Semi-grandcanonical ensemble

Other quantities can be obtained from suitable derivatives of the free energy or direct statistical mechanics averages e.g. in the semi-grandcanonical ensemble of a symmetrical mixture (NA = NB = N) (where the chemical potential difference Ap = pA — pB per effective monomer is a given independent thermodynamical variable) the order parameter defined as the relative excess in the number of A-chains (nA) over the number of B-chains (nB) in the system... 

For strongly asymmetric mixtures (e.g., mixtures where the A-chains are stiff while the B-chains are flexible) the semi-grandcanonical approach is clearly not feasible, and one must work in a canonical ensemble where both the number of A-chains nA and the number of B-chains nB are fixed. However, the finite size scaling ideas for PL(M) as exposed above still can be exploited if one considers the order parameter M in L x L subsystems of a much larger system [267]. The usefulness of this concept was demonstrated earlier for Ising models and Len-nard-Jones fluids [268-271]. Gauger and Pakula [267] find an entropy-driven phase separation without any intermolecular interactions. 

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