Temperature-composition phase diagram polymer solution

Figure 2. Temperature-composition phase diagram for a polymer solution. T = (T - 0)/0...

The binodal and spinodal data of Fig. 4.4 are presented in the temperature-composition phase diagram in Fig. 4.5. This kind of phase diagram is typical of mixtures of small-molecule substances and also in many cases of mixtures of polymers and small-molecule substances. The spinodal and binodal curves meet in the so-called upper critical solution temperature (UCST). At temperatures greater than the UCST miscibility occurs at all compositions. The critical solution temperature is obtained by applying the following condition on the mixing free energy... 

The melting point Tm is computed by solving this equation iteratively. It is often convenient to use Ec/(kBTm) as our unit of (inverse) temperature. The phase diagram of the polymer solution then depends on the molecular parameters r, q, B/Ec, and Ep/Ec, the composition parameters n and 2, and on the temperature parameter Ec/(kBTm). 

The line on the temperature vs. composition phase diagram for a mixture of two components, which separates the metastable region from the single-phase regions. Hence, it represents the limits of stability in a two-phase system, viz., a polymer solution or polymer blend. 

In addition to the molecular weight of the free polymer, there axe other variables, such as the nature of the solvent, particle size, temperature, and thickness of adsorbed layer which have a major influence on the amount of polymer required to cause destabilization in mixtures of sterically stabilized dispersions and free polymer in solution. Using the second-order perturbation theory and a simple model for the pair potential, phase diagrams relat mg the compositions of the disordered (dilute) and ordered (concentrated) phases to the concentration of the free polymer in solution have been presented which can be used for dilute as well as concentrated dispersions. Qualitative arguments show that, if the adsorbed and free polymer are chemically different, it is advisable to have a solvent which is good for the adsorbed polymer but is poor for the free polymer, for increased stability of such dispersions. Larger particles, higher temperatures, thinner steric layers and better solvents for the free polymer are shown to lead to decreased stability, i.e. require smaller amounts of free polymer for the onset of phase separation. These trends are in accordance with the experimental observations. 

Experimentally, the interaction parameter is most conveniently changed by varying temperature T [see Eq. (4.31)]. Phase diagrams are typically plotted in the temperature - composition plane. Examples of phase dia-grams for a polymer blend and a polymer solution are shown ... 

From a thermodynamic point of view, phase diagrams may be constructed by changing the temperature (ii), pressure (12). or composition of a material. The present experiments are concerned with changes in composition at constant temperature and pressure, leading to a ternary phase diagram with polymer network I at one corner, monomer II at the second corner, and polymer network II at the third corner. According to classical concepts, at first there should be a mutual solution of monomer II in network I, followed by the binodal (nucleation and growth kinetics) and finally the spinodal (spinodal decomposition kinetics). 

Thermogelation of a Two-Component Mixture. The simplest procedure for obtaining a microporous system is the thermogelation of a two component mixture. At a specific temperature, the mixture forms a homogeneous solution for all compositions but at a tower temperature shows a miscibility gap over a wide range of compositions. This behaviour is illustrated schematically in Figure 1, which shows a phase diagram of a two component mixture of a polymer and a solvent as a function of temperature. 

Figure 1.28. A phase diagram for a (hypothetical) polymer-solvent or pol5mier-polymer system showing both lower (LCST) and upper (UCST) critical solution temperatures. The boundary may be determined by locating the cloud point as a function of temperature for a fixed composition as the system moves from being a single-phase system to being a two-phase system and vice versa.

In a miscible system of two liquids it is not expected that they will remain as a single phase over all ranges of composition and temperature. Instead there will be cloud points where two phases occur and the composition of the separated material will be close to that of the original pure components. Even in so-called two-phase systems there will be a partitioning of one component in the other corresponding to a small solubility at the particular temperature. An example of a phase diagram that may occur for two liquids, a polymer solution or a polymer blend is shown in Figure 1.28. 

This figure clearly shows the temperature and composition windows where it is either a two-phase system or a single-phase system. The characteristic features of an upper critical solution temperature (UCST) and a lower critical solution temperature (LCST) corresponding to the phase transition are identified. For a particular composition of two immiscible polymers, if the temperature is increased, the UCST is the highest temperature at which two phases may co-exist in the blend. There is then a window of miscibility as the temperature is increased further, followed by phase separation again at the LCST. This type of diagram is often seen for polymer solutions, e.g. polystyrene in cyclohexane. Often polymer blends show... 

In general, the miscibility of a pair of polymers depends on temperature and composition. Figure 10.1 schematically shows three typical phase diagrams. The ordinate and the abscissa axes represent temperature and composition, respectively. The solid line in Fig. 10.1(a), below which the blend becomes immiscible (two-phase), is referred to as an upper critical solution temperature (UCST). However, Fig. 10.1(b) shows a lower critical solution temperature (LCST) behavior. Some polymer pairs display both UCST and LCST as shown in Fig. 10.1(c). As will be shown in the following, UCST is rarely observed for a polymer blend. 

Fig. 10.1. Schematic illustration of a phase diagram for a polymer blend, showing (a) upper critical solution temperature (UCST) (b) lower critical solution temperature (LCST) and (c) UCST + LCST. Ordinate and abscissa show temperature and composition, respectively.

Sophiea et al. published the first classical composition-temperature phase diagram, working with the semi-IPN net-polyurethane-mter-poly(vinyl chloride) [Sophiea et al., 1994b]. They found a lower critical solution temperature, LCST = 120°C below this temperature the system was one-phased, and above, two-phased. Such behavior is now known to be characteristic of most polymer blends (see Chapter 2). 

Liquid-liquid demixing in solutions of polymers in low molar mass solvents is not a rare phenomenon. Dembcing depends on concentration, temperature, pressure, molar mass and molar mass distribution function of the polymer, chain branching and end groups of the polymer, the chemical nature of the solvent, isotope substitution in solvents or polymers, chemical composition of copolymers and its distributions, and other variables. Phase diagrams of polymer solutions can therefore show a quite complicated behavior when they have to be considered in detail (see Ref la). 

At a given pressure and temperature, the total Gibbs free energy of mixing of a one-phase polymer-solvent system of composition 2 should be necessarily minimum, otherwise the system will separate into two phases of different composition, as it is represented in a typical AG versus cp phase diagram of a binary solution (Fig. 25.3). The volume fractions at the minima (dAGIdcp = 0), cp, and (p will vary with temperature (binodal) up to critical conditions (T and (p ) where cp = tp" (Fig. 25.3b). 

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