Advantages of the classical thermodynamic analysis of single-and multi-component Langmuir monolayers from molecules of biomedical importance-theory and applications

The Langmuir monolayer technique has been successfully used for decades to model biological membranes and processes occurring at their interfaces. Classically, this method involves surface pressure measurements to study interactions within membrane components as well as between external bioactive molecules (e.g. drugs) and the membrane. In recent years, surface-sensitive techniques were developed to investigate monolayers in situ; however, the obtained results are in many cases insufficient for a full characterization of biomolecule-membrane interactions. As result, description of systems using parameters such as mixing or excess thermodynamic functions is still relevant, valuable and irreplaceable in biophysical research. This review article summarizes the theory of thermodynamics of single- and multi-component Langmuir monolayers. In addition, recent applications of this approach to characterize surface behaviour and interactions (e.g. orientation of bipolar molecules, drug-membrane affinity, lateral membrane heterogeneity) are presented.

Unraveling the Marine Microplastic Cycle: The First Simultaneous Data Set for Air, Sea Surface Microlayer, and Underlying Water

Microplastics (MP) including tire wear particles (TWP) are ubiquitous. However, their mass loads, transport, and vertical behavior in water bodies and overlying air are never studied simultaneously before. Particularly, the sea surface microlayer (SML), a ubiquitous, predominantly organic, and gelatinous film (<1 mm), is interesting since it may favor MP enrichment. In this study, a remote-controlled research catamaran simultaneously sampled air, SML, and underlying water (ULW) in Swedish fjords of variable anthropogenic impacts (urban, industrial, and rural) to fill these knowledge gaps in the marine-atmospheric MP cycle. Polymer clusters and TWP were identified and quantified with pyrolysis-gas chromatography-mass spectrometry. Air samples contained clusters of polyethylene terephthalate, polycarbonate, and polystyrene (max 50 ng MP m-3). In water samples (max. 10.8 μg MP L-1), mainly TWP and clusters of poly(methyl methacrylate) and polyethylene terephthalate occurred. Here, TWP prevailed in the SML, while the poly(methyl methacrylate) cluster dominated the ULW. However, no general MP enrichment was observed in the SML. Elevated anthropogenic influences in urban and industrial compared to the rural fjord areas were reflected by enhanced MP levels in these areas. Vertical MP movement behavior and distribution were not only linked to polymer characteristics but also to polymer sources and environmental conditions.

The Conformational Changes of Bovine Serum Albumin at the Air/Water Interface: HDX-MS and Interfacial Rheology Analysis

The characterization and dynamics of protein structures upon adsorption at the air/water interface are important for understanding the mechanism of the foamability of proteins. Hydrogen-deuterium exchange, coupled with mass spectrometry (HDX-MS), is an advantageous technique for providing conformational information for proteins. In this work, an air/water interface, HDX-MS, for the adsorbed proteins at the interface was developed. The model protein bovine serum albumin (BSA) was deuterium-labeled at the air/water interface in situ for different predetermined times (10 min and 4 h), and then the resulting mass shifts were analyzed by MS. The results indicated that peptides 54-63, 227-236, and 355-366 of BSA might be involved in the adsorption to the air/water interface. Moreover, the residues L55, H63, R232, A233, L234, K235, A236, R359, and V366 of these peptides might interact with the air/water interface through hydrophobic and electrostatic interactions. Meanwhile, the results showed that conformational changes of peptides 54-63, 227-236, and 355-366 could lead to structural changes in their surrounding peptides, 204-208 and 349-354, which could cause the reduction of the content of helical structures in the rearrangement process of interfacial proteins. Therefore, our air/water interface HDX-MS method could provide new and meaningful insights into the spatial conformational changes of proteins at the air/water interface, which could help us to further understand the mechanism of protein foaming properties.

Donor:Acceptor Janus Nanoparticle-Based Films as Photoactive Layers: Control of Assembly and Impact on Performance of Devices

Water-processable organic semiconductor nanoparticles (NPs) are considered promising materials for the next-generation of optoelectronic applications due to their controlled size, internal structure, and environmentally friendly processing. Reasonably, the controllable assembly of donor:acceptor (D:A) NPs on large areas, quality, and packing density of deposited films, as well as layer morphology, will influence the effectiveness of charge transfer at an interface and the final performance of designed optoelectronic devices.This work represents an easy and effective approach for designing self-assembled monolayers of D:A NPs. In this self-assembly procedure, the NP arrays are prepared on a large scale (2 × 2 cm² ) at the air/water interface with controlled packing density and morphology. Due to the unique structure of individual D:A Janus particles and their assembled arrays, the Janus nanoparticle (JNP)-based device exhibits an 80% improvement of electron mobility and more balanced charge extraction compared to the conventional core-shell NP-based device. An outstanding performance of polymer solar cells with over 5% efficiency is achieved after post-annealing treatment of assembled arrays, representing one of the best results for NP-based organic photovoltaics. Ultimately, this work provides a new protocol for processing water-processable organic semiconductor colloids and future optoelectronic fabrication.

Self-Organization of Lipid-Porphyrin Conjugates at the Air/Water Interface

Lipid-porphyrin conjugates are versatile compounds which can self-assemble into liposome-like structures with multifunctional properties. Most of the conjugates that have been described so far, consisted in grafting pyropheophorbide-a (Pyro-a) or other porphyrin derivatives through the esterification of the hydroxyl group in the sn-2 position of a lysophosphatidylcholine. However, despite the versatility of these conjugates, less is known about the impact of the lipid backbone structure on their 2D phase behavior at the air/water interface and more precisely on their fine structures normal to the interface as well as on their in-plane organization. Herein, we synthesized a new lipid-porphyrin conjugate (PyroLSM) based on the amide coupling of Pyro-a to a lysosphingomyelin backbone (LSM) and we compared its interfacial behavior to that of Pyro-a and Pyro-a conjugated lysophosphatidylcholine (PyroLPC) using Langmuir balance combined to a variety of other physical techniques. Our results provided evidence on the significant impact of the lipid backbone on the lateral packing of the conjugates as well as on the shape and size of the formed domains. Compared to Pyro-a and PyroLPC monolayers, PyroLSM exhibited the highest lateral packing which highlights the role of the lipid backbone in controlling their 2D organization which in turn may impact the photophysical properties of their assemblies.

Differential Surface Adsorption Phenomena for Conventional and Novel Surfactants Correlates with Changes in Interfacial mAb Stabilization

Protein adsorption on surfaces can result in loss of drug product stability and efficacy during the production, storage, and administration of protein-based therapeutics. Surface-active agents (excipients) are typically added in protein formulations to prevent undesired interactions of proteins on surfaces and protein particle formation/aggregation in solution. The objective of this work is to understand the molecular-level competitive adsorption mechanism between the monoclonal antibody (mAb) and a commercially used excipient, polysorbate 80 (PS80), and a novel excipient, N-myristoyl phenylalanine-N-polyetheramine diamide (FM1000). The relative rate of adsorption of PS80 and FM1000 was studied by pendant bubble tensiometry. We find that FM1000 saturates the interface faster than PS80. Additionally, the surface-adsorbed amounts from X-ray reflectivity (XRR) measurements show that FM1000 blocks a larger percentage of interfacial area than PS80, indicating that a lower bulk FM1000 surface concentration is sufficient to prevent protein adsorption onto the air/water interface. XRR models reveal that with an increase in mAb concentration (0.5-2.5 mg/mL: IV based formulations), an increased amount of PS80 concentration (below critical micelle concentration, CMC) is required, whereas a fixed value of FM1000 concentration (above its relatively lower CMC) is sufficient to inhibit mAb adsorption, preventing mAb from co-existing with surfactants on the surface layer. With this observation, we show that the CMC of the surfactant is not the critical factor to indicate its ability to inhibit protein adsorption, especially for chemically different surfactants, PS80 and FM1000. Additionally, interface-induced aggregation studies indicate that at minimum surfactant concentration levels in protein formulations, fewer protein particles form in the presence of FM1000. Our results provide a mechanistic link between the adsorption of mAbs at the air/water interface and the aggregation induced by agitation in the presence of surfactants.

Insights into Extended Structures and Their Driving Force: Influence of Salt on Polyelectrolyte/Surfactant Mixtures at the Air/Water Interface

This paper addresses the effect of polyelectrolyte stiffness on the surface structure of polyelectrolyte (P)/surfactant (S) mixtures. Therefore, two different anionic Ps with different intrinsic persistence length lP are studied while varying the salt concentration (0-10-2 M). Either monosulfonated polyphenylene sulfone (sPSO2-220, lP ∼20 nm) or sodium poly(styrenesulfonate) (PSS, lP ∼1 nm) is mixed with the cationic surfactant tetradecyltrimethylammonium bromide (C14TAB) well below its critical micelle concentration and studied with tensiometry and neutron reflectivity experiments. We kept the S concentration (10-4 M) constant, while we varied the P concentration (10-5-10-3 M of the monomer, denoted as monoM). P and S adsorb at the air/water interface for all studied mixtures. Around the bulk stoichiometric mixing point (BSMP), PSS/C14TAB mixtures lose their surface activity, whereas sPSO2-220/C14TAB mixtures form extended structures perpendicular to the surface (meaning a layer of S with attached P and additional layers of P and S underneath instead of only a monolayer of S with P). Considering the different P monomer structures as well as the impact of salt, we identified the driving force for the formation of these extended structures: compensation of all interfacial charges (P/S ratio ∼1) to maximize the gain of entropy. By increasing the flexibility of P, we can tune the interfacial structures from extended structures to monolayers. These findings may help improve applications based on the adsorption of P/S mixtures in the fields of cosmetic or oil recovery.

Compression-induced Phase Transition in Adsorbed Monolayers of Alkylgalactosides at the Air/Water Interface

Compression-induced formation of condensed-phase domains in adsorbed monolayers of alkylgalactosides (AGs) at the air/water interface was observed. When an aqueous solution of AGs was poured into a Langmuir trough, the AG molecules were spontaneously adsorbed from the solution at the air/water interface to form the adsorbed or Gibbs monolayer in an expanded, liquid-like phase at equilibrium. The monolayer was subsequently laterally compressed by the barriers of the trough, while simultaneously observing the system using a Brewster angle microscope (BAM). The surface pressure-film area isotherm upon compression showed a kink at a surface pressure (π_kink) comparable to or several mN・m^-1 higher than the surface pressure at the critical micelle concentration (π_CMC), followed by a plateau region. BAM observations revealed that condensed-phase domains were formed in the homogeneous expanded phase at the plateau. Hence, the plateau corresponds to a first-order phase transition from the expanded phase to the condensed phase. As expected, the compressed adsorbed monolayer was in a metastable state because the surface pressure decreased with time, and the condensed-phase domains disappeared when compression was discontinued. The transient formation of a quasi-stable condensed phase may originate from the combined effect of the lower solubility of AG molecules in water, moderately strong attractive intermolecular interactions between AG molecules at the air/water interface, and high-rate compression.

Spin Crossover in Nickel(II) Tetraphenylporphyrinate via Forced Axial Coordination at the Air/Water Interface

Coordination-induced spin crossover (CISCO) in nickel(II) porphyrinates is an intriguing phenomenon that is interesting from both fundamental and practical standpoints. However, in most cases, realization of this effect requires extensive synthetic protocols or extreme concentrations of extra-ligands. Herein we show that CISCO effect can be prompted for the commonly available nickel(II) tetraphenylporphyrinate, NiTPP, upon deposition of this complex at the air/water interface together with a ruthenium(II) phthalocyaninate, CRPcRu(pyz)₂, bearing two axial pyrazine ligands. The latter was used as a molecular guiderail to align Ni···Ru···Ni metal centers for pyrazine coordination upon lateral compression of the system, which helps bring the two macrocycles closer together and forces the formation of Ni–pyz bonds. The fact of Ni(II) porphyrinate switching from low- to high-spin state upon acquiring additional ligands can be conveniently observed in situ via reflection-absorption UV-vis spectroscopy. The reversible nature of this interaction allows for dissociation of Ni–pyz bonds, and thus, change of nickel cation spin state, upon expansion of the monolayer.

Donor-Acceptor Interactions Induced Interfacial Synthesis of an Ultrathin Fluoric 2D Polymer by Photochemical [2+2] Cycloaddition

Two-dimensional polymers (2DPs) have attracted much interest due to their unique 2D atomic-thick covalent network with periodically linked monomers. The preparation of mono- or few-layered 2DPs with highly ordered structures is still a big challenge. Herein, we report a preparation of ultrathin 2DP film based on photo-triggered [2+2] cycloaddition at the air/water interface. The pre-assembly process induced by the D-A interactions before the polymerization plays a key role in constructing the highly ordered structure. The precise structure and chemical compositions of the continuous 2DP films were proved by selected area electron diffraction (SAED), Tip-Enhanced Raman Spectroscopy (TERS) and molecular-mechanics-based structural simulation.

Armoring the Interface with Surfactants to Prevent the Adsorption of Monoclonal Antibodies

The pharmaceutical industry uses surface-active agents (excipients) in protein drug formulations to prevent the aggregation, denaturation, and unwanted immunological response of therapeutic drugs in solution as well as at the air/water interface. However, the mechanism of adsorption, desorption, and aggregation of proteins at the interface in the presence of excipients remains poorly understood. The objective of this work is to explore the molecular-scale competitive adsorption process between surfactant-based excipients and two monoclonal antibody (mAb) proteins, mAb-1 and mAb-2. We use pendant bubble tensiometry to measure the ensemble average adsorption dynamics of mAbs with and without the excipient. The surface tension measurements allow us to quantify the rate at which the molecules "race" to the interface in single-component and mixed systems. These results define the phase space, where coadsorption of both mAbs and excipients occurs onto the air/water interface. In parallel, we use X-ray reflectivity (XR) measurements to understand the molecular-scale dynamics of competitive adsorption, revealing the surface-adsorbed amounts of the antibody and excipient. XR has revealed that at a sufficiently high surface concentration of the excipient, mAb adsorption to the surface and subsurface domains was inhibited. In addition, despite the fact that both mAbs adsorb via a similar mechanistic pathway and with similar dynamics, a key finding is that the competition for the interface directly correlates with the surface activity of the two mAbs, resulting in a fivefold difference in the concentration of the excipient needed to displace the antibody.

Long-Range Lateral Correlation between Self-Assembled Domains of Fluorocarbon-Hydrocarbon Tetrablocks by Quantitative GISAXS

The structure and lateral correlation of fluorocarbon-hydrocarbon tetrablock di(F10Hm) domains at the air/water interface have been determined by quantitative analysis of grazing incidence small-angle X-ray scattering (GISAXS) data. The measured GISAXS signals can be well represented by the full calculation of the form and structure factors. The form factor suggests that di(F10Hm) domains take a hemiellipsoid shape. Both major and minor axes of the hemiellipsoids monotonically increased in response to the elongation of the hydrocarbon blocks, which can be explained by the concominant increase in van der Waals interaction. The structure factor calculated from the GISAXS signals suggests that the domains take an orthorhombic lattice. Remarkably, the lateral correlation can reach over a distance that is more than 14 times longer than the distance to the nearest neighbors. Our data suggest that quantitative GISAXS enables the optimal design of mesoscopic self-assemblies at the air/water interface by fine-tuning of the structures of molecular building blocks.

Photochemical Creation of Covalent Organic 2D Monolayer Objects in Defined Shapes via a Lithographic 2D Polymerization

In this work we prepare Langmuir-Blodgett monolayers with a trifunctional amphiphilic anthraphane monomer. Upon spreading at the air/water interface, the monomers self-assemble into 1 nm-thin monolayer islands, which are highly fluorescent and can be visualized by the naked eye upon excitation. In situ fluorescence spectroscopy indicates that in the monolayers, all the anthracene units of the monomers are stacked face-to-face forming excimer pairs, whereas at the edges of the monolayers, free anthracenes are present acting as edge groups. Irradiation of the monolayer triggers [4 + 4]-cycloadditions among the excimer pairs, effectively resulting in a two-dimensional (2D) polymerization. The polymerization reaction also completely quenches the fluorescence, allowing to draw patterns on the monomer monolayers. More interestingly, after transferring the monomer monolayer on a solid substrate, by employing masks or the laser of a confocal scanning microscope, it is possible to arbitrarily select the parts of the monolayer that one wants to polymerize. The unpolymerized regions can then be washed away from the substrate, leaving 2D macromolecular monolayer objects of the desired shape. This photolithographic process employs 2D polymerizations and affords 1 nm-thin coatings.

Chemical Mapping of Nanodefects within 2D Covalent Monolayers by Tip-Enhanced Raman Spectroscopy

Nanoscale defects in monolayers (MLs) of two-dimensional (2D) materials, such as graphene, transition-metal dichalcogenides, and 2D polymers, can alter their physical, mechanical, optoelectronic, and chemical properties. However, detailed information about nanodefects within 2D covalent monolayers is difficult to obtain because it requires highly selective and sensitive techniques that can provide chemical information at the nanoscale. Here, we report a 2D imine-linked ML prepared from two custom-designed building blocks by dynamic imine chemistry at the air/water interface, in which an acetylenic moiety in one of the blocks was used as a spectroscopic reporter for nanodefects. Combined with density functional theory calculations that take into account surface selection rules, tip-enhanced Raman spectroscopy (TERS) imaging provides information on the chemical bonds, molecular orientation, as well as nanodefects in the resulting ML. Additionally, TERS imaging visualizes the topography and integrity of the ML at Au(111) terrace edges, suggesting possible ductility of the ML. Furthermore, edge-induced molecular tilting and a stronger signal enhancement were observed at the terrace edges, from which a spatial resolution around 8 nm could be deduced. The present work can be used to study covalent 2D materials at the nanoscale, which are expected to be of use when engineering their properties for specific device applications.

Size, Shape, and Lateral Correlation of Highly Uniform, Mesoscopic, Self-Assembled Domains of Fluorocarbon-Hydrocarbon Diblocks at the Air/Water Interface: A GISAXS Study

The shape and size of self-assembled mesoscopic surface domains of fluorocarbon-hydrocarbon (FnHm) diblocks and the lateral correlation between these domains were quantitatively determined from grazing incidence small-angle X-ray scattering (GISAXS). The full calculation of structure and form factors unravels the influence of fluorocarbon and hydrocarbon block lengths on the diameter and height of the domains, and provides the inter-domain correlation length. The diameter of the domains, as determined from the form factor analysis, exhibits a monotonic increase in response to the systematic lengthening of each block, which can be attributed to the increase in van der Waals attraction between molecules. The pair correlation function in real space calculated from the structure factor implies that the inter-domain correlation can reach a distance that is over 25 times larger than the domain's size. The full calculation of the GISAXS signals introduced here opens a potential towards the hierarchical design of mesoscale domains of self-assembled small organic molecules, covering several orders of magnitude in space.

Adsorption and Distribution of Edible Gliadin Nanoparticles at the Air/Water Interface

Edible gliadin nanoparticles (GNPs) were fabricated using the anti-solvent method. They possessed unique high foamability and foam stability. An increasing concentration of GNPs accelerated their initial adsorption speed from the bulk phase to the interface and raised the viscoelastic modulus of interfacial films. High foamability (174.2 ± 6.4%) was achieved at the very low concentration of GNPs (1 mg/mL), which was much better than that of ovalbumin and sodium caseinate. Three stages of adsorption kinetics at the air/water interface were characterized. First, they quickly diffused and adsorbed at the interface, resulting in a fast increase of the surface pressure. Then, nanoparticles started to fuse into a film, and finally, the smooth film became a firm and rigid layer to protect bubbles against coalescence and disproportionation. These results explained that GNPs had good foamability and high foam stability simultaneously. That provides GNPs as a potential candidate for new foaming agents applied in edible and biodegradable products.

Transmission X-ray scattering as a probe for complex liquid-surface structures

The need for functional materials calls for increasing complexity in self-assembly systems. As a result, the ability to probe both local structure and heterogeneities, such as phase-coexistence and domain morphologies, has become increasingly important to controlling self-assembly processes, including those at liquid surfaces. The traditional X-ray scattering methods for liquid surfaces, such as specular reflectivity and grazing-incidence diffraction, are not well suited to spatially resolving lateral heterogeneities due to large illuminated footprint. A possible alternative approach is to use scanning transmission X-ray scattering to simultaneously probe local intermolecular structures and heterogeneous domain morphologies on liquid surfaces. To test the feasibility of this approach, transmission small- and wide-angle X-ray scattering (TSAXS/TWAXS) studies of Langmuir films formed on water meniscus against a vertically immersed hydrophilic Si substrate were recently carried out. First-order diffraction rings were observed in TSAXS patterns from a monolayer of hexagonally packed gold nanoparticles and in TWAXS patterns from a monolayer of fluorinated fatty acids, both as a Langmuir monolayer on water meniscus and as a Langmuir-Blodgett monolayer on the substrate. The patterns taken at multiple spots have been analyzed to extract the shape of the meniscus surface and the ordered-monolayer coverage as a function of spot position. These results, together with continual improvement in the brightness and spot size of X-ray beams available at synchrotron facilities, support the possibility of using scanning-probe TSAXS/TWAXS to characterize heterogeneous structures at liquid surfaces.

Significant Chiral Signal Amplification of Langmuir Monolayers Probed by Second Harmonic Generation

With the development of the nonlinear optical technique such as SHG (second harmonic generation), the in situ measurements of the chirality in the monolayers at the air/water interface have become possible. However, when performing the SHG measurement of the chirality in a monolayer, it is still a great challenge to obtain the chiral signals with a good S/N (signal-to-noise) ratio. In this Letter, interfacial assemblies with induced supramolecular chirality were used to amplify the weak chiral SHG signals from the monolayers at the air/water interface. Tetrakis(4-sulfonatophenyl) porphyrin (TPPS) J aggregates were used as the subphase, and when chiral amphiphilic molecules were spread on it, chiral domains of the amphiphile/TPPS J aggregates were formed and then significantly amplified chiral signals that otherwise could not be detected. Moreover, the sign of the DCE (degree of chiral excess) changed with the chirality of the amphiphilic molecules, thus providing a possible way to obtain the absolute chiral information in situ in the monolayers.

Electron at the Surface of Water: Dehydrated or Not?

The hydrated electron is a crucial species in radiative processes, and it has been speculated that its behavior at the water surface could lead to specific interfacial chemical properties. Here, we address fundamental questions concerning the structure and energetics of an electron at the surface of water. We use the method of ab initio molecular dynamics, which was shown to provide a faithful description of solvated electrons in large water clusters and in bulk water. The present results clearly demonstrate that the surface electron is mostly buried in the interfacial water layer, with only about 10 % of its density protruding into the vapor phase. Consequently, it has a structure that is very similar to that of an electron solvated in the aqueous bulk. This points to a general feature of charges at the surface of water, namely, that they do not behave as half-dehydrated but rather as almost fully hydrated species.

Electrostatic properties of aqueous salt solution interfaces: a comparison of polarizable and nonpolarizable ion models

The effects of ion force field polarizability on the interfacial electrostatic properties of approximately 1 M aqueous solutions of NaCl, CsCl, and NaI are investigated using molecular dynamics simulations employing both nonpolarizable and Drude-polarizable ion sets. Differences in computed depth-dependent orientational distributions, "permanent" and induced dipole and quadrupole moment profiles, and interfacial potentials are obtained for both ion sets to further elucidate how ion polarizability affects interfacial electrostatic properties among the various salts relative to pure water. We observe that the orientations and induced dipoles of water molecules are more strongly perturbed in the presence of polarizable ions via a stronger ionic double layer effect arising from greater charge separation. Both anions and cations exhibit enhanced induced dipole moments and strong z alignment in the vicinity of the Gibbs dividing surface (GDS) with the magnitude of the anion induced dipoles being nearly an order of magnitude larger than those of the cations and directed into the vapor phase. Depth-dependent profiles for the trace and z z components of the water molecular quadrupole moment tensors reveal 40% larger quadrupole moments in the bulk phase relative to the vapor which mimics a similar observed 40% increase in the average water dipole moment. Across the GDS, the water molecular quadrupole moments increase nonmonotonically (in contrast to the water dipoles) and exhibit a locally reduced contribution just below the surface due to both orientational and polarization effects. Computed interfacial potentials for the nonpolarizable salts yield values 20-60 mV more positive than pure water and increase by an additional 30-100 mV when ion polarizability is included. A rigorous decomposition of the total interfacial potential into ion monopole, water and ion dipole, and water quadrupole components reveals that a very strong, positive ion monopole contribution is offset by negative contributions from all other potential sources. Water quadrupole components modulated by the water density contribute significantly to the observed interfacial potential increments and almost entirely explain observed differences in the interfacial potentials for the two chloride salts. By lumping all remaining nonquadrupole interfacial potential contributions into a single "effective" dipole potential, we observe that the ratio of quadrupole to "effective" dipole contributions range from 2:1 in CsCl to 1:1.5 in NaI, suggesting that both contributions are comparably important in determining the interfacial potential increments. We also find that oscillations in the quadrupole potential in the double layer region are opposite in sign and partially cancel those of the "effective" dipole potential.