Membrane buckling

Another issue is the membrane buckling due to internal and thermal stress of the CMOS layers, which are not optimized for high-temperature operation. The buckling of the microhotplate can generate severe problems in the adhesion of the sensitive layer. In a temperature-pulsed operation mode, the repeated bending of the membrane could cause a rehabihty problem [120]. 

Similar to beam buckling, membrane buckling is another important mechanism for thermal expansion microvalves. To investigate the bending of a membrane when heat is added to it. Fig. lb illustrates the principle of the thermal buckling of a square membrane. Considering a uniform compression condition across the membrane (i.e., the compressive stress is constant, Sx = Sy = S), the membrane buckles transversally without any additional external load when the compressive stress gradually increases with temperature and exceeds the critical stress, Sa- The critical stress is defined as... 

Figure 2(a) shows behavior of the liposomes after exposure to the MES buffer with pH 3.5 and ionic strength 0.001. The liposomes kept their shape for 5 min into the exposure, after which time the membrane buckled and folded in on itself, resulting in small inward protrusions within the stiU-spherical, yet smaller liposome. These deformations at created by pH gradients across the membrane surfaces suggests that liposomes deform not only by osmotic pressine differences. 

Figure 11.4 Magnetoliposotnes inside which the salt concentration is intermediate (Cs = 25 mM) and submitted to a magnetic field H (direction given by the arrow). The liposomes are always axisymmetric around the field direction but combine elongations both at the poles and at the equator (spinning-top shapes). The values of = 1 — can be (a) nearly zero, (b) negative or (c) positive. In that last case the sharp shape is only transient and relaxes to a more rounded one, but with (d) membrane buckling. Length of the bar is always 10 pm.

Internal-pressure design rules and formulas are given for cylindrical and spherical shells and for ellipsoidal, torispherical (often called ASME heads), hemispherical, and conical heads. The formulas given assume membrane-stress failure, although the rules for heads include consideration for buckling failure in the transition area from cylinder to head (knuckle area). 

The solution to this fourth-order partial differential equation and associated homogeneous boundary conditions is just as simple as the analogous deflection problem in Section 5.3.1. The boundary conditions are satisfied by the variation in lateral displacement (for plates, 5w actually is the physical buckle displacement because w = 0 in the membrane prebuckling state however, 5u and 8v are variations from a nontrivial equilibrium state. Hence, we retain the more rigorous variational notation consistently) ... 

Pitched roofs. Pitched roofs are typically sloped at a minimum of 6° to ensure the weather resistance of lapped sheeting without sophisticated seals or a waterproof membrane. Portal frames are also more liable to snap through buckling at very shallow pitches. A pitched roof means a greater dead volume to heat, although there is additional space for high-level service distribution. 

Care must be exercised when using metal or FRP panels for lateral support. They may have been forced into membrane action by the blast load, and may not be able to offer any resistance against lateral buckling of supporting members. The panel s inplane capacity should be evaluated, and additional bracing provided where required. 

Additional compression eventually leads to the collapse of the film. The pressure nc at which this occurs is somewhere in the vicinity of the equilibrium spreading pressure. Figure 7.7 represents schematically how this film collapse may occur. The mode of film buckling shown in Figure 7.7 is not the only possibility head-to-head as well as tail-to-tail configurations can be imagined. The second structure strongly resembles that of cell membranes, which we discuss in the next chapter. 

SEM images of the deformation around an indentation in a 90 im thick MWCNT-AI203 composite prepared by in situ formation of CNTs within the regular and very well aligned pores of an alumina membrane, (a) array of the shear bands formed, (b) close up view of lateral buckling or collapse of the CNTs in one shear band. ... 

Some materials, among the most porous, show a large volume variation due to mechanical compaction when submitted to mercury porosimetry. High dispersive precipitated silica shows, as low density xerogels and carbon black previously experimented, two successive volume variation mechanisms, compaction and intrusion. The position of the transition point between the two mechanisms allows to compute the buckling constant used to determine the pore size distribution in the compaction part of the experiment. The mercury porosimetry data of a high dispersive precipitated silica sample wrapped in a tight membrane are compared with the data obtained with the same sample without memlM ane. Both experiments interpreted by equations appropriate to the mechanisms lead to the same pore size distribution. 

Below 45 MPa, the high dispersive precipitated silica sample with or without membrane collapses without mercury intrusion. The buckling mechanism of pores edges can be assumed as in the case of low density xerogels. Consequently, equation (2) can be used to interpret the mercury porosimetry curve in this low pressure domain. The constant A, to be used in equation (2) can be calculated from the P, value using equation (4). With a mercury surface tension 0.485 N/m, a contact angle 0= 130° and P, = 45 MPa, one obtains K = 86.3 nm MPa" . 

The easiest way to measure stress in thin films after deposition is to analyze the change in the radius of curvature of the wafers before and after film deposition on one side, as first proposed by Stoney [7]. However, this technique usually requires the use of test wafers. After complete processing of the wafers, the stress can be obtained by measuring the deflection of membranes or indicator structures [8], To measure compressive stress, the buckling technique on double-side supported bridges [9] and harp-like structures [10] can be applied. 

Of the layers mentioned above, the thin films showing the widest range of stress are the PECVD oxides. The stress state of the oxide layers becomes important when such films are used as part of a membrane or as a passivation layer. Membranes that are under considerable compressive stress tend to buckle, severely changing their mechanical properties. In contrast, considerable tensile stress in membranes can lead to crack formation and fracture. The passivation properties of PECVD oxide layers, for example, towards humidity, depend sensitively on their composition, which, in turn, has a great influence on the stress. 

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