Curvature thermally induced

Another example of curvature of van t Hoff plots relates to irreversible changes in the conformation of carbamate-derivatized amylose and cellulose CSP, which was observed for the normal-phase separation of the enantiomers of a dihydropyrimidinone acid and methyl ester. The apparent conformational change was thermally induced and depended upon the polar component of the mobile phase. The irreversible change in the conformation of... 

Although a honeycomb lattice theoretically consists of sp2 atoms, the carbon s ability to represent intermediate states of hybridization leads to another kind of defect to counterbalance the strain energy induced by high curvature. This so-called rehybridization results in a higher n-character of the C-C bonds [24]. Furthermore, local sp3 hybridization can be induced though chemical treatment, such as after thermal elimination of functional groups. 

The major Poisson s ratio is vl2 and E = E2/El is the ratio of the transverse to longitudinal modulus. Equation 8.24 gives the induced curvature for anticlastic deformation of an unsymmetric cross-ply laminate. The curvature is dependent on the thermal and chemical strain mismatch (e, — e2), lamina mechanical properties (v12, E) and the half-thickness, h. 

For small curvatures, Eq. (6.15) shows that the curvature energy of a thin film is characterized by the three parameters k, k, and cq. The qualitative behavior of any system, including such properties such as the equilibrium shape, magnitude of thermal fluctuations, and any phase transitions, can of course be calculated as a function of these constants. However, the physics of the system can be radically different depending on the physical parameters e.g., a change in cq can induce shape changes in the system. It is thus of interest to relate the bending elastic moduli and the spontaneous curvature to the physics of the particular system of interest. This section first shows how these parameters are related to the pressure distribution in the membrane and then presents a simple but instructive microscopic model that relates k, and Co to more molecular properties. 

By varying several parameters such as the W/O ratio, one can induce an inversion from an O/W to a W/O microemulsion and vice versa. The type of structure in the inversion domain depends essentially on the bending constant a characteristic of the elasticity of the surfactant layer [7]. If Ke is on the order of kT (where k is the Boltzmann constant and T absolute temperature), the persistence length of the film (i.e., the distance over which the film is locally flat) is microscopically small. The interfacial film is flexible and is easily deformed under thermal fluctuations. The phase inversion occurs through a bicontinuous structure formed of water and oil domains randomly interconnected [8,9]. The system is characterized by an average curvature around zero, and the solubilization capacity is maximum. When K kT, is large and the layers are flat over macroscopic distances. The transition occurs through a lamellar phase. 

The bend stress relaxation (BSR) technique involves forcing a fiber into a loop of radius (Rq)- After thermal exposure, a creep induced radius of curvature (Rq) is observed in the fiber at room temperature. The salient parameter of the BSR test is the BSR ratio, m = 1 -Rt/R. The higher the value of m, the more creep resistant the material. For a complete description of the BSR technique, see DiCarlo and Dutta, 1995. 

Cumulative plot of the mass yields for thermal-neutron-induced fission of obtained by summing the yields from very asymmetric fission to symmetric fission for fission products (+) and fission fragments ( ). The numbers of prompt neutrons emitted [vi and for light and heavy fragments, respectively, can be obtained from the horizontal distances between the curves using slight corrections for curvature from (Terrell 1962)... 

Suppose that a thin film is bonded to one surface of a substrate of uniform thickness hs- It will be assumed that the substrate has the shape of a circular disk of radius R, although the principal results of this section are independent of the actual shape of the outer boundary of the substrate. A cylindrical r, 0, z—coordinate system is introduced with its origin at the center of the substrate midplane and with its z—axis perpendicular to the faces of the substrate the midplane is then at z = 0 and the film is bonded to the face at z = hs/2. The substrate is thin so that hs R, and the film is very thin in comparison to the substrate. The film has an incompatible elastic mismatch strain with respect to the substrate this strain might be due to thermal expansion effects, epitaxial mismatch, phase transformation, chemical reaction, moisture absorption or other physical effect. Whatever the origin of the strain, the goal here is to estimate the curvature of the substrate, within the range of elastic response, induced by the stress associated with this incompatible strain. For the time being, the mismatch strain is assumed to be an isotropic extension or compression in the plane of the interface, and the substrate is taken to be an isotropic elastic solid with elastic modulus Es and Poisson ratio Vs the subscript s is used to denote properties of the substrate material. The elastic shear modulus /Xg is related to the elastic modulus and Poisson ratio by /ig = Es/ 1 + t s). 

Residual stresses are also very important in many adhesive bonds. When adherends with similar coefficients of thermal expansion are bonded with an adhesive, a biaxial tensile stress often results within the adhesive layer. Interfacial stresses, obeying shear lag distributions, are limited to the edges and around holes and defects where free edges are present. When dissimilar adherends are bonded together, significant stresses can result in both the adherends and the adhesive, as can curvatures of the bonded system. These residual stresses can often be very significant when compared with mechanically induced stresses. 

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