Quartz-crystal microbalance-dissipation technique for the study of initial adsorption of fibronectin onto tresyl chloride-activated titanium

The immobilization of cell-adhesive proteins onto titanium implants improves biological response at the implant-tissue interface. Previous studies demonstrated the easy and direct attachment of fibronectin onto titanium with the use of a 2,2,2-trifluoroethanesulfonyl chloride (tresyl chloride) activation technique. The present study investigated the initial adsorption behavior of fibronectin on tresyl chloride-activated titanium by the quartz-crystal microbalance-dissipation (QCM-D) technique. The crystal resonant frequency and the dissipation shift of the oscillator were simultaneously measured by the injection of fibronectin/phosphate-buffered saline solution (pH = 7.4). The tresyl chloride-activated titanium surface showed a faster and greater decrease in frequency than that of untreated titanium, indicating that a greater amount of fibronectin was adsorbed in the former case during a 120-min adsorption. The dissipation-frequency plots revealed that, during the initial stage of adsorption, the bond between fibronectin and tresyl chloride-activated titanium is stronger than that between fibronectin and untreated titanium. The QCM-D technique can provide new insights into the adsorption mechanism of fibronectin.     

Adhesion of corneal epithelial cells to cell adhesion peptide modified pHEMA surfaces

Epithelialization of a corneal implant is a desirable property. In this study we compared surface modification of poly (2-hydroxyethyl methacrylate) (pHEMA) with the cell adhesion peptides RGDS and YIGSR. Various parameters in the tresyl chloride activation and modification reactions were considered in order to maximize surface coverage with the peptide including tresyl chloride reaction solvent. tresyl chloride reaction time, tresyl chloride concentration, peptide concentration, and peptide reaction pH. Surface chemistry and corneal epithelial cell adhesion to the modified surfaces were examined. X-ray photoelectron spectroscopy data suggested that while peptide modification had occurred, surface coverage with the peptide was incomplete. Acetone was found to result in a higher fraction of nitrogen and surface bound carboxyl groups compared to dioxane and ether. Furthermore, corneal epithelial cell adhesion to the surfaces for which acetone was used for the activation reaction was significantly greater. Statistical analysis of the various samples suggests that lower peptide concentrations and higher tresyl chloride reaction times result in better cell adhesion. Furthermore, modification with YIGSR resulted in higher surface concentrations and better cell adhesion than modification with RGDS. Little or no cell adhesion was noted on the unmodified pHEMA controls. Protein adsorption results suggest that the differences in cell adhesion cannot be attributed to differences in serum protein adsorption from the culture medium. We conclude that YIGSR modified surfaces have significant potential for further development in corneal applications.     

Characterization and protein-adsorption behavior of deposited organic thin film onto titanium by plasma polymerization with hexamethyldisiloxane

Plasma polymerized hexamethyldisiloxane (HMDSO) thin film was deposited onto titanium using a radio-frequency apparatus for the surface modification of titanium. A titanium disk was first polished using colloidal silica at pH=9.8. Plasma-polymerized HMDSO films were firmly attached to the titanium by heating the titanium to a temperature of approximately 250 degrees C. The thickness of the deposited film was 0.07-0.35mum after 10-60min of plasma polymerization. The contact angle with respect to double distilled water significantly increased after HMDSO coating. X-ray photoelectron spectroscopy revealed that the deposited thin film consisted of Si, C, and O atoms. No Ti peaks were observed on the deposited surface. The deposited HMDSO film was stable during 2-weeks immersion in phosphate buffer saline solution. Fourier transform reflection-absorption spectroscopy showed the formation of Si-H, Si-C, C-H, and Cz.dbnd6;O bonds in addition to Si-O-Si bonds. Quartz crystal microbalance-dissipation measurement demonstrated that the deposition of HMDSO thin films on titanium has a benefit for fibronectin adsorption at the early stage. In conclusion, plasma polymerization is a promising technique for the surface modification of titanium. HMDSO-coated titanium has potential application as a dental implant material.     

Biomimetic apatite formation on calcium phosphate-coated titanium in Dulbecco’s phosphate-buffered saline solution containing CaCl2 with and without fibronectin

Calcium phosphate (CaP) thin films with different degrees of crystallinity were coated on the surfaces of commercially pure titanium by electron beam evaporation. The details of apatite nucleation and growth on the coating layer were investigated in Dulbecco’s phosphate-buffered saline solutions containing calcium chloride (DPBS) or DPBS with fibronectin (DPBSF). The surfaces of the samples were examined by field emission scanning electron microscopy, X-ray diffraction and X-ray photoelectron spectroscopy. The concentrations of fibronectin and calcium ions (Ca²⁺) were monitored by the bicinchoninic acid method (BCA) and use of a calcium assay kit (DICA-500), respectively. Apatite initially formed at the fastest rate on the CaP-coated samples with the lowest degree of crystallinity and reached the maximum Ca²⁺ concentration after immersion in DPBS solution for 15 min. After 15 min the concentration of Ca²⁺ decreased with the growth of apatite on the coating layers. For all the samples the maximum Ca²⁺ concentration in the DPBS solutions decreased with increasing crystallinity and immersion time to reach the maximum concentration increased. The presence of fibronectin in the DPBS solutions delayed the formation and affected the morphology of the apatite. Fibronectin incorporated into apatite deposited on the surface of titanium did not affect its biological activity in terms of promoting osteoblast adhesion.     

Development and analytical characterization of cysteine-grafted polypyrrole films electrosynthesized on Pt- and Ti-substrates as precursors of bioactive interfaces.

The grafting of cysteine to polypyrrole(PPY)-coated platinum and titanium substrates has been investigated with the aim of developing innovative bioactive materials of interest for bone implants. Polypyrrole has been chosen as the coating polymer because of its suitability to be electrochemically grown directly onto metallic substrates, of any shape and dimension, leading to remarkably adherent overlayers. The effectiveness of grafting was monitored by X-ray photoelectron spectroscopy (XPS) which showed the presence of aminoacid residues onto the polymer surface. Information obtained by an accurate curve fitting of significant regions in the spectra (C1s, N1s, and O1s signals) and by a cross-check of peak area ratios, before and after the grafting process, gave evidence that cysteine forms covalent bonds to pyrrole rings, preferentially in beta-positions, via the sulfydryl group, leaving both amino and carboxylic functionalities available for further chemistry. The surface density of cysteine residues was evaluated by microgravimetric measurements performed by the electrochemical quartz crystal microbalance and was found suitable for the exploitation of these modified surfaces as bioactive systems. Some preliminary results are reported on the adhesion of neonatal rat calvarial osteoblasts onto titanium substrates after coating by a PPY film modified by a polypeptide having cysteine as a terminal residue and containing the Arg-Gly-Asp aminoacid adhesive sequence.     

Effect of the heating temperature on the corrosion resistance of alkali-treated titanium

The paper presents the results of examinations of the corrosion resistance of titanium after its being subjected to the surface modification by the alkali- and heat-treatments. The material examined was commercially pure titanium (grade 2). The samples were soaked in an aqueous 10M NaOH solution at 60 degrees C for 24 h and subsequently heated at 500, 600, or 700 degrees C for 1 h. The chemical composition of the surface layers was determined by X-ray photoelectron spectroscopy and secondary ion mass spectroscopy. The phases present in the layers were identified by XRD. The corrosion resistance was evaluated by electrochemical methods (Stern's method, potentiodynamic method, and impedance spectroscopy) at a temperature of 37 degrees C after short- and long-time exposures. The 13 h exposure was aimed to allow the corrosion potential to stabilize. The aim of the long-term exposures was to examine how the corrosion resistance of the modified samples changes during the exposure. Under the conditions prevailing during the experiments, the highest corrosion resistance was achieved with the samples heated at a temperature of 700 degrees C.     

Effect of surface chemistries and characteristics of Ti6Al4V on the Ca and P adsorption and ion dissolution in Hank's ethylene diamine tetra-acetic acid solution

This study examined the influence of chemistries and surface characteristics of Ti6Al4V on the adsorption of Ca and P species and ion dissolution behavior of the material exposed in Hank's solution with 8.0 mM ethylene diamine tetra-acetic acid at 37 degrees C. The variation of chemistries of the alloy and nano-surface characteristics (chemistries of nano-surface oxides, amphoteric OH group adsorbed on oxides, and oxide thickness) was effected by surface modification and three passivation methods (34% nitric acid passivation. 400 degrees C heated in air, and aged in 100 degrees C water). X-ray photoelectron spectroscopy and Auger electron spectroscopy were used for surface analyses. The chemistries of nano-surface oxides in a range studied should not change the capability of Ca and P adsorption. Nor is the capability affected significantly by amphoteric OH group and oxide thickness. However, passivations influence the surface oxide thickness and the early stage ion dissolution rate of the alloy. The rate-limiting step of the rate can be best explained by metal-ion transport through the oxide film, rather than hydrolysis of the film. Variation of the chemistries of titanium alloy alters the electromotive force potential of the metal, thereby affecting the corrosion and ion dissolution rate.     

Characterization of surface oxide films on titanium and adhesion of osteoblast

The relationship between surface characteristics of titanium and initial interactions of titanium-osteoblasts was investigated. Titanium plates were heat-treated in different oxidation atmospheres. The third passage rabbit osteoblasts were cultured on the titanium plates for 24h. After the heat-treatment, the crystal structure of the surface oxide films on titanium was identified using X-ray diffractometer and X-ray photoelectron spectroscopy (XPS). The surface roughness of titanium was measured with a profilometer. The surface energy was obtained by measurement of contact angles and calculation with Owens-Wendt-Kaeble's equation. The amount of surface hydroxyl (OH)(s) groups was examined using XPS. The change of binding energy of the some elements on the substrate surface suggested that the interactions between the cells and the titanium involved chemical reactions. The greater surface roughness, higher surface energy and more surface hydroxyl groups resulted in greater numbers of adhered osteoblasts and higher cell activity. Compared to the acidic hydroxyl (OH)(a) groups in (OH)(s) groups and the dispersion component of the total surface energy, the basic hydroxyl (OH)(b) groups and the polar component play more important roles in the osteoblast-titanium interaction.     

Interaction of calcium and phosphate in apatite coating on titanium with serum albumin

A Ca-deficient carbonate apatite coating on titanium was prepared by pre-calcifying titanium in a saturated Ca(OH)2 solution and then immersing in a supersaturated calcium phosphate solution. The interaction of the protein with the apatite coating on titanium was investigated by scanning electron microscopy with X-ray energy dispersion spectroscopy. X-ray photoelectron spectroscopy, X-ray diffraction and Fourier transform infrared spectroscopy. During immersion of the coating in bovine serum albumin (BSA) solution, accompanied by an adsorption of BSA onto the coating, calcium and phosphate ions dissolved and reprecipitated, resulting in the formation of the coating containing BSA from the surface to subsurface layers. The adsorption modified the structure and morphology of the apatite coating on titanium and changed the protein configuration. It was also found that the protein chemically adsorbed onto surfaces containing calcium or phosphorus, showed that both Ca and P on the apatite coating were the binding sites with protein. The BSA adsorption onto the coating involved several elements and groups. In this process. Ca played an essential role, and the interaction of Ca on the apatite coating with the protein stimulated the bond of the protein at P sites.     

Calcium phosphate naturally formed on titanium in electrolyte solution.

Surface films formed on titanium specimens immersed in electrolyte solutions (pH 4.5, 5.2, 7.4) at 37 degrees C for 1 h, 1 d, 30 d, and/or 60 d, were characterized using X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared reflection absorption spectroscopy (FTIR-RAS) to understand the reaction between titanium and inorganic ions. For comparison, the surface of Ti-6AI-4V and Ti-50Ni were also characterized. XPS data revealed that calcium phosphates were naturally formed on these specimens. In particular, compared with the calcium phosphates formed on the titanium alloys, the calcium phosphate formed on titanium immersed for 30 d in the solution with pH 7.4 was more like hydroxyapatite. The compositions of the calcium phosphates formed on the specimens changed with the immersion time and the pH value of the solution. The spectrum obtained using FTIR-RAS from titanium immersed in the solution with pH 7.4 for 60 d was similar to that obtained from carbonate-containing hydroxyapatite. The results indicate that a calcium phosphate similar to apatite is naturally formed on titanium in a neutral electrolyte solution in 30 d. In regard to titanium being a biomaterial, we found this to be an intriguing property. It is possible that this calcium phosphate is responsible for the resulting biocompatibility of titanium.     

Synthesis, analytical characterization, and osteoblast adhesion properties on RGD-grafted polypyrrole coatings on titanium substrates

The covalent attachment of an Arg-Gly-Asp (RGD) containing peptide to polypyrrole(PPy)-coated titanium substrates has been investigated in order to develop a bioactive material of potential use in orthopedic fields. Polypyrrole has been employed as the coating polymer because of its suitability to be electrochemically grown directly onto metallic substrates of different shapes, leading to remarkably adherent films. The synthetic peptide Cys-Gly-(Arg-Gly-Asp)-Ser-Pro-Lys, containing the cell-adhesive region of fibronectin (RGD), has been grafted to the polymer substrate via the cysteine residue using a procedure recently developed in the authors laboratory. The effectiveness of grafting was monitored by X-ray photoelectron spectroscopy (XPS), which assessed the presence of the peptide grafted onto the polymer surface exploiting the cysteine sulfur as target element. Neonatal rat calvarial osteoblasts were attached to RGD-modified PPy-coated Ti substrates at levels significantly greater than on unmodified PPy-coated Ti and glass coverslip substrates.     

Synthesis,analytical characterization,and osteoblast adhesion properties on RGD-grafted polypyrrole coatings on titanium substrates

The covalent attachment of an Arg-Gly-Asp (RGD) containing peptide to polypyrrole(PPy)-coated titanium substrates has been investigated in order to develop a bioactive material of potential use in orthopedic fields. Polypyrrole has been employed as the coating polymer because of its suitability to be electrochemically grown directly onto metallic substrates of different shapes, leading to remarkably adherent films. The synthetic peptide Cys-Gly-(Arg-Gly-Asp)-Ser-Pro-Lys, containing the cell-adhesive region of fibronectin(RGD), has been grafted to the polymer substrate via the cysteine residue using a procedure recently developed in the authors laboratory. The effectiveness of grafting was monitored by X-ray photoelectron spectroscopy (XPS), which assessed the presence of the peptide grafted onto the polymer surface exploiting the cysteine sulfur as target element. Neonatal rat calvarial osteoblasts were attached to RGD-modified PPy-coated Ti substrates at levels significantly greater than on unmodified PPy-coated Ti and glass coverslip substrates.     

Thin calcium phosphate coatings on titanium by electrochemical deposition in modified simulated body fluid

Adherent and optically semitransparent thin calcium phosphate (CaP) films were electrochemically deposited on titanium substrates in a modified simulated body fluid at 37 degrees C. Coatings deposited by using periodic pulsed potentials showed better adhesion and better mechanical properties than coatings deposited with use of a constant potential. Scanning electron microscopy was used to study the morphology of the coatings. The coatings displayed a polydispersed porous structure with pores in the range of a few nanometers to 1 mum. Furthermore, X-ray diffractometry and the O(1s) satellite peaks in X-ray photoelectron spectroscopy indicated that the coatings possessed a similar surface chemistry to that of natural bone minerals. These results were confirmed by inductively coupled plasma optical emission spectrometry, which yielded a Ca:P ratio of 1.65, close to that of hydroxyapatite. Contact mode atomic force microscopy (AFM) showed the average thickness of the coatings was in the order of 200 nm. Root-mean-square (RMS) roughness values, also derived by AFM, were shown to be much higher on the titanium-CaP surfaces in comparison with untreated titanium substrates, with RMS values of about 300 and 110 nm, respectively. Cell culture experiments showed that the CaP surfaces are nontoxic to MG63 osteoblastic cells in vitro and were able to support cell growth for up to 4 days, outperforming the untreated titanium surface in a direct comparison. These easily prepared coatings show promise for hard-tissue biomaterials.     

Cell attachment to PET films coated with a thermo-sensitive block co-polymer with different chemical composition

This objective of this study is to characterize the surface of poly(ethylene terephthalate) (PET) films coated with the thermo-sensitive di-block co-polymers of 2-ethoxyethyl vinyl ether and 2-phenoxyethyl vinyl ether segments (EOVE-b-PhOVE) with a high polydispersity and evaluate the behavior of cell attachment on them at different temperatures. The EOVE segment possessed a low critical solution temperature at 20 degrees C while the hydrophobic PhOVE segment functioned as the site to allow the co-polymer to adsorb onto the PET films. X-ray photoelectron spectroscopy and contact angle measurements revealed that the PET film was coated with the EOVE-b-PhOVE co-polymers. The density of co-polymers coated increased with the concentration of co-polymers used for coating. Irrespective of the co-polymer type, 3T3L1 cells attached on the surface of coated films at 37 degrees C, while the cells showed a spread shape, which is similar to that of cells attached on the original non-coated film. However, when the temperature decreased from 37 to 4 degrees C, the cell shape changed to be round, in contrast to that of the original PET film. The percent increase of round cells depended on the coating density and the polymerization degree of EOVE segment.     

The mechanisms of passive dissolution of titanium in a model physiological environment.

The surface chemistry, oxidation, and disolution kinetics of titanium were measured to establish the mechanisms of passive dissolution in physiological environments. Titanium thin films were immersed in 8.0 mM ethylenediamine-tetraacetic acid in simulated interstitial electrolyte (EDTA/SIE) and maintained at 37 degrees C, 10% O2, 5% CO2 and 7.2 pH for periods of time up to 3200 h (133 days). Two immersion schemes were employed: the integral sequentially determined the titanium released into a solution of accumulated dissolution products; and the differential continuously replenished the test solution. The solutions were analyzed for titanium by electrothermal atomic absorption spectrometry (EAAS), and the sample surfaces were analyzed by Auger electron spectroscopy (AES) and x-ray photoelectron spectroscopy (XPS) to determine oxide composition, stoichiometry, and thickness. Prior to immersion two types of hydroxyl (OH) groups were distinguished on the TiO2 surface. Upon immersion, the chemistry of the surface changed as a function of immersion: the presence of OH groups increased and P (nonelemental) was detected at the surface. The dissolution kinetics obeyed a two-phase logarithmic model, where the transition between phases occurred simultaneously with the adsorption of the P-containing species. The dissolution kinetics depended on surface reactions, electric field strength, and molecular diffusion. These mechanisms explain the observed dependence of dissolution kinetics on the properties of the surface oxide and solution ligands.     

Hydration and preferential molecular adsorption on titanium in vitro.

Surface sensitive spectroscopies, Auger electron and X-ray photoelectron (XPS), were used to determine changes in titanium oxide composition, oxide stoichiometry, and adsorbed surface species as a function of exposure to human serum in a balanced electrolyte (serum/SIE) and 8.0 mM ethylenediaminetetraacetic acid in a balanced electrolyte (EDTA/SIE) at 37 degrees C. Before immersion, the oxide was near ideal TiO2, covered by two types of hydroxyl groups: acidic OH(s) with oxygens doubly coordinated to titanium, and basic Ti-OH groups singly coordinated. After extended exposure to both solutions, up to 5000 h (ca. 208 d), the surface concentration of OH groups increased and non-elemental P appeared. The P LVV Auger transition and P 2p spectra indicated the peak positions were similar to reference phosphate compounds. The adsorbed phosphate species were presumed to be either Ti-H2PO4 or Ti-HPO4-. The XPS data suggested that a lipoprotein and/or glycolipid film was adsorbed to the specimens exposed to serum/SIE. Analysis of the preferential lipoprotein/glycolipid adsorption using electrostatic bonding concepts contributed to the refinement of the hierarchical model for the Ti-tissue interface. The salient features are that Ti metal is not in direct contact with the biological milieu, rather there is a gradual transition from the bulk metal, near-stoichiometric oxide, Ca and P substituted hydrated oxide, adsorbed lipoproteins and glycolipids, proteoglycans, collagen filaments and bundles to cells.     

Chemical interaction of polyphosphoric acid with titanium and its effect on human bone marrow derived mesenchymal stem cell behavior

The aim of this study was to evaluate the effect of treating titanium (Ti) with polyphosphoric acid on the attachment and proliferation of human bone marrow derived mesenchymal stem cells (hBMSCs). Cleaned Ti disks were immersed into three different concentrations of polyphosphoric acid solution (0.1, 1, and 10 wt %) and 10 wt % orthophosphoric acid solution for 24 h at 37 degrees C. Ti immersed in distilled water for 24 h at 37 degrees C served as control. The level of polyphosphoric acid that interacted with the Ti surface was determined by measuring the surface P/Ti ratio (atom%/atom%) using X-ray photoelectron spectroscopy. Degrees of cell attachment (1, 3, 5 h after cell seed) and proliferation (1, 3, 5, and 7 days after cell seed) on each treated Ti disk were evaluated by MTS assay. The mean surface P/Ti ratios increased in a polyphosphoric acid concentration dependent manner. A significantly higher cell attachment was found on Ti treated with polyphosphoric acid in contrast to untreated Ti (control) for all three culture periods. MTS assay also revealed that cell proliferation levels significantly increased following a polyphosphoric acid dose dependency. Ti surface treatment with orthophosphoric acid did not influence the cell attachment and proliferation. It was concluded that polyphosphoric acid treatment of Ti enhanced the attachment and proliferation of hBMSCs.     

Influence of nanometer smoothness and fibronectin immobilization of titanium surface on MC3T3-E1 cell behavior

The aim of the present study was to evaluate the influence of mechanical treatment, namely, nanometer smoothing (Ra: approximately 2.0 nm) and sandblasting (Ra: approximately 1.0 μm), as well as biochemical treatment, namely, fibronectin immobilization, of a titanium surface on osteoblast-like cell behavior. Cell proliferation was monitored by measurements of DNA content and ALP activity; osteocalcin production and mineralization behavior were also evaluated, in addition to morphological observation of attached cells. Fibronectin could be immobilized by the tresyl chloride-activation method. A sandblasted surface resulted in significantly more DNA than a nanometer-smooth surface, but fibronectin immobilization did not result in a significant increase of DNA at 52 days of cell culture. The nanometer-smooth surface showed highest ALP activity and osteocalcin production. FN immobilization decreased ALP activity for the nanometer-smooth surface, but increased it for the sandblasted surface. The nanometer-smooth surface also showed the highest osteocalcin production. Scanning electron microscopy showed interesting phenomena of the attached cells. Attached cell area was more rapidly increased on the nanometer-smooth surface than on the sandblasted surface. It was suggested that cultured cells on the nanometer-smooth surface began to spread earlier and that the proportion of spreading cells among total attached cells increased sooner on the nanometer-smooth surface than on the sandblasted rough surface. It appeared that FN immobilization influenced the arrangement of attached cells. In conclusion, the nanometer-smooth surface employed in the present study was beneficial for the differentiation of MC3T3-E1 cells. FN immobilization influenced the morphologies of attached cells.     

Fibronectin immobilization using water-soluble carbodiimide on poly-L-lactic acid for enhancing initial fibroblast attachment

The aim of this study is to evaluate the influence of fibronectin immobilization on poly-L-lactic acid (PLA) films on the initial attachment of human gingival fibroblasts. Carboxylic acid groups are chemically introduced on the PLA films' surface by surface hydrolysis with 0.5 M NaOH. The contact angle of PLA surface with respect to double-distilled water decreases significantly after NaOH hydrolysis. X-ray photoelectron spectroscopy (XPS) also reveals significantly higher intensities of C(C=O)/C(C-O) after NaOH hydrolysis. Fibronectin is immobilized onto the hydrolyzed PLA surface through a condensation reaction between the carboxylic acid groups on the hydrolyzed PLA surface and the amino groups of fibronectin using water-soluble carbodiimide. XPS analysis shows that the fibronectin-immobilized PLA surface is enriched with nitrogen atoms. The immobilization of fibronectin significantly enhances the number of initially attached human gingival fibroblasts on the PLA surface. No obvious differences in morphology are noted between fibroblasts cultured on native PLA and on fibronectin-immobilized PLA. Fibronectin can be immobilized onto the PLA surface after NaOH hydrolysis and this is effective in enhancing the initial attachment of human gingival fibroblasts.     

Solution deposition of hydroxyapatite on titanium pretreated with a sodium ion implantation.

Titanium surfaces were treated by exposing them to a beam of sodium ions. Sodium titanate was shown to be incorporated within the oxidic titanium surface. The ion-implanted surfaces were examined for their reactivity by immersion in a simulated body fluid, which showed the formation of surface-bound hydroxyapatite. The surface was characterized by X-ray diffraction, Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy, and optical and electron microscopy. The surface hydroxyl concentration was determined using the nuclear reaction (1)H((15)N, alpha gamma)(12)C. Surface-related parameters that may affect hydroxyapatite nucleation are discussed in terms of the electrical double layer.