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Lecture 21 Statistical Mechanics and Solutions

Lecture 21 Statistical Mechanics and Solutions. The model Ideal polymer solution Bragg-Williams approximation. Lattice binary solution. Distribute N A of atoms A and N B atoms B on N = N A + N B sites c - coordination number cN A = 2N AA + N AB cN B = 2N BB + N AB

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Lecture 21 Statistical Mechanics and Solutions

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  1. Lecture 21 Statistical Mechanics and Solutions • The model • Ideal polymer solution • Bragg-Williams approximation

  2. Lattice binary solution Distribute NA of atoms A and NB atoms B on N = NA + NB sites c - coordination number cNA = 2NAA + NAB cNB = 2NBB + NAB Total energy E = AANAA + BBNBB +ABNAB E = cAANA/2+ cBBNB/2+ NAB (2AB-AA- AB)/2 Interaction energy parameter w = 2AB-AA- AB

  3. Ideal solution The partition function independent on configuration An the free energy of solution Where FA and FB are free energies of pure solids

  4. Ideal solution - chemical potential Which can be written as From which the activity is given by Where PA is the partial vapor pressure of A component over solid solution

  5. Ideal solution - molar properties of mixing Helmholz free energy of mixing Since the entropy of mixing is thus the energy of mixing

  6. Regular solutions and Bragg-Williams approximation Partition function with Bragg-Williams approximation Where the average number of AB bonds is

  7. Free energy Thermodynamic function, F Which differs only by the last term for the expression for the ideal solution. Entropy is exactly the same as for ideal since we assumed regular solution

  8. Chemical potential and activity Again differs from that of ideal solution by the last term. Rewriting One obtains the activity as Or

  9. Molar properties of mixing Helmholz free energy of mixing Since the entropy of mixing is thus the energy of mixing

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