Determining Particle Size from SANS and SAXS
There are two complementary approaches to determining the particle dimensions in a dilute dispersion. By calculating the scattering from an assumed particle shape e.g. a sphere and varying the parameters e.g. radius, number of particles until a good agreement is found between measured data and model. If no agreement is found, then we assume another shape and Figure 12.12 Form factor of spherical particle. Figure 12.12 Form factor of spherical particle. repeat the fitting process. This is...
Wettability Envelopes
It maybe imagined that up until now we have a rule which tells us if wetting will occur when placing a liquid on a solid. This comes from knowing the surface tension of the liquid and the surface energy of the solid. Thus the rule which has been formulated states that 'a liquid, having a lower surface tension than the solid surface energy, will wet that solid'. In practice it is found that this is not always the case and thus it is not an immutable rule. A 2D map of wetting can be constructed...
Spreading of a Liquid on a Liquid
Spreading can also be observed for two immiscible liquids when one is placed on the surface of the other. The lens formed in this case can be described by a 'generalised Young's equation' 9.7 . This is necessary since all the surfaces involved are deformable as shown in Figure 9.11. Under these conditions we need to allow for the contact angles of each to be resolved in a horizontal direction, Ywv cos 03 Yov cos 01 Yow cos 02 9.7 The picture is relatively complicated as spreading develops with...
Wetting
Armed with the previous definitions, wetting per se can now be discussed. For some liquids a zero contact angle is obtained and might also be called perfect wetting and hence spontaneous spreading. Another possibility is partial wetting, where a contact angle is subtended somewhere between 0 and 90 . The 90 may well be thought of as an arbitrary distinction between wetting and non-wetting but nonetheless we find it an important distinction. An angle subtended between 90 and 180 in the liquid...
Surface excess and thermodynamics of adsorption
Following on the formation of an oriented surfactant monolayer, a fundamental associated physical quantity is the surface excess. This is defined as the concentration of surfactant molecules in a surface plane, relative to that at a similar plane in the bulk. A common thermodynamic treatment of the variation of surface tension with composition has been derived by Gibbs 19 . An important approximation associated with this Gibbs adsorption equation is the 'exact' location of the interface....
Info Lbo
Figure 4.3 Determination of the interfacial adsorption isotherm from surface tension measurement and the Gibbs adsorption equation. Figure 4.3 Determination of the interfacial adsorption isotherm from surface tension measurement and the Gibbs adsorption equation. of a material at an interface, its surface activity, can be determined from the measurement of the interfacial tension as a function of solute concentration. Note that in Equations 4.13 and 4.15 , for dilute surfactant systems, the...
Cohesion and Adhesion
Surface energies can also be used to define cohesion and adhesion from the condition of spontaneous spreading. Adhesion and cohesion simply define the interactions which lead to the cohesive nature of materials and the adhesive nature of one material when in contact with another material. There is no implication in these definitions of any chemical bonding. Adhesion between a solid and liquid is defined as the work required to separate the solid from the liquid. Thus, the work of adhesion...
Factors affecting the CMC
Many factors are known to strongly affect the CMC. Of major effect is the structure of the surfactant, as will be described below. Also important, but to a lesser extent, are parameters such as counterion nature, presence of additives and change in temperature. The hydrophobic group the 'tail'. The length of the hydrocarbon chain is a major factor determining the CMC. For a homologous series of linear single-chain surfactants the CMC decreases logarithmically with carbon number. The...
Microemulsion phase behaviour
Solubilisation and interfacial properties of microemulsions depend upon pressure, temperature and also on the nature and concentration of the components. The determination of phase stability diagrams or phase maps , and location of the different structures formed within these water salt -oil-surfactant-alcohol systems in terms of variables are, therefore, Figure 5.6 Film rigidities 2 K K as a function of total alkyl carbon number n-C from Winsor II micro-emulsions. The lines are guides to the...
Guinier Plots to Determine Radius of Gyration
It turns out that at low Q Q lt 1 RG the scattering from a dilute dispersion is insensitive to the shape of the particles. The intensity, I Q , only depends on contrast, number of particles, particle volume and the radius of gyration as shown in this approximate equation, known as Guinier's law 15 I Q Ap2Np Vj exp - Q2 R2G 3 12.13 The radius of gyration was introduced in Section 12.4 for light scattering and is a very convenient quantity for characterising the size of a particle. Figure 12.13...
Theoretical Models of Polymer Structure
Although the contour length of polymer chains maybe substantial, because of bond rotation and elasticity, they are rather compact. Flory first suggested that a polymer chain should undergo a random walk through space as shown in Figure 6.4. Ignoring the volume of the chain this model predicts that the end to end distance, R, is proportional to the square root of the number of bonds, n. The proof of the random walk for n steps is quite straightforward using the vector model. Each step i is...
A Mil
When the particle separation is small h 2a this reduces to a simple form of Figure 3.1 London forces between atoms in two adjacent colloidal particles. Figure 3.1 London forces between atoms in two adjacent colloidal particles. Table 3.1 Hamaker constants for various materials Particles Hamaker constant J 10 20 Media Hamaker constant J 10 20 Poly methyl Silica Titanium Metals Au, Ag, Ft, The Hamaker constant is a function of both the electronic polarisability and the density of the material....
Polar Materials
Polar materials can be treated in a similar manner by adding extra contributions to the total surface tension 8 . The surface tensions can be divided into separate independent terms, the most simple being the addition of the polar component and the dispersive component, Yp and yd thus It is also possible, if necessary, to break the surface tension down into other components, hydrogen bonding for instance. We could add the hydrogen bonding term to the dispersive term, and add in a polar term to...
The cloud point
For non-ionic surfactants, a common observation is that micellar solutions tend to become visibly turbid at a well-defined temperature. This is often referred to as the cloud point, above which the surfactant solution phase separates. Above the cloud point, the system consists of an almost micelle-free dilute solution at a concentration equal to its CMC at that temperature, and a surfactant-rich micellar phase. This separation is caused by a sharp increase in aggregation number and a decrease...
Radius of gyration
It is not straightforward to measure R directly but several experimental methods allow us to measure the radius of gyration, RG, of a polymer chain by, for example, viscosity or scattering. The value of RG depends not only on the chain length but also on the shape of the molecule. Equation 6.9 defines RG, and ri is the distance of monomer i from the centre of mass. Hence long rods have a very large radius of gyration. Figure 6.5 illustrates how shape determines RG for a random coil, a solid...
Depletion Interactions
Addition of free non-adsorbing polymer in solution induces so-called depletion interactions between colloidal particles. To gain an understanding of this we will discuss the Asakura-Oosawa AO model of depletion interactions. The particles are considered as hard spheres of diameter d and the polymers are represented by little spheres of diameter 25. Within this description the polymer coils do not interact, and hence the osmotic pressure of the polymer solution, n, can be calculated from their...
The Krafft temperature
As for most solutes in water, increasing temperature produces an increase in solubility. However, for ionic surfactants, which are initially insoluble, there is often a temperature at which the solubility suddenly increases very dramatically. This is known as the Krafft point or Krafft temperature, TK, and is defined as the intersection of the solubility and the CMC curves, i.e. it is the temperature at which the solubility of the monomeric surfactant is equivalent to its CMC at the same...