Forced rupture

Combined measurement techniques were successfully applied in the study of surface forces in microscopic foam films such as study of longitudinal electrical condictivity, study of black films with X-rays forced rupture of films by a-particles irradiation, etc. They permit to find the relation between surface forces and parameters of film structure. It is important also surface forces measurements to be performed at controlled state of the adsorption layer. As far as surface forces act normally to film surface, it is interesting to understand the role of... 

The conclusion is, therefore, that both spontaneous and forced rupture of foam bilayer by a-particles are mediated by microscopic holes of surfactant vacancies and can be described from a unified point of view with the aid of the nucleation theory of bilayer rupture [399,402,403]. However, studying the effect of a-particle irradiation of the bilayer lifetime is an independent way of proving the applicability of the hole mechanism of bilayer rupture. 

Fig. 39 Average rupture and rejoining forces (rupture, left-, rejoining, right) as a function of contour length at different loading rates (a) 60, (b) 300, (c) 1,500, (d) 6,000, and (e) 30,000 pN/s (no rejoining events are found)...

This result reflects the Kramers relation (Gardiner, 1985). A millisecond time of unbinding, i.e.. Tact 1 ms, corresponds in this case to a rupture force of 155 pN. For such a force the potential barrier AU is not abolished completely in fact, a residual barrier of 9 kcal/mol is left for the ligand to overcome. The AFM experiments with an unbinding time of 1 ms are apparently functioning in the thermally activated regime. 

This regime involves forces which are so strong that the ligand undergoes a drift motion governed by (3) in the limit that the fluctuating force aN t) is negligible compared to the applied force. In this case a force of about 800 pN would lead to rupture within 500 ps. 

These examples illustrate that SMD simulations operate in a different regime than existing micromanipulation experiments. Considerably larger forces (800 pN vs. 155 pN) are required to induce rupture, and the scaling behavior of the drift regime, characterized by (9), differs qualitatively fi om the activated regime as characterized by (7). Hence, SMD simulations of rupture processes can not be scaled towards the experimental force and time scales. 

The rupture force measured in AFM experiments is given, therefore, by the average slope of the energy profile minus a correction related to the effects of thermal fluctuations. Equation (11) demonstrates that the rupture force measured in AFM experiments grows linearly with the activation energy of the system (Chilcotti et ah, 1995). A comparison of (10) and (11) shows that the unbinding induced by stiff springs in SMD simulations, and that induced by AFM differ drastically, and that the forces measured by both techniques cannot be readily related. 

Grubmiiller et al., 1996] Grubmiiller, H., Heymann, B., and Tavan, P. Ligand binding and molecular mechanics calculation of the streptavidin-biotin rupture force. Science. 271 (1996) 997-999... 

Microscopic Interpretation of Atomic Force Microscope Rupture Experiments... 

Fig. 4. Typical AFM rupture experiment (top) Receptor molecules are fixed via linker molecules to a surface (left) in the same way, ligand molecules are connected to the AFM cantilever (right). When pulling the cantilever towards the right, the pulling force applied to the ligand can be measured. At the point of rupture of t he ligand-receptor complex the measured force abruptly drops to zero so that the rupture force can be measured.

To enable an atomic interpretation of the AFM experiments, we have developed a molecular dynamics technique to simulate these experiments [49], Prom such force simulations rupture models at atomic resolution were derived and checked by comparisons of the computed rupture forces with the experimental ones. In order to facilitate such checks, the simulations have been set up to resemble the AFM experiment in as many details as possible (Fig. 4, bottom) the protein-ligand complex was simulated in atomic detail starting from the crystal structure, water solvent was included within the simulation system to account for solvation effects, the protein was held in place by keeping its center of mass fixed (so that internal motions were not hindered), the cantilever was simulated by use of a harmonic spring potential and, finally, the simulated cantilever was connected to the particular atom of the ligand, to which in the AFM experiment the linker molecule was connected. 

Fig. 5. Theory vs. experiment rupture forces computed from rupture simulations at various time scales (various pulling velocities Vcant) ranging from one nanosecond (vcant = 0.015 A/ps) to 40 picoscconds (vcant = 0.375 A/ps) (black circles) compare well with the experimental value (open diamond) when extrapolated linearly (dashed line) to the experimental time scale of milliseconds.

In summary, our simulations provided detailed insight into the complex mcf hanisms of streptavidin-biotin rupture. They attribute the binding force... 

Fig. 6. Force profile obtained from a one nanosecond simulation of streptavidin-biotin rupture showing a series of subsequent force peaks most of these can be related to the rupture of individual microscopic interactions such as hydrogen bonds (bold dashed lines indicate their time of rupture) or water bridges (thin dashed lines).

The impact forces on car couplers put high stresses in sills, anchors, and doublers. This may start fatigue cracks in the shell, particularly at the corners of welded doubler plates. With brittle steel in cold weather, such cracks sometimes cause complete rupture of the tank. Large end radii on the doublers and tougher steels will reduce this hazard. Inspection of older cars can reveal cracks before failure. 

Gravitational force favors the separation of gas from liquid in a disperse system, causing the bubbles to rise to the hquid surface and the liquid contained in the bubble walls to drain downward to the main body of the liquid. Interfacial tension favors the coalescence and ultimate disappearance of bubbles indeed, it is the cause of bubble destruction upon the rupture of the laminae. 

As we showed in Chapter 6 (on the modulus), the slope of the interatomic force-distance curve at the equilibrium separation is proportional to Young s modulus E. Interatomic forces typically drop off to negligible values at a distance of separaHon of the atom centres of 2rg. The maximum in the force-distance curve is typically reached at 1.25ro separation, and if the stress applied to the material is sufficient to exceed this maximum force per bond, fracture is bound to occur. We will denote the stress at which this bond rupture takes place by d, the ideal strength a material cannot be stronger than this. From Fig. 9.1... 

The common tests are shown in Fig. 17.2. The obvious one is the simple tensile test (Fig. 17.2a). It measures the stress required to make the longest crack in the sample propagate unstably in the way shown in Fig. 17.3(a). But it is hard to do tensile tests on ceramics - they tend to break in the grips. It is much easier to measure the force required to break a beam in bending (Fig. 17.2b). The maximum tensile stress in the surface of the beam when it breaks is called the modulus of rupture, o for an elastic beam it is related to the maximum moment in the beam, M by... 

Effects of Water Hammer. Water hammer has a tremendous and dangerous force that can collapse floats and thermostatic elements, overstress gauges, bend mechanisms, crack trap bodies, rupture fittings and heat exchange equipment, and even expand piping. Over a period of time, this repeated stress on the pipe will weaken it to the point of rupture. 

Property of plastics that permits the material to undergo deformation permanently and continuously without rupture from a force that exceeds the yield value of the material. 

Firebox Overpressure - The firebox of a forced-draft furnace and boiler is designed to withstand the overpressure that can be generated by the fans with dampers in their closed position. This needs to be specially checked when both forced and induced-draft fans are provided to discharge combustion products through heat recovery facilities, since higher than normal fan pressures may be used to overcome pressure drop. In the case of high-pressure process furnaces, a tube rupture could also be the cause of firebox overpressure. 

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