Author s personal copy, Trends Trends in Analytical Chemistry Vol 28 No 8 2009. the course of the reaction Moreover in an ideal IMReSQ Moreover pre mixing of even a sub set of reactants. method the reaction would proceed only during the outside the capillary can lead to their degradation The. reaction step and not during the injection mix injection processes used to facilitate in capillary mixing. ing separation or quantitation steps While both namely pressure or electrokinetic injection are familiar. KCE and IMReSQ aim to study reactions in capillaries to all practitioners of CE so that there is no complexity. using an electric field the two approaches are concep added to that of operating conventional instrumenta. tually different and are not typically hybridized with the tion. exception of using the Inject Mix and React IMR part To be generic injection in IMReSQ should depend as. of IMReSQ in KCE methods that require pre equilibration little as possible on the nature of molecules so that the. before the analysis The IMR KCE combination would be process of optimizing the injection is minimized In. useful for saving reactants and for automation 1 addition to be generic an injection method has to. KCE methods were reviewed recently 2 and are not a facilitate separate injection of multiple reactants. focus of this article By contrast IMReSQ as a general To facilitate quantitative analyses injection has to be. approach has not been reviewed and is the sole subject of carried out in a perfectly controlled way so that the. this article concentration profiles of reactants along the capillary. When practical IMReSQ methods are developed it is length can be calculated The only two practical ways of. critical that correct performance criteria are taken into injection into the capillary are by electroosmosis or. consideration There are three essential performance pressure Fig 1 which we consider separately. criteria for the methods they must be generic quanti. tative and practical 2 1 Electroosmosis, To be generic IMReSQ methods have to be applicable An electroosmotic flow EOF occurs in fused silica cap. to different chemical reactions and require minimal illaries due to the deprotonation of silanol groups of sil. optimization of the five steps injection mixing reaction ica which in essence creates an immobile negative. separation and quantitation charge on the inner capillary wall and a mobile positive. To be quantitative IMReSQ methods have to produce charge in the buffer next to the wall If a voltage is ap. an output result that can be used to find quantitative plied to the ends of the capillary these positive ions move. parameters e g reaction rate constants and stoichi along the electric field dragging the buffer solution in. ometry coefficients That can only be done if all steps are the same direction thus creating EOF 4. performed in a perfectly controlled way and if a mathe EOF depends strongly on the chemistry of the inner. matical approach is available to calculate concentrations capillary wall the strength of the electric field as well as. of all reactants and products as functions of spatial the pH composition and ionic strength of the buffer The. coordinates and time volume of the injected reactant plug can be easily ad. To be practical IMReSQ methods should be imple justed by changing the strength of the electric field and. mentable with commercially available instrumentation the time of its application Fig 1A While being quite a. It is important to emphasize that due to the sequential common way of injecting reactant into capillaries EOF is. nature of processes in IMReSQ the steps earlier in the not a generic means of injection For example EOF does. sequence may influence the later steps in terms of the not occur if the inner capillary walls are coated with a. options available for technical implementation of the layer of non ionizable material such coatings are often. later steps For the same reason IMReSQ can be generic used to suppress solute adsorption to the inner capillary. and quantitative only if every step in the sequence is walls 5 The unique nature of EOF is the flat shape of its. generic and quantitative Our analysis below confirms front which does not depend on the velocity of EOF. that IMReSQ is both generic and quantitative by con Fig 1A The velocity of EOF can be measured experi. sidering these two performance criteria in individual mentally allowing the concentration profile of the in. steps of IMReSQ To address the issue of practicality we jected reactant to be well defined The length of the. also discuss the instrumentation required and available injected plug l is given by Equation 1. for IMReSQ Z tinj, l v t dt 1, 2 Injection, where v t is the velocity of EOF as function of time and. In capillary mixing has several advantages over mixing tinj is time of injection. of reactants in a container outside the capillary Most To be quantitative the injection must be free of tur. importantly in capillary mixing avoids wastage of bulence as turbulence creates vortexes i e stochastic. expensive reagents Only nL of solutions are required for hydrodynamic structures that cannot be predicted. in capillary mixing while lL are needed to mix reactants accurately Turbulence does not appear when the. outside the capillary using conventional pipetters 3 velocity of injection is low The theory of turbulence in. 988 http www elsevier com locate trac, Author s personal copy. Trends in Analytical Chemistry Vol 28 No 8 2009 Trends. E2 E1 t2 t1t, P2 P1 t2 t1, Figure 1 Representation of reactant injection into a capillary by electroosmotic flow A artistic depiction and differential pressure B computer. simulation The size of the injection plug in A is determined by the product of the electrical field strength E and the time for which it is applied. t The font size used for and reflects the strength of E In B the size of the injection plug is determined by the pressure difference between the. capillary inlet and the outlet DP and the time for which the pressure is applied The computer simulation of panel B took into account two. processes pressure driven flow and reactant diffusion in the transverse direction The quantitative parameters in the simulation were chosen. to illustrate that the front shape can range from rectangular to parabolic. EOF has not yet been developed We should appreciate hydrodynamic transfer and diffusion both longitudinal. that the standard criterion of instability for pressure and transverse Both processes are non stochastic. driven laminar flows which requires that the Reynolds allowing the exact concentration profile of the injected. number Re be greater than 2000 is not applicable to plug to be calculated. EOF Equation 2 called Poiseuille s Equation shows that. To conclude EOF as a means of injection is quanti the velocity v of a pressure driven flow inside the cap. tative for low velocities of injection a condition that is illary depends on the differential pressure Dp the fluid. easy to satisfy for narrow bore capillaries The mathe viscosity g the capillary length L the capillary inner. matics describing EOF is very simple However EOF is radius ri the distance from the center of the capillary. not a generic means of injection so its application in r and the time t. IMReSQ is limited r2i r2 Dp t, 2 2 Pressure, A reactant plug can be injected into a capillary by a At the center of the capillary r 0 Equation 3. pulse of differential pressure applied to the two ends of shows that the velocity v0 t is a maximum. the capillary Technically there are two options either r2i Dp t. pressure is applied to the injection end while the distal v0 t 3. end remains open to the atmosphere or suction is applied. to the opposite end while the injection end remains open but the velocity is zero at the inner walls of the capillary. to the atmosphere The first approach allows creation of r ri. very high differential pressures while the second ap If transverse diffusion is negligible the profile of the. proach is limited to a differential pressure of 1 atm flow is parabolic Fig 2 and the length of the injection. To be quantitative pressure driven injection has to be l r can be calculated using Equation 4. non turbulent This requirement is similar to that for Z tinj Z tinj 2. ri r2 Dp t, EOF driven injection If the velocity of injection is low l r v r t dt dt 4. enough Re 2000 which is readily achieved for, narrow bore capillaries pressure driven flow is laminar Diffusion can be neglected if the differential pressure. and controlled by two processes of mass transfer is high enough to inject the required volume of the. http www elsevier com locate trac 989, Author s personal copy. Trends Trends in Analytical Chemistry Vol 28 No 8 2009. Figure 2 Major parameters used in the theoretical consideration of pressure driven injection r is the radial distance from the center of the cap. illary ri is its internal radius v r describes the velocity profile of the injection plug v0 is the velocity along the central axis l is the length of the. injection plug and x is the distance from the inlet of the capillary in the longitudinal direction. solution during a time interval that is considerably cosity and temperature A simple approximation for D is. shorter than the characteristic time for transverse dif given by the Stokes Einstein Equation Equation 7 7. fusion to occur r, kB T kB T 3 dN A, By contrast if transverse diffusion is very fast the D 7. shape of the parabolic front is completely destroyed 6pgrh g 162p2 M. leaving it flat similar to that in Fig 1A In this case where kB 1 381 10 23 J K is Boltzmann s constant. Equation 4 simplifies to Equation 5 T is the absolute temperature and rh is the hydrodynamic. Z tinj Z tinj 2 radius of the molecule assumed to be spherical d is the. l v0 t dt dt 5 density of the reactant in kg m NA 6 022 10 23. mol is Avagadro s constant and M is the molar mass of. If diffusion cannot be assumed too slow or too fast the the reactant in kDa Most approaches to calculating. calculation of the exact concentration profile should take diffusion coefficients give only approximate values There. both the pressure driven hydrodynamic flow and diffu are also relatively simple ways to determine diffusion. sion into consideration The mass transfer by both the coefficient experimentally including a capillary based. hydrodynamic flow and diffusion is mathematically de procedure that can be realized with a commercial CE. scribed by the equations below Equation 6 instrument 8. 2 Equation 6 can be simplified to make it easier to. v r t D r analyze and to use To do so we introduce a charac. t x x2 r r r, 2 teristic length of the injected plug lchar which is related. r to the injection time tinj as lchar tinjvmax where vmax is. v r t v0 t 1 6, ri the maximum value of v0 t during the time interval of. injection If Dp constant during injection and Dp 0. D 0 before and after injection then v0 constant and. r r ri vmax v0 If we assume that lchar is much greater than. where C is the concentration of the solute D is its dif the diameter of the capillary lchar ri 1 the time re. fusion coefficient r ri v t v0 t and t are defined as quired for transverse diffusion tr will be much shorter. above in this section and x is the distance from the than the time required for longitudinal diffusion tx as. capillary inlet in the longitudinal direction While shown in Equation 8. the analytical solution of Equation 6 is challenging the tr r2i D tx l2char D. numerical solution can be found easily 6 A numerical 8. simulation of injection involving the two processes tx tr l2char r2i 1. pressure driven translational movement and diffusion The assumption leading to Equation 8 suggests that. was used to prepare Fig 1B longitudinal diffusion can be ignored This assumption is. To take diffusion of a reactant into consideration its equivalent to the assumption that 2 C x2 in the top. diffusion coefficient should be known There are a equation of Equation 6 is negligible Accordingly the. number of simple approaches to calculating a diffusion differential equation in Equation 6 can be simplified to. coefficient with the only input parameters being the size obtain the system of equations Equation 9 introduced. or the molecular weight of the reactant solvent vis by Taylor in 1953 9. 990 http www elsevier com locate trac, Author s personal copy. Trends in Analytical Chemistry Vol 28 No 8 2009 Trends. Table 1 York numbers for different diffusion coefficients D of the injected solute and different capillary radii ri but for an identical injection. time of 4 s, D cm2 s ri lm, 10 25 37 5, 10 4 10 64 28. 10 5 40 6 4 2 8, 10 6 4 0 64 0 28, 10 7 0 4 6 4 10 2 2 8 10 2. 10 8 4 10 2 6 4 10 3 2 8 10 3, 10 9 4 10 3 6 4 10 4 2 8 10 4. C C 1 C dependencies of the pressure or identical x t and iii. t x r r r similar Yo values the injection will be similar and will. r generate similar final distribution of the injected reactant. v r t v0 t 1 9 along the capillary axis, It is instructive to compare Yo values that correspond. C to a typical range of diffusion coefficients of the reactant. r r r0 and capillary radii Table 1, Yo is a dimensionless value that characterizes the. For simpler analysis Equation 9 can be transformed extent of transverse diffusion during plug injection Yo. into a dimensionless form if the following dimensionless can serve as a parameter to compare the shapes of. variables and parameters Equation 10 are introduced pressure injected plugs quickly and qualitatively for dif. the realm of kinetic capillary electropho resis KCE which is CE of species that interact during electrophoresis A requirement for KCE is that at least some of the reacting species move with different velocities in the electric eld An electric eld in KCE serves two functions First it mixes or separates interacting species thus facilitating for ward and backward processes of the

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