Flory-Huggins X parameter

The role of the solvent in polymer adsorption has been the subject of much discussion. For example, theories have made predictions about the effect of the polymer/solvent interaction (i.e. Flory Huggins x parameter) on adsorption. For many systems, x parameters had already been tabulated so that a number of adsorption studies focused attention on this parameter. In spite of much effort, available data are ambiguous, sometimes verifying and sometimes contradicting the trends predicted by theory. 

Hammers, W. E. De Ligny, C. L., "Determination of the Flory-Huggins X Parameter, the Heat of Dilution, and the Excess Heat Capacity of Some Alkanes in Polydimethylsiloxane by Gas Chromatography," J. Polym. Sci., Polym. Phys. Ed., 12, 2065 (1974). 

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. 

Calculate the steric interaction energy between the two spheres given in problem 1. Use Table 10.7 for the value of the relevant Flory-Huggins x parameter. 

Figure 4.5 Measurements of effective Flory-Huggins x parameter for deuterated polystyrene-poly(vinylmethylether) blends (Han et al, 1988) as a function of l/T. The temperature range is typically 100-150 °C, and the numbers near each set of data indicate the volume fraction of polystyrene. The observed linear dependence on 1/r provides the physical conclusion that first-order perturbation theory is a satisfactory treatment of attractive interactions here.

Here Xeff(q) is a wavevector-dependent generalization of the Flory-Huggins X parameter [78]. For q-> 0, Eq. (34) yields... 

Here we rather focus on effects of external surfaces (e.g. hard walls) on polymer blends. In general, one expects that the forces between the wall and monomers of type A will differ from those between the wall and monomers of type B, as it generally occurs at the surfaces of small-molecule mixtures as well [365]. For polymer mixtures that are partially compatible, the interactions in the bulk (as described by the Flory-Huggins x-parameter) must be relatively small, however, since the entropy of mixing is down by a factor of N (for simplicity, the following discussion is restricted to a symmetric mixture, Na = Nb = N). However, there is no reason that the difference of wall-A and wall-B forces is similarly small [125]. Thus one may expect rather pronounced surface enrichment effects in polymer mixtures [125], Indeed some experimental evidence for this prediction has been found [37, 38, 126, 127]. 

Flory-Huggins x parameter, and the volume fraction of the A block, Z. The structure-property relationship for coil-coil diblock copolymer systems is relatively well understood both experimentally [14-19] and theoretically [20-23]. Chain stretching normal to the interface leads to a positive deviation of the scaling exponent [14]. For example, scaling behavior for a conven-... 

Due to the tendency for the Flory-Huggins x parameter to be positive, miscibility between high-molar-mass polymers is rare. If homopolymers are involved, miscibility requires some kind of specific interactions of which hydrogen bonding is the... 

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,... 

An important parameter in the theory of diluted polymers, polymer mixtures, and block copolymers is the Flory-Huggins x parameter, as it determines the propensity of the system to mix or de-mix. In DPD, the x parameter is taken into account by systematically varying the conservative interaction parameter between unlike particles, whilst the repulsion between like particles remains unchanged to maintain a homogeneous compressibility. Hence, for a mixture of A and B particles one has aAA = aBB and aAB = (Iaa + Groot and Warren [24] argued on the basis of the DPD... 

The most advanced theoretical studies of micelle formation are based on numerical versions of the SCFT [32-35, 297] of polymers, and such an approach has been worked out by Cavallo et al. [125]. Since the same approach has previously been used to study interfacial properties in polymer blends and compared to corresponding bond fluctuation model simulations, the translation factor from the interaction parameter e of the simulation to the Flory-Huggins x parameter of the SCFT is already known, and is not an adjustable parameter. SCFT predicts that for large enough N, the distribution P nab) at the CMC should only depend on the ratio ab/A /. Figure 24 demonstrates that, at least in the range of sizes 48 < IV < 128,... 

The excess free energy of the mixture (relative to a pure polymer) is written as the sum of an entropy of mixing term, and an enthalpy term. In the latter, only a reduced energy parameter e enters, which is related to the Flory-Huggins x parameter... 

Observations on the interfacial retardation, decay of retardation with distance from the filler, effect of filler size, and the dependence on Flory-Huggins x parameter are in quantitative agreement with the theory. Additional data on the effect of crosslink density indicate that cohesive failure of elastomer at low cross-linking and non-Gaussian network statistics and/or failure at high crosslinking must be taken into consideration. 

The bare interactions are related to the dimensionless Flory-Huggins X-parameters through... 

SHI Shiomi, T., Tohyama, M., Endo, M., Sato, T., and hnai, K., Dependence of Flory-Huggins X-parameters on the copolymer composition for solutions of poly(methyl methacrylate-ran-n-butyl methacrylate) in cyclohexanone, J. Polym. Sci., Part B Polym. Phys., 34, 2599, 1996. 

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