Water permeability of poly(ethylene terephthalate) track membranes modified by DC discharge plasma polymerization of dimethylaniline

Water permeability of poly(ethylene terephthalate) track membranes modified by DC discharge plasma polymerization of dimethylaniline

Journal of Membrane Science 263 (2005) 127–136 Water permeability of poly(ethylene terephthalate) track membranes modified by DC discharge plasma pol...

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Journal of Membrane Science 263 (2005) 127–136

Water permeability of poly(ethylene terephthalate) track membranes modified by DC discharge plasma polymerization of dimethylaniline Lyubov Kravets a,∗ , Serguei Dmitriev a , Alla Gilman b , Alexander Drachev b , Gheorghe Dinescu c a

Joint Institute for Nuclear Research, Flerov Laboratory of Nuclear Reactions, Joliot-Curie 6, 141980 Dubna, Moscow Region, Russia b Enikolopov Institute of Synthetic Polymeric Materials, Russian Academy of Sciences, 117393 Moscow, Russia c National Institute for Laser, Plasma and Radiation Physics, 77125 Magurele, Bucharest, Romania Received 28 July 2004; received in revised form 16 March 2005; accepted 6 April 2005 Available online 31 May 2005

Abstract Poly(ethylene terephthalate) track membranes were modified by plasma polymerization of dimethylaniline in a DC discharge. The influence of the plasma treatment conditions on the basic characteristics of the membranes (pore size, wettability, surface charge, water permeability) was studied. It is shown that the obtained membranes can reversibly change their permeability properties upon the pH of the solution or when a pressure is applied. © 2005 Elsevier B.V. All rights reserved. Keywords: Poly(ethylene terephthalate) track membrane; Plasma polymerization; N,N-dimethylaniline; Swelling; Conformational changes; Controlled permeability

1. Introduction Interest has been aroused recently in membranes with controllable transport properties, whose permeability can be regulated by changing environmental conditions such as temperature [1–4], electrical [5] and magnetic [6] fields, solvent composition [7], pH [3,4,8–10] and pressure [11]. These investigations are of major practical and scientific importance, as they allow not only to gain a wide spectrum of membranes with unique properties, but also to discover synthesis opportunities for membranes that imitate the biological ones. One of the directions in this research is the preparation of hydrogel membranes [3–7,9,10] by traditional methods of polymerization or copolymerization. Such membranes represent a cross-linked polymer, whose permeability varies reversibly when changing the swelling of the matrix material; the degree of swelling leads to conformational transitions of the macromolecules that depends on the nature of the cross-linked poly∗

Corresponding author. Tel.: +7 9621 62448; fax: +7 9621 28933. E-mail address: [email protected] (L. Kravets).

0376-7388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2005.04.012

mer and its structure (quantity of cross-links and distance between them). A disadvantage of the hydrogel membranes is that the size distribution of their pores is large. Another direction in this field consists in the modification of the commercially produced membranes; it allows the regulation of the pore diameters in the modification process. In order to create membranes with controllable transport properties, one can use the ability of the macromolecules at the surface layer to make reversible conformational transitions. The research in this direction is related to a goal-directed formation of a membrane surface with tailored chemical structure. For this purpose, various methods are employed: chemical [1] or radiation-induced graft polymerization of monomers [2], preliminary activation of the surface by plasma with a subsequent grafting of polymers from the solution [8], etc. With the same goal, membranes are successfully modified by deposition on the surface of thin polymeric layers obtained by plasma polymerization [11]. The use of plasma provides a number of essential advantages such as: the control of the thickness of the polymeric layer deposited on the membrane surface, the high adhesion of the layer, the short treatment

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time and the opportunity of using of a wide list of organic and element-organic compounds for modification. Thus, the surface properties of the formed membranes appreciably depend on the type of discharge and nature of the chemical compound used for modification [12]. The most suitable for producing membranes with adjustable properties are the track membranes (TM). They are obtained by irradiation of polymeric films with a beam of high energy heavy ions, followed by a subsequent chemical etching of tracks of these particles. The peculiarity of the track membranes is the narrow distribution of the pore size. In this paper we study the surface properties and water permeability of composite membranes consisting of a porous substrate—a poly(ethylene terephthalate) track membrane and a polymeric layer deposited by plasma polymerization of dimethylaniline vapors. Dimethylaniline was chosen as a monomer, since nitrogen-containing polymers are known to be capable of forming cationic units in an acidic medium. To deposit a polymer, we selected a direct-current discharge, since the preliminary research showed that the highest concentration of functional groups playing a defining role in the process of mass transfer is reached in this case. The properties of a composite track membrane with the plasma polymerized dimethylaniline layer and than doped by iodine also were investigated. It is also known that iodine has a high electron affinity and doping with iodine increases the concentration of positively charged units in a polymeric layer.

2. Experimental 2.1. Materials The object of the investigation were poly(ethylene terephthalate) track membranes (PET TM) with the thickness of 10.0 ␮m and an effective pore diameter of 0.215 ␮m (pore density was 2 × 108 cm−2 ). In order to produce the membranes, PET films were irradiated with krypton positive ions, accelerated at ∼3 MeV/nucleon in the cyclotron U-400 (at Flerov Laboratory of Nuclear Reactions), and then subjected to physicochemical treatment on a standard procedure [13]. The pores of these membranes are cylindrical channels, crosssections of which practically independent of the depth. As precursor for modification of membranes by plasma polymerization, N,N-dimethylaniline (Fisher Scientific Co, USA) with Tboil = 193 ◦ C was used, without additional purification. 2.2. Plasma polymerization procedure Deposition of the plasma polymer from N,N-dimethylaniline (DMA) on the membrane surface was performed in DC glow discharge by using the set-up schematically presented in Fig. 1. Membrane samples (2) of size 100 mm × 100 mm were placed on the anode in the reaction chamber (1) provided with horizontal plan-parallel electrodes

Fig. 1. The scheme of the set-up used for plasma polymerization: (1) vacuum chamber; (2) a sample of a track membrane; (3) electrodes; (4) fore vacuum pump; (5) piezoelectric leak-in; (6) gas admission system; (7) ampoule with liquid monomer; (8) pressure measuring system; (9) DC power supply.

(3) of 160 mm diameter each. The chamber was evacuated by means of a forvacuum pump (4) until the residual pressure of 0.26 Pa, measured by a vacuumeter (8), was reached. Then, through a gas admission system (5) DMA (7) vapors were released, from the ampoule (6) and the DC discharge was switched on from the DC power source (9). The polymerization was carried out at a pressure of DMA vapors of 26.6 Pa and with the discharge current density 0.1 mA/cm2 for duration of 20–180 s. Only one side of the membranes was subjected to the plasma treatment. Introduction of iodine in the membrane samples after plasma modification was made by their endurance for 30 min in a desiccator in presence of saturated iodine vapors at 20 ◦ C. 2.3. Test methods The characteristics of the initial and plasma-modified membranes were determined through a series of complementary procedures. The change of the membrane thickness was measured with an electronic counter of thickness ‘Tesa Unit’ (Austria), the precision of the measuring being ±0.1 ␮m. The gas flow rate through the membranes—a flow of gas (air) passing the membrane with a square 1 cm2 in was defined at a pressure drop of 104 Pa. Gas consumption was measured by float-type flow meter. On the basis of the values obtained according to these experiments was determined the gas-dynamical pore diameter (an effective pore diameter). For calculation we used the Hagen–Poiseuille equation as

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described in [14]. The error of measurements at definition of effective pore diameter was not more 3%. The study of the samples microstructure as well as the definition of the pore diameter on the membrane surface was conducted by SEM using the JSM-840 (JEOL) with the resolution of 10 nm. Before scanning, a thin layer of gold was deposited by thermal evaporation of metal in vacuum. The contact angle (as sessile drop method) was determined with a horizontal microscope equipped with a goniometer. Water (doubly distilled) was used as a test liquid. Six measurements were made at different places on the membrane surface and averaged, the measurement accuracy was ±1◦ . Permeability experiments for water solutions with various pH values were carried out with the help of the standard filtration installation FMO-2 (Russia) on membrane samples with the area of 254 mm2 . Before filtration, the membranes were maintained in a relevant solution during 20 min. Then prepared membranes were mounted on a cell and placed below a water reservoir. Water was allowed to flow through the membranes under air atmosphere. The pH of the permeating solutions was adjusted by adding diluted hydrochloric acid. All solutions for permeability experiments had been preliminary filtered off through a PET track membrane with a pore diameter of 0.05 ␮m. The rate of water flow was determined by measuring the volume of water solution that was able to pass through the membrane per minute. Prior to each measurement, the membranes were equilibrated with the test solution under pressure until a stable flux was achieved with the difference between two subsequent readings of less than 5%. The structure of the DMA polymer, deposited on the anode, was studied by ESCA and FTIR-spectroscopy. The ESCA spectra were recorded with the spectrometer Riber SIA-100 with MAC-2 analyzer (MgK␣, 100 W, 15 kV, 20 mA). The position of peaks (the binding energy values) was calibrated against the C1s standard peak (284.6 eV). FTIR-spectra were recorded with a Bruker Equinox 50S spectrometer in the range of 400–4000 cm−1 , working with 500fold accumulation of data and a scanning step of 2 cm−1 . The absorption bands were referenced according to [15]. The spectra of the liquid DMA were obtain by using a thin dish, transparent in the IR range. In order to record the IRspectra of the DMA polymer obtained by plasma, the polymer was deposited on a thallium bromiodide plate (KRS-5) of 10 mm × 15 mm size that was placed close to the track membrane located on the anode. The measure of the electric charge of the membranes was conducted by a dynamic capacitor method [16]. For this purpose, the membrane placed between two plate electrodes, one of which was a vibrating electrode and the other was a stationary electrode. The stationary electrode is grounded. The vibrating electrode is located over the membrane surface, and is oscillated in the direction of an electric field produced by this surface. As a result, electric current appears in the external circuit. Then on the vibrating electrode from an external power source is applied a compensating potential just equal to potential on a membrane. In this case the current in

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the external circuit is equal to zero. At this moment make measurement of potential of the stationary electrode which is precisely equal to potential of a sample, and then calculate its charge. The charge of a vibrating electrode in this case is equal to zero.

3. Results and discussion 3.1. Plasma deposition of polymer on the membrane surface Results regarding the modification of the relative mass, thickness and pore diameter of the track membranes deposited by plasma polymerization of DMA (PPDMA) are presented in Table 1. An increase of the mass of the samples with the treatment time was observed. This increase is connected with the deposition of the polymeric layer on the surface. From Table 1 is observed that the thickness of the membrane increases as well, while the effective pore diameter decreases. These testify that the deposition of the polymer takes place both on the surface of the membrane and on the walls of its pores. The added area of pores of the explored TM constitutes ∼85% of the total surface of the membrane, while the relative change of the thickness of the plasma treated membrane is more than the relative decrease of the pore diameter. It indicates that the deposition of the polymer on the membrane surface prevails a little on its formation in pores. In addition, the PPDMA deposition in pores under plasma treatment of the membranes is confirmed by the following experiment. A sample of a membrane is placed on a metal plate and pressed strongly on its surface with the help of a mask. Thus, one side of the membrane placed on the anode was exposed to the gas-discharge space (treated side), and the other one was unexposed (untreated side). According to the ESCA data, nitrogen atoms were detected both on the treated and untreated sides of the membrane (Table 2). This is the proof that the deposition of the polymer under membrane plasma treatment takes place in the volume of pores, plasma species reaching the unexposed side of the sample. Table 1 Relative increase of mass and thickness and relative decrease of the effective pore diameter of PET TM upon plasma treatment time t (s)

m/m (%)

L/L (%)

|d/d| (%)

20 60 180

9.5 11.5 13.5

5 6 7

4 5 7

Table 2 Relative contents of nitrogen and iodine atoms on the treated and untreated sides of the PET TM surface with a PPDMA layer after endurance in iodine vapors Membrane side

N/C (%)

J/C (%)

Treated Untreated

13 12

0.013 0.006

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Fig. 2. SEM photographs of initial PET TM (a) and PET TM treated by plasma during 180 s (b).

The interpretation of the data mentioned above is related to the procedure of producing track membranes that comprises irradiation of a PET film by heavy ions accelerated on a cyclotron. It is known that, when irradiating a polymeric dielectric by charged particles with energy of several MeV, formation of an important electrical charge in its volume is observed [17]. This charging is due to the energy released by the ions which, when passing the polymer volume alongside with the destruction of chemical bonds, cause the ionization of the macromolecules. The chemical treatment of the area of latent tracks of ions results in formation of charged pores. The investigation performed by the dynamic capacitor method has shown that the initial PET TM has an excess positive charge, of about 30 nC/cm2 . Taking into account that the number of pores on the surface unit in the explored membrane is n = 2 × 108 cm−2 , the average charge per pore is approximately 1.5 × 10−16 C. The pores have cylindrical form with diameter d = 0.215 ␮m and the length L = 10 ␮m (membrane thickness). Assuming that the charge is distributed on the wall surface of the pore, the average charge density in such a pore is equal qs = 2.2 nC/cm2 . The intensity of the electric field established by such a charged cylinder at the distance of r = 1 ␮m, compatible with the average distance between the proximate pores (0.7 ␮m), will be 200 V/cm. Under plasma treatment the membrane samples were placed on the anode. In the DC discharge negatively charged particles are drifted to the anode. Together with electrons, negative DMA ions serve as negatively charged particles, too. Therefore, the electrostatic attraction between the negative DMA ions and the positive charged pores leads to the deposition of the polymer inside the membrane pores.

mass, there is a complete concealment of the initial surface by a layer of the deposited polymer. Moreover, SEM observations indicate the absence of erosion of the membrane surface under plasma treatment (Fig. 2); so, the increase of wettability can be related to the process of formation of additional hydrophylic groups on the surface. The analysis of the ESCA spectrum of the polymer obtained by DMA plasma (Fig. 3) testifies to the presence of carbon (284.6 eV) and nitrogen (399.2 eV) atoms and a small content of oxygen (532.2 eV). The ratio of nitrogen to carbon atoms in the polymer and the initial DMA is practically the same (Table 3). This makes possible to believe that the structural unit in the polymer is identical with that of the initial DMA. A small amount of oxygen in PPDMA can be explained by presence of residual oxygen in the plasma-forming gas and also by subsequent oxidizing of PPDMA after plasma treatment on air that is characteristic for polymers synthesized by plasma polymerization [18]. Comparison of the FTIR spectra (Fig. 4) of initial DMA (1) and PPDMA (2) supports these conclusions. For the polymer synthesized by plasma, the absorption bands connected with an aromatic ring are completely preserved: planar deformation oscillations of a skeleton at 1601, 1504 and

3.2. Surface properties and structure of polymer synthesized by plasma The study of the TM surface properties shows that after DMA plasma treatment the wettability of the surface increases. So, if the initial membrane is characterized by a value of the water contact angle (θ) equal to 65◦ , then for the modified membranes the θ value, irrespective of the discharge treatment time, will be not more than 45◦ . It means that in all cases, independent of the relative increase of the membrane

Fig. 3. ESCA spectrum of PPDMA. Table 3 Relative contents of atoms in DMA and PPDMA Sample

N/C (%)

O/C (%)

DMA (calculation) PPDMA (ESCA)

12.5 12.3

0 2

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3.3. Water permeability of the membrane modified by plasma of DMA

Fig. 4. FTIR-spectrum of DMA (1), PPDMA (2) and PPDMA doped by iodine (3).

1452 cm−1 and out-of-plane deformation oscillations of CHgroups of an aromatic ring with five unsubstituted atoms of hydrogen at 750 and 696 cm−1 . The absorption bands at 1373, 1348 and 1323 cm−1 are related to stretching vibrations of CN-group in tertiary amines. The basic changes in the PPDMA spectrum are connected to high-frequency area. The stretching vibrations of CH3 -groups (2985, 2940, 2877, 2846 and 2804 cm−1 ) are characteristic for DMA, whereas in IR-spectrum of the polymer there are the absorption bands at 2950, 2928 and 2870 cm−1 , relating to stretching vibrations of CH2 -groups. The absorption connected to the stretching vibrations of CH-groups (3080, 3055 and 3024 cm−1 ) is completely maintained. It should be noted that in the IR-spectrum of PPDMA no absorption bands characteristic for oxygencontaining groups have been observed. Apparently, it is connected to their presence only on the surface of the polymer film. Based on the investigation of the structure of the polymer synthesized by plasma, one can assume that the polymeric chains grow on the membrane surface on the expense of the anion-radicals created by the break-off of a proton from the DMA methyl groups (Fig. 5a) under activity of charged particles and the vacuum UV radiation generated by the discharge. A characteristic fragment of the formed polymeric chain is presented in Fig. 5b.

Fig. 5. Chemical structures: (a) DMA; (b) PPDMA, (c) PPDMA doped by iodine.

Previously it has been shown that the treatment of PET TM by air plasma results in changing of hydrodynamic properties of the membrane: the water permeability of the modified membranes strongly depends on the pH of the filtrated solution [19]. This dependence is connected with the presence of a modified layer with high content of carboxyl groups on the membrane surface. Referred to that, a study of the water permeability of membranes having other functional groups on the surface, in particular functional groups containing nitrogen is of special interest. It is known that in the case of viscous flow of filtrates through membranes with a hard structure (when the pore diameter is much larger than the size of water molecules) the increase of pressure results in a linear growth of the water flow rate [20]. The dependence of the water flow rate (Jw ) on the applied pressure (P), for initial PET TM membranes in acidic media (pH 1.2) showed a similar character (Fig. 6, curve 1). In addition, in the case of initial membranes in acidic medium the flow rate per unit surface differs from the calculated values. This is connected with the presence of negative charges, which are formed on the membrane surface by the ionization of the surface carboxylic groups [19]. For the membranes modified by DMA plasma, in acidic filtrate (pH 1.2), the dependence of water permeability upon pressure is not linear (Fig. 6, curves 2 and 3). Apparently, this effect is caused by a decreased diameter of the membrane pores that is explained by a change of the conformation state of PPDMA macromolecules. At low pH values, the monomer units of the macromolecules in the plasma deposited polymer layer gain a positive charge due to protonation of the nitrogen atoms. That results in its swelling—formation of gel [21] and causing a membrane pore contraction. The PPDMA macromolecules in this case represent a loose ‘glomus’. Such a conformational

Fig. 6. Dependence of water flow rate (Jw ) on the applied pressure (P) in the case of a solution with pH 1.2, for initial PET TM with a pore diameter of 0.215 ␮m (1), PET TM treated by plasma during 20 s (2), PET TM treated by plasma during 60 s (3), and PET TM treated by plasma during 60 s and doped by iodine (4). The dashed line corresponds to the calculated values of flow for initial PET TM.

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state of macromolecules resulting from the electrostatic interaction of charged monomer units with water molecules is stable. Increase of pressure up to 1.5 × 105 Pa for a membrane with the relative growth of mass of 11.5% does not change its water permeability (Fig. 6, curve 3). It should be noted that the value of pores contraction depends essentially on the relative increase of the mass of the sample. Thus, for a membrane with m/m = 9.5% a smaller deviation from a linear dependence of the flow rate on the applied pressure is observed (Fig. 6, curve 2). It is caused, apparently, by the decrease of the thickness of the plasma deposited PPDMA layer. The linear dependence of the flow rate on applied pressure for the initial membrane suggests that the swelling degree of the hard polymeric matrix is not significant in comparison with the plasma deposited polymer. Increase of the filtrate pH (the drop of H+ ion concentration in the solution) changes essentially the character of the dependence Jw upon P, for the initial membrane (Fig. 7, curve 1). At pH 4.6 the dissociation of carboxylic groups increases—pKCOOH (a negative decimal logarithm of the dissociation constant) in PET TM constitutes 3.6–3.7 [19]. This leads to the formation of a negative charge on PET TM macromolecules that causes, as result of the electrostatic repulsion, the change of their conformational state. The nonlinear character of the dependence points out at the decrease of the pores diameter of the membrane. For the modified PPDMA membrane (Fig. 7, curve 2) the increase of water permeability is related to the decrease of proton concentration in the filtrate. The content of positively charged atoms of nitrogen in PPDMA is lower in the medium with higher pH, therefore the electrostatic interaction gets weaker. With decreasing Coulomb’s interaction, the non-electrostatic interaction of hydrophobic groups [21], in this case that of non-polar CH2 -groups, increases. That results in the collapse in a gel: transition of macromolecules in a compact conformation state of a ‘globule’. This state does not cause appreciable decrease of the pores diameter, and consequently one can observe a viscous flow regime—the

Fig. 7. Dependence of water flow rate (Jw ) on the applied pressure (P) in the case of a solution with pH 4.6, for initial PET TM with a pore diameter of 0.215 ␮m (1), PET TM treated by plasma during 60 s (2), and PET TM treated by plasma during 60 s and doped by iodine (3).

dependence of the water permeability on the applied pressure has practically a linear character (Fig. 7, curve 2). It is interesting to mark that despite a lower effective diameter, the values of the flow for the modified membrane are higher than for the initial PET TM. It is related, probably, to the changing of the structure and chemical composition of the surface layer of the membrane. 3.4. Doping of plasma synthesized polymer by iodine The treatment of the membranes modified by DMA plasma, in iodine vapors leads to diffusion of the latter into the surface layers of membranes and into the pore volume. ESCA data allowed us to reveal the content of iodine also on the membrane’s side not treated by plasma (Table 2). The presence of iodine in the modified membranes is corroborated by FTIR-spectroscopy. After introduction of I2 molecules in PPDMA in concentration ∼2 × 1018 cm−3 (calculated using ESCA data), the basic absorption bands in the IR-spectrum are conserved (Fig. 4, curve 3). At the same time, changes in the ratio of planar oscillations bands of the aromatic ring skeleton (1601, 1504 and 1452 cm−1 ) are observed. They are related probably to conformation changes in macromolecules of the polymer synthesized by plasma caused by iodine presence. It is known that the introduction in polyaniline of iodine molecules possessing a high electron attachment results in the transfer of an electron from the tertiary nitrogen atom of the macromolecule to iodine. This leads to the formation of a cation radical containing a localized hole and a negatively charged contrion (A− ) [22] containing iodine polyions of various types as J3 − , J5 − , etc. [23]. The process is confirmed by the presence in the PPDMA ESCA spectrum of a shift of the N1s peak to higher binding energy values (410 eV). A similar situation occurs in our case after the doping of PPDMA by iodine (Fig. 5c). The introduction of iodine in PET TM deposited with a PPDMA layer causes the transfer of an electron from nitrogen atoms onto iodine molecules and formation of ion pairs: positively charged monomeric segments and contrions (A− ). This is reflected in the hydrodynamic characteristics of the membrane. From Fig. 6 (the curve 4) it is seen that in an aqueous medium with pH 1.2 such a membrane is not permeable up to the pressure of 2.8 × 104 Pa. This is explained by the complete pore contraction caused by an essential swelling of the plasma polymer and formation of a gel, which closes completely the pores. The iodine contrions A− that create an interior osmotic pressure are responsible for spreading the gel [21]. Apparently, in acidic medium, the PPDMA layer containing iodine in concentration of ∼2 × 1018 cm−3 is a polyelectrolyte gel behaving like a uniform three-dimensional network swelled in water, formed as result of the cooperation of macromolecules bound by covalent bonds. Alongside with the positively charged monomeric segments, the obtained polyelectrolyte gel contains iodine contrions, which remain inside the gel during the swelling. The membrane pores ‘are closed’ in this state. The

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Fig. 8. SEM photographs of PET TM with m/m = 11.5% and doped by iodine after swelling in solution with pH 1.2 during 60 min (a) and then drying on the air during 20 min (b).

complete pore contraction caused by an essential swelling of the plasma deposited polymer and the formation of gel, which closes completely the pores can observe by scanning electronic microscope. In Fig. 8 are presented SEM photographs of PET TM with m/m = 11.5% and doped by iodine after swelling in solution with pH 1.2 during 60 min (a) and then drying on the air during 20 min (b). The increase of pressure to values larger than 2.8 × 104 Pa causes a collapse of the gel, and the membrane pores transition to an ‘open’ state. The membrane in such a state is characterized by high values of the water permeability. This phenomenon is also related to the conformational transition of PPDMA macromolecules from a loose ‘glomus’ to a compact ‘globule’, which is characteristic for polymers containing charged monomeric segments [24,25]. The pressure growth results in the decrease of the distance between the fragments of macromolecules that, in turn, change the balance of hydrophobic and electrostatic forces, the forces of intermolecular attraction becoming dominant. A similar effect can occur not only at the pressure and pH solution increase, but also at the change of the solution temperature or quality of the solvent. The behavior of the water permeability of TM deposited with a PPDMA layer and doped with iodine at pH 4.6 (Fig. 7, curve 3) shows that the dependence of the flow through the membrane upon the applied pressure is of viscous character, as in the case of the modified TM not containing iodine. Apparently, at the increase of the filtrate pH, the concentration of the holes localized on nitrogen atoms decreases, leading to a sharp weakening of the electrostatic interactions and the formation of the polyelectrolyte gel does not occur. Therefore, the macromolecules of the deposited polymer, having the compact conformation, do not interfere with the penetration of solution molecules into pores. The lower values of the flow for the modified membrane are explained by presence of iodine in a polymeric film leading to conformation changes. The concentration of polar fragments of the chain increases with the concentration of iodine. The interaction between polar fragments leads to orientation of the chain in such a manner that they appear inside the globule volume, while hydrophobic ones—on its surface. According to the conducted research, the track membrane with the PPDMA layer after

doping by iodine becomes hydrophobic—the value of the water contact angle on the surface is 80◦ . 3.5. Theoretical analysis Aiming to a more detailed investigation of the transport of the solutions through membranes we carried out a theoretical analysis. For sake of simplicity we assumed that the membranes under study consist of pores of cylindrical shape, with length L, every i-th of which having a diameter di . The average pore diameter is equal in this case to: n ¯d = i=1 di (1) n According to Hagen-Poiseuille equation [14] for a stationary flux of liquid in the channel of radius ri and length L, the volume of the liquid passing it due to pressure difference P in time t, is equal to: Vi =

π P 4 r t, 8η L i

(2)

where η is a dynamic viscosity of water. Then the water volume, passing through a unit area of the membrane containing n pores, is equal to: v=

n 

vi .

(3)

i=1

Substituting (2) into (3) one obtain: n π tP  4 V = di 128η L

(4)

i=1

or V =

π tP 4 nd . 128η L

(5)

The parameter d can be described by a normal distribution of probabilities, as its value is given by the sum of a large number of independent random variables, each of them have

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an identical density of probability:   ¯ 2 (d − d) 1 , exp − f (d) = √ 2σ 2 σ 2π

(6)

where σ 2 is the dispersion of the distribution. Then according to definition of an average value,    ∞ 2 1 (d − d) 4 4 d = √ dd. (7) d exp − 2σ 2 σ 2π −∞ By replacing variable d with x = d − d in (7), we get    ∞ 1 x2 4 4 d = √ (d + x) exp − 2 dx 2σ σ 2π −∞

(8)

   ∞ d4 x2 √ exp − 2 dx 2σ σ 2π −∞    ∞ 4d¯ 3 x2 + √ x exp − 2 dx 2σ σ 2π −∞ 

0

  x2 + √ x2 exp − 2 dx 2σ σ 2π −∞    ∞ 4d¯ x2 + √ x3 exp − 2 dx 2σ σ 2π −∞ 

6d¯ 2

1 + √ σ 2π





0

  x2 x4 exp − 2 dx 2σ −∞





(9)

The integrals in 2nd and 4th terms of the Eq. (9) are equal to zero, since the integrands are odd functions. The remaining integrals are tabulated:     ∞ √ x2   exp − 2 dx = σ 2π   2σ  −∞      ∞ √ x2 (10) x2 exp − 2 dx = σ 3 2π  2σ  −∞      ∞ √  x2   x4 exp − 2 dx = σ 5 2π 2σ −∞ From (9) and (10) it follows that: d 4 = d 4 + 6σ 2 d¯ 2 + 3σ 4 .

By definition, the water permeability of the membrane is equal to Jw =

nV . t

(13)

Substituting (12) into (13), the water permeability will be:

or d4 =

Substituting (11) into (5), one obtains the following expression for the water volume passing through the unit area of the membrane: π tn ¯ 4 (d + 6σ 2 d¯ 2 + 3σ 4 )P. (12) V = 128η L

(11)

Jw =

πn ¯ 4 (d + 6σ 2 d¯ 2 + 3σ 4 )P. 128ηL

(14)

The received equation represents a Hagen–Poiseuille equation for stationary flow of liquid through a narrow channel which takes into account the fact that both initial and modified membranes have pores the diameter of which differs from the average one, i.e. have a pore distribution in sizes. Thus, the quantity Jw depends upon the pressure difference P across the membrane and a number of the TM characteristics, such as thickness, pore density and size distribution. The σ value was calculated by the statistical processing of the diameters of pores measured by SEM, and the relation σ ≈ 0.1d¯ was obtained. By using this relation, the measured dependences Jw upon P, and the Eq. (14) the values of the average pore diameter of the membranes in solutions with different pH values were calculated for the samples under study (Table 4). As expected, the obtained data show a decrease of the pore diameters. This is related to conformation changes of the polymeric chains positioned on the pore surface at their interaction with water. As it has been noticed, the decrease in the d¯ values for the initial PET TM is connected with the presence of a negative charge on the membrane surface. For membranes modified by DMA plasma polymerization large changes of the pores diameters are observed in solutions with a low pH value. That was caused by formation of positive charges on the nitrogen atoms of PPDMA. The doping of the PPDMA layer by iodine results in an additional growth of the positive charge on the nitrogen atoms; thus a sharp increase of the volume of the polyelectrolyte layer is observed and a complete closing of pores occurs. At low values of the pressure drop across membrane (less than 2.8 × 104 Pa) the diameter of pores is zero. The pressure increase leads to a sharp collapse of the polyelectrolyte gel; it results in a practically complete opening of pores and the parameter d¯ varies from 0 up to 0.205 ␮m (Table 4).

Table 4 Estimated values of the average pore diameter d¯ of the membranes in solutions with various pH values pH

CH+ (cm−3 )

1.2 4.6

3.8 × 1019 1.5 × 1016

d¯ (␮m) Initial PET TM

PET TM with the PPDMA layer

PET TM with the PPDMA layer doped by iodine

0.185–0.165 0.145–0.115

0.120–0.095 0.155–0.125

0–0.205 0.140–0.110

CH+ : concentration of protons in solution.

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4. Conclusion The study of the properties of PET TM modified by DC discharge polymerization of dimethylaniline has shown that the treatment of membranes on the anode makes available the polymer deposition both on the surface and on the walls of the pores. The polymer obtained by DMA plasma is capable of swelling in water solutions, the degree of its swelling depending essentially on the pH value of the solution. This process is related to the formation of positive charge on the nitrogen atoms. The swelling of the PPDMA layer deposited on the pore surface causes the decrease of the pores diameters. For membranes with the PPDMA layer and solutions with pH 1.2, a partial contraction of pores is observed which results in decrease in the water permeability. At pH 4.6 the formation of the charge on the nitrogen atoms is less important, and the polymer swells in a significantly smaller degree. That causes an increase of the water permeability of the membrane. The introduction of iodine in the polymeric layer results in formation of a polyelectrolyte, whose swelling in an acidic medium causes a complete contraction of pores in a specific range of pressure. With increasing pressure, the collapse of gel is observed, due to ‘glomus’–‘globule’ transition, therefore the membrane permeability abruptly increases. The obtained results testify that the PET track membrane, modified by DMA DC discharge, is capable of a reversibly change of its water permeability depending on pH of the solution and the value of the applied pressure.

Acknowledgment The authors are grateful to M.V. Aristarkhova for her help in the preparation of the paper.

Nomenclature List of symbols C H+ concentration of protons d pore diameter d¯ average pore diameter Jw water flow rate L membrane thickness m membrane mass n pore density P pressure q charge density r pore radius t time v water volume, passing through an unit area V liquid volume

Greek letters  operator η dynamic viscosity of water ν frequency σ dispersion of distribution

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