Randomization of orientational

Dipole-dipole electrostatic interaction perturbs the randomness of orientation. If the dipole on the left is pointing "up," then there is a slightly greater chance that the dipole on the right will point "down" (or vice versa both particles are equivalent in mutual perturbation). By increasing the chances of an attractive mutual orientation, the perturbation creates a net-attractive interaction energy. 

Only six students (31.6%) showed the molecules in a random orientation. But 57.9% of students drew the molecules without rotating the stencil, very much like a letter-type stencil would be used, where all the stencil shapes face in a particular (vertical) direction (see Fig. 2). These results are perhaps not surprising, since many textbooks illustrate the particle model of solids, liquids and gases using circles for particles. These structure-less particles cannot represent randomness of orientations of molecules with other shapes. 

In its simplest form the model assumes perfectly random mixing of various kinds of molecular contacts. In this form it has been applied to polystyrene-cyclohexane with partial justification from data on cyclohexane-toluene mixtures. A refinement to the random mixing assumption corrects for the influence of local surroundings on the average randomness of orientation of solvent molecules and polymer segments. With these corrections the free energy of mixing can be written ... 

Koningsveld and Stepto used an extension of Silberberg s derivation (see p. 301) of the ideal entropy of mixing in order to attach some molecular interpretation to randomness of orientation corrections. They conclude that these terms... 

The relaxation time of the rotation of a molecular direction is independent of azimuth only if the molecule is a figure of revolution about the said direction. In all other cases the rotational relaxation time of a direction may be defined by considering that all positions of the molecule obtained by rotation about the given direction enter with equal weight. Such will often be the case with molecules in solution where complete randomness of orientation prevails. The change in orientation of a molecular direction depends on rotations about two axes perpendicular to the said direction. If the frictional coefficients of the rotation about these directions are /, and the relaxation time of the k direction (normal to and j) is given by... 

The fluorescence polarization p(A-) and anisotropy r(A-) both take the value of unity for the limit of complete preservation of polarization during the excited state lifetime (e.g. if the molecules are immobile). Likewise, they both take the value of zero if there is a complete loss of polarization (i.e. a randomization of orientation). However, their values differ for states between these extremes. In principle -1 encountered negative values may be indicative of processes beyond depolarization through rotational relaxation, such as transitions to other excited states. 

One factor largely ignored in empirical approaches to fit the experimental data is the possible existence of a non-combinatorial component to the entropy of mixing. The classical combinatorial entropic contribution to is calculated assuming complete randomness of orientation and rigid molecules [8-11]. The actual distribution of molecules will not be perfectly random, however, particularly... 

Results are achieved rapidly and with much better precision when automatic diffractometers are used to record diffraction data. The X-ray tube furnishes the radiation directly (filters are generally used to obtain more nearly monochromatic radiation). The diffracting crystal is replaced by a powdered or metallic sample. To increase the randomness of orientation in the crystallites, the sample can be rotated in its own plane, that is, the plane perpendicular to the bisector of the angle between the source and detector beams. Note also that as the sample is rotated in the other plane to sweep through various 0 angles, the detector must be rotated twice as rapidly to maintain the angle 20 with the irradiating beam. 

If the orientation of the two dipoles were completely random, the average force would be zero, since attractive and repulsive orientations would occur equally. As the top of the Figure 4.5 shows, however, molecular dipoles in gases and liquids are free to rotate. This movement allows the energetically favored lower-energy attractive interactions to occur more frequently, as the dipoles tend to rotate to align. On the other hand, thermal energy leads to a randomization of orientation. 

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