Flory Huggins constants

For each sample, the Flory Huggins constants (k, Eq. 5.25) were also determined (by viscosity measurements) as function of sonication time and are given in Tab. 5.17. 

The different crosslinking behaviours of photopolymer films formed from different solvents can be explained with the help of different polymer conformations in these solvents. Studies were performed with one selected photopolymer (27). The second virial coefficients (A2), determined by light scattering, revealed the most coiled photopolymer structure in THF solution. This is to be expected since the magnitude A2 (found to be lowest in THF solution) is related to the Flory-Huggins constant Xi widely used in fundamental polymer studies as measure for the polymer-solvent interactions. If A2>0, the interactions between polymer molecules and solvent molecules are more attractive than the solvent-solvent interactions. Such solvents are considered to be thermodynamically good for the polymer. Thus, the low value for THF means that this solvent can be considered to be poor , leading to a more... 

The formation mechanism of structure of the crosslinked copolymer in the presence of solvents described on the basis of the Flory-Huggins theory of polymer solutions has been considered by Dusek [1,2]. In accordance with the proposed thermodynamic model [3], the main factors affecting phase separation in the course of heterophase crosslinking polymerization are the thermodynamic quality of the solvent determined by Huggins constant x for the polymer-solvent system and the quantity of the crosslinking agent introduced (polyvinyl comonomers). The theory makes it possible to determine the critical degree of copolymerization at which phase separation takes place. The study of this phenomenon is complex also because the comonomers act as diluents. 

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... 

Simulations [73] have recently provided some insights into the formal 5c —> 0 limit predicted by mean field lattice model theories of glass formation. While Monte Carlo estimates of x for a Flory-Huggins (FH) lattice model of a semifiexible polymer melt extrapolate to infinity near the ideal glass transition temperature Tq, where 5c extrapolates to zero, the values of 5c computed from GD theory are too low by roughly a constant compared to the simulation estimates, and this constant shift is suggested to be sufficient to prevent 5c from strictly vanishing [73, 74]. Hence, we can reasonably infer that 5 approaches a small, but nonzero asymptotic low temperature limit and that 5c similarly becomes critically small near Tq. The possibility of a constant... 

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. 

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 %. 

As pointed out in Chapter III, Section 1 some specific diluent effects, or even remnants of the excluded volume effect on chain dimensions, may be present in swollen networks. Flory and Hoeve (88, 89) have stated never to have found such effects, but especially Rijke s experiments on highly swollen poly(methyl methacrylates) do point in this direction. Fig. 15 shows the relation between q0 in a series of diluents (Rijke assumed A = 1) and the second virial coefficient of the uncrosslinked polymer in those solvents. Apparently a relation, which could be interpreted as pointing to an excluded volume effect in q0, exists. A criticism which could be raised against Rijke s work lies in the fact that he determined % in a separate osmotic experiment on the polymer solutions. This introduces an uncertainty because % in the network may be different. More fundamentally incorrect is the use of the Flory-Huggins free enthalpy expression because it implies constant segment density in the swollen network. We have seen that this means that the reference dimensions excluded volume effect. 

This result has the form of the well known Flory-Huggins approximation, evaluated in the limit of small concentrations ( dc defined chemical potential.) The term In (fdCj,(n)) can be interpreted as an entropic contribution of nonintcraeting chains and u nc is the interaction energy with a homogeneous background of other chains. The constant shift ln(4rr)d/2 is due to our normalization of the spatial integrals in the partition function. 

FIGURE I Predicted and observed DOM binding constants using the Flory-Huggins equation and methylsalicylic acid as a DOM analog. 

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