Surface diffusion rates, measurement theory

Polymer Adsorption. A review of the theory and measurement of polymer adsorption points out succinctly the distinquishing features of the behavior of macromolecules at solid - liquid interfaces (118). Polymer adsoiption and desorption kinetics are more complex than those of small molecules, mainly because of the lower diffusion rates of polymer chains in solution and the "rearrangement" of adsorbed chains on a solid surface, characterized by slowly formed, multi-point attachments. The latter point is one which is of special interest in protein adsoiption from aqueous solutions. In the case of proteins, initial adsoiption kinetics may be quite rapid. However, the slow rearrangement step may be much more important in terms of the function of the adsorbed layer in natural processes, such as thrombogenesis or biocorrosion / biofouling caused by cell adhesion. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

Finally, a number of experimental studies have been conducted in a pressure range where the polymeric solution could boil. The vapor bubbles thus created would provide a much larger surface area for mass transfer than the surface area of the wiped film alone. And therefore, for fixed values of the diffusivity and the driving force, predicted values for mass transfer rates would be substantially lower than the measured values. Conversely, for a fixed mass transfer rate and driving force, use of the wiped film surface area alone would require unusually high values of the diffusivity in order to obtain agreement between theory and experiment. 

One other measurement technique that has been used to measure Kl over a shorter time period, and is thus more responsive to changes in wind velocity, is the controlled flux technique (Haupecker et al., 1995). This technique uses radiated energy that is turned into heat within a few microns under the water surface as a proxy tracer. The rate at which this heat diffuses into the water column is related to the liquid film coefficient for heat, and, through the Prandtl-Schmidt number analogy, for mass as well. One problem is that a theory for heat/mass transfer is required, and Danckwert s surface renewal theory may not apply to the low Prandtl numbers of heat transfer (Atmane et al., 2004). The controlled flux technique is close to being viable for short-period field measurements of the liquid film coefficient. 

The only unsatisfactory aspect of this work is that it does not enable estimates of the reaction radius, R, or the mutual diffusion coefficient, D, to be made from experimentally measured rate coefficients. Nevertheless, the agreement between experiment and theory is very encouraging. Korth et al. have studied the recombination of cyano-substituted alkyl radicals and found a similar close relation between the measured rate coefficient, ft, and T/r) [45b], They presented evidence to suggest that the radicals recombine on an attractive potential energy surface. 

Between the highest and the lowest temperatures at which measurement is practicable the variation of reaction rate is many thousandfold. If the diffusion theory is applicable at all, the layer through which the reacting molecules have to pass cannot very well be less than a single molecule in thickness, even at the highest temperature, for a very simple calculation shows that the rate at which molecules of the reactant could come into contact with the bare surface is many times greater in most instances than the fastest measurable rate of reaction. At the lowest temperatures, then, the diffusion layer would have to be many thousands of molecules in thickness. This is easily shown to be a quite inadmissible supposition. No such difficulty is encountered when the variation in the observed reaction rate is attributed to the specific effect of temperature on the actual chemical transformation at the surface of the catalyst, to the uncovered portions of Cf. Langmuir, loc. cit., supra. 

In a previous paper (7), we have illustrated that diffusion in FCC takes place in the non-steady regime and that this explains the failure of several attempts to relate laboratory measurements on FCC catalysts to theories on steady state diffusion. Apart from the diffusion aspects, Nace (13) has also indicated the limited accessibility of the zeolite portal surface area by comparing the cracking rates of various model compounds with an increasing number of naphthenic rings on zeolite and amorphous FCC catalysts, figure 2. 

Ammonia is absorbed in a falling film of water in an absorption apparatus and the film is disrupted and mixed at regular intervals as it flows down the column. The mass transfer rate is calculated from the penetration theory on the assumption that all the relevant conditions apply. It is found from measurements that the mass transfer rate immediately before mixing is only 16 per cent of that calculated from the theory and the difference has been attributed to the existence of a surface film which remains intact and unaffected by the mixing process. If the liquid mixing process takes place every second, what thickness of surface film would account for the discrepancy Diffusivity of ammonia in water = 1.76 x 10 9 m2/s. 

The SECM can be used to measure the ET kinetics either at the tip or at the substrate electrode. In the former case, the tip is positioned in a close proximity of a conductive substrate (d < a). The substrate potential is kept at a constant and sufficiently positive (or negative) value to ensure the diffusion-controlled regeneration of the mediator at its surface. The tip potential is swept linearly to obtain a steady-state voltammogram. The kinetic parameters (k°, a) and the formal potential value can be obtained by fitting such a voltammogram to the theory [Eq. (22)]. A high value of the mass transfer coefficient (m) is achieved under steady-state conditions when d rate constants (k° > 1 cm-1 s) were measured with micrometersized SECM tips [92-94]. 

The rate o oxidation o ammonia at atmospheric pressure on single wires and ribbons has been determined as a function of a gas flow rate and catalyst size. In agreement with boundary layer diffusion theory the function rx, where r is the average rate of reaction/unit area, and x is the length of the surface measured in the direction of gas flow, is directly proportional to gas velocity. 

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