Molecules “feel” each

Try putting a drop of water on wax paper or glass and look at it closely. Does it look like it has a skin There really isn t a skin what you re seeing is surface tension. The molecules in water are attracted to each other, like tiny magnets, because the hydrogen atom in one molecule is attracted to the oxygen atom in another molecule. Every water molecule feels pulled towards the others, so the water molecules shrink away from the surface and cling to each other. 

Noncovalent interactions are primarily electrostatic in namre and thus can be interpreted and predicted via V (r). For this purpose, it is commonly evaluated on the surfaces of the molecules, since it is through these surface potentials, labeled VsCr), that the molecules see and feel each other. We have shown that a number of condensed-phase physical properties that are governed by noncovalent interactions—heats of phase transitions, solubilities, boiling points and critical constants, viscosities, surface tensions, diffusion constants etc.—can be expressed analytically in terms of certain statistical quantities that characterize the patterns of positive and negative regions of Vs(r) . 

To see how repulsive interactions can lead to islands of the same adsorbate let s assume that we have atoms or molecules A and B, and let s assume that they all repel each other. If the coverage is low so that all adsorbates can move so far apart that they don t feel each other, then that is what will happen and... 

Hence, A asurf is expressed in m I. Furthermore, we assume that ATiasurf is not dependent on the concentration of the compound at the surface that is, we assume that we are far from saturating the surface with compound /. This then corresponds to a linear adsorption isotherm for a homogeneous mineral surface, since the sorbate molecules do not feel each other in the gas phase or at the solid surface. Finally, we should point out that in the literature, contrary to the notation used here, gas/solid partition coefficients are often expressed in a reciprocal way that is, the reported... 

When can particles ever interact two at a time There is a remarkably easy test. If we can apply an electric field from the outside and each atom or molecule feels that externally applied electric field as though the other atoms or molecules were not there, then we can say that the particles are so dilute that they will interact two at a time. If particles are so dense that the external field felt by each particle is distorted by the presence of other particles, then we have three s-a-crowd densities. The key variable is (particle-number density) times (individual-particle polarizability). An infinitesimal value of this product ensures that the fields of neighbors dipole moments do not significantly contribute to the field felt by each particle. In practice, only dilute gases pass this test. 

Boltzmann introduces in the (x, y) plane an infinitesimal small elastic obstacle, with which the oscillating particle collides again and again. Similar procedures are used in other examples. In this respect see also Lord Rayleigh [2], It is on account of the complexity of the collisions of the molecules with each other and with the rough though perfectly elastic wall of the container that Boltzmann and Maxwell feel justified to assume that gas models are ergodic. 

Because most of you are probably too lazy to go and review stuff, we ll briefly mention a couple of pertinent points. First, the interaction between two molecules is described in terms of the potential energy (P.E.). When the molecules are too close they strongly repel, when they are too far apart they don t feel each other. There is some optimum distance apart where their interaction is a maximum, hence P.E. is a minimum, or has the largest negative or attractive value. Second, there are advanced theoretical models that deal with potential functions like this, which we will not consider, but for dispersion and weak polar forces the attractive energy varies as 1/r6, where r is the distance between the molecules. 

At the macroscopic (everyday) level, we experience this motion as atmospheric pressure . As the above calculations show, the molecules in the air around us are travelling at several hundred metres per second, and will be constantly colliding with the surface of our skin. We do not feel each collision - there are too many of them, and each impact is, in any case, rather small - but we do feel the sum total of all these collisions as the pressure exerted by the atmosphere. 

An ideal gas is a collection of atoms or molecules that do not interact with one another and occupy essentially no volume. While this is an idealized model, it turns out to describe many gases very well. The reason it works so well is that the atoms or molecules making up a gas are spread out far from one another so that the intermolecular forces between them are extremely weak (they don t feel each other). This description leads to the ideal gas law, which is a relationship between the pressure, volume, and temperature of a gas. The ideal gas law allows chemists to predict how, for example, the volume of a gas will change as its temperature is increased. The equation for the ideal gas law is... 

On any surfece molecule, there is no upward force to cancel the downward force, which means each surfece molecule feels" a net downward pull... 

On any interior molecule, each force is balanced by a force pulling in the opposite direction, which means that interior molecules feel no net pull in any direction... 

The VB model for simple molecules can also be used in solids but then there are so many resonating boundary structures that the description needs statistical methods and the model is not very user-friendly. The VB model has the advantage over the MO description that it includes some electron correlation, which means that the electrons feel each other s presence and that therefore their motion and position are interrelated. When one electron is on one atom, the other electron is on the other atom. This is different in the simple MO model, where the valence electrons are completely independent and not correlated both may be on the same atom simultaneously. 

In real liquids there is a short-range positional order because each particular molecule has nearest neighbors forming few so-called coordination spheres. Therefore, each selected molecule feels its nearest neighbors and the G-function oscillates. For simplicity, we can take only the first harmonic of density oscillation and write the density correlation function as follows ... 

When two similarly charged colloidal particles, under the influence of the EDL, come close to each another, they will begin to interact. The potentials will feel each other, and this will lead to consequences. The charged molecules or particles will be under both van der Waals and electrostatic interaction forces, van der Waals forces that operate at short distance between particles will give rise to strong attraction forces. This kind of investigation is important in various industries ... 

Maier and Saupe [13] developed a statistical theory to describe the liquid crystalline state and the molecular ordering for the nematic phase. In analogy to the treatment of ordering phenomena in ferromagnetics or ferroelectrics, this theory describes the intermolecular orientational forces by a mean field method. Each individual molecule feels a nematic potential D = f (0, S, V) which depends on the momentaneous angle 6 between its long axis and the optic axis, the order parameter S and the molar volume V. S is then given by... 

When two polar molecules are in close proximity to each other—usually in liquids or solids—the negative end of one molecule feels an attraction to the positive end of the other molecule. Similarly, the positive end of the first molecule feels an attraction to the negative end of some other molecule, and the negative end of the second molecule feels an attraction to the positive end of some other molecule. This attraction is what we call a dipole-dipole force between molecules. In bulk Uquids, the sum of all the dipole-dipole forces exerts a very strong force that is responsible for keeping the molecules together in the Uquid phase, rather than the alternative of all the molecules evaporating. 

One can readily see from Eq. (37) that in the mean field approximation each molecule feels some average mean-field potential produced by other molecules. This mean-field potential is just the pair interaction energy averaged over the position and orientation of the second molecule. 

There are several good approximations for polymer melts that considerably simplify the task. For one, many of the site-site pair correlation functions are expected to be nearly equal to each other because the internal sites on the molecule feel similar environments. In addition, the concentration of chain ends is very small (of order l/N) for long molecules and end effects can be ignored. It makes sense then to focus attention on an average site-site pair correlation function, g(r). 

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