Flory-Huggins solute-polymer interaction parameter

The Flory-Huggins solute-polymer interaction parameter may be also calculated from activity coefficients [16,39]. In the case of pure solvents the equation is ... 

The usefulness of inverse gas chromatography for determining polymer-small molecule interactions is well established (1,2). This method provides a fast and convenient way of obtaining thermodynamic data for concentrated polymer systems. However, this technique can also be used to measure polymer-polymer interaction parameters via a ternary solution approach Q). Measurements of specific retention volumes of two binary (volatile probe-polymer) and one ternary (volatile probe-polymer blend) system are sufficient to calculate xp3 > the Flory-Huggins interaction parameter, which is a measure of the thermodynamic... 

In a blend solution, the interaction parameter x of the Flory-Huggins theory is zero (the chain end effect is negligible) and independent of temperature. Otherwise, a temperature-dependent x can lead to a thermorhe-ologically complex behavior of the polymer solution sj tem, which would disallow the apphcation of the time-temperature superposition principle. A theoretical analysis indicates that if M M2, the system is free of the excluded volume effect that will cause the component-two chain to expand in other words, the chain coil remains Gaussian. Here, we consider polystyrene blend solutions with Mi slightly smaller than Mg (= 13,500 for polystyrene). In such a system, the condition M > M2 can be easily satisfied. Furthermore, the solvent, being chains of more than ten Rouse... 

The solvent-polymer interaction parameters were calculated from vapor pressure data of aqueous homopolymer solutions [25], using the Flory-Huggins expression [26] x//=6 ln/)//) —ln(l — 0) —(1 — l/N)0, where p is the vapor pressure and 6 is the polymer volume fraction. The chain length N was determined using 13/3 (EO) or 30/9 (PO) monomers per bead. This gives for the interaction parameters X s=l-4, Xi>s=l-7 (here S denotes solvent). For the EO-PO interaction parameter from group contribution methods [27] we estimated xep = 3.0. 

By applying the Flory-Huggins equations of polymer solutions to a ternary system with two polymers and one probe, the interaction parameter Xi can be related to the probe-polymer interaction parameters x" and Xu) and the polymer-polymer interaction parameter ( 23) by the following equation [41] ... 

In polymer solutions or blends, one of the most important thennodynamic parameters that can be calculated from the (neutron) scattering data is the enthalpic interaction parameter x between the components. Based on the Flory-Huggins theory [4T, 42], the scattering intensity from a polymer in a solution can be expressed as... 

Although the emphasis in these last chapters is certainly on the polymeric solute, the experimental methods described herein also measure the interactions of these solutes with various solvents. Such interactions include the hydration of proteins at one extreme and the exclusion of poor solvents from random coils at the other. In between, good solvents are imbibed into the polymer domain to various degrees to expand coil dimensions. Such quantities as the Flory-Huggins interaction parameter, the 0 temperature, and the coil expansion factor are among the ways such interactions are quantified in the following chapters. 

More fundamental treatments of polymer solubihty go back to the lattice theory developed independentiy and almost simultaneously by Flory (13) and Huggins (14) in 1942. By imagining the solvent molecules and polymer chain segments to be distributed on a lattice, they statistically evaluated the entropy of solution. The enthalpy of solution was characterized by the Flory-Huggins interaction parameter, which is related to solubihty parameters by equation 5. For high molecular weight polymers in monomeric solvents, the Flory-Huggins solubihty criterion is X A 0.5. 

According to Flory-Huggins theory, the heat of mixing of solvent and polymer is proportional to the binary interaction parameter x in equation (3). The parameter x should be inversely proportional to absolute temperature and independent of solution composition. 

Further development of the Flory-Huggins method in direction of taking into account the effects of far interaction, swelling of polymeric ball in good solvents [4, 5], difference of free volumes of polymer and solvent [6, 7] leaded to complication of expression for virial coefficient A and to growth of number of parameters needed for its numerical estimation, but weakly reflected on the possibility of equation (1) to describe the osmotic pressure of polymeric solutions in a wide range of concentrations. 

The Flory-Huggins interaction parameter, x Is the sum of enthalpic (xH) and entropic (x ) contributions to the polymer-solute interactions (28). xs is an emPitical constant related to the coordination of the polymer subunits (29). Chiou et al. (20) have selected a value of 0.25 for xs of humlc matter. From regular solution theory, xq is given by... 

Statistical thermodynamic mean-field theory of polymer solutions, first formulated independently by Flory, Huggins, and Staverman, in which the thermodynamic quantities of the solution are derived from a simple concept of combinatorial entropy of mixing and a reduced Gibbs-energy parameter, the X interaction parameter. 

Another important application of experimentally determined values of the osmotic second virial coefficient is in the estimation of the corresponding values of the Flory-Huggins interaction parameters x 12, X14 and X24. In practice, these parameters are commonly used within the framework of the Flory-Huggins lattice model approach to the thermodynamic description of solutions of polymer + solvent or polymer] + polymer2 + solvent (Flory, 1942 Huggins, 1942 Tanford, 1961 Zeman and Patterson, 1972 Hsu and Prausnitz, 1974 Johansson et al., 2000) ... 

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... 

In practice, the Flory-Huggins theory fails to predict many features of polymers solutions, either qualitatively or quantitatively, but remains widely used because of its simplicity. The Flory parameter x, assumed to be constant, often increases with interaction-energy scaled on kT, often exhibits a more complicated temperature dependence than 1/T (Flory, 1970). Such behavior stems from energetic effects, such as directional polar... 

This method is to be used to estimate the activity coefficient of a low molecular weight solvent in a solution with a polymer. This procedure, unlike the other procedures in this chapter, is a correlation method because it requires the Flory-Huggins interaction parameter for the polymer-solvent pair which must be obtained from an independent tabulation or regressed from experimental data. In addition, the specific volumes and the molecular weights of the pure solvent and the pure polymer are needed. The number average molecular weight of the polymer is recommended. The method cannot be used to estimate the activity of the polymer in the solution. 

Originally x was stated to be independent of polymer concentration. The X-parameters determined by many investigators using one or another of the methods for measuring colligative properties of polymer-liquid solutions (mentioned below) show that this is not the case (see Tables 3-22 of Reference 43) nor does x vary linearly with 1/T as stated in Eq. 7. Later [44] a quantity Aws representing an entropic contribution from contact interaction was added to the Flory-Huggins definition of x to produce a relationship linear in 1/T. 

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