Flory interaction parameter table

Table I Phase transitions, Flory interaction parameters (/), free energies (AG) and differences of Hildebrand solubility parameters (A<5) depending on the molecular structure (fluorination of the alkyl chain) [25]...

It is very important to know the value of the Flory interaction parameter X for a given mixture. Methods of measuring this parameter are discussed in Section 4.6 and tables of x parameters are listed in many reference books (see the 1996 review by Balsara). 

Table 4.3 Temperature dependence of the Flory interaction parameters of polymer blends [Eq. (4.31)1 with vq= 100 A ...

Melting point depression data are often used to determine the Huggins-Flory interaction parameter, X12 Table 3.11), that is a measure for the miscibility of the blend, i.e., X12 is negative for a miscible blend. A lack of melting point depression means that is zero. Eq 3.39 is only valid for systems in which the crystalline morphology is not affected by the composition. 

Before leaving the subject of interfacial behavior in polymers, it is instructive to consider the interfacial tension, and resulting interfacial density profiles. Making effective use of the Flory interaction parameter x, Helfand and Tagami (1972), Gaines (1972), Wu (1974), and others estimated the interfacial surface tension between incompatible polymer pairs (see Table 13.1). Also shown in Table 13.1 are theoretically estimated values of x-(See Section 4.7 and especially Sections 4.7.3 and 9.6 for related discussion.) Helfand and Tagami found that the characteristic thickness of the interface is proportional to x — y for small /. For a polystyrene/poly(methyl methacrylate) system, the value of / leads to an estimated interfacial thickness of 50 A. This value is much less than that estimated by Voyutskii and Vakula... 

From the several data obtained, Li et al. estimated the PCL/SAN-Flory interaction parameter (%), the PCL crystal surface free energy (a /(erg cm )) and the product GGg where G is the lateral surface free energy [80]. Values of x were approximately independent of SAN content up to 30 wt % with %=-0.33. Values of G and GGg, given in Table 9, decrease with increasing SAN content. The reductions in growth rate were consistent with a combination of reduced PCL concentration at the growth surface, an increase in viscosity of the amorphous material due to the... 

The Flory-Rehner equilibrium swelling method (see Section 4.2.2) was used to evaluate the change in crosslink density of the IPNs, using dioxane as the swelling agent. The Flory interaction parameter was found to be approximately 0.30 for dioxane and either polymer, simplifying the analysis. Table 6.4 gives the results for the effective crosslink densities, vj K where V is the polymer volume in cm. Table 6.4 also shows the theoretical values of vj K calculated in accordance with the law of additivity. 

Table 10.1 Flory Interaction Parameter, Xab, and Interaction Energy Density, B, for Miscible Binary Blends of Varions Polymers...

Experimental VLE data [14] for poly (acrylonitrile-co-butadiene) and its parent homopolymers are shown in Table 6. Solvent absorption in the copolymer increases as its butadiene content rises. This rise is expected because the hydrocarbon segments of pentane are better liked by hydrocarbon segments of butadiene, whereas polar segments of acrylonitrile repulse nonpolar pentane molecules. Once again, Flory interaction parameter, x. implies that with rising acrylonitrile concentration in copolymer composition. 

Here, again, we start from compressible SCFT formalism described in Section 2.2 and consider a model system in which bulk polymer consists of "free" matrix chains (Ny= 300) and "active" one-sticker chains (Na= 100). Flory-Huggins interaction parameters between various species are summarized in Table 1. This corresponds to the scenario in which surfactants, matrix chains, and functionalized chains are all hydrocarbon molecules (e.g., surfactant is a C12 linear chain, matrix is a 100,000 Da molecular weight polyethylene, and functionalized chain is a shorter polyethylene molecule with one grafted maleic group). The nonzero interaction parameter between voids and hydrocarbon monomers reflects the nonzero surface tension of polyethylene. The interaction parameter between the clay surface and the hydrocarbon monomers, Xac= 10 (a = G, F, A), reflects a very strong incompatibility between the nonpolar polymers and... 

Table 1 Flory-Huggins interaction parameters used in the calculation...

Comprehensive tables of Flory-Huggins interaction parameters and their concentration and temperature dependences have been published, e.g. by Schuld and Wolf (1999) and by Orwoll and Arnold (1996). 

Fig. 61. Correlation of the Flory-Huggins interaction parameter, %, for polystyrene-liquid systems at 25 °C with the volume fraction (v) of polymer in the system. The filled circles represent experimentally determined data recorded in Table XIX of Ref. 43. The empty circles represent estimations by interpolation or extrapolation of the linear relationships established on the basis of the experimental data shown. The value for x reported for acetone at v = 1 is placed in brackets to indicate that this point seems too high, and therefore it was not included in the data set used to establish by linear regression the equation shown for this linear relationship...

Table 3. Flory x (x ) parameters and X12 contact interaction parameters in poly(dimethyl siloxane) at 25 °C...

The comparison of the experimental solubilities [4,5] of Ar, CH4, C2H6 and CsHg in the binary aqueous mixtures of PPG-400, PEG-200 and PEG-400 with the calculated ones is presented in Figs. 1-3 and Table 2. They show that Eq. (4) coupled with the Flory-Huggins equation, in which the interaction parameter x is used as an adjustable parameter, is very accurate. The Krichevsky equation (1) does not provide accurate predictions. While less accurate than Eq. (4), the simple Eq. (2) provides very satisfactory results without involving any adjustable parameters. It should be noted that Eq. (4) coupled with the Flory-Huggins equation with X (athermal solutions) does not involve any adjustable parameters and provides results comparable to those of Eq. (2). 

Often, the Flory-Huggins solvent-polymer interaction parameter is applied instead of 1 P or G. There are some books (Refs. 1-3) giving details for such procedures as well as extensive tables of polymer solubility parameters from which the table below is extracted. Methods for calculating solubility parameters can be found in Refs. 4-7. 

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). 

Blends of AMS-AN copolymers with PVC are used to increase the heat resistance of the product. Blends of PVC and AMS-AN copolymers were formed by precipitation with THF solution into methanol. Miscible blends were found for copolymers of AMS-AN with AN composition containing 11.9-30.0 wt%. Phase separation temperatures were noted by annealing and DSC methods. Phase separation temperatures below 130°C were found. Using the characteristic EOS parameters listed in Table 3.4 and the phase separation temperatures that were measured, the AP values were calculated for the blend system. These values were found to be AP nvc = 4.30 cal/cc APamsvc = 0-26 cal/cc and APan,ams = 8.6 cal/cc. The Flory-Huggins interaction parameters at 130°C were calculated and B Nyc = 4.22 cal/cc B msvc = 0-37 cal/cc Bams,an = 8.04 cal/cc. The binary interaction parameter of the copolymer-homopolymer blend for AMS-AN copolymer and PVC homopolymer for various AN compositions in the copolymer at various volume fractions in the blend is shown in Figure 3.7. 

Table 10.1 Surface and interfacial energies (inergcm ) and Flory-Huggins interaction parameter values, X, for three block copolymer systems. The temperature (in °C) for each value is given in parentheses. References are given in square brackets.

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