Diffusion-collision mechanism

Depending on the protein, the free energy landscape differs as is illustrated in Fig. 6. For some two-state proteins, with an independently stable secondary structure, the diffusion-collision mechanism is preferred. Other proteins,for which the secondary structure is less stable on its own, fold cooperatively using the nucleation-condensation pathway. In all cases there is still two state behavior, because there is only one rate limiting barrier. 

According to the authors, the occurrence of incorrectly folded intermediates, as detected for BPTI (Creighton, 1974b,c), might be expected if the diffusion-collision mechanism plays an important role. Incorrectly folded species could occur from segments in a structure differing from the native one which collide and form relatively unstable intermediates because of the illicit interactions. 

Although it has not been demonstrated, it seems plausible that both models are operating. At each stage of the process, substructiu es may be formed by a diffusion-collision mechanism. At each level of organization and in in different parts of the molecule, a random search can conceivably lead to the formation of either right or wrong structures these last ones have to be corrected to achieve the right structure of the whole molecule. 

Welsh suggested correctly that similar transitions take place even if the molecular pair is not bound. The energy of relative motion of the pair is a continuum. Its width is of the order of the thermal energy, Efree 3kT/2. Radiative transitions between free states occur (marked free-free in the figure) which are quite diffuse, reflecting the short lifetime of the supermolecule. In dense gases, such diffuse collision-induced transitions are often found at the various rotovibrational transition frequencies, or at sums or differences of these, even if these are dipole forbidden in the individual molecules. The dipole that interacts with the radiation field arises primarily by polarization of the collisional partner in the quadrupole field of one molecule the free-free and bound-bound transitions originate from the same basic induction mechanism. 

For simulation, a 3-D random walk algorithm was developed to study diffusion-controlled mixing phenomena [160]. Several assumptions were made, i.e. only EOF carries out fluid transport, only neutral and point-like analytes are present and the transport in each dimension is fully independent. An elastic collision mechanism was applied for molecule-wall collisions. The analyte was introduced as a stream of 200 molecules ms-1. 

From the observation that the first explosion limit is lowered by inert gases such as N2 and He it is necessary to conclude that, at pressures lower than this limit, termination is predominantly at the surfaces and by a diffusion-controlled mechanism. From the further observation that this limit usually lies in the range 1 to 10 mm Hg for spherical flasks of 5 to 10 cm diameter it is further possible to show, by using our approximate analysis [Eq. (XIV.G.2)], that the efficiency of capture of the wall-terminating radicals is of order of 10 or larger (i.e., the probability of capture per collision 6 10 ). 

Two major entry models - the diffusion-controlled and propagation-controlled models - are widely used at present. However, Liotta et al. [28] claim that the collision entry is more probable. They developed a dynamic competitive growth model to understand the particle growth process and used it to simulate the growth of two monodisperse polystyrene populations (bidisperse system) at 50 °C. Validation of the model with on-line density and on-line particle diameter measurements demonstrated that radical entry into polymer particles is more likely to occur by a collision mechanism than by either a propagation or diffusion mechanism. 

A related matter concerns the physical mechanism by which radicals (primary or oligomeric) are acquired by the reaction loci. One possibility, first proposed by Garden (1968) and subsequently developed by Fitch and Tsai (1971), is that capture occurs by a collision mechanism. In this case, the rate of capture is proportional to, inter alia, the surface area of the particle. Thus, if the size of the reaction locus in a compartmentalized free-radical polymerization varies, then a should be proportional to r, where r is the radius of the locus. A second possibility (Fitch, I973) is that capture occurs by a diffusion mechanism. In this case, the rate of capture is approximatdy proportional to r rather than to r. A fairly extensive literature now exists concerning this matter (see, e.g., Ugelstad and Hansen, 1976, 1978. 1979a, b). The consensus of present opinion seems to favor the diffusion theory rather than the collision theory. The nature of the capture mechanism is not. however, relevant to the theory discussed in this chapter. It is merely necessary to note that both mechanisms predict that the rate of capture will depend on the size of the reaction locus constancy of a therefore implies that the size of the locus does not change much as a consequence of polymerization. 

The free aperture of the main 100 channels in Y-type zeolite is 0.74 nm [7] and is much larger than the diameter of CO2 and N2 molecules. If the concentrations of CO2 and N2 in the micropores of the Y-type zeolite membrane are equal to those in the outside gas phase, these molecules permeate through the membrane at a low CO2/N2 selectivity. However, this was not the case. Carbon dioxide molecules adsorbed on the outside of the membrane migrate into micropores by surface diffusion. Nitrogen molecules, which are not adsorptive, penetrate into micropores by translation-collision mechanism from the outside gas phase. 

To describe the combined bulk and Knudsen diffusion flrrxes the dusty gas model can be used [44] [64] [48] [49]. The dusty gas model basically represents an extension of the Maxwell-Stefan bulk diffusion model where a description of the Knudsen diffusion mechanisms is included. In order to include the Knudsen molecule - wall collision mechanism in the Maxwell-Stefan model originally derived considering bulk gas molecule-molecule collisions only, the wall (medium) molecules are treated as an additional pseudo component in the gas mixture. The pore wall medium is approximated as consisting of giant molecules, called dust, which are uniformly distributed in space and held stationary by an external clamping force. This implies that both the diffusive ffrrx and the concentration gradient with respect to the dust particles vanish. 

The coarsening of the phase-separated system can occur by two mechanisms. Particle diffusion, collision, and coalescence is one mechanism. Particle diffusion occurs in the quiescent melt by Brownian motion of the particles. Another mechanism is evaporation and condensation, called Ostwald ripening. Ostwald ripening occurs by molecular diffusion of the minor component, which primarily makes up the minor phase particles, through the matrix phase. This results in evaporation of particles smaller than a critical radius by diffusion of the minor component out of these and growth of particles larger than the critical radius by condensation of the diffusing molecules into these. 

An alternative mechanism for the longtime coarsening regime, which also follows a r dependence, is diffusion and coalescence. Coalescence occurs by the movement of the dispersed phase particles through the matrix by Brownian motion (diffusion), collision, and formation of fewer, larger particles (24,25). Coalescence follows the same law as stated in Equation 12.3. 

Here Tq is some reference temperature and Dpo is the pore diffusivity evaluated at that temperature. The parameter a is equal to 0.5 when Knudsen controls the pore diffusion and to 1.75 where molecular-molecular collision mechanism controls the transport. The volumetric average concentration of the adsorbed species in eq. (10.4-3 8a) is... 

The first coincides with the result obtained for the strong-collision mechanism and the second for the diffusion mechanism. Note that for the latter case the following relation between the mean transferred energy AE and the mean square of the transferred energy exists... 

Representation of the low-pressure rate constant in the form pkg, where kg is given in terms of the strong-collision mechanism and p by Eq. (17.15), provides in principle the possibility of obtaining the mean transferred energy by comparing the theoretical and experimental rate constants. It has been found that p is relatively frequently substantially lower than unity, i.e. (AE) is appreciably smaller than kT [487]. Strictly speaking, this means that the calculation of the rate constant at intermediate pressures is to be based on the diffusion equation, rather than on equation (17.4). However, the expected difference in the fall-off curves is small [487]. 

Clearly, the enhancement is observed as the pore diameter decreases. According to the Knudsen mechanism, the gas transport in a pore is governed by the colhsion between the gas molecule and the pore wall. For small CNT pores with atomically smooth pore wall, the gas-wall interaction is governed by the combination of specular and diffuse collisions. This explains the larger enhancemerrt of diffusivity over the Knudsen diffusivity for the smaller pores. 

Now encounters between molecules, or between a molecule and the wall are accompanied by momentuin transfer. Thus if the wall acts as a diffuse reflector, molecules colliding wlch it lose all their axial momentum on average, so such encounters directly change the axial momentum of each species. In an intermolecuLar collision there is a lateral transfer of momentum to a different location in the cross-section, but there is also a net change in total momentum for species r if the molecule encountered belongs to a different species. Furthermore, chough the total momentum of a particular species is conserved in collisions between pairs of molecules of this same species, the successive lateral transfers of momentum associated with a sequence of collisions may terminate in momentum transfer to the wall. Thus there are three mechanisms by which a given species may lose momentum in the axial direction ... 

The friction coefficient determines the strength of the viscous drag felt by atoms as they move through the medium its magnitude is related to the diffusion coefficient, D, through the relation Y= kgT/mD. Because the value of y is related to the rate of decay of velocity correlations in the medium, its numerical value determines the relative importance of the systematic dynamic and stochastic elements of the Langevin equation. At low values of the friction coefficient, the dynamical aspects dominate and Newtonian mechanics is recovered as y —> 0. At high values of y, the random collisions dominate and the motion is diffusion-like. 

As the density of a gas increases, free rotation of the molecules is gradually transformed into rotational diffusion of the molecular orientation. After unfreezing , rotational motion in molecular crystals also transforms into rotational diffusion. Although a phenomenological description of rotational diffusion with the Debye theory [1] is universal, the gas-like and solid-like mechanisms are different in essence. In a dense gas the change of molecular orientation results from a sequence of short free rotations interrupted by collisions [2], In contrast, reorientation in solids results from jumps between various directions defined by a crystal structure, and in these orientational sites libration occurs during intervals between jumps. We consider these mechanisms to be competing models of molecular rotation in liquids. The only way to discriminate between them is to compare the theory with experiment, which is mainly spectroscopic. 

Strictly speaking, the process of J-diffusion described by the above equation is not diffusion at all. The very first collision restores equilibrium in the whole J-space. In this sense, strong collisions represent the hopping mechanism of J-relaxation, which is the only alternative to the diffusion mechanism [20, 24, 25, 36]. Since the term J-diffusion is so pervasive, we do not like to reject it. However, it should be understood in a wider sense and used to denote J-migration . Then it remains valid for both weak and strong collisions. Still, it should be remembered that there is a considerable difference between these limits. For strong collision we obtain from Eq. (1.30)... 

For strong collisions (y = 0), is still equal to //to, but qj does not exist and the diffusion mechanism of rotational relaxation is replaced by a hopping mechanism. 

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