Polymer blends Hildebrand solubility parameter

A second part of the study of Singh and Schweizer" described in Section V.C was to investigate the validity of a solubility parameter approach to polymer blend miscibility. Solubility parameter, or Hildebrand, theory is potentially extremely useful from a practical viewpoint... 

Lohse et al. have summarized the results of recent work in this area [21]. The focus of the work is obtaining the interaction parameter x of the Hory-Huggins-Stavermann equation for the free energy of mixing per unit volume for a polymer blend. For two polymers to be miscible, the interaction parameter has to be very small, of the order of 0.01. The interaction density coefficient X = ( y/y)R7 , a more relevant term, is directly measured by SANS using random phase approximation study. It may be related to the square of the Hildebrand solubility parameter (d) difference which is an established criterion for polymer-polymer miscibility ... 

An alternate approach, which starts from blends and evaluates their interaction parameters, is the use of the Hildebrand Solubility Parameter concept (Hildebrand and Solubility, 1964 Gee, 1942, 1947). This has been used for solvent-solvent miscibility as well as for polymer-solvent mixing because it provides a more intuitive approach to predicting miscibility of polymers with solvents including solutions and gels such as swelling of vulcanized rubbers in organic liquids. Both of the models have similar deficiencies in themselves that they do not account for equation of state effects, and a consideration of speeific interactions can be added only as perturbation to these models. 

The viscosity dependence on polymer molecular weight is demonstrated in Figure 2.21 whereas Figure 2.22 shows the effect of polymer/solvent interaction. In the latter, the viscosity of solutions of a thermoplastic rubber at constant concentration and temperature is given in various hydrocarbon(blend)s. In this example hydrogen bonding or polar effects play no or only a very limited role. It is clear that in this case the solution viscosity is very much influenced by the Hildebrand solubility parameter of the solvent in relation to that of the polymer (8.2-9.1). 

Miscibility between the individual polymers is the most important factor to determine the performance characteristics of a polymer blend. Mutual solubility of the phases, the thickness and properties of the interphase formed during blending and the structure of the blend are mainly dependent on the miscibility of individual polymers within a polymer. As a result, a quantitative estimation of interactions is very much important for the prediction of blend properties. Comparison of solubility parameters of individual polymers is an effective method to predict the extent of miscibility within a blend. According to the Hildebrand solubility theory, a large difference in solubility parameters (6p) of individual matrices results in immiscibility between them in the absence of any interfacial compatibil-izer [222]. Jandas et al. have reported that PLA and PHB have Hildebrand solubility parameters (6p) of 23.5 J /cm and 19.8 J Vcm which can turn out to be partially miscibile blends in between them [35]. In case of partially miscible blends, the miscibility can be controlled by compatibili-zation using proper interactables. 

The Flory—Huggins theory, which is based upon statistical thermodynamic models, has been used to assess the miscibility of polymer blends and was developed by Flory (1941, 1942) and Huggins (1941,1942) in the 1940s. Unlike the Hildebrand solubility parameter, it provides a fundamental understanding backed with classical thermodynamic theories. 

Hildebrand solubility parameter Hansen three-dimensional solubility parameter Hydrogen bonding in polymer blends Association model Combinatorial entropy Chemical and physical forces Equilibrium rate constant... 

The Hildebrand solubility parameter is a fundamental thermodynamic property of polymers and is used extensively for the discussion of the miscibility of polymers in solvents and blends. The process of dissolving an amorphous polymer in a solvent is governed by the free energy of mixing,... 

The nature of polymer-solvent interactions plays an important role in deciding the influence of chemical and solvent effects on blends. The Hildebrand s solubility parameter, has been extended to systems that have dispersive (subscript d), polar (subscript p) and hydrogen bonding (subscript h) interactions, i.e., 5, 5p, and 5j, respectively [Hildebrand and Scott, 1949 Burrel and Hansen, 1975]. 

In real systems, nonrandom mixing effects, potentially caused by local polymer architecture and interchain forces, can have profound consequences on how intermolecular attractive potentials influence miscibility. Such nonideal effects can lead to large corrections, of both excess entropic and enthalpic origin, to the mean-field Flory-Huggins theory. As discussed in Section IV, for flexible chain blends of prime experimental interest the excess entropic contribution seems very small. Thus, attractive interactions, or enthalpy of mixing effects, are expected to often play a dominant role in determining blend miscibility. In this section we examine these enthalpic effects within the context of thermodynamic pertubation theory for atomistic, semiflexible, and Gaussian thread models. In addition, the validity of a Hildebrand-like molecular solubility parameter approach based on pure component properties is examined. 

The first two terms represent the combinational entropy of mixing. Since these entropy terms are usually small in polymer blends, AG, is dominated by the balance between the third and fourth terms. The third term represents physical forces that can be estimated using Hildebrand s approach from solubility parameters calculated using group contribution methods for a set of carefully chosen groups which are free from association (see also Section 2.1.6) [8,15]. The fourth term represents the favorable hydrogen-bonding contribution to AG - Its... 

---