Diffusion of water in nanoporous NF polyamide membrane

Chemical Physics Letters 478 (2009) 56–60

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Diffusion of water in nanoporous NF polyamide membrane V.K. Sharma a, P.S. Singh b, S. Gautam a, S. Mitra a, R. Mukhopadhyay a,* a b

Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India Central Salt and Marine Chemicals Research Institute (CSIR), Bhavnagar 364002, India

a r t i c l e

i n f o

Article history: Received 10 June 2009 In final form 13 July 2009 Available online 16 July 2009

a b s t r a c t Diffusion of water sorbed in a nanofiltration (NF) polyamide membrane as studied by quasielastic neutron scattering (QENS) is reported here. The trimesoyl chloride–piperazine based NF membrane was synthesized by interfacial polymerization technique and was characterized by positron annihilation lifetime spectroscopy (PALS) and SEM techniques. PALS data shows that the membrane has an average pore size 4.6 Å. QENS data from water sorbed NF membrane show that the diffusion in the sorbed water occurs through jump diffusion with the jump lengths distributed randomly. Translational diffusion coefficient obtained for water sorbed in the NF membrane is found to be smaller than that of bulk water. Ó 2009 Published by Elsevier B.V.

1. Introduction Diffusion of liquid in restricted geometries is determined by a combination of two factors: chemical effect (surface interaction) and physical effect (limitation by geometry). The interplay of these two effects depends on many factors such as size of confining medium, concentration of guest molecules, hydrophilic and hydrophobic nature of substrates and so forth. The modification in dynamics of liquids in confined geometry compared to its bulk state has attracted considerable interest in scientific research, not only for fundamental aspects but also for practical applications in many pertinent industrial problems, in petroleum industries, catalysis, water purification, building optical switches and so forth. An example of confined fluids is provided by water sorbed in polyamide membranes, which is used for removal of organic substance from natural and waste water [1], desalination of sea and brackish waters [2], treatment of industrial effluents [3] and so forth. These membranes are also used in catalysis; food and dairy industries, chemical processing industries, pulp and paper industries, textile dye effluent, landfill leach treatment, and so forth. An irregular interlinking of polymer chains in these membranes can give rise to polymer free void spaces – pores having a variety of structures – open, closed, circular, non-circular, and so forth. PALS is an excellent technique for measuring the pore size in reverse osmosis (RO) and nanofiltration (NF) membranes which is generally in order of angstroms [4–7]. We have earlier used PALS technique to find the pore size of RO membrane [7]. The technique of QENS has found a wide use in the study of dynamics of confined liquids for its ability to give spatial as well as temporal information on a wide range of time (1010–1013 s) and length (few angstroms) scales [7,8–14]. It is very well suited * Corresponding author. Fax: +91 22 25505151. E-mail address: [email protected] (R. Mukhopadhyay). 0009-2614/$ - see front matter Ó 2009 Published by Elsevier B.V. doi:10.1016/j.cplett.2009.07.045

to study the diffusion of hydrogenous material in confined geometries such as hydrocarbons adsorbed in zeolites [13], water confined in porous media [7,9–12], reverse micelles [14] and so forth. This technique provides quantitative as well as qualitative information about the dynamics of fluids. The quantitative information entails the information about the correlation time of motion, length scale, and activation energy while qualitative information pertains to the geometrical mechanism of the motion. Recently we have reported a QENS study of diffusivity of water in a trimesoyl chloride–m-phenylene diamine based reverse osmosis polyamide membrane (ROPM) [7]. We found that water diffusion occurs via jump diffusion with random distribution of jump lengths, and time spent by sorbed water molecules between two consecutive jumps is larger by a factor of two as compared to that of bulk water. In other words chemical effect (hydrophilic nature of ROPM) plays a key role in determining the dynamical behavior of sorbed water as also corroborated by differential scanning calorimetry (DSC) measurements. To understand the detailed mechanism of the diffusion of water in such membrane systems we have carried out QENS experiment on water confined in other membrane systems such as nanofiltration (NF) and so forth. Here we report diffusion of water confined in nanoporous NF polyamide membrane (trimesoyl chloride–piperazine based), as studied by QENS technique. Chemical structure of this membrane is shown in Fig. 1. The piperazine monomer used in the case of the porous NF has both cross-linking sites at linear positions (180°) forming a relatively linear polymer network, whereas the cross-linking sites of m-phenylenediamine monomer of the RO are at an angular position (120°). Surface microstructure of NF membrane was studied by scanning electron microscope (SEM) and compared with ROPM. SEM pictures indicate that NF membrane has relatively smoother surface microstructure (Fig. 2) compared to ROPM, which has rough surface showing hill–valley microstructure morphology [7].

V.K. Sharma et al. / Chemical Physics Letters 478 (2009) 56–60

O C N

O N

COOH

C C O

Linear structure

Crosslinked structure N N C

O

O

N C

C N

O

Fig. 1. Chemical structure of nanofiltration polyamide membrane.

2. Experimental The trimesoyl chloride–piperazine based NF polyamide was prepared by interfacial polymerization techniques [15]. A 2% (w/v) solution of piperazine (Aldrich) in water was contacted with n-hexane solution of 0.1% (w/v) trimesoyl chloride (Aldrich), which resulted in the formation of polyamide layer at the water–organic interface. SEM pictures of the samples were taken on LEO 1430VP scanning electron microscope with 5 kV accelerating voltage. For PALS measurement, 22Na positron source in the form of aqueous solution of NaCl folded in kapton foil was sandwiched between the layers of polymer film samples and kept in between two scintillation detectors. The positrons, having acquired kinetic energy from the 22Na radioisotope source, are injected into the sample. The energy of positron gradually decreases upon interacting with the counter-particle in the sample before it is completely annihilated. A substantial fraction of such thermalized positrons may form positronium at the bulk-pore interface having two different spin states, either anti-parallel; i.e., para-positronium (p-Ps), or parallel, known as ortho-positronium (o-Ps) that diffuse and localize in pores or regions of low electron density of the sample. Positron annihilation lifetime measurements were carried out using plastic scintillators coupled to fast–fast coincidence system with resolving time of 230 ps as measured with 60Co source in 22Na energy window settings. PATFIT program [16] was used for data analysis.

57

Quasielastic neutron scattering measurements were carried out using the QENS spectrometer at Dhruva reactor, Trombay [17]. The spectrometer is used in multi angle reflecting crystal (MARX) mode, which uses a combination of a large analyser crystal for energy analysis and a position sensitive detector for detecting the scattered neutrons. In the present configuration this instrument has an energy resolution of 200 leV with incident neutron energy of 5 meV as obtained from standard vanadium sample. The quasielastic data were recorded in the wave vector transfer (Q) range of 0.67 Å1–1.8 Å1 at 300 K. QENS measurements were performed on both dehydrated (bare) as well as water sorbed NF membrane. 3. Results and discussion Compared to the RO membrane, the NF membrane has relatively larger porosity that has molecular weight cut-off of 180– 200 Daltons as determined by aqueous solution of 500 ppm concentration of organic solutes such as glucose, sucrose, polyethylene glycol, etc. To measure pore size and porosity of NF membrane we have carried out PALS measurement, which is based on the principle of detecting c-rays, which are produced during the annihilation of positrons inside the porous material. In PALS, o-Ps or p-Ps formed by positron at bulk-pore interface in which p-Ps have a very short lifetime of 0.125 ns, as compared to o-Ps, which have a reasonably long lifetime of 142 ns in vacuum. In the presence of matter, ortho-positronium (o-Ps) can seek out an electron of opposite spin from the pore surface and annihilate through twophoton mode known as pick-off annihilation within the time range 1–10 ns. This component of positron lifetime has paramount importance, because it enables its use as nano-probe to study the micro structural properties of porous material. The released photons mostly come out from open spaces such as holes or voids. So by measuring Ps pick-off lifetime sp, one can find out the radius of hole R according to the semi empirical equation as given below introduced by Tao and Eldrup [18,19],

sp ¼

  1 1 R 1 2p R sin 1 þ 2 R þ DR 2p R þ DR

ð1Þ

where DR = 1.66 Å is the thickness of the homogeneous electron layer inside the wall of free-volume hole, which is considered to

Fig. 2. SEM micrograph of nanofiltration polyamide membrane.

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be an infinite spherical potential well of radius R0 (=R + DR). In the present case, pore size in the NF membrane is found to be 4.58 Å, which is close to the value obtained for similar polymers [20,21]. It was found that lifetime of o-Ps is slightly larger in NF membrane (1.45 ns) than RO membrane (1.38 ns) [7] and therefore, slightly larger pore size in NF membrane was observed. It is interesting to note that the intensity I, which is a measure of density of cavities is found to be larger in NF membrane (10.49%) compared to RO membrane (2.34%). Besides their porosity differences, RO and NF membranes have different electrical potentials as a result of different thickness of charged layers, which then have a direct relationship to membrane separation performances. While the RO membrane rejects (95–99%) all the electrolytes including monovalent ions, the rejection selectivity (90–99%) of the NF membrane towards the divalent and multivalent ions, and less rejection towards monovalent ions (<50%) is suited for separating mixture of ions containing monovalent and divalent/multivalent ions. Therefore NF membranes are suitably used for softening of hard water, separation of monovalent from divalent ions, treatment of dye containing wastewater, desalting of protein and amino acids [22]. Mechanism of self-diffusion of water molecules changes on filtration through a membrane as a result of a complicated process occurring in filtration [23]. So it is of interest to study the uptake of water and its diffusion in these membranes that can be conveniently studied using neutron scattering technique. In a neutron scattering experiment with a hydrogenous sample, the measured intensity is proportional to the double differential scattering cross section, which in turn is proportional to the incoherent scattering law S(Q, x). Here Q is the wavevector transfer and x is the angular frequency corresponding to the energy transfer,  hx ¼ Ef  Ei , Ei and Ef being the initial and final energies respectively of the neutrons. In general, this scattering law can be written as [8],

SðQ; xÞ ¼ AðQ ÞdðxÞ þ ½1  AðQ ÞLðC; xÞ

where the first term is the elastic part and the second is the quasielastic one. L(C, x) is a Lorentzian function with a half width at half maxima (HWHM) C. The variation of HWHM, C provides information about the time scale of the motion. It is convenient to analyse the data in terms of elastic incoherent structure factor (EISF), which is the fraction of the elastic intensity present in the total S(Q, x). Therefore, A(Q) in Eq. (2) is nothing but the EISF. Information about the geometry of the molecular motion can be directly obtained by analysing the behavior of EISF. In case of localized motion, e.g., rotational motion, this term is expected to have a non-zero value. It may be noted that in a QENS experiment the measured data is inherently convoluted with the resolution function of the instrument. To analyse the QENS data, it is customary to assume a theoretical scattering function (Eq. (2)), convolute with the instrumental resolution function and then obtain the dynamical parameters involved in the model scattering function by least squares fit to the experimental data. The quasielastic spectra were recorded in the wave vector transfer (Q) range of 0.67–1.8 Å1 at 300 K for both anhydrous (dry) as well as water sorbed NF membrane using QENS spectrometer [17] at Dhurva, Trombay. Significant quasielastic broadening was observed in case of water sorbed NF membrane whereas dry membrane did not show any broadening over the instrument resolution. Thus, this broadening observed in case of water sorbed NF membrane is related to the dynamical motion of water molecules inside the membrane. To analyse the data, first the contributions of the elastic and quasielastic components were estimated using Eq. (2). The spectra as obtained from dry/anhydrous membrane were used to estimate the elastic contribution from the membrane alone to the spectra. The parameters, A(Q) and C(Q) were obtained by least squares fit. The resulting fits are shown in Fig. 3. In the present case, the elastic intensity other than that from the anhydrous sample was found to be negligible and a single Lorentzian function was good enough to describe the quasielastic part,

ð2Þ

140 120

Q=1.58 Å

-1

100 80 60 40

300 250

Q=1.08 Å

20

-1

0 -1.0

200

-0.5

0.0

0.5

1.0

150 400 350

100

Q=0.8 Å

-1

50

S(Q,ω)(arb. units)

300 250

0 -1.0

200

-0.5

0.0

0.5

1.0

150 100 50 0 -1.0

-0.5

0.0

0.5

1.0

Energy Transfer (meV) Fig. 3. Fitted QENS spectra from the water sorbed nanofiltration membrane at some typical Q values. Instrument resolution is shown by dashed line in the middle panel.

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indicating that the observed dynamics correspond to the translational diffusion of the sorbed water molecules. The simplest model of translational motion is Brownian diffusion, which is described by Fick’s law, in which HWHM (C) of the quasielastic component (Lorentzian function) varies linearly with Q2, C(Q) = DQ2, where D is the self-diffusion coefficient of fluids. This occurs when the interactions between the particles are weak. In Brownian diffusion it is assumed that motion occurs via infinitely small, elementary jumps. When the intermolecular interactions are significant, the diffusion mechanism is affected by the environment of the particle under consideration. For example, in case of a periodic lattice, the particle is more likely to be found at some energy minima, which are regularly distributed throughout the crystal. Motion of the particle in such an environment is likely to occur as jumps between these energy minima. This gives rise to a jump diffusion in which the particle remains at a site for some time called the residence time, before jumping to another site instantly. The distance covered by the particle in a jump is called the jump length. This model of jump diffusion can then be classified depending upon the degree of order in the environment, which in turn determines the distribution of jump lengths. In case of a more disordered environment like the present one where water molecules are confined within a membrane, the jump lengths could be a random or a Gaussian distribution. The corresponding jump diffusions are known as Singwi–Sjölander [24] and Hall and Ross [25] jump diffusions, respectively. It may be noted that in all these jump diffusion models, the difference is that of a microscopic detail. In case the system is studied at a larger length scales or equivalently at smaller Q values, the information about these finer details is lost and the diffusion process looks very much like the Brownian diffusion. The variation of C(Q) with Q2 is therefore linear at low Q values and the diffusion coefficient can be obtained simply from the slope of this curve in the region of small Q values. At higher Q values however, as finer details of the jump diffusion start to emerge, the variation of C(Q) with Q2 is no more linear and saturates to a value, which is indicative of the residence times involved in the jump process. In the present case, the variation of C(Q) with Q2 obtained from the experimental data was found to be described well by the Singwi–Sjölander model of jump diffusion, which employs a random distribution of jump lengths. In this model the variation of C(Q) with Q2 is given by [24],

CðQ Þ ¼

DQ 2

ð3Þ

1 þ DQ 2 s

The variation of C as obtained from the fit is plotted in Fig. 4 as a function of Q2 along with the experimental values. The deviation of the graph from the linear behavior at high Q justifies the jump

NF membrane Bulk [26] ROPM [9] Nafion [16]

s (ps)

D (105 cm2/s)

1.1 ± 0.3 1.1 2.8 ± 0.6 2.5 ± 0.4

1.4 ± 0.2 2.5 1.9 ± 0.4 2.0 ± 0.1

diffusion model. The solid line in Fig. 4 corresponds to the least squares fit of the above equation with the experimentally obtained values. The values of the parameters, D and s as obtained from the fit are shown in Table 1, which is compared with bulk water [26]. It was found that diffusion of water in NF membrane is smaller compared to bulk water, which can be explained in terms of the combined effect of confinement and hydrophilic interaction with membranes. Earlier we have studied dynamics of sorbed water in ROPM. However, the pore size in case of NF membrane is slightly larger than ROPM, therefore diffusion coefficient of water in NF membrane should be slightly larger. But as indicated in Table 1, diffusion coefficient of water is found to be lower in NF membrane compared to ROPM. It needs to be mentioned here that this comparison is not so straight forward as Devanathan et al. [27] showed by MD simulation that hydration may alter the nanostructure of the membrane depending on its constituents and hydration levels. Although saturation loading was used for both the membranes in the present study, constituents of the two membranes are not the same and hydration could lead to a very different nanostructure. It was also found that water molecules sorbed in ROPM has larger residence time compared to that in NF membranes suggesting that the ROPM is more hydrophilic in nature as compared to the NF membrane. This is consistent to the DSC results, as no upward shift in freezing point of water was observed in NF membrane vis-à-vis RO membrane [7]. Lot of work has been done for fluorinated inomer membrane – Nafion. Detailed QENS study is reported by Perrin et al. [11] in Nafion with different hydration levels and it was found that with increased amount of adsorbed water, the residence times are reduced and the diffusion coefficients are increased. The local diffusion coefficient and residence time obtained at the highest hydration level in this system are also given in Table 1 for comparison. It was found that the residence time of water molecules in Nafion membrane is larger compared to NF membrane which indicates that NF membrane used in our QENS study is less hydrophilic in nature compared to Nafion membrane.

The surface microstructure and porosity of NF membrane was studied using SEM and PALS techniques. Results are compared with our earlier study on ROPM. It was found that NF membrane has smoother surface with higher porosity compared to ROPM. Diffusion of water sorbed in NF membrane has been studied using QENS technique. It was found that water molecules undergo jump diffusion as described by Singwi–Sjölander model wherein jump length is distributed randomly. Diffusion coefficient of confined water was found to be lower than that of bulk water, which can be understood in terms of combined effect of geometrical restriction and chemical effects.

0.2 Γ (meV)

Water

4. Summary

0.3

0.1

0.0

Table 1 Comparison of the residence time (s) and diffusion coefficient (D) obtained for water molecules in different membranes with bulk water.

0

1

2 2

3

4

-2

Q (Å )

Acknowledgement 2

Fig. 4. Variation of HWHM C, as obtained from the fitting shown in Fig. 3, with Q . The solid line corresponds to the fit as per the random jump diffusion model. The variation expected as per Fick’s law is shown by dashed line.

We would like to acknowledge Dr. P.K. Pujari for PALS measurements and fruitful discussions.

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