Three-dimensional dualistic model

The heat of mixing of two liquids is expressed by the classical theory of regular polymer solutions using Eq. [4.1.10]. This expression is not adequate for systems with specifie interae-tions. Sueh interaetions are expressed as a product of the donor parameter and the aceeptor parameter. The eontribution of H-bonding to the enthalpy of mixing can be written in terms of volume units as follows  

Hence enthalpy of mixing of two liquids per volume unit ean be expressed by  

This equation is used for the ealeulation of the enthalpy eontribution to the Huggins parameter (see Subehapter 4.2) for a polymer-solvent system  

Results of ealeulations using Eq. [4.1.44] of three-dimension dualistie model eoineide with the experimental values of %h nd the %h values ealeulated by other methods. Values A, D, and S ean been obtained from IR-speetroseopy evaluations and Hansen s parameters.Values of the TDM parameters are presented in Tables 4.1.3, 4.1.4. It should be noted that Hansen parameters are used for estimation of values of TDM parameters from equation 5, -t S = 5 Si = A.  

8 can be separated into donor and acceptor components using values of enthalpies of the hydrogen bond formation between proton-donors and proton-acceptors. In the absence of such data it is possible to evaluate TDM parameters by means of analysis of parameters of compounds similar in the chemical structure. For example, propyl acetate parameters can been calculated by the interpolation of corresponding parameters of butyl acetate and ethyl acetate, parameters of benzene can be calculated by decomposition of S, into acceptor and donor components in the way used for toluene elsewhere.  

62 dispersion-polar components of solubility parameters (values of solubility parameters 

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For certain polymers Rider has drawn solubility maps. Thus the area of solubility was represented by a pair of symmetric quarters of a plane lying in coordinates b,C. Values of parameters were defined from data for enthalpies of hydrogen bonds available from the earlier works. The model is a logical development of the Hansen method. A shortcoming of this model is in neglecting all other factors influencing solubility, namely dispersion and polar interactions, change of entropy, molecular mass of polymer and its phase condition. The model was developed as a three-dimensional dualistic model (see Section 4.1.5). 4.1.4 HANSEN S SOLUBILITY... 

The Rider s approach was developed into the three-dimensional dualistic model in which the eqnation for estimation of an enthalpy contribntion to the Huggins parameter for a polymer-solvent system was given ... 

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