Dynamic polymer membranes displaying tunable transport properties on constitutional exchange

Journal of Membrane Science 321 (2008) 8–14

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Dynamic polymer membranes displaying tunable transport properties on constitutional exchange Gihane Nasr a , Mihail Barboiu a,∗ , Takashi Ono b , Shunsuke Fujii b , Jean-Marie Lehn b,∗∗ a Adaptative Supramolecular Nanosystems Group, Institut Europ´ een des Membranes – ENSCM/UM2/CNRS 5635, IEM/UM2, CC 047, Place Eug`ene Bataillon, F-34095 Montpellier, Cedex 5, France b ISIS, CNRS UMR 7006, Universit´ e Louis Pasteur, 8 All´ee Gaspard Monge, 67083 Strasbourg, France

a r t i c l e

i n f o

Article history: Received 12 November 2007 Received in revised form 2 February 2008 Accepted 7 March 2008 Available online 13 March 2008 Keywords: Dynamers Supramolecular membranes Dialysis Molecular constitutional variation

a b s t r a c t Functional dynamic polymers, “dynamers”, are used to design new membrane materials. Our efforts involve the synthesis and the fabrication of dynamic thin-layer supported solid membrane films. The transport performances of (permeability, selectivity and partition coefficients) are evaluated by using the solution-diffusion model. The membrane performances designed to transport ionic salts NaCl and KCl depend and are based on encoded molecular features of the monomeric subcomponents. Thanks to the possibility to combine the structural and functional features of different monomers, the heteropolymeric membrane materials can exhibit very different properties from their original homopolymeric components. In the examples developed here, this strategy revealed itself as a versatile way for the synthesis of new membranes presenting different permeabilities and preserving their selectivity (SK+ /Na+ ∼ 1.4).

1. Introduction Membrane-mediated separations are an attractive alternative to other chemical methods (i.e., ion exchange and chromatographic processes) for purification, recovery, etc. [1–3]. Numerous artificial membrane transport systems using carriers or channel-forming structures have been developed in the last decades. The design and application of new polytopic receptors capable of recognition of cations, anions or molecular species has attracted a great deal of interest as these systems have many potential functions such as solubilization, extraction and membrane transport [2–8]. Concurrently, convergent multidimensional self-assembly strategies have been used for the synthesis of non-covalent self-organized devices, designed to mimic natural ion channel proteins [9–11]. Crown-ethers [2–8], cyclic peptides [9], oligophenyl barrel-stave structures [10] and oligoester bola-amphiphiles [11] have all been used in this context. All these systems illustrate the convergence of molecular recognition and of supramolecular self-organization and supramolecular transport function. The extension of molecular recognition and self-assembly concepts and features of supramolecular chemistry [1] from discrete

∗ Corresponding author. Fax: +33 467 149119. ∗∗ Corresponding author. Fax: +33 390 245140. E-mail addresses: [email protected] (M. Barboiu), [email protected] (J.-M. Lehn). 0376-7388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2008.03.005

© 2008 Elsevier B.V. All rights reserved.

carriers and ion-channels transporting devices to polymolecular entities define the field of supramolecular membrane materials. Of particular interest are the potential ability of such supramolecular membrane films to present polyfunctional properties such as solute molecular recognition [11–14] and the generation of directional diffusion pathways by self-assembling at the supramolecular level [15–18]. This represents a rational approach for building molecular channels in hybrid organic–inorganic materials via the inorganic (sol–gel) transcription of dynamic self-assembled superstructures. The basic and specific molecular information encoded in the molecular precursors (i.e., crown ethers [11–16], amino acid [17] and nucleobase [16,18] ureido-silsesquioxanes) results in the generation of isotropic superstructures in solution and in the solid state which can be “frozen” in a polymeric hybrid matrix by sol–gel process. These systems have been successfully employed to design solid dense membranes, functioning as ion-channels and illustrate how a self-organized hybrid material performs interesting and potentially useful transport functions. On the other hand, supramolecular chemistry is by nature a dynamic chemistry in view of the lability of the noncovalent interactions connecting the molecular components of a supramolecular entity [1,19]. Importing such dynamic features into molecular as well as supramolecular polymeric materials implies looking at dynamic polymers “dynamers”, which are dynamic by nature (supramolecular) or by design (molecular) [20–24] and are capable of undergoing exchange, incorporation or decorporation of their

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Fig. 1. Structural comparative features between classical mixtures of polymers (a) and the dynamic features of dynamers capable of undergoing exchange, incorporation or decorporation of their monomeric subunits, (b) resulting in the formation of specific recognition superstructures (for example, the AAAA signature (c)).

monomeric subunits, linked together by respectively labile noncovalent interactions or reversible covalent bonds. Compared with a physical mixture of classical polymers (Fig. 1a), the mixtures of dynamers give access to new homogenous species presenting controllable modulation of their structure at molecular level in response to external stimuli or experimental conditions. They are capable of undergoing exchange, incorporation or decorporation of their monomeric subunits (Fig. 1b), linked together by respectively labile non-covalent interactions or reversible covalent bonds. This might play an important role in the ability to more finely mutate the mechanical or functional properties of such new molecularly tunable dynamers, compared with physical mixtures of polymers [22–24]. By this way, specific recognition superstructures (for example,

the AAAA signature in Fig. 1c) would be of much interest, giving access to a new class of functional membrane materials. For all these reasons, functional dynamic polymers “dynamers” may be used to conceive novel membrane materials. Our efforts involve the synthesis and the fabrication of “dynameric” thin-layer supported solid membrane films. Then, their transport performances (permeability, selectivity and partition coefficients) are evaluated by using the solution-diffusion model. The membrane performances designed to transport ionic salts NaCl and KCl depend and are based on encoded molecular features of the monomeric subcomponents. The sodium/potassium pump is a good example of biological relevance of active transport of molecules across a membrane where this transport is coupled to the ATP hydrolysis

Fig. 2. Structures of the dialdehydes M1 –M3 and of the bis-hydrazide monomers M4 –M7 .

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to obtain enough free energy to transport other ions against their concentration gradient [30]. In the present study we are exploiting the dynamic reversible covalent exchange processes of the constituent dynameric subcomponents in solution during the membrane synthesis. The resulted solid-thin layer structure of the membrane is stable and is conserved during and after the membrane transport experiments. 2. Experimental 2.1. Materials and methods The dialdehydes M1 –M3 were obtained from the corresponding hydroxybenzaldehydes and bis[2-(2-chloroethoxy)ethyl]ether. The bis-hydrazide monomers M4 –M7 were obtained by treatment of the corresponding methylesters with hydrazine monohydrate in methanol [22,23] (Fig. 2). Polycondensation between the monomers M1 and M4 , M2 and M3 , M2 and M5 , and M3 and M6 gave respectively, the homopolymers, P1 , P2 , P3 and P4 , as transparent films after solvent evaporation (Table 1). The random copolymers P5 –P7 were also prepared starting from the homopolymers P1 and P2 by simply mixing at room temperature (P5 ), in the presence of pentadecafluorooctanoic acid as catalyst (molar ratio 0.01 with respect to the total acylhydrazone bonds in the polymers) (P6 ) and by refluxing at 60 ◦ C (P7 ), respectively. The 1 H NMR spectra of M1 –M7 and P1 –P7 are in agreement with the proposed formula as previously reported [22,23]. The structures of P1 –P7 are stable after the transport experiments as confirmed by NMR spectroscopy. The membrane materials were characterized by X-ray powder diffraction, Thermogravimetric Analysis (Hi-Res TGA 2950, TA Instruments) and Differential Scanning Calorimetry (DSC 2920 Modulated DSC, TA Instruments). 2.2. Preparation and characterization of membranes The membranes were obtained by coating a 1 M chloroformic solution of each homopolymer P1 to P4 or random heteropolymers P5 to P7 onto planar polyvinylidenefluoride (PVDF) microporous supports by using a tape casting method. The membranes were then dried for 1 h at room temperature and for 3 h at 90 ◦ C. Scanning electron microscopy (SEM) allowed the thickness and the quality of the active deposited layer to be determined. 2.3. Dialysis transport procedure Membrane transport experiments were performed with a bicompartmental device, magnetically stirred at room temperature (Fig. 3). It consists of two PTFE cell device separated by the solid membrane oriented with the active dense film to the feed phase. Nitrogen permeation measurements were performed to ensure that they were dense and defect free. The feed phase was an aque-

Fig. 3. Experimental device used in diffusion membrane transport experiments.

ous (V = 50 ml) equimolar of 10−1 M (NaCl + KCl) solution for the competitive cation transport experiments. The membrane consisted of supported “dynamer” dense material (S = 5.32 cm2 ) while the receiving phase consisted of 50 ml of deionized water. The Na+ and K+ concentrations were monitored at different time intervals using the atomic absorption spectrophotometry. The permeabilities P and the partition coefficient ratio ˛ of Na+ and K+ ions have been determined from experimental concentration versus time profiles using the solution-diffusion model [12]. 3. Results and discussions 3.1. Membrane material characterization Structural insights on the morphology of the membrane materials P1 –P3 were obtained by X-ray powder diffraction (XRPD). Fig. 3 shows the XRPD patterns of the homopolymers P1 –P3 All these samples display a broad Bragg diffraction peak at ˚ representative for the parallel packing 2 = 21–23◦ (d = 4.5–4.8 A) of the hydrogen-bonded polymeric chains presenting a tight van de Waals contact (Fig. 4). Adsorbtion/desorbtion nitrogen experiments showed that all P1 –P7 dynamers do not exhibit the absorbtion/desorbtion isotherms, revealing dense non-porous structures. They are structurally more similar with conventional dense polymers rather than the inorganic porous [28] or organic pseudo-microporous materials [31] presenting free-volume voids spanning the sample. SEM confirmed that the active layer of “dynamer” membrane films P1 –P7 (thickness of about 2–6 ␮m) were dense without micropinholes (Fig. 5). Fig. 5a and b depicts the typical SEM images of the cross-section and the surface of P1 film and shows wellresolved bulk crystalline areas at nanometric scale. The P2 –P4 films present a very similar morphology (see the cross-section and the

Table 1 Structures and glass transition temperatures, Tg of the homopolymer P1 –P4 and heteropolymeric P5 –P7 membranes

Tg (◦ C) M1 M2m M2m M2p M1 + M2 M1 + M2 M1 + M2

M4 M3 M5 M6 M3 + M4 M3 + M4 M3 + M4

P1 P2 P3 P4 P5 = P1 + P2 (mix) P6 = P1 + P2 (H+ ) P7 = P1 + P2 (60 ◦ C)

65.5 19.1 23.5 37.5 20.2 47.1 n.d.

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exchange of the monomers in the presence of added acidic catalyst (P6 ) or at 60 ◦ C (P7 ). Exchange within the polymeric films was followed by observing the changes of the 1 H NMR spectra. The mechanical properties of these resulting heteropolymers were thus similar with the flexible P2 homopolymer in the case of simple mixing (P5 ) or markedly different from those of the parent homopolymers P1 or P2 in the case of chemical exchange (P6 and P7 ) proving that the properties of the membrane films are adjustable via the nature of the incorporated polymeric chains. The acylhydrazone dynamers are capable of interchanging their bonds mutually even as neat polymers, inducing crossover between polymeric chains (Fig. 6). Such polymers have promising potential as smart adaptive membrane materials. 3.2. Dialysis membrane transport experiments

Fig. 4. XRD patterns of P1 –P3 homopolymers.

surface of P2 in Fig. 5c and d) with a homogeneous dense structure at the nanometric scale. These results were confirmed by ATG and DSC experiments (see glass transition temperatures, Tg of P1 –P7 in Table 1). The homopolymer P1 resulting from polycondensation between M1 and the rigid M4 monomer, gave a hard and very fragile membrane film (Tg = 65.5 ◦ C). The homopolymers P2 (Tg = 19.1 ◦ C) and P3 (Tg = 23.5 ◦ C) obtained by polycondensation between M2 , M3 and M3 , M5 monomers, containing a highly flexible ethyleneglycolderived spacer units as soft components, yielded the soft and quite stretchy films. Introduction of M6 rigid macrocyclic spacer groups into homopolymer P4 led to an increased glass transition temperature (Tg = 37.5 ◦ C). The occurrence of bond exchange and crossover component recombination was demonstrated by the use of P1 and P2 polymer blends either by simple physical mixing (P5 ) or by chemical

In order to study the transport properties of the “dynamer” membrane films we carried out dialysis transport experiments (Table 2). The competitive transport of Na+ and K+ across the membranes P1 –P7 according to the solution-diffusion mechanism [11–16] and was evaluated using passive transport conditions. We have recently reported a model based on a solution-diffusion (Fick’s law) which can be described for different membrane processes such as dialysis, reverse osmosis, gas permeation, pervaporation, etc. [12]. This model assumes that the chemical potential gradient across the membrane is only due to a concentration gradient. The flux of the solute “i” can be expressed as follows: Ji = −Di

dci dx

(1)

By integrating over the thickness l of the membrane, the flux of solute “i” is: Ji = −

Di m,s (c − cim,f ) l i

Fig. 5. SEM images of (a), (c) the cross-section and (b), (d) the surface of the P1 and P2 membrane films.

(2)

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Table 2 Transport parameters: the permeability P, the diffusion coefficient D and the partition coefficient ratio ˛ of solutes Na+ and K+ in P1 –P7 membranes Membrane

PNa+ × 109 (cm2 s−1 )

DNa+ × 108 (cm2 s−1 )

˛Na+

PK+ × 109 (cm2 s−1 )

DK+ × 108 (cm2 s−1 )

˛K+

SK+ /Na+

P1 P2 P3 P4 P5 P6 P7

– 7.6 4.0 15.7 11.7 1.9 0.5

– 0.84 0.51 1.18 0.68 0.38 0.24

– 0.76 0.62 0.89 0.90 0.28 –

– 10.3 6.3 20.8 16.4 2.6 0.62

– 1.24 0.86 1.51 0.55 0.46 0.33

– 0.80 0.56 1.07 1.02 0.56 –

– 1.35 1.57 1.32 1.43 1.32 1.12

with cim,s , cim,f the concentrations of the solute in the membrane at the strip and the feed phase interfaces, respectively. The concentration gradient in the membrane can be deduced by assuming thermodynamical equilibria at the interfaces:

By combining Eq. (2) with Eqs. (3) and (4), we obtain the flux according to the concentrations in the feed and the strip phases:

cim,s = Kis × cis

(3)

cim,f = Kif × cif

(4)

Di and Ki , the effective diffusion and partition coefficients of this macroscopic approach, can be correlated with the physical and chemical structure of the dense membrane. If we suppose that the transport rate is governed by diffusion and that the complexation–decomplexation reactions are kinetically rapid, then the accumulation of the solute in the membrane can be neglected. In a quasi-stationary regime (Fig. 4) the transport rate across each interface becomes approximately equal to:

with cis and cif the concentrations of the solute “i” in the strip and

feed phases, respectively, and Kis and Kif the partition coefficients at the strip and feed phase interfaces with the membrane, respectively. If we suppose that the transport rate is governed by diffusion and that the complexation–decomplexation reactions are kinetically rapid, then the accumulation of the solute in the membrane can be neglected.

Ji =

Di f f (Ki ci − Kis cis ) l

−J1 = a J2 = a

dcif dt

dcis dt

=−

=−

(5)

Di f f (Ki ci − Kis cis ) l

(6)

Di f f (Ki ci − Kis cis ) l

(7)

with a = V/A the compartment length (we suppose a simple geometry), V the compartment volume, and A the active surface of the membrane. The solute flux density across the membrane is then simply Jm ∼ = J1 = J2 . With Di Kif /al = , Kis /Kif = ˛ and the initial conditions (c1,t=0 = c10 and c2,t = 0 = 0) Eqs. (6) and (7) yield: c2 (t) =

Kis

c10 1+˛

[1 − e−(1+˛)t ]

(8)

Note that as ˛ → 0 (i.e., Kis  Kif ), C2 (∞) → C10 and as ˛  1 (i.e.,

 Kif ), C2 (∞) → 0. The fitting of experimental concentration versus time data in the strip phase allows the permeability P (it express the evaluation of the transport performances), the diffusion coefficients Di and the partition coefficient ratio ˛ of solute “i” (it express the affinity of the membrane toward the solute), to be determined: Pi = Di Kif =  × a × l ˛=

(9)

Kis

(10)

Kif

The diffusion coefficient is obtained from Eq. (11), derived from Eq. (8) where the Ci0 is the initial concentration in the feed phase, Cit the concentration in the strip phase Am the membrane area, V the volume of the receiving phase, and dm the thickness of the active layer of the membrane. ln

Fig. 6. (a) Permeability values of Na+ and K+ cations in the homopolymeric P2 –P4 membranes; (b) permeability values of Na+ and K+ cations in the homopolymeric P2 and heteropolymeric P5 –P7 membranes.

c10 − (1 + ˛)c2 (t) c10

= −(1 + ˛)

Am · Dm t Vr · l

(11)

The transport parameters, the permeability P the diffusion coefficients Di , and the partition coefficient ratio ˛ of solutes Na+ and K+ are determined for all dialysis transport experiments performed by using P1 –P7 supported membrane films (Table 2). The transport experiments of Na+ and K+ through P1 –P7 membranes present the

G. Nasr et al. / Journal of Membrane Science 321 (2008) 8–14

Fig. 7. (a) Diffusion coefficients values of Na+ and K+ cations in the homopolymeric P2 –P4 membranes; (b) diffusion coefficients values of Na+ and K+ cations in the homopolymeric P2 and heteropolymeric P5 –P7 membranes.

non-linear saturation behaviours of the transport profile concentration versus time, indicating a strong affinity of the membrane towards the solutes [12]. In all experiments the K(H2 O)n + ions are preferentially transported through P1 –P7 membranes (Table 2). The dialysis transport experiments were performed by pre-equilibrating the membranes with the water. At equilibrium the water uptake influencing the ion transport rates, might depend on the hydrophilic nature of membrane constituents, but the thickness of our active hybrid thinlayers 2–6 ␮m are not permitting an accurate determination of water amount with the reference of the supporting membrane. Since self-diffusion coefficients of hydrated ions are DNa(H O) + < 2 n DK(H O) + [25], and the dehydration free energy is thermodynam2

13

the hydrophilic polyethyleneoxyde pathways of the P1 –P7 membranes (Table 2). This seems to be true when we compare the transport performances of P2 and P3 membranes: the introduction of an increasing number of repeating oxyethylene units (monomer M3 → P2 compared with monomer M5 → P3 ) decrease the permeabilities and the diffusions coefficients of both cations by a factor of ∼2 (Fig. 6a). The macrocyclic moiety of the monomer M6 → P4 drastically increases by a factor of ∼2 the permeabilities of both cations through membrane P4 compared with membrane P3 ; this may reflect the dominant contribution of the preorganization (macrocyclic) effect in the specific complexation of the alkali cations selectively increasing the diffusion of K+ over Na+ cations through the membrane [1]. The transport of Na+ and K+ is facilitated by introducing the macrocyclic complexant into the membrane, without changing significantly the transport selectivity. The transport properties of the heteropolymers resulting from the crossover component recombination of the parent homopolymers P1 and P2 are strongly dependent on the different synthetic approaches used for the membrane film preparation. The simple mixing of P1 and P2 results in the formation of P5 heteropolymer in which the P1 and P2 parent polymers are physically mixed without any structural exchange between the monomeric subunits. The P5 heteropolymer (Tg = 20.2 ◦ C), presenting almost similar mechanical features as the flexible P2 homopolymer (Tg = 19.1 ◦ C) but increased permeabilities for Na+ and K+ cations, keeping almost the same order for the values of the diffusion coefficients (Table 2; Fig. 7). The physical introduction of the most rigid P1 homopolymer in the matrix of P5 heteropolymer probably induces a favourable reorganization of the conducting pathways in the membrane film, expressed in an increased solubility of the ions within the membrane. The possibility of bond exchange by chemical exchange of the monomers in the presence of added acidic catalyst (P6 , Tg = 47.1 ◦ C) or at 60 ◦ C (P7 , Tg = n.d.) leads to the crosslinked hard membrane materials. The transport permeability as well as the diffusion coefficients of such membrane materials are both strongly decreasing compared with the initial P2 homopolymer (Table 2; Figs. 6 and 7). Taking into account the transport mechanism diffusionally controlled through cross-linked polymers, presenting dense transport corridors, it can be found normal that ionic diffusion in such membranes is markedly slowed-down when the exchange processes between the subcomponents (P6 and P7 compared with P5 ) occur, affecting both by the microstructure of the matrix and by solutes interaction with the polymeric network. However, for all three heteropolymeric membrane films P5 –P7 , the selectivity SK+ /Na+ is preserved, showing that the trade off in the low permeability/high selectivity or vice versa balance is not still present for this kind of dynamic membrane systems of tunable superstructures, as is generally observed for glassy polymers used for gas and ion separations [28,29].

n

ically more favourable for K(H2 O)n + than for Na(H2 O)n + [26], a substantial contribution to K+ selectivity is due to the interaction of the partially hydrated ions with the hydrated ethyleneoxide groups within the polymeric matrix of the membrane. This is totally reflected in the diffusion coefficient values determined from transport experiments showing that the diffusion is more favourable for K(H2 O)n + than for Na(H2 O)n + (Table 2; Fig. 7) The complexation of alkali cations by polyethyleneoxide (POE) chains is strongly influenced by protic solvents and the K+ –POE complexes are two orders of magnitude more stable than the Na+ –POE complexes in methanol [27]. In all studied transport experiments the partition coefficient ratios are ˛ ≤ 1 for both Na+ and K+ cations, except for the macrocyclic based membrane, P4 . This suggests that they may stick within

4. Conclusions The present results report a first example of “dynamer” membrane films. The proposed strategy for using dynamic covalent polymers films provides a very useful methodology for modifying the transport properties, giving access to smart and adaptive dynamic membrane materials. In addition to conventional polymeric properties such as stability and strength, these dynamic polymeric membranes present the distinctive ability to exchange, incorporate and/or decorporate monomeric components linked by reversible acylhydrazone covalent bonds depending on the external conditions. In the present study we have demonstrated that the dynamic reversible

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covalent exchange processes between the constituent dynameric subcomponents during the membrane synthesis results in the formation of stable solid-thin layer membranes conserving their structural properties during and after the membrane transport experiments. Thanks to the possibility to combine the structural and functional features of different monomers, the heteropolymeric membrane materials can exhibit very different properties from their original homopolymeric components. In the above-developed examples, this strategy revealed itself to be a versatile way for the synthesis of new membranes presenting different permeabilities and preserving their selectivity (SK+ /Na+ ∼ 1.4). This feature offers to membrane science perspectives towards functional materials that involve modification and control of the intrinsic structural properties of dynamic entities correlated with the dynamic features of the diffusional controlled transport. Prospects for the future include the development of these original methodologies towards for such dynamic tunable membrane materials, presenting a greater degree of structural complexity and their application to different membrane processes. Acknowledgments This work, conducted as part of the award “Dynamic adaptive materials for separation and sensing Microsystems” (M.B.) made under the European Heads of Research Councils and European Science Foundation EURYI (European Young Investigator) Awards scheme in 2004, was supported by funds from the Participating Organizations of EURYI and the EC Sixth Framework Program. See www.esf.org/euryi. We thank Dr. John Palmeri for his valuable assistance on modelisation of the transport experimental data. References [1] J.-M. Lehn, Supramolecular Chemistry–Concepts and Perspectives, VCH, Weinheim, 1995. [2] G.W. Gokel, A. Mukhopadhyay, Synthetic models of cation-conducting channels, Chem. Soc. Rev. 30 (2001) 274–286. [3] N. Voyer, The Development of Peptide Nanostructures, Top. Curr. Chem., vol. 184, Springer Verlag, Berlin/Heidelberg, 1996, pp. 1–35. [4] J.-M. Lehn, J.P. Behr, Transport of amino acids through organic liquid membranes, J. Am. Chem. Soc. 95 (1973) 6108–6110. [5] M. Barboiu, G. Vaughan, A. van der Lee, Self-organized heteroditopic macrocyclic superstructures, Org. Lett. 5 (2003) 3073–3076. [6] M. Barboiu, Supramolecular polymeric macrocyclic receptors—hybrid carrier vs. channel transporters in bulk liquid membranes, J. Incl. Phenom. Mol. Rec. 49 (2004) 133–137. [7] A. Cazacu, C. Tong, A. van der Lee, T.M. Fyles, M. Barboiu, Columnar selfassembled ureidocrown-ethers—an example of ion-channel organization in lipid bilayers, J. Am. Chem. Soc. 128 (29) (2006) 9541–9548. [8] D.T. Bong, T.D. Clark, J.R. Granja, M.R. Ghadiri, Self-assembling organic nanotubes, Angew. Chem. Int. Ed. Engl. 40 (2001) 988–1011. [9] S. Matile, En route to supramolecular functional plasticity: synthetic ␤-barrels, the barrel-stave motif, and related approaches, Chem. Soc. Rev. 30 (2001) 158–167.

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