Dilute polymer solutions thermodynamics

The thermodynamic behavior of the dilute polymer solution depends on three factors (1) the molecular weight, (2) the thermodynamic interaction parameters and ki, or ipi and 0, which characterize the segment-solvent interaction, and (3) the configuration, or size, of the... 

Parameter occurring in thermodynamic relations for dilute polymer solutions (Chaps. XII and XIV). 

Below a critical concentration, c, in a thermodynamically good solvent, r 0 can be standardised against the overlap parameter c [r)]. However, for c>c, and in the case of a 0-solvent for parameter c-[r ]>0.7, r 0 is a function of the Bueche parameter, cMw The critical concentration c is found to be Mw and solvent independent, as predicted by Graessley. In the case of semi-dilute polymer solutions the relaxation time and slope in the linear region of the flow are found to be strongly influenced by the nature of polymer-solvent interactions. Taking this into account, it is possible to predict the shear viscosity and the critical shear rate at which shear-induced degradation occurs as a function of Mw c and the solvent power. 

W. H. Stockmayer, Problems of the statistical thermodynamics of dilute polymer solutions, Makromol. Chem. 35, 54 (1960). 

A characteristic feature of a dilute polymer solution is that its viscosity is considerably higher than that of either the pure solvent or similarly dilute solutions of small molecules. The magnitude of the viscosity increase is related to the dimensions of the polymer molecules and to the polymer-solvent interactions. Viscosity measurements thus provide a simple means of determining polymer molecular dimensions and thermodynamic parameters of interactions between polymer and solvents. These aspects will also be considered in a later part of this chapter. 

Other thermodynamic parameters can be obtained from osmotic pressure. For example, the chemical potential of the solvent in the solution is given by -x/rtV,. From the foregoing discussion, it is evident that the thermo(% namic behavior of the dilute polymer solution depends on the following factors ... 

G. C. Berry and E. F. Casassa, Thermodynamic and hydrodynamic behavior of dilute polymer solutions, Macromol. Rev. 4, I (1970). 

D. Patterson, Thermodynamics of non-dilute polymer solutions. Rubber Chem. Technol. 40, 1 (1967). 

Vapor-pressure osmometry is, from its name, compared with membrane osmometry by considering the vapor phase to act like the semipermeable membrane, however, from its principles it is based on vapor pressure lowering or boiling temperature elevation. Sinee the direct measure of vapor pressure lowering of dilute polymer solutions is impractieal because of the extreme sensitivity that is required, VPO is in widespread use for oligomer solutions (Mn less than 20,000 g/mol) by employing the thermoeleetrie method as developed by Hill in 1930. In the thermoelectric method, two matched temperature-sensitive thermistors are placed in a chamber that is thermostated to the measuring temperature and where the atmosphere is saturated with solvent vapor. If drops of pure solvent are placed on both thermistors, the thermistors will be at the same temperature (zero point ealibration). If a solution drop is placed on one thermistor, a temperature differenee AT oeeurs whieh is caused by condensation of solvent vapor onto the solution drop. From equilibrium thermodynamics follows that this temperature increase has its theoretical limit when the vapor pressure of... 

TREF was developed before Crystaf. In TREF, a very dilute polymer solution (TCB is generally the solvent of choice) is transferred at high temperature to a column packed with an inert support. The polymer solution is then cooled very slowly, typically from 120-140°C to room temperature. As the temperature decreases, chains with higher crystallization temperatures crystallize and precipitate, followed by chains with lower crystallization temperatures. Crystallization is the most important step in TREF. A slow cooling rate (2.0-6.0°Ch is a recommended range) allows the polymer chains to crystallize near thermodynamic... 

Flory s analysis focuses on the thermodynamic interactions between polymers, and defines the theta point at the critical polymer concentration for phase separation (equal to the critical concentration of chain units within a single chain upon collapse transition), similar to the Boyle point of the non-ideal gas. We can perform Virial expansion on the osmotic pressure of dilute polymer solutions, as... 

Flory PJ (1965) Statistical thermodynamics of liquid mixtures. J Am Chem Soc 87 1833-1838 Flory PJ (1970) Thermodynamics of polymer solutions. Faraday Discuss Soc 49 7-29 Flory PJ (1982) Treatment of disordered and ordered systems of polymer chains by lattice methods. Proc Natl Acad Sci USA 79 4510-4514 Flory PJ, Krigbaum WR (1950) Statistical mechanics of dilute polymer solutions II. J Chem Phys 18 1086-1094... 

Some implicit databases are provided within the Polymer Handbook by Schuld and Wolf or by Orwoll and in two papers prepared earlier by Orwoll. These four sources list tables of Flory s x-fiinction and tables where enthalpy, entropy or volume changes, respectively, are given in the literature for a large number of polymer solutions. The tables of second virial coefficients of polymers in solution, which were prepared by Lechner and coworkers (also provided in the Polymer Handbook), are a valuable source for estimating the solvent activity in the dilute polymer solution. Bonner reviewed vapor-hquid equilibria in concentrated polymer solutions and listed tables containing temperature and concentration ranges of a certain number of polymer solutions. Two CRC-handbooks prepared by Barton list a larger number of thermodynamic data of polymer solutions in form of polymer-solvent interaction or solubility parameters." ... 

Many attempts have been made to find theoretical explanations for the non-ideal behavior of polymer solutions. There exist books and reviews on this topic, e.g., Refs. " " Therefore, only a short summary of some of the most important thermodynamic approaches and models will be given here. The following explanations are restricted to concentrated polymer solutions only because one has to describe mainly concentrated polymer solutions when solvent activities have to be calculated. For dilute polymer solutions, with the second virial coefficient region, Yamakawa s book provides a good survey. 

The treatment presented here devolves from the thermodynamics of dilute polymer solutions developed by Huggins [25, 26] and by Flory [27-29], now... 

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