Exit rate

Xu Xj = amount of drug in compartment 1 and j, respectively ky, kjt = first-order transfer rate constants from compartment 1 to j and from compartment j to 1, respectively Fi0, kj0 = first-order exit rate constants from compartment 1 and j, respectively... 

The first-order transfer and exit rate constants can be replaced by nonlinear terms dependent on the amount or concentration of drug in a particular compartment. For instance, saturable metabolism of drug in compartment 1 (the central compartment) would result in the Michaelis-Menten equation... 

FI = continued product where any term is defined as equal to 1 when the index takes a forbidden value, i.e., i = 1 in the numerator or m = j in the denominator X = summation where any term is defined as equal to zero when the index j takes a forbidden value, i.e., j = 1 ky, kji = first-order intercompartmental transfer rate constants Eh Em = sum of exit rate constants from compartments i or m n = number of driving force compartments in the disposition model, i.e., compartments having exit rate constants... 

Disposition rate constants are functions of the intercompartmental transfer rate constants and exit rate constants and can be expressed as such by equating the denominators of Eqs. (5) and (6). Common input functions, in, are as follows. 

Fluorescence quenching studies in micellar systems provide quantitative information not only on the aggregation number but also on counterion binding and on the effect of additives on the micellization process. The solubilizing process (partition coefficients between the aqueous phase and the micellar pseudo-phase, entry and exit rates of solutes) can also be characterized by fluorescence quenching. 

The rate constant for the reentry is of the magnitude expected for a diffusion-controlled reaction as in Eq. (5.6). This means that the exit rate is determined by the partition coefficient of the solubilizate in its triplet state between the micelle and the aqueous solution. Table 5.2 shows the exit rate constants k for several systems. The water solubilities of the probes are also given to show the correlation between kt and the solubility in water. These studies give further support to the view that the micelle has a very dynamic structure, which makes it easy for the solubilizate to enter and leave the aggregate. 

Table 5.2. Exit rate constants ki for solubilizates in micellar systems. (From Ref.77 )...

The inhomogeneity of the micellar aggregate also affords assisted spin trapping and the exploitation of magnetic field effects on the charge separated ion pairs [48]. Optical modulation spectroscopy can be used, for example, to follow the decay of radicals formed in homogeneous solution and in SDS micelles. Enhancements of a factor of about 50 in the lifetimes and the steady state concentrations of the radical were observed in the micelle, and a kinetic analysis led to a value of 2 x 103 s 1 for the exit rate constant from the micelle [49]. 

If we estimate the time required for S-T mixing and recombination for a radical pair to be 100 ns( and the lifetime of the plvaloyl radical at 31°C to be v6 ps(i5., we can estimate the rate constant for the exit of t-butyl/plvaloyl radicals from HDTCl micelles to be on the order of 10 -10 sec . This Is nicely In line with exit rates of small phosphorescent probe molecules from similar micelle systems. 

Monteiro et al. [293] also studied the effect of xanthates (RAFT agents with low transfer constants) with styrene, in ab initio styrene polymerizations. Again rate retardation was observed throughout the polymerization. This is not surprising, since the low transfer constants of these RAFT agents mean that they are present during the whole polymerization, which results in an increased exit rate throughout the reaction. 

This was later confirmed by Smulders et al. [294], who experimentally determined the exit rate in similar systems using y-relaxation experiments. The exit rate was found to increase Hnearly with the RAFT concentration, although the decrease in rate could not be ascribed to the increase in exit rate alone. 

Fluorescence quantum-yield and lifetime measurements have established that oxygen penetrates micelles (Geiger and Turro, 1975). Entrance- and exit-rate constants have been determined for a cationic (CTAB) and an anionic (SLS) micelle system using I, S-dimethylnaphthalene as the fluorescing species (Hautala et al., 1973). Of general importance is that the solubility of oxygen is higher in the micelle than in the aqueous phase. 

When a positive exit rate of the concentrated suspension is obtained in the starting conditions, an important reduction in the filtrate flow rate will be expected, as shown in Fig. 3.17. 

The results of this study show that ultrasonic absorption techniques, when used in conjunction with other aggregate properties, provide important kinetic information about the partitioning process of alcohols tetween ionic micelles and the bulk phase. The effect of hydrocarbon chain length of the alcohol on the exit rates of monomer surfactant and alcohol components from the mixed micelles, aggregate size distribution, and the electrostatic stabilization of the head group region of the micelles will be considered. As well, previously unreported data for water- 1-butoxyethanol-DTAB will be used to extend conclusions based on previous work [2,3]. 

The data in Tables II and m show that the exit rate of the monomer surfactant decreases in a linear manner with increasing chain length of the n-alcohol in the mixed micelle. It is also evident from the rate constant data in these tables that the value of k for the DTAB-BE system does not readily fit into the above trend. In fact kj has a value near to that for the exit rate of a monomer surfactant from regular micelles of DTAB. At the same time the magnitude of the exit rate of BE from the mixed micelles is between the values for Bu and Pe. 

The data in Table III indicate that the magnitude of for BE is approximately in the range of values for Bu and Pe. This suggests that the butyl segment of BE is embedded in the mixed micelle. However, the magnitude of the exit rate constant for DTAB from mixed... 

If we exclude the results for BE and assume for the other alcohols that the forward rate constant kj is diffusion controlled and approximately constant, the decrease in the exit rate of the surfactant represents a measure of the Gibbs energy of stabilization per CH2 group of the alcohol. From AGs = RT din (kj")/dnc, AGs = -450 J mol l per CH2. A similar calculation using data derived from the Hall model gives an estimate of AGs = -220 J mol-1 per CH2. 

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