Solubility parameters, polymer melts

The various approaches to estimating diffusion coefficients and solubilities of drugs in polymers have been reviewed. The polymers typically used for drug delivery have diffusion coefficients that are characteristic of the polymer and relatively constant for drugs of a similar molecular size. Drug solubilities in a polymer can be estimated from the solubility parameters and melting points (steroids), from the melting point alone, or from the correlation of partition coefficients. 

Many properties of pure polymers (and of polymer solutions) can be estimated with group contributions (GC). Examples of properties for which (GC) methods have been developed are the density, the solubility parameter, the melting and glass transition temperatures, as well as the surface tension. Phase equilibria for polymer solutions and blends can also be estimated with GC methods, as we discuss in Section 16.4 and 16.5. Here we review the GC principle, and in the following sections we discuss estimation methods for the density and the solubility parameter. These two properties are relevant for many thermodynamic models used for polymers, e.g., the Hansen and Flory-Hug-gins models discussed in Section 16.3 and the free-volume activity coefficient models discussed in Section 16.4. 

In the case of crystalline polymers better results are obtained using an amorphous density which can be extrapolated from data above the melting point, or from other sources. In the case of polyethylene the apparent amorphous density is in the range 0.84-0.86 at 25°C. This gives a calculated value of about 8.1 for the solubility parameter which is still slightly higher than observed values obtained by swelling experiments. 

Since polyethylene is a crystalline hydrocarbon polymer incapable of specific interaction and with a melting point of about 100°C, there are no solvents at room temperature. Low-density polymers will dissolve in benzene at about 60°C but the more crystalline high-density polymers only dissolve at temperatures some 20-30°C higher. Materials of similar solubility parameter and low molecular weight will, however, cause swelling, the more so in low-density polymers Table 10.5). 

Let us examine the connection between Pcr and gas solubility parameters. When gas content in the polymer does not change with time, gas solubility in the melt is described by Henry s Law ... 

It is possible to determine C quantitatively using Hildebrand s theory of microsolutes. An example of the accuracy that can be achieved is provided by the calculation of the solubilities of a series of p-aminobenzoate esters in hexane (17,18). Michaels, et al. (19) used this approach to estimate the solubility of steroids in various polymers. The solubilities of seven steroids in six polymers were calculated from the steroid melting points, heats of fusion, and solubility parameters. Equation 8 was derived, where Jjj is the maximum steady state flux, h is the membrane thickness, x is the product of V, the molar volume of the liquid drug, and the square of the difference in the solubility parameters of the drug and polymer, p is the steroid density, T is melting point (°K), T is the temperature of the environment, R is the gas constant, and AH and ASf are the enthalpy and entropy of fusion, respectively. 

Figure 5. Correlation of permeabilities (J ) of steroids in various polymers with their melting points (T ) and a solubility parameter term x (Reproduced with permission from Ref. 19. Copyright 1975 American Institute of Chemical Engineers.)...

Solubility can be expected if(5 -(52 is less than about 2(calcm ) / [4(Mpa) ] and there are no strong polar or hydrogen-bonding interactions in either the polymer or solvent. Crystalline polymers, however, will be swollen or softened by solvents with matching solubility parameters but will generally not dissolve at temperatures much below their crystal melting points. 

For some applications, polymers are blended to provide a balance of properties. Some polymers blend well due to mutual solubility, but if the solubility parameter of the candidate polymers is different by more than about 3 SI units, the polymers must be blended with an intermediate material to improve compatibility. Typically, this involves an intermediate polymer with a low molecular weight. In the melt, this serves to reduce the surface tension between two incompatible polymers, thus improving dispersion. Low molecular weight polyethylene is an example of a polymer blending aid. In other cases, metal stearates or salts can be used to aid dispersion. Examples include zinc stearate and calcium stearate. 

Polytetrafluoroethylene (PTFE Teflon) was discovered accidently by PlunkettCZ nd commercialized by DuPont in the 1940 s. This polymer has a solubility parameter of about 6H and a high melting point of 327°C and is not readily moldable. Poly-chlorotrifluoroethylene (CTFE, Kel-F), the copolymer of tetrafluoroethylene and hexafluoropropylene (FEP), polyvinylidene fluoride (PVDF, Kynar), the copolymer of tetrafluoroethylene and ethylene (ETFE), the copolymer of vinylidene fluoride and hexafluoroisobutylene (CM-1), perfluoroalkoxyethylene (PFA) and polyvinyl fluoride (PVF, Tedlar) are all more readily processed than PTFE. However, the lubricity and chemical resistance of these fluoropolymers is less than that of PTFE. 

Considering Table 1.16, only the first polymer, polyethylene, has non-polar contributions alone the next three have also polar components and the last, nylon-6,6, has contributions from all three forces. The largest solubility parameter for this polymer also corresponds to the highest melting point and stiffness, reflecting the importance of cohesive energy density as a measure of intermolecular forces. 

Many databases (some available in computer form) and reliable GC methods are available for estimating many pure polymer properties and phase equilibria of polymer solutions such as densities, solubility parameters, glass and melting temperatures, and solvent activity coefficients. 

Melt viscosity is critically affected by the difference in segmental solubility parameters, that is, by the interaction parameter between blocks. The deviation from normal behavior is dependent on the composition and block structure of the particular block polymer examined. It is most dramatic when the block polymer is capable of forming a three-dimensional network in the bulk state and the different polymer segments have high mutual incompatibility as evidenced by diverse solubility parameters. 

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