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1.
Langmuir ; 37(5): 1902-1912, 2021 Feb 09.
Artigo em Inglês | MEDLINE | ID: mdl-33502872

RESUMO

The temperature dependence of nanomechanical properties of adsorbed poly-NIPAm microgel particles prepared by a semibatch polymerization process was investigated in an aqueous environment via indentation-based atomic force microscopy (AFM) methods. Poly-NIPAm microgel particles prepared by the classical batch process were also characterized for comparison. The local mechanical properties were measured between 26 and 35 °C, i.e., in the temperature range of the volume transition. Two different AFM tips with different shapes and end radii were utilized. The nanomechanical properties measured by the two kinds of tips showed a similar temperature dependence of the nanomechanical properties, but the actual values were found to depend on the size of the tip. The results suggest that the semibatch synthesis process results in the formation of more homogeneous microgel particles than the classical batch method. The methodological approach reported in this work is generally applicable to soft surface characterization in situ.

2.
Langmuir ; 37(32): 9826-9837, 2021 Aug 17.
Artigo em Inglês | MEDLINE | ID: mdl-34355909

RESUMO

Understanding the wear of mineral fillers is crucial for controlling industrial processes, and in the present work, we examine the wear resistance and nanomechanical properties of bare calcite and stearic acid-modified calcite surfaces under dry and humid conditions at the nanoscale. Measurements under different loads allow us to probe the situation in the absence and presence of abrasive wear. The sliding motion is in general characterized by irregular stick-slip events that at higher loads lead to abrasion of the brittle calcite surface. Bare calcite is hydrophilic, and under humid conditions, a thin water layer is present on the surface. This water layer does not affect the friction force. However, it slightly decreases the wear depth and strongly influences the distribution of wear particles. In contrast, stearic acid-modified surfaces are hydrophobic. Nevertheless, humidity affects the wear characteristics by decreasing the binding strength of stearic acid at higher humidity. A complete monolayer coverage of calcite by stearic acid results in a significant reduction in wear but only a moderate reduction in friction forces at low humidity and no reduction at 75% relative humidity (RH). Thus, our data suggest that the wear reduction does not result from a lowering of the friction force but rather from an increased ductility of the surface region as offered by the stearic acid layer. An incomplete monolayer of stearic acid on the calcite surface provides no reduction in wear regardless of the RH investigated. Clearly, the wear properties of modified calcite surfaces depend crucially on the packing density of the surface modifier and also on the air humidity.

3.
Langmuir ; 35(48): 15515-15525, 2019 12 03.
Artigo em Inglês | MEDLINE | ID: mdl-31310126

RESUMO

Mussel adhesive polymers owe their ability to strongly bind to a large variety of surfaces under water to their high content of 3,4-dihydroxy-l-phenylalanine (DOPA) groups and high positive charge. In this work, we use a set of statistical copolymers that contain medium-length poly(ethylene oxide) side chains that are anchored to the surface in three different ways: by means of (i) electrostatic forces, (ii) catechol groups (as in DOPA), and (iii) the combination of electrostatic forces and catechol groups. A nanotribological scanning probe method was utilized to evaluate the wear resistance of the formed layers as a function of normal load. It was found that the combined measurement of surface topography and stiffness provided an accurate assessment of the wear resistance of such thin layers. In particular, surface stiffness maps allowed us to identify the initiation of wear before a clear topographical wear scar was developed. Our data demonstrate that the molecular and abrasive wear resistance on silica surfaces depends on the anchoring mode and follows the order catechol groups combined with electrostatic forces > catechol groups alone > electrostatic forces alone. The devised methodology should be generally applicable for evaluating wear resistance or "robustness" of thin adsorbed layers on a variety of surfaces.

4.
Langmuir ; 35(3): 653-661, 2019 01 22.
Artigo em Inglês | MEDLINE | ID: mdl-30605339

RESUMO

The adsorption of hydrophilic or amphiphilic multiblock copolymers provides a powerful means to produce well-defined "smart" surfaces, especially if one or several blocks are sensitive to external stimuli. We focus here on an A-B-A-B-A copolymer, where A is a cationic poly((3-acrylamido-propyl)-trimethylammonium chloride) (PAMPTMA) block containing 15 (end blocks) or 30 (middle block) repeat units and B is a neutral thermosensitive water-soluble poly(2-isopropyl-2-oxazoline) (PIPOZ) block with 50 repeat units. X-ray reflectivity and quartz crystal microbalance with dissipation monitoring were employed to study the adsorption of PAMPTMA15-PIPOZ50-PAMPTMA30-PIPOZ50-PAMPTMA15 on silica surfaces. The latter technique was employed at different temperatures up to 50 °C. Surface forces and friction between the two silica surfaces across aqueous pentablock copolymer solutions at different temperatures were determined with the atomic force microscopy colloidal probe force and friction measurements. The cationic pentablock copolymer was found to have a high affinity to the negatively charged silica surface, leading to a thin (2 nm) and rigid adsorbed layer. A steric force was encountered at a separation of around 3 nm from hard wall contact. A capillary condensation of a polymer-rich phase was observed at the cloud point of the solution. The friction forces were evaluated using Amontons' rule modified with an adhesion term.

5.
Soft Matter ; 15(38): 7704-7714, 2019 Oct 14.
Artigo em Inglês | MEDLINE | ID: mdl-31508653

RESUMO

The mechanical properties of hydrogels are of importance in many applications, including scaffolds and drug delivery vehicles where the release of drugs is controlled by water transport. While the macroscopic mechanical properties of hydrogels have been reported frequently, there are less studies devoted to the equally important nanomechanical response to local load and shear. Scanning probe methods offer the possibility to gain insight on surface nanomechanical properties with high spatial resolution, and thereby provide fundamental insights on local material property variations. In this work, we investigate the local response to load and shear of poly(2-hydroxyethyl methacrylate) hydrogels with two different cross-linking densities submerged in aqueous solution. The response of the hydrogels to purely normal loads, as well as the combined action of load and shear, was found to be complex due to viscoelastic effects. Our results show that the surface stiffness of the hydrogel samples increased with increasing load, while the tip-hydrogel adhesion was strongly affected by the load only when the cross-linking density was low. The combined action of load and shear results in the formation of a temporary sub-micrometer hill in front of the laterally moving tip. As the tip pushes against such hills, a pronounced stick-slip effect is observed for the hydrogel with low cross-linking density. No plastic deformation or permanent wear scar was found under our experimental conditions.

6.
Langmuir ; 34(45): 13615-13625, 2018 11 13.
Artigo em Inglês | MEDLINE | ID: mdl-30350704

RESUMO

Mucins are high molar mass glycoproteins that assume an extended conformation and can assemble into mucus hydrogels that protect our mucosal epithelium. In nature, the challenging task of generating a mucus layer, several hundreds of micrometers in thickness, from micrometer-sized cells is elegantly solved by the condensation of mucins inside vesicles and their on-demand release from the cells where they suddenly expand to form the extracellular mucus hydrogel. We aimed to recreate and control the process of compaction for mucins, the first step toward a better understanding of the process and creating biomimetic in vivo delivery strategies of macromolecules. We found that by adding glycerol to the aqueous solvent, we could induce drastic condensation of purified mucin molecules, reducing their size by an order of magnitude down to tens of nanometers in diameter. The condensation effect of glycerol was fully reversible and could be further enhanced and partially stabilized by cationic cross-linkers such as calcium and polylysine. The change of structure of mucins from extended molecules to nano-sized particles in the presence of glycerol translated into macroscopic rheological changes, as illustrated by a dampened shear-thinning effect with increasing glycerol concentration. This work provides new insight into mucin condensation, which could lead to new delivery strategies mimicking cell release of macromolecules condensed in vesicles such as mucins and heparin.


Assuntos
Mucinas/química , Nanopartículas/química , Animais , Cálcio/química , Glicerol/química , Mucinas/isolamento & purificação , Tamanho da Partícula , Polilisina/química , Conformação Proteica/efeitos dos fármacos , Solventes/química , Suínos , Viscosidade
7.
Phys Chem Chem Phys ; 19(35): 23642-23657, 2017 Sep 13.
Artigo em Inglês | MEDLINE | ID: mdl-28589979

RESUMO

Surface science, which spans the fields of chemistry, physics, biology and materials science, requires information to be obtained on the local properties and property variations across a surface. This has resulted in the development of different scanning probe methods that allow the measurement of local chemical composition and local electrical and mechanical properties. These techniques have led to rapid advancement in fundamental science with applications in areas such as composite materials, corrosion protection and wear resistance. In this perspective article, we focussed on the branch of scanning probe methods that allows the determination of surface nanomechanical properties. We discussed some different AFM-based modes that were used for these measurements and provided illustrative examples of the type of information that could be obtained. We also discussed some of the difficulties encountered during such studies.

8.
Langmuir ; 31(45): 12390-400, 2015 Nov 17.
Artigo em Inglês | MEDLINE | ID: mdl-26501836

RESUMO

The aim of this study was to develop a fundamental understanding of the adsorption behavior of metal ions on cellulose surfaces using experimental techniques supported by computational modeling, taking Ag(I) as an example. Force interactions among three types of cellulose microspheres (native cellulose and its derivatives with sulfate and phosphate groups) and the silica surface in AgNO3 solution were studied with atomic force microscopy (AFM) using the colloidal probe technique. The adhesion force between phosphate cellulose microspheres (PCM) and the silica surface in the aqueous AgNO3 medium increased significantly with increasing pH while the adhesion force slightly decreased for sulfate cellulose microspheres (SCM), and no clear adhesion force was observed for native cellulose microspheres (CM). The stronger adhesion enhancement for the PCM system is mainly attributed to the electrostatic attraction between Ag(I) and the negative silica surface. The observed force trends were in good agreement with the measured zeta potentials. The scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS), and attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR) analyses confirmed the presence of silver on the surface of cellulose microspheres after adsorption. This study showed that PCM with a high content of phosphate groups exhibited a larger amount of adsorbed Ag(I) than CM and SCM and possible clustering of Ag(I) to nanoparticles. The presence of the phosphate group and a wavenumber shift of the P-OH vibration caused by the adsorption of silver ions on the phosphate groups were further confirmed with computational studies using density functional theory (DFT), which gives support to the above findings regarding the adsorption and clustering of Ag(I) on the cellulose surface decorated with phosphate groups as well as IR spectra.

9.
Microsc Microanal ; 20(1): 33-41, 2014 Feb.
Artigo em Inglês | MEDLINE | ID: mdl-24397939

RESUMO

Sodium-activated calcium bentonite is used as a binder in iron ore pellets and is known to increase strength of both wet and dry iron ore green pellets. In this article, the microstructure of bentonite in magnetite pellets is revealed for the first time using scanning electron microscopy. The microstructure of bentonite in wet and dry iron ore pellets, as well as in distilled water, was imaged by various imaging techniques (e.g., imaging at low voltage with monochromatic and decelerated beam or low loss backscattered electrons) and cryogenic methods (i.e., high pressure freezing and plunge freezing in liquid ethane). In wet iron ore green pellets, clay tactoids (stacks of parallel primary clay platelets) were very well dispersed and formed a voluminous network occupying the space available between mineral particles. When the pellet was dried, bentonite was drawn to the contact points between the particles and formed solid bridges, which impart strength to the solid compact.

10.
J Colloid Interface Sci ; 672: 133-141, 2024 Oct 15.
Artigo em Inglês | MEDLINE | ID: mdl-38833733

RESUMO

HYPOTHESIS: Organohydrogel emulsions display unique rheological properties and contain hydrophilic and lipophilic domains highly desirable for the loading of active compounds. They find utility in various applications from food to pharmaceuticals and cosmetic products. The current systems have limited applications due to complex expensive formulation and/or processing difficulties in scale-up. To solve these issues, a simple emulsification process coupled with unique compounds are required. EXPERIMENTS: Here, we report an organohydrogel emulsion based only on a low concentration of 12-hydroxystearic acid acting as a gelling agent for both oil and water phases but also as a surfactant. The emulsification process is based on in-situ surfactant transfer. We characterize the emulsification process occurring at the nanoscale by using tensiometry experiments. The emulsion structure was determined by coupling Small Angle X-ray and neutron scattering, and confocal Raman microscopy. FINDINGS: We demonstrate that the stability and unique rheological properties of these emulsions come from the presence of self-assembled crystalline structures of 12-hydroxystearic acid in both liquid phases. The emulsion properties can be tuned by varying the emulsion composition over a wide range. These gelled emulsions are prepared using a low energy method offering easy scale-up at an industrial level.

11.
Materials (Basel) ; 16(16)2023 Aug 10.
Artigo em Inglês | MEDLINE | ID: mdl-37629845

RESUMO

The development of rechargeable lithium-ion battery (LIB) technology has facilitated the shift toward electric vehicles and grid storage solutions. This technology is currently undergoing significant development to meet industrial applications for portable electronics and provide our society with "greener" electricity. The large increase in LIB production following the growing demand from the automotive sector has led to the establishment of gigafactories worldwide, thus increasing the substantial consumption of fossil-based and non-sustainable materials, such as polyvinylidene fluoride and/or styrene-butadiene rubber as binders in cathode and anode formulations. Furthermore, the use of raw resources, such as Li, Ni, and Mn in cathode active materials and graphite and nanosilicon in anodes, necessitates further efforts to enhance battery efficiency. To foster a global sustainable transition in LIB manufacturing and reduce reliance on non-sustainable materials, the implementation of bio-based binder solutions for electrodes in LIBs is crucial. Bio-based binders such as cellulose, lignin, alginate, gums, starch, and others can address environmental concerns and can enhance LIBs' performance. This review aims to provide an overview of the current progress in the development and application of bio-based binders for LIB electrode manufacturing, highlighting their significance toward sustainable development.

12.
Nanoscale Adv ; 5(13): 3453-3462, 2023 Jun 27.
Artigo em Inglês | MEDLINE | ID: mdl-37383076

RESUMO

Micro- and nanoplastic pollution has emerged as a global environmental problem. Moreover, plastic particles are of increasing concern for human health. However, the detection of so-called nanoplastics in relevant biological compartments remains a challenge. Here we show that Raman confocal spectroscopy-microscopy can be deployed for the non-invasive detection of amine-functionalized and carboxy-functionalized polystyrene (PS) nanoparticles (NPs) in Daphnia magna. The presence of PS NPs in the gastrointestinal (GI) tract of D. magna was confirmed by using transmission electron microscopy. Furthermore, we investigated the ability of NH2-PS NPs and COOH-PS NPs to disrupt the epithelial barrier of the GI tract using the human colon adenocarcinoma cell line HT-29. To this end, the cells were differentiated for 21 days and then exposed to PS NPs followed by cytotoxicity assessment and transepithelial electrical resistance measurements. A minor disruption of barrier integrity was noted for COOH-PS NPs, but not for the NH2-PS NPs, while no overt cytotoxicity was observed for both NPs. This study provides evidence of the feasibility of applying label-free approaches, i.e., confocal Raman mapping, to study PS NPs in a biological system.

13.
Glob Chall ; 7(4): 2200235, 2023 Apr.
Artigo em Inglês | MEDLINE | ID: mdl-37020627

RESUMO

Wood is an inherently hygroscopic material which tends to absorb moisture from its surrounding. Moisture in wood is a determining factor for the quality of wood being employed in construction, since it causes weakening, deformation, rotting, and ultimately leading to failure of the structures resulting in costs to the economy, the environment, and to the safety of residents. Therefore, monitoring moisture in wood during the construction phase and after construction is vital for the future of smart and sustainable buildings. Employing bio-based materials for the construction of electronics is one way to mitigate the environmental impact of such electronics. Herein, a bio-graphene sensor for monitoring the moisture inside and around wooden surfaces is fabricated using laser-induced graphitization of a lignin-based ink precursor. The bio-graphene sensors are used to measure humidity in the range of 10% up to 90% at 25 °C. Using laser induced graphitization, conductor resistivity of 18.6 Ω sq-1 is obtained for spruce wood and 57.1 Ω sq-1 for pine wood. The sensitivity of sensors fabricated on spruce and pine wood is 2.6 and 0.74 MΩ per % RH. Surface morphology and degree of graphitization are investigated using scanning electron microscopy, Raman spectroscopy, and thermogravimetric analysis methods.

14.
Adv Mater ; 35(16): e2205377, 2023 Apr.
Artigo em Inglês | MEDLINE | ID: mdl-36373490

RESUMO

Conjugated polymer field-effect transistors are emerging as an enabling technology for flexible electronics due to their excellent mechanical properties combined with sufficiently high charge-carrier mobilities and compatibility with large-area, low-temperature processing. However, their electrical stability remains a concern. ON-state (accumulation mode) bias-stress instabilities in organic semiconductors have been widely studied, and multiple mitigation strategies have been suggested. In contrast, OFF-state (depletion mode) bias-stress instabilities remain poorly understood despite being crucial for many applications in which the transistors are held in their OFF-state for most of the time. Here, a simple method of using an antisolvent treatment is presented to achieve significant improvements in OFF-state bias-stress and environmental stability as well as general device performance for one of the best performing polymers, solution-processable indacenodithiophene-co-benzothiadiazole (IDT-BT). IDT-BT is weakly crystalline, and the notable improvements to an antisolvent-induced, increased degree of crystallinity, resulting in a lower probability of electron trapping and the removal of charge traps is attributed. The work highlights the importance of the microstructure in weakly crystalline polymer films and offers a simple processing strategy for achieving the reliability required for applications in flexible electronics.

15.
Small Methods ; 7(11): e2300476, 2023 Nov.
Artigo em Inglês | MEDLINE | ID: mdl-37661594

RESUMO

Organic semiconductors are a family of pi-conjugated compounds used in many applications, such as displays, bioelectronics, and thermoelectrics. However, their susceptibility to processing-induced contamination is not well understood. Here, it is shown that many organic electronic devices reported so far may have been unintentionally contaminated, thus affecting their performance, water uptake, and thin film properties. Nuclear magnetic resonance spectroscopy is used to detect and quantify contaminants originating from the glovebox atmosphere and common laboratory consumables used during device fabrication. Importantly, this in-depth understanding of the sources of contamination allows the establishment of clean fabrication protocols, and the fabrication of organic field effect transistors (OFETs) with improved performance and stability. This study highlights the role of unintentional contaminants in organic electronic devices, and demonstrates that certain stringent processing conditions need to be met to avoid scientific misinterpretation, ensure device reproducibility, and facilitate performance stability. The experimental procedures and conditions used herein are typical of those used by many groups in the field of solution-processed organic semiconductors. Therefore, the insights gained into the effects of contamination are likely to be broadly applicable to studies, not just of OFETs, but also of other devices based on these materials.

16.
Adv Sci (Weinh) ; 9(32): e2203898, 2022 11.
Artigo em Inglês | MEDLINE | ID: mdl-36104216

RESUMO

Mucus is a self-healing gel that lubricates the moist epithelium and provides protection against viruses by binding to viruses smaller than the gel's mesh size and removing them from the mucosal surface by active mucus turnover. As the primary nonaqueous components of mucus (≈0.2%-5%, wt/v), mucins are critical to this function because the dense arrangement of mucin glycans allows multivalence of binding. Following nature's example, bovine submaxillary mucins (BSMs) are assembled into "mucus-like" gels (5%, wt/v) by dynamic covalent crosslinking reactions. The gels exhibit transient liquefaction under high shear strain and immediate self-healing behavior. This study shows that these material properties are essential to provide lubricity. The gels efficiently reduce human immunodeficiency virus type 1 (HIV-1) and genital herpes virus type 2 (HSV-2) infectivity for various types of cells. In contrast, simple mucin solutions, which lack the structural makeup, inhibit HIV-1 significantly less and do not inhibit HSV-2. Mechanistically, the prophylaxis of HIV-1 infection by BSM gels is found to be that the gels trap HIV-1 by binding to the envelope glycoprotein gp120 and suppress cytokine production during viral exposure. Therefore, the authors believe the gels are promising for further development as personal lubricants that can limit viral transmission.


Assuntos
HIV-1 , Animais , Bovinos , Humanos , HIV-1/metabolismo , Herpesvirus Humano 2/metabolismo , Mucinas/metabolismo , Géis , Muco/metabolismo
17.
Nat Commun ; 13(1): 3076, 2022 Jun 02.
Artigo em Inglês | MEDLINE | ID: mdl-35654891

RESUMO

The field of organic electronics has profited from the discovery of new conjugated semiconducting polymers that have molecular backbones which exhibit resilience to conformational fluctuations, accompanied by charge carrier mobilities that routinely cross the 1 cm2/Vs benchmark. One such polymer is indacenodithiophene-co-benzothiadiazole. Previously understood to be lacking in microstructural order, we show here direct evidence of nanosized domains of high order in its thin films. We also demonstrate that its device-based high-performance electrical and thermoelectric properties are not intrinsic but undergo rapid stabilization following a burst of ambient air exposure. The polymer's nanomechanical properties equilibrate on longer timescales owing to an orthogonal mechanism; the gradual sweating-out of residual low molecular weight solvent molecules from its surface. We snapshot the quasistatic temporal evolution of the electrical, thermoelectric and nanomechanical properties of this prototypical organic semiconductor and investigate the subtleties which play on competing timescales. Our study documents the untold and often overlooked story of a polymer device's dynamic evolution toward stability.

18.
J Phys Chem B ; 125(34): 9860-9869, 2021 09 02.
Artigo em Inglês | MEDLINE | ID: mdl-34428041

RESUMO

Poly-NIPAm microgel particles with two different cross-linking densities were prepared with the classical batch polymerization process. These particles were adsorbed onto modified silica surfaces, and their nanomechanical properties were measured by means of atomic force microscopy. It was found that these particles have a hard core-soft shell structure both below and above the volume transition temperature. The core-shell-like structure appears due to a higher reaction rate of the cross-linker compared to that of the monomer, leading to depletion of cross-linker in the shell region. The microgel beads with lower average cross-linking density were found to be less stiff below the volume transition temperature than the microgel with higher cross-linking density. Increasing the temperature further to just above the volume transition temperature led to lower stiffness of the more highly cross-linked microgel compared to its less cross-linked counterpart. This effect is explained with the more gradual deswelling with temperature for the more cross-linked microgel particles. This phenomenon was confirmed by dynamic light scattering measurements in the bulk phase, which showed that the larger cross-linking density microgel showed a more gradual collapse in aqueous solution as the temperature was increased.


Assuntos
Microgéis , Resinas Acrílicas , Géis , Temperatura
19.
Nanoscale Adv ; 3(15): 4388-4394, 2021 Jul 27.
Artigo em Inglês | MEDLINE | ID: mdl-36133465

RESUMO

The electrical properties of an all-oxide core-shell ZnO-Co3O4 nanorod heterojunction were studied in the dark and under UV-vis illumination. The contact potential difference and current distribution maps were obtained utilizing new methods in dynamic multifrequency atomic force microscopy (AFM) such as electrostatic and conductive intermodulation AFM. Light irradiation modified the electrical properties of the nanorod heterojunction. The new techniques are able to follow the instantaneous local variation of the photocurrent, giving a two-dimensional (2D) map of the current-voltage curves and correlating the electrical and morphological features of the heterostructured core-shell nanorods.

20.
J Colloid Interface Sci ; 583: 414-424, 2021 Feb 01.
Artigo em Inglês | MEDLINE | ID: mdl-33011410

RESUMO

Frictional and nanomechanical properties of nanostructured polymer surfaces are important to their technological and biomedical applications. In this work, poly(ethylene terephthalate) (PET) surfaces with a periodic distribution of well-defined nanopillars were fabricated through an anodization/embossing process. The apparent surface energy of the nanopillared surfaces was evaluated using the Fowkes acid-base approach, and the surface morphology was characterized using scanning electron microscope (SEM) and atomic force microscope (AFM). The normal and lateral forces between a silica microparticle and these surfaces were quantified using colloidal probe atomic force microscopy (CP-AFM). The friction-load relationship followed Amonton's first law, and the friction coefficient appeared to scale linearly with the nanopillar height. Furthermore, all the nanopillared surfaces showed pronounced frictional instabilities compared to the smooth sliding friction loop on the flat control. Performing the stick-slip amplitude coefficient (SSAC) analysis, we found a correlation between the frictional instabilities and the nanopillars density, pull-off force and work of adhesion. We have summarised the dependence of the nanotribological properties on such nanopillared surfaces on five relevant parameters, i.e. pull-off force fp, Amontons' friction coefficient µ, RMS roughness Rq, stick-slip amplitude friction coefficient SSAC, and work of adhesion between the substrate and water Wadh in a radar chart. Whilst demonstrating the complexity of the frictional behaviour of nanopillared polymer surfaces, our results show that analyses of multiparametric nanotribological properties of nanostructured surfaces should go beyond classic Amontons' laws, with the SSAC more representative of the frictional properties compared to the friction coefficient.

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