Effective concentration difference model to study the effect of various factors on the effective diffusion coefficient in the dialysis membrane

Cellulose acetate dialysis membrane (CDM) has been used in the diffusive gradients in thin films (DGT) technique, where accurate diffusion coefficients are essential for the assessment of the concentrations of labile metal in solution. Effective concentration difference model (ECDM), based on the assumption that the effective diffusion coefficient of metal ion in the dialysis membrane is determined by the effective concentration difference (ΔC(e)) across the dialysis membrane, is proposed and applied to study the effect of ionic strength, binding agent, ligands and Donnan potential on the effective diffusion coefficient. The effective diffusion coefficients of Cd(2+) through the dialysis membrane immersed in receptor solutions with binding agent were almost the same as those in receptor solutions without binding agent at higher ionic strengths (0.01-1 M) but much higher than those at lower ionic strengths (0.001-0.0001 M). The effective diffusion coefficients of Cd(2+) through the dialysis membrane immersed in deionized water receptor solutions with binding agent were not significantly different from those in synthetic receptor solutions (receptor solutions with various ionic strengths) with binding agent. The DGT-labile fractions were measured in synthetic solutions and natural waters, which indicated that the effective diffusion coefficients, through the dialysis membrane immersed in the deionized water solution with binding agent as receptor solution and in the spiked natural water as source solution, were more suitable for DGT application.     

Use of the diffusion gradient thin film method to measure trace metals in fresh waters at low ionic strength

The diffusion gradients in thin films (DGT) method was investigated and used to measure trace metal concentrations in river water. The principle of DGT is that trace metal ions diffuse through a thin polyacrylamide gel film (the diffusion gel layer) and are subsequently immobilised and concentrated on a layer of Chelex-100 resin embedded in another polyacrylamide gel film (the resin gel layer). These layers are mounted in a plastic holder, which exposes a fixed area of the diffusion gel layer to the water being monitored. Replacement of the normal agarose cross-linked diffusion gel with bisacrylamide cross-linked gel altered the ion uptake properties of DGT. The bisacrylamide cross-linked gel weakly, and with little selectivity, bound metal ions prior to their irreversible binding to Chelex-100. Trace metal ion uptake by these DGT devices was thus dependent on ionic strength and temperature, although the ionic strength effect is relatively small for most natural waters and negligible in sea water. The concentrations of Cd, Co, Cu, Ni, Pb, and Zn in the Water of Leith, an urban stream in Dunedin, New Zealand, were measured by DGT and the results compared with total dissolved concentrations of these metals measured in conventional (bottle) samples collected in parallel with the DGT monitoring. Greater than 90% of the total dissolved Cd and Zn; 20-40% of the total dissolved Co, Ni, and Pb; and 5% of the total dissolved Cu was available to the DGT method.     

Diffusion and partitioning of cations in an agarose hydrogel

Self- and mutual diffusion were measured in a low-melt 1.5% agarose hydrogel as a function of ionic strength (0.1-100 mM) and pH (3-7) for Cd(2+) and a charged rhodamine derivative. Self-diffusion was measured by fluorescence correlation spectroscopy, whereas mutual diffusion was evaluated using a diffusion cell. In contrast to the results observed for the diffusion cell, self-diffusion of rhodamine 6G increased from 50 to 90% of that found in water as the ionic strength increased from 0.1 to 100 mM (pH = 6). The combined observations of decreasing diffusive flux in parallel with an increasing diffusion coefficient were attributed to the gel's Donnan potential. Donnan potentials obtained voltammetrically using a Au amalgam microelectrode varied from -30 to 0 mV as the ionic strength increased from 0.1 to 100 mM (pH = 6). At the low ionic strengths, Donnan potentials of this magnitude accounted for a 13× enhancement of Cd(2+) concentrations in the hydrogel, which was consistent with measurements obtained by a nitric acid extraction of the gel (15×) and able to explain the apparent discrepancy between mutual and self-diffusion measurements. The overall diffusion of the positively charged substrates decreased as the pH was decreased from 12 to 3.     

Performance of the diffusive gradients in thin films technique for measurement of trace metals in low ionic strength freshwaters

A series of experiments were undertaken to investigate the effect of ionic strength and the concentration of free sodium ions in the resin gel on the performance of the diffusive gradients in thin films (DGT) technique. When the free sodium ion concentration in the resin gel was estimated by the time-dependent release into solution, it agreed with a previous estimate. However, equilibration with different volumes of water gave a higher value, suggesting that inherent averaging in the time-dependent release method underestimates the free concentration. DGT measurements of Cu and Cd were made over a wide range of ionic strengths (from 3 μmol l⁻¹ to 0.8 mol l⁻¹). For all the ionic strengths above 100 μmol l⁻¹ there was no significant difference between measurements made by DGT and measurements made directly on the solution using atomic absorption spectroscopy. Below 100 μmol l⁻¹ results were erratic. They did not comply with a theory that predicts high results for DGT based on enhancement of the diffusion coefficient of trace metal cations by counter diffusion of sodium ions. When Cd in solutions with a range of ionic strengths was measured by DGT there was no difference whether the resin gels were in Na or Ca form. Rather than counter diffusion of Na ions, it is suggested that the spurious behaviour at low ionic strength is due to interactions of the trace metals with the diffusion gel when there are insufficient excess cations present.     

Effect of acid-base equilibria on the donnan potential of layer-by-layer redox polyelectrolyte multilayers

In polymer films carrying an excess of fixed charge the electrostatic penalty to bring ions of same charge from the bathing electrolyte into the film sets a membrane potential (Donnan Potential) across the film-electrolyte interface. This potential is responsible for the ionic permselectivity observed in polyelectrolyte membranes. We have used electrochemical measurements to probe the dependence of the Donnan potential on the acid-base equilibrium in layer-by-layer self-assembled polyelectrolyte multilayers. The voltammperogram peak position of the Os(III)/Os(II) couple in self-assembled polyelectrolyte multilayers comprised of poly(allylamine) derivatized with Os(bpy)(2)PyCl+ and poly(vinylsulfonate) was recorded in solutions of increasing ionic strength for different assembly and testing solution pH. Protonation-deprotonation of the weak redox poly(allylamine) changes the fixed charge population in the as prepared (intrinsic) self-assembled redox polyelectrolyte multilayers. For films assembled in solutions of pH higher than the test solution pH, the Donnan plots (E(app) vs log C) exhibit a negative slope (anionic exchanger) while for films assembled at lower pH than that of the test solution positive slopes (cationic exchanger) are apparent. The ion exchange mechanism has been supported by complementary electrochemical quartz crystal microbalance. X-ray photoelectron spectroscopy and infrared reflection-absorption spectroscopy experiments demonstrated that the as prepared films have a memory effect on their protonation state during assembly, which leads to the observed dependence of the Donnan potential on the adsorption pH.     

Electrokinetics of diffuse soft interfaces. III. Interpretation of data on the polyacrylamide/water interface

Streaming potential measurements were carried out on a family of polyacrylamide-co-sodium acrylate gels cross-linked with N,N'-methylenebisacrylamide in a homemade electrokinetic cell. Measurements of the ionic conductivity within thin films of these gels allowed the equilibrium Donnan potential difference between the bulk gel and the bulk electrolyte environments to be estimated at various ionic strengths. The resulting Donnan potential data were combined with the directly measurable streaming potential data and used to evaluate the diffuse soft interface model of electrokinetics (Langmuir 2004, 20, 10324). The model introduces the concept of a gradual decay of polymer density and fixed charge density within a narrow inter-phase at the gel/solution interface. The nature of the decay at the interface has a dramatic effect on the magnitude of the streaming potential as predicted by the diffuse soft interface model. In this investigation, the gradual decay of polymer density within the inter-phase is described with a hyperbolic tangent function. For the gels mentioned, the characteristic length scale of the decay, alpha, as calculated from the fit to the model, increases significantly with decreasing ionic strength, suggesting an osmotically driven swelling of the loosely cross-linked polymer chains at the interface. The experimental data and the results of the fitting are discussed in terms of the physical picture of the interface and compared to fitting results for a model which assumes a simple step function at the gel-solution interface.     

Cobalt(II) and Nickel(II) Transfer through Charged Polysulfonated Cation Exchange Membranes

The transport of Co(II) and Ni(II) ions through charged polysulfonated ion exchange membranes under Donnan dialysis conditions has been studied as a function of pH gradient at 25 degrees C. In the Donnan dialysis process, the membrane is bounded by two electrolyte solutions, the one side (donor phase) initially containing metal salts and the other H(2)SO(4) with no external potential field applied. The transport of metal ions through membranes was correlated with the flux data as well as with estimated diffusion coefficients and was found to depend on the interaction between the fixed groups in the membrane and the metal ions. It was observed that the pH gradient influences the transport of metals and the flux of ions increases with H ion concentration in the receiver phase. Copyright 2000 Academic Press.     

Ion transport in sulfonated nanoporous colloidal films

The surface of self-assembled nanoporous silica colloidal crystalline films comprised of 184-nm-diameter silica spheres has been sulfonated using 1,3-propanesultone. The transport of ions through the sulfonated films has been studied using cyclic voltammetry in water as a function of ion charge, pH, and solution ionic strength. We found that the flux of anions through the sulfonated colloidal films is reduced, while the flux of cations is increased, compared to the unmodified colloidal films. This behavior is pH-dependent and is due to electrostatic repulsion/attraction that can be modulated by changing the ionic strength of the contacting solution.     

Segmented sediment probe for diffusive gradient in thin films technique

A new modification of a constrained sediment probe was tested for application in the diffusive gradient in thin films technique (DGT). The sediment probes packed with agarose based resin and diffusive gels were exposed under laboratory conditions to well-mixed test solutions of cadmium and nickel as model elements. The reproducibility of metal uptake in segments (strips) of resin gel with anchored 8-hydroxyquinoline functional groups (Spheron-Oxin? ion exchanger) was studied. The relative yield of uptake of metals in resin gel strips, determined as the ratio of the time-averaged DGT-measured metal concentration and the concentration of a metal in the test solution, showed that the effective sampling area was larger than the geometric area of the resin gel strip. This relative yield is in very good agreement with the theoretical value obtained by the Finite Element Method (FEM) in calculation of diffusion processes. The performance of the modified constrained probe is demonstrated by an example of uranium, iron and manganese depth profiling in a spiked sediment core. Utilization of the new segmented sediment probe in the DGT technique is very simple. Its application does not require special devices and labor-intensive procedures. It can provide sediment depth profiles of metals with the resolution down to the millimetre level.     

Chemodynamics of metal complexation by natural soft colloids: Cu(II) binding by humic acid

The chemodynamics of Cu(II) complexation by humic acid is interpreted in terms of recently developed theory for permeable charged nanoparticles. Two opposing electric effects are operational with respect to the overall rate of association, namely, (i) the conductive enhancement of the diffusion of Cu(2+), expressed by a coefficient f(el), which accounts for the accelerating effect of the negative electrostatic field of the humic particle on the diffusive transport of metal ions toward it, and (ii) the ionic Boltzmann equilibration with the bulk solution, expressed by a factor f(B), which quantifies the extent to which Cu(2+) ions accumulate in the negatively charged particle body. These effects are combined in the probability of outer-sphere metal-site complex formation and the covalent binding of the metal ion by the complexing site (inner-sphere complex formation) as in the classical Eigen mechanism. Overall "experimental" rate constants for CuHA complex formation, k(a), are derived from measurements of the thermodynamic stability constant, K*, and the dissociation rate constant, k(d)*, as a function of the degree of metal ion complexation, θ. The resulting k(a) values are found to be practically independent of θ. They are also compared to theoretical values; at an ionic strength of 0.1 mol dm(-3), the rate of diffusive supply of metal ions toward the particles is comparable to the rate of inner-sphere complex formation, indicating that both processes are significant for the observed overall rate. As the ionic strength decreases, the rate of diffusive supply becomes the predominant rate-limiting process, in contrast with the general assumption made for complexes with small ligands that inner-sphere dehydration is the rate-limiting step. The results presented herein also resolve the discrepancy between experimentally observed and predicted dissociation rate constants based on the above assumption.     

Fabrication of mesoporous metal chalcogenide nanoflake silica thin films and spongy mesoporous CdS and CdSe

Mesoporous silica metal oxide (ZnO and CdO) thin films have been used as metal ion precursors to produce the first examples of mesoporous silica metal sulfide (meso-SiO(2) @ZnS, meso-SiO(2) @CdS) or silica metal selenide (meso-SiO(2) @ZnSe, meso-SiO(2) @CdSe) thin films, in which the pore walls are made up of silica and metal sulfide or metal selenide nanoflakes, respectively. A gentle chemical etching with a dilute HF solution of the meso-SiO(2) @CdS (or meso-SiO(2) @CdSe) produces mesoporous cadmium sulfide (meso-CdS) (or cadmium selenide, meso-CdSe). Surface modified meso-CdS displays bright blue photoluminescence upon excitation with a UV light. The mesoporous silica metal oxides are formed as metal oxide nanoislands over the silica walls through a self-assembly process of a mixture of metal nitrate salt-two surfactants-silica source followed by calcination step. The reactions, between the H(2) S (or H(2) Se) gas and solid precursors, have been carried out at room temperature and monitored using spectroscopy and microscopy techniques. It has been found that these reactions are: 1)?taking place through the diffusion of sulfur or selenium species from the top metal oxide layer to the silica metal oxide interface and 2)?slow and can be stopped at any stage to obtain mesoporous silica metal oxide metal sulfide or silica metal oxide metal selenide intermediate thin films.     

Bulk conductivity of soft surface layers: experimental measurement and electrokinetic implications

Conductivity measurements were carried out on a family of polyacrylamide-co-sodium acrylate gels cross-linked with N,N'-methylenebisacrylamide in a homemade electrokinetic cell. The conductivity data allowed the equilibrium Donnan potential difference between the bulk gel and the bulk electrolyte solution to be estimated at various ionic strengths. The data were fit to a simple model assuming full dissociation of functional groups as well as to a more complete model (Dukhin, S. S.; Zimmerman, R.; Werner, C. J. Colloid Interface Sci. 2004, 274, 309) that accounts for the weak electrolyte nature of the acrylate groups fixed within the gel structure. The conductivity of the gel layers was observed to be significantly larger than the conductivity of the bulk electrolyte solutions at low ionic strengths. The increased conductivity reflects the enhanced concentration of ions within the gel structure due to Donnan equilibrium and the mobility of ions within the high water content gel layers. The electrokinetic implications of the bulk conductivity of gel-like soft surface layers are discussed in terms of the influence of the gel conductance on the resulting streaming potential.     

An electrodynamics-based model for ion diffusion in microbial polysaccharides

An electrodynamics-based model was formulated for simulation of ion diffusion in microbial polysaccharides. The fixed charges and electrostatic double layers that may associate with microbial polysaccharides and their effects on ion diffusion were explicitly built into the model. The model extends a common multicomponent ion diffusion formulation that is based on irreversible thermodynamics under a zero ionic charge flux condition, which is only applicable to the regions without fixed charges and electrostatic double layers. An efficient numerical procedure was presented to solve the differential equations in the model. The model well described key features of experimental observations of ion diffusion in negatively charged microbial polysaccharides including accelerated diffusive transport of cations, exclusion of anions, and increased rate of cation transport with increasing negative charge density. The simulated diffusive fluxes of cations and anions were consistent with a cation exchange diffusion concept in negatively charged polysaccharides at the interface of plant roots and soils; and the developed model allows to mathematically study such diffusion phenomena. An illustrative example was also provided to simulate dynamic behavior of ionic current during ion diffusion within a charged bacterial cell wall polysaccharide and the effects of the ionic current on the compression or expansion of the bacterial electrostatic double layer at the interface of the cell wall and bulk solution.     

Lability of a mixture of metal complexes under steady-state planar diffusion in a finite domain

The rigorous analytical solution for the fluxes from a mixture of 1:1 metal complexes toward an active surface under steady-state planar diffusion in a finite domain and excess ligand conditions allows for the computation of the global degree of lability of the system as well as particular degrees of lability of each complex in the mixture. This kind of system is found in a variety of fields ranging from electrochemical techniques (such as stripping chronopotentiometry at scanned deposition potential, SSCP) to analytical devices (such as diffusion gradients in thin-film gels, DGT). Among the specific effects arising from the presence of a mixture of ligands competing for the metal we highlight the following: (i) The degree of lability of a complex in the mixture differs from its degree of lability in an unmixed system with the same ligand concentration, and (ii) the degree of lability of one complex depends on (i.e., can be modified with) the concentrations of the ligands in the mixture. The impact of these characteristics on the metal flux crossing the active surface reaches the highest value when both complexes are partially labile. The complex contribution to the metal flux goes through a maximum when the thickness of the diffusion domain is varied. Thus, the thickness of the diffusion domain can be chosen to enhance the contribution of one particular complex. Lability criteria for each complex of the mixture within the reaction layer approximation are also reported. In particular, the reaction layer formulation for a complex is discussed in detail for two limiting cases: the rest of complexes are all nonlabile or the rest of complexes are all labile.     

Diffusion characteristics of agarose hydrogel used in diffusive gradients in thin films for measurements of cations and anions

The agarose hydrogel has been increasingly used as a diffusive layer in diffusive gradients in thin films (DGT) measurements. However its diffusive characteristics have not been examined in detail. In this study, the performance of agarose gel was tested in DGT measurements of eight cations (Fe(II), Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Pb(II), and Cd(II)) and eight anions (P(V), As(V), Cr(VI), Mo(VI), Sb(V), Se(VI), V(V), and W(VI)). It was found that the thickness of agarose, a key parameter in the calculation of DGT measured concentration, remained unchanged after hydration followed by storage under the following conditions: pH 2–11, ionic strength 0–1.0 M, temperature 4–40 °C, and with the storage time extending to 300 d. Enrichment of cations and repelling of anions were observed in the gel under the ionic strengths of < 2–3 mM and <1 mM (NaNO₃), respectively, which was attributed to the electrostatic interactions of these ions with the fixed negatively charged groups (mainly pyruvate) in the gel. The diffusion coefficients of cations and anions through the agarose gel (plus a PVDF filter membrane) were on average 1.10 ± 0.04 times of the reported diffusion coefficients through the agarose cross-linked polyacrylamide (APA) hydrogel, typically used in DGT technique. The working pH ranges for the agarose gel-assembled DGTs were 4–10 and 5–9 for anions and cations, respectively. The use of agarose gel, either individually or along with different filter membranes, affected the overall diffusion rates of cations and anions. The measured DGT concentrations of cations and anions in filtered natural freshwater and seawater were mostly in line with those measured directly. The results showed that the agarose gel can be used as one of the standard diffusive layers in DGT measurements for a wide range of inorganic and organic analytes.     

Polarization of a diffuse soft particle subjected to an alternating current field

The polarization of a diffuse soft particle submerged in an aqueous electrolyte and subjected to a uniform alternating electric field is theoretically analyzed with the standard electrokinetic model (the Poisson-Nernst-Planck equations). The particle consists of a rigid uncharged core and a charged diffuse polyelectrolytic shell (soft layer) permeable to ions and solvent. Our focus is on the impact of the characteristics of the soft layer including the Donnan potential, the soft layer thickness, and the friction coefficient of the soft layer on the dipole coefficient, characterizing the strength of the polarization. Under the limits of thin double layers and thin polyelectrolytic shells, approximate analytical expressions to evaluate the dipole moment coefficients are derived for high-frequency and low-frequency ranges, respectively. The analytical results are compared and agree favorably with those numerically computed by the standard model. Interestingly, we discover that when the double layer is comparable to the soft layer the dipole moment behaves qualitatively differently at different Donnan potentials. When the Donnan potential is small, the dipole moment decreases as the double layer increases. In contrast, at large Donnan potentials, the dipole moment increases with the increase in the double layer. The distinct responses to Donnan potentials are attributed to the impact of the associated double layer on the charge distribution of mobile ions inside the soft layer. The theoretical model provides a fundamental basis for interpreting the polarization of heterogeneous systems, including environmental or biological colloids or microgel particles.     

Simulations of film growth and diffusion during the corrosion process

A simple model is proposed to describe some general aspects concerning the formation of films at metal ionic solution interfaces. Working on a mesoscopic scale, three main processes are retained: the metal corrosion, the reduction of one species present in the ionic solution and the diffusion of one species from the corrosion front to the growth front where the reduction takes place. This model differs from those devoted to the growth on a surface by the existence of two fronts and their coupling. Moreover, a coupling between the diffusive species is taken into account. To emphasize the role of the diffusion, the predictions of the model are compared with those obtained from a simple extension of the Eden model. Due to diffusion a dissymetry is created between the two fronts which obeys different scaling laws. The internal structure of the film during its formation is investigated via the concentration of diffusive species.     

Donnan permselectivity in layer-by-layer self-assembled redox polyelectrolye thin films

Redox polyelectrolyte multilayers have been assembled with use of the layer-by-layer (LBL) deposition technique with cationic poly(allylamine) modified with Os(bpy)(2)ClPyCHO (PAH-Os) and anionic poly(styrene)sulfonate (PSS) or poly(vinyl)sulfonate (PVS). Different behavior has been observed in the formal redox potential of the Os(II)/Os(III) couple in the polymer film with cyclic voltammetry depending on the charge of the outermost layer and the electrolyte concentration and pH. The electrochemical quartz crystal microbalance (EQCM) has been used to monitor the exchange of ions and solvent with the external electrolyte during redox switching. At low ionic strength Donnan permselectivity of anions or cations is apparent and the nature of the ion exclusion from the film is determined by the charge of the topmost layer and solution pH. At high electrolyte concentration Donnan breakdown is observed and the osmium redox potential approaches the value for the redox couple in solution. Exchange of anions and water with the external electrolyte under permselective conditions and salt and water under Donnan breakdown have been observed upon oxidation of the film at low pH for the PAH-Os terminating layer. Moreover, at high pH values and with PVS as the terminating layer EQCM mass measurements have shown that cation release was masked by water exchange.     

Interaction of different metal ions with carboxylic acid group: a quantitative study

The binding strength of the carboxylic acid group (-COOH) with different divalent metal ions displays considerable variation in arachidic acid (AA) thin films. It is considered that in AA thin films the metal ions straddle the hydrophilic regions of the stacked bilayers of AA molecules via formation of carboxylates. In this study first the uptake of different divalent cations in films of AA is estimated by atomic absorption spectroscopy (AAS). Through the amount of cation uptake, it is found that the strength of binding of different cations varies as Ca2+>Co2+>Pb2+>Cd2+. Variation in the binding strength of different ions is also manifested in experiments where AA thin films are exposed to metal ion mixtures. The higher binding strength of AA with certain metal ions when exposed individually, as well as the preference over the other metal ions when exposed to mixtures, reveal some interesting deviation from the expected behavior based on considerations of ionic radii. For example, Pb2+ is always found to bind to AA much more strongly than Cd2+ even though the latter has smaller ionic radius, indicating that other factors also play an important role in governing the binding strength trends apart from the effects of ionic radii. Then, to get a more meaningful knowledge regarding the binding capability, first-principles calculations based on density functional theory have been applied to study the interaction of different cations with the simplest carboxylic acid, acetic acid, that can result in formation of metal diacetates. Their electronic and molecular structures, cohesive energies, and stiffness of the local potential energy well at the cation (M) site are determined and attempts are made to understand the diversity in geometry and the properties of binding of different metal ions with -COOH group. We find that the calculated M-O bond energies depend sensitively on the chemistry of M atom and follow the experimentally observed trends quite accurately. The trends in M-O bond energies and hence the total M-acetate binding energy trends can actually be related to their molecular structures that fall into different categories: Ca and Cd have tetrahedral coordination; Fe, Ni, and Co exhibit planar 4-fold coordination; and Pb is off-centered from the planar structure (forming pyramidal structure) due to its stereochemically active lone pair of electrons.     

Lability criteria for successive metal complexes in steady-state planar diffusion

The lability of sequential metal complexes, ML, ML2, ML3, ... , up to a general 1:n metal/ligand stoichiometric ratio is considered for the case of metal ions (M) being accumulated at a surface (analytical sensor or organism). The analytical solution for the steady-state diffusion of M within a sequential complexation scheme allows quantification of the contribution from the dissociation of all of the complex species to the metal flux through the so-called lability degree, xi. A lability degree for each sequential complexation step is also defined which, due to the sequential character of the complexation scheme, depends not only on the proper kinetic constants of the given complexation step but also on the kinetics of the previous ones. When all contributions from the complexes are diffusion limited, the system is fully labile and xi=1. To provide simple lability criteria, the reaction layer approximation is extended to specifically deal with this sequential complexation scheme, so that a reaction layer thickness is defined when the existence of one particular rate-limiting step is assumed. Expressions for the classical lability parameter, L, are formulated using the reaction layer approximation. The change of the lability of the system as the diffusion layer thickness is modified is analyzed in detail. The contribution of the complex flux reflects the evolution of the system from labile to inert as the thickness of the sensor is appropriately decreased.