Particles as molecules

An activity which illustrates this general point in relation to particle theory (the topic of Chapter 2) is included in a publication available from SEP (the Science Enhancement Programme, details of which are given in the Other resources section at the end of this introduction). The first of two group-work tasks in this activity Judging models in science asks students to consider two types of particle models - particles like tiny hard billiard balls particles as molecules with soft electron clouds - and to consider which model better explains a range of evidence based on the observable properties of matter. Students will find that each model is useful for explaining some phenomena, but neither fits all the evidence - and of course both models are stiU found useful in science. 

The process by which particles (as molecules and ions) in solution spread throughout the solution and across separating membranes from the places of highest concentration to lowest concentration. 

In special cases (as in colloidal solutions) some particles can be considered as essential and other particles as irrelevant , but in most cases the essential space will itself consist of collective degrees of freedom. A reaction coordinate for a chemical reaction is an example where not a particle, but some function of the distance between atoms is considered. In a simulation of the permeability of a lipid bilayer membrane for water [132] the reaction coordinate was taken as the distance, in the direction perpendicular to the bilayer, between the center of mass of a water molecule and the center of mass of the rest of the system. In proteins (see below) a few collective degrees of freedom involving all atoms of the molecule, describe almost all the... 

Taking atomic sputtering into account the proportion of the particles emitted as molecules is negligible and the partial sputtering yield for element A in sputter equilibrium can be determined by use of ... 

The theory of the structure of ice and water, proposed by Bernal and Fowler, has already been mentioned. They also discussed the solvation of atomic ions, comparing theoretical values of the heats of solvation with the observed values. As a result of these studies they came to the conclusion that at room temperature the situation of any alkali ion or any halide ion in water was very similar to that of a water molecule itself— namely, that the number of water molecules in contact with such an ion was usually four. At any rate the observed energies were consistent with this conclusion. This would mean that each atomic ion in solution occupies a position which, in pure water, would be occupied by a water moldfcule. In other words, each solute particle occupies a position normally occupied by a solvent particle as already mentioned, a solution of this kind is said to be formed by the process of one-for-one substitution (see also Sec. 39). 

As shown in Example 5.10, the average speed of an N2 molecule at 25°C is 515 m/s that of H2 is even higher, 1920 m/s. However, not all molecules in these gases have these speeds. The motion of particles in a gas is utterly chaotic In the course of a second, a particle undergoes millions of collisions with other particles. As a result, the speed and direction of motion of a particle are constantly changing. Over a period of time, the speed will vary from almost zero to some very high value, considerably above the average. 

The properties of a solution differ considerably from those of the pure solvent Those solution properties that depend primarily on the concentration of solute particles rather than their nature are called colligative properties. Such properties include vapor pressure lowering, osmotic pressure, boiling point elevation, and freezing point depression. This section considers the relations between colligative properties and solute concentration, with nonelectrolytes that exist in solution as molecules. 

Thus we find that each of these gases has distinctive properties. If these gases are made up of particles, then the particles must be distinctive. The particles that are present in ammonia cannot be like the particles in hydrogen chloride, or like those in the other gases. The nature of the ammonia particles, then, is the key to the properties of ammonia. The particles that make up a gas determine its chemistry. They are so important to the chemist that they are given a special name. A gas is described as a collection of particles called molecules. 

Here p is the radius of the effective cross-section, (v) is the average velocity of colliding particles, and p is their reduced mass. When rotational relaxation of heavy molecules in a solution of light particles is considered, the above criterion is well satisfied. In the opposite case the situation is quite different. Even if the relaxation is induced by collisions of similar particles (as in a one-component system), the fraction of molecules which remain adiabatically isolated from the heat reservoir is fairly large. For such molecules energy relaxation is much slower than that of angular momentum, i.e. xe/xj > 1. 

The structures of phases such as the chiral nematic, the blue phases and the twist grain boundary phases are known to result from the presence of chiral interactions between the constituent molecules [3]. It should be possible, therefore, to explore the properties of such phases with computer simulations by introducing chirality into the pair potential and this can be achieved in two quite different ways. In one a point chiral interaction is added to the Gay-Berne potential in essentially the same manner as electrostatic interactions have been included (see Sect. 7). In the other, quite different approach a chiral molecule is created by linking together two or more Gay-Berne particles as in the formation of biaxial molecules (see Sect. 10). Here we shall consider the phases formed by chiral Gay-Berne systems produced using both strategies. 

Consider a particle (a molecule or atom) for which the different degrees of freedom are independent and the energy is simply the sum of the energies contained in the different degrees of freedom. We can then write the partition function as the product of the partition functions for the various degrees of freedom. For an atom this is rather trivial ... 

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