Rotational and translational diffusion

The motions of a molecular system, for example a solution, occur on many time scales. There are very fast electronic motions, the basic mechanism in chemical reactions then, the nuclear motions, vibrations, librations, rotations, and translations (diffusion). In the Bom-Oppenheimer spirit, one can consider the electronic motion as separated from the nuclear motions, thus one can talk of micro-deformations to be treated quantum mechani-... 

However, picosecond resolution is insufficient to fully describe solvation dynamics. In fact, computer simulations have shown that in small-molecule solvents (e.g. acetonitrile, water, methyl chloride), the ultrafast part of solvation dynamics (< 300 fs) can be assigned to inertial motion of solvent molecules belonging to the first solvation layer, and can be described by a Gaussian func-tiona) b). An exponential term (or a sum of exponentials) must be added to take into account the contribution of rotational and translational diffusion motions. Therefore, C(t) can be written in the following form ... 

The second explanation for the solvent isotope effect arises from the dynamic medium effect . At 25 °C the rotational and translational diffusion of DjO molecules in D20 is some 20% slower than H20 molecules in H20 (Albery, 1975a) the viscosity of D20 is also 20% greater than H20. Hence any reaction which is diffusion controlled will be 20% slower in D20 than in H20. This effect would certainly apply to transition state D in Fig. 3 where in the transition state the leaving group is diffusing away. A similar effect may also apply to the classical SN1 and SN2 transition states, if the rotational diffusion of water molecules to form the solvation shell is part of the motion along the reaction co-ordinate in the transition state. Robertson (Laughton and Robertson, 1959 Heppolette and Robertson, 1961) has indeed correlated solvent isotope effects for both SN1 and SN2 reactions with the relative fluidities of H20 and D20. However, while the correlation shows that this is a possible explanation, it may also be that the temperature variation of the solvent isotope effect and of the relative fluidities just happen to be very similar (see below). 

The absolute and relative rates at which these processes occur depend on the molecular stmctures of the radicals in a pair, their initial spin multiplicity and rates of intersystem crossing, their rates of both rotational and translational diffusion within and outside their initial cages, and the nature of the radical centers. In addition, they can be affected enormously by external factors, such as temperature, the nature of... 

Diffusional motion. Many rotational and translational diffusion processes for hydrocarbons within zeolites fall within the time scale that is measurable by quasielastic neutron scattering (QENS). Measurements of methane in zeolite 5A (24) yielded a diffusion coefficient, D= 6 x lO" cm at 300K, in agreement with measurements by pulsed-field gradient nmr. Measurements of the EISF are reported to be consistent with fast reorientations about the unique axis for benzene in ZSM-5 (54) and mordenite (26). and with 180 rotations of ethylene about the normal to the molecular plane in sodium zeolite X (55). Similar measurements on methanol in ZSM-5 were interpreted as consistent with two types of methanol species (56). 

A major result of this work is that we quantitatively assessed the relevant role played by H-bond dynamics to determine the long-time diffusional properties. Indeed, both the rotational and translational diffusion processes are driven by a secondary time-dependent process the H-bond dynamics simulated by the stochastic variable %... 

In the popular fluid mosaic model for biomembranes, membrane proteins and other membrane-embedded molecules are in a two-dimensional fluid formed by the phospholipids. Such a fluid state allows free motion of constituents within the membrane bilayer and is extremely important for membrane function. The term "membrane fluidity" is a general concept, which refers to the ease of motion for molecules in the highly anisotropic membrane environment. We give a brief description of physical parameters associated with membrane fluidity, such as rotational and translational diffusion rates, order parameters etc., and review physical methods used for their determination. We also show limitations of the fluid mosaic model and discuss recent developments in membrane science that pertain to fluidity, such as evidence for compartmentalization of the biomembrane by the cell cytoskeleton. 

Generation of the Brownian trajectories for rodlike molecules requires simulation of the anisotropic translational diffusion and rotational diffusion. The rotational and translational diffusion are coupled in this case, however, taking a sufficiently small time step enables the computation of the different components... 

W. Eimer and R. Pecora, Rotational and translational diffusion of short rodlike molecules in solution - oligonucleotides, J. Chem. Phys. 94 (1991) 2324-2329. 

The magnetic dipole interaction between two protons (7, 5) depends on their relative distance rj s and on the orientation of the molecule in a laboratory-fixed frame. Both protons vary in time due to rotational and translational diffusion depending on whether the two spins reside on the same molecule (intra) or on different molecules (inter). The total dipole relaxation rate for any neat liquid thus consists of two terms. 

These structures appear well suited for investigations of intramembrane charge redistributions associated with receptor protein function and for applications that use receptors as the active element in biosensor systems. The receptor protein is retained in these structures by its hydrophobic interaction with the core of the membrane, and the environment around the receptor mimics that of a natural membrane. The receptor protein is thus free to undergo rotational and translational diffusion in the plane of the membrane. This should aid in retention of function relative to systems in which the receptor is directly immobilized on a surface. 

Ruiter A G T, Veerman J A, Garcia-Parajo M F and van Hulst N F 1997 Single molecule rotational and translational diffusion observed by near-field scanning optical microscopy J. Chem. Phys. A 101 7318-23... 

In this chapter it is assumed that the center of mass position and the orientation of a molecule are statistically independent. This assumption is not completely justified since the interaction potential between any two molecules is not separable in the relative position and orientations of the two molecules. The problem may, however, be treated in the special case of the translational and rotational diffusion approximations where one considers both the rotational and translational diffusion coefficients to be tensors (see Appendix 7. A). With the assumption of statistical independence of molecular rotation and translation Eq. (7.1.1) becomes... 

In Chapter 5 we found/ (q, t) = exp — q2Dt for translational diffusion. Combining this with Eqs. (7.2.16) and (7.2.6) gives for combined rotational and translational diffusion... 

Inspection of Table I reveals two further trends, impUcit in the apparent linearity of the hydrodynamic plot in Fig. 5. The solvation time t, increases with increasing viscosity (tj) and decreasing average number density (pj) of OH dipoles cm". By studying the effects of lowering both the viscosity and density, the role of rotational and translational diffusion and short-range solvent structure should become more apparent. 

The study encompassed measurements of rotational and translational diffusion rates of different parts of PHC molecules (by C NMR) and OD, CH2OD and D2O hydration phase (by H NMR) over a range... 

Dale and Eisinger have analyzed the effect of rotational mobility Stryer presents an analysis of the errors introduced by assuming = 2/3 and van der Meer et al. present a treatment on the effects of restricted rotational and translational diffusion. Experimentally, one determines the rotational mobility of the dyes by a steady-state or time-resolved fluorescence depolarization experiment. ... 

Proton, deuteron and carbon spin relaxation measurements of liquid crystals have provided detailed information about the molecular motions of such anisotropic liquids (anisotropic rotation and translation diffusion of individual molecules), and about a peculiar feature of liquid crystalline phases, namely collective molecular reorientations or order fluctuations. Spin relaxation in liquid crystalline mesophases has challenged NMR groups since the early 1970s, shortly after the publication of theoretical predictions that order fluctuations of the director (OFD, OF), i.e. thermal excitations of the long-range orientational molecular alignment (director), may play an important unusual role in nuclear spin relaxation of ordered liquids. Unique to these materials, which are composed of rod-like or disc-like (i.e. strongly anisotropic molecules), it was predicted that such thermal fluctuations of the director should, at the frequencies of these fluctuation modes, produce rather peculiar Ti(p) dispersion profiles. For example in the case of uniaxial nematic... 

In the implementation of the model, it is further assumed that as the bound water molecule is immobilized by the protein surface, it cannot rotate or translate. Thus, it must become free to move. The bound to free (and free to bound) transition is described as a chemical reaction. The free water molecules, on the other hand, are assumed to behave as molecules in bulk water, although their rotation and translation diffusion are generally modified due to their interaction with the protein. This surface layer of bound and free water is coupled to the bulk water outside the layer. Although this is a key feature, it is ignored in many other models. In addition, we allow the possibility of the bound water having a preferred orientation due to its interaction with the protein. 

As mentioned earlier, the first signature of the influence of the protein surface on the dynamics of water came from the measurements of the rotational and translational diffusion coefficients of water in aqueous protein solutions. Analysis based on hydrodynamic formulas (such as Stokes-Einstein and Debye-Stokes-Einstein (DSE)) showed that an explanation of the observed values required a larger than actual radius of the protein to be used in the Stokes expression of the friction (from hydrodynamics). This indicated the presence of a substantially rigid water layer around the protein surface. However, the story turned out to be more complex. We have already discussed some of these aspects - we now turn to a more detailed discussion of several experimental results. 

In the time window between the absorption and emission of a photon, a number of molecular processes can occur. They concern either (a) the fluorophore itself (its rotational and translational diffusion, conformational changes, transition between electronic states differing in dipole moment) or (b) molecules in its immediate vicinity (reorganization of the solvent shell, diffusion of quenchers, etc.). All these processes influence the fluorescence properties (position and shape of the emission band, quantum yield, decay time, etc.). In most cases, both the fluorophore and the surrounding molecules participate in the process and fluorescence characteristics are in fact influenced by their mutual interactions. Figure 3 shows a survey of important... 

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