Repulsive, but sticky - Insights into the non-ionic foam stabilization mechanism by superchaotropic nano-ions.

HYPOTHESIS: The superchaotropic Keggin polyoxometalate α-SiW12O404- (SiW) was recently shown to stabilize non-ionic surfactant (C18:1E10) foams owing to electrostatic repulsion that arises from the adsorption of SiW-ions to the foam interfaces. The precise mechanism of foam stabilization by SiW however remained unsolved. EXPERIMENTS: Imaging and conductimetry were used on macroscopic foams to monitor the foam collapse under free drainage and small angle neutron scattering (SANS) at a given foam height allowed for the tracking of the evolution of film thickness under quasi-stationary conditions. Thin film pressure balance (TFPB) measurements enabled to quantify the resistance of single foam films to external pressure and to identify intra-film forces. FINDINGS: At low SiW/surfactant ratios, the adsorption of SiW induces electrostatic repulsion within foam films. Above a concentration threshold corresponding to an adsorption saturation, excess of SiW screens the electrostatic repulsion that leads to thinner foam films. Despite screened electrostatics, the foam and single foam films remain very stable caused by an additional steric stabilizing force consistent with the presence of trapped micelles inside the foam films that bridge between the interfaces. These trapped micelles can serve as a surfactant reservoir, which promotes self-healing of the interface leading to much more resilient foam films in comparison to bare surfactant foams/films.

Application of Population Balance Models in Particle-Stabilized Dispersions.

In this study, a first approach to model drop size distributions in agitated nanoparticle-stabilized liquid/liquid systems with population balance equations is presented. Established coalescence efficiency models fail to predict the effect of steric hindrance of nanoparticles at the liquid/liquid interface during the film drainage process. A novel modified coalescence efficiency is developed for the population balance framework based on the film drainage model. The elaborate submodel considers the desorption energy required to detach a particle from the interface, representing an energy barrier against coalescence. With an additional implemented function in the population balance framework, the interface coverage rate by particles is calculated for each time step. The transient change of the coverage degree of the phase interface by particles is thereby considered in the submodel. Validation of the modified submodel was performed with experimental data of agitated water-in-oil (w/o) dispersions, stabilized by well-defined spherical silica nanoparticles. The nanospheres with a size of 28 nm are positively charged and were hydrophobized by silanization with dimethyloctadecyl[3-(trimethoxysilyl)propyl]ammoniumchloride. This modeling approach is a first step toward predicting time-resolved dynamic drop size distributions of nanoparticle-stabilized liquid/liquid systems.

Light-Controlled Lyotropic Liquid Crystallinity of Polyaspartates Exploited as Photo-Switchable Alignment Medium.

Two polyaspartates bearing ortho-fluorinated azobenzenes (pFAB) as photo-responsive groups in the side chain were synthesized: PpFABLA (1) and co-polyaspartate PpFABLA-co-PBLA [11, 75%(n/n) PpFABLA content]. As a consequence of the E/Z-isomerization of the side chain, PpFABLA (1) undergoes a visible-light-induced reversible coil-helix transition in solution: Green light (525 nm) affords the coil, and violet light (400 nm) affords the helix. pFAB significantly increases the thermal stability of the Z-isomer at 20 °C (t1/2 = 66 d for the Z-isomer) and effectively counters the favored back formation of the helix. At 20%(w/w) polymer concentration, the helical polymer forms a lyotropic liquid crystal (LLC) that further orients unidirectionally inside a magnetic field, while the coil polymer results in an isotropic solution. The high viscosity of the polymer solution stabilizes the coexistence of liquid crystalline and isotropic domains, which were obtained with spatial control by partial light irradiation. When used as an alignment medium, PpFABLA (1) enables (i) the measurement of dipolar couplings without the need for a separate isotropic reference and (ii) the differentiation of enantiomers. PpFABLA-co-PBLA (11) preserves the helical structure, by intention, independently of the E/Z-isomerization of the side chain: Both photo-isomers of PpFABLA-co-PBLA (11) form a helix that─at a concentration of 16%(w/w)─form an LLC. Despite the absence of a change in the secondary structure, the E/Z-isomerization of the side chain changes the morphology of the liquid crystal and leads to different sets of dipolar coupling for the same probe molecule.

When Bulk Matters: Disentanglement of the Role of Polyelectrolyte/Surfactant Complexes at Surfaces and in the Bulk of Foam Films.

Foam films display exciting systems as on one hand they dictate the performance of macroscopic foams and on the other hand they allow studies of surface forces. With regard to surface forces, we attempt to disentangle the effect of the foam film surfaces and the foam film bulk. For that, we study the influence of salt (LiBr) on foam films formed by mixtures of oppositely charged polyelectrolyte and surfactant: anionic monosulfonated polyphenylene sulfone (sPSO2-220) and cationic tetradecyltrimethylammonium bromide (C14TAB). Adding a small amount of salt (≤10-3 M) decreases the foam film stability due to a weakened electrostatic net repulsion. In contrast, a large amount of salt (10-2 M) unexpectedly increases the foam film stability. Disjoining pressure isotherms reveal that the increased stability is due to an additional steric stabilization, which is attributed to sPSO2-220/C14TAB complexes in the film bulk. These bulk complexes also contribute to the measured apparent surface potential between the two air/water interfaces. We find, for the first time, the formation of Newton black films for mixtures of anionic polyelectrolytes and cationic surfactants.

Structure formation of PNIPAM microgels in foams and foam films.

Responsive aqueous foams are very interesting from a fundamental point of view and for various applications like foam flooding or foam flotation. In this study thermoresponsive microgels (MGs) made from poly(N-isopropyl-acrylamide) (PNIPAM) with varying cross-linker content, are used as foam stabilisers. The foams obtained are thermoresponsive and can be destabilised by increasing the temperature. The structuring of MGs inside the foam films is investigated with small-angle neutron scattering and in a thin film pressure balance. The foam films are inhomogeneous and form a network-like structure, in which thin and MG depleted zones with a thickness of ca. 30 nm are interspersed in a continuous network of thick MG containing areas with a thickness of several 100 nm. The thickness of this continuous network is related to the elastic modulus of the individual MGs, which was determined by atomic force microscopy indentation experiments. Both, the elastic moduli and foam film thicknesses, indicate a correlation to the network elasticity of the MGs predicted by the affine network model.

Frequency-Dependent Ultrasonic Stimulation of Poly(N-Isopropylacrylamide) Microgels in Water.

As a novel stimulus, we use high-frequency ultrasonic waves to provide the required energy for breaking hydrogen bonds between Poly(N-isopropylacrylamide) (PNIPAM) and water molecules while the solution temperature is maintained below the volume phase transition temperature (VPTT = 32 °C). Ultrasonic waves propagate through the solution and their energy will be absorbed due to the liquid viscosity. The absorbed energy partially leads to the generation of a streaming flow and the rest will be spent to break the hydrogen bonds. Therefore, the microgels collapse and become insoluble in water and agglomerate, resulting in solution turbidity. We use turbidity to quantify the ultrasound energy absorption and show that the acousto-response of PNIPAM microgels is a temporal phenomenon that depends on the duration of the actuation. Increasing the solution concentration leads to a faster turbidity evolution. Furthermore, an increase in ultrasound frequency leads to an increase in the breakage of more hydrogen bonds within a certain time and thus faster turbidity evolution. This is due to the increase in ultrasound energy absorption by liquids at higher frequencies.

Maximum Incorporation of Soft Microgel at Interfaces of Water in Oil Emulsion Droplets Stabilized by Solid Silica Spheres.

The incorporation of soft hydrophilic particles at the interface of water in non-polar oil emulsion droplets is crucial for several applications. However, the stabilization of water in non-polar oil emulsions with hydrophilic soft material alone is, besides certain exceptions, not possible. In our previous works, we showed that stabilizing the emulsions with well-characterized spherical hydrophobic silica nanospheres (SNs) and soft equally charged microgel particles (MGs) is a robust strategy to stabilize w/o emulsions while still incorporating a large amount of MGs at the interface. In the present study, we address the question of what the maximum amount of MGs at the interface in these kinds of emulsion droplets can be. By using well-characterized mono-disperse SNs, we are able to calculate the fraction of interface covered by the SNs and complementary that of the present MG. We found that it is not possible to decrease the SN coverage below 56% irrespective of MG softness and SN size. The findings elucidate new perspectives to the broader topic of soft/solid stabilized emulsions.

A new model to describe small-angle neutron scattering from foams.

The modelling of scattering data from foams is very challenging due to the complex structure of foams and is therefore often reduced to the fitting of single peak positions or feature mimicking. This article presents a more elaborate model to describe the small-angle neutron scattering (SANS) data from foams. The model takes into account the geometry of the foam bubbles and is based on an incoherent superposition of the reflectivity curves arising from the foam films and the small-angle scattering (SAS) contribution from the plateau borders. The model is capable of describing the complete scattering curve of a foam stabilized by the standard cationic surfactant tetradecyltrimethylammonium bromide (C14TAB) with different water contents, i.e. different drainage states, and provides information on the thickness distribution of liquid films inside the foam. The mean film thickness decreases with decreasing water content because of drainage, from 28 to 22 nm, while the polydispersity increases. These results are in good agreement with the film thicknesses of individual horizontal foam films studied with a thin-film pressure balance.

Amphiphilic Polymer Conetwork Gel Films Based on Tetra-Poly(ethylene Glycol) and Tetra-Poly(ε-Caprolactone).

The preparation and investigation of gel films from a model amphiphilic polymer conetwork (ACN) grant a deeper control and understanding of the structure-property relationship in the bulk phase and at the interface of materials with promising applications. In order to allow the simultaneous transport of hydrophilic and hydrophobic substances, polymeric networks with finely distributed hydrophilic and hydrophobic components are very suitable. When designing new soft materials such as coatings, in addition to the structure in the bulk phase, the structure at the interface plays a critical role. In this study, two alternating tetra-arm star polymers poly(ε-caprolactone) (tetra-PCL-Ox) and amino-terminated poly(ethylene glycol) (tetra-PEG-NH2) form an amphiphilic polymer conetwork. The correlation between different synthesis strategies for gel films of this ACN model system and their resulting properties will be described. Through various spin coating techniques, control over film thickness and roughness is achievable and highlights differences to macroscopic gel samples. Atomic force microscopy (AFM) measurements reveal the effect of solvents of different polarities on the swelling ability and surface structure. This correlates with AFM investigations of the mechanical properties on ACN gel films, demonstrating a strong effect on the resulting elastic modulus E, depending on the presence or absence of a good solvent during synthesis. Furthermore, a higher E modulus is obtained in the presence of the selective solvent water, compared to the non-selective solvent toluene. This observation is explained through selective swelling of the tetra-arm star polymers displaying a different hydrophobicity.

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.

Cohesion Gain Induced by Nanosilica Consolidants for Monumental Stone Restoration.

Mineral nanoparticle suspensions with consolidating properties have been successfully applied in the restoration of weathered architectural surfaces. However, the design of these consolidants is usually stone-specific and based on trial and error, which prevents their robust operation for a wide range of highly heterogeneous monumental stone materials. In this work, we develop a facile and versatile method to systematically study the consolidating mechanisms in action using a surface forces apparatus (SFA) with real-time force sensing and an X-ray surface forces apparatus (X-SFA). We directly assess the mechanical tensile strength of nanosilica-treated single mineral contacts and show a sharp increase in their cohesion. The smallest used nanoparticles provide an order of magnitude stronger contacts. We further resolve the microstructures and forces acting during evaporation-driven, capillary-force-induced nanoparticle aggregation processes, highlighting the importance of the interactions between the nanoparticles and the confining mineral walls. Our novel SFA-based approach offers insight into nano- and microscale mechanisms of consolidating silica treatments, and it can aid the design of nanomaterials used in stone consolidation.

Copolymerization Kinetics of Dopamine Methacrylamide during PNIPAM Microgel Synthesis for Increased Adhesive Properties.

Combining stimuli-responsive properties of gels with adhesive properties of mussels is highly interesting for a large field of applications as, e.g., in life science. Therefore, the present paper focuses on the copolymerization of poly(N-isopropylacrylamide) (PNIPAM) microgels with dopamine methacrylamide (DMA). A detailed understanding of reaction kinetics is crucial to figure out an optimized synthesis strategy for tailoring microgels with adhesive properties. The present study addresses the influence of relevant synthesis parameters as the injection time of DMA during the microgel synthesis and the overall reaction time of the microgel. Reaction kinetics were studied by mass spectrometry of time samples taken during the microgel synthesis. This allowed us to determine the monomer consumption of NIPAM, the cross-linker N,N'-methylenebisacrylamide (BIS), and DMA. A second-order reaction kinetics was found for DMA incorporation. The amount of DMA incorporated in the resulting microgel was successfully determined by a combination of UV-vis and NMR spectroscopy to level off limitations of both methods. The dependence of the hydrodynamic radius on temperature was determined by DLS measurements for the microgels. While an early injection of DMA stops the PNIPAM polymerization due to scavenging, it greatly enhances the reaction speed of DMA. The faster reaction of DMA and the incomplete NIPAM and BIS conversion also compensate for shorter reaction times with respect to the incorporated amount of DMA. On the contrary, a later injection of DMA leads to a full NIPAM monomer and BIS cross-linker consumption. An overall reaction time of 60 min ensures the DMA incorporation. Longer reaction times lead to clumping. First adhesion tests show an increased adhesion of P(NIPAM-co-DMA) microgels compared to pure PNIPAM microgels, when mechanical stress is applied.

Magnetic response of CoFe2O4 nanoparticles confined in a PNIPAM microgel network.

The paper addresses coupling of magnetic nanoparticles (MNPs) with the polymer matrix of temperature-sensitive microgels and their response to magnetic fields. Therefore, CoFe2O4@CA (CA = citric acid) NPs are embedded within N-isopropylacrylamid (NIPAM) based microgels. The volume phase transition (VPT) of the magnetic microgels and the respective pure microgels is studied by dynamic light scattering and electrophoretic mobility measurements. The interaction between MNPs and microgel network is studied via magnetometry and AC-susceptometry using a superconducting quantum interference device (SQUID). The data show a significant change of the magnetic properties by crossing the VPT temperature (VPTT). The change is related to the increased confinement of the MNP due to the shrinking of the microgels. Modifying the microgel with hydrophobic allyl mercaptan (AM) affects the swelling ability and the magnetic response, i.e. the coupling of MNPs with the polymer matrix. Modeling the AC-susceptibility data results in an effective size distribution. This distribution represents the varying degree of constraint in MNP rotation and motion by the microgel network. These findings help to understand the interaction between MNPs and the microgel matrix to design multi responsive systems with tunable particle matrix coupling strength for future applications.

Shape and Structure Formation of Mixed Nonionic-Anionic Surfactant Micelles.

Aqueous solutions of a nonionic surfactant (either Tween20 or BrijL23) and an anionic surfactant (sodium dodecyl sulfate, SDS) are investigated, using small-angle neutron scattering (SANS). SANS spectra are analysed by using a core-shell model to describe the form factor of self-assembled surfactant micelles; the intermicellar interactions are modelled by using a hard-sphere Percus-Yevick (HS-PY) or a rescaled mean spherical approximation (RMSA) structure factor. Choosing these specific nonionic surfactants allows for comparison of the effect of branched (Tween20) and linear (BrijL23) surfactant headgroups, both constituted of poly-ethylene oxide (PEO) groups. The nonionic-anionic surfactant mixtures are studied at various concentrations up to highly concentrated samples (ϕ ≲ 0.45) and various mixing ratios, from pure nonionic to pure anionic surfactant solutions. The scattering data reveal the formation of mixed micelles already at concentrations below the critical micelle concentration of SDS. At higher volume fractions, excluded volume effects dominate the intermicellar structuring, even for charged micelles. In consequence, at high volume fractions, the intermicellar structuring is the same for charged and uncharged micelles. At all mixing ratios, almost spherical mixed micelles form. This offers the opportunity to create a system of colloidal particles with a variable surface charge. This excludes only roughly equimolar mixing ratios (X≈ 0.4-0.6) at which the micelles significantly increase in size and ellipticity due to specific sulfate-EO interactions.

Understanding near-surface polymer dynamics by a combination of grazing-incidence neutron scattering and virtual experiments.

Neutron spin-echo spectroscopy is a unique experimental method for the investigation of polymer dynamics. The combination of neutron spin-echo spectroscopy with grazing-incidence geometry (GINSES) opens the possibility to probe the dynamics of soft-matter materials in the vicinity of the solid substrate in the time range up to 100 ns. However, the usage of the GINSES technique has some peculiarities and, due to the novelty of the method and complexity of the scattering geometry, difficulties in further data analysis occur. The current work discusses how virtual experiments within the distorted-wave Born approximation using the BornAgain software can improve GINSES data treatment and aid the understanding of polymer dynamics in the vicinity of the solid surface. With two examples, poly(N-isopropyl acrylamide) brushes and poly(ethylene glycol) microgels on Si surfaces, the simulation as well as the application of the simulation to the GINSES data analysis are presented. The approach allowed a deeper insight to be gained of the background effect and scattering contribution of different layers.

Model Surfaces for Paper Fibers Prepared from Carboxymethyl Cellulose and Polycations.

For tailored functionalization of cellulose based papers, the interaction between paper fibers and functional additives must be understood. Planar cellulose surfaces represent a suitable model system for studying the binding of additives. In this work, polyelectrolyte multilayers (PEMs) are prepared by alternating dip-coating of the negatively charged cellulose derivate carboxymethyl cellulose and a polycation, either polydiallyldimethylammonium chloride (PDADMAC) or chitosan (CHI). The parameters varied during PEM formation are the concentrations (0.1-5 g/L) and pH (pH = 2-6) of the dipping solutions. Both PEM systems grow exponentially, revealing a high mobility of the polyelectrolytes (PEs). The pH-tunable charge density leads to PEMs with different surface topographies. Quartz crystal microbalance experiments with dissipation monitoring (QCM-D) reveal the pronounced viscoelastic properties of the PEMs. Ellipsometry and atomic force microscopy (AFM) measurements show that the strong and highly charged polycation PDADMAC leads to the formation of smooth PEMs. The weak polycation CHI forms cellulose model surfaces with higher film thicknesses and a tunable roughness. Both PEM systems exhibit a high water uptake when exposed to a humid environment, with the PDADMAC/carboxymethyl cellulose (CMC) PEMs resulting in a water uptake up to 60% and CHI/CMC up to 20%. The resulting PEMs are water-stable, but water swellable model surfaces with a controllable roughness and topography.

The quantitative impact of fluid vs. solid interfaces on the catalytic performance of pickering emulsions.

Pickering emulsions (PEs), i.e. particle stabilized emulsions, are used as reaction environments in biphasic catalysis for the hydroformylation of 1-dodecene into tridecanal using the catalyst rhodium (Rh)-sulfoxantphos (SX). The present study connects the knowledge about particle-catalyst interactions and PE structure with the reaction results. It quantifies the efficiency of the catalytic performance of the catalyst localized in the voids between the particles (liquid-liquid interface) and the catalyst adsorbed on the particle surface (liquid-solid interface) using a new numerical approach. First, it is ensured that the overall packing density and geometry at the droplet interface and the size of the water droplets of the resulting w/o PEs are predictable. Second, it is shown that approximately all particles assemble at the droplet surface after emulsion preparation and neither the packing parameter nor the droplet size change with the particle surface charge or size when the total particle cross section is kept constant. Third, studies on the influence of the catalyst on the emulsion structure reveal that irrespective of the particle charge the surface active and negatively charged catalyst Rh-SX reduces the PE droplet size significantly and decreases the particle packing parameter from s = 0.91 (hexagonal packing in 2D) to s = 0.69 (shattered structure). In this latter case, large voids of the free w/o interface form and become covered with the catalyst. With a deep knowledge about the PE structure the reaction efficiencies of the liquid-liquid vs. the solid-liquid interface are quantified. By excluding any other influence factors, it is shown that the activity of the catalyst is the same at the fluid and solid interface and the performance of the reaction is explained by the geometry of the system. After the reaction, the catalyst retention via membrane filtration is shown to be successfully achieved without damaging the emulsions. This enables the continuous recovery of the catalyst, i.e. the most expensive compound in PE-based catalytic reactions, being a crucial criterion for industrial applications.

Exploring water in oil emulsions simultaneously stabilized by solid hydrophobic silica nanospheres and hydrophilic soft PNIPAM microgel.

A general drawback of microgels is that they do not stabilize water-in-oil (w/o) emulsions of non-polar oils. Simultaneous stabilization with solid hydrophobic nanoparticles and soft hydrophilic microgels overcomes this problem. For a fundamental understanding of this synergistic effect the use of well defined particle systems is crucial. Therefore, the present study investigates the stabilization of water droplets in a highly non-polar oil phase using temperature responsive, soft and hydrophilic PNIPAM microgel particles (MGs) and solid and hydrophobic silica nanospheres (SNs) simultaneously. The SNs are about 20 times smaller than the MGs. In a multiscale approach the resulting emulsions are studied from the nanoscale particle properties over microscale droplet sizes to macroscopic observations. The synergy of the particles allows the stabilization of water-in-oil (w/o) emulsions, which was not possible with MGs alone, and offers a larger internal interface than the stabilization with SNs alone. Furthermore, the incorporation of hydrophilic MGs into a hydrophobic particle layer accelerates the emulsions sedimentation speed. Nevertheless, the droplets are still sufficiently protected against coalescence even in the sediment and can be redispersed by gentle shaking. Based on droplet size measurements and cryo-SEM studies we elaborate a model, which explains the found phenomena.

Non-monotonic speed-dependence of microswimmers on wall distance.

While substrates naturally occur in most microswimmer experiments, their impact on the swimming performance is not well understood. In the present study, we functionalize substrates with polymer brushes of varying swelling properties, grafting densities and brush lengths to systematically modify and explore the substrate-swimmer interactions. Notably, the swimming speed does not monotonically change with brush thickness, but shows a distinct maximum at a certain intermediate thickness, which results from two counteracting factors: surface charge and surface roughness. The results show that the speed of thermophoretic microswimmers does not only depend on the particle properties but is also strongly influenced by the properties of the underlying substrate. This provides a route to control the speed of microswimmers via the underlying substrate, which could be applied in the future e.g. to design complex motility landscapes by patterning substrates with polymer brushes. It is expected that similar effects would occur for diffusio- and electrophoretic particles.

Untangling superposed double layer and structural forces across confined nanoparticle suspensions.

The description of forces across confined complex fluids still holds many challenges due to the possible overlap of different contributions. Here, an attempt is made to untangle the interaction between charged surfaces across nanoparticle suspensions. Interaction forces are measured using colloidal-probe atomic force microscopy. The experimental force profiles are considered as a superposition of double layer and structural forces. In order to independently describe the decay of the double layer force, the ionic strength of the suspension is determined by electrolytic conductivity measurements. Jellium approximation is used to define the impact of the fluid on screening the surface potential. There, the nanoparticles are considered homogeneously distributed across the fluid and screening is only carried out via the particles counterions and added salt. The structural force follows a damped oscillatory profile due to the layer-wise expulsion of the nanoparticles upon approach of both surfaces. The description of the oscillatory structural force is extended by a depletion layer next to the confining surfaces, with no nanoparticles present. The thickness of the depletion layer is related to the electrostatic repulsion of the charged nanoparticles from the like-charged surfaces. The results show that the total force profile is a superposition of independent force contributions without any mutual effects. Using this rather simple model describes the complete experimentally determined interaction force profiles very well from surface separations of a few hundred nanometres down to the surfaces being almost in contact.