Difference between revisions of "Cohan Mechanism"

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The Cohan mechanism, also known as the Cohan theory of capillary condensation, describes the condensation of liquid in a cylindrical pore. The Cohan mechanism states that on adsorption, pores do not fill vertically, but instead fill radially. This it thought to explain the hysteretic behavior seen in the adsorption-desorption process for porous materials.  
 
The Cohan mechanism, also known as the Cohan theory of capillary condensation, describes the condensation of liquid in a cylindrical pore. The Cohan mechanism states that on adsorption, pores do not fill vertically, but instead fill radially. This it thought to explain the hysteretic behavior seen in the adsorption-desorption process for porous materials.  
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Typically for larger structures, the adsorption and desorption process is understood by the Kelvin equaiton:
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<math>p/p0 = exp (-2\sigma * v_m / rRT) </math>
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Figure 1 shows a typical adsorption-desorption isotherm is shown for a porous solid. A hysteresis is evident, indicating that some adsorbate is retained during desorption and released at p/p0 value less than that required to cause adsorption.
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When the first layer of liquid is condensed, the radius of the pores is decreased, thus causing further condenstion at a fixed p/p0. Rebalancing the surface area to volume ratios of the new sized pores gives a modified version of the Kelvin equation p_{adsorption}.
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[[Image:Porous.jpg|thumb|300px|Figure 1 - Isotherm for a porous solid of uniform pore radius.]]
  
  
 
For a given pore radius r, adsorption with radial capillary condensation occurs at  
 
For a given pore radius r, adsorption with radial capillary condensation occurs at  
  
<math>p_{adsorption} = p_0 exp (- \Sigma * v_m / rRT) </math>
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<math>p_{adsorption} = p_0 exp (-\sigma * v_m / rRT) </math>
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whilst for desportion,
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<math>p_{desorption} = p_0 exp (-2\sigma * v_m / rRT) </math>
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[[Image:Cohan_Mechanism.jpg|thumb|300px|Figure 2 - Radial filling of pores during adsorption (left) and desorption (right) as explained by the Cohan Mehanism]]
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==References==
  
<math>\Delta \mu_{desorption} = 2 \gamma / n R</math>
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[1] Cohan, L.H., J. Am. Chem. Soc. 66, 98 (1944)
[[Image:Cohan_Mechanism.jpg|thumb|300px| Radial filling of pores during adsorption (left) and desorption (right) as explained by the Cohan Mehanism]]
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[2] "Principles of adsorption and adsorption processes" D. M. Ruthven

Latest revision as of 21:31, 5 October 2009

The Cohan mechanism, also known as the Cohan theory of capillary condensation, describes the condensation of liquid in a cylindrical pore. The Cohan mechanism states that on adsorption, pores do not fill vertically, but instead fill radially. This it thought to explain the hysteretic behavior seen in the adsorption-desorption process for porous materials.

Typically for larger structures, the adsorption and desorption process is understood by the Kelvin equaiton:

<math>p/p0 = exp (-2\sigma * v_m / rRT) </math>


Figure 1 shows a typical adsorption-desorption isotherm is shown for a porous solid. A hysteresis is evident, indicating that some adsorbate is retained during desorption and released at p/p0 value less than that required to cause adsorption.

When the first layer of liquid is condensed, the radius of the pores is decreased, thus causing further condenstion at a fixed p/p0. Rebalancing the surface area to volume ratios of the new sized pores gives a modified version of the Kelvin equation p_{adsorption}.

Figure 1 - Isotherm for a porous solid of uniform pore radius.


For a given pore radius r, adsorption with radial capillary condensation occurs at

<math>p_{adsorption} = p_0 exp (-\sigma * v_m / rRT) </math>

whilst for desportion,

<math>p_{desorption} = p_0 exp (-2\sigma * v_m / rRT) </math>

Figure 2 - Radial filling of pores during adsorption (left) and desorption (right) as explained by the Cohan Mehanism

References

[1] Cohan, L.H., J. Am. Chem. Soc. 66, 98 (1944) [2] "Principles of adsorption and adsorption processes" D. M. Ruthven