Ruptures

Though foam and emulsion films might exist for a long time, on some timescale they will collapse. The rupture of foam and emulsion films has been studied by various methods both experimentally [797] and theoretically [798]. It is obvious that the stability of foam films is influenced by surface forces. For example, in 1924 Bartsch reported that electrolytes decrease the life time of certain foams [799], presumably by decreasing electrostatic stabilization. Surface forces alone, however, do not determine the life time of a soap film. 

Several experiments indicate that the life time of a foam film is correlated with the surface elasticity [738, 786, 800]. One explanation is that high surface elasticities dampen fluctuations in the film [786, 791]. Fluctuations are one possible reason for film rupture. For the same reason, surface viscosity influences the stability of Aims [792, 800]. In particular for large surface-active molecules such as proteins, this has been analyzed for emulsion films due to the importance in food science [721, 793]. The rupture of thin films has been extensively studied for liquid films on solid surfaces. Therefore, we describe it in more detail in Section 7.6.3. 

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For vehicles, special attention is most often focused on the knocking potential encountered at high motor speeds in excess of 4000 rpm for which the consequences from the mechanical point of view are considerable and lead very often to mechanical failure such as broken valves or pistons, and rupture of the cylinder head gasket. Between RON and MON, it is the latter which better reflects the tendency to knock at high speeds. Conversely, RON gives the best prediction of the tendency to knock at low engine speeds of 1500 to 2500 rpm. 

The mechanical properties of waxes and solid paraffins are of considerable importance for most applications and numerous tests have been developed for characterizing the hardness, the brittleness, and resistance to rupture. 

Ductility of bituminous materials NF T 66-006 ASTM D 113 Test-sample elongation at the point of rupture... 

Fault seals are known to have been ruptured by excessive differential pressures created by production operations, e.g. if the hydrocarbons of one block are produced while the next block is kept at original pressure. Uncontrolled cross flow and inter-reservoir communication may be the result. 

Storage tanks should always be closely surrounded by bund walls to contain crude in the event of a spillage incident, such as a ruptured pipe or tank, and to allow fire fighting personnel and equipment to be positioned reasonably close to the tanks by providing protected access. 

The speed of wetting has been measured by running a tape of material that is wetted either downward through the liquid-air interface, or upward through the interface. For a polyester tape and a glycerol-water mixture, a wetting speed of about 20 cm/sec and a dewetting speed of about 0.6 cm/sec has been reported [37]. Conversely, the time of rupture of thin films can be important (see Ref. 38). 

There have been some studies of the equilibrium shape of two droplets pressed against each other (see Ref. 59) and of the rate of film Winning [60, 61], but these are based on hydrodynamic equations and do not take into account film-film barriers to final rupture. It is at this point, surely, that the chemistry of emulsion stabilization plays an important role. 

The rupture process of a soap film is of some interest. In the case of a film spanning a frame, as in Fig. XIV-15, it is known that rupture tends to originate at the margin, as shown in the classic studies of Mysels [207, 211]. Rupture away from a border may occur spontaneously but is usually studied by using a spark [212] as a trigger (a-radia-tion will also initiate rupture [213]). An aureole or ridge of accumulated material may be seen on the rim of the growing hole [212, 214] (see also Refs. 215, 216). Theoretical analysis has been in the form of nucleation [217, 218] or thin-film instability [219]. 

Variational RRKM theory is particularly important for imimolecular dissociation reactions, in which vibrational modes of the reactant molecule become translations and rotations in the products [22]. For CH —> CHg+H dissociation there are tlnee vibrational modes of this type, i.e. the C—H stretch which is the reaction coordinate and the two degenerate H—CH bends, which first transfomi from high-frequency to low-frequency vibrations and then hindered rotors as the H—C bond ruptures. These latter two degrees of freedom are called transitional modes [24,25]. C2Hg 2CH3 dissociation has five transitional modes, i.e. two pairs of degenerate CH rocking/rotational motions and the CH torsion. 

This illustrates the steps of energy transfer from the initially highly-excited C-H bond to other parts of the molecule, subsequent concentration of energy in one part of the molecule and finally rupture of the... 

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.

Both the AFM rupture experiments as well as our simulation studies focussed on the streptavidin-biotin complex as a model system for specific ligand binding. Streptavidin is a particularly well-studied protein and binds its ligand biotin with high affinity and specificity [51]. Whereas previous experiments (see references in Ref. [49]) and simulation studies [52] referred only to bound/unbound states and the associated kinetics, the recent AFM... 

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).

Fig. 7. Snapshots of rupture taken (A) at the start of the simulation (zcant = 0), (li) at ZcB.nl = 2.8 A, (C) at Zcnm = 4.1 A, (D) at Zcnm = 7.1 A, and (E) at Zcant = 10.5 A. The biotin molecule is drawn as a ball-and-stick model within the binding )ocket (lines). The bold dashed lines show hydrogen bonds, the dotted lines show selected water bridges.

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