Polymer-solvent pairs

Theta temperature (Flory temperature or ideal temperature) is the temperature at which, for a given polymer-solvent pair, the polymer exists in its unperturbed dimensions. The theta temperature, , can be determined by colligative property measurements, by determining the second virial coefficient. At theta temperature the second virial coefficient becomes zero. More rapid methods use turbidity and cloud point temperature measurements. In this method, the linearity of the reciprocal cloud point temperature (l/Tcp) against the logarithm of the polymer volume fraction (( )) is observed. Extrapolation to log ( ) = 0 gives the reciprocal theta temperature (Guner and Kara 1998). 

Values obtained for and a for a number of polymer-solvent pairs are given in Table XXX. It will be observed that the exponent a varies with both the polymer and the solvent. It does not fall below 0.50 in any case and seldom exceeds about 0.80. Once K and a have been established for a given polymer series in a given solvent at a specified temperature, molecular weights may be computed from intrinsic viscosities of subsequent samples without recourse to a more laborious absolute method. 

The value of dn/dc is constant for a given polymer — solvent pair and independent of M except for oligomers, in which case dn/dc only attains constancy above a certain molecular weight35, as illustrated in Fig. 4. 

It is however possible to find conditions, called unperturbed or theta conditions (because for each polymer-solvent pair they correspond to a well-defined temperature called d temperature) in which a tends to 1 and the mean-square distance reduces to Q. In 6 conditions well-separated chain segments experience neither attraction nor repulsion. In other words, there are no long-range interactions and the conformational statistics of the macromolecule may be derived from the energy of interaction between neighboring monomer units. For a high molecular weight chain in unperturbed conditions there is a simple relationship between the mean-square end-to-end distance < > and the mean-... 

This method is to be used to estimate the activity coefficient of a low molecular weight solvent in a solution with a polymer. This procedure, unlike the other procedures in this chapter, is a correlation method because it requires the Flory-Huggins interaction parameter for the polymer-solvent pair which must be obtained from an independent tabulation or regressed from experimental data. In addition, the specific volumes and the molecular weights of the pure solvent and the pure polymer are needed. The number average molecular weight of the polymer is recommended. The method cannot be used to estimate the activity of the polymer in the solution. 

In effect, different calibration curves are necessary for different polymer solvent pairs, or even the same polymer/solvent pair if the microstructure of the polymer is different to that of the standards that are available (Figure 12-41). Sometimes, molecular weight averages based upon linear polystyrene standards are reported, but this can obviously lead to large errors. 

Barton [41] has assembled a well-referenced source book for the derivation and use of x and cohesion parameters for various polymer solvent pairs. There are many ways to measure solvent activity, the simplest being boiling point elevation, freezing point depression, and osmotic pressure discussed in Section 11.5, Solution and Suspension Colligative Properties. ... 

Solution viscosities for a particular polymer and solvent are plotted in the form (rj — j o)/(cr o) against c where rj is the viscosity of a solution of polymer with concentration c g cm and /o is the solvent viscosity. The plot is a straight line with an intercept of 1.50 cm g and a slope of 0.9 cm g. Give the magnitude and units of Huggins s constant for this polymer-solvent pair. 

For the substituted polysilylenes, (SiRR ) , the coupling constant can be varied systematically by changing the side groups (this change affects e and Vd via the backbone polarizability) or the solvent (this change affects Vj) via the London dispersion forces e is expected to be only weakly solvent dependent for nonpolar systems). Therefore, in principle, the three distinct phase behaviors predicted by the theory may be observed by judicious choice of polymer-solvent pairs. 

The chains have nearly ideal conformations at the -temperature because there is no net penalty for monomer-monomer contact. Polystyrene in cyclohexane at = 34.5 C is an example of a polymer-solvent pair at the -temperature. 

The selection of solvents for the treatment trains is based on the thermodynamics and dissolution/precipitation kinetics of polymer-solvent pairs as well as the toxicity, cost, and solvent recovery feasibility. By selecting solvents which are optimal for each polymer stream, cross-contamination is minimized and expenses reduced. In this way, polymer/solvent compatibility is achieved by solvent selection rather than elevated pressures and temperatures. 

Originally, it was assumed that the FH interaction parameter was a constant, characteristic for each polymer-solvent pair. In this case, it can be proved based on thermodynamics that the FH equation for the activity coefficient of a solvent in a binary solvent(l)-polymer(2) system is... 

However, UCST and LCST values of a given polymer/solvent pair depend strongly on the molar mass of the polymer. In the case of monodisperse polymers, this dependency can be described in good approximation by the so-called Shultz-Flory plot (see Refs. 6 and 8) ... 

We determine the values of the empirical constants K and a by plotting logioE ] versus log o M for a given polymer-solvent pair, using measurements on fractions having... 

The excess free energy per solvent molecule of polymer solutions is characterized by a semi-empirical Flory-Huggins parameter, X) which is a function of temperature for a given polymer-solvent pair. To estimate the compatibility parameter experimentally, it is necessary to define the x value for each polymer-solvent pair and compare it to its critical value calculated by the equation... 

Table 4. Miscibility of polymer-solvent pairs as a function of the difference in solubility parameters A(5...

For the proposed technique community verification, namely, the equation (29), the authors [24] used the literary data for polymer-solvent 16 pairs in reference to polymers of different kinds polyearbonate (PC), poly(methyl methacrylate) (PMMA), poly(vinyl ehloride) (PVC), polydimethylsiloxane (PDMS), polyarylate (PAr) and polystirene (PS) [5, 17, 18, 20]. The solubility parameters 6 of the indieated polymers is accepted according to the data [16, 32]. The eomparison of ealeulated according to the Eqs. (4) and (29) Devalues for these polymer-solvent pairs... 

The prediction of Z) according to the Eq. (13) results is presented in Table 8 for the indicated 16 polymer-solvent pairs. As it follows from the Table 8 data, a good enough correspondence of theory and experiment is obtained. The average discrepancy between theoretical and experimental Z) values is equal to 3.9% and maximum—10.1%. In other words, such error is comparable with calculation according to the Eq. (29) error (see Table 7). 

The proportionality coefficient in the Eq. (33) can be received from the following considerations. As it is known through Ref [22], a polymer ceases to dissolve in solvent at I 6 6j >2. 5 (cal/cm ). This is the criterion for poor solvent with 8 =1.0, that allows one to accept the indicated coefficient as equal to approx. 0.4. The comparison of theoretical and experimental data of value for 18 polymer-solvent pairs has shown their good correspondence [33]. 

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