Thermodynamic interaction parameter

The thermodynamic linear expansion factor has been related to Flory or thermodynamic interaction parameter, %, and the entropy of dilution parameter, Xs, through the Flory-Fox [10] equations. 

Guner, A., Kibarer, G. 2001. The important role of thermodynamic interaction parameter in the determination of theta temperature, dextran/water system. European Polymer Journal, 37, 619-622. 

The thermodynamic behavior of the dilute polymer solution depends on three factors (1) the molecular weight, (2) the thermodynamic interaction parameters and ki, or ipi and 0, which characterize the segment-solvent interaction, and (3) the configuration, or size, of the... 

Melting-point-depression data plotted in accordance with the above equation are shown schematically in Figure 2.44. The intercept gives the heat of fusion, and the slope gives the thermodynamic interaction parameter... 

Typical thermodynamic properties of the polysloxanes, such as heat capacities, solubility parameters, thermodynamic interaction parameters, and so on, have been extensively tabulated.46,182,212 Of particular interest in this area are the thermodynamics of mixing,... 

The quantity %s is the thermodynamic interaction parameter "/ between the constituent polymers at the stability limit and AT = (T — Ts) is the quench depth. 

Heat-resistant [218] soft foams were prepared from the blends of hdPE with E-P random copolymers. The azodicarbanamide acts as a thermal antioxidant and the crosslinking of the blend was increased by electron beam radiations and foamed at 225 °C with 2320% expansion. A blend of 35 wt.% PE-PP (8 92), 15 wt.% E-P block copolymers, and 50 wt.% EPDM showed accelerated weathering resitance [219] 1000 h probably due to crosslinking between constituents of the block copolymer, polyblend and EPDM. The effect of filler and thermodynamic compatibility on kaolin-filled PE-PP blend was studied by Lipatov and coworkers [220]. The thermodynamic interaction parameter (%) decreased and thermodynamic stability increased by filler addition, the degree of crystallinity decreased with increasing thermodynamic compatibility of the components due to sharp decrease in the phase separation rate during cooling. 

Since its introduction some years ago, inverse gas chromatography (IGC) has been recognized as a convenient route to the determination of thermodynamic interaction parameters for polymeric or other non-volatile stationary phases in contact with selected vapor probes (1,2). The principles of IGC experiments have also been extended to two-component stationary phases (3), thereby making it possible to specify thermodynamic interaction parameters for the components of polymer blends (4,5), as well as for filled polymers and other mu 11i-component systems. Despite these attractive features, limitations must by recognized on the general... 

On the basis of the SANS results, a molecular mechanism has been recently proposed for the toughness enhancement of DN gels [34]. This mechanism rationalizes the changes in molecular structure of the DN gel constituents observed via in-situ neutron scattering measurements, the composition dependence of the solution viscosity, and the thermodynamic interaction parameters of PAMPS and PAAm molecules obtained previously from neutron scattering studies. More specifically, this proposed mechanism provides an explanation for the observed periodic compositional fluctuations in the micrometer range induced by large strain deformation. 

Schultz, A.R. and Flory, P.J., Phase equilibria in polymer-solvent systems. II. Thermodynamic interaction parameters from critical miscibility data, J. Am. Chem. Soc., 75, 496, 1953. 

For high molecular weight (M — °o) binary blends, the Helfand and Tagami theory predicts that in binary blends (i) the interfacial thickness, A/ is inversely proportional to the interfacial tension coefficient,v , the product, A/ v being independent of the thermodynamic interaction parameter, X, (ii) the surface free energy is proportional to (iii) the chain-ends of both polymers concentrate at the interface (iv) any low molecular... 

As seen in Part 4.2, several theoretical approaches have been proposed for the description of the interfacial phenomena. The lattice theories by Helfand, Roe, Noolandi and their collaborators are based on the study of conformation and molecular environment. The derived relations are written in terms of the binary thermodynamic interaction parameter %i2 and the lattice constants. The theories do agree that the interfacial tension coefficient is a function of but the predicted functional dependencies are different Vj %"l2> with exponent n = 1/2 to 3/2, depending on the assumptions. 

The values of the 5 -components can be calculated for any chemical substance from the tabulated group and bond contributions. Once 8j is known for both polymers in the blend, the Huggins-Flory binary thermodynamic interaction parameter, can be calculated from ... 

There is an upper limit for the Flory-Huggins thermodynamic interaction parameter X if the polymer solution is homogeneous ... 

A.A. Tager [110] determined the change of AG k by producing thermodynamic cycles using static sorption of solvent vapors on the polymeric specimens. However, in solution the polymer compatibihty is influenced by the difference of the thermodynamic interaction parameters of the common solvent with each indvidual polymer. Additionally, compatibility in solution does not always correspond to that in the solid state (without a solvent). These shortcomings limit the applicability of the AG ix estimation method that Tager developed. 

Quantitative estimation of the compatibility of polymers and oligomers can be made from the concentration dependence of the Flory— Huggins thermodynamic interaction parameter X2,a- The shape of the phase diagram is judged to a certain extent by the type of this dependence in that there is a relation AG ix = RTx2,3 P2 Pa between the... 

S.3.2.4 Mechanical properties of epoxy rubber compounds. The shape of the phase diagram can be judged to some extent by the type of concentration dependence of the thermodynamic interaction parameter X2,3 of the cured polymeric compound. The parameter X2,3 for the UP-637 system (cured by the UP-0639 crosslinking agent) with SKD-KTRA rubber is positive and essentially does not change when 5 0% of the rubber is added. But the evaluation of the fraction of the rubber (which is in the form of a dispersion in the epoxy matrix) by determination of the enthalpy component of /2,3 (Xh = 9X2,3 /9/ ... 

Comparison of the concentration dependence of the Kic values of the compounds obtained by the above two methods with the concentration dependence of the X2,z thermodynamic interaction parameter of oligomer mixtures (epoxy resin-modifier and curing agent—modifier) displays the same dependences. The maximum value of of l.lMPa m / is observed at 5% content of the SKD-KTRA rubber. This is the region of maximal thermodynamic instabihty of the oligomer mixture. 

As seen from Pig. 3.22, the concentration dependence of the thermodynamic interaction parameter X2,3 of the above mixtures is nonmonotonic and is bimodal in character (the maxima are observed at 20% and 70% of Laproxide 703M). The existence of two maxima indicates that these systems have two regions of composition with least-stable thermodynamic equilibrium, which is a function of temperature. It follows from the temperature dependence of X2,3 that the thermodynamic compatibiliiy of these mixtures of polymers declines as the temperature drops—there is the top mixture critical temperature. Whereas at the blending stage there is thermodynamic compatibility of the ED-20 oligomers and Laproxide 703M for modifier contents up to 40% at 298 K, the parameter X2,3 of the mixture of the two epoxy... 

Compounds of this type are characterized by the fact that enhancement of the adhesion strength (Fig. 3.23a) and increase of the breaking strength (Fig. 3.23b) are accompanied by decrease of the impact viscosity (Fig. 3.23c) and vice versa. Apparently, this effect can be related to the beginning of microphase separation of two crosshnked polymers, which occurs at more than 5% of the modifier (Laproxide 703M) content. This assumption is also confirmed by electron-microscopic analysis and by the positive values of the thermodynamic interaction parameter X2,3 (see Fig. 3.22). 

Starting from a thickness of 0.3 x 10 m, the properties of the boundary layer of the polymer approach the voliunetric values. The data enable determination of specific changes of the retention voliune Vg with change in the film thickness. For the polymer located on the surfactant-treated basalt surface we observe a neghgible change of Vg with variation of the film thickness. When the imtreated basalt flakes with a film thickness of 0.03 x 10 m are used, we observe a sharp increase of Vg that can be explained by the decrease of structme density. Figure 9.2 presents the dependence of the thermodynamic interaction parameter of polymer solvent Xi,2 the film thickness. As is... 

The data presented indicate the complex thermodyn unic behavior of the system. Actu dly, as Fig 2.3 shows, the Floiy-Huggins thermodynamic interaction parameter between the system components has a value lower than the critical value in the region of surfactant concentrations up to 30% that characterizes the thermodynamic stability of the system. The xl,3 critical parameter for the given oligomeric system was calculated using the equation... 

The data can be used for the quantitative evaluation of thermodynamic compatibility of solvents with elastomers and for calculation of AZ, the thermodynamic interaction parameter. These data can be recalculated to the network density distinguished by the network density value, given in Table 6.3.1, using Eq. [4.2.9]. Network density values can be used for the calculation of the interaction parameter. It should be noted that each rubber has specific ratio for the equilibrium swelling values in various solvents. This can help to identify rubber in polymeric material. 

Commercial BCs are prepared from monomers that, upon polymerization, yield immiscible macromolecular blocks, one rigid and the other flexible, that separate into a two-phase system with rigid and soft domains. The concentration and molecular weights provide control of the size of the separated domains, thus the morphology and the interconnection between the domains. The existence of a dispersed rigid phase in an elastomeric matrix is responsible for its thermoplastic elastomer behavior. For symmetric block copolymers, Leibler (1980) showed that a sufficient condition for microphase separation is (XabN) = 10.5, where Xab is the binary thermodynamic interaction parameter and N is the degree of BC polymerization (Folkes 1985). 

Bab Reduced binary thermodynamic interaction parameter, Bab = Xab TA B Droplet width bi Segment length... 

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