Surface elastic moduli forces

The elastic and viscoelastic properties of blends of PP and ethylene-propylene (EP) were investigated with the force modulation technique by Nysten and co-workers (250,251). In addition to a mapping of the distribution of the rubbery nodules of EP at the surface, the subsurface distribution of these nodules could be estimated. While the FMM data yielded qualitative data, more recent indentation mapping based on f-d curves allowed Nysten and co-workers to obtain quantitative information of the surface elastic modulus (252). 

Force-Curves Measurements In force curve measurements, a vertical displacement of the sample, z, is imposed and the subsequent tip displacement, d, is measured. The tip-sample interaction force, F, is deduced by means of the Hooke s relation, F = -kcd, where is the cantilever stiffness. Force curves arc generally divided into different regions (7). If the part where the electrostatic repulsion forces are dominant is only considered, with silicon tips much stiffer than polymers, tips penetrate the sample surface and an indentation depth, 5, equal to Z d, can be measured. The lower the sample elastic modulus, the greater will be the indentation depth. By using the Hertz mechanical model adapted to the geometry of the tip-sample system (8,9) surface elastic modulus could be deduced from the following equations corresponding respectively to a spherical, a paraboloid and a conical tip ... 

In this relation, k. is the cantilever stiffness and ki is the tip-surface effective stiffness given by dFIBS. From the relations (1.1 to 1.3), it can be seen that k depends on the static contact force, the tip geometry and the surface elastic modulus. Knowing the cantilever stiffness, the static contact force and the tip geometry and dimensions, it is thus theoretically possible to determine the surface elastic modulus from the dynamic response. 

Tan delta(S) TDI Tear strength material from its surface. Usually expressed in milligrams loss per number of cycles per a given load. The viscous modulus/elastic modulus. An abbreviation for toluene diisocyanate. The maximum force required to tear a specified specimen, the force acting mainly parallel to the major axis of the test specimen. 

A Models to describe microparticles with a core/shell structure. Diametrical compression has been used to measure the mechanical response of many biological materials. A particular application has been cells, which may be considered to have a core/shell structure. However, until recently testing did not fully integrate experimental results and appropriate numerical models. Initial attempts to extract elastic modulus data from compression testing were based on measuring the contact area between the surface and the cell, the applied force and the principal radii of curvature at the point of contact (Cole, 1932 Hiramoto, 1963). From this it was possible to obtain elastic modulus and surface tension data. The major difficulty with this method was obtaining accurate measurements of the contact area. 

Compositional contrast, as well as modulus, can also be assessed by laterally resolved imaging of normal or lateral forces in the contact mode AFM. In the corresponding mapping [121] (see also Chap. 4), force-displacement curves are recorded for each pixel. Subsequently, the pull-off forces, as a measure for adhesion, and the indentation part of the loading curves, to extract/fit the elastic modulus, are evaluated for each pixel. In particular for adhesion mapping, the use of chemically functionalized AFM probe tips [122], has been shown to be a suitable approach to map chemical composition and functional group distributions down to the sub-50 nm scale [123]. The mapping of adhesion, friction, and surface mechanical properties will be treated in more detail in Chap. 4. 

Indentation force measurements utilize the indentation part of a force-displacement curve (Fig. 4.19). In the case of a non-compliant sample surface, the SFM tip does not indent the sample and hence the deflection vs. piezo position curve in the contact region has a slope of 1.0. For compliant samples, the slope is <1.0 and can be used to obtain the elastic modulus of the sample by fitting the measured... 

The relationship between the force, Fc, the surface tension, a, (which in this case represents the work required to form a new interface), crack length, /, thickness, h, width, d, and Young s elasticity modulus, E, of the cleaved layer... 

In Chapter 3 we will show that the modulus of surface elasticity is really quite a complex quantity. Whereas the flow properties of liquid/air and liquid/liquid interfaces are determined strongly by elastic forces, the solid/liquid interface is mainly related to wetting processes. 

The technological importance of thin films in such areas as semiconductor devices and sensors has led to a demand for mechanical property information for these systems. Measuring the elastic modulus for thin films is much harder than the corresponding measurement for bulk samples, since the results obtained by traditional indentation methods are strongly perturbed by the properties of the substrate material. Additionally, the behaviour of the film under conditions of low load, which is necessary for the measurement of thin-film properties, is strongly influenced by surface forces [75]. Since the force microscope is both sensitive to surface forces and has extremely high depth resolution, it shows considerable promise as a technique for the mechanical characterization of thin films. 

The mechanisms of debonding of viscoelastic materials from a soHd surface when adhesion is simply due to van der Waals forces should be the starting point of our analysis. Two types of mechanism are typically observed either the viscoelastic material has a relatively high elastic modulus of the order of 1 MPa or above and one typically observes propagation of a crack as described schema-... 

A plate of high-density polyethylene has a surface crack 7.5 pm in one face. The plate fractures in a brittle fashion when a force of 6 X 10 N m is apphed in a direction perpendicular to the crack. The elastic modulus of the polyethylene is 0.95 GPa. Estimate the surface energy of the material. 

Sun, Y., Akhremitchev, B., and Walker, G. C., Using the adhesive interaction between atomic force microscopy tips and polymer surfaces to measure the elastic modulus of compliant samples, Langmuir, 20, 5837-5845 (2004). 

---