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150
Q
Im3m
Q
Im3m
100
H
L
H
50
Q
la3d
CPS
CPS
DIS
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
f
A
Figure 1.3
Theoretical phase diagram for a diblock copolymer system [Readapted
with permission from Matsen and Bates (1996). Copyright 1996, American Chemical
Society.]
This explains why microphase segregation in lipid-water mixtures is nearly
always observed. Therefore, the loss of entropy in packing together the differ-
ent lipid molecules is always small compared to the enthalpic gain driving
microphase segregation, and self-assembly is driven nearly entirely by enthalpy
gain. These concepts are summarized in Figure 1.4.
Another important difference between block copolymers and lipids is the
sequence of phases found, for example, on a isothermal, concentration-titrating
experiment. Matsen has formulated a theoretical phase diagram for an A-B
block copolymer plus an A homopolymer pair (Matsen, 1995a,b), which is
exactly the system needed to draw direct comparisons with the lipid-water
system of interest.
Consider the arrow in Figure 1.5 in which the phase diagram of such a
system, an A-B diblock copolymer, is reported as a function of the block
copolymer volume fraction of block A,
f
, versus the volume fraction
of the
additional homopolymer A. Upon adding the homopolymer A, the system
goes through spheres, hexagonal, gyroid, and lamellar, which is also referred
to as a “normal” sequence since the curvature is progressively decreasing as
a consequence of the increasing overall A fraction. The analog experiment
ϕ
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