Copolymer-solvent systems phase behavior

For the modeling of the phase behavior of copolymer-solvent systems, the copolymer can be treated as a homopolymer with effective pure component parameters. Examples of this approach are given by McHugh and co-workers [79, 80]. The disadvantage of this approach is that the pure component polymer parameters depend on the type and composition of the copolymer. Pure component polymer parameters are obtained from binary polymer-solvent phase equilibrium data. With these parameters it is possible to model the phase behavior of the same polymer with another solvent. 

There are two different situations for the liquid-liquid equilibrium in copolymer/solvent systems (i) the equilibrium between a dilute copolymer solution (sol) and a copolymer-rich solution (gel) and (ii) the equilibrium between the pure solvent and a swollen copolymer network (gel). Only case (i) is considered here. To understand the results of LLE experiments in copolymer/solvent systems, one has to take into account the strong influence of distribution functions on LLE, because fi actionation occurs during demixing, both with respect to chemical distribution and to molar mass distribution. Fractionation during demixing leads to some effects by which the LLE phase behavior differs fi om that of an ordinary, strictly binary mixture, because a common copolymer solution is a multicomponent system. Cloud-point curves are measured instead of binodals and per each individual feed concentration of the mixture, two parts of a coexistence curve occur below or above (UCST or LCST behavior) the cloud-point curve, i.e., to produce an infinite number of coexistence data. 

Tailoring block copolymers with three or more distinct type of blocks creates more exciting possibilities of exquisite self-assembly. The possible combination of block sequence, composition, and block molecular weight provides an enormous space for the creation of new morphologies. In multiblock copolymer with selective solvents, the dramatic expansion of parameter space poses both experimental and theoretical challenges. However, there has been very limited systematic research on the phase behavior of triblock copolymers and triblock copolymer-containing selective solvents. In the future an important aspect in the fabrication of nanomaterials by bottom-up approach would be to understand, control, and manipulate the self-assembly of phase-segregated system and to know how the selective solvent present affects the phase behavior and structure offered by amphiphilic block copolymers. 

SAM Samii, A.A., Karlstrbm, G., and Lindman, B., Phase behavior of nonionic block copolymer in a mixed-solvent system, J. Phys. Chem., 95, 7887, 1991. 

Since then. Dr. Woldfarth s main researeh has been related to polymer systems. Currently, his research topics are molecular thermodynamics, continuous thermodynamics, phase equilibria in polymer mixtures and solutions, polymers in supercritical fluids, PVT behavior and equations of state, and sorption properties of polymers, about which he has published approximately 100 original papers. He has written the following books Vapor-Liquid Equilibria of Binary Polymer Solutions, CRC Handbook of Thermodynamic Data of Copolymer Solutions, CRC Handbook of Thermodynamic Data of Aqueous Polymer Solutions, CRC Handbook of Thermodynamic Data of Polymer Solutions at Elevated Pressures, CRC Handbook of Enthalpy Data of Polymer-Solvent Systems, and CRC Handbook of Liquid-Liquid Equilibrium Data of Polymer Solutions. 

Adidharma and Radosz provides an engineering form for such a copolymer SAFT approach. SAFT has successfully applied to correlate thermodynamic properties and phase behavior of pure liquid polymers and polymer solutions, including gas solubility and supercritical solutions by Radosz and coworkers Sadowski et al. applied SAFT to calculate solvent activities of polycarbonate solutions in various solvents and found that it may be necessary to refit the pure-component characteristic data of the polymer to some VLE-data of one binary polymer solution to calculate correct solvent activities, because otherwise demixing was calculated. GroB and Sadowski developed a Perturbed-Chain SAFT equation of state to improve for the chain behavior within the reference term to get better calculation results for the PVT - and VLE-behavior of polymer systems. McHugh and coworkers applied SAFT extensively to calculate the phase behavior of polymers in supercritical fluids, a comprehensive summary is given in the review by Kirby and McHugh. They also state that characteristic SAFT parameters for polymers from PVT-data lead to... 

An interesting phase behavior was observed experimentally [38] for the system poly(ethylene-co-methyl acrylate) in the solvent ethylene (Figure 10.13). Starting from low-density polyethylene, an increasing content of methyl acrylate in the copolymer shifts the demixing curve to lower pressures up to 13 mol% of methyl acrylate in the copolymer, whereas with further addition of methyl acrylate the solubility again decreases. In this case, the binary parameter is a linear function of the copolymer composition [38]. Figure 10.13 demonstrates the performance of the PC-SAFT EOS. The model is able to describe the observed dependence on temperature and molar mass as well as the nonmonotonic dependence on copolymer composition. 

At first glance, one might consider the effect of compressed CO2 on the phase behavior of multi-component polymer systems to be a simple combination of the known effects of liquid solvents and hydrostatic pressure. Solvent effects are primarily enthapic in nature and typically manifest in upper critical solution behavior. Common solvents mitigate unfavorable interactions between dissimilar segments and enhance miscibility. In blends, the addition of highly selective solvents, e.g. a non-solvent for one component, can lead to precipitation of the unfavored species at high dilution. In block copolymers, the effect of selective solvents is less clear, but studies to date reveal a collection of the solvent at the domain interface, selective dilation of one phase, and stabilization of the disordered phase via depression of the UODT. The systems we have studied each exhibit a lower critical transition. For these specific systems, previous work indicates the hydrostatic pressure suppresses free volume differences between the components and expands the region of miscibility. 

In practice, the existence of both UCST and LCST has been established for polymer-solvent systems. About 10 years ago, Schmitt discussed UCST, LCST and combined UCST and LCST behavior in blends of poly(methyl methacrylate) with poly(styrene-co-acrylonitrile) (PMMA-PSAN), Ueda and Karasz reported the existence of UCST in chlorinated polyethylene (CPE) blends using DSC, Inoue found that elastomer blends of cis-l,4-polybutadiene and poly(styrene-co-butadiene) exhibit both UCST and LCST behavior and Cong et al. (72) observed that blends of polystyrene and carboxylated poly(2,6-dimethyl-l,4-phenylene oxide) copolymers with a degree of carboxylation between molar fraction 8% and 10% exhibit both UCST and LCST behavior. They used DSC to establish the phase diagram. 

Copolymers can be mixed with other copolymers, homopolymers, or solvents. Broadly speaking, there are three general problems related to the phase behavior of these blends the microphase behavior, the interplay between microphase and macrophase separation, and micelle formation at low copolymer concentration. The mixtures sometimes form one phase, which can be either ordered or disordered, and sometimes they separate into two macrophases. In the latter case, each of the macrophases can be ordered or disordered. For example, there could be coexisting phases of spheres and cylinders. The phase behavior of a two component system can be summarized by a temperature-composition phase diagram [102,103], that of a three component system by a series of ternary phase diagrams, and so on. Space permits touching only briefly on a small sample of these possibilities in this chapter. Copolymers can also be used as surfactant in homopolymer-homopolymer blends, but that topic is beyond the scope of this chapter. 

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