Local Elastic Modulus Research Articles

Assessing Mg/Si3N4 biodegradable nanocomposites for osteosynthesis implants with a focus on microstructural, mechanical, in vitro corrosion and bioactivity aspects

Magnesium-based biodegradable implant materials for the osteosynthesis process (fixation or stabilizing of a fractured bone) are on the verge of being used clinically. However, the rapid degradation of magnesium-based materials in the physiological environment results in a loss of mechanical integrity before the complete healing of the fracture site. To address this issue, the present study used Silicon Nitride (Si3N4) nanoparticles to improve the in-vitro degradation resistance along with the mechanical strength and ductility of Magnesium. The Si3N4 nanoparticles were homogeneously reinforced in the pure Magnesium matrix through the ultrasonic-assisted stir casting method. Moreover, the effect of Si3N4 nanoparticles on microstructure, mechanical, in-vitro corrosion and bioactivity response of Mg/Si3N4 nanocomposites was studied. Notably, the inclusion of 1.0 vol% Si3N4 nanoparticles increased tensile strength by 1.4 times and ductility by two times. In addition, the elastic modulus of Mg/Si3N4 nanocomposites is within the range of local cortical bone elastic modulus. In-vitro immersion experiments in simulated physiological fluids revealed a 2.2-fold reduction in degradation rate compared to pure Magnesium. Moreover, the addition of Si3N4 nanoparticles enhanced the in-vitro bioactivity, as the surface of the nanocomposites showed a high needle-like Ca–P apatite layer with a 1.41 Ca/P ratio of the deposited layer close to hydroxyapatite's Ca/P ratio (1.64). Overall, this study provides the basis for the fabrication of stable yet completely biodegradable Mg/Si3N4 nanocomposite bone implants for the osteosynthesis process.

Effect of Carbon Nanofiber Clustering on the Micromechanical Properties of a Cement Paste.

The use of carbon nanofibers (CNFs) in cement systems has received significant interest over the last decade due to their nanoscale reinforcing potential. However, despite many reports on the formation of localized CNF clusters, their effect on the cement paste micromechanical properties and relation to the mechanical response at the macroscopic scale are still not fully understood. In this study, grid nanoindentation coupled with scanning electron microscopy and energy dispersive spectroscopy was used to determine the local elastic indentation modulus and hardness of a portland cement paste containing 0.2% CNFs with sub-micro and microscale CNF clusters. The presence of low stiffness and porous assemblage of phases (modulus of 15–25 GPa) was identified in the cement paste with CNFs and was attributed primarily to the interfacial zone surrounding the CNF clusters. The CNFs favored the formation of higher modulus C–S–H phases (>30 GPa) in the bulk paste at the expense of the lower stiffness C–S–H. Nanoindentation results combined with a microscale–macroscale upscaling homogenization method further revealed an elastic modulus of the CNF clusters in the range from 18 to 21 GPa, indicating that the CNF clusters acted as compliant inclusions relative to the cement paste.

Effects of long-term loading on Moabi wood beams in the tropical environment of Gabon: variability in properties and effects of exposure conditions on mechanical properties in 3-point bending tests

This work is devoted to 3-point bending tests performed on tropical specimens of Moabi (Baillonella toxisperma) from Gabon. The beams are formerly subjected to long-term loading in three media (air-conditioned, unsheltered and sheltered outdoor) in a tropical environment. The beams were sawn into nine 340 mm long sections and subdivided into three sections in the vertical direction (top section, middle section and bottom section). From each section, two specimens were extracted for the bending test, two for the tensile test and four for the compression test. In the present study, 81 bending specimens with a cross-section of 15 x 15 mm2 and a length of 300 mm were used. The tests for the determination of the local modulus of elasticity and failure strength in bending were carried out according with NF EN 408. The results obtained show a strong influence of time and exposure environments on the mechanical parameters (bending strength and modulus of elasticity). There is also a strong variability of these mechanical parameters along the length of the beams with a clear correlation between the sampling areas and the level of exposure; this confirms quite well the level of complexity of the wood material.

A link between mechanical heterogeneity and nontrivial local structural power-law response in a model metallic glass

The structural heterogeneity and mechanical inhomogeneity of metallic glasses at the nanoscale have been demonstrated by extensive experimental investigations, while their inherent correlation remains ambiguous. Based on elasticity theory, a model is developed to describe the local structural response of metallic glasses under hydrostatic deformation. We establish a linear relationship between the local bulk modulus and the nontrivial power-law exponent of the structural response and further verify this relationship by molecular dynamics simulations. The intrinsic link between the local structural response and elastic modulus reveals that the mechanical heterogeneity reflects not only the static atomic packing but also the dynamic evolution of the amorphous structure. Our findings provide direct evidence that mechanical heterogeneity is a feasible indicator for describing the structural heterogeneity of metallic glasses and shed some light on the non-cubic structural power law of disordered materials.

A method for generating finite element models of wood boards from X-ray computed tomography scans

A method is presented for reconstructing the geometry, the pith, the knots and the local fibre orientations in timber boards, based on X-ray computed tomography scans. The local fibre deviations around knots were found by a new algorithm, based on image analysis. The experimental data comprised tomography scans, eigenfrequency measurements and four-point bending tests of 20 Norway spruce boards. 3D and 1D finite element models of the pure bending zone of the bending tests were created, accounting for the exact board geometry and the reconstructed fibre deviations. A purely density based, a purely eigenfrequency based, and a mixed constitutive law were compared. Model estimations showed a high coefficient of determination (R2) for global modulus of elasticity (MoE) (R2⩽0.93), local MoE (R2⩽0.87), bending strength (R2⩽0.83), and the location of initial failure. Constitutive laws accounting for eigenfrequency showed the most accurate results. In the future, adapting the method for logs could enable analyses of boards before sawing.

Presenting in-situ AFM investigations for the evolution of micro-surface topography and elastic modulus of rock under variable loads

Understanding the micro and nano-scale surface deformation and mechanical properties of rock under load possess enormous significance for underground engineering research and provides strong basis for comprehending rock failure as well. According to the documented research, the in-situ observation of micro-surface under dynamic load has not been yet reported. With this motive, a novel approach is presented in this work that takes advantages of combined Atomic Force Microscope (AFM) and customized micro-loading device for in-situ characterization of the the micro-surface topography and elastic modulus of rocks under different load strength. The in-situ comparison of micro-surface properties is carried out using interactive tools of AFM image post-processing software including crop and split, and section analysis. Taking the typical observation results of igneous rock and shale as an example, the results show that the micro-surface topography undulations of rock can reach up to tens of nanometers. Although no apparent fracture occurred, the local fluctuation of the rock samples’ micro-surface changed with the increasing load strength at nanometer level, and in the measurement area of 5 × 5 μm2, the topographies of different pixel points are various, showing significant local difference. With the increasing load strength, the elastic modulus distribution of the rock’s micro-surface shows heterogenity, and the local elastic modulus also increases or decreases, while the variation difference at different pixel points reaches hundreds of MPa. Additionally, the macroscopic fracture characteristics of rock under load, especially the non-uniform crack propagation and its mechanism are discussed. The analysis indicates that the heterogeneous distribution of the rock’s micro-surface elastic modulus and its local complex change with load are accounting for the complexity of the macroscopic crack path and the numerous crack branches. This study provides a novel insight into micro-surface behavior in rock and presents a new method for the investigation of the fracture mechanism of rock.

An experimental investigation into the physical, thermal and mechanical degradation of a polymeric bioresorbable scaffold

This study presents a comprehensive evaluation of the mechanical, micro-mechanical and physical properties of Reva Medical Fantom Encore Bioresorbable Scaffolds (BRS) subjected to a thermally-accelerated degradation protocol. The Fantom Encore BRS were immersed in phosphate buffered saline solution at 50 °C for 112 days with radial compression testing, nanoindentation, differential scanning calorimetry, gel permeation chromatography and mass loss characterisation performed at consecutive time points. In the initial stages of degradation (Days 0–21), the Fantom Encore BRS showed increases in radial strength and stiffness, despite a substantial reduction in in molecular weight, with a slight increase in the melt temperature also observed. In the second phase (Days 35–54), the radial strength of the BRS samples were maintained despite a continued loss in molecular weight. However, during this phase, the ductility of the stent showed a reduction, with stent fracture occurring earlier in the crimp process and with lower amounts of plastic deformation evident under visual examination post-fracture. In the final phase (Days 63–112), the load-bearing capacity of the Fantom Encore BRS showed continued reduction, with decreases in radial stiffness and strength, and drastic reduction in the work-to-fracture of the devices. Throughout each phase, there was a steady increase in the relative crystallinity, with limited mass loss until day 112 and only minor changes in glass transition and melt temperatures. Limited changes were observed in nano-mechanical properties, with measured local elastic moduli and hardness values remaining largely similar throughout degradation. Given that the thermally-accelerated in vitro conditions represented a four-fold acceleration of physiological conditions, these results suggest that the BRS scaffolds could exhibit substantially brittle behaviour after ∼ one year of implantation.

Instrumented Nanoindentation Tests Applied to Bulk Metallic Materials: From Calibration Issue to Pile-Up Phenomena.

Instrumented nanoindentation tests have reached an effective level of theoretical and practical knowledge to become an interesting and useful tool for determining hardness, H, and local elasticity (reduced Young’s modulus), Er, of a variety of materials, from coatings and thin films to bulk metallic materials. Nanoindentation instruments are equipped with analysis software for raw data for hardness and reduced Young’s modulus evaluation, generally based on the Oliver and Pharr analysis method. On the other hand, it is widely known and recognized that prior data acquisition, a tip-dependent calibration procedure of compliance, and area function are needed. With this in view, an accurate and sound calibration protocol is here reported. Hardness and local elastic modulus is measured on different bulk metallic materials, showing the distinctive strengths of using nanoindentation. Finally, a local elastic-plastic phenomenon mostly induced by the nanoindentation tip on ductile metallic material (i.e., pile-up) is also reported and modelled. This manuscript is thus intended to favor and account for the importance of using the instrumented nanoindentation tests for H and Er measurements of metallic materials.

New Perspectives for LVL Manufacturing from Wood of Heterogeneous Quality—Part 2: Modeling and Manufacturing of Variable Stiffness Beams

This paper presents a new strategy in the use of wood of heterogeneous quality for composing LVL products. The idea is to consider veneers representative of the resource variability and retain local stiffness information to control panel manufacturing fully. The placement of veneers is also no longer random as in the first part of this group of papers but optimized for the quality of veneers according to the requirement of bending stresses along the beam. In a four-point bending test arrangement, this means the high-quality veneer is concentrated in the center of the beam in the area between the loading points where the bending moments are the most important, and the low quality is located at the extremities. This initiates the creation of variable stiffness beams. This is driven by an algorithm developed and tested on representative veneer samples from the resource. Four LVL panels were manufactured by positioning the veneers in the same positions as in an analytical calculation model, which allowed the calculation of beam mechanical properties in four-point bending. The proposed optimization of LVL manufacturing from variable quality veneers should help for more efficient usage of forest resources. This optimization strategy showed notable gains for modeled and experimental mechanical properties, whether in terms of stiffness or strength. The analytical calculation of the local modulus of elasticity from modelized beams was satisfactory compared to the tests of the manufactured beams test results, allowing the reliability of the model for this property to be confirmed.

Comparison of two techniques (in vivo and ex-vivo) for evaluating the elastic properties of the ascending aorta: Prospective cohort study

IntroductionAneurysms of the ascending aorta (AA) correspond to a dilatation of the ascending aorta that progressively evolves over several years. The main complication of aneurysms of the ascending aorta is type A aortic dissection, which is associated with very high rates of morbidity and mortality. Prophylactic ascending aorta replacement guidelines are currently based on maximal AA diameter. However, this criterion is imperfect. Stretching tests on the aorta carried out ex-vivo make it possible to determine the elastic properties of healthy and aneurysmal aortic fragments (tension test, resistance before rupture). For several years now, cardiac magnetic resonance imaging (MRI) has provided another means of evaluating the elastic properties of the aorta. This imaging technique has the advantage of being non-invasive and of establishing aortic compliance (local measurement of stiffness) without using contrast material by measuring the variation of the aortic surface area during the cardiac cycle, and pulse wave velocity (overall stiffness of the aorta).Materials and methodsProspective single-center study including 100 patients with ascending aortic aneurysm requiring surgery. We will perform preoperative cine-MRI and biomechanical laboratory stretching tests on aortic samples collected during the cardiac procedure. Images will be acquired with a 3T MRI with only four other acquisitions in addition to the conventional protocol. These additional sequences are a Fast Low Angle Shot (FLASH)-type sequence performed during a short breath-hold in the transverse plane at the level of the bifurcation of the pulmonary artery, and phase-contrast sequences that encodes velocity at the same localization, and also in planes perpendicular to the aorta at the levels of the sino-tubular junction and the diaphragm for the descending aorta. For ex-vivo tests, the experiments will be carried out by a biaxial tensile test machine (ElectroForce®). Each specimen will be stretched with 10 times of 10% preconditioning and at a rate of 10 mm/min until rupture. During the experiment, the tissue is treated under a 37°C saline bath. The maximum elastic modulus from each sample will be calculated.ResultsThe aim of this study is to obtain local patient-specific elastic modulus distribution of the ascending aorta from biaxial tensile tests and to assess elastic properties of the aorta using MRI, then to evaluate the correlation between biaxial tests and MRI measurements.DiscussionOur research hypothesis is that there is a correlation between the evaluation of the elastic properties of the aorta from cardiac MRI and from stretching tests performed ex-vivo on aorta samples collected during ascending aorta replacement.

Ultrasonic characterization of localized passive elastic properties of human pennate muscle with a single-probe setup

Quantitative evaluation of passive elastic properties of an individual skeletal muscle in vivo is among the major challenges of biomechanics, and its clinical application is severely limited. By combining shear-wave elastography (SWE) and B-mode imaging techniques, this study develops a novel non-invasive method to measure the local elastic modulus-fascicle strain curve of human pennation muscle during passive stretching using a single probe. Physiologically meaningful parameters are estimated and compared in subjects with different ages or pathological conditions. The in vivo experimental group comprised 12 healthy subjects (four children, four adults, and four seniors) and eight patients (four suffering from pseudohypertrophy, four from atrophy). Their gastrocnemius muscles were passively stretched using an ankle joint motion instrument. Local elastic moduli of the muscle were measured using SWE imaging frames and a built-in ‘F-ROI’ tool. The corresponding fascicle strains were simultaneously obtained using B-mode imaging frames and a gradient Radon transform. Three parameters (η, μ, G0) were estimated from a normalized elastic modulus-strain curve using the Gauss–Newton method. The measured elastic modulus-strain curves all agreed with models of the estimated parameters (0.910 < R2 < 0.999) and presented different patterns among normal and diseased subjects. η values were lower for pseudohypertrophies (1.93 ± 0.12), but higher for atrophies (63.40 ± 98.89), compared with normal ones (6.02 ± 2.53). In addition, μ values were higher for pseudohypertrophies (22.65 ± 16.40), but lower for atrophies (0.28 ± 0.41), compared with normal ones (1.07 ± 1.22). The proposed method may provide novel insight into the biomechanics of pennate muscle and has the potential to serve for clinical musculoskeletal medical diagnosis, as the single-probe scanning setup is broadly accepted.

A Study on the Failure Behavior of Sand Grain Contacts with Hertz Modeling, Image Processing, and Statistical Analysis.

The crushing behavior of particles is encountered in a large number of natural and engineering systems, and it is important for it to be examined in problems related to hydraulic fracturing, where proppant–proppant and proppant–rock interactions are essential to be modeled as well as geotechnical engineering problems, where grains may crush because the transmitted stresses at their contacts exceed their tensile strength. Despite the interest in the study of the crushing behavior of natural particles, most previous experimental works have examined the single-grain or multiple-grain crushing configurations, and less attention has been given in the laboratory investigation of the interactions of two grains in contact up to their failure as well as on the assessment of the methodology adopted to analyze the data. In the present study, a quartz sand of 1.18–2.36 mm in size was examined, performing a total of 244 grain-to-grain crushing tests at two different speeds, 0.01 and 1 mm/min. In order to calculate stresses from the measured forces, Hertz modeling was implemented to calculate an approximate contact area between the particles based on their local radii (i.e., the radius of the grains in the vicinity of their contact). Based on the results, three different modes of failure were distinguished as conservative, fragmentary, and destructive, corresponding to micro-scale, meso-scale, and macro-scale breakage, respectively. From the data, four different classes of curves could be identified. Class-A and class-B corresponded to an initially Hertzian behavior followed by a brittle failure with a distinctive (single) peak point. The occurrence of hardening prior to the failure point distinguished class-B from class-A. Two additional classes (termed as class-C and class-D) were observed having two or multiple peaks, and much larger displacements were necessary to mobilize the failure point. Hertz fitting, Weibull statistics, and clustering were further implemented to estimate the influence of local radius and elastic modulus values. One of the important observations was that the method of analysis adopted to estimate the local radius of the grains, based on manual assessment (i.e., eyeball fitting) or robust Matlab-based image processing, was a key factor influencing the resultant strength distribution and m-modulus, which are grain crushing strength characteristics. The results from the study were further compared with previously reported data on single- and multiple-grain crushing tests.

Relación entre el Módulo de Elasticidad Global y Local en Elementos Estructurales de Populus Deltoides ‘Australiano 129/60’ y ‘Stoneville 67’ Cultivados en Argentina

En este trabajo se compara el valor del módulo de elasticidad local obtenido experimentalmente con el determinado a partir del módulo de elasticidad global de acuerdo a tres criterios reconocidos internacionalmente (UNE-EN 384 2016, INTI-CIRSOC 2016 y Danzler et al. 2008). El programa experimental se desarrolló de acuerdo a normas europeas sobre 396 elementos estructurales de madera aserrada de Populus deltoides, clones ‘Australiano 129/60’ y ‘Stoneville 67’, cultivados en el delta del río Paraná en Argentina. Se confirmó la alta correlación entre el módulo de elasticidad local y el módulo de elasticidad global. Se constató la incidencia que, en la relación entre ambos módulos, tiene la exigencia normativa de ubicar los mayores defectos en el tercio central al ensayar las piezas. La determinación a partir del módulo de elasticidad global presentó resultados menores a los experimentales con una aproximación superior al 95%.

Clustering of Major Histocompatibility Complex-Class I Molecules in Healthy and Cancer Colon Cells Revealed from Their Nanomechanical Properties.

The activation of the T cell mediated immune response relies on the fine interaction between the T cell receptor on the immune cell and the antigen-presenting major histocompatibility complex (MHC) molecules on the membrane surface of antigen-presenting cells. Both the distribution and quantity of MHC/peptide complexes and their adequate morphological presentation affect the activation of the immune cells. In several types of cancer the immune response is down-regulated due to the low expression of MHC-class I (MHC-I) molecules on the cell's surface, and in addition, the mechanical properties of the membrane seem to play a role. Herein, we investigate the distribution of MHC-I molecules and the related nanoscale mechanical environment on the cell surface of two cell lines derived from colon adenocarcinoma and a healthy epithelial colon reference cell line. Atomic force microscopy (AFM) force spectroscopy analysis using an antibody-tagged pyramidal probe specific for MHC-I molecules and a formula that relates the elasticity of the cell to the energy of adhesion revealed the different population distributions of MHC-I molecules in healthy cells compared to cancer cells. We found that MHC-I molecules are significantly less expressed in cancer cells. Moreover, the local elastic modulus is significantly reduced in cancer cells. We speculate that these results might be related to the proven ability of cancer cells to evade the immune system, not only by reducing MHC-I cell surface expression but also by modifying the local mechanical properties affecting the overall morphology of MHC-I synapse presentation to immune cells.

Characterization of the local mechanical texture of animal meat and meat replacements using multi-point indentation

Over consumption of animal meat is a large contributor to environmental change and should be reduced. This reduction can be achieved by replacing high environmental impact animal meat with an alternative produced from plant-based products or innovative in vitro techniques that have negligible environmental impact. However, the general public will likely consume only meat replacements that mimic the aesthetic qualities of animal meat, with a challenging parameter to tune being the local mechanical response which defines the food texture. In this work, we present a method to characterize the local mechanics of food by using multi-point indentation to spatially measure the local elastic modulus. The resulting heterogeneous mechanical maps are quantified using the established auto-correlation method Moran's I, which can be used to quantify the resemblance of food texture between samples. The presented technique holds the potential to correlate production parameters such as shear rate and chemical composition with perceived food texture.

Multipoint indentation for material identification in three-dimensional observation based on serial sectioning

Three-dimensional (3D) observations of internal structures are important for evaluating material properties. Serial sectioning with destructive processes is traditionally employed as a 3D observation method. Identifying the boundaries of elements in microscope images and measuring the mechanical properties of each element are required for the evaluation of the mechanical properties of composite materials. This study provides a system for measuring the local hardness and elastic modulus by conducting indentation tests during serial sectioning processes. An automatic serial sectioning observation was performed during a combination process of precision cutting in high-speed milling with a single-crystal diamond tool and microscopic observation. A Vickers indenter was attached to a tool spindle table, and indentation tests were conducted under a displacement control process at submicron spatial resolution. The indentation modulus was obtained by analyzing the force–displacement profile measured during the unload process. The scale effects relating to the indentation depth in the measurements of the indentation modulus were confirmed for an Al alloy sample measured in this system. This study focused on the identification of components by using hardness information measured under the same indentation depth on a two-dimensional flat surface after precision cutting of the material. Three types of metal wires (1 mm diameter) embedded in plastic resin were used in the experiment. The hardness distributions on the serial sectioning surfaces were measured, and the values measured at each wire area on 3D positions were used for the identification of their material properties. This serial sectioning observation creates a 3D microstructural model including not only microscopic images, but also hardness and elastic modulus information for the identification of components in the microscopic area.

Photodegradation pathways of CH3NH3PbI3 organic perovskite polycrystalline film observed by in-situ scanning probe microscopy

In this study, the in-situ observation of degradation-induced local elastic modulus (Young’s modulus) variation in CH3NH3PbI3 (MAPbI3) polycrystalline film was conducted using the continuous scanning by scanning probe microscopy (SPM). We pointed out that the observed degradation in MAPbI3 film under the SPM continuous scanning is a photo-excited process due to the stray laser effect induced by the scattering of the SPM-equipped red laser. The degradation rate was highly accelerated by light illumination when the MAPbI3 polycrystalline films were aged in humid air, O2, dry air, and N2 atmosphere. Significantly, the SPM analysis result shows that several hours is sufficient for MAPbI3 film to undergo red light degradation in N2. Otherwise, under light illumination, the result provides evidence that hydrate, which is the critical intermediate phase to trigger humid degradation, did not occur even in the presence of H2O. It identifies H2O is not the preferential species to react with the photo-excited MAPbI3. Though the laser effect must be carefully taken into account, this study indicates that SPM is an appropriate analysis technique to examine the infinitesimal variation of surface property in organic perovskite material, clarifying the degradation mechanism in the initial period.

Intrinsic properties of osteomalacia bone evaluated by nanoindentation and FTIRM analysis

Osteomalacia is a pathological bone condition consisting in a deficient primary mineralization of the matrix, leading to an accumulation of osteoid tissue and reduced bone mechanical strength. The amounts, properties and organization of bone constituents at tissue level, are known to influence its mechanical properties. It is then important to investigate the relationship between mechanical behavior and tissue composition at this scale in order to provide a better understanding of bone fragility mechanisms associates with this pathology.Our purpose was to analyze the links between ultra-structural properties and the mechanical behavior of this pathological bone tissue (osteomalacia) at tissue level (mineral and osteoid separately, or global). Four bone biopsies were taken from patients with osteomalacia, and subsequently embedded, sectioned, and polished. Then nanoindentation tests were performed to determine local elastic modulus E, contact hardness Hc and true hardness H for both mineralized and organic bone phases and for the global bone. The creep of the bone was also studied using a special indentation procedure in order to assess visco-elasto-plastic (creep) bone behavior. This allowed a detailed study of the rheological models adapted to the bone and to calculate the parameters associated to a Burgers model. Ultra-structural parameters were measured by Fourier Transform InfraRed Microspectroscopy (FTIRM) on the same position as the indents.The use of rheological models confirmed a significant contribution from the organic phase on the viscous character of bone tissue. The elastic E and the elasto-plastic Hc deformation were correlated to both collagen maturity and Mineral/Matrix. The pure plastic deformation H was only correlated to the mineral phase. Our data show that mineral phase greatly affects mechanical variables (moduli and viscosities) and that organic phase (as illustrated in osteoid tissue) may play an important role in the creep behavior of bone. In conclusion, this study brings mechanical and physicochemical values for osteoid and mineral phases.

Analysis of Thickness Dependence of Nanoscaled Thin Film and Substrate by Ultrasonic Atomic Force Microscopy

Nanoscaled thin films are typically deposited on various substrates to achieve their unique characteristics. These thin film systems can be affected by the thickness variations between the thin film and the accompanying substrate. To investigate the thickness dependence of a nanoscaled thin film system, ultrasonic atomic force microscopy (Ultrasonic-AFM) which can evaluate the localized elastic modulus using the contact resonance frequency of a vibrating cantilever is applied. Copper thin films of low elastic modulus were deposited on silicon substrates of high elastic modulus. By contrast, Si3N4 and Ti thin films of high elastic modulus were deposited on GaAs and glass substrates of low elastic modulus, respectively. Experimental results showed that the thin films with different thickness were affected significantly by the substrate and the contact resonance frequency changes as a result of the varying thickness of the thin films. This research demonstrate that Ultrasonic-AFM may be a novel technique for the nondestructive measurement of nanoscale thin film thickness by considering substrate features.

Microscopic theory for elastic modulus of colloidal polymers: Effect of bond length

Colloidal polymers have attracted increasing attention in condensed physics, statistical mechanics and polymer science and engineering due to their advances in synthesis and visualization. Many useful properties and applications of colloidal polymers make them an ideal model to explore fundamental problems in slow dynamics and rheology of chain-like molecules in supercooled regime. With temperature decreasing or density rapidly increasing, amorphous materials often exhibit nonzero shear moduli. In this article, we are to investigate the nonzero shear modulus and bulk modulus of colloidal polymer in supercooled regime based on recent microscopic theoretical development. At the segmental-scale level, an analytical derivation for elastic modulus of colloidal polymer is constructed based on the standard approximation in naïve mode-coupling theory (NMCT). In the framework of nonlinear Langevin equation theory (NLET), the derivation combines the concept of dynamic free energy, localization and NMCT crossover volume fraction. Taking the chain connectivity into account, an explicit expression for shear modulus including intrachain structure factor, interchain correlation and localized length is formulated. Bulk modulus can be obtained by relating it to long wavelength part of static structure factor. Firstly, our calculation for discrete wormlike chain shows that intrachain structure factor has a power law decay at intermediate wavevector which is similar to flexible linear chain. Secondly, we find that colloidal polymer with long bond length has a lower NMCT crossover volume fraction. Furthermore, inputting the localized length, long wavelength density fluctuation and static intrachain and interchain structures into the theoretical expression, the effect of bond length on shear modulus and bulk modulus are investigated. Interestingly, we find the bond length plays a critical and unique role in localized length and bulk modulus. For instance, when the supercooling degree is used as an independent variable, the local length and bulk elastic modulus of the chain with the same bond length can be collapsed onto a universal curve, which is independent of chain length and local bending energy. However, in the aspect of shear modulus, the bond length is not a unique quantity and the above universal curve cannot be found. The shear modulus depends on other parameters of chain, such as chain length and rigidity. According to the universal behavior of zero-wavevector static structure factor versus bond length, we guess that the nonuniversal curve of shear modulus is due to the bond length effect on long wavevector static structure factor. This work provides a theoretical foundation for controlling various properties of chain-like supercooled materials in the future.