Competitive hydrogen bonds in mixed solvents

Some water-soluble polymers, such as PEO and PNIPAM, exhibit a peculiar conformational change in water upon mixing of a second water-miscible good solvent such as 

Considering that methanol molecules are also H-bonded onto the chain, we expect that there is a competition in forming the p-w and p-m H-bonds. The statistical weight of a sequence for each is given by 

To take into consideration the difference in molecular volume of the solvents, let p be the volume of methanol molecule relative to that of water. It has a numerical value of between 2 and 3. We assume that the chain segments covered by bound water and bound 

the number of different ways to choose such sequences from the finite total 

The canonical partition function of a chain for given numbers of bound water 

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