Self-diffusion transition

Micellization is a second-order or continuous type phase transition. Therefore, one observes continuous changes over the course of micelle fonnation. Many experimental teclmiques are particularly well suited for examining properties of micelles and micellar solutions. Important micellar properties include micelle size and aggregation number, self-diffusion coefficient, molecular packing of surfactant in the micelle, extent of surfactant ionization and counterion binding affinity, micelle collision rates, and many others. 

The order parameter values calculated from the data of Fig. 4 are illustrated in Fig. 5. The data there suggest the existence of two continuous transitions, one at a = 0.85 and another at a = 0.7. The first transition at a = 0.85, denoted by the arrow labeled a in Fig. 5, is assigned to the formation of percolating clusters and aggregates of reverse micelles. The onset of electrical percolation and the onset of water proton self-diffusion increase at this same value of a (0.85) as illustrated in Figs. 2 and 3, respectively, are qualitative markers for this transition. This order parameter allows one to quantify how much water is in these percolating clusters. As a decreases from 0.85 to 0.7, this quantity increases to about 2-3% of the water. 

Another more abrupt transition in this order parameter occurs at a = 0.7 under the arrow labeled b. This transition is assigned to the onset of irregular bicontinuous microstructure formation, and is indicated qualitatively by the marker illustrated in Fig. 3, where the onset in AOT self-diffusion increase occurs. 

FIG. 7 Order parameter for disperse pseudophase water derived from self-diffusion data for water, decane, and AOT reverse microemulsion illustrated in Fig. 6. The Op and arrow denote the approximate onset of percolation in low-frequency conductivity and a breakpoint in water self-diffusion increase. The arrow labeled AOT shows a second continuous transition corresponding to the onset of AOT self-diffusion increase. 

While the order parameters derived from the self-diffusion data provide quantitative estimates of the distribution of water among the competing chemical equilibria for the various pseudophase microstructures, the onset of electrical percolation, the onset of water self-diffusion increase, and the onset of surfactant self-diffusion increase provide experimental markers of the continuous transitions discussed here. The formation of irregular bicontinuous microstructures of low mean curvature occurs after the onset of conductivity increase and coincides with the onset of increase in surfactant self-diffusion. This onset of surfactant diffusion increase is not observed in the acrylamide-driven percolation. This combination of conductivity and self-diffusion yields the possibility of mapping pseudophase transitions within isotropic microemulsions domains. 

In spite of the problems associated with the static structure, the coarsegrained model for BPA-PC did reproduce the glass transition of this material rather well the self-diffusion constant of the chains follows the Vogel-Fulcher law [187] rather nicely (Fig. 5.10),... 

The non-collective motions include the rotational and translational self-diffusion of molecules as in normal liquids. Molecular reorientations under the influence of a potential of mean torque set up by the neighbours have been described by the small step rotational diffusion model.118 124 The roto-translational diffusion of molecules in uniaxial smectic phases has also been theoretically treated.125,126 This theory has only been tested by a spin relaxation study of a solute in a smectic phase.127 Translational self-diffusion (TD)29 is an intermolecular relaxation mechanism, and is important when proton is used to probe spin relaxation in LC. TD also enters indirectly in the treatment of spin relaxation by DF. Theories for TD in isotropic liquids and cubic solids128 130 have been extended to LC in the nematic (N),131 smectic A (SmA),132 and smectic B (SmB)133 phases. In addition to the overall motion of the molecule, internal bond rotations within the flexible chain(s) of a meso-genic molecule can also cause spin relaxation. The conformational transitions in the side chain are usually much faster than the rotational diffusive motion of the molecular core. 

These experiments suggest that as the long time self-diffusion coefficient approaches zero the relaxation time becomes infinite, suggesting an elastic structure. In an important study of the diffusion coefficients for a wide range of concentrations, Ottewill and Williams14 showed that it does indeed reduce toward zero as the hard sphere transition is approached. This is shown in Figure 5.6, where the ratio of the long time diffusion coefficient to the diffusion coefficient in the dilute limit is plotted as a function of concentration. 

Large amplitude motions in molecular crystals such as phase transitions and self-diffusion of solid adamantane have also been treated by a MM method (322). However, the program used in this work is useful only for the calculation of intermolecular interactions. 

We review Monte Carlo calculations of phase transitions and ordering behavior in lattice gas models of adsorbed layers on surfaces. The technical aspects of Monte Carlo methods are briefly summarized and results for a wide variety of models are described. Included are calculations of internal energies and order parameters for these models as a function of temperature and coverage along with adsorption isotherms and dynamic quantities such as self-diffusion constants. We also show results which are applicable to the interpretation of experimental data on physical systems such as H on Pd(lOO) and H on Fe(110). Other studies which are presented address fundamental theoretical questions about the nature of phase transitions in a two-dimensional geometry such as the existence of Kosterlitz-Thouless transitions or the nature of dynamic critical exponents. Lastly, we briefly mention multilayer adsorption and wetting phenomena and touch on the kinetics of domain growth at surfaces. 

Figure 19 shows the pressure effeets on the lateral self diffusion eoeffieient of sonicated DPPC and POPC vesicles. The lateral diffusion coefficient of DPPC in the LC phase decreases with increasing pressure from 1 to 300 bar at 50 °C. A sharp decrease in the D-value occurs at the LC to GI phase transition pressure. From 500 bar to 800 bar in the GI phase, the values of the lateral diffusion coefficient 1 x 10 cm /s) are approximately constant. There is another sharp decrease in the value of the lateral diffusion coefficient at the... 

Figure 2. Plot of self-diffusion coefficient, D (in m /s, log scale) of toluene in a 24.4 wt% aPS sample as a function of temperature. The arrow indicates the reported gel transition temperature for this concentration (ref. 1).

TRANSITION STRUCTURE TRANSKETOLASE Translational self-diffusion,... 

Self-diffusion in simple monatomic liquids at temperatures well above their glass-transition temperatures may be interpreted in a simple manner.1 Within such liquids, regions with free volume appear due to displacement fluctuations. Occasionally, the fluctuations are large enough to permit diffusive displacements. 

If equimolecular counterdiffusion takes place N = -N B (see Volume 1, Chapter 10) and the total pressure is constant, we obtain from equation 3.5 an expression for the effective self-diffusion coefficient in the transition region ... 

The change in the two-state distribution is easily monitored by a convenient one-wavelength measurement of the neutral form fluorescence, and this can be used for probing the membrane. The fairly large differences in wavelengths of excitation (300 nm), fluorescence of the neutral form (360 nm), and fluorescence of the anion form (480 nm) makes the fluorescence free from spectral interference. The variation of the P form fluorescence intensity with temperature showed a maximum at phase-transition temperatures (Tc) for both DMPC (23°C) (Fig. 2) and DPPC (42°C) membranes (Fig. 3). Figures 2 and 3 show a very nice correspondence of this variation with DPH fluorescence polarization and self-diffusion rate [93] of 22Na+. The coexistence of solid gel and fluid liquid-crystalline phases at Tc and the consequent imperfection of the membrane [93] result in a redistribution of... 

The results of estimation of coefficient of self-diffusion due to simulation for macromolecules with different lengths are shown in Fig. 12. The introduction of local anisotropy practically does not affect the coefficient of diffusion below the transition point M, the position of which depends on the coefficient of local anisotropy. For strongly entangled systems (M > M ), the value of the index —2 in the reptation law is connected only with the fact of confinement of macromolecule, and does not depend on the value of the coefficient of local anisotropy. At the particular value ae = 0.3, the simulation reproduces the results of the conventional reptation-tube model (see equation (5.21)) and corresponds to the typical empirical situation (M = 10Me). 

The delocalized state can be considered to be a transition state, and transition state theory [105], a well-known methodology for the calculation of the kinetics of events, [12,88,106-108] can be applied. In the present model description of diffusion in a zeolite, the transition state methodology for the calculation of the self-diffusion coefficient of molecules in zeolites with linear channels and different dimensionalities of the channel system is applied [88], The transition state, defined by the delocalized state of movement of molecules adsorbed in zeolites, is established during the solution of the equation of motion of molecules whose adsorption is described by a model Hamiltonian, which describes the zeolite as a three-dimensional array of N identical cells, each containing N0 identical sites [104], This result is very interesting, since adsorption and diffusion states in zeolites have been noticed [88],... 

Figure 7. Schematic diagram comparing the behavior of self-diffusion coefficients of oil (D0), water (Dw), and surfactant (Ds) expected for the droplet inversion transition and the bicontinuous transition of microemulsion depicted in Fig. 6.

Figure 8. Self-diffusion coefficients of the components of a microemulsion of sodium dodecyl sulfate (SDS), butanol, toluene, and NaCl brine. Vertical lines denote 2,3 and 3,2 phase transitions. Reprinted with permission from P. Guering and B. Lindman, Langmuir 1,464 (1985) [14]. Copyright 1985 American Chemical Society.

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