J. Phys. Chem. C 2007, 111, 2965-2973
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pH and Ionic Strength Effects on Amino Acid Transport through Au-Nanotubule Membranes Charged with Self-Assembled Monolayers Jie-Ren Ku,†,‡ Shih-Ming Lai,†,§ Nazar Ileri,† Patricio Ramı´rez,| Salvador Mafe´ ,⊥ and Pieter Stroeve*,† Department of Chemical Engineering and Materials Science, UniVersity of California DaVis, DaVis, California 95616, Departament de Fı´sica Aplicada, UniVersidad Polite´ cnica de Valencia, E-46022 Valencia, Spain, and Departament de Fı´sica de la Terra i Termodina` mica, UniVersitat de Vale` ncia, E-46100 Burjassot, Spain ReceiVed: October 23, 2006; In Final Form: December 19, 2006
The transport of the amino acids tyrosine and phenylalanine through Au-nanotubule membranes with selfassembled monolayers of alkanethiols is theoretically and experimentally studied. The membranes are prepared by electroless deposition of gold on porous polycarbonate track-etched membranes with control of the inner pore size, followed by self-assembly of acid-functionalized thiols (final mean average pore radius: 7 nm). The capability of switchable ion-transport selectivity by external control (e.g., by changing the pH, ionic strength, and amino acid concentration) is discussed. The flux changes with the pH and the ionic strength of the solution clearly show that electrical charges play a key role in the amino acid transport through the nanopores. Remarkably, an uphill transport of the amino acid is observed when a pH difference is imposed in the external solutions. The theoretical approach based on the Nernst-Planck flux equations considers all of the charged species present in the system (the cationic, anionic, and zwitterionic forms of the amino acid, the hydrogen and hydroxide ions, and the two salt ions) and allows a qualitative understanding of the transport phenomena in the charged nanopores.
1. Introduction Self-assembled monolayers (SAMs) of alkanethiols provide a convenient way to attach functional groups to metal substrates such as Au, Ag, and Cu1 which can be used in membrane technology, especially in nanofiltration. Recently, Au-nanotubule membranes have attracted attention because they have the capability of switchable ion-transport selectivity by external control (e.g., by changing the pH, ionic strength, and applied potential2-9). The Au-nanotubule membranes have been prepared by electroless deposition of gold on porous polycarbonate track-etched (PCTE) membranes with control of the inner pore size,10-12 followed by self-assembly of acid-functionalized thiols. Since the membrane has fixed charges, electrostatic interactions lead to ionic selectivity depending on the thickness of the electrical double layer, the charge of the transported ions, and the membrane surface charge.13-15 Further, the gold surface layers allow for electrical contact with the gold nanotubules inside the membrane for controlling the electrostatic potential.3 Amino acids are amphoteric compounds16 having more than one ionizable group that can exist in cationic, anionic, and zwitterionic forms depending on the aqueous solution pH. We theoretically and experimentally study the transport of two amino acids, L-tyrosine and L-phenylalanine, through the above nanoporous membranes as a function of the external pH and * Author to whom correspondence should be addressed. E-mail: pstroeve@ ucdavis.edu. † University of California Davis. ‡ Permanent address: ITRI, Energy and Environmental Laboratories, Industrial Technology Research Institute, Hsinchu, Taiwan 310. § On leave from the Department of Chemical Engineering, National Yunlin University of Science and Technology, Touliu, Yunlin, Taiwan 640. | Universidad Polite ´ cnica de Valencia. ⊥ Universitat de Vale ` ncia.
ionic strength. Phenylalanine is hydrophobic, but tyrosine is less hydrophobic because of the polar nature of the OH in the R group (the amino acid side chain). The study of the amino acid pH-dependent transport is of interest not only for a better understanding of a variety of metabolic processes in biological membranes but also for devising efficient separation processes employing artificial membranes.17-33 Some theoretical studies on amino acid transport through charged membranes have employed a solution-diffusion approach where the membrane fixed site complexant assists the solute diffusion by complexation-decomplexation reactions, increasing thus the solute partition in the membrane.18,19,28 Although the above approach has proved to be useful, the amino acid is a charged species whose ionic fractions within the membrane are coupled with the other ionic species by the local electroneutrality condition. For instance, application of the Donnan equilibrium33-35 at the membrane/solution interface for membranes with fixed charges gives significantly different membrane and external solution pH values,31,36-38 and this should be important for the amino acid dissociation equilibrium. Also, the amino acid transport through the membrane follows an electrodiffusional mechanism rather than a pure diffusional mechanism, and the effect of the electric potential gradient on the amino acid flux should be considered. There is clear experimental evidence that electrical charge effects play a key role in the amino acid transport through hydrophilic charged pores.17,20-26,30-33 In particular, these effects are theoretically predicted to be crucial for amino acid transport at a zero concentration gradient and against its external concentration difference (uphill transport33). This transport should occur for certain combinations of the pH and salt concentration in the external solutions and has previously been studied for small ions in fixed-charge membranes.38,39 Uphill transport is also typical of biological membranes because of the coupling of the
10.1021/jp066944d CCC: $37.00 © 2007 American Chemical Society Published on Web 01/30/2007
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flux of the species being transported to other processes (e.g., hydrogen transport due to a pH gradient). We report here preliminary experimental data showing nonzero values of the flux at zero amino acid concentration difference when a pH difference is imposed in the external solutions. The theoretical approach employed is based on the NernstPlanck flux equations40,41 with the Goldman constant electric field (GCF) assumption42,43 and considers all of the species present in the system: the cationic, anionic, and zwitterionic forms of the amino acid, the hydrogen and hydroxide ions, and the two salt ions. These equations are coupled by the amino acid dissociation equilibrium and the local electroneutrality condition within the membrane. We are aware that short range interactions between the amino acid, the water molecules, and the membrane constituents18-20,28 are important for the amino acid transport through fixed-charge membranes. In particular, the shape and chemical properties of the R group are responsible for the unique properties of each amino acid,16 which explains the highly specific nature of amino acid transport through some fixed-charge membranes.19,25 However, we do not consider these interactions with detail as a first approximation (they could be incorporated indirectly via the amino acid membrane/solution partition coefficient) and concentrate on the effects of the pH and the ionic strength on the electrostatic interaction between the amino acid and the membrane charges. This interaction dictates the transport of ions through the hydrophilic, charged nanopores.44 2. Experimental Section Commercial PCTE membranes (Poretics, Inc.) were used as received as substrates for the electroless plating of gold. These membranes had a hydraulic pore radius of 28 nm, a pore density of 6 pores/µm2, and a thickness of 6 µm.4,5 The PCTE membranes had approximately parallel, cylindrical pores with a narrow distribution of pore sizes. The compounds SnCl2 (98%), AgNO3 (99+%), Na2SO3 (98+%), NH4OH, trifluoroacetic acid (99%), formaldehyde, methanol (HPLC grade), and ethanol (HPLC grade) were obtained from Aldrich and were used as received. A commercial gold-containing solution of Na3Au(SO3)2 (Oromerse Part B, Technic, Inc.) was used after dilution with water (40 times). The thiol 11-mercaptoundecanoic acid (95%) was used to form the SAMs on the gold surfaces. Milli-Q water (18 MΩ) was employed for rinsing and the preparation of all solutions. The amino acids L-tyrosine and L-phenylalanine were purchased from Aldrich Chemical Company (Milwaukee, WI) and used without further purification. Gold was deposited on the pore walls and both faces of the PCTE membranes using the electroless plating method.2,11,12 The temperature of the gold solution was fixed at 1 °C during the deposition process, and the pH of the gold solution was 10. After the gold plating on the membrane surfaces, all membranes were thoroughly rinsed with water. The PCTE membranes with electroless gold were immersed in an aqueous solution of 25% HNO3, stored overnight, and then rinsed with pure water. This treatment is necessary to clean the electroless gold without delaminating the gold from its substrate.12b,35 In order to form thiol monolayers on the gold surface, the gold-coated membrane was thoroughly rinsed with ethanol and then immersed in an ethanolic solution of alkanethiol (5 mM) for 12 h to form a SAM on the inside gold surface.2,6,7 The average hydraulic pore radius of the final PCTE/Au/HSC10H20COOH membranes was measured to be 7 nm by flow experiments.2 Most of the experiments were conducted with identical pH values for the aqueous solutions in both the reservoir and the sink. The actual
Figure 1. (a) Schematic view of the membrane system. (b) The amino acids L- tyrosine and L-phenylalanine.
pH values, in the range 2-11, were measured with an Orion Research pH meter (model 601A). The PCTE/Au/HSC10H20COOH membranes are very robust.2,6,7 The PCTE/Au/HSC10H20COOH membranes are stable for a couple of months. 2-5,12a (Our flux measurements for the same membrane were repeatable to within 3%, 2 months apart in time.) The gold nanotubules themselves are also robust, and the SAM on the gold surface can be removed with an aqueous solution of 25% HNO3, stored overnight, and then rinsed with pure water. A new SAM can then be deposited by immersion in an ethanolic solution of an alkanethiol (5 mM) for 12 h. The membrane can then be used again for flow and transport experiments. The membrane separated the diffusion cell into two compartments, reservoir and sink. In the first set of experiments, the reservoir contained an aqueous solution (35 mL) of amino acid, and the sink contained an aqueous solution (35 mL), initially without amino acid. The area of the membrane was 1.77 cm2. For eliminating the concentration polarization in the diffusion cell, vigorous stirring (400 rpm) was carried on in both compartments in all experiments by using two magnetic stirrers and a Corning stirring plate. For the reservoir solutions, the amino acid was dissolved in aqueous solutions of NaOH or HCl at known pH values with the initial amino acid concentration fixed at 1 mM (the sink compartment contained an aqueous solution with the same pH value as the reservoir side but without the amino acid). The ionic strength of the solutions in both compartments was balanced either at 2 mM or at 200 mM by the addition of NaCl salt. The concentration of amino acid passing from the reservoir to the sink was measured by UVvisible light spectrophotometry (Varian, Cary 3) in the sink compartments at 275 nm (tyrosine) and 257 nm (phenylalanine). Finally, some experiments with an imposed pH difference (pHL ) 11.5 and pHR ) 2.4) were also conducted at the fixed
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ionic strength IL ) IR ) 4 mM (see Figure 1a). In this second set of experiments, the concentration of tyrosine in the reservoir solution was varied between cA,L ) 0.1 mM and cA,L ) 1.1 mM while the sink solution concentration was initially set to cA,R ) 0.1 mM in all cases.
where K3 ) 10-pK3 must also be considered in addition to the equilibria in eqs 4a,b. From eqs 4a,b, the concentrations of the phenylalanine species in the external solutions are
cA-,j )
3. Theoretical Model Figure 1 shows a sketch of the system under study. A goldcoated PCTE membrane with monodisperse cylindrical pores of radius r after plating extends from x ) 0 to x ) d separating two solutions containing the salt (NaCl in the experiments) and the amino acid. This can be in zwitterionic (A(), cationic (A+), and anionic form (A- in the case of phenylalanine, A- and A2in the case of tyrosine). The membrane ionic selectivity is achieved by chemisorption of the acid-terminated thiols (the negatively charged carboxylic groups in Figure 1a) onto the gold layers. The volume concentration of these fixed-charge groups in the membrane is XCT, with σ the (absolute) value of the negative surface-charge density. Also, ci(x) is the local concentration of the species i (i ) Na+, Cl-, H+, OH-, A+, A-, A2-, A() at a point of coordinate x within the membrane and ci,j is the concentration of the species i in the external solution j (j ) L for the left reservoir solution, and j ) R for the right sink solution). φj and pHj (j ) L, R) are respectively the electric potential and the pH of solution j, with φ(x) as the local electric potential in the membrane. The potential drops ∆φL ) φ(0) - φL and ∆φR ) φR - φ(d) are respectively the Donnan potential differences through the left and right interfaces, and ∆φD ) φ(d) - φ(0) is the diffusion potential within the membrane. Finally, cA(x) is the total concentration of amino acid at a point of coordinate x within the membrane, and cA,j (j ) L, R) refers to this concentration in solution j. The solutions are assumed to be perfectly stirred, and the whole system is isothermal. The pH of the external solutions is controlled by adding either an acid (HCl) or a base (NaOH) to these solutions. The H+ and OH- ions follow the water dissociation equilibrium: KW
H2O {\} H+ + OH-
(1)
where KW ) 10-14 mol2 L-2. The concentrations of H+ and OH- in the external solutions are
cH+,j ) 10-pHj
j ) L, R
(2)
KW cH+,j
j ) L, R
(3)
cOH-,j )
The zwitterionic and net charge forms of phenylalanine are assumed to be in equilibrium with the H+ ions according to the schemes K1
A+ {\} A( + H+ K2
A( {\} A- + H+
K3
A {\} A
2-
+H
+
cA(,j )
(cH+,j)2/K1K2
j ) L, R (5) j ) L, R
cA,j
1 + cH+,j/K2 + (cH+,j)2/K1K2 cH+/K2
(6) j ) L, R
cA,j
1 + cH+,j/K2 + (cH+,j)2/K1K2
(7)
where
cA+,j + cA-,j + cA(,j ) cA,j
j ) L, R
(8)
Analogously, solving the equilibria in eqs 4a-c, the concentrations of tyrosine species in the external solutions are
cA-,j )
cH+,j/K3
cA,j 1 + cH+,j/K3 + (cH+,j)2/K2K3 + (cH+,j)3/K1K2K3 j ) L, R (9)
cA2-,j )
cA+,j )
cA(,j )
1 cA,j 1 + cH+,j/K3 + (cH+,j) /K2K3 + (cH+,j)3/K1K2K3 j ) L, R (10) 2
(cH+,j)3/K1K2K3
cA,j 1 + cH+,j/K3 + (cH+,j)2/K2K3 + (cH+,j)3/K1K2K3 j ) L, R (11) (cH+,j)2/K2K3
cA,j 1 + cH+,j/K3 + (cH+,j)2/K2K3 + (cH+,j)3/K1K2K3 j ) L, R (12)
where
cA+,j + cA-,j + cA2-,j + cA(,j ) cA,j
j ) L, R (13)
NaCl was used to keep fixed the ionic strength of the external solutions j at a value Ij for all pHj. Also, the electroneutrality condition in the external solutions is
∑i zici,j ) 0
j ) L, R
(14)
where zi is the charge number of the ionic species i. This gives
(4a)
cNa+,j ) Ij - cH+ - cA+
j ) L, R
(15)
(4b)
cCl-,j ) Ij - cOH- - cA-
j ) L, R
(16)
j ) L, R
(17)
where K1 ) 10-pK1 and K2 ) 10-pK2 are the equilibrium constants of the dissociation reactions. In the case of tyrosine, the dissociation equilibrium -
cA+,j )
1 cA,j 1 + cH+,j/K2 + (cH+,j)2/K1K2
(4c)
in the case of phenylalanine and
cNa+,j ) Ij - cH+ - cA+ cCl-,j ) Ij - cOH- - cA- - 2cA2in the case of tyrosine.
j ) L, R (18)
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External and membrane/solution concentrations are connected through the Donnan equilibrium conditions42,43 at the interfaces x ) 0 and x ) d (see Figure 1a):
(
ziF ci(0) ) kici,L exp - ∆φL RT ci(d) ) kici,R exp
(
ziF ∆φ RT R
)
)
[
]
[
KN
)
kNa+cNa+,j kA+cA+,j XCT/cH+,j + uj - (kCl-cCl-,j + cH+,j kH+cH+,j kH+cH+,j 1+ u KN j kH+ 1 kOH-cOH-,j + kA-cA-,j) )0 j ) L, R (29) cH+,j uj
in the case of phenylalanine and
] (21)
(22)
through the membrane/solution interfaces at x ) 0 and x ) d (see Figure 1a). Because of the SAMs of acidic thiols, the nanopore’s surfaces are lined with weak acid carboxylic groups. We assume that these groups are homogeneously distributed on the pore surface. The neutral -COOH and dissociated -COO- forms of the carboxylic groups are in equilibrium with the H+ ions of the membrane solution:
R-COOH {\} R-COO- + H+
1+
(20)
is the partition coefficient of species i, µ0i is the reference chemical potential, and constants F, R, and T have their usual meaning.42,43 Note that ki does not include the effect of the electric potential difference across the interface, as can be seen from the definition of the Donnan potential differences in eqs 19 and 20. Equations 19 and 20 result from the quasi-equilibrium condition that assumes a constant value for the electrochemical potential
µ˜ i ) µ0i + RT ln ci + ziFφ
(
(19)
where
1 1 ki ≡ exp (µ0i,L - µ0i (0)) ) exp (µ0i,R - µ0i (d)) RT RT
we obtain
(
1+
)
kNa+cNa+,j kA+cA+,j kA2-cA2-,j 2 1 + uj - 2 k kH+cH+,j kH+cH+,j cH+,j H+ u 2
in the case of tyrosine, where uL ≡ cH+(0)/cH+,L and uR ≡ cH+(d)/cH+,R. Equations 29 and 30 can be readily solved for uj using a numerical procedure. After determining uj, the inner membrane concentrations ci(0) and ci(d) and the Donnan potential differences through the left (x ) 0) and right (x ) d) interfaces, ∆φL and ∆φR, can be obtained from eqs 19 and 20 (see also Figure 1a). The electric potential and the ion fluxes through the membrane can be calculated solving the Nernst-Planck equations40-43
dci F dφ Ji ) -Di - ziDici dx RT dx
XNC cH+ X0C
∑i ziJi ) 0
(23)
(25)
the effective membrane fixed-charge concentration is44
XNC )
1 X 1 + cH+/KN CT
(26)
The (absolute) value of the surface density of ionizable groups, σ, is related to the volume concentration of these groups, XCT, through the pore electroneutrality condition44
σ2πr ) FXCTπr2
(27)
Combining eqs 19, 20, and 26, together with the electroneutrality condition within the membrane
∑i zici - XNC ) 0
(32)
Also, the (unknown) total amino acid flux is
(24)
where XNC and X0C are respectively the concentration of the negative and neutral forms of the carboxylic groups. From eq 24 and the total concentration,
XCT ) XNC + X0C
(31)
where Di and Ji are the diffusion coefficient in the membrane and the flux of species i, respectively. The fluxes of eq 31 are subjected to the condition of zero total current (no external electric field is applied)
where KN is the dissociation constant. From eq 23, we obtain
10-pKa ≡ KN )
j
k H+ 1 XCT/cH+,j - (kCl-cCl-,j + kOH-cOH-,j + kA-cA-,j) )0 cH+,j cH+,j uj 1+ uj KN j ) L, R (30)
(28)
J A ) J A- + J A+ + J A(
(33a)
in the case of phenylalanine and
JA ) JA- + JA2- + JA+ + JA(
(33b)
in the case of tyrosine. Fluxes JNa+, JCl-, and JA are constant through the membrane under steady-state conditions because of the continuity (mass conservation) equations. On the contrary, fluxes JH+, JOH-, JA(, JA-, JA2-, and JA+ are not constant through the membrane because these ions participate in the local dissociation reactions that are sources and sinks for these ions. Equations 31-33 constitute a set of algebraic and differential equations subject to the boundary conditions above. This boundary value problem could be solved using an iterative scheme,45 but as a first approximation, we have estimated the ionic fluxes assuming that they are constant and using the GCF approximation.42 Although these assumptions are crude, the results obtained give the qualitative trends of the model, as reported previously.31,37 The fluxes of the ionic species can then be written approximately in the form
Ji ≈
ziF Di∆φD ci(0) exp(-ziF∆φD/RT) - ci(d) (34) RT d 1 - exp(-ziF∆φD/RT)
Amino Acid Transport through Au-Nanotube Membranes Substituting eq 34 for each species into eq 32 we obtain
zi2F Di∆φD ci(0) exp(-ziF∆φD/RT) - ci(d)
∑i RT
1 - exp(-ziF∆φD/RT)
d
)0 (35)
Equation 35 can be solved for ∆φD using a numerical procedure. Once ∆φD has been determined, the ion fluxes and the membrane potential
∆φM ) ∆φL + ∆φD + ∆φR
(36)
can be also obtained. 4. Results and Discussion Figure 1b shows the two amino acids used in the experiments. Amino acids can be classified according to the type of side chain associated with the R group: phenylalanine is hydrophobic, but tyrosine is less hydrophobic because of the polar nature of the OH in the R group. Their isoelectric points are pH 5.64 (tyrosine) and pH 5.48 (phenylalanine). Figure 2 gives the concentrations of tyrosine (Figure 2a,b) and phenylalanine (Figure 2c,d) in the sink solution versus time at different pH ≡ pHL ) pHR values for the ionic strengths I ≡ IL ) IR ) 2 and 200 mM, respectively. The amino acids were dissolved in the reservoir at each pH value, and their initial concentrations were fixed at cA,L ) 1 mM. The ionic strength of the solutions in both compartments was kept constant using NaCl for all pH values. The higher scatter in the phenylalanine experimental data compared with that of tyrosine is caused by a lower absorbance of phenylalanine in the UV-visible spectrometer measurements compared to tyrosine. Figure 3 shows the fluxes of tyrosine (Figure 3a) and phenylalanine (Figure 3b) across the PCTE/Au/HS(CH2)10COOH membrane (mean pore radius: 7 nm) as a function of external pH at the two ionic strengths I ) 2 and 200 mM. The fluxes were obtained from the slopes of the straight lines in Figure 2. In all cases, the flux decreases with the pH because of the electrostatic repulsion between the negative charges in the amino acid and those in the nanopore surface. This trend is more marked for tyrosine than for phenylalanine because of the higher membrane exclusion of the more negative tyrosine compared with that of phenylalanine. The decrease of the amino acid flux with the pH is less pronounced at the higher ionic strength because of the more effective Debye screening of the electrostatic interactions at high electrolyte concentrations. Note also that both amino acids show the same qualitative behavior with the pH and the ionic strength despite their different hydrophobic nature. All of these experimental facts clearly point out the importance of the electrostatic interaction between the amino acid charges and the fixed charges in the hydrophilic nanopores. The theoretical fluxes of tyrosine (Figure 4a) and phenylalanine (Figure 4b) as a function of external pH at I ) 2 and 200 mM reproduce qualitatively the experimental results of Figure 3. The ionic diffusion coefficients introduced in the calculations are those characteristic of an infinitely dilute aqueous solution: DN+ ) 1.33 × 10-9 m2/s, DCl- ) 2.03 × 10-9 m2/s, DH+ ) 9 × 10-9 m2/s, and DOH- ) 4.5 × 10-9 m2/ s. The surface pKa (pKN) of the carboxylic groups of the mercaptoundecanoic acid SAM on gold has been measured and reported to be 4.8-5.5.46 We have used pKN ) 5 in the calculations of Figure 5a,b, with σ ) 1 e/nm2, in agreement with previous studies using similar membranes44 that gave values
J. Phys. Chem. C, Vol. 111, No. 7, 2007 2969 of σ in the range 0.1-1 e/nm2. (Note that the effective, pHdependent value of the fixed-charge density XNC is lower than XCT in eq 27, as shown in eqs 23-25.) The amino acid pKa values are pK1 ) 2.11 and pK2 ) 9.13 (phenylalanine) and pK1 ) 2.20, pK2 ) 9.11, and pK3 ) 10.10 (tyrosine).47 The aqueous solution diffusion coefficients DA+ ) DA- ) DA( ) 7.1 × 10-10 m2/s (phenylalanine) and DA+ ) DA- ) DA2- ) DA( ) 7 × 10-10 m2/s (tyrosine)48 are used, as a first approximation. The differences between the phenylalanine and the tyrosine theoretical fluxes are minor (except for the more marked electrostatic exclusion and the concomitant lower flux of the more negative tyrosine at high pH values). Since all partition coefficients in eq 21 are assumed to be unity and the two amino acids considered have almost equal isoelectric points, the model predicts a similar pH dependence of the fluxes, as confirmed by the experimental data. The theoretical fluxes begin to decrease at pH ≈ 8, also in agreement with the experiments. Note that, because of the negative fixed charges in the nanopore, the local hydrogen concentration can be higher than that in the external solution (the local pH is lower than the external pH; see, e.g., refs 36-38). The Debye screening effect (increasing the ionic strength decreases the electrostatic exclusion and, therefore, increases the fluxes at high pH) is clearly shown in Figure 4. Although the model calculations tend to underestimate the experimental fluxes, especially for I ) 200 mM, we must emphasize that no particular fitting parameters (fixed-charge concentration, partition and diffusion coefficients, etc.) were used for the membrane and amino acid characteristics (the pore radius and the surface density of ionizable groups were estimated from independent measurements44). The discrepancies between theory and experiment could be due to both the experimental uncertainties in the membrane characteristics (thickness, porosity, and effective radius) and the crude nature of the model assumptions. In particular, mass transport at the nanoscale may have additional effects that were not incorporated in the classical approach employed. (For instance, Holt et al.49 have recently shown high transport rates of water in nanoporous membranes made from carbon nanotubes with an internal pore diameter of less than 2 nm.) Also, the model used considers only the amino acid charge number and ignores then the dipolar character of the charge distribution in the molecule. This dipolar contribution might be important in the interaction of the amino acid with the nanopore fixed charges. In a final effort to show further the effects of the nanopore fixed charges on the amino acid transport, some preliminary experiments with an imposed pH difference (pHL ) 11.5 and pHR ) 2.4) were also conducted at the ionic strength IL ) IR ) 4 mM. In these experiments, the concentration of tyrosine in the reservoir solution was varied between cA,L ) 1.1 mM and cA,L ) 0.1 mM while the sink solution concentration cA,R was initially set to 0.1 mM in all cases. The experimental fluxes of Figure 5a show that amino acid uphill transport (negative fluxes) can occur when a pH difference is imposed in the external solutions. Indeed, Figure 5a shows that the amino acid flux changes its sign from positive to negative (see Figure 1a) for small enough amino acid concentration differences between the reservoir and the sink solutions. To our knowledge, this is the first time that amino acid uphill transport is reported in charged nanopores. An attempt to rationalize the observed phenomena is given in Figure 5b where the amino acid flux is calculated according to the simplified model used here (the experimental points of Figure 5a are redrawn for a better comparison with theory). Overall, the model predicts significantly lower fluxes than those
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Figure 2. Concentration of tyrosine (Figure 2a,b) and phenylalanine (Figure 2c,d) in the sink solution vs time at different pH values for two ionic strengths (2 and 200 mM). The PCTE/Au/HS(CH2)10COOH membrane has a mean pore radius of 7 nm.
Figure 3. Experimental fluxes of (a) tyrosine and (b) phenylalanine across the PCTE/Au/HS(CH2)10COOH membrane (mean pore radius: 7 nm) as a function of external pH at ionic strengths 2 and 200 mM. The fluxes are obtained from the slopes of the straight lines in Figure 2 and the membrane characteristics (thickness, surface area, porosity, and effective radius).
observed experimentally (as noticed previously in Figure 4) although it shows clearly that the theoretical fluxes can assume negative values if the amino acid concentration difference is small enough, in qualitative agreement with the experimental data. The quantitative agreement is however poor because of the model limitations. In particular, the GCF assumption could not be suitable when large concentration gradients occur through the membrane,38,42 as it is the case of the data in Figure 5b for the highest values of cA,R - cA,L and pHL > pHR. More importantly, the model ignores the (local) reaction-diffusion transport of hydrogen through the nanopore. This process should decrease the effective fixed-charge concentration because of the hydrogen association to the (negative) carboxylic acid groups.50 Figure 5b shows indeed that if we arbitrarily decrease the effective surface-charge density in the nanopore, then the model calculations become closer to the observed qualitative trends.
(A more quantitative theory is probably not justified because of the preliminary nature of the uphill transport experiments.) Remarkably, no negative flux is obtained if the fixed-charge density is zero regardless of the concentration difference imposed, which emphasizes once again the importance of the electrostatic interactions for the amino acid transport. Figure 6 shows schematically the effects of the pH gradient and the Donnan and diffusion potentials on the uphill transport of amino acid for cA,L ) 0.3 mM, cA,R ) 0.1 mM, and σ ) 1 e/nm2 (other model parameters as in Figure 5). The concentration and potential profiles are not to scale. When pHL ) pHR ) 11.5 (Figure 6a), most of the amino acid is in anionic form (the calculated values for tyrosine are cA2-,L ≈ 0.29 mM, cA-,L ≈ 0.01 mM, cA2-,R ≈ 0.096 mM, and cA-,R ≈ 0.004 mM). Also, the membrane fixed-charge groups are deprotonated (XNC ≈
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J. Phys. Chem. C, Vol. 111, No. 7, 2007 2971
Figure 4. Theoretical fluxes of (a) tyrosine and (b) phenylalanine as a function of external pH at ionic strengths 2 and 200 mM.
Figure 5. Experimental (a) and theoretical (b) fluxes of tyrosine across the PCTE/Au/HS(CH2)10COOH membrane (mean pore radius: 7 nm) as a function of the amino acid concentration difference between the reservoir and the sink solutions at ionic strength 4 mM. The theoretical fluxes are obtained for the same amino acid and membrane characteristics used in Figure 4 with the values of the surface-charge density σ (e/nm2) shown in the figure.
Figure 6. Effects of the pH gradient and the diffusion and Donnan potentials on the uphill transport of amino acid through the nanoporous membrane (see explanation in the text).
0.47 M). These (negative) membrane fixed charges are compensated by the Na+ ions from the bathing solutions, and the resulting Donnan potential drops ∆φL ) -121 mV ) -∆φR exclude the negative amino acid species from the membrane (cA(0) ≈ 1.6 × 10-4 mM > cA(d) ≈ 5.5 × 10-5 mM). Therefore, the diffusion potential ∆φD ≈ 0 ≈ ∆φM and the (downhill) amino acid flux is very low (JA ≈ 1.3 × 10-12
mol/cm2 s). When pHL ) 11.5 and pHR ) 2.4 (see Figure 6b), the Donnan potential and the total amino acid concentration at the left membrane/solution interface are the same as in Figure 6a, but the corresponding values at the right membrane/solution interface are very different. For pHR ) 2.4, most of the amino acid is in cationic and neutral form (the calculated values are now cA+,R ≈ 0.039 mM and cA(,R ≈ 0.061 mM). Also, most of
2972 J. Phys. Chem. C, Vol. 111, No. 7, 2007 the membrane fixed-charge groups at this interface are now protonated giving a small effective concentration XNC ≈ 1 mM. The corresponding Donnan potential ∆φR ≈ 3 mV allows the positive and neutral forms of the amino acid to enter the membrane (the calculated values are now cA(d) ≈ 0.11 mM > cA(0) ≈ 1.6 × 10-4 mM; note that these values give a concentration gradient within the membrane opposite to that imposed in the external solutions; see Figure 6b). At the same time, the diffusion potential ∆φD ≈ 69 mV drives also the positive form of the amino acid from right to left in Figure 6b. The net result is an uphill flux of amino acid (the calculated value is JA ≈ -2.22 × 10-9 mol/cm2 s). Finally, when pHL ) pHR ) 2.4 (see Figure 6c), most of the amino acid is in cationic and neutral forms (we estimate cA+,L ≈ 0.12 mM, cA(,L ≈ 0.18 mM, cA+,R ≈ 0.039 mM, and cA(,R ≈ 0.061 mM). Also, the fixed-charge groups are protonated throughout the membrane, giving a low effective concentration XNC ≈ 1 mM and small Donnan potentials (∆φL ) -3 mV ) -∆φR). The calculated amino acid concentrations at the membrane/solution interfaces cA(0) ≈ 0.32 mM > cA(d) ≈ 0.11 mM are now close to the external solution concentrations (see Figure 6c), and the net result is a downhill amino acid flux JA ≈ 2.5 × 10-9 mol/ cm2s. Therefore, Figure 6 shows that the uphill transport should be observed when the amino acid concentration gradient in the membrane is opposite to that imposed in the external solutions and the diffusion potential ∆φD > 0. In conclusion, the experimental trends of Figures 3 and 5 can be explained qualitatively taking into account the ionic nature of both the amino acid and the membrane fixed groups, although a quantitative theoretical analysis could require the consideration of the short-range interactions between the amino acid, the water molecules, and the membrane thiol chains.18,19,28,50-57 It is also likely that not only the bulk diffusion through the membrane but also the interfacial kinetics might play a role on the amino acid transport;20,21,26-29,47,51 therefore, the simple Donnan equilibrium assumed here could not be valid. Finally, the set of transport equations should be extended to incorporate the hydrogen reaction-diffusion and solved locally to obtain the axial profiles of the concentrations as well as the fluxes. In any case, the experimental results show that the electrostatic interaction between the amino acid and the nanopore charges significantly influence the transport through the hydrophilic nanopores. The key role of the membrane-charge density has been emphasized previously for the case of uphill transport of ions through ion-exchange membranes58 (see also refs 38 and 39). Also, the pH and ionic strength effects have recently been found to dominate protein transport in the same charged nanopores employed here.59 Acknowledgment. Financial support from the CICYT, Ministerio de Ciencia y Tecnologı´a (Project Nos. MAT200501441 and MAT2006-03097), is acknowledged. References and Notes (1) Ulman, A. An Introduction to ultrathin Organic Films; Academic Press: San Diego, CA, 1991. (2) Hou, Z.; Abbott, N. L.; Stroeve, P. Langmuir 2000, 16, 2401. (3) (a) Chun, K.-Y.; Stroeve, P. Langmuir 2001, 17, 5271. (b) Nishizawa, M.; Menon, V. P.; Martin, C. R. Science 1995, 268, 700. (4) Chun, K.-Y.; Stroeve, P. Langmuir 2002, 18, 4653. (5) Ku, J.; Stroeve, P. Langmuir 2004, 20, 2030. (6) Jirage, K. B.; Hulteen, J. C.; Martin, C. R. Anal. Chem. 1999, 71, 4913. (7) Hulteen, J. C.; Jirage, K. B.; Martin, C. R. J. Am. Chem. Soc. 1998, 120, 6603. (8) Liu, Y.; Zho, M.; Bergbreiter, D. E.; Crooks, R. M. J. Am. Chem. Soc. 1997, 119, 8720.
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