Anisotropic translational diffusion

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... 

Figure 17 Variation of reaction probability with the orientation angle (0) and angular position (9,) for pairwise Brownian dynamics simulation of rodlike molecules for anisotropic translational diffusion.

J. Srinivasalu Gupta and D. V. Khakhar, Brownian dynamics simulation of diffusion-limited polymerization of rodlike molecules Anisotropic translational diffusion, J. Chem. Phys., 108 (1998) 5626-5634. 

A quantitative, albeit indirect, approach to capture the dynamical signature of the coupling between orientational and translational order is to compare the D and D data obtained from our simulations with those predicted by the existing dynamical models, which ignore such coupling. In Fig. 29, we do so by considering two theoretical models [163, 164] that have been applied to trace experimental and molecular dynamics simulation data of anisotropic translational diffusion in the nematic phase of liquid crystalline systems [26-28, 163-165] the Hess-Frenkel-Allen (HFA) model and the Chu and Moroi... 

Rod-like polymers may be represented by rods or rods capped with hemispheres at both ends. In rod-like molecules, anisotropic translational diffusion arising from the airisotropic particle shape is coupled with rotational diffusion to appear in a < i dependence of the initial decay rate of DLS, which has experimentally been observed for the tobacco mosaic vims. °° By finding a proper model, we can characterize the particle shape and size through Rg, Rh, and Rg/Rh, along with P(g) and r(g], which could contain more information. 

The choice of method depends on the system to be investigated. The methods of intermolecular quenching and intermolecular excimer formation are not recommended for probing fluidity of microheterogeneous media because of possible perturbation of the translational diffusion process. The methods of intramolecular excimer formation and molecular rotors are convenient and rapid, but the time-resolved fluorescence polarization technique provides much more detailed information, including the order of an anisotropic medium. 

The studies of Hasinoff [53] on the recombination rate of carbon monoxide and the heme units after photodissociation of carboxy ferrous microperioxidase come close to satisfying the requirements for observing the effects of anisotropic reactivity and rotational diffusion on the rate of a translational diffusion-limited reaction. In Chap. 2, Sect. 5.6, the details of this study were briefly mentioned. Hasinoff found that the rate of recombination was substantially diffusion-limited in all three aqueous solvents used at 260 K, but at higher temperatures, the rate of reaction of the encounter pair, feact, was a significant factor in determining the overall rate of recombination (see Fig. 9). The observed rate coefficient of recombination, feobs, was separated into the rate coefficient of diffusive formation of encounter pairs, feD, and the rate coefficient of reaction of encounter pairs, fcact, with the Collins and Kimball expression, eqn. (26)... 

Molecular motions in low molecular weight molecules are rather complex, involving different types of motion such as rotational diffusion (isotropic or anisotropic torsional oscillations or reorientations), translational diffusion and random Brownian motion. The basic NMR theory concerning relaxation phenomena (spin-spin and spin-lattice relaxation times) and molecular dynamics, was derived assuming Brownian motion by Bloembergen, Purcell and Pound (BPP theory) 46). This theory was later modified by Solomon 46) and Kubo and Tomita48 an additional theory for spin-lattice relaxation times in the rotating frame was also developed 49>. 

Discussion. We can now propose a coarse description of the paraffinic medium in a lamellar lyotropic mesophase (potassium laurate-water). Fast translational diffusion, with D 10"6 at 90 °C, occurs while the chain conformation changes. The characteristic times of the chain deformations are distributed up to 3.10"6 sec at 90 °C. Presence of the soap-water interface and of neighboring molecules limits the number of conformations accessible to the chains. These findings confirm the concept of the paraffinic medium as an anisotropic liquid. One must also compare the frequencies of the slowest deformation mode (106 Hz) and of the local diffusive jump (109 Hz). When one molecule wants to slip by the side of another, the way has to be free. If the swinging motions of the molecules, or their slowest deformation modes, were uncorrelated, the molecules would have to wait about 10"6 sec between two diffusive jumps. The rapid diffusion could then be understood if the slow motions were collective motions in the lamellae. In this respect, the slow motions could depend on the macroscopic structure (lamellar or cylindrical, for example)... 

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. 

Diffusion is the random movement of a particle because of an exchange of thermal energy with its environment. Membrane lipids and proteins participate in highly anisotropic translational and rotational diffusion motion. Translational diffusion in the plane of the membrane is described by the mean square lateral displacement after a time At (r ) = TD At. Lipid lateral diffusion coefficients in fluid phase bilayers are typically in the range Dj 10 to 10 cm /s (3). 

Hensel Bielowka, S., Psurek, T., Ziolo, J., and Paluch, M. (2001) Test of the fractional Debye-Stokes-Einstein eqnation in low-molecnlar-weight glass-forming liqnids nnder condition of high compression, Phys. Rev. E 63, 062301 Wang, C. H. (2002) Enhancement of translational diffusion coefficient of a probe in a rotationally anisotropic fluid, Phys. Rev. E 66, 021201... 

As stated above, this theory assumes that translational diffusion is isotropic that is, in a molecule-fixed frame, the diffusion constant parallel to the long molecular axis is the same as that perpendicular to it. For highly anisotropic large molecules this is probably not a good assumption. Maeda and Saito (1969) have calculated the spectrum taking into account the anisotropy of the translational diffusion constant. Their resulting expressions are rather complex and will not be given here. Their results are expressed as a power series in the translational diffusion coefficient anisotropy,... 

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... 

At high E/N, the rotational diffusion of ions is anisotropic like the translational diffusion (2.2.4) the temperatures for J E rotation (7r ) and the two J J. E modes (7r,x) are unequal. To relate them to translational temperatures (2.2.4), we note that only collisions in the plane orthogonal to E can influence the J E mode while the J E mode is affected equally by collisions along and perpendicular to E (Figure 2.28). Then ... 

The similarity exhibited here between the multi-variable and the memory hierarchy formulations of the orientational problem is obviously not a general result in fact, it derives from the choice of a variable and its time derivative in the multi-variable theory. Other variations on these themes can readily be devised for example, one could couple Q, and 4 (orthogonal ized to Qj, however) (8) or one could combine higher-order memory functions with a multi-variable theory or one could couple translational and rotational variables (9), The enormous flexibility of the G,L,E, means that the intuition of the user will play a particularly significant role in determining the success of the outcome. To illustrate this point, we now briefly recapitulate how the 6,L,E, applies to a quite different orientational problem namely, anisotropic rotational diffusion (10). 

When the distance h between a spherical particle of radius a and a solid boundary becomes sufficiently small h/a 1), hydrodynamic interactions between the particle and wall hinder the Brownian motion (diffusion) of the particle. Such effects are critical to fundamental near-waU measurements and the accuracy of micro-velocimetry techniques, which rely on the accurate measurement of micro/nano particle displacements to infer fluid velocity. By applying the 3D TIRV technique to freely suspended fluorescent particles, simultaneous observation of three-dimensional anisotropic hindered diffusion has heen measured for particle gap sizes /i/a 1 with 200 nm diameter particles [6] and h/a 1 with 3 xm diameter particles [7]. The latter results confirm the increase of hydrodynamic drag when a particle approaches a sohd boundary, and such correction shall be applied to not only diffusion but also other translational motion of particles where the drag force is of concern. 

Detailed molecnlar dynamics simnlations have been carried out also for GB particles in the sea of spheres. These studies have indicated anisotropic diffusion for the ellipsoids at higher density. In addition, the ratio between parallel and perpendicular diffusion coefficients rises from unity to the value of aspect rado as density of the system increases [19-21]. The product of the translational diffusion coefficient and reorientational correlation time behaves in a manner similar to that found for pure GB fluid. 

---