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Colloid chemistry - Chapter 4: Thermodynamics of surface - Ngo Thanh An

•The presence of an interface influences generally all thermodynamic parameters of a system

•To consider the thermodynamic of a system with an interface, we divide that system into three parts: The two bulk phases with volumes Vα and Vβ and the interface

•In Gibbs convention the two phases are thought to be separated by an infinitesimal thin boundary layer, the Gibbs dividing plane (this is of course an idealization)

•Gibbs dividing plane also called an ideal interface

•In Gibbs model the interface is ideally thin (Vσ = 0) and the total volume is

  V = Vα + Vβ

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Nội dung text: Colloid chemistry - Chapter 4: Thermodynamics of surface - Ngo Thanh An

  1. 1. Surface excess • The presence of an interface influences generally all thermodynamic parameters of a system • To consider the thermodynamic of a system with an interface, we divide that system into three parts: The two bulk phases with volumes Vα and Vβ and the interface σ
  2. 1. Surface excess ∞ 푒 Γ = න 휌 − 휌 − න 휌 − 휌 = 0 푒 0 • In Gibbs convention the two phases α and β are separated by an ideal interface σ which is infinitely thin: Guggenheim explicitly treated an extended interphase with a volume
  3. 1. Surface excess    N1 = N1 − c1 V + (c1 − c1 )V (1)    N2 = N2 − c2 V + (c2 − c2 )V (2) c − c Multiply both sides of equation (1) by 2 2  c1 − c1 c − c c − c c − c N  2 2 = N 2 2 − c V 2 2 1  1  1  c1 − c1 c1 − c1 c1 − c1 c − c + c − c V  2 2 (3) ( 1 1 )  c1 − c1
  4. 1. Surface excess Finally, dividing through by the interfacial area A, gives: N  N  c − c 1 c − c  2 − 1 2 2 = N − c V − N − c V 2 2  ( 2 2 ) ( 1 1 )   A A c1 − c1 A c1 − c1  N  N  c − c 1 c − c  2 − 1 2 2 = N − c V − N − c V 2 2  ( 2 2 ) ( 1 1 )   A A c1 − c1 A c1 − c1   (1)   c2 − c1 2 = 2 − 1  c1 − c1  (1)   ci − ci i = i − 1  c1 − c1
  5. 2. Fundamentals of thermodynamic relations V = V +V  dV = dV + dV  dV = dV − dV  U = U +U  +U    Ni = Ni + Ni + Ni S = S + S  + S 
  6. 2. Fundamentals of thermodynamic relations dU = T (dS + dS  + dS  )− P dV − P  dV      +  i dNi +  i dNi +  i dNi + dA dU = TdS − P dV − (P  − P )dV      +  i dNi +  i dNi +  i dNi + dA
  7. 2. Fundamentals of thermodynamic relations   Ni = Ni + Ni + Ni (dNi = 0)   dNi = −dNi − dNi    dF = −(P − P )dV + dA + (i − i )dNi    + (i − i )dNi
  8. 2. Fundamentals of thermodynamic relations   dF = −(P − P )dV + dA +  idNi
  9. 2. Fundamentals of thermodynamic relations    dU = TdS +  idNi + dA    U = TS +  i Ni + A   F = A +  i Ni    dF = −S dT +  idNi + dA S   − = A  T A,N  T ,Ni i
  10. 2. Fundamentals of thermodynamic relations Application of Euler’s theorem On the interface, we have: 휎 휎 휎 푈 = 푆 + ෍ 휇푖 푛푖 + 훾 Integrate both sides of the above equation: 휎 휎 휎 න 푈 = න 푆 + ෍ 휇푖 න 푛푖 + 훾 න 휎 휎 휎 푈 = 푆 + ෍ 휇푖푛푖 + 훾
  11. 3. Gibbs adsorption isotherm 휎 If dT = 0, then: σ 푛푖 휇푖 = − 훾 푛휎 Or: 훾 = − σ 푖 휇 푖 푛휎 If 푖 = Γ , then: 푖 훾 = − ෍ Γ푖 휇푖
  12. 4. Application of Gibbs adsorption isotherm ൗ 휇 = 푅 × 표 = 푅 × 2 ൗ 표 푅 훾 = −Γ(1) × 2 Therefore, 훾 Γ(1) = − × 2 푅
  13. 5. Surfactant Traube’s rule: In homologous series each additional CH2 group increases the surface tension reduction effect three fold.
  14. 5. Surfactant