Zeta potential Henry equation

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. 

With these relations, zeta potentials can be calculated for many practical systems. Note that within each set of limiting conditions the electrophoretic mobility is independent of particle size and shape as long as the zeta potential is constant. For intermediate values of Ka another equation, the Henry equation (4.10) can be used other such equations are available in the literature as well [81,253,264],... 

Henry [3] derived the mobility equations for spheres of radius a and an infinitely long cylinder of radius a, which are applicable for low ( and any value of Ka. Henry s equation for the electrophoretic mobility p of a spherical colloidal particle of radius a with a zeta potential C is expressed as ... 

Henry Equation A relation expressing the proportionality between electrophoretic mobility and zeta potential for different values of the Debye length and size of the species. See also Electrophoresis, Hiickel Equation, Smoluchowski Equation. 

DLS instruments can be used to measure the size of particle aggregates in water, as described previously. DLS can also measure the movement of nanoparticles in an electric field to determine the zeta potential, which provides information about the surface charge on a particle. The zeta potential will affect the distribution of the nanoparticles in solution and influence surface reactive properties. The zeta potential can be calculated using the Henry equation ... 

Figure 4.10 Illustration of the Henry equation parameter (for zeta potential) with ica. (Adapted from Shaw [17].)...

Henry s equation (2.6) assumes that is low, in which case the double layer remains spherically symmetrical during electrophoresis. For high zeta potentials, the double layer is no longer spherically symmetrical. This effect is called the relaxation elfect. Henry s equation (2.6) does not take into account the relaxation effect, and thus this equation is correct to the first order of Ohshima et al. [19] derived an accurate analytic mobility expression correct to order 1/ka in a symmetrical electrolyte of valence z and bulk concentration (number density) n with the relative error less than 1% for 10 < Ka < 00, which is... 

Henry [25] was the first author who solved the problem for spheres of any radius (also for infinite cylinders), that is, of any Ka value, although for small zeta potentials. Restricting ourselves to the case of spheres, Henry s equation for nonconducting particles reads... 

The zeta potential (Q can be determined from the electrophoretic mobility by using the Henry equation in which the electrophoretic mobility is seen to be a function of the double layer thickness,/(k ) ... 

Eq. (4) and (5) can only be valid if the reciprocal of Debye length (Kr)" is very high >100 or very low 1. If the zeta potential is not so high, e.g., smaller than 50 mV, Henry s equation should be used ... 

Meastuements were performed at 20°C as a function of pH in the range of 3-10 by addition of 0.01 M HCl or 0.01 M NaOH using a Malvern Zetasizer Nano ZS. Microgel solutions with a concentration of 5 mg/mL were dialyzed in standard 1 mM KCl solution and measured in disposable polystyrene cuvettes. One hundred scans were made for each sample and the zeta potential was calculated using Henry s equation. Expert System software was used for data interpretation. 

A potential is simply the work done in bringing a point charge from infinity to the particle surface. Potentials are always relative to ground (i.e. at an infinite distance from the surface). The surface potential is very important and is approximated by the so-called zeta potential, which can be estimated by (micro)electrophoresis experiments, at least for some special cases (small and large particles via the so-called Hiickel and Smoluchowski equations). In the general case, the zeta potential is calculated from values of the electrophoretic mobility, using graphical solutions or the Henry equation, which requires a correction factor. 

As the value of kR is neither below 0.1 (sometimes less than 1 is sufficient) or above 100, we cannot use the Hiickel or Smoluchowski equations for estimating the smface or zeta potential. We have to use the Henry equation (see Equation 10.10) with a correction parameter/, which we can obtain from the available data (by interpolation) ... 

Eq. 6.3 with f(Kr) taking the value of either 3/2 for large partilces when Kr > 200, called the Smoluchowski equation, which was derived even earlier than Henry s function [20], or 1 for small particles when Kr <0.01, called the Hiickel equation, is still the most popular way to convert a mobility distribution to a zeta potential distribution. Electrophoretic mobility can also be presented by particle s surface charge density s [21]... 

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