Free volume suspension

Analysis of mixture models, established techniques, 61 Analysis of styrene suspension polymerization continuous models, 210-211 efficiency, 211,212f,213 free volume theory, 215,217 initiator conversion vs. 

Most coatings are applied as solutions, emulsions, or suspensions of the pigment, and are converted to solid films after application, usually by allowing the solvent to evaporate. Latex, one of the simplest of paint formulations, is simply a dispersion of high molar mass polymer particles in water. In the first stage of solvent evaporation, the rate of evaporation is essentially independent of the presence of the dissolved or dispersed pigment. As the solvent evaporates, the viscosity increases and the free volume decreases, so that the rate of evaporation becomes dependent on how rapidly solvent molecules can diffuse to the surface of the film [782],... 

Aqueous suspensions (ca. 50 mg of sample) were irradiated with a 200W Osram HBO bulb with a total energy output at the flat window of the flask of 470 mW/cm2. Analysis of H2 and 02 evolved into the flask free volume (ca. 17.6 cm3) was made by GC using a molecular sieve 5 A column and Ar as carrier gas. Detection limit was 1 pmo 1 for 02 and 0.1 pmo 1 for HL in that volume. 

In some more recent theories, it was suggested that the free volume of the system could really be taken into account in describing the rheological properties of suspensions. This direction, however, is not sufficiently developed. 

The central point of the present survey is an attempt to show a complete analogy between the free volume of suspensions and that of molecular systems. It is characteristic that the limiting volume fraction of spherical filler particles leaves in the system another 25-40% of unoccupied volume. Precisely the same unoccupied volume exists in molecular systems if we liken them to a volume filled with spheres whose radii are calculated taking into account the Lennard-Jones potential. 

The glass transition in a molecular system sets in at the moment the free volume (about 2.5% of the free volume in glass transition of polymers) disappears. Loss of fluidity ( glass transition ) in suspensions occurs when the free volume of suspensions tends to zero. 

The experimental data obtained by us, presented in this survey and compared with literature data show that the free volume is, presumably, a structure parameter characterizing most reliably the properties of highly-loaded suspensions. Using this parameter is most beneficial when we have to deal with a polydisperse suspension and it is difficult to describe it by means of a model. 

Consider a dilute suspension of parallel cyhndrical particles of radius a with a surface charge density a or total surface charge Q = 2naa per unit length in a salt-free medium containing only counterions. We assume that each cylinder is surrounded by a cylindrical free volume of radius R, within which counterions are distributed so that electroneutrality as a whole is satisfied. We define the particle volume fraction 6 as... 

So far we have discussed electrophoresis of particles and drops in electrolyte solutions, i.e., salt-containing media. For those in salt-free media containing only counterions (e.g., nonaqueous media [63]), special consideration is needed. To treat a suspension of spherical particles in a salt-free medium, one usually employs a free volume model, in which each sphere of radius a is surrounded by a spherical free volume of radius R within which counterions are distributed so that electrical neutrality as a whole is satisfied. The particle volume fraction is given by 4>= (fl// ). We treat the case of dilute suspensions, viz., < C lara/R< 1. Let the concentration (number density) and valence of the counterions be n and — z, respectively. For a spherical particle carrying surface charge density a or total surface charge Q = 4ira a, it follows from the electroneutrality condition that... 

For the free volume fraction a of interacting polymers in a suspension of hard spherocylinders we can write down a revised form of (6.39),... 

Eq.(17) shows how the viscosity of a liquid changes with the temperature and other physical parameters. It also indicates that the constant A in Eq.(lO) is dependent on the temperature. The free volume concept is important and will be used again to treat the colloidal suspension systems later. 

Before the ER effect of suspensions is addressed, the viscosity of suspensions without the application of an external electric field is introduced for comparison. There is a tremendous amount of literature on the viscosity of colloidal suspensions [14,15]. An exhaustive literature survey on this subject is beyond the scope of this book. Instead, the free volume concept is a very important and intriguing idea, and is thus focused on in the following sections for deriving the viscosity equation. 

Where Vjp is the volume of individual particle, and is equal to Am" ) , r is the particle radius. The total volume that each particle occupies in the suspension is the volume of each individual particle plus the free volume per particle ... 

Eq. (42) is only valid when < ><1%. Ball [26] assumed that the effect of the panicle in a concentrated suspension is the sum of the effect of the particle added sequentially. The free volume unoccupied by the particle relative to the maximum packing fraction is ... 

When the particle volume fraction is increased by an amount of d<(), the particles already in the suspension suffer a erowding effeet, which causes the viscosity increase by (1. A small free volume decrease results in a large viscosity increase. Since Rq. (42) can be written in the form ... 

In the previous section, the free volume concept is used to treat the viscosity of a pure liquid. This important concept will be used again to treat the viscosity of a suspension. The main idea is that the viscosity of a suspension should be inversely proportional to the free volume of the suspension. In other words, more free volume is available for the particle to move freely, a much less viscous force or viscosity will be generated. The term (l- /( ,) to some extent represents the normalized free volume in the equations shown above. However, this term may not accurately... 

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