Polymer systems volume fraction

In order that the deviation from ideality expressed as the activity coefficient may be significant, the selection of a reference for systems should be consistent. The activity coefficient depends, besides the variables of state associated with it, on the concentration units employed (mole fraction, molality etc.). In the case of polymer solutions volume fractions segment fractions and weight fractions Wt are the most convenient [15]. 

Although the properties of specific polymer/wall systems are no longer accessible, the various phase transitions of polymers in confined geometries can be treated (Fig. 1). For semi-infinite systems two distinct phase transitions occur for volume fraction 0 = 0 and chain length N oo, namely collapse in the bulk (at the theta-temperature 6 [26,27]) and adsorp-... 

Recently efficient techniques were developed to simulate and analyze polymer mixtures with Nb/Na = k, k > I being an integer. Going beyond meanfield theory, an essential point of asymmetric systems is the coupling between fluctuations of the volume fraction (j) and the energy density u. This coupling may obscure the analysis of critical behavior in terms of the power laws, Eq. (7). However, it turns out that one can construct suitable linear combinations of ( ) and u that play the role of the order parameter i and energy density in the symmetrical mixture, ... 

Dt and the mutual diffusion coefficient, D, are interconvertible by correcting for the penetrant activity in the polymer [12], For highly concentrated systems where the penetrant volume fraction, < >, is low,/can be approximated by... 

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 above values are applicable only in the limiting case of infinite dilution. The interaction parameter varies with the volume fraction of polymer network as has been demonstrated for the PDMS-benzene system by Flory (47) and PDMS-methyl ethyl ketone, PDMS-methyl isobutyl ketone, PDMS-ethyl-n-butyl ketone, and PDMS-diisobutyl ketone by Shiomi et al. (48). Theoretically calculated and experimentally observed values of X as a function of volume fraction of polymer are given for PDMS in alkanes, aromatic hydrocarbons, and dimethyl siloxane oligomers by Gottlieb and Herskowitz (49). In the case of PDMS-alkanes, x was practically independent of the volume fraction of polymer. 

Figures 3 and 4 give displacement isotherms of PVP adsorbed on pyrogenic silica. The polymer surface excess is plotted versus the volume fraction of displacer < >d. Results in Figure 3 are for water as the solvent and in Figure 4 for dioxane as the solvent. Various displacers were used, as indicated in the figures. One of the displacers was N-ethyl pyrrolidone (NEP), which can be considered as the monomer of PVP. From the isotherm in dioxane, it was found that In = 0.14. The aqueous system shows strong...

The crucial question is at what value of <)> is the attraction high enough to induce phase separation De Hek and Vrij (6) assume that the critical flocculation concentration is equivalent to the phase separation condition defined by the spinodal point. From the pair potential between two hard spheres in a polymer solution they calculate the second virial coefficient B2 for the particles, and derive from the spinodal condition that if B2 = 1/2 (where is the volume fraction of particles in the dispersion) phase separation occurs. For a system in thermodynamic equilibrium, two phases coexist if the chemical potential of the hard spheres is the same in the dispersion and in the floe phase (i.e., the binodal condition). 

Remarkably, the use of a fluorous biphasic solvent system in combination with a [Rh(NBD)(DPPE)]+-type catalyst (NBD = norbornadiene) copolymerized into a porous nonfluorous ethylene dimethacrylate polymer, resulted in an increased activity of the catalyst relative to a situation when only toluene was used as solvent [30]. The results were explained by assuming that fluorophobicity of the substrate (methyl-trans-cinnamate) leads to a relatively higher local substrate concentration inside the cavities of the polymer when the fluorous solvent is used. That is, the polymer could be viewed as a better solvent than the fluorous solvent system. This interpretation was supported by the observations that (i) the increase in activity correlates linearly with the volume fraction of fluorous solvent (PFMCH) and (ii) the porous ethylene dimethacrylate polymer by itself lowers the concentration of decane in PFMCH from 75 mM to 50 mM, corresponding to a 600 mM local concentration of decane in the polymer. Gas to liquid mass transport limitation of dihydrogen could be mled out as a possible cause. 

---