Direct Force Measurements Research Articles

Impact of adhesive area on cellular traction force and spread area.

Cells integrate endogenous and exogenous mechanical forces to sense and respond to environmental signals. In particular, cell-generated microscale traction forces regulate cellular functions and impact macroscale tissue function and development. Many groups have developed tools for measuring cellular traction forces, including microfabricated post array detectors (mPADs). mPADs are a powerful tool that provides direct traction force measurements through imaging post deflections and utilizing Bernoulli-Euler beam theory. In this technical note, we investigated how mPADs presenting two different top surface areas but similar effective stiffness influence cellular spread area and traction forces for murine embryonic fibroblasts and human mesenchymal stromal cells. When focal adhesion size was restricted via mPAD top surface area, we observed a decrease in both cell spread area and cell traction forces as the mPAD top surface area decreased, but the traction force-cell area linear relationship was maintained, which is indicative of cell contractility. We conclude that the mPAD top surface area is an important parameter to consider when utilizing mPADs to measure cellular traction forces. Furthermore, the slope of the traction force-cell area linear relationship provides a useful metric to characterize cell contractility on mPADs.

Hardware-in-the-Loop Test Bench for Simulation of Catenary-Pantograph Interaction (CPI) with Linear Camera Measurement.

Catenary-pantograph contact force is generally used for assessment of the current collection quality. A good current collection quality not only increases catenary lifetime but also keeps a stable electric supply and helps to avoid accidents. Low contact forces lead to electric arcs that degrade the catenary, and high contact forces generate excessive wear on the sliding surfaces. Railway track operators require track tests to ensure that catenary-pantograph force remains between safe values. However, a direct measure of the contact force requires an instrumented pantograph which is generally costly and complicated. This paper presents a test bench that allows testing virtual catenaries over real pantographs. Therefore, the contact point force behavior can be tested before the track test to guarantee that the test is passed. Moreover, due to its flexibility, the system can be used for model identification and validation, catenary testing, or contact loss simulation. The test bench also explores using computer vision as an additional sensor for each application. Results show that the system has high precision and flexibility in the available tests.

Image-Guided Measurement of Radiation Force Induced by Focused Ultrasound Beams.

The radiation force balance (RFB) is a widely used method for measuring acoustic power output of ultrasonic transducers. The reflecting cone target is attractive due to its simplicity and long-term stability, at a reasonable cost. However, accurate measurements using this method depend on the alignment between the ultrasound beam and cone axes, especially for highly focused beams utilized in therapeutic applications. With the advent of dual-mode ultrasound arrays (DMUAs) for imaging and therapy, image-guided measurements of acoustic output using the RFB method can be used to improve measurement accuracy. In this article, we describe an image-guided RFB measurement of focused DMUA beams using a widely used commercial instrument. DMUA imaging is used to optimize the alignment between the acoustic beam and reflecting cone axes. In addition to image-guided alignment, DMUA echo data is used to track the displacement of the cone, which provides an auxiliary measurement of acoustic power. Experimental results using a DMUA prototype with [Formula: see text] shows that 1-2 mm of misalignment can result in 5%-14% error in the measured acoustic power. In addition to the use of B-mode image guidance for improving measurement accuracy, we present preliminary results demonstrating the benefit of displacement tracking using real-time DMUA imaging during the application of (sub)therapeutic focused beams. Displacement tracking provides a direct measurement of the radiation force with high sensitivity and follows the expected dependence on changes in amplitude and duty cycle (DC) of the focused ultrasound (FUS) beam. This could lead to simpler, more reliable methods for measuring acoustic power based on the radiation force principle. Combined with appropriate computational modeling, the direct measurement of acoustic radiation force could lead to reliable dosimetry in situ in emerging applications such as transcranial FUS (tFUS) therapies.

Experimental research on the contact force of the bi-directional pig in oil and gas pipeline

The migration process of the pig in oil and gas pipeline is a complex dynamic problem. During the pigging operation, the variation of friction force caused by the nonlinear contact between the sealing disc and the pipe wall is the key factor affecting the dynamic characteristics of the pig motion. At present, the existed pigging models for predicting pigging behavior regard friction as an invariant constant. Experimental research indicates that the friction force of the pig varies with the contact force and the lubrication conditions. Therefore, the assumption that the friction force is constant cannot reflect the friction dynamic characteristics of the pig during pigging, and will also affect the accuracy of the pigging model. Exploring the variation of friction force of pig under different conditions is the basis of establishing the transient dynamic model of a pig. As a result, in this paper, a method of direct measurement of contact force between the pig and the pipeline is presented, the contact force, the friction force, as well as the friction coefficient of the pig are obtained from the experiment. Research results in this paper can help to establish a more accurate dynamic model of pig.

Direct measurement of three-dimensional forces at the medial meniscal root: A validation study

The posterior medial meniscal root (PMMR) experiences variable and multiaxial forces during loading. Current methods to measure these forces are limited and fail to adequately characterize the loads in all three dimensions at the root. Our novel technique resolved these limitations with the installation of a 3-axis sensing construct that we hypothesized would not affect contact mechanics, would not impart extraneous loads onto the PMMR, would accurately measure forces, and would not deflect under joint loads. Six cadaveric specimens were dissected to the joint capsule and a sagittal-plane, femoral condyle osteotomy was performed to gain access to the root. The load sensor was placed below the PMMR and was validated across four tests. The contact mechanics test demonstrated a contact area precision of 44 mm2 and a contact pressure precision of 5.0 MPa between the pre-installation and post-installation states. The tibial displacement test indicated an average bone plug displacement of < 1 mm in all directions. The load validation test exhibited average precision values of 0.7 N in compression, 0.5 N in tension, 0.3 N in anterior-posterior shear, and 0.3 N in medial–lateral shear load. The bone plug deflection test confirmed < 2 mm of displacement in any direction when placed under a load. This is the first study to successfully validate a technique for measuring both magnitude and direction of forces experienced at the PMMR. This validated method has applications for improving surgical repair techniques and developing safer rehabilitation and postoperative protocols that decrease root loads.

Ternary Synergy of Lys, Dopa, and Phe Results in Strong Cohesion of Peptide Films.

Synergistic interactions between 3,4-dihydroxyphenylalanine (Dopa, Y*), cationic residues, and the aromatic rings have been recently highlighted as influential factors that enhance the underwater adhesion strength of mussel foot proteins and their derivatives. In this study, we report the first ever evidence of a cation-catechol-benzene ternary synergy between Y*, lysine (Lys, K), and phenylalanine (Phe, F) in adhesive peptides. We synthesized three hexapeptides containing a different combination of Y*, K, and F, i.e., (KY*)3, (KF)3, and (KY*F)2, respectively, exploring the relationship between the cohesive performance and molecular architecture of peptides. The peptide with the (KY*F)2 sequence displays the strongest underwater cohesion energy of 10.3 ± 0.3 mJ m-2 from direct nanoscale surface force measurements. Combined with molecular dynamics simulation, we demonstrated that there are more bonding interactions (including cation-π, π-π, and hydrogen bond interactions) in (KY*F)2 compared to the other two peptides. In addition, peptide (KY*F)2 still shows the strongest cohesive energies of 7.6 ± 0.7 and 3.7 ± 0.5 mJ m-2 in acidic and high-ionic strength environments, respectively, although the cohesive energy decreases compared to the value in pure water. Our results further explain the underwater cohesion mechanisms combining multiple interactions and offer insights on designing Dopa containing underwater adhesives.

Direct Measurement of Kinetic Force Generated by Mycoplasma.

Optical tweezers enable us to measure the force generated by bacterial motility and motor proteins. Here, we describe a method, using optical tweezers and related techniques, to measure the force generated during Mycoplasma gliding. An avidin-conjugated polystyrene bead trapped by a focused laser beam is bound to the surface-biotinylated Mycoplasma cell, which pulls the bead from the trap center of the laser. The force generated by Mycoplasma is calculated from a displacement measured and a spring constant of the laser trap.

Fluid droplet spreading and adhesion studied with a microbalance: a review

A contact angle observed for a liquid–solid system is not necessarily a unique value, and a few contact angles need to be considered carefully in relation to liquid spreading, adhesion and phase separation. Understanding of the significance of different contact angles has improved in the last few years through direct measurements of interactive forces between droplets/bubbles and solids together with the simultaneous visualization of the changes in their shapes. A microelectronic balance system is employed to measure the force of spreading after either liquid droplet or gas bubble attachment to a substrate surface and the droplet/bubble–substrate adhesion forces after droplet/bubble compression, retraction and detachment. Equipped with a camera in flank and data-acquisition software, the instrument measures directly the forces, monitors droplet/bubble–surface separation with respect to distances over which the droplet/bubble stretches and collects optical images simultaneously. The images are used to analyze capillary pressure and surface tension forces based on the measured droplet/bubble dimensions, shapes of surfaces and values of contact angles. These measurements allow researchers to correlate the advancing, receding and most stable contact angles with liquid–solid interactive forces and analyze their scientific meaning. This review summarizes the very recent literature reports on measurements and interpretation of liquid droplet/gas bubble interactive forces and associated contact angles.

Rotor performance enhancement by alternating current dielectric barrier discharge plasma actuation

An experimental system was established to explore the plasma flow control effect for helicopter rotors in hover mode. With the plasma actuator applied at the leading edge of the rotor blades, alternating current dielectric barrier discharge (AC-DBD) plasma actuation was generated by a sinusoidal AC high-voltage generator. By direct force measurement, the influence of actuation parameters on the aerodynamic performance of the rotor was investigated at a tip Reynolds number of 1.7 × 105. AC-DBD actuation can delay the blade stall to more than 3° with a 20% increase of about in the thrust coefficient at the post-stall pitch. At a constant motor power driving the rotor, AC-DBD actuation could reduce the rotor’s torque at the stalled pitch and increase the rotational speed of the rotor. Also, AC-DBD actuation could maintain a relatively high hover efficiency of the rotor at large collective pitches. In a wide range of actuation parameters, AC-DBD plasma actuation could improve the rotor’s aerodynamic performance at large blade pitches. High-speed photography of the tuft motion on the blade’s upper surface showed that AC-DBD plasma actuation could promote the reattachment of the blade’s separation flow.

Experiments on the localized interaction at the interface fuel rod/spacer grid in pressurized water reactors

The release of fissile material into the coolant caused by fretting of the fuel rods at the interface with spacer grids is a significant safety issue and cause of financial losses in the operation of Pressurized Water Reactors (PWRs). Each fuel rod is kept in position inside spacer grids through friction from the preload exerted by retaining elements (springs and dimples). Fretting of the fuel rods occurs at the contact with the springs and dimples. In severe fretting cases the integrity of the fuel rod cladding is compromised and fission byproducts enter the primary coolant circuit. The reciprocating motion at the contact interface of the fuel rods and spacer grids resulting in material fretting is due to the Flow-Induced Vibrations (FIV) of fuel rods, caused by the unstable surrounding coolant flow, which in PWRs is predominantly parallel to the length of fuel rods (axial flow). Under specific flow conditions, fretting develops rapidly. The vibrations of fuel rods, as well as the relationship of fretting wear mechanisms with several factors associated with the fission process and coolant flow dynamics and stability (vibration amplitude, preload, oscillating loads, irradiation, axial slip, spring relaxation, temperature, oxidation, material of spacer grids and fuel rods), have been considered in the literature. However, direct experimental measurements of the contact force and axial slip during FIV have not been treated in the literature, likely because of the absence of suitable measurement methods. This gap in experimental measurement techniques is addressed in this work, specifically for the analysis of PWR fuel assemblies, by installing a piezoelectric stack and aiming laser Doppler vibrometers on a one-meter-long fuel rod, supported by two full-scale spacer grids, in-air or immersed in quiescent water. In the presence of small- and large- amplitude forced vibrations, the signal of the piezoelectric force transducer increases with the amplitude of vibration, but it is also affected by vibrations perpendicular to the excitation, which appear for large-amplitude excitations. The axial motion of the fuel rod at the spacer grid has a complex evolution and is significant for large-amplitude vibrations only. At any rate, the time histories of contact force and axial motion display the effects of impacts and slips, particularly during the tests in water. The measurement system shows that the severity of the interaction at the spacer grid interfaces is influenced strongly by the amplitude of the forced fuel rod vibrations. Since fuel rods and fuel assemblies are prone to several nonlinear phenomena, as demonstrated by recent studies, it follows that the usage of nonlinear models will be essential to numerically estimating the severity of fretting.

Using colloidal AFM probe technique and XDLVO theory to predict the transport of nanoplastics in porous media

The plastic concentration in terrestrial systems is orders of magnitude higher than that found in marine ecosystems, which has raised global concerns about their potential risk to agricultural sustainability. Previous research on the transport of nanoplastics in soil relied heavily on the qualitative prediction of the mean-field extended Derjaguin–Landau–Verwey–Overbeek theory (XDLVO), but direct and quantitative measurements of the interfacial forces between single nanoplastics and porous media are lacking. In this study, we conducted multiscale investigations ranging from column transport experiments to single particle measurements. The maximum effluent concentration (C/C0) of amino-modified nanoplastics (PS–NH2) was 0.94, whereas that of the carboxyl-modified nanoplastics (PS–COOH) was only 0.33, indicating PS-NH2 were more mobile than PS-COOH at different ionic strengths (1–50 mM) and pH values (5–9). This phenomenon was mainly attributed to the homogeneous aggregation of PS-COOH. In addition, the transport of PS-NH2 in the quartz sand column was inhibited with the increase of ionic strength and pH, and pH was the major factor governing their mobility. The transport of PS-COOH was inhibited with increasing ionic strength and decreasing pH. Hydrophilicity/hydrophobicity-mediated interactions and particle heterogeneity strongly interfered with interfacial forces, leading to the qualitative prediction of XDLVO, contrary to experimental observations. Through the combination of XDLVO and colloidal atomic force microscopy, accurate and quantitative interfacial forces can provide compelling insight into the fate of nanoparticles in the soil environment.

Probing and Manipulating Noncovalent Interactions in Functional Polymeric Systems.

Noncovalent interactions, which usually feature tunable strength, reversibility, and environmental adaptability, have been recognized as driving forces in a variety of biological and chemical processes, contributing to the recognition between molecules, the formation of molecule clusters, and the establishment of complex structures of macromolecules. The marriage of noncovalent interactions and conventional covalent polymers offers the systems novel mechanical, physicochemical, and biological properties, which are highly dependent on the binding mechanisms of the noncovalent interactions that can be illuminated via quantification. This review systematically discusses the nanomechanical characterization of typical noncovalent interactions in polymeric systems, mainly through direct force measurements at microscopic, nanoscopic, and molecular levels, which provide quantitative information (e.g., ranges, strengths, and dynamics) on the binding behaviors. The fundamental understandings of intermolecular and interfacial interactions are then correlated to the macroscopic performances of a series of noncovalently bonded polymers, whose functions (e.g., stimuli-responsiveness, self-healing capacity, universal adhesiveness) can be customized through the manipulation of the noncovalent interactions, providing insights into the rational design of advanced materials with applications in biomedical, energy, environmental, and other engineering fields.

Modelling wave attenuation through submerged vegetation canopies using a subgrid canopy flow model

Coastal canopies formed by aquatic vegetation can significantly modify nearshore wave processes, which has motivated numerous laboratory and field studies investigating how wave attenuation occurs for a wide range of canopies as a function of wave conditions and canopy properties. To predict wave dissipation by canopies, numerous formulations have been derived to describe canopy drag through use of empirical drag coefficients. In many cases, drag coefficients are used as a tuning parameter to account for complex processes that govern how wave-driven flows interact with individual plants within canopies. This approach, however, can greatly limit the predictive capabilities of both empirical and numerical models. In this study, we extend a non-hydrostatic (phase-resolving) depth-integrated wave model (XBeach non-hydrostatic) with an efficient and robust subgrid canopy flow model to account for the important properties of submerged canopy flows that govern canopy drag forces and wave dissipation. A combination of wave heights, velocities and direct canopy force measurements, as well as data obtained from literature, were used to validate the model, showing the model has good skill in capturing the governing flow dynamics for both rigid and flexible vegetation canopies. By incorporating the canopy flow dynamics, the extended model allows for application of well-established drag coefficients for individual canopy elements to accurately predict wave attenuation over submerged vegetation canopies, rather than relying on empirical formulations or calibration. With the current extension, the model remains computationally efficient, allowing for use on coastal (∼km) scales. • A canopy flow subgrid model was implemented in the open-source XBeach model. • The model was verified using observed wave heights, velocities and canopy forces. • It can accurately predict wave evolution over rigid and flexible submerged canopies. • The model is robust and computationally efficient for use in large scale applications. • Not accounting for canopy flow can lead to substantial errors in wave predictions.

Cell-substratum and cell-cell adhesion forces and single-cell mechanical properties in mono- and multilayer assemblies from robotic fluidic force microscopy

The epithelium covers, protects, and actively regulates various formations and cavities of the human body. During embryonic development the assembly of the epithelium is crucial to the organoid formation, and the invasion of the epithelium is an essential step in cancer metastasis. Live cell mechanical properties and associated forces presumably play an important role in these biological processes. However, the direct measurement of cellular forces in a precise and high-throughput manner is still challenging. We studied the cellular adhesion maturation of epithelial Vero monolayers by measuring single-cell force-spectra with high-throughput fluidic force microscopy (robotic FluidFM). Vero cells were grown on gelatin-covered plates in different seeding concentrations, and cell detachment forces were recorded from the single-cell state, through clustered island formation, to their complete assembly into a sparse and then into a tight monolayer. A methodology was proposed to separate cell-substratum and cell-cell adhesion force and energy (work of adhesion) contributions based on the recorded force-distance curves. For comparison, cancerous HeLa cells were also measured in the same settings. During Vero monolayer formation, a significantly strengthening adhesive tendency was found, showing the development of cell-cell contacts. Interestingly, this type of step-by-step maturation was absent in HeLa cells. The attachment of cancerous HeLa cells to the assembled epithelial monolayers was also measured, proposing a new high-throughput method to investigate the biomechanics of cancer cell invasion. We found that HeLa cells adhere significantly stronger to the tight Vero monolayer than cells of the same origin. Moreover, the mechanical characteristics of Vero monolayers upon cancerous HeLa cell influence were recorded and analyzed. All these results provide insight into the qualitative assessment of cell-substratum and cell-cell mechanical contacts in mono- and multilayered assemblies and demonstrate the robustness and speed of the robotic FluidFM technology to reveal biomechanical properties of live cell assemblies with statistical significances.

Abstract P2031: Evaluation Of Adenosine Monophosphate-activated Protein Kinase Activator MK-8722 In Human Induced Pluripotent Stem Cell Derived Cardiomyocyte Monolayer And Microtissue (Biowire II) Models

MK-8722, a systemic pan-AMPK activator improves glucose homeostasis in animal models of diabetes, but causes cardiac hypertrophy # . Two- and 3-dimensional tissue (2D,3D) constructs of human induced pluripotent stem cell derived cardiomyocytes (CM) (iCells, Fujifilm/CDI) were used to probe the translatability of cardiac hypertrophy and the role of AMPK in cardiomyocyte function. Chronic 10-day exposure (2 μM and 10 μM MK-8722) of iCell cardiomyocyte 2D monolayers, probed via monitoring of cellular impedance (CardioECR, Agilent), revealed a decrease in beat amplitude (-13%,2μM;-49%,10μM) as well as an increase in excitability, based on the ability to follow higher pacing frequencies (+81%,2uM;+34%,10uM). Direct force measurements in 3D iCell CM tissues (Biowire II, TARA Biosystems) reported loss of contractility when stimulated at 1Hz (-74%,2μM;-90%,10 μM), as well as changes in passive resting tension (+18%,2μM;-75%,10 μM) over chronic six-week exposure. MK-8722 caused a marked increase in Biowire excitability as revealed by a large drop in the voltage threshold of entrainment of paced tissues (-36%,2μM;-43%,10 μM). The increased excitability of both 2D and 3D CM models suggests a cellular correlate of the increased electrocardiographic QRS amplitude observed in rhesus monkeys upon chronic dosing with MK-8722 # . Hypertrophy of the Biowires could be clearly observed at the end of the 6-week incubation and presented as increased microtissue widths (+5%,2μM; +10%,10μM) and thickened regions of attachment to the chamber force sensors at each end of the Biowire. Volume estimation revealed increases (+22.3%, 2μM; +31.4%, 10 μM) in Biowire tissue volumes that were comparable to heart hypertrophic changes in preclinical test species # (mouse, rat, and rhesus monkey). The effect of 10μM MK-8722 was more pronounced when treatment began before tissues had completed a multi-week electrical stimulation maturation protocol, rather than after. The functional effects in both 2D and 3D CM models, and the contractile and structural readouts of the 3D Biowire model were highly informative in the interpretation of the clinical applicability of the pleiotropic cardiac effects of MK-8722 observed in preclinical testing. # Myers, et al. Science 357, p 507-511 (2017)

Robust prediction of force chains in jammed solids using graph neural networks

Force chains are quasi-linear self-organised structures carrying large stresses and are ubiquitous in jammed amorphous materials like granular materials, foams or even cell assemblies. Predicting where they will form upon deformation is crucial to describe the properties of such materials, but remains an open question. Here we demonstrate that graph neural networks (GNN) can accurately predict the location of force chains in both frictionless and frictional materials from the undeformed structure, without any additional information. The GNN prediction accuracy also proves to be robust to changes in packing fraction, mixture composition, amount of deformation, friction coefficient, system size, and the form of the interaction potential. By analysing the structure of the force chains, we identify the key features that affect prediction accuracy. Our results and methodology will be of interest for granular matter and disordered systems, e.g. in cases where direct force chain visualisation or force measurements are impossible.

Direct force measurement of microscopic droplets pulled along soft surfaces

When a droplet is placed on a soft surface, surface tension deforms the substrate, creating a capillary ridge. We study how the motion of the ridge dissipates energy in microscopic droplets. Using a micropipette based method, we are able to simultaneously image and measure forces on a microscopic droplet moving at a constant speed along a soft film supported on a rigid substrate. Changing the thickness of the thin film tunes the effective stiffness of the substrate. Thus we can control the ridge size without altering the surface chemistry. We find that the dissipation depends strongly on the film thickness, decreasing monotonically as effective stiffness increases. This monotonic trend is beyond the realm of small deformation theory, but can be explained with a simple scaling analysis.

Data-Driven Derivation of Sheet Metal Properties Gained from Punching Forces Using an Artificial Neural Network

The ongoing digitization of production processes provides new possibilities and potentials for process monitoring of forming and stamping processes. The component quality achievable by these processes is strongly dependent on the properties of the sheet metal material, so that a permanent digital recording of material data offers high potential for monitoring each component produced. In this context, presented paper deals with a novel AI-based method for the direct determination of ma-terial parameters from measured punching force curves. Using software systems Python and Tensor-Flow, an artificial neural network was first set up to determine mechanical material parameters (out-put data) from punching force curves (input data). As data basis for the adopted neural network, force curves were measured during punching of various sheet metal materials using a punching tool equipped with a direct force measurement device. Punching force curves were experimentally deter-mined for the sheet metal materials DP1200, DP1000, DP800, DP600, HX380LA, DC03 and DX54. Additionally, tensile tests were performed for these sheet metal materials to determine ultimate tensile strengths (Rm), yield strengths (Rp0.2, Re), uniform strains (Ag), elongations at break (At) and strain hardening exponents (n). The presented paper reveals that neural networks can accurately quantify the relationship between characteristic parameters of punching force curves and the mentioned me-chanical material properties.

Experimental Investigation of Flow Interaction Dynamics in Supersonic Retropropulsion

Supersonic retropropulsion experiments were performed using a 12.7-cm-diameter 70 deg sphere–cone body with a single jet in the center of the model with a 4:1-area-ratio Laval nozzle directed into a Mach 4 freestream. Data were acquired using high-speed schlieren imaging and direct axial force measurements. Spectral analyses of the total axial force, jet total pressure, and bow shock standoff distance were performed, resulting in the observation of three characteristic modes. For all tests, a dominant frequency in the axial force, independent of the jet and tunnel flow, of 1.9 kHz was observed, which was determined to be a structural vibration mode. A mode at 4.2 kHz in the axial force is observed to correspond to the motion of flow structures, suggesting a coupling between the jet flow and the freestream. A dependency on the presence of the jet and the selection of jet gas is shown for a 13.7 kHz mode, indicating it is acoustic in nature. Proper orthogonal decomposition on the schlieren image data is used to show that the flowfield structures in which dominant modes manifest are dependent on the thrust coefficient.

Depletion of Polyelectrolytes near Like-Charged Substrates Probed by Optical Reflectivity

Salt-free polyelectrolyte solutions form a polyelectrolyte-free depletion layer near like-charged solid interfaces. This evidence is provided by optical reflectivity measurements from planar silica substrates in contact with aqueous solutions of sodium poly(styrene sulfonate). Analysis of the observed reflectivity signal, which features unusual negative signals and optical matching points, with a two-slab model demonstrates the existence of such a polyelectrolyte-free depletion layer. Moreover, the applied model permits the extraction of the corresponding layer thickness, which typically is several tenths of nanometers. This thickness decreases as the inverse square root of the polyelectrolyte concentration, but the actual values exceed the expected Debye length substantially. These results clearly provide independent evidence for the existence of a polyelectrolyte-free depletion layer, as previously suggested on the basis of direct force measurements with the atomic force measurement.