Transport rate constants

In Equation (4.31) the rate constant is either the reaction rate constant or the transport rate constant, depending on which rate controls the dissolution process. If the reaction rate controls the dissolution process, then k. t becomes the rate of the reaction while if the dissolution process is controlled by the diffusion rate, then k j becomes the diffusion coefficient (diffusivity) divided by the thickness of the diffusion layer. It is interesting to note that both dissolution processes result in the same form of expression. From this equation the dependence on the solubility can be seen. The closer the bulk concentration is to the saturation solubility the slower the dissolution rate will become. Therefore, if the compound has a low solubility in the dissolution medium, the rate of dissolution will be measurably slower than if the compound has a high solubility in the same medium. 

The membrane potential increased with increasing hydrocarbon chain length. Figure 7 shows the transport rate constants of various phosphonium ions as a function of the membrane potential. The selectivity coefficient of tpp+ has also been determined using a nitrobenzene—based membrane electrode45 a value of log KPot = 8.75 was reported, which is lower than that obtained with the arsenic analogue. 

The chemical kinetics approach provides us with more insight with respect to the range of validity. We see from Table 4 that Fick s law indeed results without approximations (l.h.s.). For the pure electrical conduction (r.h.s.) we have to linearize the exponentials (Eqs. 98 and 99), i.e., to assume Ifa I RT which is definitely a good approximation for transport in usual samples it fails at boundaries or for ultrathin samples. Hence the application of Eq. (103) has to presuppose sufficiently thick samples and not too high fields. Table 4 also reveals the connection between Dk, uk and the transport rate constant kk and hence their microscopic meaning ... 

When the tubes are very long, the molecules reside in the tubes for a substantial amount of time, leading to a time-dependent transport rate constant km It can be shown that the decay in concentration is given by Ck t) oc (Dkit) for short times, i.e. t << Ttransp. [20]. 

Figure 6-2. Left Correlations between photo-induced hole transport rate constants and structural distances in synthetic capped hair-pin double-strand oligonucleotides for charge separation (open symbols) and charge recombination (filled symbols). Right Free energy plots for charge separation (filled symbols) and recombination (open symbols) Circles and triangles represent different sensitizer molecular units. Reprinted from ref. 52 with permission.

Mass transport Rate constants Reaction kinetics Sensor Sirnface plasmon resonance... 

Dissociation Constant PK, Apparent Partition Coefficient4 Transport Rate Constant (min 1)... 

The nature of the dissolution medium can profoundly affect the shape of a dissolution profile. The relative rates of dissolution and the solubilities of the two polymorphs of 3-(3-hydroxy-3-methylbutylamino)-5-methyl-a5-triazino[5,6-Z)7indole were determined in USP artificial gastric fluid, water, and 50% ethanol solution [69]. In the artificial gastric fluid, both polymorphic forms exhibited essentially identical dissolution rates. This behavior has been contrasted in Fig. 6 with that observed in 50% aqueous ethanol, in which Form II has a significantly more rapid dissolution rate than Form I. If the dissolution rate of a solid phase is determined by its solubility, as predicted by the Noyes-Whitney equation, the ratio of dissolution rates would equal the ratio of solubilities. Because this type of behavior was not observed for this triazinoindole drug, the different effects of the dissolution medium on the transport rate constant can be suspected. 

Eqs. 95 and 96 could be derived for the dependence of the transport rate constants ki (from the aqueous phase into the organic phase) and the reverse rate constants kj (from the organic phase into the aqueous phase) on lipophilicity [444]. According to eq. 95, the rate constants ki are thermodynamically controlled, they linearly increase with lipophilicity. With further increase in lipophilicity the diffusion of the solutes becomes rate-limiting a plateau is reached because now thermodynamic control is replaced by kinetic control. The reverse holds true for the rate constants k2 (eq. 96) (Figure 16). 

In general, one will not be surprised to find a marked asymmetry in transport parameters. The transport rate constants can have any values subject only to the constraint that in the absence of an external source of energy there is no net movement of substrate when the concentration at each face of the membrane is the same. This implies that h,/2 = for the simple pore or that h,/2k = 2/1 2 for the simple carrier. It is the value of the transport resistance / ,2 and /(ji hat will determine whether or not the system will behave asymmetrically. This can be seen by taking the ratio of the derivable half-saturation concentration and maximum velocities as follows ... 

To define in precise terms the concept of rapidity of a redox couple for an E mechanism, one says that a redox couple is fast (respectively slow) if the standard rate constant of the redox reaction is very high (respectively very low) compared to the mass transport rate constant (denoted by mand expressed In m s ) ... 

In the simple examples considered here, the mass transport rate constant is the ratio of the diffusion coefficient of the species in question to the diffusion layer thickness of the latter ... 

Rigorously speaking, one should take into account all the mass transport rate constants of the various electroactive species. 

The concept of fast or slow couples is therefore independent of the potential applied, since it is intrinsic to the system. However it does depend on other experimental parameters through the mass transport rate constant. The latter parameter is in fact a function of the quantities specific to the mass transport of the species in question (diffusion coefficient or electrochemical mobility), but it also depends on other characteristics in the system which vary according to each type of experiment, as illustrated in the examples below. 

In process engineering this parameter is called the mass transfer constant. It Is denoted by some authors by (a notation which has the advantage of underlining the parallel shown with the reaction rate constants denoted by k). To be precise, this quantity is not based on the diffusion layer thickness as defined in this document, but rather the value calculated from the interfaclal slope of the concentration profile (see section 4.3.1.4). For example. In the case of an experiment involving forced convection, one should use the thickness of the Nernst layer In order to define the mass transport rate constant. 

If the diffusion coefficients of the two reactive species are very close, then their mass transport rate constants are also very close and the half-wave potential is equal to the standard potential of the redox couple % =E°... 

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