As illustrated in Figure 17.14d the value of the modulus increases with
decreasingtemperature, once a gel has formed. This is as observed for casein
gels, but the explanation for heat-set gels is uncertain.
Large deformationproperties also vary widely. The strain at fracture
efris mostly between 0.3 and 1.0; the fracture stress can be up to 25 kPa.
b-Lactoglobulin gels formed at a pH close to the pI are brittle, whereas
rubberlike gels are formed at high pH; this qualitatively agrees with the
difference in gel structure discussed. Again, relations have to be established
separately for each protein system.
Question
Consider the situation given in Figure 17.19 at the moment that a gel is formed. (a)
What would be the size of the particles making the fractal gel, i.e., what is the value
ofaeff? (b) Assuming that unhindered perikinetic aggregation occurs (i.e.,W¼1),
what would be the aggregation time needed to form a gel? (c) Is the latter value a
reasonable one?
Answer
(a) According to Eq. (17.16),B¼ða^2 eff=KÞj^2 =ðD^3 Þ. We assumeK&80 andD¼2.4,
as were given above. The figure givesB& 10 ^13 m^2. The concentration of aggregating
material was about 1.4%; taking into account that the molecules are denatured and
hence have an increased voluminosity, and remembering that the molecules in the
particles are probably not closely packed, a mass fraction of 0.014 may correspond to
a volume fraction of about 0.05. This then would yieldaeff&20 nm. (Electron
micrographs show that the particles have a diameter of at least 50 nm, i.e., about the
same.) (b) Equation (13.20) givestcr¼t 0 : 5 qD. Equation (13.3) gives an expression for
t0.5, and assuming that the viscosity was 1 Pa?s, we arrive att0.5¼0.13 ms.q¼
Rgel/aeff ¼j1/(D3), according to Eq. (13.15). Henceq&150 and we arrive at
tcr& 0 :02 s. (c) The value fortcris not reasonable, simply because we assumedW¼1,
whereas it was concluded above that gel formation will not occur unless the particles
show some mutual repulsion, henceW>>1. Even forW¼ 104 , for instance,tcr
would be 200 s, i.e., small compared to the time needed to form a sufficient number
of particles.
17.2.5 Mixed Systems
In practice, various mixtures of gel forming materials are applied, giving rise
to gels of widely varying properties. We will briefly mention some types; the
discussion is for the most part qualitative.