Polymer Flory-Huggins interaction paramete

Zhao, L and Choi, P. (2002) Measurement of solvent-independent polymer-polymer Flory-Huggins interaction parameters with the use of non-random partitioning solvents in inverse gas chromatography. Polymer, 43, 6677-6681. 

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. 

The Flory-Huggins Interaction Parameter. These ideas, based on a study of polymer miscibility, have been appHed to plasticizers according to the foUowiag equation ia which is the molar volume of the plasticizer, obtaiaed from molar mass figures and density values at T, and represents the iateraction parameter (11). 

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. 

The toughness of interfaces between immiscible amorphous polymers without any coupling agent has been the subject of a number of recent studies [15-18]. The width of a polymer/polymer interface is known to be controlled by the Flory-Huggins interaction parameter x between the two polymers. The value of x between a random copolymer and a homopolymer can be adjusted by changing the copolymer composition, so the main experimental protocol has been to measure the interface toughness between a copolymer and a homopolymer as a function of copolymer composition. In addition, the interface width has been measured by neutron reflection. Four different experimental systems have been used, all containing styrene. Schnell et al. studied PS joined to random copolymers of styrene with bromostyrene and styrene with paramethyl styrene [17,18]. Benkoski et al. joined polystyrene to a random copolymer of styrene with vinyl pyridine (PS/PS-r-PVP) [16], whilst Brown joined PMMA to a random copolymer of styrene with methacrylate (PMMA/PS-r-PMMA) [15]. The results of the latter study are shown in Fig. 9. 

Helfand and Tagami [75,76] introduced a model which considered the probability that a chain of polymer 1 has diffused a given distance into polymer 2 when the interactions are characterised by the Flory-Huggins interaction parameter x They predicted that at equilibrium the thickness , d c, of the interface would depend upon the interaction parameter and the mean statistical segment length, b, as follows ... 

Here % is the Flory-Huggins interaction parameter and ( ), is the penetrant volume fraction. In order to use Eqs. (26)—(28) for the prediction of D, one needs a great deal of data. However, much of it is readily available. For example, Vf and Vf can be estimated by equating them to equilibrium liquid volume at 0 K, and Ku/y and K22 - Tg2 can be computed from WLF constants which are available for a large number of polymers [31]. Kn/y and A n - Tg can be evaluated by using solvent viscosity-temperature data [28], The interaction parameters, %, can be determined experimentally and, for many polymer-penetrant systems, are available in the literature. 

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... 

Several authors have attempted to corrolate the degradation rate with such solvent parameters as osmotic coefficient [35], viscosity [36-38] and the Flory Huggins interaction parameter, % [39,40] - a low % value indicates a good solvent in which the polymer is expected to exhibit an open conformation (as opposed to coiled) and therefore is more susceptible to degradation (Fig. 5.15). 

The Flory-Huggins interaction parameter, x, indicates the water affinity of the polymer while Ch is a measure of the fraction of bound water in the... 

In addition to the solubility parameter model to treat SEC adsorption effects, an approach based on Flory-Huggins interaction parameters has also been proposed (24-27). For an excellent review of both mechanisms, see reference 28.- A general treatment of polymer adsorption onto chromatographic packings can be found in Belenkii and Vilenchik s recent book (29). 

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) ... 

Here Vi and v are the partial specific volumes of the polymer (/ = 2,4) and the solvent, respectively M is the molar weight of the solvent and Xu and 724 are the Flory-Huggins interaction parameters, quantifying the energy of interaction between unlike lattice-based polymer segments (%24) or between polymer segments and solvent molecules (%u). 

In the above equation, % is the Flory-Huggins interaction parameter, R is the universal gas constant, 02a is the average volume fraction of polymer in the adsorbed layer, and 2b is the bulk polymer concentration. 

Since there had not been any measurements of thermal diffusion and Soret coefficients in polymer blends, the first task was the investigation of the Soret effect in the model polymer blend poly(dimethyl siloxane) (PDMS) and poly(ethyl-methyl siloxane) (PEMS). This polymer system has been chosen because of its conveniently located lower miscibility gap with a critical temperature that can easily be adjusted within the experimentally interesting range between room temperature and 100 °C by a suitable choice of the molar masses [81, 82], Furthermore, extensive characterization work has already been done for PDMS/PEMS blends, including the determination of activation energies and Flory-Huggins interaction parameters [7, 8, 83, 84],... 

Once the second virial coefficient has been obtained for a given polymer - solvent system one can calculate the corresponding Flory - Huggins interaction parameter, X, from the equation ... 

We can also summarized a method for calculating the Flory - Huggins interaction parameter, x, for a given polymer and solvent using the solubility parameters 8. 

Determining the Flory-Huggins Interaction Parameter %n Charge a 1-liter vessel with 250 g polymer (p = 1.37), heat, and evacuate to 1 torr. Add 3.6 mL nitromethane, agitate at 180°C at final pressure of 560 torr. What is %n f°r the polymer-nitromethane system ... 

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