Diffusion-collision

When the entering ligand, L, is uncharged, the stability of the outer-sphere complex M OH2 L2+ may be so low that its concentration does not differ significantly from that arising from diffusive collisions between M OH2m+ and L. Under these conditions, entry of L into the... 

Transport processes - diffusion, collisions and shock fronts transiting the cloud. Magnetic turbulence must be considered for mixing molecules. 

Maximum intrapellet temperatures, 25 305 effect of diffusion collision integral on, 25 301-303... 

Bashford D Weaver D. L. and Karplus M. Diffusion-collision model for the folding kinetics of the lambda-repressor operatorbinding domain. J. Biomol. Str. Dyn. (1984) 1 1243-1255. 

Karplus M. and Weaver D. L. Protein-folding dynamics - the diffusion-collision model and experimental-data. Prot. Sri. (1994) 3(4) 650-668. 

Short-Lived Species in Fluid Solution. - In fluid solution, radical cations derived from saturated hydrocarbons are highly reactive oxidizing species and the rates of their bimolecular reactions are often determined by the frequency of diffusion collisions in solutions. It is known that the reactions of primary radical... 

A more quantitative measure of stability, known as the stability ratio, can be obtained by setting up and solving the equation for diffusive collisions between the particles. Quantitative formulations of stability, known as the Smoluchowski and Fuchs theories of colloid stability, are the centerpieces of classical colloid science. These and related issues are covered in Section 13.4. 

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. 

The collision integral for diffusion depends upon the choice of the intermolecular force law between colliding molecules and is a function of temperature. The characteristic length also depends upon the intermolecular force law selected. In comparison with the simple Eq. (6-2) for perfect gases, Eq. (6-3) takes into account the interactive forces between real molecules. But, while in the first case only two specific parameters are needed, the diffusion collision integral, Q0, is a complicated function of several parameters. 

The other explanation is the diffusion-collision model in which the secondary structure forms very fast [5,17]. These secondary structure elements then diffuse in a random walk fashion until they collide in the proper way and form the tertiary structure. Islam et al. used this model to analyze the folding of a three helix bundle proteins [17]. 

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. 

S. Islam, M. Karpins, D. Weaver (2002) Application of the diffusion-collision model to the folding of three-helix bundle proteins. J. Mol. Biol. 318, pp. 199-215... 

For Knudsen diffusion collisions between particles are negligible and molecules of different species move entirely independent of each other under the action of their own concentration (or partial pressure) gradient. There is no fundamental difference between flow and diffusion. The resulting expression for the total flux of a mixture with component fluxes and is... 

The parameter the diffusion collision integral, is a function of k T/e, where is the Boltzmann constant and e is a molecular energy parameter. Values of tabulated as a function of k T/e, have been published (Hirschfelder et al., 1964 Bird et al., 1960). Neufeld et al., (1972) correlated using a simple eight parameter equation that is suitable for computer calculations (see, also, Danner and Daubert, 1983 Reid et al., 1987). Values of a and e/k (which has units of kelvin) can be found in the literature—for only a few species—or estimated from critical properties (Reid et al., 1987 Danner and Daubert, 1983). The mixture a is calculated as the arithmetic average of the pure component values. The mixture e is taken to be the geometric average of the pure component values. 

The diffusion-collision model considers the protein molecule to be divided... 

Figure 39. Probabilities of significantly populated intermediate states for the folding of the X-repressor in the diffusion collision model as a function of time for 0 = 0.01. The states are labeled as described in the text.

---