Flory-Huggins interaction parameter, stability

Flory-Huggins interaction parameter and is less than A for the steric repulsion or above the 0-point. Therefore, in steric stabilization in a nonaqueous suspension, Eq. (22) for Vr should be replaced by Eq. (31). Since the steric repulsion increases sharply (hard-sphere type of repulsion) when two adsorbed polymer layers interpenetrate each other under the condition of this provides a... 

It is clear from equation (16.23) that when the Flory-Huggins interaction parameter x is less than 0.5, i.e. the stabilizing chains are in good solvent conditions. 

It is clear from Equation 14.18 that when the Flory-Huggins interaction parameter, % is <0.5, that is, the chains are in good solvent conditions, is positive, and the interaction is repulsive and increases very rapidly with decreasing h, when the latter is lower than 28. This explains why polymeric surfactants such as Hypermer CG6 (a graft copolymer of polymethylmethacrylate backbone and PEO side chains, produced by ICl) are ideal for stabilizing dispersions in aqueous media. For stabilization of dispersions in nonaqueous media, such as w/o emulsions, the stabilizing chains have to be soluble in the oil phase (normally a hydrocarbon). In this case, polyhydroxystearic acid (PHS) chains are ideal. A polymeric surfactant such as Aralcel P135 (an ABA block copolymer of PHS-PEO-PHS produced by ICl) is an ideal w/o emulsifier. 

Xm,p Flory-Huggins interaction parameter between monomer and polymer Xs cpi Flory-Huggins interaction parameter between the stabilizing polymer and the continuous phase e permittivity... 

Pajula K, Taskinen M, Lehto VP, Ketolainen J, Korhonen O (2010) Predicting the formation and stability of amorphous small molecule binary mixtures from computationally determined Flory-Huggins interaction parameter and phase diagram. Mol Pharm 7 795-804 Pajula K, Lehto VP, Ketolainen J, Korhonen O (2012) Computational approach for fast screening of small molecular candidates to inhibit crystallization in amorphous drugs. Mol Pharm 9 2844-2855... 

In the case of low-molecular-weight polar resins such as VE resins, relatively thin and dense adsorption layers can be assiuned. This should result in low viscosities due to low effective phase volumes of the dispersed phase and weak interparticulate interactions forces according to steric stabilization. However, addition of a solvent like styrene will influence the Hamaker constant of the liquid medium and of the adlayer and the structure of the adlayer in terms of swelling and/or multilayer formation. In particular, any multilayer formation could result in surface layer entanglement depending on the solvency of the liquid medium expressed in terms of the Flory-Huggins parameter % [11]. These effects should dramatically influence the viscosity and rest structure of the dispersion, as seen in the experiments. 

The lattice fluid equation-of-state theory for polymers, polymer solutions, and polymer mixtures is a useful tool which can provide information on equa-tion-of-state properties, and also allows prediction of surface tension of polymers, phase stability of polymer blends, etc. [17-20]. The theory uses empty lattice sites to account for free volume, and therefore one may treat volume changes upon mixing, which are not possible in the Flory-Huggins theory. As a result, lower critical solution temperature (LCST) behaviors can, in principle, be described in polymer systems which interact chiefly through dispersion forces [17]. The equation-of-state theory involves characteristic parameters, p, v, and T, which have to be determined from experimental data. The least-squares fitting of density data as a function of temperature and pressure yields a set of parameters which best represent the data over the temperature and pressure ranges considered [21]. The method,however,requires tedious experiments to deter-... 

One further difficulty not touched upon in the foregoing discussion is the absence of a truly quantitative theory describing polymer solution thermodynamics. Even a second generation theory, such as the equation-of-state theory, probably only represents a qualitative or, at best, a semi-quantitative theory of polymer solution thermodynamics (Casassa, 1976). In the absence of a fully quantitative theory, it seems justifiable to make do with the classical Flory-Huggins theory, provided that the cracks that have appeared in its superstructure are papered over. These include using the concentration dependent interaction parameter % that is determined experimentally. Most of the theories of steric stabilization that have been developed to-date have unfortunately been based upon a concentration independent interaction parameter (see Table 10.1), although there are some exceptions (see, e.g. Evans and Napper, 1977). 

The simple Flory-Huggins %-function, combined with the solubility parameter approach may be used for a first rough guess about solvent activities of polymer solutions, if no experimental data are available. Nothing more should be expected. This also holds true for any calculations with the UNIFAC-fv or other group-contribution models. For a quantitative representation of solvent activities of polymer solutions, more sophisticated models have to be applied. The choice of a dedicated model, however, may depend, even today, on the nature of the polymer-solvent system and its physical properties (polar or non-polar, association or donor-acceptor interactions, subcritical or supercritical solvents, etc.), on the ranges of temperature, pressure and concentration one is interested in, on the question whether a special solution, special mixture, special application is to be handled or a more universal application is to be foxmd or a software tool is to be developed, on munerical simplicity or, on the other hand, on numerical stability and physically meaningftd roots of the non-linear equation systems to be solved. Finally, it may depend on the experience of the user (and sometimes it still seems to be a matter of taste). 

Stability, and the B parameter must be negative to have miscibility in high molecnlar weight blends. Interaction parameters used in the ensuing sections are not limited to the Flory-Huggins framework and can be viewed as free of equation of state effects. 

Controlling the spontaneous formation of ordered domains in soft materials such as block copolymers [189] may lead to the development of stimuli-responsive materials for applications such as actuators [190] and photonics [191] due to the reversible nature of order formation. However, the stimuli that are typically used to control the morphology of block copolymers are e.g., temperature, pressure, solvent type and concentration... Pioneering work by Abbott and co-workers used the chemical oxidation approach to control the self-assembly of small-molecule amphiphiles containing ferrocene [192]. Rabin and co-workers have shown that the introduction of dissociated charges on one of the blocks of a diblock copolymer leads to stabilization of the disordered phase [193]. They also quantified the increase in x at the order-disorder transition (ODT), xodt, due to the entropic contribution of the dissociated counterions. The Flory-Huggins parameter,x, that is used to quantify interactions between polymer chains is assumed to be proportional to the difference in the polarizibility of the blocks [194]. The polarizibility of polyferrocenyldimethylsilane, which is larger than that of either polystyrene or polyisoprene [195], must increase upon oxidation due to the presence of the NO ions. 

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