Hydrocarbon radius

Below, we will be concerned with spherical microemulsion droplets, composed of a core of decane and covered by the surfactant C12E5. For this system, there exists an extensive set of accurate experimental data and we can identify three different characteristic radii for these droplets, as illustrated in Figure 17.13. We define a hydrocarbon radius, rhc, which corresponds to the radius at the polar-apolar interface that essentially is located in... 

From self-diffusion data, we have found that the structure is composed of closed droplets. NMR data and SANS data, analysed at higher q values, have demonstrated that the droplets have a concentration-independent size. The SANS data have also given us one size of the droplets, i.e. the hydrocarbon radius (and the shape), while collective and self-diffusion data have provided us with a value for the hydrodynamic radius. Knowing that we have identified a dilution line of spherical droplets of constant size, we can now turn to investigate the interactions. The latter affect properties such as osmotic pressure, diffusion and viscosity. The osmotic pressure, jr, can be measured, for example, in a membrane osmometer. A more common experiment for colloidal systems, however, is to measure the osmotic compressibility (97t/90) For a binary system, the osmotic compressibility is proportional to the structure factor at = 0, as follows ... 

The interface separating oil and the alkyl chain of C12E5 from the ethylene oxide chain and water is known to have an essentially invariant area, per molecule, independent of the curvature. It is therefore useful to define the curvature at this particular interface, and the corresponding sphere radius, which we denote the hydrocarbon radius, becomes... 

For predicting liquid diffiisivities of binary nonpolar liquid systems at high solute dilution, Umesi " developed a method that only depends on the viscosity of the solvent (2) and the radius of gyration of the solvent (2) and the solute (1). The Technical Data Book— Petroleum Refining gives the method and values of the radii of gyration for common hydrocarbons. Errors average 16 percent but reach 30 percent at times. 

Two physically reasonable but quite different models have been used to describe the internal motions of lipid molecules observed by neutron scattering. In the first the protons are assumed to undergo diffusion in a sphere [63]. The radius of the sphere is allowed to be different for different protons. Although the results do not seem to be sensitive to the details of the variation in the sphere radii, it is necessary to have a range of sphere volumes, with the largest volume for methylene groups near the ends of the hydrocarbon chains in the middle of the bilayer and the smallest for the methylenes at the tops of the chains, closest to the bilayer surface. This is consistent with the behavior of the carbon-deuterium order parameters,. S cd, measured by deuterium NMR ... 

The interfacial activity is determined by the sterical properties of the molecule. At the interface the spatial demand A0 of the hydrophobic part of the molecule is higher because of the second chain of the internal sulfonate compared with the terminal sulfonate. Thus, the surface concentration of the surfactant molecules is lower. That means that the hydrocarbon chains are laterally oriented and therefore cover the interface between the solution surface and air more completely. Because the ratio of the spatial demand of the head group to the volume of the alkyl chain governs the radius of the micellar surface, it... 

Highly monodisperse reversed micelles are formed by sodium bis(2-ethylhexyl) sul-fosuccinate (AOT) dissolved in hydrocarbons that are in equilibrium with monomers whose concentration (cmc) is 4 X 10 M, have a mean aggregation number of about 23, a radius of 15 A, exchange monomers with the bulk in a time scale of 10 s, and dissolve completely in a time scale of 10 s [1,2,4,14], Other very interesting surfactants able to form reversed micelles in a variety of apolar solvents have been derived from this salt by simple replacing the sodium counterion with many other cations [15,16],... 

By small-angle neutron scattering experiments on water/AOT/hydrocarbon microemulsions containing various additives, the change of the radius of the miceUar core with the addition of small quantities of additives has been investigated. The results are consistent with a model in which amphiphilic molecules such as benzyl alcohol and octanol are preferentially adsorbed into the water/surfactant interfacial region, decreasing the micellar radius, whereas toluene remains predominantly in the bulk hydrocarbon phase. The effect of n-alcohols on the stability of microemulsions has also been reported [119],... 

With the development of new instrumental techniques, much new information on the size and shape of aqueous micelles has become available. The inceptive description of the micelle as a spherical agglomerate of 20-100 monomers, 12-30 in radius (JJ, with a liquid hydrocarbon interior, has been considerably refined in recent years by spectroscopic (e.g. nmr, fluorescence decay, quasielastic light-scattering), hydrodynamic (e.g. viscometry, centrifugation) and classical light-scattering and osmometry studies. From these investigations have developed plausible descriptions of the thermodynamic and kinetic states of micellar micro-environments, as well as an appreciation of the plurality of micelle size and shape. 

The more incisive calculation of Springett, et al., (1968) allows the trapped electron wave function to penetrate into the liquid a little, which results in a somewhat modified criterion often quoted as 47r/)y/V02< 0.047 for the stability of the trapped electron. It should be noted that this criterion is also approximate. It predicts correctly the stability of quasi-free electrons in LRGs and the stability of trapped electrons in liquid 3He, 4He, H2, and D2, but not so correctly the stability of delocalized electrons in liquid hydrocarbons (Jortner, 1970). The computed cavity radii are 1.7 nm in 4He at 3 K, 1.1 nm in H2 at 19 K, and 0.75 nm in Ne at 25 K (Davis and Brown, 1975). The calculated cavity radius in liquid He agrees well with the experimental value obtained from mobility measurements using the Stokes equation p = eMriRr], with perfect slip condition, where TJ is liquid viscosity (see Jortner, 1970). Stokes equation is based on fluid dynamics. It predicts the constancy of the product Jit rj, which apparently holds for liquid He but is not expected to be true in general. 

The properties of the micelle are very well defined so, for example, the maximum micelle radius is a simple function of the hydrocarbon chain in the monomer. 

Figure 23. Radial segment density profile through a cross-section of a highly curved spherical vesicle. The origin is at r = 0, and the vesicle radius is very small, i.e. approximately r = 25 (in units of segment sizes). The head-group units, the hydrocarbons of the tails and the ends of the hydrocarbon tails are indicated. Calculations were done on a slightly more simplified system of DPPC molecules in the RIS scheme method (third-order Markov approximation), i.e. without the anisotropic field contributions...

The Dp and Dq are the diffusion coefficients of probe and quencher, respectively, N is the number molecules per millimole, andp is a factor that is related to the probability of each collision causing quenching and to the radius of interaction of probe and quencher. A more detailed treatment of fluorescence quenching including multiexponential intensity decays and static quenching is given elsewhere/635 There are many known collisional quenchers (analytes) which alter the fluorescence intensity and decay time. These include O2/19 2( 29 64 66) halides,(67 69) chlorinated hydrocarbons/705 iodide/715 bromate/725 xenon/735 acrylamide/745 succinimide/755 sulfur dioxide/765 and halothane/775 to name a few. 

Fig. 3 Electrochemical and homogeneous standard free energies of activation for self-exchange in the reduction of aromatic hydrocarbons in iV.A -dimethylformamide as a function of their equivalent hard sphere radius, a. 1, Benzonitrile 2, 4-cyanopyridine 3, o-toluonitrile 4, w-toluonitrile 5, p-toluonitrile 6, phthalonitrile 7, terephthalonitrile 8, nitrobenzene 9, w-dinitrobenzene 10, p-dinitrobenzene 11, w-nitrobenzonitrile 12, dibenzofuran 13, dibenzothiophene 14, p-naphthoquinone 15, anthracene 16, perylene 17, naphthalene 18, tra 5-stilbene. Solid lines denote theoretical predictions. (Adapted from Kojima and Bard, 1975.)...

---