Permeation of a Fully Ionized Species Across a Polarized Supported

Article pubs.acs.org/ac

Permeation of a Fully Ionized Species Across a Polarized Supported Liquid Membrane Matěj Velický,† Kin Y. Tam,‡ and Robert A. W. Dryfe*,† †

School of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, U.K. AstraZeneca, Mereside, Alderley Park, Macclesfield, Cheshire SK10 4TG, U.K.

‡

ABSTRACT: An analytical technique for the detection of permeation of a fully ionized analyte across a lipophilic membrane is reported. The system, which is comprised of two aqueous compartments (donor and acceptor) separated by a supported liquid membrane, is based on the parallel artificial membrane permeation assay (PAMPA), widely used in the drug discovery process to estimate permeability in vivo. The in situ spectroelectrochemical method developed here employs mechanical stirring of the solution phases on either side of the membrane, external polarization of the membrane, and in situ detection of the analyte via UV−vis spectrophotometry. The flux of the crystal violet cation across the membrane is simultaneously measured via UV−vis spectrophotometry and voltammetry/chronoamperometry as a function of applied potential. The relative contribution of two permeation modes, i.e., that due to naked ions and ion-pairs, is thereby quantified. The open circuit potential difference between the two aqueous compartments and the cyclic voltammetric response are also recorded as a function of time and compared with the predicted values.

S

to reconsider the pH-partition hypothesis, widely cited in the pharmaceutical community. This hypothesis assumes that only the neutral fraction of an ionizable molecule can permeate through lipophilic membranes.14,15 The pH-partition is a good “rule of thumb” for permeation/partition of drugs. It has, however, been criticized as being an oversimplification, neglecting the fact that ionized species can also permeate biological/artificial membrane, albeit at much slower rates than nonionized species.16,17 Specifically a number of partition, permeation, and diffusion studies in the last 2 decades have presented evidence that both ionic and ion-pair flux across lipophilic barriers does occur.18−23 The hydrodynamically controlled version of the membrane permeation assay also showed indirect evidence of ion/ion-pair transfer across the lipophilic SLM when the permeability-pH profiles of ionizable drugs were studied.5 The presented permeation/polarization method has been applied to a fully ionized species, crystal violet (tris(4(dimethylamino)phenyl)methylium) cation, in order to investigate ionic flux across the lipophilic membrane without masking effects of any highly permeable uncharged fraction, as can occur with ions formed from weak bases or acids. An earlier attempt was made to apply this method to a partially ionized drug molecule, cetirizine, but the high flux of its uncharged fraction effectively hindered the detection of the ionic flux across the membrane. Also, the complex membrane

ystems with a supported liquid membrane (SLM) separating two aqueous compartments are of interest to fields as diverse as pharmaceutical research, liquid/liquid electrochemistry, and liquid/liquid extraction/separation processes. Notably the parallel artificial membrane permeation assay (PAMPA) is a passive diffusion experiment, which has become popular for high-throughput screening in the early stages of drug discovery, since it is believed to mimic the transfer of a drug molecule across the intestinal wall. It is comprised of two aqueous phases, donor and acceptor, which are separated by a lipid solution immobilized on the hydrophobic membrane.1−4 This passive diffusion method was recently altered to an assay with controlled hydrodynamics in our laboratories,5 following earlier implementations of stirring in PAMPA.6 Electrochemical methods have been applied extensively to SLM systems to study ion transfer across the membrane.7−10 The application of potential differences in the range of 1−300 V, in dc mode, between the two aqueous phases adjacent to the SLM was used for liquid/liquid extraction of drugs from model and biological samples.11−13 There are, however, no reports directly related to electrochemical polarization of SLMs in permeability studies. The method presented here combines hydrodynamically controlled permeation with electrochemical polarization of the membrane. A pair of reference and counter electrodes is placed in both the donor and acceptor phases, allowing application of the potential difference between the two aqueous phases and detection of the current/charge passed through the organic membrane, which is rotated at a constant rate of 120 rpm (12.6 rad s−1). Simultaneously, the total flux across the SLM is detected in the acceptor compartment using UV−vis spectrophotometry. This experiment was motivated by a need © 2012 American Chemical Society

Received: January 3, 2012 Accepted: January 29, 2012 Published: January 30, 2012 2541

dx.doi.org/10.1021/ac300016n | Anal. Chem. 2012, 84, 2541−2547

Analytical Chemistry

Article

Figure 1. (Left) Schematic diagram of the modified permeation cell adapted for spectrophotoelectrochemical analysis: 1, rotation controller; 2, paddle; 3, glass tube (donor compartment); 4, spacer disk; 5, PTFE cogwheel attached to the glass tube; 6, supported liquid membrane; 7, acceptor solution; 8, Ag/AgCl reference electrode; 9, platinum counter electrode; 10, saturated KCl solution (inner reference electrode solution); 11, glass frit; 12, PTFE acceptor cell; 13, steel pad; 14, steel pad screw; 15, quartz window; 16, quartz lens; 17, fiber-optic cable; 18, UV−vis optical path. Electrode connections to potentiostat terminals are shown. (Right) Schematic of the various possible mode of analyte permeation across lipophilic membranes, via uncharged, ion-pair and ionic pathways. The method presented here focused on the fully ionized species and therefore latter two modes of transport.

system, consisting of a pair of reference and counter electrode in each aqueous phase, is depicted in Figure 1. The counter− reference electrode pairs were shorted together with a 100 nF capacitor to reduce the induced electrical noise (Farnell, Leeds, U.K.). UV−vis spectra were acquired in the acceptor using a DH-2000-BAL spectrometer (supplied by Ocean Optics, Duiven, The Netherlands) equipped with a DH-2000-BD deuterium bulb, DH-2000-BH tungsten halogen bulb, and fiber-optic cable and controlled using a USB2000 interface (Micropack GmbH, Ostfildern, Germany). Reagents and Solutions. Sodium dihydrogen phosphate (98.5%), buffer solutions for pH meter calibration (pH 4.00, 7.00, 10.0), crystal violet (tris(4-(dimethylamino)phenyl)methylium, VETRANAL, analytical standard, purchased as the chloride salt), 1,9-decadiene (98%), and tetradodecylammonium tetrakis(4-chlorophenyl)borate (TDDATPBCl4 ) (≥98%) were purchased from Sigma-Aldrich, U.K. Potassium chloride (99%), sodium hydroxide (98.8%), and hydrochloric acid (analytical reagent grade, 38%) were obtained from Fisher Scientific UK Ltd. Water, of 18.2 MΩ cm resistivity, purified by a “PURELAB” Ultrafiltration unit (Elga Process Water, Marlow, U.K.) was used for solution preparation.

composition, i.e., solvent, electrolyte, and mixture of lipids, is a difficult system for an initial study.24 Therefore, we have chosen a simple model membrane, only containing a nonpolar solvent and supporting electrolyte. Conceptually, the method reported here is analogous to an ion selective electrode with a liquid membrane. Figure 1 depicts the permeation cell setup and a scheme with three possible modes of transport of an ionizable molecule.

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EXPERIMENTAL SECTION Apparatus. The general design of the permeation cell has been reported previously.5 The upper aqueous compartment, i.e., the donor, containing the analyte prior to the start of the experiment was made of precision ground glass (Glass Precision Engineering Ltd., Leighton Buzzard, U.K.). The lower aqueous compartment, i.e., the acceptor, which was made of polytetrafluoroethylene (PTFE), was built in-house. Rotation of the donor compartment, i.e., the supported liquid membrane, was controlled using a model 616 rotating-disk controller (EG&G Parc). Solution pH was measured using a HI991300 pH meter (Hanna Instruments). The present modified cell, which was equipped with a four electrode 2542



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Membrane Preparation. “Durapore” Poly(vinylidene fluoride) (PVDF) hydrophobic membrane filters (0.45 μm pore size, 125 μm thickness, 75% porosity, 13 mm diameter) supplied by Millipore, were attached to the donor glass tubes using Araldite Rapid glue (Bostik Ltd., Stafford, U.K.) and cut to fit the tube outer diameter after 2 h of drying (acceptor-side membrane area = 1.04 cm2, donor-side membrane area = 0.79 cm2). The adhesive-free area of the membrane, corrected for its porosity, was 0.68 cm2. The membrane was then soaked with a solution of 1 × 10−2 M TDDATPBCl4 in 1,9-decadiene. TDDATPBCl4 served as the supporting electrolyte for the organic phase as well as a source of counterions for crystal violet ion pairing. Electrochemical Measurements. The permeation cell can be described as follows:

organic phase (nitrobenzene).26 Crystal violet is an organic dye with an absorbance maximum at 590 nm and a corresponding molar absorption coefficient of 8.70 × 104 M−1 cm−1 (water) at neutral pH.25 The molar absorption coefficient in the pH 7.4 sodium phosphate buffer (3 × 10−2 M buffer concentration) was determined to be 8.11 × 104 (± 700) M−1 cm−1 (at 590 nm). The potential difference between the acceptor and donor phase was varied between limits of −1 and +1 V while the membrane was rotated at a constant rate of 120 rpm (12.6 rad s−1). The cyclic voltammogram of the crystal violet transfer is shown in Figure 2. Initially, a blank cyclic voltammogram on a system with

Ag(s)|AgCl(s)|3 × 10−2 M NaH2PO4 , (cD(0) − x) M crystal violet, pH 7.4(aq) ||(1 × 10−2 M TDDATPBCl 4(1,9‐decadiene)|| (3 × 10−2 M NaH2PO4 , (VD/VA × x) M crystal violet, pH 7.4(aq) AgCl(s) Ag(s)

where cD(0) is the initial concentration of crystal violet in the donor (100 μM), x is the time dependent concentration disappearance of crystal violet from the donor, and VD and VA are the volumes of the donor and acceptor, respectively. Sodium phosphate acts as a supporting electrolyte as well as pH buffer. The four electrodes were connected to the potentiostat (Autolab PGSTAT 100, Metrohm-Autolab BV, Utrecht, The Netherlands) as follows: Counter 1, working; Reference 1, sense; Counter 2, counter; Reference 2, reference. In addition to the cyclic voltammetric and chronoamperometric measurements performed with the four-electrode configuration, opencircuit potential experiments were also performed using the reference electrodes to measure the potential difference across the SLM in the absence of current flow. The Ag/AgCl reference electrodes were made of a silver wire covered with layer of silver chloride in contact with saturated KCl solution. The reference electrode was enclosed in a glass tube ensuring the contact with the surrounding liquid via a glass frit (SciMed Ltd., Cheadle, U.K.). Silver wire (0.75 mm diameter, 99.99%), platinum wire (0.5 mm diameter, 99.99%), and platinum mesh (0.1 mm plain weave wire, 420 per cm2, open area 62.7%) were obtained from Advent Research Materials (Oxford, U.K.). The nonpolar solvent, 1,9-decadiene, immobilized on the PVDF membrane, is the main source for high resistivity of the permeation cell. Even after addition of the organic supporting electrolyte, TDDATPBCl4, the resistivity of the membrane was found to be 30−50 kΩ m. The resistivity of the membrane was found from the solution resistance measured via a potentiostat and the approximate membrane thickness (the resistivity of the aqueous phase was considered negligible in comparison). Internal IR compensation was applied (∼10 kΩ) via the potentiostat to correct the potential values.

Figure 2. Cyclic voltammogram of crystal violet transfer across the supported liquid membrane. The current flowing through the membrane is recorded as a function of the potential difference between the acceptor and donor phase at a scan rate of 20 mV s−1. The voltammetric cycle was swept in both directions from the starting potential difference of 0 V: green dashed curve, negative potentials first; red dotted curve, positive potentials first. A blank cyclic voltammogram of a system without the analyte was also recorded (black solid curve).

no analyte was recorded. The potential window, limited by the transfer of the organic electrolyte ions into and out of the supported liquid membrane, was found to be about −0.7 V to +0.6 V (black solid curve). The transfer of the crystal violet across the membrane was measured, starting from 0 V toward the negative potential first (green dashed curve). As crystal violet is positively charged at these conditions, it transfers from the donor phase to the acceptor as the potential difference between the acceptor and donor is swept to negative values. The direction of the flux induced by the polarization of the membrane is therefore identical with the flux induced from the concentration gradient, and a transfer peak with the current maximum of −4 μA (relative to the background current seen in the “blank” case) is observed at −0.73 V. On the reverse shoulder of the cyclic voltammogram, a current maximum of 2.5 μA (corrected for the blank) is observed at +0.3 V. This peak corresponds to the reverse transfer of crystal violet from the acceptor to the donor phase (against the concentration gradient). The red dotted curve in Figure 2 shows the cyclic voltammogram with the sweep direction toward a positive potential first. Because of the fact that some crystal violet transfer occurs spontaneously (even at slow rate) across the membrane, a small transfer peak is observed at about +0.2 V. The size of the peak indicates that the amount of analyte transferring from acceptor-to-donor is smaller than in the

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RESULTS AND DISCUSSION Cyclic Voltammetry. Cyclic voltammetry was used to study the transfer of the crystal violet cation across the supported liquid membrane. It is noted that the tetraphenylborate salt of crystal violet has been previously used in liquid/ liquid electrochemistry as a supporting electrolyte for the 2543



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potential was applied. At 600 s the potential was stepped to, and held at, a set value between −0.6 and +0.4 V for another 600 s. The absorbance profiles show that the analyte flux across the membrane in the donor-to-acceptor direction increases progressively for applied potentials between 0 and −0.6 V. Note that a fresh permeation cell was set up for each experiment. At 1200 s, a positive potential difference of +0.4 V was applied. Figure 3a shows that the decrease in absorbance signal corresponds to the induced reverse flux of the analyte from acceptor-to-donor. The corresponding current response for some of these absorbance curves is shown in Figure 3b. The current−time curves show a brief transient for about 30 s and then remain at a relatively constant value for the first course of the experiment (600−1200 s). The second part of the chronoamperometric measurement (1200−1600 s, potential difference of +0.4 V) shows the current decaying exponentially with time. The inset in Figure 3a shows a detail of the absorbance profiles acquired for the potential difference +0.4 V (upper, black curve) and also for the case where no potential difference was applied (lower, red curve). Note that the fully ionized analyte transfers across the supported liquid membrane only due to the concentration gradient between the donor and acceptor phase. This result supports previous observations of ion/ion-pairs transfer across lipophilic barriers,17,20−23 which was originally disputed by the pH-partition hypothesis.15 Comparison of the two absorbance traces shows that application of the positive potential difference effectively stops the flux of the analyte across the supported liquid membrane that occurs due to the concentration gradient between the two aqueous phases. Charge and Permeability Analysis. The overall charge passed through the membrane at various applied potential differences was determined from integration of the chronoamperometric curves in Figure 3b. The crystal violet permeability coefficient can be found from the analyte concentration (absorbance measurement) in the acceptor compartment. The detailed procedure of ionic permeability coefficient determination from the concentration−time dependence has been reported previously.5 Briefly, the concentration was transformed into a function, k, (see below) whose logarithm is linearly dependent on time, t:

previous case (green dashed curve), where application of negative potentials induced the transfer of the analyte to the acceptor. The negative potential shoulders of the two cyclic voltammograms (green dashed and red dotted) are almost identical. Combined Spectrophotometry and Chronoamperometry. A series of chronoamperometric measurements were combined with spectrophotometric monitoring of the acceptor composition change, based on the results from cyclic voltammetry. Figure 3 shows the experiment where the UV−vis

Figure 3. Chronoamperometric and simultaneous spectrophotometric measuremement of crystal violet transfer across the supported liquid membrane. The graph shows (a) UV−vis absorbance (590 nm) recorded in the acceptor as a function of time for the applied potential difference (acceptor/donor) in the range of −0.6 to +0.4 V, (b) corresponding current response. No potential was applied during the first 600 s of the experiment, and then a potential difference was applied for another 600 s. At 1200 s, a positive potential of +0.4 V was applied (for −0.6 to 0 V potentials only in the 600−1200 s period). The inset graph of part (a) shows UV−vis absorbance recorded at 590 nm in the acceptor phase as a function of time. Upper (red) curve, no potential difference applied during the course of the experiment. Lower (black) curve, no potential difference applied for the first 600 s, and then a potential difference of +0.4 V was applied.

ln(k) = −at

(1)

and the ionic permeability coefficient in the donor-to-acceptor direction, PiD→A, was determined from the slope parameter of eq 1, a, defined as follows: a=

V ⎞ APiD → A ⎛ ⎜1 + D ⎟ VD ⎝ VA ⎠

(2)

where A is the membrane area and VD and VA are the donor and acceptor phase volumes, respectively. The function k can be approximated by the following equation (assuming negligible membrane retention of the analyte):

absorbance was measured in the acceptor compartment simultaneously with the applied potential difference between the two aqueous phases, ΔEacc/don. The applied potential difference was varied between −0.6 and +0.4 V. The UV−vis absorbance recorded at 590 nm as a function of time is shown in Figure 3a. During the first 600 s of the experiment, only membrane rotation at 120 rpm was maintained and no

V b − A cA(t ) a VD b cD(0) − a

cD(0) − k=

(3)

where cD(0) is the analyte concentration in the donor phase at the beginning of the experiment, cA(t) is the analyte 2544



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Table 1. Charge, Current, and Permeability Coefficient Determined for the Crystal Violet Cation As a Function of Applied Potential Differencea PiD→A (elchem)/10−6 cm s−1

PiD→A (UV−vis)/10−6 cm s−1

permeability ratio (UV−vis/elchem)

0.032 0.003

−0.005 −0.001

−0.054 −0.485 −0.858 −1.480 −3.267 −4.619

0.009 0.074 0.131 0.219 0.496 0.700

−0.1 1.1 7.9 8.5 64.3 111.9 147.1 317.7 400.4

983 869 854 673 640 572

ΔEapp/V

ΔEcor/V

Q/mC

Iave/μA

0.400 0.200 none 0.100 0.000 −0.100 −0.200 −0.400 −0.600

0.397 0.200 none 0.106 0.053 −0.006 −0.037 −0.041 −0.092

0.019 0.002 −0.034 −0.291 −0.515 −0.859 −1.952 −2.750

a

The permeability coefficients are found from two different methods, and the ratio between the two is given, as explained in the text. The correction of the potential difference term is also explained below.

data and eqs 1−4, is marked “UV−vis”, and the second, using chronoamperometric data and eqs 5−7, is denoted “elchem”, in Table 1. Comparison of the ionic permeability values obtained using the two techniques shows that the overall permeability determined via UV−vis in the acceptor compartment (corresponding to the overall analyte transfer) is several orders of magnitude higher than those determined via the charge passed through the membrane (corresponding to purely ionic transfer). The ratio between the permeabilites is also listed in Table 1. Its value suggests that, although the applied potential significantly increases the flux of crystal violet from the donor to acceptor, the main transport mechanism across the membrane is most likely to be via ion-pairs. The applied potential difference most likely provides extensive polarization of the organic phase which increases the amount of counterions (anions) on the donor side of the membrane. As a result, more ion pairs between crystal violet (tris(4-(dimethylamino)phenyl)methylium) and tetrakis(4-chlorophenyl)borate are formed and permeate through the membrane, driven by the concentration gradient between the donor and acceptor. The fact that the ratio decreases for potentials below 0.1 V indicates that the ion-pair transfer mechanism becomes less dominant when moving to more negative potential difference. At the most positive potential differences, a flux reversal is seen in the electrochemical permeability, where the applied potential is sufficient to reverse the overall flux arising from the concentration gradient. The permeability ratios for the first three entries in Table 1 are therefore not listed as the ratio becomes more difficult to interpret because of the opposing flux direction, due to the different sensitivities of ions and ionpairs to the applied potential. Most charge transfer rates are assumed to be exponentially dependent on the driving force, in this case, the applied potential difference. Hence plotting the logarithm of the current or permeability against the applied potential difference should yield a linear dependence.27 However, a semilogarithmic current−potential analysis showed otherwise. One source of deviation is the high resistivity of the supporting liquid membrane; hence, an attempt was made to correct the apparent potential difference, ΔEapp, for the ohmic IR-drop using the following equation:

concentration in the acceptor phase at time t, and the term b/a is defined as: V cD(0) b = D ⎛ a VA V ⎞ ⎜1 + D ⎟ VA ⎠ ⎝

(4)

The charge, Q, passed through the membrane is related to the molar diffusive flux of the ionic species, Ji, by the following equation:27 Ji =

Q z iFAt

(5)

where zi is the charge of the transferred ionic species i and F is the Faraday constant. Equation 5 assumes that the current flowing through the membrane (and therefore molar diffusive flux) is constant with time t. On the basis of the experimental data (Figure 3), this is a reasonable assumption for times longer than 30 s allowing an approximate quantification of the potentialinduced permeation. Applying Fick’s first law of diffusion to a homogeneous membrane, we arrive at:28 Ji = PiD → AcD − PiA → DcA

(6)

where PiD→A and PiA→D denote the ionic permeability coefficients for the donor-to-acceptor and acceptor-to-donor transport, respectively, and cD and cA are the bulk concentrations of the ions in the donor and acceptor phases, respectively. Assuming that the ion concentration in the acceptor phase is negligible compared to the donor phase value and therefore bulk concentration in the donor phase has practically not changed from the initial value, cD(0), we can calculate the donor-to-acceptor permeability coefficient of the transferred ion as:

PiD → A =

Ji cD(0)

(7)

The charge passed, the average current, and ionic permeability coefficient values, obtained at different applied potentials, are listed in Table 1. It should be noted that the permeability coefficient, determined when no potential difference is applied, falls between the permeability coefficients obtained at applied potential differences of +0.1 and +0.2 V. This corresponds well with the measured open-circuit potential of +0.1 V (see below). Since the experimental method comprised of two independent techniques, i.e., electrochemical and UV−vis spectrophotometric, the ionic permeability coefficient has been determined using two different approaches. The first approach, using UV−vis spectrophotometric

ΔEcor = ΔEapp − IR

(8)

where ΔEcor is the potential difference applied (for the system of infinite conductivity), I is the current flowing through the membrane, and R is the resistance of the membrane. The 2545



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resistance, R, was obtained from the best linear fit of currentcorrected potential dependence. Briefly, a range of resistance values (0−200 kΩ) were used to plot logarithm of the current (or permeability) as a function of the corrected potential (eq 8). The optimal resistance corresponding to the best linear fit was determined to be 110 kΩ, which corresponds to resistivity of 37 kΩ m (assuming a membrane thickness of 200 μm and an area of 0.68 cm2 for the SLM). The corrected potential values are also listed in Table 1. Potential Measurement. As mentioned earlier, the permeability coefficient obtained without an applied potential difference corresponds to the one obtained at a potential difference between +0.1 and +0.2 V (Table 1). This was confirmed via measurement of the open circuit potential difference between the aqueous phases. The graph in Figure 4

ment, allows the standard potential difference to be determined 0 as the best fit of eq 9. The value of ΔEacc/don = − 0.115 V was found. The time-dependent potential difference based on the 0 calculated ΔEacc/don and the measured cA(t) is also plotted in Figure 4 (blue, dashed curve) and shows an excellent agreement with the experimental curve for times >250 s. The inset in Figure 4 shows a comparison of the concentration in the acceptor, which was the solid black line measured via UV−vis absorbance the dashed blue line calculated retrospectively from eq 9.

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CONCLUSIONS A hydrodynamically controlled permeation method combining electrochemical and UV−vis spectrophotometric detection was used to study the transfer of a fully ionized solute through a supported liquid membrane separating two aqueous compartments. The effect of membrane polarization on permeation was studied using cyclic voltammetry and chronoamperometry with simultaneous detection of the analyte flux in the acceptor phase. The analysis of both electrochemical and UV−vis results shows that a small applied potential (0−100 mV) in the direction corresponding to the passive flux of the analyte, i.e., donor to acceptor, significantly enhances the permeability of the analyte. The advantage of using combined electrochemical and UV−vis detection is that these methods allow separation of the two transfer mechanisms, due to naked ions and ion-pairs, since the former detects the ionic flux, while the latter detects the total flux of analyte. More detailed analysis of the two detection techniques thus shows that transfer via ion-pairs occurs at a rate that is close to 3 orders of magnitude higher than the ionic one. The open circuit potential measurements have confirmed that the two detection methods are mutually consistent and the potential−concentration dependence follows the Nernst equation. The above results are a valuable confirmation of the limited applicability of the pH-partition hypothesis, which has been a subject of debate within the pharmaceutical community for some time.

Figure 4. Open circuit potential difference between the acceptor and donor phase. The dotted curves (red, green, and black) are three repeated measurements started immediately upon the permeation cell assembly. The blue solid curve is the potential difference calculated from eq 9, using the concentration data acquired simultaneously with the potential measurement. The inset graph shows the analyte concentration measured in the acceptor (black, solid curve) and the concentration calculated retrospectively using eq 9 (blue, dashed curve).

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AUTHOR INFORMATION

Corresponding Author

*Phone: +44 (0)161-306-4522. Fax: +44 (0)161-275-4734. E-mail: [email protected].

shows three repeats of an open-circuit potential difference between the acceptor and donor phase, ΔEacc/don(t), measured immediately after the permeation cell was assembled and rotation started (the dotted points in Figure 4). All three repeats follow the same trend and converge between about +0.09 and +0.11 V. This value corresponds well with the observation that the permeability coefficient obtained without membrane polarization falls between permeability coefficients obtained for a potential difference +0.1 and +0.2 V (Table 1). The Nernst equation relates the time-dependent potential difference to the concentration of the permeating analyte in the acceptor phase as follows:

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank our industrial collaborator, AstraZeneca, and EPSRC for funding for M.V.

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REFERENCES

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RT ⎛ cD(0) − cA(t ) ⎞ 0 ΔEacc/don(t ) = ΔEacc/don + ln⎜ ⎟ z iF ⎝ cA(t ) ⎠ (9) 0 ΔEacc/don

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Permeation of a Fully Ionized Species Across a Polarized Supported

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