Interparticle structure factor

The structure factor accounts for interparticle interferences. It relates to the so-called pair distribution function, g(r), of particles through ... 

The function S(Q) in the above equation is known as the (interparticle) structure factor or static structure factor (the label static is used to differentiate S(Q) from its time-dependent version, known as the dynamic structure factor) and contains information on how the particles are spatially distributed in the dispersion. When there are no interparticle effects, S(Q) becomes unity and we recover Equation (60) from Equation (79). 

V p is the volume of one scattering body (Ap)2 is the contrast term, which is described later P(q) is a function known as the form or shape factor S(q) is commonly called the interparticle structure factor Bmc is the incoherent background signal... 

Table 12 Peak positions from structure factor maxima, ds, and mean interparticle distances,...

For small particles, g r) is substantially different from unity only at interparticle distances r Then, the structure factor is equal to the inverse osmotic compressibility of the suspension ... 

The kinetic factor D(q) characterizes the average particle flux, and S(q), the interparticle structure factor, is equivalent to the integrated scattered light intensity. When the range of interparticle interactions a is comparable with d, the mean interparticle distance, then D(q) may exhibit angle-dependent behavior. In the limits q- 0, co, D(q) reduces to the translational diffusion constant Dt (93), The data of Berne and... 

The interparticle structure factor, S(Q), is also a dimensionless function describing the modulation of the scattered intensity by interference effects between radiation scattered from different scattering units in the sample. It therefore gives information on the relative positions of the scattering objects. 

This describes the interparticle correlations and gives access to the interaction between the entities. Ri is the vector to the centre of mass coordinate of particle i. The structure factor is close to unity at all Q values for dilute systems and, hence, Eq. 63 can be written as ... 

In this work we will mostly focus on dilute systems where interparticle interactions are negligible. A more detailed discussion concerning structure factors can be found in, e.g., [71, 75, 77]. 

This kinetic zero average contrast (KZAC) experiment [100-102] is an extension to the static zero average contrast (ZAC) described in Sect. 3.1.7. ZAC is used to effectively remove the structure factor such that interparticle correlations are eliminated and the single entities are visible, whereas in KZAC the trick is used to render mixing processes hence, diffusion and transport become observable without perturbing the system in any substantial way. 

However, the structure and composition of microdroplets in which the reaction takes place are not the only parameters controlling polymerisation. We shall see later that particles in the initial microemulsion cannot be considered as independent reactors since interparticle interactions play an important role. Small angle light and neutron scattering experiments have shown that these interactions are attractive [6.20]. There is a clear increase in these attractive interparticle forces as the proportion of acrylamide is raised. In particular, this has two consequences the second virial coefficient of osmotic pressure takes negative values the peak in the structure factor which characterises a hard sphere system is no longer present. 

As Friman and Rosenholm are aware, there is substantial interparticle spatial correlation at the solution conditions studied by them. Their measurements extend out to scattering vectors s (= 2 sin 6/X) of 0.5 nm" equivalent to a momentum transfer Q (= 47rsin 6/X) of 3.1 nm" As shown by Hayter and Zemb [43] for the same system, the structure factor describing intermicellar spatial correlations, S(Q), shows considerable structure out to this value of Q (see figure 2, Hayter and Zemb). 

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