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Perfluorinated hybrid membranes modified by metal decorated clay nanotubes
Journal of Membrane Science 582 (2019) 172–181
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Perfluorinated hybrid membranes modified by metal decorated clay nanotubes
T
D.A. Petrovaa,∗, A.N. Filippova, N.A. Kononenkob, S.A. Shkirskayab, M.O. Timchenkob, E.V. Ivanova, V.A. Vinokurova, Yu.M. Lvova,c a
Laboratory of Functionalized Aluminosilicate Materials, Gubkin University, Leninsky Prospect 65-1, Moscow, 119991, Russia Department of Physical Chemistry, Kuban State University, Stavropol'skaya 149, Krasnodar, 350040, Russia c Institute for Micromanufacturing, Louisiana Tech University, 911 Hergot Ave., Ruston, LA, 71272, USA b
A R T I C LE I N FO
A B S T R A C T
Keywords: Perfluorinated sulfocationic membrane Hybrid membrane Metal-ceramic hybrid halloysite nanotubes Diffusion permeability Current-voltage curve Modelling transport through a membrane
A number of one-layer perfluorinated cation-exchange membranes modified by halloysite clay nanotubes were prepared using two different solvents: dimethylformamide and isopropanol. The modifier is hybrid Pd, Pt/clay nanotubes doped at 4 wt % into the polymeric matrix. Metal nanoparticles of platinum or palladium were deposited onto the surface of the nanotubes then embedded into membranes providing composite materials which are promising for solid polymer fuel cells. At the first time the distribution of water, effective pore radius, electrical conductivity, selectivity, diffusion and electroosmotic permeability, contact angles (hydrophilicity/hydrophobicity) were investigated for the presented different types of nanocomposite membranes. It is shown that hybrid cation-exchange membranes demonstrate improved thermal, mechanical and transport properties synergistically combining separation. The optimized halloysite-perfluorinated polymer membranes meet the conditions for electro-transport properties needed for solid electrolytes in separation diaphragms for low-temperature membrane electrolyzers. Introduction of Pt-halloysite into the perfluorinated matrix results in preservation of high selectivity and constant value of the limiting electrodiffusion current density. Comparing the theoretically calculated parameters, like the limiting current density, selectivity, transport numbers of water to the experimentally measured ones for samples we can conclude that the hybrid membrane with platinum nanoparticles is promising for nanocomposite cation-exchange perfluorinated films both as the separating membrane in fuel cells and other electric devices.
1. Introduction The development of electro catalysts is important for the transition from a carbon to a hydrogen-based economy where hydrogen can be extracted from renewable energy sources and used in fuel cells to generate electricity and heat. Hydrogen power fuel cell engineering has a high demand for membranes with special mechanical, physicochemical and transport properties. Perfluorinated membranes (PM) are widely used as solid polymer electrolytes in low-temperature fuel cells and separation diaphragms in membrane electrolyzers, electrodialyzers, and sensors [1]. Nevertheless, even the best cation-exchange perfluorinated membranes like Nafion-117® (DuPont de Nemours, USA) and its Russian analog MF-4SC (LTD Plastpolymer, Russia) need to be modified for enhanced water retention and maintenance of hydrophilic pathways for proton transfer. Surface and bulk modification of ion-
∗
exchange membranes by incorporation of organic or inorganic dopants enables the fine tuning of their characteristics, improving stability, ion and molecular transport [2]. Polyaniline [3], nanosized zirconia [4], silica [5], carbon and clay nanotubes [6,7], which are able to change transport properties of ion-exchange membranes, were used as such dopants. Nanoparticles of noble metals [8], can also be used to impart catalytic properties to modified membranes. Ones of the promising modifiers in addition to carbon materials are the abundantly available natural halloysite nanotubes (HNT) with the high porosity, dual positive/negative inner-outer surface charge enhancing ion-channeling, and good dispersibility in perfluorinated polymers [9,10]. The structural features of these 50-nm diameter and 1 μm long aluminosilicate nanotubes allow one to obtain unique composite additives with catalytic properties due to deposition of metal nanoparticles on the inner or
Corresponding author. Department of Physical and Colloid Chemistry, Gubkin University, Leninsky Prospect 65-1, 119991, Moscow, Russia. E-mail address: [email protected] (D.A. Petrova).
https://doi.org/10.1016/j.memsci.2019.03.084 Received 19 February 2019; Received in revised form 25 March 2019; Accepted 27 March 2019 Available online 08 April 2019 0376-7388/ © 2019 Elsevier B.V. All rights reserved.
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hexahydrate (99.9%), palladium (II) chloride and H2PtCl6·6H2O (99%), toluene (99.8%), sodium tetrahydridoborate (98%) – all Sigma Aldrich, Saint Louis, MO, USA.
outer surface of the nanotubes [11,12]. The resulting hybrid membranes doped with halloysite are characterized by improved mechanical properties, thermal stability and are able to retain water at high temperatures [13]. Due to these properties, perfluorinated membranes modified by halloysite can be effectively used as solid polyelectrolytes in low-temperature fuel cells. This task requires reversed engineering via theoretical modelling and computer simulation to select the optimal synthesis conditions. For this, two independent and mutually inconsistent models were studied: the two-phase model of an ion-exchange membrane [14] and the homogeneous model of a fine porous membrane [15,16]. It is a known fact that Pd, Pt and other metals from platinum group are catalytically active and there are numerous articles confirming this [12,17–19]. Based on that we believe the nanocomposite membranes we have synthesized here should be a prospective catalytic system. Moreover, the catalytic properties of our membranes can be confirmed by shortening the plateau of the limiting current on current-voltage curves that might be associated with the catalytic action of platinum/ palladium on the process of water splitting, which leads to the appearance of additional charge carriers—protons and hydroxyl ions [20]. As the dopants, shell Pt/Pd–halloysite nanotubes were synthesized to use in polymer solution with different nature of solvents: dimethylformamide and isopropanol. It is necessary to mention that previously [7,16,20] we have synthesized and investigated hybrid cation-exchange membranes containing halloysite nanotubes doped with platinum and iron nanoparticles using only dimethylformamide as a solvent. Halloysite nanotubes of 4% by weight were added to the membrane film during its formation by the casting method. Halloysite clay is a safe natural tubular material formed by rolled kaolin sheets; it is available in tons at a low price [9]. Halloysite is an aluminosilicate which is chemically identical to kaolin but typically contains minor amount (less than 1 wt %) of iron ions. Prior to the composite membrane formation, hybrid Pt/Pd–halloysite systems were produced as described in Refs. [11,16]. Thus, halloysite nanotubes were used not only as a container for encapsulation, but also as a hydrophilic, polar particles (zeta-potential −30 mV) which contain water and increases the moisture of the membrane [9,20,21]. Based on our theoretical models, we were able to explain the change in the features of modified MF-4SC membranes doped with Pt and Pd and revealed the distinct effects that the hybrid nanosystems based on two metal have on the structure and transport properties of perfluorinated membranes with halloysite clay nanotubes. This allowed for the effective use of the designed hybrid MF-4SC - Pd,Pt/halloysite membranes not only as separating films in fuel cells and electromembrane devices, but also as promising catalytic systems. The goal of this work was to study the effect of modifying perfluorinated membranes with halloysite nanotubes (varying the nature of the perfluoropolymer solvent, doping halloysite nanotubes with palladium and platinum nanoparticles) on their electrotransport properties and structural characteristics.
2.2. Instruments Modified halloysite nanotubes were investigated with means of transmission electron microscopy (TEM) analyses at voltage of 10 kV with JEM-2100 (JEOL, Tokyo, Japan). Atomic force microscopy (AFM) studies were carried out with the SmartSPM®-1000 (AIST-NT, Novato, CA, USA) in semi-contact mode using fpN11 cantilever (beam length 130 μm, hardness 2.6–9.8 N/m, resonance frequency of 118–190 kHz, radius of curvature of the needles 10–25 nm). The wettability and hydrophilicity of membranes were studied with contact angle instrument. The contact angle between membrane and water was measured with a Drop Shape Analyser – DSA100 (Kruss, Germany) operated at room temperature in air. The images and data were recorded after 1.0 μL distilled water or monoethylene glycol being deposited on the surface of membrane (the measurements were carried out at three different locations). Contact angle data were fitted with the Ellipse (Tangent-1) method. 2.3. Metal-ceramic shell halloysite synthesis Halloysite nanotubes surface-modified with Pt and Pd-nanoparticles were synthesized by method described in Ref. [18]. Metals were obtained from acid H2PtCl6·6H2O and salt PdCl2. TEM images of metal particles onto halloysite nanotubes are given in Fig. 1 (b,c). The content of the modifying metal was 2 wt % of the nanotubes' mass. Such percentage of Pt and Pd was chosen based on previous research [7]. The modified halloysite was washed with water, dried and mixed with selected polymers for further membrane formation process. 2.4. Membrane synthesis Monolayer membranes were formed by casting method from sulfopolymer solution in IPA or DMF described in Refs. [5,7]. The polymer solution was placed into a glass former with a flat bottom and kept for 2 h for uniform material distribution and to air bubbles remove. Then, the polymer solution was dried at gradually increasing temperature from 50 to final 120 °C (about 6 h). After drying, the film was carefully removed from the glass surface. For modified membranes nanotubes suspension was obtained as follows: the polymer solution was mixed with halloysite nanotubes with magnetic stirrer (30 min) and ultrasonicated to achieve enough homogeneity. The content of the halloysite was 4 wt % which allowed an optimal mechanical properties [20,22]. The membrane was visually homogeneous over the entire area (Fig. 1); a slight bending of the membrane was possible. The membrane color resulted from the color of halloysite nanotubes modified by different metals. The total thickness of the membranes was 200 ± 20 μm. The total thickness of the membranes was measured by micrometer (SCHUT 908.750, China). Composition of the MF-4SC samples is given in Table 1.
2. Experimental 2.1. Chemicals
2.5. Membrane characterization General membrane synthesis was carried out from sulfopolymer solution of the MF-4SC in lithium form (7.2 wt % in dimethylformamide, DMF solution, 0.98 mgeq/g exchange capacity, Plastpolymer, St.Petersburg, Russia) or MF-4SC in protonic form (10.0 wt % in isopropanol, IPA solution, 0.95 mgeq/g exchange capacity, Plastpolymer, St.-Petersburg, Russia) and dehydrated halloysite nanotubes (Applied Minerals Inc., New York, NY, USA). MF-4SC is constructed from tetrafluoroethylene and perfluorinated sulfocontainning monomers. For synthesis of metal-ceramic hybrid nanosystems the following chemicals were used: furfural (99%), hydrazine hydrate (50–60%), 3aminopropyltriethoxysilane (99%), hexachloroplatinic acid
The method of standard contact porosimetry was used for the determination of water volume distribution in the membrane on the water binding energy or the effective pore radii [23,24]. The membrane samples were piled in a special clamping device between two standards, having the known pore-size distribution obtained by an independent method (e.g. mercury porosimetry). After partial evaporation of water and achieving capillary equilibrium, the standards and samples are weighed, and their water volume is calculated using the mass balance. The pore radius corresponding to a given water volume is found with the use of the standards. 173
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Fig. 1. TEM images of pristine halloysite, for comparison (a), HNT@Pd (b), HNT@Pt (c) and optical images of modified membranes (3), MF-4SC/HNT@Pd (c) and (4), MF-4SC/HNT@Pt (d) obtained from DMF polymer solution.
characterizes the membrane heterogeneity and the fraction of microand mesopores volume in the total pore volume of the membrane; (Vmicro/V0) characterizes the membrane ion selectivity [25]. Here Vsw.m. is the volume occupied by swelled membrane. Schematic drawings of the electrochemical cells, the equations used for calculations and some experimental parameters are summarized in Table 2. The membrane conductivity (κ, S/m) of the membranes in solutions of sodium chloride was measured by the mercury-contact method as the active part of the cell impedance. Integral diffusion permeability (Pm, m2/s) of all membranes was determined in twocompartment cell filled with electrolyte solution and water in opposite chambers. The diffusion flux through the membrane was determined based on kinetic dependencies of electrolyte concentration in chamber with water measured by conductometric method [26]. Electroosmotic permeability (W, m3/C) of the membranes in NaCl
The value of total porosity is determined from the obtained porosimetric curves as water volume per gram of the dry sample (V0, cm3/ g). The specific internal surface area (S, m2/g) is calculated by the formula: rmax
S=2
∫
rmin
r
max dV (r ) 1 ⎛ dV ⎞ dr = 2 , 2 r r ⎝ d ln r ⎠ r
∫
(1)
min
where rmin and rmax are the minimum and maximum pore radii, respectively. The lower limit of integration is estimated as 1 nm, which corresponds to the lowest limit of this method applicability. The volume of hydrophilic unselective macropores filled with unbound, “free” water (Vmacro) was found from the porosimetric curve and the volume of micro and mesopores (Vmicro) having diameter below 50 nm and nearly ideal selectivity was found as well. The volume fraction of macropores in swollen membrane (Vmacro/Vsw.m.) Table 1 Composite membrane samples. No
Membrane
Solvent of polyelectrolyte
Thickness l, μm, ± 2
Modifier
1 2 3 4 5 6 7 8
MF-4SC MF-4SC/HNT MF-4SC/HNT@Pd MF-4SC/HNT@Pt MF-4SC MF-4SC/HNT MF-4SC/HNT@Pd MF-4SC/HNT@Pt
DMF DMF DMF DMF IPA IPA IPA IPA
196 176 182 194 180 176 186 180
– 4% 4% 4% – 4% 4% 4%
174
HNT HNT+ 2% Pd HNT +2% Pt HNT HNT+ 2% Pd HNT +2% Pt
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Table 2 Schematic drawings of the experimental set-up. Cell schematics
Calculation equation
Km =
Experimental conditions AC frequency 200 kHz
l RS
l, membrane thickness; S, area; R, resistance;
Pm =
Vl Δ c Sc Δ t
V, chamber volume; c, concentration; t, time;
W=
V• t Sit w
=
WF 18
i, current density; F, Faraday number; V*, volume of water transfer
i=0 Δc≠0 Δp = 0
i≠0 Δc = 0 Δp = 0
Graphic determination of limiting current and other parameters of current-voltage curve
i≠0 Δc = 0 Δp = 0
Determination of volume of sorbed water as a function of the effective pore radius and the water binding energy
Membranes and standards are in equilibrium with the water vapor within the vessel
solutions and the water transport numbers (tw, mol Н2О/F) were measured in a two-chamber cell with reversible silver chloride electrodes by the volumetric method. The current voltage curves (CVC) were obtained in a cell equipped with platinum polarizing and silver chloride measuring electrodes. Parameters of CVC were found graphically: the angular slope of the ohmic section of the CVC (tgOhmic), the magnitude of the limiting diffusion current (ilim), the extent of the plateau of the limiting current (Δ, V) and its slope (tgplateau). The isothermal experiments were carried out at 25 °С. The measurement errors for all determined parameters amounted to 3–5%.
3. Results and discussion Concentration dependencies of the integral coefficient of diffusion permeability of the initial and modified membranes in NaCl solutions are presented in Fig. 2а. The presence of the modifier results in an increase of the diffusion characteristics of the membrane by almost 2 times in the investigated range of NaCl solution concentrations, except for the sample (4) which has almost the same diffusion characteristics as the unmodified membrane (1). Although Pt and Pd belong to same group of effective catalysts, the 175
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Fig. 2. Dependencies of the integral coefficient of diffusion permeability Pm for perfluorinated membranes (1)–(4) (а) and diffusion flux Jm for membranes (2) and (6) (b) on concentration of NaCl solution. The curve numbers correspond to the sample numbers in Table 1.
diffusion permeabilities of the membranes (3) and (4) are differed (Fig. 2a). The homogeneous model of fine porous membrane was used to explain the reason for this phenomenon [15]. In accordance with the model, the determination of the physicochemical parameters of membranes, such as the equilibrium distribution coefficient γm of a salt molecule inside the membrane and the diffusion coefficient Dm of the electrolyte molecules in the membrane pores, was carried out by minimizing the deviation of theoretically predicted magnitudes of the integral coefficient Pm of diffusion permeability from its experimental dependence on concentration of NaCl solution:
Pm =
2(Dm /γm) C (ργm)2 + 4C 2 + ργm
, (2)
where C - concentration of electrolyte, mol/l; ρ - volume charge density of the membrane, mol/dm3. The results of the calculations are given in Table 3. The volume charge density ρ in the membrane was calculated based on the experimentally determined exchange capacity and the density of the membrane using the standard method [26]. The magnitude of Φm = ln γm expressed in kBT units (kB is Boltzmann's constant, T is absolute temperature), represents the interaction potential of a pair of ions with the ion-exchange membrane matrix. It is negative, since there is a positive ion sorption inside cation-exchange membranes. The most extended structure has membrane (2) with the highest diffusion coefficient of NaCl molecules (Table 3). The addition of palladium to the HNT surface slightly shrinks the structure, but not so tightly as original membrane (1). Membrane (3) with palladium has the highest positive ion sorption (lowest distribution coefficient γm) that is confirmed by its electrical conductivity which is somewhat higher than that of membrane (4) (Fig. 3). At the same time, the diffusion properties of membrane (3) are two times worse than those of membranes (1) (pristine) and (4) (with platinum), that does not allow to recommend the membrane with palladium for use in fuel cells. It is also interesting to note that the functionalization of halloysite nanotubes with palladium does not change the diffusion permeability of the membrane compared with the case of pure halloysite (membrane (2)). Membrane (4) with platinum slightly differs in the physicochemical
Fig. 3. Concentration dependences of the specific electrical conductivity of membranes (3) and (4) and NaCl electrolyte solution (straight line). The curve numbers correspond to the sample numbers in Table 1.
properties from the original membrane (1) (Table 3). Thus, the modification of the perfluorinated membrane by the HNT with platinum nanoparticles covered on the surface does not lead to a noticeable change in the membrane structure and does not weaken their transport properties. This allows predicting the application prospects of hybrid membranes based on MF-4SC with HNT modified by platinum nanoparticles, not only as separating diaphragms in fuel cells and electromembrane devices, but also as catalytic systems. Fig. 2b indicates the influence of the polymer solvent on the diffusion characteristics of perfluorinated membranes modified by pure HNT. Both membranes (2) and (6) contained 4 wt % of HNT and were synthesized from DMF and IPA polymer solutions, accordingly. The diffusion flux through the membrane (6), which was cast from the IPA polymer solution, is higher than for membrane (2) casting from the DMF polymer solution in the whole range of concentrations of NaCl solution. So, to obtain samples with lower diffusion permeability, membranes should be cast from the DMF polymer solution. The electroosmotic permeability of membranes (3)-(4) (solvent DMF) and membranes (5)-(8) (solvent IPA) has been studied to find the changes between these membranes as it was done for the integral coefficient of diffusion permeability. The concentration dependences of the water transport numbers for the mentioned membranes in a constant electric field at a current of 20 mA are given in Fig. 4. They have a classic form of downward curves: the water transport numbers decrease along with the rise of electrolyte concentration [27]. As for the membranes which are cast from the polymer solution in IPA (Fig. 4b), the water transport numbers of the modified membranes (6)–(8) in the dilute solutions are higher than for the original membrane (5).
Table 3 Calculated and measured physicochemical characteristics of membranes (1)–(4). Membrane
γm
Фm
ρ, mol/dm3
Dm, μm2/s
1 2 3 4
0.51 0.45 0.36 0.54
−0.67 −0.79 −1.01 −0.62
1.08 1.15 1.22 1.22
4.9 8.4 6.1 4.9
176
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Table 4 The main structural characteristics of the membranes. Membrane
V0, mm3/ g
Vmacro, mm3/ g
Vmacro/Vsw.m., %
Vmicro/V0, %
S, m2/g
1 2 3 4 5 6 7 8
310 304 294 299 374 345 357 382
44 46 44 39 59 63 59 62
10.7 9.4 7.0 8.6 4.2 6.1 4.1 3.3
86 85 84 86 83 92 83 82
193 181 173 223 227 202 205 221
from DMF polymer solution. The results of experimental study of the diffusion and electroosmotic permeability are consistent with a change in the structural characteristics of the membranes after modification using HNT. The curves of water volume distribution on the water binding energy and the effective pore radii for the membranes (1)–(8) are given in Fig. 6. Some structural parameters of the pristine and modified membranes were found from porosimetric curves (Table 4). As one can see from Table 4 and Fig. 5, the nature of the polymer solvent has a significant effect: the MF-4SC membranes cast from the DMF polymer solution (1–4) have a lower total porosity (V0) and a
Fig. 4. The water transport numbers (in NaCl solution) of hybrid membranes which were cast from the polymer solution in DMF (a) and IPA (b). The curve number corresponds to the membrane number given in Table 1.
Apparently, the introduction of HNT leads to extend of transport channels and the increasing of the specific moisture capacity of the membranes, which is the number of moles of water per mole of functional groups. It is known that the higher the specific moisture capacity of membranes the higher water transport numbers are in dilute solutions [27]. In the case of membranes with moisture capacity above 20 mol of H2O/mole of SO3− the exponential concentration dependences of tw are observed (Fig. 4). Therefore, modifying perfluorinated membranes by HNT enhances the moisture capacity and it is more than 20 mol of H2O per mole of SO3−. The electroosmotic permeability of the membranes (7) and (8) modified by HNT with palladium and platinum nanoparticles correspondingly is higher than for the initial membrane (5), but lower than for membrane (6) modified by pure HNT only. It can be explained by the partial blocking of transport channels by metal nanoparticles. The increase of the NaCl solution concentration to 1 M leads to a decrease of the electroosmotic permeability of the original membrane (5) and modified membranes, so the water transport numbers reach almost the same value: 9 mol H2O/F. Comparing curves (3) and (4) in Fig. 4a with corresponding curves (7) and (8) in Fig. 4b built for two types of membranes modified with HNT containing Pd (3,7) and Pt (4,8) nanoparticles one can conclude, that the electroosmotic permeability as well as the diffusion permeability is significantly higher for samples cast from IPA polymer solution than
Fig. 5. Integral functions of water distribution on the water binding energy and the effective pore radii for membranes (1)–(8), obtained from DMF (a) and IPA (b) polymer solution. The curve numbers correspond to the membrane numbers in Table 1. 177
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Table 5 Physicochemical characteristics and model parameters of modified perfluorinated membranes (3) and (4).
L+∗ (C )
1−
(3)
L−∗ (C ) =
κ dm (C ) ⎛ ⎜1 − 2F 2 ⎝
1−
2P ∗ (C ) CF 2 ⎞ ⎟, R 0 T κ dm (C )π± ⎠
(4)
2P ∗ (C ) CF 2 ⎞ ⎟, R 0 T κ dm (C )π± ⎠
(5)
– electrical conductivity of the membrane measured at direct Here, current; P* – the differential coefficient of diffusion permeability; F – the Faraday number; R0 – universal gas constant; π ± – correction factor that accounts for the non-ideality of the electrolyte solution. The differential coefficient (P*) of diffusion permeability was calculated from the experimentally obtained concentration dependences of the diffusion flux to estimate selectivity of the modified membranes (2), (3) and (4) using also data on the electrical conductivity of the samples in NaCl solutions of the same concentration. To calculate the differential coefficient of diffusion permeability we used the link equation [28]:
κ dm
P ∗ = βPm,
P*·1012, m2/s
κ dm , S/m
L+ ·1012
L-·1014
t+∗ (C )
3
1.58
0.13
4
1.60
0.13
0.1 0.5 0.1 0.5
5.7 17.4 2.8 7.7
0.70 0.82 0.64 0.79
75.2 86.4 68.5 84.1
13.3 208.4 6.5 91.2
0.998 0.976 0.999 0.989
(7)
where t+ is the transfer number of counterions in the solution; f2 - is the volume fraction of the solution inside the membrane in the framework of the two-phase model of conductivity for inhomogeneous ion-exchange membrane [14]. The experimental values of the electrical conductivity of membranes (3) and (4) modified with palladium and platinum nanoparticles in the range of NaCl solution concentrations from 0.01 M to 0.5 M are shown in Fig. 3. The values of κ dm calculated for the same membranes at concentrations of 0.1 M and 0.5 M NaCl solution are presented in Table 5. As seen from Fig. 3 and Table 5, the electrical conductivity at the direct current is 10–15% lower than at the alternating current. The volume fraction (parameter f2) of electrolyte solution in the membranes was calculated as an angular slope of the specific electrical conductivity dependence of the membranes on the electrical conductivity of solution in bilogarithmic coordinates [14]. The obtained values of parameter f2 are presented in Table 5. Electrodiffusion coefficients L+ and L- were calculated based on formulas (4)–(5). The values of L+ and L- as well as transfer numbers t+∗ (C ) of counter-ions through the membranes, calculated on their basis, are presented in Table 5. Analyzing the results obtained, we conclude that the addition of metal-ceramic hybrid halloysite nanotubes allows to preserve the membrane selectivity. In order to assess the use efficacy of ion-exchange membranes under external electric field, the current-voltage curves (CVC) of the electromembrane system (EMS) must be known. Membranes prepared by casting method possess the different roughness of air-contacted and glass-contacted sides. It is easy to see that air-contacted membrane side is brighter, i.e. rougher, in accordance with the height scale shown on the right edge of Fig. 7. This phenomenon is due to the solvent evaporation from the air-contacted membrane side, creating the inhomogeneities on it. As a result, the glass-contacted side was more uniform than the air-contacted side for all samples. Since the heterogeneity of the membrane surface has a significant effect on their polarization behavior, the CVC were registered for each sample for different orientation of the membrane in the measuring cell. Parameters of CVC are shown in Table 6. The resulting polarization curves are shown in Fig. 8 (arrows point out the side of membrane which is oriented towards the cation flux). In case of pristine membrane (1) the earlier transition to the overlimiting state is observed when the rougher membrane surface (“air”) is oriented toward the flux of counterions. The difference in the plateau lengths is about 0.2 V (see Fig. 8 and Table 6). More pronounced difference for sample (1) is observed in the slope of the plateau of the limiting current: the tgplateau value is 19% greater in case of inhomogeneous surface (“air”) than in case of smooth surface
and are the electrodiffusion coefficients of the Where counter- and co-ions, which are calculated from concentration dependences of electrical conductivity and diffusion permeability of these membranes, according to the following formulas [26]:
κ dm (C ) ⎛ ⎜1 + 2F 2 ⎝
C, M
f
L−∗ (C )
L+∗ (C ) =
f2
κ dm = κ m⋅t+2
smaller volume of macropores (Vmacro) than the MF-4SC membranes cast from the IPA polymer solution. It is important to consider possible application these materials as a solid polymer polyelectrolyte in lowtemperature air-hydrogen fuel cells because of the lower probability of a hydrogen crossover. Table 4 shows that the fraction of selective micro- and mesopores (Vmicro/V0) in the MF-4SC membranes casted from the DMF polymer solution is higher than in the MF-4SC membranes cast from the IPA polymer solution. This allows predicting the application prospects of hybrid membranes based on MF-4SC membrane cast from the DMF polymer solution in electromembrane processes. To confirm last assumption the selectivity of two membranes modified by palladium (3) and platinum (4) nanoparticles was evaluated based on the data of their electrical conductivity and diffusion permeability. The calculation of the transfer numbers of counter-ions t+∗ (C ) in the membranes was carried out according to the formula:
L+∗ (C ) , L+∗ (C ) + L−∗ (C )
β
diffusion flux in bilogarithmic coordinates. The values of coefficient β found from the experimental data are presented in Table 5; the concentration dependences of the differential diffusion permeability coefficient of the membranes in the NaCl solution are shown in Fig. 6. To calculate the electrical conductivity κ dm at the direct current the experimental data of appropriate conductivity κ m obtained on the alternating current were used in accordance with the formula:
Fig. 6. Dependences of the differential coefficient of diffusion permeability on concentration of NaCl solution. The curve numbers correspond to the membrane numbers in Table 1.
t+∗ (C ) =
Membrane
(6)
where β is the angular slope of the concentration dependence of the 178
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Fig. 8. Current-voltage characteristics of membranes (1) – (a), and (2) – (b) in 0.05 M NaCl solution. Arrows indicate the membrane side where the limiting state occurred.
[29,34], 10% distortion of the flat membrane surface results in 30% increase of the overlimiting mass transfer. It is known that hydrophilic-hydrophobic properties of the membrane surface influence the CVC parameters. In Ref. [31] it was shown that in case of samples whose surfaces did not differ in roughness but had different surface energies, the length of the plateau varied by 0.2 ± 0.3 V, depending on the orientation of the membrane to the flux of counterions. Herewith the plateau of the limiting current is shorter for hydrophobic membrane surface [29,34,35]. According to these observations, the comparison of the contact angles of wetting for both surfaces (“glass” and “air”) of the membranes under investigation was carried out. The results are shown in Fig. 9. As can be seen from Fig. 9, the rough side membrane faced to air is more hydrophobic and, therefore, its plateau of the limiting current is shorter (Table 6). Inhomogeneous surface and larger contact angle lead to the shortening of the plateau of the limiting current. Thus, in case of pristine membrane (1) the membrane system transfers to the overlimiting state earlier when the more heterogeneous and hydrophobic side of the membrane faces the counterion flux. Introduction of halloysite nanotubes into membrane (1) reduces the hydrophobicity of the sample. The similar effect was previously observed in Ref. [34] when the Nafion solution was modified by carbon nanotubes. Electrochemical behavior of membrane (2) modified by
Fig. 7. AFM images of the surface of the base membrane (1): air-contacted side (a), glass-contacted side (b). Table 6 Parameters of CVC of membranes (1) and (2). CVC parameters
tgOhmic (1/R), S/m2 ilim, A/m2 Δ, V tgplateau (1/R), S/m2
Membrane (1)
Membrane (2)
air
glass
air
glass
374.2 ± 0.2 40.8 ± 0.6 1.10 ± 0.05 5.6
356.3 ± 0.1 40.7 ± 0.6 1.50 ± 0.05 3.4
329.8 ± 0.1 40.4 ± 0.6 1.60 ± 0.05 2.7
337.7 ± 0.1 39.3 ± 0.6 1.40 ± 0.05 3.0
of the sample (“glass”). The results obtained for pure (pristine) membrane (1) are consistent with the literature data [29–33]. Particularly, in work [32] it was shown that the membrane surface influences the slope and length of the limiting current plateau, as well as the behavior of the membrane in the overlimiting state. The earlier onset of the overlimiting state in case of relief membrane can be explained by the fact that profiling of the membrane surface contributes to a more intensive motion of the liquid because of partial destruction of the diffusion layer. According to Refs. 179
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modification of the membrane using HNT, the membrane thickness, the diffusion layer thickness and the ions transport numbers in the solution also remain constant. Substituting the values D, C, h, δ and P* into Eq. (8), the contribution of the second term to the value of the limiting current density can be found. In case of the modified membrane the ratio of two terms in Eq. (8) is equal to:
DFC P ∗FC = 500: 1 : (t¯i − ti ) δ (t¯i − ti ) l
(9)
Last expression means that the contribution of the second term is only 0.2%. For comparison, in case of the pristine membrane, whose diffusion permeability is twice lower, this value is 0.1%. The experimental error and the error of graphical estimation of the ilim value are much higher (Table 6). Thus, the theoretical calculation explains the identical values of the limiting current densities obtained in the experiments for modified and unmodified membranes, despite the differences in their diffusion permeability. 4. Conclusion The composite membranes modified with hybrid Pt/Pd-halloysite nanotubes were prepared by casting method from sulfopolymer solution in isopropanol or dimethylformamide. A comparative study of diffusion permeability and water transport numbers for membranes modified by HNT@Pt and HNT@Pd is carried out. The effect of the polymer solvent on diffusion and electroosmotic permeability is revealed in comparison with membranes modified by HNT@Pt and HNT@Pd. It is found that the water transport numbers of the hybrid membranes obtained from isopropanol polymer solution are higher by 30% in dilute electrolytes as compared to the membranes obtained from dimethylformamide polymer solution. This correlates with the structural characteristics of membranes measured by the standard contact porosimetry. It is better to cast the composites from the dimethylformamide for lower diffusion and electroosmotic permeability of the resulted membranes in order to use them in fuel cells. The electrical conductivity of membranes containing clay nanotubes modified with platinum and palladium particles was determined in NaCl solutions. The volume fraction of the solution in the swollen membrane was calculated based on the concentration dependence of the conductivity in the framework of the two-phase model of a membrane. It is shown that introducing 4 wt% of the Pd, Pt modified nanotubes does not affect the structural heterogeneity of the composite membranes. The differential coefficient of diffusion permeability and electrical conductivity under direct current were calculated and applied to estimate the modified membranes selectivity. The introduction of halloysite nanotubes modified by Pt and Pd nanoparticles into perfluorinated membranes aids in preservation of the membrane selectivity. It is found the behavior of the current-voltage curves depends on the surface irregularity correlated with the conditions of solvent evaporation during the membrane formation, as well as the hydrophobic-hydrophilic properties of the membrane surface. It was shown also that addition of 4 wt% of halloysite nanotubes does not lead to a significant change of the limiting electrodiffusion current density as compared to the pristine sulfopolymer membrane. A preservation of high selectivity and constant value of the limiting electrodiffusion current density by introducing the Pt-halloysite nanotubes into the perfluorinated matrix makes hybrid MF-4SC membranes promising not only as a solid polyelectrolyte films in fuel cells and other electro-devices, but also as prospective separating diaphragms in electromembrane processes.
Fig. 9. Contact angles of membranes (1) – pristine sample and (2) – sample modified by pure halloysite for “glass” and “air” sides, using water (a) and monoethylene glycol (b).
HNT differs from that of unmodified membrane (1) (Fig. 8). Despite the circumstance that the values of contact angles (Fig. 9) and the heterogeneity of the surface obey the same law for membrane (2) as for pristine membrane (1), the parameters of their current-voltage characteristics change in the opposite directions. Thus, the overlimiting state for the membrane (2) occurs earlier for the side facing the glass than for the side facing the air during synthesis and evaporation of the solvent. The difference in the length of the limiting current plateau is 0.2 V. Since the HNT-modified MF-4SC membrane differs from the original membrane only by the presence of halloysite we may conclude that the deviation in the polarization behavior is caused by the influence of HNT, which contributes to earlier transition of the EMS to the overlimiting state. It can be assumed that halloysite nanotubes precipitating in the process of membrane synthesis under the action of gravity on the side facing the glass, thereby forming a surface enriched with HNT. As a result, regions with high and low conductivity are formed in the membrane. According to the model concepts [35] it contributes to the enhancement of electroconvection in the overlimiting current regimes, which causes the decrease of the transition electric potential of EMS to the overlimiting state. Interestingly, the limiting current value does not change after the membrane modification by HNT. To explain this, the theoretical estimate of the ilim value was completed using the Pierce-Gnusin equation, considering the actual values of the parameters:
ilim =
DFC P ∗FC + , (t¯i − ti )δ (t¯i − ti ) l
(8)
where D – diffusion coefficient of a salt molecule in a dilute solution; C – concentration of salt in the solution; δ – thickness of the diffusion layer; l – membrane thickness, t¯i and ti – the transport numbers of the ith counterion in the membrane and in the solution, respectively. The introduction of nanotubes changes only the differential diffusion permeability P∗ (Fig. 6) which is involved in the second term of Eq. (8). The selectivity of membranes found from porosimetric curves through the Vmicro/V0 parameter does not change (Table 3). Upon
Funding This work was supported by the Ministry of Science and Higher Education of the Russian Federation (Grant No. 14.Z50.31.0035). 180
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Acknowledgments [26]
The authors thank Anna Stavitskaya for synthesis of Pd/Pt - halloysite nanoparticles and Y. Darrat (Louisiana Tech) for the manuscript editing.
[27]
[28]
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.memsci.2019.03.084.
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Bagotsky, Structural Properties of Porous Materials and Powders Used in Different Fields of Science and Technology, Springer, London, 2014. [24] Y.M. Volfkovich, V.S. Bagotzky, V.E. Sosenkin, I.A. Blinov, The standard contact porosimetry, Colloids Surf. A Physicochem. Eng. Asp. 187–188 (2001) 349–365. [25] N.A. Kononenko, M.A. Fomenko, Y.M. Volfkovich, Structure of perfluorinated
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List of main symbols Latin A: water binding energy, J/mol C: concentration of electrolyte, mol/l D, Dm: diffusion coefficients of a salt molecule in a dilute solution and inside a membrane, correspondingly, m2/s F: Faraday number f2: volume fraction of the solution inside the membrane l: membrane thickness, m ilim: density of the limiting diffusion current, A/m2 Jm: transmembrane flux, mol/m2 s kB: Boltzmann's constant L+∗, L−∗ : electrodiffusion coefficients of the counter- and co-ions Pm: integral coefficient of diffusion permeability, m2/s P*: differential coefficient of diffusion permeability, m2/s r: pore radius, nm S: specific internal surface membrane's area, m2/g T: absolute temperature t¯i, ti : transport numbers of the i-th counterion in the membrane and in the solution t+∗ : transport number of counter-ions tgOhmic: slope of the ohmic section of the current voltage curve tgplateau: slope of the plateau of the limiting current tw: water transport number, mol Н2О/F R0: gas constant V0: total volume of water in the membrane per gram of the dry sample, cm3/g Vmacro: volume of macropores having the pore radius > 50 nm, cm3/g Vmicro: volume of micro and mesopores having the pore radius ≤50 nm, cm3/g Vsw.m: volume of swollen membrane, cm3/g Δ: extent of the plateau of the limiting current, V W: electroosmotic permeability, m3/C
Greek β: the angular slope of the concentration dependence of the diffusion flux in bilogarithmic coordinates δ: thickness of the diffusion layer, m κ: membrane conductivity measured under alternating current, S/m κ dm : membrane conductivity measured under direct current, S/m γm: distribution coefficient of a salt molecule inside a membrane Φm: interaction potential of a pair of ions with the ion-exchange membrane matrix in kBT units ρ: volume charge density of a membrane, mol/dm3
Subscripts +: cation -: anion m: membrane
181
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Perfluorinated hybrid membranes modified by metal decorated clay nanotubes
T
D.A. Petrovaa,∗, A.N. Filippova, N.A. Kononenkob, S.A. Shkirskayab, M.O. Timchenkob, E.V. Ivanova, V.A. Vinokurova, Yu.M. Lvova,c a
Laboratory of Functionalized Aluminosilicate Materials, Gubkin University, Leninsky Prospect 65-1, Moscow, 119991, Russia Department of Physical Chemistry, Kuban State University, Stavropol'skaya 149, Krasnodar, 350040, Russia c Institute for Micromanufacturing, Louisiana Tech University, 911 Hergot Ave., Ruston, LA, 71272, USA b
A R T I C LE I N FO
A B S T R A C T
Keywords: Perfluorinated sulfocationic membrane Hybrid membrane Metal-ceramic hybrid halloysite nanotubes Diffusion permeability Current-voltage curve Modelling transport through a membrane
A number of one-layer perfluorinated cation-exchange membranes modified by halloysite clay nanotubes were prepared using two different solvents: dimethylformamide and isopropanol. The modifier is hybrid Pd, Pt/clay nanotubes doped at 4 wt % into the polymeric matrix. Metal nanoparticles of platinum or palladium were deposited onto the surface of the nanotubes then embedded into membranes providing composite materials which are promising for solid polymer fuel cells. At the first time the distribution of water, effective pore radius, electrical conductivity, selectivity, diffusion and electroosmotic permeability, contact angles (hydrophilicity/hydrophobicity) were investigated for the presented different types of nanocomposite membranes. It is shown that hybrid cation-exchange membranes demonstrate improved thermal, mechanical and transport properties synergistically combining separation. The optimized halloysite-perfluorinated polymer membranes meet the conditions for electro-transport properties needed for solid electrolytes in separation diaphragms for low-temperature membrane electrolyzers. Introduction of Pt-halloysite into the perfluorinated matrix results in preservation of high selectivity and constant value of the limiting electrodiffusion current density. Comparing the theoretically calculated parameters, like the limiting current density, selectivity, transport numbers of water to the experimentally measured ones for samples we can conclude that the hybrid membrane with platinum nanoparticles is promising for nanocomposite cation-exchange perfluorinated films both as the separating membrane in fuel cells and other electric devices.
1. Introduction The development of electro catalysts is important for the transition from a carbon to a hydrogen-based economy where hydrogen can be extracted from renewable energy sources and used in fuel cells to generate electricity and heat. Hydrogen power fuel cell engineering has a high demand for membranes with special mechanical, physicochemical and transport properties. Perfluorinated membranes (PM) are widely used as solid polymer electrolytes in low-temperature fuel cells and separation diaphragms in membrane electrolyzers, electrodialyzers, and sensors [1]. Nevertheless, even the best cation-exchange perfluorinated membranes like Nafion-117® (DuPont de Nemours, USA) and its Russian analog MF-4SC (LTD Plastpolymer, Russia) need to be modified for enhanced water retention and maintenance of hydrophilic pathways for proton transfer. Surface and bulk modification of ion-
∗
exchange membranes by incorporation of organic or inorganic dopants enables the fine tuning of their characteristics, improving stability, ion and molecular transport [2]. Polyaniline [3], nanosized zirconia [4], silica [5], carbon and clay nanotubes [6,7], which are able to change transport properties of ion-exchange membranes, were used as such dopants. Nanoparticles of noble metals [8], can also be used to impart catalytic properties to modified membranes. Ones of the promising modifiers in addition to carbon materials are the abundantly available natural halloysite nanotubes (HNT) with the high porosity, dual positive/negative inner-outer surface charge enhancing ion-channeling, and good dispersibility in perfluorinated polymers [9,10]. The structural features of these 50-nm diameter and 1 μm long aluminosilicate nanotubes allow one to obtain unique composite additives with catalytic properties due to deposition of metal nanoparticles on the inner or
Corresponding author. Department of Physical and Colloid Chemistry, Gubkin University, Leninsky Prospect 65-1, 119991, Moscow, Russia. E-mail address: [email protected] (D.A. Petrova).
https://doi.org/10.1016/j.memsci.2019.03.084 Received 19 February 2019; Received in revised form 25 March 2019; Accepted 27 March 2019 Available online 08 April 2019 0376-7388/ © 2019 Elsevier B.V. All rights reserved.
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hexahydrate (99.9%), palladium (II) chloride and H2PtCl6·6H2O (99%), toluene (99.8%), sodium tetrahydridoborate (98%) – all Sigma Aldrich, Saint Louis, MO, USA.
outer surface of the nanotubes [11,12]. The resulting hybrid membranes doped with halloysite are characterized by improved mechanical properties, thermal stability and are able to retain water at high temperatures [13]. Due to these properties, perfluorinated membranes modified by halloysite can be effectively used as solid polyelectrolytes in low-temperature fuel cells. This task requires reversed engineering via theoretical modelling and computer simulation to select the optimal synthesis conditions. For this, two independent and mutually inconsistent models were studied: the two-phase model of an ion-exchange membrane [14] and the homogeneous model of a fine porous membrane [15,16]. It is a known fact that Pd, Pt and other metals from platinum group are catalytically active and there are numerous articles confirming this [12,17–19]. Based on that we believe the nanocomposite membranes we have synthesized here should be a prospective catalytic system. Moreover, the catalytic properties of our membranes can be confirmed by shortening the plateau of the limiting current on current-voltage curves that might be associated with the catalytic action of platinum/ palladium on the process of water splitting, which leads to the appearance of additional charge carriers—protons and hydroxyl ions [20]. As the dopants, shell Pt/Pd–halloysite nanotubes were synthesized to use in polymer solution with different nature of solvents: dimethylformamide and isopropanol. It is necessary to mention that previously [7,16,20] we have synthesized and investigated hybrid cation-exchange membranes containing halloysite nanotubes doped with platinum and iron nanoparticles using only dimethylformamide as a solvent. Halloysite nanotubes of 4% by weight were added to the membrane film during its formation by the casting method. Halloysite clay is a safe natural tubular material formed by rolled kaolin sheets; it is available in tons at a low price [9]. Halloysite is an aluminosilicate which is chemically identical to kaolin but typically contains minor amount (less than 1 wt %) of iron ions. Prior to the composite membrane formation, hybrid Pt/Pd–halloysite systems were produced as described in Refs. [11,16]. Thus, halloysite nanotubes were used not only as a container for encapsulation, but also as a hydrophilic, polar particles (zeta-potential −30 mV) which contain water and increases the moisture of the membrane [9,20,21]. Based on our theoretical models, we were able to explain the change in the features of modified MF-4SC membranes doped with Pt and Pd and revealed the distinct effects that the hybrid nanosystems based on two metal have on the structure and transport properties of perfluorinated membranes with halloysite clay nanotubes. This allowed for the effective use of the designed hybrid MF-4SC - Pd,Pt/halloysite membranes not only as separating films in fuel cells and electromembrane devices, but also as promising catalytic systems. The goal of this work was to study the effect of modifying perfluorinated membranes with halloysite nanotubes (varying the nature of the perfluoropolymer solvent, doping halloysite nanotubes with palladium and platinum nanoparticles) on their electrotransport properties and structural characteristics.
2.2. Instruments Modified halloysite nanotubes were investigated with means of transmission electron microscopy (TEM) analyses at voltage of 10 kV with JEM-2100 (JEOL, Tokyo, Japan). Atomic force microscopy (AFM) studies were carried out with the SmartSPM®-1000 (AIST-NT, Novato, CA, USA) in semi-contact mode using fpN11 cantilever (beam length 130 μm, hardness 2.6–9.8 N/m, resonance frequency of 118–190 kHz, radius of curvature of the needles 10–25 nm). The wettability and hydrophilicity of membranes were studied with contact angle instrument. The contact angle between membrane and water was measured with a Drop Shape Analyser – DSA100 (Kruss, Germany) operated at room temperature in air. The images and data were recorded after 1.0 μL distilled water or monoethylene glycol being deposited on the surface of membrane (the measurements were carried out at three different locations). Contact angle data were fitted with the Ellipse (Tangent-1) method. 2.3. Metal-ceramic shell halloysite synthesis Halloysite nanotubes surface-modified with Pt and Pd-nanoparticles were synthesized by method described in Ref. [18]. Metals were obtained from acid H2PtCl6·6H2O and salt PdCl2. TEM images of metal particles onto halloysite nanotubes are given in Fig. 1 (b,c). The content of the modifying metal was 2 wt % of the nanotubes' mass. Such percentage of Pt and Pd was chosen based on previous research [7]. The modified halloysite was washed with water, dried and mixed with selected polymers for further membrane formation process. 2.4. Membrane synthesis Monolayer membranes were formed by casting method from sulfopolymer solution in IPA or DMF described in Refs. [5,7]. The polymer solution was placed into a glass former with a flat bottom and kept for 2 h for uniform material distribution and to air bubbles remove. Then, the polymer solution was dried at gradually increasing temperature from 50 to final 120 °C (about 6 h). After drying, the film was carefully removed from the glass surface. For modified membranes nanotubes suspension was obtained as follows: the polymer solution was mixed with halloysite nanotubes with magnetic stirrer (30 min) and ultrasonicated to achieve enough homogeneity. The content of the halloysite was 4 wt % which allowed an optimal mechanical properties [20,22]. The membrane was visually homogeneous over the entire area (Fig. 1); a slight bending of the membrane was possible. The membrane color resulted from the color of halloysite nanotubes modified by different metals. The total thickness of the membranes was 200 ± 20 μm. The total thickness of the membranes was measured by micrometer (SCHUT 908.750, China). Composition of the MF-4SC samples is given in Table 1.
2. Experimental 2.1. Chemicals
2.5. Membrane characterization General membrane synthesis was carried out from sulfopolymer solution of the MF-4SC in lithium form (7.2 wt % in dimethylformamide, DMF solution, 0.98 mgeq/g exchange capacity, Plastpolymer, St.Petersburg, Russia) or MF-4SC in protonic form (10.0 wt % in isopropanol, IPA solution, 0.95 mgeq/g exchange capacity, Plastpolymer, St.-Petersburg, Russia) and dehydrated halloysite nanotubes (Applied Minerals Inc., New York, NY, USA). MF-4SC is constructed from tetrafluoroethylene and perfluorinated sulfocontainning monomers. For synthesis of metal-ceramic hybrid nanosystems the following chemicals were used: furfural (99%), hydrazine hydrate (50–60%), 3aminopropyltriethoxysilane (99%), hexachloroplatinic acid
The method of standard contact porosimetry was used for the determination of water volume distribution in the membrane on the water binding energy or the effective pore radii [23,24]. The membrane samples were piled in a special clamping device between two standards, having the known pore-size distribution obtained by an independent method (e.g. mercury porosimetry). After partial evaporation of water and achieving capillary equilibrium, the standards and samples are weighed, and their water volume is calculated using the mass balance. The pore radius corresponding to a given water volume is found with the use of the standards. 173
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Fig. 1. TEM images of pristine halloysite, for comparison (a), HNT@Pd (b), HNT@Pt (c) and optical images of modified membranes (3), MF-4SC/HNT@Pd (c) and (4), MF-4SC/HNT@Pt (d) obtained from DMF polymer solution.
characterizes the membrane heterogeneity and the fraction of microand mesopores volume in the total pore volume of the membrane; (Vmicro/V0) characterizes the membrane ion selectivity [25]. Here Vsw.m. is the volume occupied by swelled membrane. Schematic drawings of the electrochemical cells, the equations used for calculations and some experimental parameters are summarized in Table 2. The membrane conductivity (κ, S/m) of the membranes in solutions of sodium chloride was measured by the mercury-contact method as the active part of the cell impedance. Integral diffusion permeability (Pm, m2/s) of all membranes was determined in twocompartment cell filled with electrolyte solution and water in opposite chambers. The diffusion flux through the membrane was determined based on kinetic dependencies of electrolyte concentration in chamber with water measured by conductometric method [26]. Electroosmotic permeability (W, m3/C) of the membranes in NaCl
The value of total porosity is determined from the obtained porosimetric curves as water volume per gram of the dry sample (V0, cm3/ g). The specific internal surface area (S, m2/g) is calculated by the formula: rmax
S=2
∫
rmin
r
max dV (r ) 1 ⎛ dV ⎞ dr = 2 , 2 r r ⎝ d ln r ⎠ r
∫
(1)
min
where rmin and rmax are the minimum and maximum pore radii, respectively. The lower limit of integration is estimated as 1 nm, which corresponds to the lowest limit of this method applicability. The volume of hydrophilic unselective macropores filled with unbound, “free” water (Vmacro) was found from the porosimetric curve and the volume of micro and mesopores (Vmicro) having diameter below 50 nm and nearly ideal selectivity was found as well. The volume fraction of macropores in swollen membrane (Vmacro/Vsw.m.) Table 1 Composite membrane samples. No
Membrane
Solvent of polyelectrolyte
Thickness l, μm, ± 2
Modifier
1 2 3 4 5 6 7 8
MF-4SC MF-4SC/HNT MF-4SC/HNT@Pd MF-4SC/HNT@Pt MF-4SC MF-4SC/HNT MF-4SC/HNT@Pd MF-4SC/HNT@Pt
DMF DMF DMF DMF IPA IPA IPA IPA
196 176 182 194 180 176 186 180
– 4% 4% 4% – 4% 4% 4%
174
HNT HNT+ 2% Pd HNT +2% Pt HNT HNT+ 2% Pd HNT +2% Pt
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Table 2 Schematic drawings of the experimental set-up. Cell schematics
Calculation equation
Km =
Experimental conditions AC frequency 200 kHz
l RS
l, membrane thickness; S, area; R, resistance;
Pm =
Vl Δ c Sc Δ t
V, chamber volume; c, concentration; t, time;
W=
V• t Sit w
=
WF 18
i, current density; F, Faraday number; V*, volume of water transfer
i=0 Δc≠0 Δp = 0
i≠0 Δc = 0 Δp = 0
Graphic determination of limiting current and other parameters of current-voltage curve
i≠0 Δc = 0 Δp = 0
Determination of volume of sorbed water as a function of the effective pore radius and the water binding energy
Membranes and standards are in equilibrium with the water vapor within the vessel
solutions and the water transport numbers (tw, mol Н2О/F) were measured in a two-chamber cell with reversible silver chloride electrodes by the volumetric method. The current voltage curves (CVC) were obtained in a cell equipped with platinum polarizing and silver chloride measuring electrodes. Parameters of CVC were found graphically: the angular slope of the ohmic section of the CVC (tgOhmic), the magnitude of the limiting diffusion current (ilim), the extent of the plateau of the limiting current (Δ, V) and its slope (tgplateau). The isothermal experiments were carried out at 25 °С. The measurement errors for all determined parameters amounted to 3–5%.
3. Results and discussion Concentration dependencies of the integral coefficient of diffusion permeability of the initial and modified membranes in NaCl solutions are presented in Fig. 2а. The presence of the modifier results in an increase of the diffusion characteristics of the membrane by almost 2 times in the investigated range of NaCl solution concentrations, except for the sample (4) which has almost the same diffusion characteristics as the unmodified membrane (1). Although Pt and Pd belong to same group of effective catalysts, the 175
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Fig. 2. Dependencies of the integral coefficient of diffusion permeability Pm for perfluorinated membranes (1)–(4) (а) and diffusion flux Jm for membranes (2) and (6) (b) on concentration of NaCl solution. The curve numbers correspond to the sample numbers in Table 1.
diffusion permeabilities of the membranes (3) and (4) are differed (Fig. 2a). The homogeneous model of fine porous membrane was used to explain the reason for this phenomenon [15]. In accordance with the model, the determination of the physicochemical parameters of membranes, such as the equilibrium distribution coefficient γm of a salt molecule inside the membrane and the diffusion coefficient Dm of the electrolyte molecules in the membrane pores, was carried out by minimizing the deviation of theoretically predicted magnitudes of the integral coefficient Pm of diffusion permeability from its experimental dependence on concentration of NaCl solution:
Pm =
2(Dm /γm) C (ργm)2 + 4C 2 + ργm
, (2)
where C - concentration of electrolyte, mol/l; ρ - volume charge density of the membrane, mol/dm3. The results of the calculations are given in Table 3. The volume charge density ρ in the membrane was calculated based on the experimentally determined exchange capacity and the density of the membrane using the standard method [26]. The magnitude of Φm = ln γm expressed in kBT units (kB is Boltzmann's constant, T is absolute temperature), represents the interaction potential of a pair of ions with the ion-exchange membrane matrix. It is negative, since there is a positive ion sorption inside cation-exchange membranes. The most extended structure has membrane (2) with the highest diffusion coefficient of NaCl molecules (Table 3). The addition of palladium to the HNT surface slightly shrinks the structure, but not so tightly as original membrane (1). Membrane (3) with palladium has the highest positive ion sorption (lowest distribution coefficient γm) that is confirmed by its electrical conductivity which is somewhat higher than that of membrane (4) (Fig. 3). At the same time, the diffusion properties of membrane (3) are two times worse than those of membranes (1) (pristine) and (4) (with platinum), that does not allow to recommend the membrane with palladium for use in fuel cells. It is also interesting to note that the functionalization of halloysite nanotubes with palladium does not change the diffusion permeability of the membrane compared with the case of pure halloysite (membrane (2)). Membrane (4) with platinum slightly differs in the physicochemical
Fig. 3. Concentration dependences of the specific electrical conductivity of membranes (3) and (4) and NaCl electrolyte solution (straight line). The curve numbers correspond to the sample numbers in Table 1.
properties from the original membrane (1) (Table 3). Thus, the modification of the perfluorinated membrane by the HNT with platinum nanoparticles covered on the surface does not lead to a noticeable change in the membrane structure and does not weaken their transport properties. This allows predicting the application prospects of hybrid membranes based on MF-4SC with HNT modified by platinum nanoparticles, not only as separating diaphragms in fuel cells and electromembrane devices, but also as catalytic systems. Fig. 2b indicates the influence of the polymer solvent on the diffusion characteristics of perfluorinated membranes modified by pure HNT. Both membranes (2) and (6) contained 4 wt % of HNT and were synthesized from DMF and IPA polymer solutions, accordingly. The diffusion flux through the membrane (6), which was cast from the IPA polymer solution, is higher than for membrane (2) casting from the DMF polymer solution in the whole range of concentrations of NaCl solution. So, to obtain samples with lower diffusion permeability, membranes should be cast from the DMF polymer solution. The electroosmotic permeability of membranes (3)-(4) (solvent DMF) and membranes (5)-(8) (solvent IPA) has been studied to find the changes between these membranes as it was done for the integral coefficient of diffusion permeability. The concentration dependences of the water transport numbers for the mentioned membranes in a constant electric field at a current of 20 mA are given in Fig. 4. They have a classic form of downward curves: the water transport numbers decrease along with the rise of electrolyte concentration [27]. As for the membranes which are cast from the polymer solution in IPA (Fig. 4b), the water transport numbers of the modified membranes (6)–(8) in the dilute solutions are higher than for the original membrane (5).
Table 3 Calculated and measured physicochemical characteristics of membranes (1)–(4). Membrane
γm
Фm
ρ, mol/dm3
Dm, μm2/s
1 2 3 4
0.51 0.45 0.36 0.54
−0.67 −0.79 −1.01 −0.62
1.08 1.15 1.22 1.22
4.9 8.4 6.1 4.9
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Table 4 The main structural characteristics of the membranes. Membrane
V0, mm3/ g
Vmacro, mm3/ g
Vmacro/Vsw.m., %
Vmicro/V0, %
S, m2/g
1 2 3 4 5 6 7 8
310 304 294 299 374 345 357 382
44 46 44 39 59 63 59 62
10.7 9.4 7.0 8.6 4.2 6.1 4.1 3.3
86 85 84 86 83 92 83 82
193 181 173 223 227 202 205 221
from DMF polymer solution. The results of experimental study of the diffusion and electroosmotic permeability are consistent with a change in the structural characteristics of the membranes after modification using HNT. The curves of water volume distribution on the water binding energy and the effective pore radii for the membranes (1)–(8) are given in Fig. 6. Some structural parameters of the pristine and modified membranes were found from porosimetric curves (Table 4). As one can see from Table 4 and Fig. 5, the nature of the polymer solvent has a significant effect: the MF-4SC membranes cast from the DMF polymer solution (1–4) have a lower total porosity (V0) and a
Fig. 4. The water transport numbers (in NaCl solution) of hybrid membranes which were cast from the polymer solution in DMF (a) and IPA (b). The curve number corresponds to the membrane number given in Table 1.
Apparently, the introduction of HNT leads to extend of transport channels and the increasing of the specific moisture capacity of the membranes, which is the number of moles of water per mole of functional groups. It is known that the higher the specific moisture capacity of membranes the higher water transport numbers are in dilute solutions [27]. In the case of membranes with moisture capacity above 20 mol of H2O/mole of SO3− the exponential concentration dependences of tw are observed (Fig. 4). Therefore, modifying perfluorinated membranes by HNT enhances the moisture capacity and it is more than 20 mol of H2O per mole of SO3−. The electroosmotic permeability of the membranes (7) and (8) modified by HNT with palladium and platinum nanoparticles correspondingly is higher than for the initial membrane (5), but lower than for membrane (6) modified by pure HNT only. It can be explained by the partial blocking of transport channels by metal nanoparticles. The increase of the NaCl solution concentration to 1 M leads to a decrease of the electroosmotic permeability of the original membrane (5) and modified membranes, so the water transport numbers reach almost the same value: 9 mol H2O/F. Comparing curves (3) and (4) in Fig. 4a with corresponding curves (7) and (8) in Fig. 4b built for two types of membranes modified with HNT containing Pd (3,7) and Pt (4,8) nanoparticles one can conclude, that the electroosmotic permeability as well as the diffusion permeability is significantly higher for samples cast from IPA polymer solution than
Fig. 5. Integral functions of water distribution on the water binding energy and the effective pore radii for membranes (1)–(8), obtained from DMF (a) and IPA (b) polymer solution. The curve numbers correspond to the membrane numbers in Table 1. 177
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Table 5 Physicochemical characteristics and model parameters of modified perfluorinated membranes (3) and (4).
L+∗ (C )
1−
(3)
L−∗ (C ) =
κ dm (C ) ⎛ ⎜1 − 2F 2 ⎝
1−
2P ∗ (C ) CF 2 ⎞ ⎟, R 0 T κ dm (C )π± ⎠
(4)
2P ∗ (C ) CF 2 ⎞ ⎟, R 0 T κ dm (C )π± ⎠
(5)
– electrical conductivity of the membrane measured at direct Here, current; P* – the differential coefficient of diffusion permeability; F – the Faraday number; R0 – universal gas constant; π ± – correction factor that accounts for the non-ideality of the electrolyte solution. The differential coefficient (P*) of diffusion permeability was calculated from the experimentally obtained concentration dependences of the diffusion flux to estimate selectivity of the modified membranes (2), (3) and (4) using also data on the electrical conductivity of the samples in NaCl solutions of the same concentration. To calculate the differential coefficient of diffusion permeability we used the link equation [28]:
κ dm
P ∗ = βPm,
P*·1012, m2/s
κ dm , S/m
L+ ·1012
L-·1014
t+∗ (C )
3
1.58
0.13
4
1.60
0.13
0.1 0.5 0.1 0.5
5.7 17.4 2.8 7.7
0.70 0.82 0.64 0.79
75.2 86.4 68.5 84.1
13.3 208.4 6.5 91.2
0.998 0.976 0.999 0.989
(7)
where t+ is the transfer number of counterions in the solution; f2 - is the volume fraction of the solution inside the membrane in the framework of the two-phase model of conductivity for inhomogeneous ion-exchange membrane [14]. The experimental values of the electrical conductivity of membranes (3) and (4) modified with palladium and platinum nanoparticles in the range of NaCl solution concentrations from 0.01 M to 0.5 M are shown in Fig. 3. The values of κ dm calculated for the same membranes at concentrations of 0.1 M and 0.5 M NaCl solution are presented in Table 5. As seen from Fig. 3 and Table 5, the electrical conductivity at the direct current is 10–15% lower than at the alternating current. The volume fraction (parameter f2) of electrolyte solution in the membranes was calculated as an angular slope of the specific electrical conductivity dependence of the membranes on the electrical conductivity of solution in bilogarithmic coordinates [14]. The obtained values of parameter f2 are presented in Table 5. Electrodiffusion coefficients L+ and L- were calculated based on formulas (4)–(5). The values of L+ and L- as well as transfer numbers t+∗ (C ) of counter-ions through the membranes, calculated on their basis, are presented in Table 5. Analyzing the results obtained, we conclude that the addition of metal-ceramic hybrid halloysite nanotubes allows to preserve the membrane selectivity. In order to assess the use efficacy of ion-exchange membranes under external electric field, the current-voltage curves (CVC) of the electromembrane system (EMS) must be known. Membranes prepared by casting method possess the different roughness of air-contacted and glass-contacted sides. It is easy to see that air-contacted membrane side is brighter, i.e. rougher, in accordance with the height scale shown on the right edge of Fig. 7. This phenomenon is due to the solvent evaporation from the air-contacted membrane side, creating the inhomogeneities on it. As a result, the glass-contacted side was more uniform than the air-contacted side for all samples. Since the heterogeneity of the membrane surface has a significant effect on their polarization behavior, the CVC were registered for each sample for different orientation of the membrane in the measuring cell. Parameters of CVC are shown in Table 6. The resulting polarization curves are shown in Fig. 8 (arrows point out the side of membrane which is oriented towards the cation flux). In case of pristine membrane (1) the earlier transition to the overlimiting state is observed when the rougher membrane surface (“air”) is oriented toward the flux of counterions. The difference in the plateau lengths is about 0.2 V (see Fig. 8 and Table 6). More pronounced difference for sample (1) is observed in the slope of the plateau of the limiting current: the tgplateau value is 19% greater in case of inhomogeneous surface (“air”) than in case of smooth surface
and are the electrodiffusion coefficients of the Where counter- and co-ions, which are calculated from concentration dependences of electrical conductivity and diffusion permeability of these membranes, according to the following formulas [26]:
κ dm (C ) ⎛ ⎜1 + 2F 2 ⎝
C, M
f
L−∗ (C )
L+∗ (C ) =
f2
κ dm = κ m⋅t+2
smaller volume of macropores (Vmacro) than the MF-4SC membranes cast from the IPA polymer solution. It is important to consider possible application these materials as a solid polymer polyelectrolyte in lowtemperature air-hydrogen fuel cells because of the lower probability of a hydrogen crossover. Table 4 shows that the fraction of selective micro- and mesopores (Vmicro/V0) in the MF-4SC membranes casted from the DMF polymer solution is higher than in the MF-4SC membranes cast from the IPA polymer solution. This allows predicting the application prospects of hybrid membranes based on MF-4SC membrane cast from the DMF polymer solution in electromembrane processes. To confirm last assumption the selectivity of two membranes modified by palladium (3) and platinum (4) nanoparticles was evaluated based on the data of their electrical conductivity and diffusion permeability. The calculation of the transfer numbers of counter-ions t+∗ (C ) in the membranes was carried out according to the formula:
L+∗ (C ) , L+∗ (C ) + L−∗ (C )
β
diffusion flux in bilogarithmic coordinates. The values of coefficient β found from the experimental data are presented in Table 5; the concentration dependences of the differential diffusion permeability coefficient of the membranes in the NaCl solution are shown in Fig. 6. To calculate the electrical conductivity κ dm at the direct current the experimental data of appropriate conductivity κ m obtained on the alternating current were used in accordance with the formula:
Fig. 6. Dependences of the differential coefficient of diffusion permeability on concentration of NaCl solution. The curve numbers correspond to the membrane numbers in Table 1.
t+∗ (C ) =
Membrane
(6)
where β is the angular slope of the concentration dependence of the 178
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Fig. 8. Current-voltage characteristics of membranes (1) – (a), and (2) – (b) in 0.05 M NaCl solution. Arrows indicate the membrane side where the limiting state occurred.
[29,34], 10% distortion of the flat membrane surface results in 30% increase of the overlimiting mass transfer. It is known that hydrophilic-hydrophobic properties of the membrane surface influence the CVC parameters. In Ref. [31] it was shown that in case of samples whose surfaces did not differ in roughness but had different surface energies, the length of the plateau varied by 0.2 ± 0.3 V, depending on the orientation of the membrane to the flux of counterions. Herewith the plateau of the limiting current is shorter for hydrophobic membrane surface [29,34,35]. According to these observations, the comparison of the contact angles of wetting for both surfaces (“glass” and “air”) of the membranes under investigation was carried out. The results are shown in Fig. 9. As can be seen from Fig. 9, the rough side membrane faced to air is more hydrophobic and, therefore, its plateau of the limiting current is shorter (Table 6). Inhomogeneous surface and larger contact angle lead to the shortening of the plateau of the limiting current. Thus, in case of pristine membrane (1) the membrane system transfers to the overlimiting state earlier when the more heterogeneous and hydrophobic side of the membrane faces the counterion flux. Introduction of halloysite nanotubes into membrane (1) reduces the hydrophobicity of the sample. The similar effect was previously observed in Ref. [34] when the Nafion solution was modified by carbon nanotubes. Electrochemical behavior of membrane (2) modified by
Fig. 7. AFM images of the surface of the base membrane (1): air-contacted side (a), glass-contacted side (b). Table 6 Parameters of CVC of membranes (1) and (2). CVC parameters
tgOhmic (1/R), S/m2 ilim, A/m2 Δ, V tgplateau (1/R), S/m2
Membrane (1)
Membrane (2)
air
glass
air
glass
374.2 ± 0.2 40.8 ± 0.6 1.10 ± 0.05 5.6
356.3 ± 0.1 40.7 ± 0.6 1.50 ± 0.05 3.4
329.8 ± 0.1 40.4 ± 0.6 1.60 ± 0.05 2.7
337.7 ± 0.1 39.3 ± 0.6 1.40 ± 0.05 3.0
of the sample (“glass”). The results obtained for pure (pristine) membrane (1) are consistent with the literature data [29–33]. Particularly, in work [32] it was shown that the membrane surface influences the slope and length of the limiting current plateau, as well as the behavior of the membrane in the overlimiting state. The earlier onset of the overlimiting state in case of relief membrane can be explained by the fact that profiling of the membrane surface contributes to a more intensive motion of the liquid because of partial destruction of the diffusion layer. According to Refs. 179
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modification of the membrane using HNT, the membrane thickness, the diffusion layer thickness and the ions transport numbers in the solution also remain constant. Substituting the values D, C, h, δ and P* into Eq. (8), the contribution of the second term to the value of the limiting current density can be found. In case of the modified membrane the ratio of two terms in Eq. (8) is equal to:
DFC P ∗FC = 500: 1 : (t¯i − ti ) δ (t¯i − ti ) l
(9)
Last expression means that the contribution of the second term is only 0.2%. For comparison, in case of the pristine membrane, whose diffusion permeability is twice lower, this value is 0.1%. The experimental error and the error of graphical estimation of the ilim value are much higher (Table 6). Thus, the theoretical calculation explains the identical values of the limiting current densities obtained in the experiments for modified and unmodified membranes, despite the differences in their diffusion permeability. 4. Conclusion The composite membranes modified with hybrid Pt/Pd-halloysite nanotubes were prepared by casting method from sulfopolymer solution in isopropanol or dimethylformamide. A comparative study of diffusion permeability and water transport numbers for membranes modified by HNT@Pt and HNT@Pd is carried out. The effect of the polymer solvent on diffusion and electroosmotic permeability is revealed in comparison with membranes modified by HNT@Pt and HNT@Pd. It is found that the water transport numbers of the hybrid membranes obtained from isopropanol polymer solution are higher by 30% in dilute electrolytes as compared to the membranes obtained from dimethylformamide polymer solution. This correlates with the structural characteristics of membranes measured by the standard contact porosimetry. It is better to cast the composites from the dimethylformamide for lower diffusion and electroosmotic permeability of the resulted membranes in order to use them in fuel cells. The electrical conductivity of membranes containing clay nanotubes modified with platinum and palladium particles was determined in NaCl solutions. The volume fraction of the solution in the swollen membrane was calculated based on the concentration dependence of the conductivity in the framework of the two-phase model of a membrane. It is shown that introducing 4 wt% of the Pd, Pt modified nanotubes does not affect the structural heterogeneity of the composite membranes. The differential coefficient of diffusion permeability and electrical conductivity under direct current were calculated and applied to estimate the modified membranes selectivity. The introduction of halloysite nanotubes modified by Pt and Pd nanoparticles into perfluorinated membranes aids in preservation of the membrane selectivity. It is found the behavior of the current-voltage curves depends on the surface irregularity correlated with the conditions of solvent evaporation during the membrane formation, as well as the hydrophobic-hydrophilic properties of the membrane surface. It was shown also that addition of 4 wt% of halloysite nanotubes does not lead to a significant change of the limiting electrodiffusion current density as compared to the pristine sulfopolymer membrane. A preservation of high selectivity and constant value of the limiting electrodiffusion current density by introducing the Pt-halloysite nanotubes into the perfluorinated matrix makes hybrid MF-4SC membranes promising not only as a solid polyelectrolyte films in fuel cells and other electro-devices, but also as prospective separating diaphragms in electromembrane processes.
Fig. 9. Contact angles of membranes (1) – pristine sample and (2) – sample modified by pure halloysite for “glass” and “air” sides, using water (a) and monoethylene glycol (b).
HNT differs from that of unmodified membrane (1) (Fig. 8). Despite the circumstance that the values of contact angles (Fig. 9) and the heterogeneity of the surface obey the same law for membrane (2) as for pristine membrane (1), the parameters of their current-voltage characteristics change in the opposite directions. Thus, the overlimiting state for the membrane (2) occurs earlier for the side facing the glass than for the side facing the air during synthesis and evaporation of the solvent. The difference in the length of the limiting current plateau is 0.2 V. Since the HNT-modified MF-4SC membrane differs from the original membrane only by the presence of halloysite we may conclude that the deviation in the polarization behavior is caused by the influence of HNT, which contributes to earlier transition of the EMS to the overlimiting state. It can be assumed that halloysite nanotubes precipitating in the process of membrane synthesis under the action of gravity on the side facing the glass, thereby forming a surface enriched with HNT. As a result, regions with high and low conductivity are formed in the membrane. According to the model concepts [35] it contributes to the enhancement of electroconvection in the overlimiting current regimes, which causes the decrease of the transition electric potential of EMS to the overlimiting state. Interestingly, the limiting current value does not change after the membrane modification by HNT. To explain this, the theoretical estimate of the ilim value was completed using the Pierce-Gnusin equation, considering the actual values of the parameters:
ilim =
DFC P ∗FC + , (t¯i − ti )δ (t¯i − ti ) l
(8)
where D – diffusion coefficient of a salt molecule in a dilute solution; C – concentration of salt in the solution; δ – thickness of the diffusion layer; l – membrane thickness, t¯i and ti – the transport numbers of the ith counterion in the membrane and in the solution, respectively. The introduction of nanotubes changes only the differential diffusion permeability P∗ (Fig. 6) which is involved in the second term of Eq. (8). The selectivity of membranes found from porosimetric curves through the Vmicro/V0 parameter does not change (Table 3). Upon
Funding This work was supported by the Ministry of Science and Higher Education of the Russian Federation (Grant No. 14.Z50.31.0035). 180
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Acknowledgments [26]
The authors thank Anna Stavitskaya for synthesis of Pd/Pt - halloysite nanoparticles and Y. Darrat (Louisiana Tech) for the manuscript editing.
[27]
[28]
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.memsci.2019.03.084.
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List of main symbols Latin A: water binding energy, J/mol C: concentration of electrolyte, mol/l D, Dm: diffusion coefficients of a salt molecule in a dilute solution and inside a membrane, correspondingly, m2/s F: Faraday number f2: volume fraction of the solution inside the membrane l: membrane thickness, m ilim: density of the limiting diffusion current, A/m2 Jm: transmembrane flux, mol/m2 s kB: Boltzmann's constant L+∗, L−∗ : electrodiffusion coefficients of the counter- and co-ions Pm: integral coefficient of diffusion permeability, m2/s P*: differential coefficient of diffusion permeability, m2/s r: pore radius, nm S: specific internal surface membrane's area, m2/g T: absolute temperature t¯i, ti : transport numbers of the i-th counterion in the membrane and in the solution t+∗ : transport number of counter-ions tgOhmic: slope of the ohmic section of the current voltage curve tgplateau: slope of the plateau of the limiting current tw: water transport number, mol Н2О/F R0: gas constant V0: total volume of water in the membrane per gram of the dry sample, cm3/g Vmacro: volume of macropores having the pore radius > 50 nm, cm3/g Vmicro: volume of micro and mesopores having the pore radius ≤50 nm, cm3/g Vsw.m: volume of swollen membrane, cm3/g Δ: extent of the plateau of the limiting current, V W: electroosmotic permeability, m3/C
Greek β: the angular slope of the concentration dependence of the diffusion flux in bilogarithmic coordinates δ: thickness of the diffusion layer, m κ: membrane conductivity measured under alternating current, S/m κ dm : membrane conductivity measured under direct current, S/m γm: distribution coefficient of a salt molecule inside a membrane Φm: interaction potential of a pair of ions with the ion-exchange membrane matrix in kBT units ρ: volume charge density of a membrane, mol/dm3
Subscripts +: cation -: anion m: membrane
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