Phases behavior

The knowledge of the phase behavior of surfactants or polymers in water or in oils is a basic understanding of the properties of these systems, and it is very important for surfactant industrial applications. It has been found that depending on the temperature or composition, the surfactants form a variety of self-assembled structures in water and oils or in both [54-63]. In comparison to the aqueous systems, the surfactant/oil systems offer less variety of self-assembled structures [9, 64—68]. In the following sections, the phase behavior of mono- and diglycerol fatty acid esters in a variety of organic oils will be described. 

Phase Behavior oT Monoglycerol Fatty Acid Ester/Oil Systems 

The phase behavior of monoglycerol fatty acid esters with different alkyl chain length in liquid paraffin oil, squalane, and squalene is described first, then the phase behavior in the dilute regions of the monoglycerol fatty acid esters in linear chain alkanes is discussed. This section is based on Ref. [64], and [69], respectively. 

Understanding surfactant phase behavior is important because it controls physical properties such as rheology and freeze-thaw stability of formulations. It is also closely related to the ability to form and stabilize emulsions and microemulsions. Micelles, vesicles, mi-croemulsions and liquid crystal phases have all been used as delivery vehicles for perfumes or other active ingredients. 

Few studies exist for ionic silicone surfactants. Several trisiloxane anionic, cationic and zwitterionic surfactants have been found to form micelles, vesicles and lamellar liquid crystals. As would be expected, salt shifts the aggregates toward smaller curvature structures [40]. 

The aggregation behavior of AB silicone surfactants in nonpolar oils including several hydrocarbon oils has been reported by Rodriguez [46]. They found that inverse micelles were formed in all oils, adjacent to the inverse cubic phase formed by the neat copolymers and by concentrated mixtures of copolymer and oil. The CMC depended strongly on the length of the pEO chain but only weakly on the pDMS chain. Inverse hexagonal phase was also observed. 

To demonstrate the general freezing behavior of a binary mixture, we present the solid-liquid phase diagram for systems of ethanol and water at 1 atm in Fig. 8.1. The solid line with the filled symbols is the freezing curve of water in the mixture. Above the curve the solution is completely liquid below the curx-e, it is a liquid mixture coexists with solid water (i.e., ice). At this pressure, pure water freezes at 273.15 K. As ethanol is added to the solution, the temperature at which ice begins to form in gradually decreases. 

The dotted line with the open symbols on the right side of the diagram is the freezing curve of ethanol in tire mixture. As one passes downward through this curve, solid ethanol precipitates from the solution. Note that the temperature at which ethanol begins to freeze decreases as the amount of water in the solution increases. Therefore, we see that the addition of impurities decreases the freezing temperature of a substance. This phenomena is known as freezing point depression. 

The point where the two freezing curves intersect with each other is called the eutectic point. This is the lowest temperature at which a binary mixture can remain in liquid without either of its components precipitating. 

Finally, we note that below the dotted line in Fig. 8.1 the system exists as two coexisting solid phases one consisting of pure ice, and the other composed of pure solid ethanol. The relative amounts of these two phases is given by the lever rule. 

In addition to these lattices composed of spheres, cylinders and layers, under special conditions periodic structures occur where both phases are continuous. In the example presented in the figure both have the symmetry of a 

To be sure, the figure depicts the structures observed for polystyrene-6Zocfc-polyisoprene, but these are quite typical. Spherical, cylindrical and layer-like domains are generally observed in all block copolymers. Less is known about how general special types like the OBDD lattices are. Observations are rare, since these exist in small regions only, positioned in-between the extended stability ranges of the major structures. 

The majority of synthesized compounds are di-block copolymers composed of one A- and one B-chain, however, tri-blocks and multiblocks, comprising an arbitrary number of A- and B-chains, can be prepared as well. One can also proceed one step further and build up multiblocks which incorporate more than two species, thus again increasing the variability. The question may arise as to if all these modifications result in novel structures. In fact, this is not the case. The findings give the impression that at least all block copolymers composed of two species exhibit qualitatively similar phase behaviors. Changes then occur for ternary systems. For the latter, the observed structures still possess periodic orders, but the lattices are much more complex. Here, we shall only be concerned with the simplest systems, the di-block copolymers. 

from the same A- and B-chains, a symmetric di-block copolymer is formed, the transition between the homogeneous phase and the microphase-separated 

The complete phase-diagram of a block copolymer is displayed in Fig. 3.40 in a schematic representation. Variables are the volume fraction of the A-blocks 

To conclude this section we will simply note that the relationship given above in Equation 11-36 does not work well for polymer solutions. A comparison of calculated values of x to those obtained experimentally has led to the suggestion that a fudge factor df about 0.34 be included (Equation 11-39)  

A more general approach is to consider the Flory x parameter to be a free energy term that has the form (Equation 11-40)  

Coleman and P. C. Painter, Miscible Polymer Blends, CD-ROM. DEStech Publications, Lancaster, PA (2006). 

Now we turn our attention to the phase behavior of polymer solutions and blends and the questions we asked right at the beginning of this chapter will a particular polymer dissolve in a given solvent or mix with another chosen polymer  

It makes things easier to see if we consider the free energy on a per mole of lattice sites basis by dividing the Flory-Huggins expression for the free energy by the number of moles of lattice sites, VI V. Recall that the 

The change in the volume upon mixing for an ideal mixture is 

These are well-established thermodynamic relations that describe the properties of mixing as a function of the molar fractions of mixing components. Typically, these relations are presented in an ad hoc manner in thermodynamics textbooks. In this section, we have demonstrated that they can be naturally derived from first principles of statistical mechanics. Properties of non-ideal mixtures can also be derived, but, as expected, the derivations, which include particle interactions, quickly become cumbersome. The interested reader is referred to the literature at the end of the chapter for more details. 

Typical pressure-volume isotherms of real fluids are shown in Fig. 10.2. For temperatures higher than the critical temperature, the fluid exists in 

For temperatures below the critical pressure, there are ranges of values of the system volume where there are two distinct phases, a high-density liquid phase and alow-density gas phase, as illustrated in Fig. 10.3. How can this behavior be explained in terms of molecular interactions  

At temperatures higher than a characteristic temperature, Tc, the critical temperature, the vdW pressure isotherms monotonically decrease with the molar volume. The slope of the curve is always negative 

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To illustrate, predictions were first made for a ternary system of type II, using binary data only. Figure 14 compares calculated and experimental phase behavior for the system 2,2,4-trimethylpentane-furfural-cyclohexane. UNIQUAC parameters are given in Table 4. As expected for a type II system, agreement is good. 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

R. G. Laughlin, The Aqueous Phase Behavior of Surfactants, Academic, London, 1994. 

These fascinating bicontinuous or sponge phases have attracted considerable theoretical interest. Percolation theory [112] is an important component of such models as it can be used to describe conductivity and other physical properties of microemulsions. Topological analysis [113] and geometric models [114] are useful, as are thermodynamic analyses [115-118] balancing curvature elasticity and entropy. Similar elastic modulus considerations enter into models of the properties and stability of droplet phases [119-121] and phase behavior of microemulsions in general [97, 122]. 

An essential component of cell membranes are the lipids, lecithins, or phosphatidylcholines (PC). The typical ir-a behavior shown in Fig. XV-6 is similar to that for the simple fatty-acid monolayers (see Fig. IV-16) and has been modeled theoretically [36]. Branched hydrocarbons tails tend to expand the mono-layer [38], but generally the phase behavior is described by a fluid-gel transition at the plateau [39] and a semicrystalline phase at low a. As illustrated in Fig. XV-7, the areas of the dense phase may initially be highly branched, but they anneal to a circular shape on recompression [40]. The theoretical evaluation of these shape transitions is discussed in Section IV-4F. 

Orkoulas G and Panagiotopoulos A Z 1999 Phase behavior of the restricted primitive model and square-well fluids from Monte Carlo simulations in the grand canonical ensemble J. Chem. Phys. 110 1581... 

Muller M and Sohiok M 1998 Caloulation of the phase behavior of lipids Phys. Rev. E 57 6973... 

Larson R G 1996 Monte Carlo simulations of the phase behavior of surfaotant solutions J. Physique 116 1441... 

Stadler C and Sohmid F 1999 Phase behavior of grafted ohain moleoules influenoe of head size and ohain length J. Chem. Phys. 110 9697... 

Janert P Kand Sohiok M 1997 Phase behavior of ternary homopolymer/diblook blends miorophase unbinding in the symmetrio system Macromolecules 30 3916... 

Fluse D A and Leibler S 1988 Phase behavior of an ensemble of noninterseoting random fluid films J. Physique 49 605... 

Veerman J A C and Frenkei D 1992 Phase-behavior of disk-iike hard-oore mesogens Phys.Rev. A 45 5632-48... 

Most of the envisioned practical applications for nonlinear optical materials would require solid materials. Unfortunately, only gas-phase calculations have been developed to a reliable level. Most often, the relationship between gas-phase and condensed-phase behavior for a particular class of compounds is determined experimentally. Theoretical calculations for the gas phase are then scaled accordingly. 

Solids can be crystalline, molecular crystals, or amorphous. Molecular crystals are ordered solids with individual molecules still identihable in the crystal. There is some disparity in chemical research. This is because experimental molecular geometries most often come from the X-ray dilfraction of crystalline compounds, whereas the most well-developed computational techniques are for modeling gas-phase compounds. Meanwhile, the information many chemists are most worried about is the solution-phase behavior of a compound. 

PHARMSEARCH Phase behavior Phase change recording Phase contrast Phase diagram Phase diagrams... 

For nonionic amphiphiles, the effects of temperature on the phase behavior are large and the effects of inorganic electrolytes are very small. However, for ionic surfactants temperature effects are usually small, but effects of inorganic electrolytes are large. Most common electrolytes (eg, NaCl)... 

Basic Thermodynamics. Equilibrium-phase behavior of mixtures is governed by the free energy of mixing and how this quantity, consisting of enthalpic... 

Equatioa-of-state theories employ characteristic volume, temperature, and pressure parameters that must be derived from volumetric data for the pure components. Owiag to the availabiHty of commercial iastmments for such measurements, there is a growing data source for use ia these theories (9,11,20). Like the simpler Flory-Huggias theory, these theories coataia an iateraction parameter that is the principal factor ia determining phase behavior ia bleads of high molecular weight polymers. 

Ternary Blends. Discussion of polymer blends is typically limited to those containing only two different components. Of course, inclusion of additional components may be useful in formulating commercial products. The recent Hterature describes the theoretical treatment and experimental studies of the phase behavior of ternary blends (10,21). The most commonly studied ternary mixtures are those where two of the binary pairs are miscible, but the third pair is not. There are limited regions where such ternary mixtures exhibit one phase. A few cases have been examined where all three binary pairs are miscible however, theoretically this does not always ensure homogeneous ternary mixtures (10,21). 

A variety of experimental techniques have been used to prepare and characterize polymer blends some of the mote important ones for estabHshing the equiHbtium-phase behavior and the energetic interactions between chain segments ate described here (3,5,28,29). 

The hterature contains extensive reports on investigations of the equiUbrium-phase behavior for an enormous number of polymer—polymer pairs (1,97). The number of blends known to be miscible has grown so rapidly since the mid-1980s that it is more instmctive to attempt to understand these observations in terms of the molecular stmctures of the components rather than to catalog them. 

One proposed approach (75) to modeling the phase behavior for hydrogen bonding pairs uses the following expression for the free energy of mixing (eq. 7). 

Table 1. Phase Behavior of Halogenated Polymers With Families of Polymers Containing Ester Units, ...

Fig. 5. Phase behavior of blends of a styrene—acrylonitrile copolymer containing 19 wt % of acrylonitrile with other SAN copolymers of varying AN content and as a function of the molecular weight of the two copolymers (° ) one-phase mixture ( ) two-phase mixtures as judged by optical clarity. Curve...

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