Semidilute solution chemical potential

Chemical Potential We find here how the excess chemical potential depends on p, where is the dilference of the chemical potential p. from the chemical potential in the ideal solution of the same concentration. We note that 5p is calculated from the nonideal part of the free energy. In the semidilute solution, it is approximately given by Iiy, where II is given by Eq. 4.12. Because pV/N is the number of polymer chains in volume V, Sp, is obtained as... 

The following equation can be used for the overall chemical potential p. It is an approximate formula valid from dilute to semidilute solutions ... 

From the partition function the free energy Fjy follows and hence all thermodynamic quantities of interest can be estimated (entropy, chemical potential, osmotic pressure...). Ottinger applied this technique to test the osmotic equation of state for dilute and semidilute polymer solutions for N <60. Extension of this technique to off-lattice systems has also been made. ... 

The coexistence curve that describes (see Fig. 1) the coexistence between a dilute polymer solution of volume fraction coL and a semidilute polymer solution of volume fraction for T < Tent, can be found by equating the chemical potentials = kBT(dg(cf>)/8cf>)T and the osmotic pressures [1, 2, 3]... 

Figure 3.23 allows us make a conclusion that increase of n-oxiethylene-dimetacrylate in a system will be accompanied by decrease of Aiai, though fall down, they don t (in both phases) stay positive (curve 1). Let s note that considerable differences observed at the scale of variation of residual chemical potential in phases Api as a function of i decreases on 2 -2.5 decimal orders in semidiluted solutions (for various systems), while decrease of in diluted solutions stays within one decimal order for all range of binodal concentrations. However, it s half as little in the second case. 

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