Difference between revisions of "Intermolecular and interparticle forces"

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(Interactions from molecular attraction)
(Flow properties from molecular energies)
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| [[Image:Vicosity_at_short_times.png |100px|]]  
 
| [[Image:Vicosity_at_short_times.png |100px|]]  
| For short time scales and simple liquids.  
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| For short time scales and simple liquids, the viscosity &eta; can be approximated by the product of the instantaneous modulus G<sub>0</sub> and the relaxation time &tau;.  
 
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| [[Image:Erying_model_of_flow.png |300px|]]
 
| [[Image:Erying_model_of_flow.png |300px|]]
| Erying model: When the strain is generated molecules are "trapped" and "jump" to a relaxed state. [[Image:Relaxation_time_in_Eyring_model.png |150px| ]]
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| Erying model: When the strain is generated molecules are "trapped" inside an energy barrier of size &epsilon; and "jump" to a relaxed state with the characteristic time &tau;. While inside the barrier, the molecule vibrates with the characteristic frequency &nu; of the solid. [[Image:Relaxation_time_in_Eyring_model.png |150px| ]]
 
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| [[Image:Viscosity_with_Erying_model.png |200px| ]]
 
| [[Image:Viscosity_with_Erying_model.png |200px| ]]
| &nu; is the characteristic frequency in the solid and &epsilon; is the heat of vaporization of the liquid.
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| Combining these equations yields the Arrhenius behavior. In this case, &epsilon; is the heat of vaporization of the liquid, which is the upper bound of the energy barrier. This behavior can be seen experimentally by plotting the logarithm of viscosity as a function of the reciprocal of the temperature.
 
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Revision as of 18:02, 24 September 2008

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Intermolecular energies

3D Pressure-volume isotherms 2D Spreading pressure-area isotherms
Hirschfelder Fig 4-1-1.gif Gaines Fig 4-7.gif
Hisrshfelder, Fig. 4.1.1 Gaines, Fig. 4.7






Flow properties from molecular energies

Vicosity at short times.png For short time scales and simple liquids, the viscosity η can be approximated by the product of the instantaneous modulus G0 and the relaxation time τ.
Erying model of flow.png Erying model: When the strain is generated molecules are "trapped" inside an energy barrier of size ε and "jump" to a relaxed state with the characteristic time τ. While inside the barrier, the molecule vibrates with the characteristic frequency ν of the solid. Relaxation time in Eyring model.png
Viscosity with Erying model.png Combining these equations yields the Arrhenius behavior. In this case, ε is the heat of vaporization of the liquid, which is the upper bound of the energy barrier. This behavior can be seen experimentally by plotting the logarithm of viscosity as a function of the reciprocal of the temperature.






Forces near surfaces

  • Bulk phases are characterized by density, free energy and entropy – not by forces.
  • Molecular forces average out.
  • Not so at surfaces.

Galileo Surface Forces.png Galileo reference.png







(Modern) forces near sufaces

  • (a) This potential is typical of vacuum interactions but is also common in liquids. Both molecules and particles attract each other.
  • (b) Molecules attract each other; particles effectively repel each other.
  • (c) Weak minimum. Molecules repel, particles attract.
  • (d) Molecules attract strongly, particles attract weakly.
  • (e) Molecules attract weakly, particles attract strongly.
  • (f) Molecules repel, particles repel.

Israelachvili Fig 10-1.gif
Israelachivili Fig.10.1






Interactions from molecular attraction

Eqn molecular attraction.png
Israelachvili Fig 10-2.gif
Israelachivili Fig.10.2

  • (a) A molecule near a flat surface.
  • (b) A sphere near a flat surface.
  • (c) Two flat surfaces.


Eqn Molecule surface attraction.png
Eqn Sphere Surface Attraction.png
Eqn Surface Surface Attraction.png






Derjaguin Force Approximation

Israelachvili Fig 10-3.gif
Israelachivili Fig.10.3
Eqn Derjaguin Force Equation.png
Eqn Derjaguin Force Equation-II.png

Where W(D)is the energy of interaction of two flat plates.







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