Interaction parameter from osmometry

This stipulation of the interaction parameter to be equal to 0.5 at the theta temperature is found to hold with values of Xh and Xs equal to 0.5 - x < 2.7 x lO-s, and this value tends to decrease with increasing temperature. The values of = 308.6 K were found from the temperature dependence of the interaction parameter for gelatin B. Naturally, determination of the correct theta temperature of a chosen polymer/solvent system has a great physic-chemical importance for polymer solutions thermodynamically. It is quite well known that the second viiial coefficient can also be evaluated from osmometry and light scattering measurements which consequently exhibits temperature dependence, finally yielding the theta temperature for the system under study. However, the evaluation of second virial... 

Nn0 is the number of solvent molecules, xn is a dimensionless DP function, and x is the Flory-Huggins interaction parameter calculable from osmometry data (Ulrich, 1975) ... 

Vapour pressure depression and membrane osmometry are the most common methods to determine the polyer-solvent interaction parameter. The latter method will be described briefly. In a membrane osmometer a dilute polymer solution has been separated from pure solvent by means of a membrane. The membrane is penneable for solvent molecules but not for polymer molecules. Due to a chemical potential difference solvent molecules will diffuse from the diluted phase to the concentrated phase and this results in a pressure increase which is called the osmotic pressure ti (see also section VI - 2 for a more detaUed description of osmosis). The osmotic pressure is given by... 

Measurements performed to determine the molar masses of polymers yield - as a valuable byproduct - information on the pair interaction between the macromolecules [30]. The composition dependence of the osmotic pressure Tiosm observed via membrane osmometry is directly related to the chemical potential of the solvent [cf. (14) of Sect. 2] and provides the second osmotic virial coefficient A2, from which Xo> Ihe Flory-Huggins interaction parameter in the limit of high dilution becomes accessible [cf. (15)]. Such data are particularly valuable because they can be measured with higher accuracy than the x values for concentrated polymer solutions and because they represent a solid starting point for the sometimes very complex function xiV )- In principle, membrane osmometry can also be operated with polymer solutions of different composition in the two chambers (differential osmometry) to gain data for higher polymer concentrations however, little use is made of this option. 

In cases where the contact energy is temperature-independent, the entropy of mixing is purely combinatorial, i.e. it is expressed by the first two terms in eq. (4.48) and the third term in the Flory-Huggins equation is only enthalpic. Osmometry data from Schulz and Doll (1952) treated according to eq. (4.45) showed that the entropy part of the interaction parameter was significantly larger than the enthalpic part for solutions of polymethylmethacrylate in various solvents, e.g. for toluene as solvent at 20°C Xhu 0.03 and Xsu 0.42. 

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