CALCULATION OF THE YOUNG’S MODULUS OF AN ADSORBED POLYMER LAYER

 Polymer layers adsorbed to a surface or in a confined environment often change their mechanical properties. There is even the possibility of solidification of the confined layer. To judge the stiffness of such a layer, we used the Hertz model to calculate the Young’s modulus of the polymer layer in the confinement of AFM experiments with silicon nitride tip with a radius of curvature of R » 50 nm and a glass sphere attached to the cantilever R = 5 mm. Since there is no visible indentation of the layer in the AFM experiments, the layer is either penetrated very easily, or the indentation is too small to be seen in a force curve. The latter would be the case for a polymer layer with a Young’s modulus above 4 ´ 10⁸ Pa in case of an experiment with a silicon nitride tip and 4 ´ 10⁵ Pa in case of a glass sphere.     

Extreme hardening of PDMS thin films due to high compressive strain and confined thickness

Polymers confined to small dimensions and that undergo high strains can show remarkable nonlinear mechanics, which must be understood to accurately predict the functioning of nanoscale polymer devices. In this paper we describe the determination of the mechanical properties of ultrathin polydimethylsiloxane (PDMS) films undergoing large strains, using atomic force microscope (AFM) indentation with a spherical tip. The PDMS was molded into extremely thin films of variable thickness and adhered to a hard substrate. We found that for films below 1 μm in thickness the Young's modulus increased with decreasing sample thickness with a power law exponent of 1.35. Furthermore, as the soft PDMS film was indented, significant strain hardening was observed as the indentation depth approached 45% of the sample thickness. To properly quantify the nonlinear mechanical measurements, we utilized a pointwise Hertzian model which assumes only piecewise linearity on the part of the probed material. This analysis revealed three regions within the material. A linear region with a constant Young's modulus was seen for compression up to 45% strain. At strains higher than 45%, a marked increase in Young's modulus was measured. The onset of strain induced stiffening is well modeled by finite element modeling and occurs as stress contours expanding from the probe and the substrate overlap. A third region of mechanical variation occurred at small indentations of less than 10 nm. The pointwise Young's modulus at small indentations was several orders of magnitude higher than that in the linear elasticity region; we studied and ruled out causes responsible for this phenomenon. In total, these effects can cause thin elastomer films to become extremely stiff such that the measured Young's modulus is over a 100-fold higher than the bulk PDMS. Therefore, the mechanics of a polymer can be changed by adjusting the geometry of a material, in addition to changing the material itself. In addition to understanding the mechanics of thin polymer films, this work provides an excellent test of experimental techniques to measure the mechanics of other nonlinear and heterogeneous materials such as biological cells.     

Effect of aminoglycoside on mechanical properties of zwitterionic phospholipid vesicles

The effect of the aminoglycoside (streptomycin) incorporation on the nanomechanical properties of pure dipalmitoylphosphatidylcholine (DPPC) vesicles was studied using atomic force microscope (AFM) on mica surface. The vesicles were prepared by extrusion and adsorbed on the mica surface. The forces, measured between an AFM tip and the vesicle, presented that the breakthrough of the tip into the vesicles occurred two times. Each breakthrough represented each penetration of the tip into each bilayer. Force data prior to the first breakthrough were fitted well with the Hertzian model to estimate Young's modulus and bending modulus of the vesicles. It was found that the Young's modulus and bending modulus were not varied with the incorporation of AGs (streptomycins) up to the 1:1 AG/DPPC vesicle system. This result may suggest that the AGs do not lead to the disruption of DPPC packing.     

Micromechanical testing of individual collagen fibrils

A novel method based on AFM was used to attach individual collagen fibrils between a glass surface and the AFM tip, to allow force spectroscopy studies of these. The fibrils were deposited on glass substrates that are partly coated with Teflon AF. A modified AFM tip was used to accurately deposit epoxy glue droplets on either end of the collagen fibril that cross the glass-Teflon AF interface, as to such attach it with one end to the glass and the other end to the AFM tip. Single collagen fibrils have been mechanically tested in ambient conditions and were found to behave reversibly up to stresses of 90 MPa. Within this regime a Young's modulus of 2-7 GPa was obtained. In aqueous media, the collagen fibrils could be tested reversibly up to about 15 MPa, revealing Young's moduli ranging from 0.2 to at most 0.8 GPa.     

Interaction forces between adsorbed polymer layers

The interaction forces between adsorbed polymer layers were investigated. Two types of graft copolymers that were adsorbed on hydrophobic surfaces have been investigated: (i) a graft copolymer consisting of polymethylmethacrylate/polymethacrylic acid back bone (the B chain) on which several poly(ethylene oxide) chains are grafted (to be referred to as PMMA/PEO_n); and (ii) a graft copolymer consisting of inulin (linear polyfructose with degree of polymerization > 23) (the A chain) on which several C₁₂ chains are grafted (INUTEC SP1). In the first case adsorbed layers of the graft copolymer were obtained on mica sheets and the interaction forces were measured using the surface force apparatus. In the second case the interaction forces were measured using Atomic Force Microscopy (AFM). For this purpose a hydrophobically modified glass sphere was attached to the tip of the cantilever of the AFM and the glass plate was also made hydrophobic. Both the sphere and the glass plate contained an adsorbed layer of INUTEC SP1.In the surface forces apparatus one essentially measures the energy E(D)–distance D curves for the graft copolymer of PMMA/PEO_n between mica surfaces bearing the graft copolymer and this could be converted to interaction energy between flat surfaces. Using the de Gennes scaling theory, it is possible to calculate the interaction energy between the polymer layers. The same graft copolymer was used in latex dispersions and the high frequency modulus G′_∝ was measured as a function of the volume fraction ? of the dispersion. This high frequency modulus could be related to the potential of mean force. In this way one could compare the results obtained from rheology and those obtained from direct measurement of interaction forces.In the AFM method, the interaction forces are measured in the contact area between two surfaces, i.e. a spherical glass particle and a glass plate. Both glass spheres and plates were hydrophobized using dichlorodimethylsilane. Results were obtained for adsorbed layers of INUTEC SP1 in water and in the presence of various concentrations of Na₂SO₄ (0.3, 0.8, 1.0 and 1.5 mol dm^{− 3}). All results showed a rapid increase of force with a decrease of separation distance and the forces were still repulsive up to the highest Na₂SO₄ concentration. This explains the high stability of dispersions when using INUTEC SP1 as stabilizer.     

AFM nanoindentation to determine Young’s modulus for different EPDM elastomers

AFM nanoindentation was investigated as a method for determining the micromechanical properties of polymer materials. It is generally accepted that the shape of the tip of the cantilever undergoes a change in a standard AFM setup. The shape defines the projected contact area, so it is a parameter directly proportional to the elastic modulus; any change in the shape thus affects the accuracy of the results. The method suggested in this paper relies on the introduction of an experimentally determined tip-area function. Values for Young’s modulus were calculated for EPDM samples with different degrees of cure and crystallinity. The degree of crystallinity has a greater impact on the mechanical properties of the material than the degree of cure. Depending on the amplitude of the indentation, the E-moduli determined by AFM are systematically higher. When studying different regions of polymer materials, the values of the E-modulus determined by AFM become identical to those measured by means of DMA on extrapolation of the modulus at zero indentation.     

A comparison of JKR-based methods to analyze quasi-static and dynamic indentation force curves

The Johnson-Kendall-Roberts (JKR) theory of elastic contact, extended to take viscoelastic effects into account, is used to evaluate work of adhesion and modulus of elastomeric films. In this paper, we present a comparison of five approaches to analyze quasi-static and dynamic JKR force curve data obtained using instrumented indentation. The load-displacement experiments were performed using a 200-microm radius borosilicate glass sphere against poly(dimethyl siloxane) (PDMS). By applying a small oscillation to the tip during indentation, dynamic stiffness vs load data were also obtained for frequencies between 25 and 160 Hz. Direct curve fitting as well as simplified 2- and 3-point analysis methods were used to compare modulus values obtained from load-displacement and stiffness-load data. Fit methods not requiring determination of the initial point of tip-sample contact ("zero" displacement) provided modulus values closest to those obtained by direct curve fitting. The dynamic stiffness-load data revealed a frequency dependent modulus; load-displacement measurements obtained simultaneously were consistent with the relaxed, or low-frequency, modulus of the PDMS sample. These experiments demonstrate that both the frequency dependent and relaxed modulus can be obtained from a single experiment.     

EFFECT OF DISPERSION OF MICA IN MATRIX ON YOUNG''''S MODULUS OF MICA FILLED POLYETHYLENE

The correlation between Young's modulus of mica-filled high density polyethylene (HDPE), low density polyethylene(LDPE) and the state of dispersion of plasma-treated mica in the polymer matrices was studied. The modulus and the number average diameter of mica aggregates in matrix were determined with tensile testing and image analysis respectively. The interface structure of the filler/matrix and the bulk structure of matrix were examined through the dielectric spectrometry, differential scanning calorimetry (DSC) and dynamic viscoelastic spectrometry. The results show that the Young's modulus of the filial polyethylene depends to a great extent upon the state of dispersion of filler in matrix, but it is independent of the interface structure and bulk structure. The better the dispersion, the higher the Young's modulus.     

Nano-mechanical methods in biochemistry using atomic force microscopy

The atomic force microscope has been extensively used not only to image nanometer-sized biological samples but also to measure their mechanical properties by using the force curve mode of the instrument. When the analysis based on the Hertz model of indentation is applied to the approach part of the force curve, one obtains information on the stiffness of the sample in terms of Young's modulus. Mapping of local stiffness over a single living cell is possible by this method. The retraction part of the force curve provides information on the adhesive interaction between the sample and the AFM tip. It is possible to functionalize the AFM tip with specific ligands so that one can target the adhesive interaction to specific pairs of ligands and receptors. The presence of specific receptors on the living cell surface has been mapped by this method. The force to break the co-operative 3D structure of globular proteins or to separate a double stranded DNA into single strands has been measured. Extension of the method for harvesting functional molecules from the cytosol or the cell surface for biochemical analysis has been reported. There is a need for the development of biochemical nano-analysis based on AFM technology.     

Mechanical Properties of Poly(dimethylsiloxane)-block-poly(2-methyloxazoline) Polymersomes Probed by Atomic Force Microscopy

Poly(dimethylsiloxane)-block-poly(2-methyloxazoline) (PDMS-b-PMOXA) vesicles were characterized by a combination of dynamic light scattering (DLS), cryogenic transmission electron microscopy (cryo-TEM), and atomic force microscopy imaging and force spectroscopy (AFM). From DLS data, a hydrodynamic radius of ～150 nm was determined, and cryo-TEM micrographs revealed a bilayer thickness of ～16 nm. In AFM experiments on a silicon wafer substrate, adsorption led to a stable spherical caplike conformation of the polymersomes, whereas on mica, adsorption resulted also in vesicle fusion and formation of bilayer patches or multilayer stacks. This indicates a delicate balance between the mechanical stability of PDMS-b-PMOXA polymersomes on one hand and the driving forces for spreading on the other. A Young's modulus of 17 ± 11 MPa and a bending modulus of 7 ± 5 × 10(-18) J were derived from AFM force spectroscopy measurements. Therefore, the elastic response of the PDMS-b-PMOXA polymersomes to external stimuli is much closer to that of lipid vesicles compared to other types of polymersomes, such as polystyrene-block-poly(acrylic acid) (PS-b-PAA).     

Investigation of Viscoelastic Properties of Amorphous Selenium near Glass Transition Using Depth‐Sensing Indentation

Abstract

New procedures involving depth‐sensing indentation are used to measure the submicron scale elastic modulus, hardness, viscosity, and activation energy and volume for creep of amorphous selenium below glass transition. The accurate measurement of Young's modulus in a highly viscoelastic situation using depth‐sensing indentation remains a challenge, and a creep correction procedure is employed here to measure the modulus. The measured Young's modulus exhibits a strong decreasing trend from ～10 GPa to 4.4 GPa as temperature increases from ～302 K to 309 K, in reasonably good agreement with bulk behavior. Two new procedures are also proposed here to measure the viscosity. The measured shear viscosity decreases from ～1×10¹² Pa‐s to ～2×10¹⁰ Pa‐s when the temperature increases over the same range, and the variation with temperature is found to obey an Arrehnius rate equation. The activation energy for the viscous creep process is found to be ～463 kJ/mol. Both the viscosity and the activation energy are lower than the bulk values, and this is thought to be due to the much higher stress levels of over 200 MPa involved in the nanoindentation experiments here. The apparent activation volume exhibits a rising trend from 1.04×10^?31 to 2.35×10^?30 m³ over the same temperature range.     

Atomic force microscopy measurement of the elastic properties of the kidney epithelial cells

Direct interaction force measurements using atomic force microscopy (AFM) were carried out between a silicon nitride tip and renal epithelial cells (Madin-Darby Canine Kidney-MDCK and proximal tubular epithelial cells derived from pig kidneys, LLC-PK1). The approaching (extending) portion of the force/distance curves is considered, and repulsive forces in the long range of 2-3 microm were seen in both MDCK as well as LLC-PK1 cells growing under normal conditions. The repulsive force in the shorter distance range of 50-200 nm was also observed, when cells were damaged exposing the underlying basal membrane. LLC-PK1 cells were more prone to damage than the MDCK cells, hence short-range forces were common in the former and long-range forces in the latter cells. The functional dependence of repulsive force on the indentation depth changes, at small indentation depth the force increases linearly, while at larger indentations the force is a quadratic function of the distance, which is attributed to the elasticity of the membrane and the solid-like response of cells, respectively. The oxalate treatment of cells for 2-4 h gives rise to an increase in the elastic modulus of the cells.     

Probing small unilamellar EggPC vesicles on mica surface by atomic force microscopy

Sonicated small unilamellar egg yolk phosphatidylcholine (EggPC) vesicles were investigated using atomic force microscopy (AFM) imaging and force measurements. Three different topographies (convex, planar, and concave shape) of the EggPC vesicles on the mica surface were observed by tapping mode in fluid, respectively. It was found that the topography change of the vesicles could be attributed to the interaction force between the AFM tip and vesicles. Force curves between an AFM tip and an unruptured vesicle were obtained in contact mode. During approach, two breaks corresponding to the abrupt penetration of upper and lower bilayer of vesicle were exhibited in the force curve. Both breaks spanned a distance of around 4 nm close to the EggPC bilayer thickness. Based on Hertz analysis of AFM approach force curves, the Young's modulus (E) and the bending modulus (kc) for pure EggPC vesicles were measured to be (1.97 +/- 0.75) x 10(6)Pa and (0.21 +/- 0.08) x 10(-19)J, respectively. The results show that the AFM can be used to obtain good images of intact and deformed vesicles by tapping mode, as well as to probe the integrity and bilayer structure of the vesicles. AFM force curve compare favorably with other methods to measure mechanical properties of soft samples with higher spatial resolution.     

Alternative method for fabricating chemically functionalized AFM tips: silane modification of HF-treated Si3N4 probes

An alternative method for fabricating functionalized, atomic force microscopy (AFM) tips is presented. This technique is simple and requires only minimal preparation and tip modification to generate chemically sensitive probes that have a robust organic monolayer of flexible terminal chemistry attached to the surface. Specifically, commercially microfabricated Si3N4 AFM tips were modified with self-assembled monolayers (SAMs) of octadecyltrichlorosilane and (11-bromoundecyl)trichlorosilane after removing the native silicon oxide surface layer with concentrated hydrofluoric acid. The structure of these SAM films on solid silicon nitride surfaces was studied using contact angle goniometry and Fourier transform infrared spectroscopy. Pull-off force measurements on various bare (mica, graphite, and silicon) and SAM-functionalized substrates confirm that mechanically robust, long-chain organic silane SAMs can be formed on HF-treated Si3N4 tips without the presence of an intervening oxide layer. Adhesion experiments show that the integrity of the organic film on the chemically modified tips is maintained over repeated measurements and that the functionalized tips can be used for chemical sensing experiments since strong discrimination between different surface chemistries is possible.     

小形变时杨氏模量等于三倍的剪切模量

尽管高聚物是黏弹性材料,具有时间依赖性和温度依赖性,但在小形变时,弹性理论中的一些假定和定理仍能用来讨论黏弹性高聚物的形变。应力与应变之比是模量,在小形变时,单向拉伸的杨氏模量约等于三倍的剪切模量,E≈3G。     

Viscoelastic response of poly(dimethylsiloxane) in the adhesive interaction with AFM tips

As follow-up to a previous study,(1) the viscoelastic response of cross-linked poly(dimethylsiloxane) (PDMS) in the adhesive interaction with AFM tips is reported. The indentation of the AFM tip into the polymer caused by adhesion is monotonically dependent on the loading speed. During the unloading process, the adherence force between the AFM tip and the polymer has a turning point at a specific unloading speed. It is found that the viscoelastic relaxation processes in the bulk polymer, which may have more than one component, cause the monotonic rate dependence of the adhesion-induced indentation; the competition between the bulk relaxation and the interfacial relaxation results in the turning point of the adherence force at a specific ramp speed. Experiments at different dwell times provide additional evidence for the existence of material relaxation. Methyl- and hydroxyl-functionalized AFM tips were used to study PDMS samples and indicated strong dipolar attractions formed at the tip-sample interface.     

Surface elastic properties of human retinal pigment epithelium melanosomes

Atomic force microscope (AFM) imaging and nanoindentation measurements in water were used to probe the mechanical properties of retinal pigment epithelium melanosomes isolated from 14-year-old and 76-year-old donors. Topographic imaging reveals surface roughness similar to previous measurements on dry melanosomes. Force-indentation measurements show different types of responses that were catalogued into four different categories. In these measurements no permanent surface damage of melanosomes was observed as revealed by imaging before and after indentation measurements. The indentation measurements that exhibited nearly elastic responses were used to determine the Young's modulus of melanosomes. The average Young's modulus values are similar for 14-year-old and 76-year-old melanosomes with a somewhat narrower distribution for the 14-year-old sample. These elastic modulus values are considerably higher than the modulus of organelles with cytoplasm (<1 MPa) and approaching values of the modulus of protein crystals (approximately 100 MPa) indicating rather high packing density of biologic material in melanosomes. The width of the Young's modulus distributions is considerable spanning from few megapascals to few tens of megapascals indicating large heterogeneity in the structure. A fraction of the force curves cannot be described by the homogeneous elastic sample model; these force curves are consistent with approximately 10 nm structural heterogeneity in melanosomes. The approach-withdraw hysteresis indicates a significant viscoelasticity, particularly in the samples from the 14-year-old sample. Adhesion of the AFM probe was detected on approximately 3% and approximately 20% of the surface of 14-year-old and 76-year-old samples, respectively. In light of previous studies on these same melanosomes using photoelectron emission microscopy, this adhesion is attributed to the presence of lipofuscin on the surface of the melanosomes. This suggestion indicates that part of the difference in photochemical properties between the old and young melanosomes originates from surface lipofuscin.     

Quantifying adhesion bond parameters to distinguish interactions of hydrophilic and hydrophobic blocks of polystyrene-poly-2-vinylpyridine with a silicon nitride surface

An analysis of the loading rate dependence of the forces required to rupture an AFM tip from a block copolymer surface has provided insight into the structure of the surface-macromolecule contact, differentiation of the block contacting the tip, a measure of the polymer-surface binding energy, and the rigidity of the contact. Polystyrene-poly-2-vinylpyridine block copolymers were studied adsorbing to silicon nitride. Polystyrene makes stiff van der Waals contact with the silicon nitride surface in aqueous solution, while the bond of poly-2-vinylpyridine to the surface is more flexible and may involve a bridging water.     

Nanomechanical properties of globular proteins: lactate oxidase

We report on the study of the nanomechanical properties of a lactate oxidase (LOx) monolayer immobilized on gold substrates by atomic force microscopy techniques operating under buffer conditions. Topographical contact mode imaging evidenced the protein deformation under the applied tip load. We performed approaching force curves with both stiff and soft cantilevers by imposing maximum loads of 1.6 nN and 400 pN, respectively. We found that the experimental data were well fitted by the Hertz model for a conical indenter. The use of two types of cantilevers allowed us to check further the consistency of the applicability of the Hertz model to the experimental data. After analyzing 180 curves, we obtained an average value of Young's modulus for the LOx layer in the 0.5-0.8 GPa range. These results agreed with those obtained for LOx submonolayer deposits on mica substrates, which allows discarding any important contribution from the underlying substrate on the measured properties. This range of values is closer to those obtained by other techniques on other globular proteins in comparison with those reported in previous AFM studies on similar systems. We found that for our experimental conditions the force curves can be, in principle, well fitted by the Hertz model for both conical and spherical indenter geometries. However, as the Young's modulus obtained for both geometries can differ appreciably, it becomes necessary to assess which indenter geometry is more adequate to explain the experimental data. For such purpose a systematic study of the indentation versus applied force curves obtained from both fittings for all the experimental curves was done.     

热致液晶高分子微纤的形貌特征和一个模量分析的方法

热致液晶高分子微纤的形貌特征和一个模量分析的方法益小苏，沈烈（浙江大学高分子科学与工程学系，杭州，３１００２７）关键词热致液晶高分子，原位复合，弹性模量，注塑由于主链型热致液晶高分子（ＬＣＰ）的高模量、高强度、易取向、低粘度等特性，当将这种高分子以较...