Small angle neutron scattering from droplets

3 Small angle neutron scattering from droplets 

The theoretical description in terms of spherical harmonics also yields a relation between the size polydispersity index p of the microemulsion droplets and the bending elastic constants [43]. The quantity p is accessible by SANS [51, 52, 59-61]. For polydisperse shells as obtained by using deuterated oil and heavy water for the preparation of the microemulsion (contrast variation), one can account for the droplet polydispersity by applying an appropriate form factor, e.g. containing a Gaussian function to model the size distribution [52, 59, 62]. A possible often-used choice is the following form factor 

t is a parameter describing the thickness of the surfactant layer and a (or p) contains the information about the size polydispersity of the micro emulsion drops. R0 is the mean value of the shell inner and outer radii. Besides this approach other distribution functions were also already applied to model the droplet polydispersity [52]. The absolute scattering intensity I(q), which is the experimentally observed quantity is given by 

In this relation, N is the number density of the scattering microemulsion droplets and S(q) is the static structure factor. Equation (2.12) is only strictly valid for the case of monodisperse spheres. However, for the case of low polydispersities the occurring error is small [63, 64]. S(q) describes the interactions between and the spatial correlations of the droplets. These are in general well approximated by hard sphere interactions in microemulsion systems [65], The influence of inter-particle interactions as described by S(q) canbe estimated at least for S(0) using the Carnahan-Starling expression [52,64,66] 

In this equation, f hs is the hard sphere volume fraction which is about 14% larger in o/w-droplet microemulsions of non-ionic surfactant than the dispersed volume fraction. This is caused by the water penetration in the surfactant layer [64]. S(q) approaches unity for q values smaller than the minimum of I(q). This behaviour occurs even for fairly high volume fractions in non-ionic surfactant systems (see for example Fig. 8 in Ref. [64]). Seeing that the value of the radius is fixed by the position of the minimum of I(q), the approximation of S(q) 1 in Eq. (2.12) does not lead to a significant error in the determination of Rq if the low q part of the experimental curve is not taken into 

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Even in dilute solutions they associate (49, 50). Published sizes of the micelles vary from 2 to 4 run. Sophisticated analytical techniques such as small-angle X-ray diffraction (SAXS), small-angle neutron scattering (SANS), and NMR were used to study the asphaltene particle or micelle sizes (51). MacKay (15) reported that a MWtof 10,000 g/mol would correspond to a 2 to 4-nm cluster. This is very much smaller than a 1-pm water droplet, and considered to be 1/100 to 1/1000 the droplet diameter. This topic is worthy of a review on its own. However, the colloidal properties of asphaltenes, micelles, and... 

Figure 13.8 shows the first separation of small molecules by FFF. Ascorbic acid was separated from toluene through a secondary chemical equilibrium with field-retained microemulsiom droplets. Once again, the exchange between the aqueous phase and the swollen micelles is low, i. e., the efficiency is low and broad peaks are obtained (Figure 13.8). There are so many powerful techniques for small molecule separation that micellar FFF was not used for this purpose. Its interest could be in the physicochemical study of the micellar or microemulsion structure. For example, in the case of the Figure 13.8 experiment, the separation allowed the estimation of the average mass of the mobile phase microemulsion droplets (1.4x 10 %) and consequently, its radius (35 nm) [38], These values can be obtained by heavy methods such as small angle neutron scattering or high resolution NMR [38]. Micellar FFF can be an easy alternative in such studies.

Details are given of a number of indirect techniques for characterising droplet or particle sizes before and after PS polymerisation without diluting the system. Data from small angle neutron scattering on PS microemulsions are presented. 15 refs. 

In the 2 region only the surface area of the droplets is preserved their volume can be adjusted so that the droplets take their optimum size i.e., a radius that locally minimizes the interfacial free energy. depends only on temperature it is independent of composition [23]. At the emulsification boundary / op( = R , whereas in the 20 region / optl < For temperatures sufficienUy below those corresponding to the micellar size and several degrees away from T, the optimum radius has been determined by small-angle neutron scattering (SANS) experiments to vary as [31]... 

Nevertheless, much is known about the structure of adsorbed 6-casein, certainly more flian is known for any other food protein, and various techniques have been used to study the adsorbed protein. The first evidence from DLS showed that 6-casein adsorbed to a polystyrene latex caused an increase in the radius of the particle by 10 to 15 nm (84). Later studies using small-angle X-ray scattering confirmed this and showed, in addition, that the bulk of the mass of the protein was close to the interface, so the interfacial layer was not of uniform density throughout (85). Neutron-reflectance studies also showed that most of the mass of protein was close to the interface (86). Only a relatively small portion of the mass of the adsorbed protein extends from the tightly packed interface into the solution, but it is this part which determines the hydrodynamics of the particle and which is almost certainly the soiuce of the steric stabilization which the 6-casein affords to emulsion droplets (84). It is to be noted that all of the studies just described were performed on latex particles or on planar interfaces however, it has also been demonstrated that the inter-facial structiues of 6-casein adsorbed to emulsion dro plets resemble those of the model particles (39, 85). Although detailed control of emulsion droplets dining their... 

The variation of the average water droplet size can be deduced from small-angle X-ray or neutron scattering, as well as by classical light scattering measurements. The maximum water content can be obtained by titration and gives the evolution of W ax at a given temperature. Hence, the effect of the solute on the spontaneous curvature of the surfactant film in the presence of solute can also be deduced in the quaternary final state (32, 33). 

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