Self-diffusion 662 INDEX

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). 

Figure 4 Self diffusion coefficient of the small probe, CH3-CH2-CH2-NBD, versus the PDMS polymerization index (now only unlabelled PDMS is used). Given the low accuracy of the experiment at such high values of the diffusion coefficient (relative uncertainty larger than 10%, contrary to the data on figure 3, which are all slower by more than one decade and thus far easier to measure accurately), it seems that there is no significant change of the friction...

Over 50 methods have been employed in the literature to determine CMC values of bile salt solutions (reviewed in [6]). These can be divided into two broad categories (a) methods requiring no physical or chemical additive in the bulk solution and (b) methods involving the use of an additive in the bulk solution. The former methods, also called non-invasive, include surface tension and the measurements of a variety of colligative bulk properties (conductivity, turbidimetry, osmometry, self-diffusion, refractive index, modal volumes, electrometric force) or electromagnetic bulk properties (NMR, sound velocity and adsorption, etc.), all as functions of bile salt concentration. The second set of methods, also called invasive, depends upon a change in some physical or chemical property of an additive which occurs with the formation of micelles. These include the spectral change of a water-soluble dye, micellar solubilization of a water-insoluble dye, interfacial tension at liquid-liquid interfaces, and partition coefficients between aqueous and immiscible non-polar phases. Whereas a detailed discussion of the merits and demerits of both approaches can be found elsewhere [6], non-invasive methods which are correctly utilized provide the most reliable CMC values. 

The thermophysical and thermodynamic properties of liquid water as well as its chemical properties, all depend on the temperature and the pressure. The thermophysical and thermodynamic properties include the density p, the molar volume V = M/p, the isothermal compressibility/ct = P (dp/d P)t = —V (dV/dP)T, the isobaric expansibility ap = —p dp/dT)p = V dV/dT)p, the saturation vapour pressure p, the molar enthalpy of vapourization Ayf7, the isobaric molar heat capacity Cp, the Hildebrand solubility parameter 3h = [(Ay// —RT)/ the surface tension y, the dynamic viscosity rj, the relative permittivity Sr, the refractive index (at the sodium D-line) and the self-diffusion coefficient T>. These are shown... 

Two groups have used physical measurements e.g. density, viscosity, refractive index, and optical rotation) to determine the compositions of solutions of water-sucrose-D-glucose (or invert sugar) at various temperatures. The diffusion coefficient for self-diffusion of D-fructose in an aqueous system has been measured over a range of concentrations and temperatures. The yields of trapped electrons and radicals have been determined following y-irradiation of frozen aqueous solutions of sugars. ... 

The index of refraction of the material in the layer can be estimated to be 1.333. The total intensity of the quasi elastically scattered light is proportional to the isothermal compressibility. From intensity measurements we estimate it to be about a factor 500 higher than the compressibility of water at O C. A diffusion constant, which describes the dynamics of the entropy fluctuations, has been determined to be about 3 10" cm /s. This value has to be compared with the thermal diffusivity in water a 10 cm /s or the constant for self diffusion in water Djj20 lO" cm /s. 

Isothermal frontal polymerization (IFP) is a self-sustaining, directional polymerization that can be used to produce gradient refractive index materials. Accurate detection of frontal properties has been difficult due to the concentration gradient that forms from the diffusion and subsequent polymerization of the monomer solution into the polymer seed. A laser technique that detects tiny differences in refractive indices has been modified to detect the various regions in propagating fronts. Propagation distances and gradient profiles have been determined both mathematically and experimentally at various initiator concentrations and cure temperatures for IFP systems of methyl methacrylate with poly(methyl methacrylate) seeds and wilh the thermal initiator 2,2 -azobisisobutryonitrile. 

II.4 Self-consistency removing the hypothesis of fixed obstacles Obviously the hypothesis of fixed obstacles, crucial for the application of reptation ideas to melts or entangled polymer solutions, and which makes it possible to reduce the real many-body problem to a one-chain problem, might not be valid and has to be carefully tested experimentally. Diffusion measurement techniques in which labelled chains are used are unique tools to do so, as labelled and unlabelled chains of different polymerization index (respectively N and P) can be used systematically, to... 

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