Effectiveness single-file systems

Combining eqs. 2, 5, 7, and 9, for sufficiently large Thiele moduli (i.e. in the transport-limited case), the effectiveness factor of single-file systems is found to obey the relation... 

With this more general equation, representation of the effectiveness factor in terms of the Thiele modulus also becomes possible for single-file diffusion. As an example. Fig. 16 shows the result of a computer simulation of diffusion and reaction within a single-file system consisting of A = 100 sites for different occupation numbers in comparison with the dependence... 

As in the case of tracer exchange, quantitative information about the correlated effect of transport and catalytic reactions in single-file systems has... 

SO far only been attained by Monte Carlo simulations. Figure 5 illustrates the situation due to the combined effect of diffusion and catalytic reaction in a single-file system for the case of a monomolecular reaction A B [1]. For the sake of simplicity it is assumed that the molecular species A and B are completely equivalent in their microdynamic properties. Moreover, it is assumed that in the gas phase A is in abimdance and that, therefore, only molecules of type A are captured by the marginal sites of the file. Figure 5 shows the concentration profile of the reaction product B within the singlefile system imder stationary conditions. A parameter of the representation is the probabiUty k that during the mean time between two jump attempts (t), a molecule of type A is converted to B. It is related to the intrinsic reactivity k by the equation... 

Before the introduction of measuring techniques such as pulsed field gradient (PEG) NMR ([14,16,45], pp. 168-206) and quasielastic neutron scattering (QENS) [49,50], which are able to trace the diffusion path of the individual molecules, molecular diffusion in adsorbate-adsorbent systems has mainly been studied by adsorption/desorption techniques [ 16]. In the case of singlefile systems, adsorption/desorption techniques cannot be expected to provide new features in comparison to the case of normal diffusion [51,52]. In adsorption/desorption measurements it is irrelevant whether or not two adjacent molecules have exchanged their positions. But it is this effect which makes the difference between normal and single-file diffusion. 

In complete agreement with the fact that the product molecules in a singlefile system are prevented from leaving the system by their file neighbors, the concentration profiles in the single-file cases show a much more pronounced tendency of accumulation of the reaction products in the file center than in the case of normal diffusion. Under stationary conditions, the effective reactivity k is related to the intrinsic reactivity k by the equation... 

Fig. 13.21. Self-organization of the tobacco virus. The virus consists of an RNA helix (shown as a single file ) contaming about 7000 nucleotides, which is sufficient genetic material to code the production of 5 — 10 proteins (first level of supramolecular self-organization). The RNA strand interacts very effectively with a certain protein (shown as a drop, which is the second level). The protein molecules associate with the RNA strand forming a kind of necklace, and then the system folds (third level) into a rodUke shape typical for this virus. The rods are able to form a crystal (level four, not shown here), which melts after heating but is restored when cooled down.

If molecules can pass one another in the pore, then an increased pore occupation may increase the diffusion rates since molecule-molecule interactions may be weaker than moleculi zeolite channel interactions. When molecules cannot pass one another, the phenomenon known as single file diffusion may arise. In single file diffusion, which tends to occur in one dimensional porous systems, the large reduction in diffusion rate is represented by an effective diffusion constant proportional to the center of mass of the file of molecules occluded in the zeolite channel. 

The photochemistry of conjugated polyenes has played a central role in the development of modern molecular photochemistry, due in no small part to its ultimate relevance to the electronic excited state properties of vitamins A and D and the visual pigments, as well as to pericyclic reaction theory. The field is enormous, tremendously diverse, and still very active from both experimental and theoretical perspectives. It is also remarkably complex, primarily because file absorption spectra and excited state behavior of polyene systems are strongly dependent on conformation about the formal single bonds in the polyene chain, which has the main effect of turning on or off various pericyclic reactions whose efficiencies are most strongly affected by conformational factors. 

Since we are interested in cellular activities where several motors could be involved, a simplified mean-filed model emerge with the assumption that motors a) work independent of each other b) share the applied load equally. These equations are able to predict the transport properties of cargo particles such as their effective velocity and average run length. Two most important quantities that need to be mentioned here are the force-velocity relation and detachment rate of motor when a load is applied to the cargo. Several experiments have shown that velocity Vn(F) of a single motor in system of n bound motors decreases almost linearly with the force F applied against the motor movement. 

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