Flory-Huggins parameter concentration dependence

The advantage of expressing H in terms of the Flory-Huggins parameter Xn is that the latter is often insensitive to temperature, and may better reflect the dependence on concentration than H. Its disadvantage is that it does not apply near and above the critical temperature of the volatile component. 

Schotsch, K. Wolf, B. A. Jeberien, H. -E. Klein, J., "Concentration Dependence of the Flory-Huggins Parameter at Different Thermodynamic Conditions," Makromol. Chem., 185, 2169 (1984). 

The Flory-Huggins parameter Xi was initially derived as an experimentally determined interaction enthalpy parameter which was supposed to be independent of poljnner concentration. However, experiments have shown that it is dependent on pol5mier concentration. Evans and Napper [40] have shown that the polymer volume fraction dependence of X can be given by... 

Another very interesting problem concerns the concentration dependence of the effective Flory-Huggins parameter XeffM T) that can be extracted from small angle scattering data by fitting Eqs. (37), (46) or (55) to them. It has been found that Xrff T) for symmetric mixtures (such as mixtures of protonated and... 

Thus what is known as the Flory-Huggins parameter x is, by definition, a measure of the interaction energy A e. However, A e is in reality a measure of the Gibbs energy and not of the enthalpy. Consequently, x also contains an entropy contribution, which is often found to depend on the concentration. A linear dependence of the interaction parameter on the volume fraction 2 of the solute can be assumed as a first approximation (see also Fig. 6-4) ... 

These findings are confirmed by study of the thermodynamic parameters of mixing of the cured epoxy resin with OP-20. At 6-7% content of surfactant, corresponding to the maximum surface tension of the polymer, a kink and an area of decrease of the Flory-Huggins parameter are observed in the dependence of X2,s on the surfactant concentration. This anomalous dependence can be explained in terms of the rearrangement of the intermolecular bonds in the polymer-surfactant system. With ED-20 initial resin, there are no extrema on the curve. Alteration of the macromolecular conformation affects the supermolecular structure of the polymer. Adding surfactant to ED-20 resin changes the form and causes a noticeable decrease of the size of the polymeric supermolecular formations. 

The Flory-Huggins X parameter has been one of the most widely used quantities, characterizing a variety of polymer-solvent and polymer-polymer interactions. It is a unitless number. Sometimes the Flory-Huggins parameter is written Xi,2< sometimes just plain x- While the original theory proposed that x-y be concentration independent, many polymer-solvent systems exhibit increases ofxi with polymer concentration (21). In that case the analytical representation of the experimentally found concentration dependence can be written as a power series,... 

Schotsch K, Wolf BA, Jeberien H-E, Klein J (1984) Concentration dependence of the Flory-Huggins parameter at different thermodynamic conditions. Makromol Chem 185 2169... 

The reference state dimensions unperturbed dimensions, because of the unknown influence of the presence of crosslinks, possibly specific diluent effects, and perhaps at high swelling even an excluded volume effect. We have pointed out that (r2)0 may depend on the concentration of the diluent. Therefore the reference state is in general not a constant. We have also pointed out that, if (r2)0 contains a molecular expansion term due to an excluded volume effect, the use of the Flory-Huggins free enthalpy of dilution is no longer adequate. A difference between the % parameter in a network and the X parameter of the same polymer material but then in solution, may occur because the presence of crosslinks may modify %. 

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). 

For isothermal ternary systems, Geveke and Danner (1991) have modified the Flory-Huggins theory to account for the concentration dependency of the parameters. The reduced total Gibbs free energy of mixing is given by... 

For the Flory-Huggins model of the activity, Equations (2C-4)-(2C-6), the data are reported in terms of a concentration dependent chi parameter. Data must be taken or extrapolated to the 6 = 0 limit in order to remove solution structure effects. 

As well as the above quoted studies this method has also been used to study the interaction between poly(vinylidene fluoride) and poly(methyl methacrylate) , between poly(ethylene oxide) and the hydroxy ether of bisphenol A ° , and between poly(ethylene oxide) and a poly(ether sulphone) The above equations have also been reformulated in terms of the equation-of-state theory to obtain the interaction energy, which is concentration independent rather than the Flory-Huggins X parameter which is composition dependent. 

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