Flory-Huggins type solution theory

The role of asphaltene deposition in miscible flooding processes is also examined. Experimental data together with coupled equation of state models and Flory-Huggins polymer solution theory have been used to illustrate the effect of various parameters such as solvent type, solvent/oll ratio and pressure on the amount of asphaltene precipitation during addition of solvents to heavy oil. 

The deficiencies of the Flory-Huggins theory result from the limitations both of the model and of the assumptions employed in its derivation. Thus, the use of a single type of lattice for pure solvent, pure polymer and their mixtures is clearly unrealistic since it requires that there is no volume change upon mixing. The method used in the model to calculate the total number of possible conformations of a polymer molecule in the lattice is also unrealistic since it does not exclude self-intersections of the chain. Moreover, the use of a mean-field approximation to facilitate this calculation, whereby it is assumed that the segments of the previously added polymer molecules are distributed uniformly in the lattice, is satisfactory only when the volume fraction (f>2 of polymer is high, as in relatively concentrated polymer solutions. 

One can see that when p = I, this equation can be reduced to the Flory-Huggins-Scott equation for binary polymer blends. The lattice fluid theory can predict both UCST and LOST (lower critical solution temperature) types of phase diagrams for polymer blends, with further considerations of speciflc interactions (Sanchez and Balazs 1989), see more introductions about LOST in Sect. 9.1. 

The infortnation provided in this chapter can be divided into four parts 1. introduction, 2. thermodynamic theories of polymer blends, 3. characteristic thermodynamic parameters for polymer blends, and 4. experimental methods. The introduction presents the basic principles of the classical equilibrium thermodynamics, describes behavior of the single-component materials, and then focuses on the two-component systems solutions and polymer blends. The main focus of the second part is on the theories (and experimental parameters related to them) for the thermodynamic behavior of polymer blends. Several theoretical approaches are presented, starting with the classical Flory-Huggins lattice theory and, those evolving from it, solubility parameter and analog calorimetry approaches. Also, equation of state (EoS) types of theories were summarized. Finally, descriptions based on the atomistic considerations, in particular the polymer reference interaction site model (PRISM), were briefly outlined. 

Gibbs principle of multiple phase equihbria is applied to model polymer solutions to explore the possible types of heterophase coexistence and phase transitions. The fundamental properties of dilute polymer solutions and hquid-hquid phase separation driven by van der Waals-type interaction is reviewed within the framework of Flory-Huggins theory. No specific molecular interactions are assumed. Refinement of the polymer-solvent contact energy beyond Flory-Huggins description is attempted to study the glass transition of polymer solutions at low temperatures. The scaling description of semiconcentrated polymer solutions is summarized. 

The same positive AH, which arises from interactions between different species, usually prevails in polymer mixtures and most polymer pairs are mutually immiscible. The strengths of the interactions between components is usually expressed in terms of an interaction parameter Xab (Eq- 3), which originates from Flory-Huggins theory of polymer solutions. The enthalpy of mixing, or interaction energy term, arises in a van Laar type expression of heats of mixing and is of the form... 

Phase Diagrams. The phase diagrams reported so far in Figures 2, 3, and 5 refer to UCS behavior. These types of phase equilibria are those predicted on the basis of the Flory-Huggins theory and are observed experimentally for solutions of small molecules as well as polymer solutions. This situation implies that mixing is favored by heating and that it is accompanied by a decrease of the interaction parameter, while cooling may lead to a two-phase system. 

In the case of copolymer solutions, the melting temperature also depends on interactions between the different monomeric imits and the solvent. Considering the case in which the crystalline phase is pure (i.e., only monomeric units of a single type crystallize and no solvent is present in the lattice), the decrease in the melting temperature can be derived in a similar manner as for the homopolymer solution case using the Flory-Huggins theory with an appropriate modification [15]. To take into accoimt the interactions between both comonomers and solvent, the net interaction parameter for binary copolymers should be calculated as follows ... 

Linear alkane solutions of 60a (n = 300, M = 3.1 x 10", Mw/Mn = 1.15) showed highly sensitive UCST-type phase separation irrespective of the solvent [222]. Interestingly, the cloud point temperature of 60a increased linearly with the number of carbon atoms in the alkane, which is in reasonable agreement with the Flory-Huggins theory. Similar phase separation occurred for poly(vinyl ether)s with various pendant groups, such as alkyl (in alcohols and esters), ester (in alcohols and toluene), and silyloxy groups (in alcohols). The combination of polymer and solvent was the decisive factor in sensitive phase separation. Nonpolar polymers underwent phase separation in polar solvent, and polar ones became thermosensitive in nonpolar media. 

When one tries to account for real polymer systems in terms of models of the type of Eqs. (1.1)-(1.8) the situation is rather unsatisfactory however, when one fits data on the coexistence curve or on (0 (AF/kBT)/0(() )j., the latter quantity being experimentally accessible via small angle scattering, one finds that one typically needs an effective y-parameter that does not simply scale proportional to inverse temperature, as Eq. (1.5) suggests. Moreover, there seems to be a pronounced (])-dependence of x, in particular for (]) — 1. Near (]) = (]) ", on the other hand, there are critical fluctuations (which have been intensely studied by Monte Carlo simulations [11-13,15] and also in careful experiments of polymer blends [16-18] and polymer solutions [19]). Sometimes in the literature a dependence of the x parameter on pressure [18] or even chain length is reported, too. Thus, there is broad consensus that the Flory-Huggins theory and its closely related extensions [20] are too crude as models to provide predictive descriptions of real polymer solutions and blends. A more promising approach is the lattice cluster approach of Freed and coworkers [21-23], where effective monomers block several sites on the lattice and have complicated shapes to somehow mimic the local chemical structure. However, this approach requires rather cumbersome numerical calculations, and is still of a mean-field character, as... 

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