Polymer/solvent interaction parameter

Polyisobutylene is readily soluble in nonpolar Hquids. The polymer—solvent interaction parameter Xis a. good indication of solubiHty. Values of 0.5 or less for a polymer—solvent system indicate good solubiHty values above 0.5 indicate poor solubiHty. Values of X foi several solvents are shown in Table 2 (78). The solution properties of polyisobutylene, butyl mbber, and halogenated butyl mbber are very similar. Cyclohexane is an exceUent solvent, benzene a moderate solvent, and dioxane a nonsolvent for polyisobutylene polymers. 

Table 2. Polymer—Solvent Interaction Parameters for Polyisobutylene and Butyl Rubber...

Here x is the polymer-solvent interaction parameter defined by Flory for polymeric swelling its value becomes more negative as the interaction between the solvent and the polymer increases. By comparing Eqs. (45) and (46), we arrive at... 

The polymer-solvent interaction parameter, which is a key constant defining the physical chemistry of every polymer in a solvent, can be obtained from electrochemical experiments. Definition and inclusion of this interaction was a milestone in the development of polymer science at the beginning of the 1950s. We hope that Eq. 47 will have similar influence in the development of all the cross-interactions of electrochemistry and polymer science by the use of the ESCR model. A second point is that Eq. 47 provides us with an efficient tool to obtain this constant in electroactive... 

Since the equilibrium volume degree of swelling Q equals l 2, this equation shows that the parameters which control swelling are the polymer-solvent interaction parameter % and the effective cross-link density pt. Figure 2 shows that Q falls as either % or p) increases, although the influence of the cross-link density becomes negligible in poor solvents. 

The polymer-solvent interaction parameter can be estimated by using the solubility parameters for the polymer and solvent. An approximate relationship between these parameters is... 

RA Orwell. The polymer-solvent interaction parameter %. Rubber Chem Technol 50 451-456, 1977. 

Here, AGeiastic is the contribution due to the elastic retractive forces developed inside the gel and A6mixi g is the result of the spontaneous mixing of the fluid molecules with the polymer chains. The term AGmjXjng is a measure of the compatibility of the polymer with the molecules of the surrounding fluid. This compatibility is usually expressed by the polymer-solvent interaction parameter, xi (Flory, 1953). 

Here k and T have their usual meaning, x is the ratio between the molecular volumes of a polymer chain and a solvent molecule and X is the polymer-solvent interaction parameter. 

A comparison between the Eg values listed in tables I and II with theoretical Gg values is not possible at present, since for calculation of Gg one needs to know the polymer-solvent interaction parameter as a function of Na2S04 concentration. Moreover, an assumption must be made about the segment distribution of the adsorbed layer. In the absence of such information, it is not possible to calculate Gg. However, the values of Eg obtained from rheology (tables I and II) are reasonable, considering the approximation made and the crude model used for calculating Es. 

Roult s law is known to fail for vapour-liquid equilibrium calculations in polymeric systems. The Flory-Huggins relationship is generally used for this purpose (for details, see mass-transfer models in Section 3.2.1). The polymer-solvent interaction parameter, xo of the Flory-Huggins equation is not known accurately for PET. Cheong and Choi used a value of 1.3 for the system PET/EG for modelling a rotating-disc reactor [113], For other polymer solvent systems, yj was found to be in the range between 0.3 and 0.5 [96],... 

For the solubility of TPA in prepolymer, no data are available and the polymer-solvent interaction parameter X of the Flory-Huggins relationship is not accurately known. No experimental data are available for the vapour pressures of dimer or trimer. The published values for the diffusion coefficient of EG in solid and molten PET vary by orders of magnitude. For the diffusion of water, acetaldehyde and DEG in polymer, no reliable data are available. It is not even agreed upon if the mutual diffusion coefficients depend on the polymer molecular weight or on the melt viscosity, and if they are linear or exponential functions of temperature. Molecular modelling, accompanied by the rapid growth of computer performance, will hopefully help to solve this problem in the near future. The mass-transfer mechanisms for by-products in solid PET are not established, and the dependency of the solid-state polycondensation rate on crystallinity is still a matter of assumptions. 

Fractional Precipitation of Cellulose Triacetate. The reported partial or non-fractionation of cellulose triacetate from chlorinated hydrocarbons or acetic acid may be explained in terms of the polymer-solvent Interaction parameter x (1-11) The x values for cellulose triacetate-tetrachloroethane and cellulose triacetate-chloroform systems are reported (10,21) as 0.29 and 0.34 respectively. The lower values of x for such systems will result in a smaller or negative heat of mixing (AHm) and therefore partial or non-fractionation of the polymer in question results. 

Xi and X2 are the mole fractions of solvent and polymer, respectively g is the polymer-solvent interaction parameter... 

Table 2.5 Some Polymer-Solvent Interaction Parameters at 25° C...

Vs = molar volume of the solvent = volume fraction of polymer in the swollen gel % = polymer-solvent interaction parameter... 

X is the polymer solvent interaction parameter, which is a dimensionless quantity characterizing a polymer solvent system, x may generally depend on temperature, pressure, concentration, but only a little on the functionality/ h2>3 is the memory term, already discussed ... 

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. 

In the above equations, % is the polymer-solvent interaction parameter, kB the Boltzmann constant, T the absolute temperature, NA Avogadro s number, v, the molar volume of solvent. If the network is made up only of neutral monomers, 7im and 7te sum up to generate the total osmotic pressure it . On the other hand, when ionizable species are contained in the network, the osmotic pressure due to ions must be considered. The contribution from counter ions [5,10,11] is... 

Fig 4. Polymer-solvent interaction parameter % calculated from Eq. (10) using the experimental swelling ratio as a function of inverse absolute temperature. Dashed lines represent fits to straight lines which should be obeyed in a highly swollen state. NIPA/water, O NIPA/ethanol, NIPA/n-propanol. (Reproduced with permission from Ref. 19)... 

Table 1. Changes in the enthalpy (Ah) and the entropy (As) parameters appearing in the polymer-solvent interaction parameter % of NIPA-water system...

In contrast to swollen homopolymer films, only a limited number of studies on thin films of block copolymers have been reported in which the degree of the film swelling has been directly accessed. In situ SE has been used to evaluate the polymer-solvent interaction parameters [144], to construct phase diagrams of surface structures [49, 51], and to control the mechanism of lamella reorientation in thick swollen films [118, 163, 164], Spectroscopic reflectometry combined with real-time GISAXS has been used to follow structural instabilities in swollen lamella films [165], Recently, it was demonstrated that swelling of diblock copolymer films in organic selective and non-selective solvents follows the same physical behavior as in thin films of homopolymers [119]. 

One of the most characteristic properties of crosslinked rubbers is the ability to swell in appropriate solvents to a constant volume. Not only is this property exploited for estimation of parameters such as crosslink densities and polymer-solvent interaction parameters, but the resultant change in nuclear magnetic resonance (NMR) parameters allows a large number of new and interesting NMR experiments. It is the aim of this chapter to introduce some simple concepts of polymer swelling and to examine the information obtainable for the range of NMR experiments possible on swollen gels. 

---