Liquid-expanded solid state

Most of us think of matter as being segregated into one of three states gas, liquid, or solid. Gases flow easily and expand to fill their container. Liquids also flow, but they take the shape of their container and have a fixed volume. Solids have a fixed shape and do not flow. As a general rule, polymers do not fall neatly into any of these categories. Most uncrosslinked (or lightly crosslinked) polymers do not behave exactly either as liquids or solids. Their behavior has characteristics of both liquid and solid states. We call this state the viscoelastic state, the same term we applied to certain solutions in Chapter 6. 

Their derivation consisted in expanding the pressure in a power series of the parameter A, and was valid only for small values of A. The procedure which will now be adopted in this paper is not so refined as de Boer and Blaisse s theory, but it will not be required that A is small. The procedure is the same as that adopted by Prigogine and Philippot27 in their theory of energies of liquid helium, and it will be applied to other liquids than liquid helium. These substances are, of course, solid at 0° K except for helium. However, it will be assumed that the same method can be applied to these substances in the following treatment, considering the comparative crudeness of our theory which does not discriminate between liquid and solid states. 

Gas A state of matter in which the material has a very low density and viscosity, can expand and contract greatly in response to changes in temperature and pressure, easily diffuses into other gases, and readily and uniformly distributes itself throughout any container. A gas can be changed to the liquid or solid state only by the combined effect of increased pressure and decreased temperature below the critical temperature). 

The phenomenon of phase transitions in two dimensions is of great fundamental interest and has therefore drawn a considerable amount of attention.i 2 insoluble monomolecular layers at a water-air interface provide a quite ideal two-dimensional model system with an isotropic substrate and an easily controllable density of molecules. At low densities they often exhibit a two-dimensional gas behavior,3 whereas at higher densities transitions to liquid and solid states can be found. In many systems, the liquid phase is further divided into the so-called liquid-expanded (LE) and liquid-condensed (LC) phases.4 Though observed and intensively studied, the nature of the LE-LC phase transition is still controversial. 

L. The liquid-expanded, L phase is a two-dimensionally isotropic arrangement of amphiphiles. This is in the smectic A class of liquidlike in-plane structure. There is a continuing debate on how best to formulate an equation of state of the liquid-expanded monolayer. Such monolayers are fluid and coherent, yet the average intermolecular distance is much greater than for bulk liquids. A typical bulk liquid is perhaps 10% less dense than its corresponding solid state. 

Again, if we consider the initial substances in the state of liquids or solids, these will have a definite vapour pressure, and the free energy changes, i.e., the maximum work of an isothermal reaction between the condensed forms, may be calculated by supposing the requisite amounts drawn off in the form of saturated vapours, these expanded or compressed to the concentrations in the equilibrium box, passed into the latter, and the products then abstracted from the box, expanded to the concentrations of the saturated vapours, and finally condensed on the solids or liquids. Since the changes of volume of the condensed phases are negligibly small, the maximum work is again ... 

Initially, the compression does not result in surface pressure variations. Molecnles at the air/water interface are rather far from each other and do not interact. This state is referred to as a two-dimensional gas. Farther compression results in an increase in snrface pressure. Molecules begin to interact. This state of the monolayer is referred as two-dimensional liquid. For some compounds it is also possible to distingnish liqnid-expanded and liquid-condensed phases. Continnation of the compression resnlts in the appearance of a two-dimensional solid-state phase, characterized by a sharp increase in snrface pressure, even with small decreases in area per molecule. Dense packing of molecnles in the mono-layer is reached. Further compression results in the collapse of the monolayer. Two-dimensional structure does not exist anymore, and the mnltilayers form themselves in a non-con trollable way. 

For example, we know that water (a liquid) will chemge to ice (a solid) if its internal temperature falls below a certain temperature. Likewise, if its internal temperature rises above a certain point, water changes to steam (a gas). Because water is so abundant on the Earth, it was used in the past to define Changes of State and even to define Temperature Scales. However, the concept of "heat" is also involved, and we need to also define the perception of heat as it is used in this context. Note that defining heat implies that we have a reproducible way to measure temperature. A great deal of work was required in the past to reach that stage. First, you have to establish that certcun liquids expand when heated. Then you must establish... 

The techniques used for handling various materials depend on their physical states as well as their chemical properties. While it is comparatively easy to handle liquids and solids, it is not as convenient to measure out a quantity of a gas. Fortunately, except under rather extreme conditions, all gases have similar physical properties, and the chemical identity of the substance does not influence those properties. For example, all gases expand when they are heated in a nonrigid container and contract when they are cooled or subjected to increased pressure. They readily diffuse through other gases. Any quantity of gas will occupy the entire volume of its container, regardless of the size of the container. 

Graham s definitions were expanded, and the concept of a colloidal state of matter evolved. According to this view, a substance could occur in a colloidal state just as it could occur under various conditions as a gas, liquid, or solid. If a colloidal solution was, at that time, defined as a solution in which the dispersed particles were comprised of large molecules, the ascertion would have been more acceptable. 

Antimony is unique in that when it solidifies from a molten liquid state to a solid state, it expands, which is just the opposite of most metals. This is useful in making some typesetting castings in which the expansion assures an accurate reproduction of the letter mold. 

When the area available for each molecule is many times larger than molecular dimension, the gaseous-type film [state 1] would be present. As the area available per molecule is reduced, the other states, for example, liquid-expanded [Lex], liquid-condensed [Lco], and, finally, the solid-like [S or solid-condensed] states would be present. 

FIGURE 4.6 II versus A isotherms for different types of states (a) gas film (b) liquid-expanded (Lex) and liquid-condensed (Lco) solid films collapse state. 

Liquid Expanded Films (Lexp) In general, there are two distinguishable types of liquid films. The first state is called the liquid expanded (Lexp) (Gaines, 1966 Chattoraj and Birdi, 1984 Adamson and Gast, 1997). If the Il-A isotherm is extrapolated to zero n, the value of A obtained is much larger than that obtained for close-packed films, shows that the distance between the molecules is much larger than that in the solid him (to be discussed in later text). These films exhibit very characteristic elasticity. 

Liquid Condensed Films (Lco) As the area per molecule (or the distance between molecules) is further decreased, a transition to a so-called liquid condensed (Lco) state is observed. These states have also been called solid expanded films (Adam, 1941 Gaines, 1966 Birdi, 1989, 1999 Adamson and Gast, 1997). The n versus A isotherms of n-pentadecylic acid (amphiphile with a single alkyl chain) have been studied, as a function of temperature (Birdi, 1989). 

From these descriptions, it is seen that the films may, under given experimental conditions, show three first-order transition states, such as (i) transition from the gaseous film to the liquid-expanded (Lex), (ii) transition from the liquid-expanded (Lex) to the liquid-condensed (Lco), and (iii) from Lex or Lco to the solid state if the temperature is below the transition temperature. The temperature above which no expanded state is observed has been found to be related to the melting point of the lipid monolayer. 

Devaux also advanced the important theory that the characteristics of the solid, liquid and gaseous states of matter are retained so long as one continuous layer of molecules remains unbroken. This conception has been partially confirmed by the work shortly to be described. A film may be solid, liquid, expanded or gaseous, and one kind is readily distinguished from another. In certain properties, a solid film of unimolecular thickness resembles quantitatively a three-dimensional solid mass of the same substance, but these properties are necessarily limited to such as can be measured in any given direction. 

The M-NM transition has been a topic of interest from the days of Sir Humphry Davy when sodium and potassium were discovered till then only high-density elements such as Au, Ag and Cu with lustre and other related properties were known to be metallic. A variety of materials exhibit a transition from the nonmetallic to the metallic state because of a change in crystal structure, composition, temperature or pressure. While the majority of elements in nature are metallic, some of the elements which are ordinarily nonmetals become metallic on application of pressure or on melting accordingly, silicon is metallic in the liquid state and nonmetallic in the solid state. Metals such as Cs and Hg become nonmetallic when expanded to low densities at high temperatures. Solutions of alkali metals in liquid ammonia become metallic when the concentration of the alkali metal is sufficiently high. Alkali metal tungsten bronzes... 

If the area of an insoluble monolayer is isothermally reduced still further, the compressibility eventually becomes very low. Because of the low compressibility, the states observed at these low values of a are called condensed states. In general, the isotherm is essentially linear, although it may display a well-defined change in slope as tt is increased, as shown in Figure 7.6. As menlioned above, the (relatively) more expanded of these two linear portions is the liquid-condensed state LC, and the less expanded is the solid state S. It is clear from the low compressibility of these states that both the LC and S states are held together by strong intermolecular forces so as to be relatively independent of the film pressure. 

Only a few materials fit into this category they seldom can be categorized into one of the above material classes. Water fits into the category of materials with unusual behavior. Water is one of the few materials that expands upon freezing. It changes volume by approximately 8% transiting from the liquid to the solid state. 

As the compression of the surface continues, the vapor phase disappears and the film is in the liquid state, also referred to as liquid expanded (LE, E or Li) state. The area per molecule in this state is in the range of 25-40 A2 for fatty acid films, which is intermediate between those in gaseous and solid (i.e. condensed) states. The surface pressure increases as the area per molecule decreases. The molecules in the liquid expanded state interact strongly with each other but are not closely packed. Defects, such as gauche conformations, can be found in the alkyl tails of the molecules. 

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