Coefficient, polymer- solvent expansion

There are some smdies (23,24) which link the magnitude of the Huggins and Sehulz-Blasehka coefficients to the coefficient of polymer- solvent expansion,, of the Fox and Flory treatment of polymer coil properties (25). 

In addition, hybrid materials have been made by doping diketonate cluster complexes of lanthanide hydroxide into organic polymers. The resulting materials exhibit lowered coefficients of thermal expansion, increased moduli, reduced solvent sensitivity while preserving acceptable thermal and mechanical properties [110]. 

The data shown in Table 1.1 were experimentally determined from solutions under 0-temperature conditions. This involves measuring the properties when a solution has the characteristic properties which allow the polymer chain to approach ideality most closely. When a polymer chain is in solution the coil will expand due to polymer-solvent interactions and an expansion coefficient, a, is defined so that the actual mean square end-to-end distance [/ rms]act becomes... 

If the difference between the coefficients of thermal expansion of the solvent above and below Tgs is unknown, Equation 3.7 can be used to provide a first estimate by substituting the quantities referring to the solvent instead of those referring to the polymer into this equation. This procedure amounts to making the assumption that the free volume arguments underlying Equation 3.7 are just as valid for simple molecular liquids as they are for amorphous polymers. If this assumption is made, Equation 6.12 is simplified into Equation 6.13 which should only be used if the necessary thermal expansion data are unavailable for the solvent. 

We have a dilemma we need a high-quality solvent to insure that the polymer remains in solution when it is formed but we need a solvent whose quality can be easily adjusted to induce the polymer to drop out of solution. How can we resolve it First, we need to know the thermodynamic variables that cause the occurrence of an LCST (chapter 3). The key variable in this instance is the chemical nature of the solvent or, to a first approximation, the critical properties of the solvent. Decreasing the solvent quality shifts the LCST curve to lower temperatures, and it is this variable that we wish to manipulate to force the polymer out of solution. To demonstrate the effect of solvent quality on the location of the LCST curve, consider the difference in LCST behavior for the same polymer, polyisobutylene, in two different solvents, n-pentane and cyclooctane. The LCST curve for the polyisobutylene-rt-pentane system begins at 70°C, while for the polyisobutylene-cyclooctane system it begins at 300°C (Bardin and Patterson, 1969). Cyclooctane, which has a critical temperature near 300°C, is a much better solvent than n-pentane, which has a critical temperature near 200°C, probably because cyclooctane has a greater cohesive energy density that translates into a lower thermal expansion coefficient, or equivalently, a lower free volume. Numerous examples of LCST behavior of polymer-solvent mixtures are available in the literature, demonstrating the effect of solvent quality on the location of the LCST (Freeman and Rowlinson, 1960 Baker et al., 1966 Zeman and Patterson, 1972 Zeman et al., 1972 Allen and Baker, 1965 Saeki et al., 1973, 1974 Cowie and McEwen, 1974). 

Volumetric data can be essential in the thermodynamic treatment of the "polymer-solvent" interaction process. The lack of them for many important fibrous proteins is due to the difficulty of measuring the density, at controlled temperature and hydration degree, for these systems. As far as elastin is concerned, it has been reported that when completely hydrated this protein has a negative and very large coefficient of thermal expansion (15), a result which has been interpreted as evidence of a hydrophobic character of the protein (16). 

Polymer-solvent interactions have been examined by viscometric studies of polymer-solvent-non-solvent mixtures in dilute solution84 86). The Fox-Flory model which relates the molecular parameters of the unperturbed dimension and the linear expansion coefficient to the total sorption parameter has been used. The latter can be obtained by the simultaneous solution of several Equations when the intrinsic viscosities of the mixtures are known. This method is in an early stage of development and pro-... 

Expansion Factor The second virial coefficient, A2, is a measure of solvent-polymer compatibility. Thus, a large positive value 0/A2 indicates a good solvent for the polymer favoring expansion of its size, while a law value (sometimes even negative) shows that the solvent is relatively poor. The value of A2 will thus fell... 

When the actual experimental temperature used is equal to 6, xi = 1/2, at which point all excess contributions to the solution thermodynamics disappear and the solution exhibits ideal behaviour since the second virial coefficient has a value of zero. At this point the excluded volume effects that cause an expansion of the polymer molecule are exactly balanced by the unfavourable polymer-solvent interactions and the molecule adopts imperturbed, random walk dimensions. The influence on polymer dimensions and the highly detailed theories of polymer configuration in relation to the excluded volume parameter are beyond the scope of this book but are extensively covered by Yamakawa (1971) and to some extent by des Cloizeaux and Jannink (1990). 

The second osmotic virial coefficient of the expansion, A2, is a measure of the thermodynamic quality of the solvent for the polymer and accounts for binary... 

Stress evolution in polymers stems fi om a number of factors in addition to mismatched coefficients of thermal expansion. Curing-induced shrinkage, contraction due to the evaporation of solvents and volatile by-products, and relaxation accompanying physical aging are three examples. Stress concentration near topographically sharp features, viscoelasticity, competition between curing kinetics and thermal processing history, as well as ambient environment further complicate the issue. 

Usp = ass + A.a. For negative Aa the polymer-polymer interaction was more repulsive than the polymer-solvent interaction, and the polymers were observed to swell to v 0.61. The opposite case of positive Aa saw the polymers collapse to v 0.31 (theory 1/3). A smooth transition between the two extremes was observed by varying Aa. Defining the expansion coefficient k = Rg/Rg, with Rg the radius of gyration in the theta solvent, a qualitative agreement was found with Flory s expression. 

Mahabadi and O Driscoll also studied the effect of dissolved polymer upon the termination rate coefficient [82, 83]. They derived a theoretical relationship for the dependence of kt upon conversion [82], based on a previously derived segmental diffusion model [100] that allowed for a concentration dependent linear expansion coefficient and polymer-solvent interactions. Also Mahabadi and O Driscoll pointed out that the rate of segmental diffusion would increase if the segment density gradient was increased as a result of coil shrinkage. In a simplified form, the dependence of kt upon polymer concentration, C, could be represented by ... 

Liquid Ciystailine Polymers (LCPs) are of considerable into-est inasmuch as their inherent molecular ordering has dramatic consequences on their macroscopic properties. LCPs are utilized in many high performance applications due to their superior strength and stiffness, excellent solvent resistance, low coefficient of thermal expansion, and low viscosity, Since molecular alignment affects the macroscopic properties and is easily achieved during flow, the rheology and relation between an applied flow field and molecular orientation of LCPs are an area of great interest. " Over twenty years ago, Kiss and Porter discovered the unique phenomenon of a... 

---