Biomedical Engineering Reference
In-Depth Information
20
15
Δ T ( ° C)
-8.5
-4.5
-3.0
-2.5
q m 2
10
5
0
0
10
20
30
40
q 2
× 10 6 (nm -2 )
Cahn - Hilliard plots of the early stages of phase separation of the ternary mixture PS - PB - Tol at
solvent volume fraction 0.925 (nearly critical mixture) quenched to various depths Δ T from 2.5°C
to 8.5°C below the cloud point temperature. The arrows indicate the position of the maximum q m .
From Sasaki and Hashimoto ( 1984 ) © 1984 American Chemical Society.
Figure 10.4
100 s), the relaxation (or growth) rate of the
intensity or of concentration can be measured from the slope of scattered intensity versus
q. Later (t
In the early stage of phase separation (t
150 s), the intensity change with time deviates from exponential, owing to the
onset of coarsening processes. As phase separation progresses further, the peak position
starts to shift towards small angles, indicating that the periodicity of
fluctuations, as well
as the amplitude of
fluctuations, increases further with time.
ω q /q 2 versus q 2 are shown in Figure 10.4 , and different temper-
ature jumps at the early stages help to determine D eff . This is found to be independent of
Δ
Cahn
-
Hilliard plots of
T up to 10°C, for various proportions of these ternary systems. In measurements
performed at large quench depths, deviations from a straight line appear in the plots of
ω q /q 2 versus q 2 , suggesting the limitations of linearized theory.
10.3.6
Kinetics of demixing and gelation in ternary systems
In both biological and application systems, polysaccharides and proteins are often
present together. When a certain concentration of these biopolymers in the mixture is
exceeded, phase separation often results (Tolstoguzov et al., 1985 ; Zasypkin et al., 1997 ;
Doublier et al., 2000 ; Scholten et al., 2002 ). A very large number of ternary systems
containing proteins and polysaccharides in aqueous medium are described as thermo-
dynamically incompatible. When the Flory
-
Huggins interaction parameter for biopol-
-
ymer A
biopolymer B interactions is positive, indicating a net repulsion between the
biopolymers, segregation occurs, so that the system
finally demixes into two phases, each
enriched with one of the biopolymers. This occurs for most such biopolymer systems,
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