The relaxation effect

In the absence of an electric field the ionic atmosphere is symmetric about the central ion with the charge distribution fading exponentially to zero with distance from the central ion. When the ion moves under the influence of an applied external field, it will normally still have an ionic atmosphere associated with it. However, at each stage of movement, a new ionic atmosphere must be built up around the moving ion, and it takes time for this to happen. The ionic atmosphere has to build up in front of the moving ion and to decay behind it. Because this process cannot occur instantaneously, the net result is that the ionic atmosphere 

There are two processes involved in the bmld up of this asymmetry  

The process giving rise to this asymmetry is called the relaxation effect, and the time taken for the ion to build up its new ionic atmosphere is called the relaxation time. As the ion moves, the build up and decay are occurring continuously. Since the process is a relaxation phenomenon, then the build up of the asymmetry in the ionic atmosphere under the influence of the external field and the decay of the asymmetry to the symmetrical ionic atmosphere once the external field is removed will be first order processes. The overall rate constant for a first order relaxation process can be shown to be given by feoveraii = buildup + decay, and the relaxation time is given by t = l/(fcbuiidup + decay)- This applies even if the rate constants for build up and decay are different. This has the consequence that the same relaxation time is applicable to both build up and decay. 

The effect of the asymmetry of the ionic atmosphere when a cation is moving forward in the direction of the applied field, or potential, is to pull the cation back . The velocity of the ion in the forward direction is, therefore, less than it would be if the ionic atmosphere were symmetrical. The same effect will occur when an anion is moving in a direction opposite to the applied field, i.e. the ionic atmosphere will pull the anion back . This results in the velocity of the anion also being less than it would be in the absence of the asymmetry. The ionic conductivity of the ions is therefore less than it would be if the ionic atmosphere were symmetrical. 

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L is Avagadro s constant and k is defined above. It can be seen that there are indeed two corrections to the conductivity at infinite dilution tire first corresponds to the relaxation effect, and is correct in (A2.4.72) only under the assumption of a zero ionic radius. For a finite ionic radius, a, the first tenn needs to be modified Falkenliagen [8] originally showed that simply dividing by a temr (1 -t kiTq) gives a first-order correction, and more complex corrections have been reviewed by Pitts etal [14], who show that, to a second order, the relaxation temr in (A2.4.72) should be divided by (1 + KOfiH I + KUn, . The electrophoretic effect should also... 

K, L, M,. ..), 5 is the energy shift caused by relaxation efiects and cp is the work fimction of tlie spectrometer. The 5 tenn accounts for the relaxation effect involved in the decay process, which leads to a final state consisting of a heavily excited, doubly ionized atom. 

Overbeek and Booth [284] have extended the Henry model to include the effects of double-layer distortion by the relaxation effect. Since the double-layer charge is opposite to the particle charge, the fluid in the layer tends to move in the direction opposite to the particle. This distorts the symmetry of the flow and concentration profiles around the particle. Diffusion and electrical conductance tend to restore this symmetry however, it takes time for this to occur. This is known as the relaxation effect. The relaxation effect is not significant for zeta-potentials of less than 25 mV i.e., the Overbeek and Booth equations reduce to the Henry equation for zeta-potentials less than 25 mV [284]. For an electrophoretic mobility of approximately 10 X 10 " cm A -sec, the corresponding zeta potential is 20 mV at 25°C. Mobilities of up to 20 X 10 " cmW-s, i.e., zeta-potentials of 40 mV, are not uncommon for proteins at temperatures of 20-30°C, and thus relaxation may be important for some proteins. 

Ideas concerning the ionic atmosphere can be used for a theoretical interpretation of these phenomena. There are at least two effects associated with the ionic atmosphere, the electrophoretic effect and the relaxation effect, both lowering the ionic mobilities. Formally, this can be written as... 

The relaxation effect arises because a certain time, is required for the formation or collapse of an ionic atmosphere around the central ion. When an ion moves in an electric held, its ionic atmosphere lags somewhat behind, as it were its center (Fig. 7.7, point B) is at a point where the central ion had been a little earlier. The conhgurahon of the ionic atmosphere around the central ion (point A) will no longer be spherical but elongated (ovoid). Because of this displacement of the charges, the ionic atmosphere has an electrostahc effect on the central ion which acts in a direction opposite to the ion s motion. A rigorous calculation of this effect was made in 1927 by Lars Onsager. His solution was... 

An analysis of Eq. (7.49) shows that the electrophoretic effect accounts for about 60 to 70% of the decrease in solution conductivity, and the relaxation effect for the remaining 40 to 30%. 

These rules are based on the theory of conductivity of strong electrolytes accounting for the electrophoretic effect only (the relaxation effect terms outbalance each other). 

Fig. 4.2. Effects of triphenylethylene SERMs on spontaneous and depolarization-induced contractions in visceral smooth muscle. Tamoxifen (a) and ethylbromide tamoxifen (EBTx, b) rapidly and reversibly inhibit spontaneous peristaltic activity in duodenal muscle. Both compounds also inhibit depolarization-induced tonic contraction of uterine muscle (c). The inhibition of L-type voltage-dependent calcium channels underlies the relaxing effects illustrated here. Drugs concentrations were 10 xM in all cases. %RA percent of activity related to maximal activity...

The relaxation effects of the cation are throughout rather small, of the order of 2-10 kcal mol-1. The reason for this is that most aromatic compounds retain their planarity on ionization, and thus structural reorganizations are small. Similar observa-... 

The SE term accounts for the relaxation effects involved in the decay process, which leads to a final state consisting of a heavily excited, doubly ionized atom. 

In this section, we shall first give a brief review of the phenomenological theory of these effects.5 -6 26 We shall then show how the methods we have discussed in the previous sections may be extended to derive a microscopic theory of the relaxation effect the microscopic theory of electrophoresis will be considered in the next section. 

In this section, we shall only discuss the relaxation term however, before performing the detailed calculations corresponding to the precise Brownian model we have in mind, we shall first consider simpler cases, which already give a qualitatively correct description of the relaxation effect. 

From what we have seen above, the plasma-dynamical model of Section V-C provides a rigorous formulation of the relaxation effect under the following conditions ... 

Fig. 19. Logical connection between the theories of the relaxation effect.

Finally, we wish to close this section by indicating briefly the connection between the present work and other theories of the relaxation effect this is illustrated in Fig. 19. 

Kim HJ, Woo DS, Lee G, Kim JJ. (1998). The relaxation effects of ginseng saponin in rabbit corporal smooth muscle is it a nitric oxide donor BrJ Urology. 82 744-48. 

A rare genetic variant is found in some patients who possess a form of butyrylcholinesterase, the metabolizing enzyme, for which succinylcholine has a very low affinity. The consequences are greatly prolonged duration of achon of the relaxant. Patients fail to resume spontaneous respiration, and often have to be artihcially ventilated, sometimes for days, before the relaxant effect disappears. 

When in motion, the diffnse electrical donble-layer aronnd the particle is no longer symmetrical and this canses a rednction in the speed of the particle compared with that of an imaginary charged particle with no donble-layer. This rednction in speed is cansed by both the electric dipole field set np which acts in opposition to the applied field (the relaxation effect) and an increased viscons drag dne to the motion of the ions in the donble-layer which drag liqnid with them (the electrophoretic retardation effect). The resnlting combination of electrostatic and hydrodynamic forces leads to rather complicated eqnations which, nntil recently, conld only be solved approximately. In 1978, White and O Brien developed a clever method of nnmerical solntion and obtained detailed cnrves over the fnll range of Ka valnes (0 °°)... 

Activation of endothelial cell muscarinic receptors by acetylcholine (Ach) releases endothelium-derived relaxing factor (nitric oxide), which causes relaxation of vascular smooth muscle precontracted with norepinephrine, 10-8M. Removal of the endothelium by rubbing eliminates the relaxant effect and reveals contraction caused by direct action of Ach on vascular smooth muscle. (NA, noradrenaline [norepinephrine]. Numbers indicate the log concentration applied at the time indicated.)... 

When the primary electron donation pathway in photosystem II is inhibited, chlorophyll and p-carotene are alternate electron donors and EPR signals for Chl+ and Car+ radicals are observed.102 At 130 GHz the signals from the two species are sufficiently resolved to permit relaxation time measurements to be performed individually. Samples were Mn-depleted to remove the relaxation effects of the Mn cluster. Echo-detected saturation-recovery experiments were performed with pump pulses up to 10 ms long to suppress contributions from cross relaxation and spin or spectral diffusion. The difference between relaxation curves in the absence of cyanide, where the Fe(II) is S = 0, and in the presence of cyanide, where the Fe(II) is S = 2, demonstrated that the relaxation enhancement is due to the Fe(II). The known distance of 37 A between Fe(ll) and Tyrz and the decrease of the relaxation enhancement in the order Tyrz > Car+ > Chl+ led to the proposal of 38 A and > 40A for the Fe(II)-Car+ and Fe(II)-Chl+ distances, respectively. Based on these distances, locations of the Car+ and Chl+ were proposed. 

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