Handbook of Solvents - George Wypych - ChemTech - Ventech!

112 Valery Yu. Senichev, Vasiliy V. Tereshatov
2
2
[ ( dS . d. P) ( pS . pP . ) ]
VS
χH = δ − δ + δ −δ
RT
[4.1.19]
where δd. S , δd.P , δp. S , δp.P
are Hansen’s parameters of solvent and polymer (see the next section).
Chen implied that χH was the enthalpy contribution to the Flory-Huggins parameter χ1 and plotted the solubility data in a δh −χH diagram where δh was the H-bond parameter in
the Hansen approach. In these diagrams sphere-like volumes of Hansen’s solubility have
degenerated to circles.
The disadvantage of this method lies in the beforehand estimating characteristics of
the polymer. Among other two-dimensional methods used for the representation of solubility
data was the δp-δh diagram proposed by Henry 19 and the δ-δh diagram proposed by
Hoernschemeyer, 20 but their representations of the solubility region were less correct. All
these approaches involving hydrogen bond parameter ignored the fact that hydrogen bond
interaction was the product of hydrogen bonding donating and accepting capability. 21-23
On the basis of chemical approach to hydrogen bonding, Rider proposed a model of
solubility for liquids in which the enthalpy limited the miscibility of polymers and solvents.
24,25 For substances capable to form hydrogen bonds, Rider proposed a new factor relating
miscibility with an enthalpy of mixing which depends on an enthalpy of the hydrogen
bond formation. He has introduced the quantity of a hydrogen bond potential (HBP). If the
quantity of HBP is positive it promotes miscibility and if it is negative it decreases miscibility.
( )( )
HBP = b −bC −C
1 2 1 2 [4.1.20]
where:
b1,b2 donor parameters of solvent and solute, respectively
C1,C2 acceptor parameters of solvent and solute, respectively
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. 24 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 Hansen approach 26-30 assumed that the cohesive energy can be divided into contributions
of dispersion interactions, polar interactions, and hydrogen bonding.
E = Ed + Ep + Eh
[4.1.21]
where:
E total cohesive energy
Ed,Ep,Eh contributions of dispersion forces, permanent dipole-permanent dipole forces, and
hydrogen bonds.
Dividing this equation by the molar volume of solvent, V1, gives: