Flory-Huggins theory of polymer

The formation mechanism of structure of the crosslinked copolymer in the presence of solvents described on the basis of the Flory-Huggins theory of polymer solutions has been considered by Dusek [1,2]. In accordance with the proposed thermodynamic model [3], the main factors affecting phase separation in the course of heterophase crosslinking polymerization are the thermodynamic quality of the solvent determined by Huggins constant x for the polymer-solvent system and the quantity of the crosslinking agent introduced (polyvinyl comonomers). The theory makes it possible to determine the critical degree of copolymerization at which phase separation takes place. The study of this phenomenon is complex also because the comonomers act as diluents. 

The polymer solubility can be estimated using solubility parameters (11) and the value of the critical oligomer molecular weight can be estimated from the Flory-Huggins theory of polymer solutions (12), but the optimum diluent is still usually chosen empirically. 

According to the Flory-Huggins theory of polymer solutions, if the mixing process were driven only by an entropic gradient (nonpolar solvent) the solubility coefficient... 

The Flory-Huggins theory of polymer solutions has been documented elsewhere [26, 27]. The basic parameters necessary to predict polymer miscibility are the solubility parameter 6, the interaction parameter %, and the critical interaction parameter ( ) . 

It should also be mentioned that polymer-solvent interactions can be characterized by the second virial coefficients that appear in equations (8) and (13) and by the free energy of interaction parameter Z1 that appears in the Flory-Huggins theory of polymer solution thermodynamics.1,61... 

To apply the procedure outlined above to a polymer, it is necessary to use the Flory-Huggins theory of polymer solution, which takes into account the entropy of mixing of solutes in polymers caused by the large difference in molecular size... 

The Flory-Huggins theory of polymer solubility suggests that if a polymer is growing in a poor solvent, when it reaches a critical molecular weight, a phase separation will occur in which a polymer-rich or gel phase... 

A general treatment of the dependence of M,. on the nature of solvent and the volume fraction of polymer was outlined by Ivin and Leonard184. Adopting the Flory-Huggins theory of polymer solutions to ternary systems, they derived the relation... 

Flory-Huggins-Theory of Polymer Mixtures and Its Extensions. 184... 

The terms between the brackets correspond to the osmotic contribution to the Gibbs free energy (AG), and they also constitute the standard expression for AG of the Flory-Huggins theory of polymer solutions [61], where < p is the volume fraction of polymer and the ratio of the equivalent number of molecular segments of solvent to polymer (usually expressed as the ratio of molar volumes of solvent and polymer). Xap is the Flory-Huggins interaction parameter of solvent and polymer and the last term of Equation 14.1 is the interfacial free energy contribution where y is the interfacial tension, the molar volume of solvent, and r the particle radius. T is temperature in Kelvin and R is the universal gas constant. 

The simplest description of swelling is based on equilibrium thermodynamics (Equation 25.21), and considers as the driving force the affinity of the monomer to the polymer via the Flory-Huggins theory of polymer solutions and as counteracting contribution the increase in the interfacial free energy due to the growth of swelling particles. Equation 25.21 was derived by Morton-Kaizerman-Altier (MKA equation) over 50 years ago [22, 23] ... 

G.H. Fredrickson, A.J. Liu, F.S. Bates, Entropic corrections to the Flory-Huggins theory of polymer blends architectural and conformational effects. Macromolecules 27, 2503-2511 (1994)... 

The same positive AH, which arises from interactions between different species, usually prevails in polymer mixtures and most polymer pairs are mutually immiscible. The strengths of the interactions between components is usually expressed in terms of an interaction parameter Xab (Eq- 3), which originates from Flory-Huggins theory of polymer solutions. The enthalpy of mixing, or interaction energy term, arises in a van Laar type expression of heats of mixing and is of the form... 

The thermodynamic properties of concentrated polymer solutions were studied by Floryi and independently by Huggins. The Flory-Huggins theory of polymer solutions still forms the basis for much discussion of these solutions in industry and even in academic research. Understanding this model is important for making coimections to much of the literature. Flory also substantially improved this model to include compressible fluids. The Flory-OrwoU theory of polymer solutions is still transparent and easily applicable, predicting both upper and lower critical solution temperatures. More-empirically adequate theories of concentrated solutions do not lend themselves to simple lecture presentation and often require detailed computer calculations to obtain any results. Concentrated solutions also introduce the phenomenon of viscoelasticity. An extensive treatment of the full distribution of relaxation times necessary to imderstand the dynamic properties of polymers in concentrated solution is presented. 

The melting mechanism of such systems is described by the Flory-Huggins theory of polymer-diluent interaction, which correlates the melting temperature of the dilute polymer (Tm) to that of the undiluted polymer T°ni as a function of the volume... 

The well-known mean-field incompressible Flory-Huggins theory of polymer mixtures assumes random mixing of polymer repeat units. However, it has been demonstrated that the radial distribution functions gay(r) of polymer melts are sensitive to the details of the polymer architecture on short length scales. Hence, one expects that in polymer mixtures the radial distribution functions will likewise depend on the intramolecular structure of the components, and that the packing will not be random. Since by definition the heat of mixing is zero for an athermal blend, Flory-Huggins theory predicts athermal mixtures are ideal solutions that exhibit complete miscibility. 

While Eq. (4.74) contained an expression for based on the Flory-Huggins theory of polymer mixtures, in a more general view afc can be considered as representing a general modulus. Equation (A.83) can also be presented in the form... 

While for the first 30 years after the introduction (in 1941) of the Flory-Huggins theory of polymer blends (and polymer solutions) experimentalists had to exclusively rely on this approach and its refinements for the interpretation of their data, in the two decades from about 1970 to about 1990 basic steps were taken to go beyond this phenomenological description, both via the formulation of more detailed and refined... 

---