Joule Heating
The conduction of electric current through an electrolytic solution generates heat via frictional collisions between migrating ions and buffer molecules. Since high field strengths are employed in HPCE, ohmic or Joule heating can be substantial. There are two problems that can result from Joule heating:
1. Temperature changes due to ineffective heat dissipation
2. Development of thermal gradients across the capillary
If heat is not dissipated at a rate equal to its production, the temperature inside the capillary will rise and eventually the buffer solution will outgas. Even a small bubble inside of the capillary disrupts the electrical circuit. At moderate field strengths, outgassing is not usually a problem, even for capillaries that are passively cooled.
The rate of heat production inside the capillary can be estimated by
where L = capillary length and A = the cross-sectional area. Rearranging this equation using I = V/R, where the resistance R = L/kA and k = the conductivity, dH _ kV2 dT ~ L2
The amount of heat that must be removed is proportional to the conductivity of the buffer, as well as the square of the field strength.
Lacking catastrophic failure (bubble formation), the problem of thermal gradients across the capillary can result in substantial band broadening (29-31). This problem is illustrated in Figure 2.13. The second law of thermodynamics states heat flows from warmer to cooler bodies. In HPCE, the center of the capillary is hotter than the periphery. Since the viscosity of most fluids decreases with increasing temperature, Eq. (2.4) and (2.8) predict that both mobility and EOF increase as the temperature rises.
This situation becomes similar to laminar flow where the electrophoretic or electroosmotic velocity at the center of the capillary is greater than the velocity near the walls of the capillary. The temperature differential of the buffer between the middle and the wall of the capillary can be estimated from where W = power, r = capillary radius, and K = thermal conductivity of the buffer, capillary wall, and polyimide cladding. A 2-mm-i.d. capillary filled with 20 mM CAPS buffer draws 18 mA of current at 30 kV, giving a AT of 75°C. A 50-|im-i.d. capillary filled with the same buffer draws only 12 |aA of current, yielding a AT of 50 m°C. Since the thermal gradient is proportional to the square of the capillary radius, the use of narrow capillaries facilitates high resolution. On the other hand, the use of dilute buffers or isoelectric buffers (32) permits the use of wider bore capillaries, but the loading capacity of the separation is reduced.
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