Thermodynamics of Semidilute Polymer Solutions

IRV Irvine, P. and Gordon, M., Graph-like state of matter. 14. Statistical thermodynamics of semidilute polymer solution. Macromolecules, 13, 761, 1980. 

For example, at MW = 4 X 10, c = 12 g/liter, and at MW = 5 X 10, c " = 62 g/liter. A polymer solution with concentration c > c is called a semidilute solution because mass concentration is low yet repulsive interactions between solutes are strong. Thermodynamics, viscoelasticity, and diffusion properties of semidilute polymer solutions have been studied extensively since the 1960s. 

In mixtures of low-molar-mass components, the structure of the components will not depend on concentration. However, the structure of the polymer depends on solvent concentration. At a certain polymer concentration (overlapping concentration c ), entanglements of the polymer chains will occur (semidiluted polymer solution). This effect is neglected in most thermodynamic equations. 

From the partition function the free energy Fjy follows and hence all thermodynamic quantities of interest can be estimated (entropy, chemical potential, osmotic pressure...). Ottinger applied this technique to test the osmotic equation of state for dilute and semidilute polymer solutions for N <60. Extension of this technique to off-lattice systems has also been made. ... 

In this chapter, our understanding of ideal chain conformations (Chapter 2), real chain conformations (Chapter 3), and thermodynamics (Chapter 4) will be combined to describe the conformations of polymer solutions at all concentrations and temperatures. In this chapter, the focus is on semidilute and concentrated solutions that span the large range of concentrations between dilute solutions and melts.-------------... 

The star architecture effects are more important for I q 0) than for Dc because the ratio of the corresponding correction terms, k / k — k, is large when k k. Nevertheless, the experimental Dc c/c reveals a stronger speed-up of Dc with concentration in multiarm stars compared to the semidilute linear polymer solutions. The hard core contribution to the osmotic pressure is essentially hidden in the inhomogeneous density profile and the thermodynamic properties of the star solutions are primarily determined by their polymeric character. 

There have been also some recent theoretical approaches addressing mainly the thermodynamic properties of binary and ternary polymer blends. Campos et al. (1996) extended the Flory-Huggins theory to predict the thermodynamic properties of binary polymer blends and blends in solution. Their approach was applied for PVDF/PS dry blend and in solutirm in dimethylformamide (DMF) with inclusion of an interaction functirai. It could be inferred that this blend behave as slightly incompatible under envirorunental cruiditions, in agreement with previously reported data. That incompatibility was suppressed when a low molar mass component, such as DMF, was added, reaching the semidilute regime (total... 

Beyond Semidilute Solutions. Further increase of concentration gives the concentrated regime and the melt regime. Beyond the semidilute regime, the minimal model mentioned above is not adequate, because the volume fraction is now finite and it really exerts entropic forces (53). If the static model is not in a good shape, it should be clear that we do not have a reliable minimal model for dynamics of nondilute solutions. We must take into account entanglement and direct friction as well as the hydrodynamic interactions. Thus, from the statistical thermodynamic point of view, real understanding of many polymer chain systems is still beyond our reach. 

This chapter is about semidilute solutions, c > c. We learn both thermodynamics and dynamics. The properties of semidilute solutions are drastically different from those of dilute solutions. With a mere tenfold increase in the concentration, the osmotic pressure can easily increase by a factor of several hundred. In the ideal solution, in contrast, the osmotic pressure is proportional to c. Furthermore, the overall chain motion is slow in semidilute solutions because the chains are entangled semidilute solutions of a high-molecular-weight polymer can barely flow. The solutions are highly viscous and may even behave like elastic rubber. 

A third class of new polymer integral equation theories have been proposed by Kierlik and Rosinberg. Their work is an extension of a density functional theory of inhomogeneous polyatomic fluids to treat the homogeneous phase. The Wertheim thermodynamic pertubation theory of polymerization is employed in an essential manner. Applications to calculate the intermolecular structure of rather short homopolymer solutions and melts have been made. Good results are found for short chains at high densities, but the authors comment that their earlier theory appears to be unsuited for long chains at low to moderate (semidilute) densities. ... 

CL. Strazielle Docteur s-Sciences, University of Strasbourg, France (1966). Laboratory Institut C. Sadron (CRM), CNRS, Strasbourg (since 1961). Field of interest Physicochemical properties of polymer solutions (dilute and semidilute solutions = Characterization of polymers, thermodynamic of solutions and conformation of polymers - Ternary systems Polymer - polymer - solvent and polymer - solvent - solvent. 

We do not dwell more on the thermodynamic consequences of chain interpenetration in the crowded semidilute and concentrated polymer solutions, as we will mainly focus on the translocation phenomenon involving single chains in this book. 

In recent years, studies of solutions of polymer blends and of copolymers have aroused a substantial theoretical and experimental interest. This is motivated by both numerous applications and more fundamental issues concerning the usefulness of the scaling and universality concepts to describe the thermodynamic properties and the phase transitions in these systems. In this lecture, chain interactions in dilute and semidilute solutions are reviewed and it is discussed how and when the interactions between chemically different monomers lead to a macroscopic phase separation in the case of ternary polymer A-polymer B- solvent systems and to a mesophase formation in diblock-copolymer solutions. The important conclusion is that due to both the overall monomer concentration fluctuations (excluded volume effects) and the composition fluctuations, the classical Flory theory often fails. This requires the use of the renormalization method and of scaling concepts to give a correct description of the phase diagrams and the critical phenomena observed in these complex systems. We give only here a brief outline, a complete review has been published elsewhere, ... 

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