Fracture Mechanics Studies of Adhesion in Biological Systems

A fracture mechanics based methodology for quantifying adhesive interactions between soft solids, or between a soft solid and a rigid substrate, is reviewed. An emphasis is placed on the application of these techniques to the characterization of adhesive interactions in biological systems. Results from experiments involving the adhesion of gelatin hydrogels to hydrophilic and hydrophobic substrates are described as an illustration of the application of these methods. In these experiments a hemispherical gelatin cap is brought into contact with a flat surface. Separation of the two materials is described in terms of crack propagation along the gelatin/substrate interface. Simultaneous measurements of the applied load, the resulting displacement, and the contact area between the two materials enable us to determine the elastic modulus of the cap, in addition to the crack driving force, or energy release rate. The adhesive behavior of the interface is quantified by the relationship between the energy release rate and the crack velocity. Analogies are made to information obtained from contact angle measurements, and from measurements made with the Israelachvili surface forces apparatus.     

Valid strain measurements for structural dynamic testing

Experimental Techniques -     

Scaling analysis of the magnetocaloric effect in Gd5Si2Ge1.9X0.1 (X=Al, Cu, Ga, Mn, Fe, Co)

The field dependence of the magnetic entropy change has been studied for a series of doped Gd₅Si₂Ge₂ alloys, which possess a magnetic phase transition that is either entirely second order or a combination of primarily second-order mixed to a very minor degree with a first-order transition arising from a magneto-structural phase change. By analyzing the field scaling of the refrigerant capacity as well as of the reference temperatures used for constructing a universal scaling curve, a procedure for estimating the values of the critical exponents for the alloys was developed. For the cases where the transition is entirely second order, the results obtained from this procedure are comparable to the values obtained from the Kouvel–Fisher method. For the case of Fe-doped alloys which partially possess a first-order phase change, the Kouvel–Fisher method is inapplicable. However, their critical exponents determined by our developed procedure can be used to estimate the Curie temperature of the orthorhombic majority phase.     

Antisymmetric magnetoresistance in magnetic multilayers with perpendicular anisotropy

While magnetoresistance (MR) has generally been found to be symmetric in applied field in nonmagnetic or magnetic metals, we have observed antisymmetric MR in Co/Pt multilayers. Simultaneous domain imaging and transport measurements show that the antisymmetric MR is due to the appearance of domain walls that run perpendicular to both the magnetization and the current, a geometry existing only in materials with perpendicular magnetic anisotropy. As a result, the extraordinary Hall effect gives rise to circulating currents in the vicinity of the domain walls that contributes to the MR. The antisymmetric MR and extraordinary Hall effect have been quantitatively accounted for by a theoretical model.     

Chirality of a forming spin spring and remagnetization features of a bilayer ferromagnetic system

Distribution of a magnetic moment in an exchange-coupled bilayer Fe/SmCo epitaxial structure grown on a (110) MgO substrate is visualized by the magnetooptic indicator film technique. The direction and the magnitude of the effective magnetization in this structure are determined both under external magnetic fields of variable magnitude and direction and after the removal of these fields. It is shown that such a heterostructure is remagnetized by a nonuniform rotation of a magnetic moment both along the thickness of a sample and in its plane. A field antiparallel to the axis of unidirectional anisotropy gives rise to spin springs with opposite chiralities in different regions of the magnetically soft ferromagnetic layer. The contributions of these springs to the net magnetization cancel out, thus decreasing the averaged magnetic moment and the remanent magnetization without their rotation. When the external field deviates from the easy axis, the balance is violated and the sample exhibits a quasi-uniform rotation of the magnetic moment. Asymmetry in the rotation of the magnetic moment is observed under the reversal of the field as well as under repeated remagnetization cycles. It is established that a monochiral spin spring is also formed in a rotating in-plane magnetic field when the magnitude of the field exceeds the critical value. Possible mechanisms of remagnetization in this system are discussed with regard to the original disordered orientation of magnetization of the magnetically soft layer with respect to the easy axis, which is defined by the variance of unidirectional anisotropy axes of this layer on the interface.     

Contact studies of weakly compressed PEG brushes with a quartz crystal resonator

A quartz crystal resonator was used to characterize the contact of an elastomeric polymer membrane with a grafted poly(ethylene glycol) (PEG) brush in an aqueous environment. A two-layer model of the acoustic impedance of the system was used to measure the brush thickness before and after contact with the membrane. This model was further extended to include multiple layers, allowing characterization of other monomeric density profiles along the brush thickness. The polymer brush maintains a hydrated layer between the membrane and the quartz crystal surface, the thickness of which could be determined to within 1 nm. We show that the technique is very well suited for studying the properties of highly hydrated layers with thicknesses between 0 and 100 nm at low contact pressures corresponding to a very weak compression of the PEG brush.     

Range of the Fractional Weak Discrepancy Function

In this paper we describe the range of values that can be taken by the fractional weak discrepancy of a poset and characterize semiorders in terms of these values. In [6], we defined the fractional weak discrepancy of a poset to be the minimum nonnegative for which there exists a function satisfying (1) if then and (2) if then . This notion builds on previous work on weak discrepancy in [3, 7, 8]. We prove here that the range of values of the function is the set of rational numbers that are either at least one or equal to for some nonnegative integer . Moreover, is a semiorder if and only if , and the range taken over all semiorders is the set of such fractions .The third author's work was supported in part by a Wellesley College Brachman Hoffman Fellowship.     

Extreme strain localization and sliding friction in physically associating polymer gels

Model physically associating gels deformed in shear over a wide range of reduced rates displayed evidence of strain localization. The nonlinear stress responses and inhomogeneous velocity profiles observed during shear rheometry coupled with particle tracking velocimetry were associated with the occurrence of rate-dependent banding and fracture-like responses in the gel. Scaling law analysis from traditional sliding friction studies suggests that, at the molecular level, deformation is confined to a shear zone with thickness comparable to the mesh size of the gel, the smallest structurally relevant length scale in the gel.     

Quartz crystal microbalance studies of the contact between soft, viscoelastic solids

Mechanical contact between a viscoelastic lens and a viscoelastic film has been probed by means of a quartz crystal microbalance operated in the impedance analysis mode. The frequency shift induced by the formation of the contact decreases with increasing film thickness because of the finite penetration depth of the acoustic shear wave. The dependence of frequency and bandwidth on film thickness and contact area is described within a sheet-contact model, which can be employed to quantitatively analyze mechanical contact in a wide range of materials problems. The model was tested by bringing a quartz crystal coated with an elastomeric gel into contact with a hemispherical cap of a similar gel. Both gels consisted of the thermoreversible gel Kraton G swollen in mineral oil. The experiments support the model well.