The Role of Thermal Fluctuations

In the preceding discussion, we have neglected the thermal fluctuations of the triple line. Such fluctuations are in fact unobservable on a macroscopic scale (roughly, for objects larger than micron). They can, nevertheless, play a role when one studies the hysteresis due to small defects. We proceed to discuss the possible role of thermal vibrations in overcoming an anchor point for the triple line. 

Even when Young s force 7(cos — cos0 ) is quite weak, it is possible to see the line of contact move if the anchor points can be overcome by thermally activated jumps. The corresponding Boltzmann factor is exp(—W/feT), where kT is the thermal energy and W is the energy stored in the line at the instant of break off [equation (3.22)]. Based on equations (3.25) and (3.27), we have roughly 

Conclusion Only for very small defects can thermal vibrations provide enough energy to overcome hysteresis. The reader is encouraged to consult the literature for a documented case involving very small defects (helium on cesium).  

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The role of thermal fluctuations in bubble nucleation of pool boiling was shown experimentally by Dougall and Lippert (1967) see Figure 2.4. Their experiments were conducted using water, at atmospheric pressure, boiled from a 2-in. (5 cm)-diameter copper surface that was located in the bottom plate of a 2-gal (7.6-liter) aluminum container. The copper boiling surface was prepared by pol-... 

The role of thermal fluctuations for membranes interacting via arbitrary potentials, which constitutes a problem of general interest, is however still unsolved. Earlier treatments G-7 coupled the fluctuations and the interaction potential and revealed that the fluctuation pressure has a different functional dependence on the intermembrane separation than that predicted by Helfrich for rigid-wall interactions. The calculations were refined later by using variational methods.3 8 The first of them employed a symmetric functional form for the distribution of the membrane positions as the solution of a diffusion equation in an infinite well.3 However, recent Monte Carlo simulations of stacks of lipid bilayers interacting via realistic potentials indicated that the distribution of the intermembrane distances is asymmetric 9 the root-mean-square fluctuations obtained from experiment were also shown to be in disagreement with this theory.10... 

III.B. The Role of Thermal Fluctuations on the Transition from Common Black Films to Newton Black Films. The method described in the previous section will be now applied to thin films with fluctuating interfaces, with the interaction energy calculated as in section II.G. For low values ofthe external pressure, the enthalpy has two metastable minima at Zk and 2c, and a stable one at 2 - 0 (the former two correspond to the Newton and to the common black films, respectively, and the latter implies the rupture of the film), separated by two maxima located at Z and 22 (see Figure 7a). At metastable equilibrium the distances between the surfaces are distributed between 21 and 22 for the Newton black film and between z2 and 2 —°° for the common black film. The stability of the metastable states depends on the chance for a small area S of the interface to reach the... 

Zeldovich Ya B 1977 The role of thermal fluctuations of concentration in the kinetics of bimolecular reactions Elektrokhimia 13 677-9... 

In our most recent work, we investigated the impact of thermal fluctuations mi the driven translocation dynamics, theoretically and by means of extensive MD simulation [88]. Indeed, the role of thermal fluctuations is by no means self-evident. Our theoretical consideration is based on the Fokker-Planck equation (FPE) Eq. (6), which has a nonlinear drift term and a diffusion term with a time-dependent diffusion coefficient... 

Under the conditions of a gradual failure, such as in creep, the kinetic aspects of the physical-chemical processes are revealed, and the role of thermal fluctuations is emphasized. Thermal fluctuations are the primary reason for the activation of elementary acts of cleavage and rearrangements of the interatomic bonds. They determine the probability (i.e., frequency) of these acts overcoming the potential barrier. Here, we deviate from a macroscopic description of mechanical testing and move to a description at a microscopic and nanolevels. 

Some statistical properties of defect turbulent states in EHC were studied experimentally [42, 133, 134] and, as pointed out before, the role of thermal fluctuations slightly below threshold was measured and analyzed. Of the numerous investigations of far-off threshold effects we only mention the study of phase waves in the oscillatory bimodal state [135, 136] and the transition between strongly turbulent states [60]."... 

Vorberg, J. and Herminghaus, S. (2001) Adsorption isotherms of hydrogen the role of thermal fluctuations. Physical Review Letters, 87,1-4. 

Since Ca is transferred from one side of the membrane to the other side in association with the Ca -ATPase, thermal fluctuation of critical regions of the Ca -ATPase influenced in specific ways through the phosphorylation of the enzyme by ATP may play a role in Ca translocation. Similar ideas have been proposed some time ago by Huxley [419] in relationship to crossbridge movements during muscle contraction and by Welch and others on the role of protein fluctuations in enzyme action [420-430]. 

The preceding considerations are restricted to the case of zero temperature. To understand the role of the temperature, we now evaluate the effect of thermal fluctuations on the equilibrium position of the tube. 

Radiation probes such as neutrons, x-rays and visible light are used to see the structure of physical systems through elastic scattering experiments. Inelastic scattering experiments measure both the structural and dynamical correlations that exist in a physical system. For a system which is in thermodynamic equilibrium, the molecular dynamics create spatio-temporal correlations which are the manifestation of thermal fluctuations around the equilibrium state. For a condensed phase system, dynamical correlations are intimately linked to its structure. For systems in equilibrium, linear response theory is an appropriate framework to use to inquire on the spatio-temporal correlations resulting from thermod5mamic fluctuations. Appropriate response and correlation functions emerge naturally in this framework, and the role of theory is to understand these correlation functions from first principles. This is the subject of section A3.3.2. 

The spontaneous emergence of avalanches, droplets and rivulets is very difficult to simulate with classical fluid dynamical models, due to the critical nature (self-organized criticality) and threshold character of these nonlinear phenomena. Therefore, the role of statistical fluctuations in thin-film dynamics cannot be underestimated, especially in the mesoscale. Unlike the classical approaches, we need not introduce any external and artificial perturbations. All phenomena occur spontaneously due to thermal noise inherent in the nonlinearly interacting particle dynamics. 

When the string is subject to thermal fluctuations (due to the surrounding air) y(x) becomes a random function, x playing the role of the variable called so far t. One expects that the probability for any particular y(x) to materialize will be proportional to... 

As was shown in Section 2.1, in some cases thermal fluctuations of reactant densities affect the reaction kinetics. However, the equations of the formal chemical kinetics are not suited well enough to describe these fluctuations in fact they are introduced ad hoc through the initial conditions to equations. The role of fluctuations and different methods for incorporating them into formal kinetics equations were discussed more than once. 

After thermalization, the electron may recombine with a positive ion or be captured by a molecule forming a negative ion, or it may be locked in a trap the role of which may be played by fluctuation cavities or structural disturbances in the medium, or by polarization pits that the electron digs when it interacts with surrounding molecules. Such captured electrons are called solvated electrons (in water they are sometimes called hydrated electrons).31,32 According to the data obtained in picosecond pulsed-radiolysis sets,33 34 the solvation time of an electron is 2 x 10-12 s in water and —10 11 s in methanol. 

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