is 1 ppm. The ratio τ

_{2}′/τ

_{1}′ = 3, i.e., there exists a very good correlation with the ratio of the times τ

_{2}/τ

_{1}taken from Table 1 and Table 2; see above.

## 5. Conclusions

- The rate of MB adsorption on the Nafion surface depends on the isotopic composition of the MB aqueous solution, which is associated with the effect of unwinding polymer fibers from the membrane surface into the liquid bulk. This is due to the fact that adsorption is controlled by diffusion, and diffusion processes are slowed down inside the layer of unwound fibers, whereas the unwinding effect is controlled by the isotopic composition of liquid.
- Certain bands of the absorption spectrum of MB, adsorbed on the Nafion surface, are redshifted as compared to the same bands in the MB solution. The effect is associated with the formation of molecular complexes between MB, water, and Nafion. These complexes are formed due to short-range dispersion forces and long-range Coulomb forces; Coulomb forces are caused by the presence of negative charge on the membrane surface, resulting from the dissociation of terminal sulfonic groups and the transfer of protons into the liquid bulk. When the Nafion plate is removed from the liquid, the charge on the membrane surface is reduced to zero level, which leads to the disappearance of the Coulomb attraction and, accordingly, to a decrease in the desorption barrier for water molecules. The decrease in charge on the membrane surface is controlled by the diffusion kinetics. This is manifested in the behavior of the derivative dκ‘/dt. We can claim that in the case of polymer fibers, unwound into the bulk of liquid, the charge on the surface decreases slower than in the absence of the unwinding effect.
- We can claim that it is possible to control the dynamics of adsorption and desorption processes by infinitesimal changes in the deuterium content (from 3 to 157 ppm) in an aqueous solution, in which a polymer membrane swells.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A and B | Dimensional constants in Equations (6) and (7); |

C_{b} | The concentration of adsorbed substance in the bulk of the solution in Equation (1); |

C_{0} | The value of C_{b} at t = 0; |

C_{S0} | The number of free adsorption sites per the surface unit before the beginning of the adsorption process in Equation (1); |

C(t) | Time-dependent dimensional parameter in Equations (6) and (7); |

d′ | Dipole moment of complex “MB + water”; |

D | The diffusivity of adsorbing particles in Equation (3); |

E | The electric field strength vector near the Nafion surface; |

n_{i0} | The equilibrium volume number density of ions in MB solution; |

n | The number of adsorbed molecules on the surface unit in Equation (1); |

R_{D} | The Debye screening radius; |

Y_{01} | The equilibrium percentage of MB, removed from the solution based on natural water; |

Y_{02} | The equilibrium percentage of MB, removed from the solution based on DDW; |

σ | The area of adsorbed molecules in Equation (1); |

σ′(t) | The surface charge density on the Nafion membrane; |

φ | The subsurface concentration of adsorbed substance in Equation (4); |

κ(t) | The absorption coefficient of MB solution; |

κ′(t) | The absorption coefficient of Nafion after removing from MB solution; |

η and ξ | Variables of integration in Equation (4); |

τ_{1} | The characteristic time of MB adsorption from MB solution based on natural water; |

τ_{1}′ | The characteristic time of water desorption from MB solution based on natural water; |

τ_{2} | The characteristic time of MB adsorption from MB solution based on DDW; |

τ_{2}′ | The characteristic time of water desorption from MB solution based on DDW; |

ω | The oscillator frequency. |

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**Figure 1.**The process of soaking Nafion in the MB solution with concentration 0.015 mg/mL. Panel (

**a**) corresponds to the start of soaking. Panel (

**b**) corresponds to the end of soaking.

**Figure 3.**The absorptivity spectrum of the MB solution with concentration 0.015 mg/mL, based on natural water and DDW.

**Figure 4.**The absorptivity spectrum of Nafion membrane immediately after removing the plate out of the MB solution with weight concentration 0.015 mg/mL based on natural water, and DDW.

**Figure 5.**Absorption spectrum of the MB solution with concentration 0.015 mg/mL. The inset shows the time of soaking t. Panel (

**a**)—the MB solution is based on natural water. Panel (

**b**)—the MB solution is based on DDW.

**Figure 6.**The dependences {[κ(t = 0) − κ(t)]/κ(t = 0)} × 100%. Panel (

**a**)—the MB solution is based on natural water. Panel (

**b**)—the MB solution is based on DDW.

**Figure 7.**Absorptivity spectra of Nafion plate soaked in the MB solution with concentration 0.015 mg/mL. The inset shows the soaking time t. Panel (

**a**)—the MB solution is based on natural water. Panel (

**b**)—the MB solution is based on DDW.

**Figure 8.**The triplet structures of the absorptivity spectra. Panel (

**a**)—the MB solution with concentration 0.015 mg/mL is based on natural water, t = 12 min. Panel (

**b**)—the MB solution with concentration 0.015 mg/mL is based on DDW, t = 4 min.

**Figure 9.**Dynamics of drying the Nafion plate after soaking in the MB solution based on natural water (black curves) and DDW (red curves). Panel (

**a**)—dependences κ‘(t). Panel (

**b**)—dependences dκ‘/dt.

**Figure 10.**Potential energy of “MB + water + Nafion” complexes near the surface of Nafion. Panel (

**a**) is related to the case C(t) = 0 (Equation (7), W

_{2}(x)). Panel (

**b**) is related to the case t = 0 (Equation (8), W

_{1}(x,0)).

C_{0}, mg/mL | Y_{01}, % | τ_{1}, min |
---|---|---|

0.015 | 98.6 | 113.7 |

0.02 | 90.8 | 121.6 |

0.025 | 83.7 | 130.2 |

C, mg/mL | Y_{02}, % | τ_{2}, min |
---|---|---|

0.015 | 92 | 42.7 |

0.02 | 81 | 46.3 |

0.025 | 73 | 54.3 |

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**MDPI and ACS Style**

Bunkin, N.F.; Bolotskova, P.N.; Gladysheva, Y.V.; Kozlov, V.A.; Timchenko, S.L.
Adsorption of Methylene Blue on the Surface of Polymer Membrane; Dependence on the Isotopic Composition of Liquid Matrix. *Polymers* **2022**, *14*, 4007.
https://doi.org/10.3390/polym14194007

**AMA Style**

Bunkin NF, Bolotskova PN, Gladysheva YV, Kozlov VA, Timchenko SL.
Adsorption of Methylene Blue on the Surface of Polymer Membrane; Dependence on the Isotopic Composition of Liquid Matrix. *Polymers*. 2022; 14(19):4007.
https://doi.org/10.3390/polym14194007

**Chicago/Turabian Style**

Bunkin, Nikolai F., Polina N. Bolotskova, Yana V. Gladysheva, Valeriy A. Kozlov, and Svetlana L. Timchenko.
2022. "Adsorption of Methylene Blue on the Surface of Polymer Membrane; Dependence on the Isotopic Composition of Liquid Matrix" *Polymers* 14, no. 19: 4007.
https://doi.org/10.3390/polym14194007