Flory-Rehner parameter

Fig. 4 The Flory-Rehner parameter / characterizes the interaction between the polymer and the solvent. High values of X indicate that separation of polymer and solvent is energetically favorable while low values indicate that nuxing is favorable. Shown here is the temperature and polymer volume fraction dependence of/ for PNIPAAm and water...

The Flory-Rehner phenomenological theory [9,10] has beei most widely used to analyze the volume phase transition of gels. This theory, extended [11] to take into account the concentration dependence of the polymer-solvent interaction parameter x, can predict basic features of the phase transition. 

Fig. 5. Linear swelling ratio calculated for neutral NIPA gels on the basis of the Flory-Rehner theory. The structural parameters used in the calculation were determined from the preparation condition of (a) gel A, and ( >) gel B. The curve (c) represents the critical transition. (Reproduced with permission from Ref 20)...

While one of the < 2 values is equal to the peak position of envelope I, the other value cannot be determined accurately from Figure 1 due to the uncertainty of the peak position and low intensity of the broad peak (envelope II) Yeo has thus calculated (3) the interaction (X) parameter based on the modified Flory-Rehner equation (16) ... 

The Flory-Rehner equation (2,13) was used to interpret the swelling of the polyurethane networks in pure dioxane in order to calculate, the molecular weight between crosslinks. Here, we set qQ= 1 and x the network-solvent interaction parameter, constant and assumed equal to 0.35 (3). Networks with degrees of swelling (q ) of 6.41, 11 and 21.1 yielded Mc values of 7,700,... 

D. Patterson in 1968 based on an analysis of Flory-Rehner theory. It took ten years for the phenomenon to be experimentally observed after prediction. It was found by T. Tanaka that, when a critical amount of an organic solvent was added to a water-swollen poly(acrylamide) gel, the gel collapses. Many gels of synthetic and natural polymers have been studied. Subsequent experiments showed that a volume phase transition (swelling/collapse) could also be brought about by changes in other environmental parameters such as pH, ionic strength, and temperature. 

Moreover, such a hnear relationship tends to demonstrate that the actual cross-linking degree of the APCNs is only dependent on the initial molar fraction in PCLDMA crosshnkers introduced in the polymerization medium and therefore attests for the absence of additional (physical) cross-links that could be due to polymer chain entanglements. Therefore and owing to the control over the molecular parameters of the APCNs, a correlation between gel stracture and swelling behavior could be predicted from the Flory-Rehner relationship in the particular case of this study with a constant composition in PCL of about 30%. 

As with moisture absorption, solvent ingress will occur through diffusion processes which are driven by thermodynamic considerations. Thus in agreement with Flory-Rehner considerations, the degree of swelling will be a function of the Flory interaction parameter and the crosslink density [29]. For this discussion, the most important consideration is the relative polarity... 

Chemical potentials inside the membrane are determined by the Flory-Rehner-Donnan equation of state for one-dimensional swelling (5), since the clamped membrane s area. A, is constant. The polymer-solvent interaction parameter, f, is a linear function of the polymer volume fraction, i.e. J + Xi as proposed by Hirotsu (/ 7). Transport of water into and out of the hydrogel membrane causes its thickness, I, to change at a rate that is proportional to the difference in chemical potential of water between the membrane and Cell I and Cell II. 

Nonionic hydrogels can be analyzed with Flory-Rehner theory to determine the quantitative parameters described previously. In Flory-Rehner analysis, hydrogel swelling is dictated by the thermodynamic free energies of mixing and... 

The eorrelation between thermodynamic parameters and the value of an equilibrium swelling is given by Flory-Rehner equation used now in a modified form ... 

If the Xi23 value is considered as a criterion of existence of a maximum of equilibrium swelling of polymer in the mixed solvent, a maximum of Q should correspond to the minimum of %i23. For practical use of Eq. [6.2.2] it is necessary to know parameters 5 13,5 23, and Xn- The values X13 and X23 can be determined by the Flory-Rehner equation, with data on swelling of a crosslinked elastomer in individual solvents 1 and 2. The evaluation of the Xn value can be carried out with use of results of the experimental evaluation of vapor pressure, viscosity and other characteristics of a binary mixture. ... 

The values of parameters Xn and X23 were calculated from the Flory-Rehner equation, using data on swelling of crosslinked polymer in individual solvents, the values Xn X23 > and %i23 were estimated from Eqs. [6.2.3-6.2.5). Then equilibrium swelling of elastomer in SL was calculated from the equation similar to Flory-Rehner equation, considering the mix-... 

The calculation of equilibrium swelling of SPU-1 (after its deformation up to 700 % and subsequent unloading) in a given solvent was carried out using the Flory - Rehner equation. In our calculations we used values of the parameter of interaction between solvents... 

As expected,preferential sorption was observed, with the essential distinction of molar volumes Vi and Vj of components of the mixed solvent (hexane-DBP, DOS-DEP). For swelling of the crosslinked elastomer SCN-26 in the mixture of components, having similar molar volumes Vj and Vj (e.g., amyl acetate-dimethyl phthalate) the preferential sorption of components of SL is practically absent. Influence of Vj and V2 and the influence of double interaction parameters on the sorption of binary liquids by crosslinked elastomers was examined by the method of mathematical experiment. Therewith the set of equations describing swelling of crosslinked elastomers in binary mixture, similar to the equations obtained by Bristow from the Flory-Rehner theory and from the work of Schulz and Flory, were used ... 

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. 

A hydrogel network is obtained through the physical or chemical interactions that occur between polymer chains. According to the Flory—Rehner theory, fundamental structural parameters of hydrogels are (Fig. 10.2) (Hu et ah, 2009 Flory, 1953) ... 

Total crosslink density of the irradiated samples was determined taking advantage of equilibrium swelling in toluene and calculated on the basis of Flory-Rehner equation [21]. The Flory-Huggins interaction parameter used in the calculations for toluene - NBR rubber was 0.435 [22]. 

The solubility parameter of a new polymer may be determined by any of several means. If the polymer is cross-Unked, the solubility parameter may be determined by swelling experiments (7). The best solvent is defined for the purposes of the experiment as the one with the closest solubility parameter. This solvent also swells the polymer the most. Several solvents of varying solubility parameters are selected, and the cross-linked polymer is swelled to equilibrium in each of them. The swelling coefficient, Q, is plotted against the various solvent s solubility parameter, the maximum defining the solubility parameter of the polymer. The theoretical extent of swelling is predicted by the Flory-Rehner theory on the basis of the cross-link density and the attractive forces between the solvent and the polymer (see Section 9.12). 

By microscopic measurements of the degree of swelling (Flory-Rehner theory) or rather by compression measurements (rubber elasticity theory (RET)) the network parameters, such as cross-linking density or the molecular weight of network chains Me can also be determined vc = p2lMc) (Flory et al. 1976 James and Guth 1943 Wall 1942, 1943, 1951 Hermans 1947). 

The density of cross-links in the elastomer network was determined by the method of equilibrium swelling according to standard PN-74/C-04236. The samples of the composite material were subjected to equilibrium swelling in toluene for 48 h at room temperature. Then, the swollen samples were weighed on a torsion balance, next dried at a temperature of 60 to a constant weight and after 48 h they were reweighed. Based on the Flory-Rehner s equation [20] the crosslink density was determined, assuming the elastomer-solvent interactions parameter as x = 0.501 + 0.273 Vr, where Vr is the volume fraction of the elastomer in the swollen gel. 

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