ENGR-1100 Introduction to Engineering Analysis

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Lecture 21 Statistical Mechanics and Solutions

• The model
• Ideal polymer solution
• Bragg-Williams approximation

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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
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Ideal solution
The partition function independent on
configuration An the free energy of
solution Where FA and FB are free energies of
pure solids
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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
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Ideal solution - molar properties of mixing
Helmholz free energy of mixing Since the
entropy of mixing is thus the energy of
mixing
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Regular solutions and Bragg-Williams approximation
Partition function with Bragg-Williams
approximation Where the average number of AB
bonds is
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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
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Chemical potential and activity
Again differs from that of ideal solution by
the last term. Rewriting One obtains the
activity as Or
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Molar properties of mixing
Helmholz free energy of mixing Since the
entropy of mixing is thus the energy of
mixing