Molecular motion in liquids

Because the rate at which molecules move in solution may be a controlling factor of the maximum rate of a biochemical reaction in the intracellular medium, we need to understand the factors that limit molecular motion in a liquid. 

A molecule in a liquid is surrounded by other molecules and can move only a fraction of a diameter in each step it takes, perhaps because its neighbors briefly move aside. Molecular motion in liquids is a series of short steps, with ever-changing directions, like people in an aimless, milling crowd. 

The process of migration by means of a random jostling motion through a liquid is called diffusion. We can think of the motion of the molecule as a series of short jumps in random directions, a so-called random walk (Fig. 8.11). If there is an initial concentration gradient in the liquid (for instance, a solution may have a high concentration of solute in one region), then the rate at which the molecules spread out is proportional to the concentration gradient and we write 

To express this relation mathematically, we introduce the flux, /, which is the number of particles passing through an imaginary window in a given time interval, divided by the area of the window and the duration of the interval  

The flux may also be expressed in terms of the amount (in moles) of molecules amount of particles passing through window 

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U. Buontempo, S. Cunsolo, P. Dore and P. Maselli, Molecular motions in liquids. In J. van Kranendonk, ed., Intermodular Spectroscopy and Dynamical Properties of Dense Systems - Proceedings of the Int. School of Physics Enrico Fermi , Course LXXV, p. 211, 1980. 

Steffen T, Duppen K. Femtosecond two-dimensional spectroscopy of molecular motion in liquids. Phys Rev Lett 1996 76 1224-1227. 

Reactions in Solution Molecular motion in liquids is diffusional in place of free flight but the concept of activation energy and stearic requirements survive. Molecules have to jostle their way through the solvent and so the encounter frequency is drastically less than in a gas. Since a molecule migrates only slowly into the region of a possible reaction partner, it also migrates only slowly away from it. 

One of the simplest examples of this type of calculation involves the study of a system of rare-gas atoms, as in, e.g., calculations carried out on liquid argon. The relaxation time after a colhsion was found to be on the order of 10 s, which is about the same time as that for rather large ions (e.g., of 500 pm). Thus, much of what one learns from the MD study of molecular motion in liquid argon should be applicable to ionic diffusion. 

This chapter will focus on the specific research area of combining MD simulations and experimental NMR relaxation studies to obtain information about intermolecular interactions and molecular motion in liquids and solutions [4]. To combine MD simulations and NMR relaxation measurements is an ideal tool in many respects. In spite of the fact that it enables studies of the most fundamental molecular properties in liquids, difficult to obtain using other methods, it has re-... 

H. Dardy, V. Volterra, and T. A. Litovitz. Molecular motions in liquids Comparison of light scattering and infra-red absorption. Faraday Symposia Chem. Soc., 6 71-81 (1972). 

P. Lallemand. fitude des mouvements moleculaires par diffusion de la lumiere. In J. Lascombe (ed.). Molecular Motion in Liquids, D. Reidel, Dordrecht, 1974, pp. 517-534. 

Unfortunately, the usefulness of NMR for the investigation of chemical problems was strictly limited to liquid samples, so solid samples first had to be dissolved or melted. This is because of the anisotropic nuclear interactions which strongly depend on molecular orientation, and are therefore averaged by molecular motion. In liquids, the molecules reorient randomly very quickly a water molecule requires ca. 10 s for complete reorientation. Although certain solids have sufficient molecular motion for their NMR spectra to be obtainable without resorting to special techniques, in the general case of a true solid, there is no such motion, and conventional NMR, instead of sharp spectral lines, yields a broad hump which conceals most information of interest to chemists. For example, the width of the H NMR resonance in the spectrum of water is ca. 0.1 Hz, while the line from a static sample of ice is ca. 100 kHz wide, i.e., a million times broader. Andrew et al. [ 12], and independently Lowe [ 13], had the idea of substituting the insufficient molecular motion in solids for the macroscopic rotation of the sample. 

According to the hole theory of liquids, first developed by Eyring [31], molecular motion in liquids depends on the presence of holes or voids, i.e., places where there are vacancies. When a molecule moves into a hole, a... 

According to the hole theory of liquids (Eyring, 1936), molecular motion in liquids depends on the presence of holes or voids, i.e., places where there are vacancies, as illustrated in Fig. 2.22. For real materials, however. Fig. 2.22 has to be visualized in three dimensions. A similar model can also be constructed for the motion of polymer chains, the main difference being that more than one hole will now be required to be in the same locality for the movement of polymer chain segments. On this basis, the observed specific volume of a sample, v, can be described as a sum of the volume actually occupied by the polymer molecules, vq, and the free volume (empty spaces), uy, in the system [see Fig. 2.23(a)], i.e.,... 

The application of molecular spectroscopic techniques to an elucidation of molecular reorientations and interactions of halogenomethanes in the liquid phase has been described. The usefulness of Raman spectroscopy in probing the details of molecular motion in liquids has been demonstrated for... 

R 778 M. E. G. Porto and A. A. de Sousa, Molecular Motions in Liquids Studied by Nuclear Spin Relaxation and Dielectric Relaxation , Anais da Associacao Brasileira de Quimica, 2002, 51,113... 

Quadrupole relaxation studies of the mobility of covalent compounds have almost exclusively dealt with the pure compounds and medium effects on halogen quadrupole relaxation are virtually unknown. Furthermore, we have seen in the above description of models of molecular motion in liquids and the interpretation of correlation times that the effect of specific intermolecular forces has in most cases been disregarded. For the understanding of the influence of different types of intermolecular interactions on molecular reorientation, systematic studies of quadrupole relaxation in liquid mixtures should be helpful. Halogen relaxation investigations of this type are nonexistent in the literature but a preliminary investigation in our... 

The study of quadrupolar nuclei can provide unique and very valuable information on a variety of physico-chemical and biological systems. For one thing the relaxation of quadrupolar nuclei is in many ways easier to interpret than the relaxation of non-quadrupolar nuclei, since the former is in many cases caused by purely intramolecular interactions modulated by the molecular motion. Studies of quadrupolar relaxation have therefore furnished important information about molecular reorientation and association in liquids and have played - and will certainly play for many years - an important role in testing new theoretical models of molecular motion in liquids. 

We next evaluate the lineshape function (8.16) for two concrete situations in gases, (The complexity of molecular motions in liquids precludes computation of their dipole correlation functions in a text of this scope.) In the first situation, we imagine that we are examining lineshapes in the far-infrared spectrum of a collision-free, rotating polar molecule. Its dipole moment /Iq is assumed to rotate classically without interruption with angular frequency cwq about an axis normal to /Iq. In a dilute gas, we would then have... 

Miiller, K., Etique, P. and Kneubiihl, F. 1974, in Molecular Motions in Liquids, Lascombe, J. Editor, Reidel Publ. Comp., Dordrecht, p. 265. 

To summarize the main contents of this section, we show in Figure 2.7 the typical appearance of NMR spectra in liquid substances, evidencing the role played by chemical shift and /-coupling interactions, which, as discussed above, are the only ones that survive to the random molecular motion in liquids. On the other hand. Figure 2.8 exhibits some typical powder patterns associated with the anisotropic nature of these interactions, as commonly found in solid-state NMR spectra of polycrystalline samples. 

The isothermal time dependence of relaxation and fluctuation due to molecular motions in liquids at equilibrium usually cannot be described by the simple linear exponential function exp(-t/r), where t is the relaxation time. This fact is well known, especially for polymers, from measurements of the time or frequency dependence of the response of the equilibrium liquid to external stimuli such as in mechanical [6], dielectric [7, 33], and light-scattering [15, 34] measurements, and nuclear-magnetic-resonance spectroscopy [14]. The correlation or relaxation function measured usually decays slower than the exponential function and this feature is often referred to as non-exponential decay or non-exponentiality. Since the same molecular motions are responsible for structural recovery, certainly we can expect that the time dependence of the structural-relaxation function under non-equilibrium conditions is also non-exponential. An experiment by Kovacs on structural relaxation involving a more complicated thermal history showed that the structural-relaxation function even far from equilibrium is non-exponential. For example (Fig. 2.7), poly(vinyl acetate) is first subjected to a down-quench from Tq = 40 °C to 10 °C, and then, holding the temperature constant, the sample... 

J. Lamb, in Molecular Motions in Liquids, edited by J. Lascombe, Reidel Publishing Company, Dordrecht, 1974, p. 29 J. Rheol.. 22,317 (1978). 

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