macrophase separation. However, BCPs do undergo microphase separation and form
a variety of self-assembled ordered nanostructures at much smaller length scales
(typically 10-100 nm). The nanostructure formation process is the cumulative result
of enthalpy gain due to polymer segregation (into domains) and the corresponding
loss in entropy due to chain stretching away from the interface. The chemical bond
between the two blocks becomes the boundary between the two nanodomains. The
dimensions of these nanodomains are a function of the radius of gyration (R g ) of the
polymer chains (which in turn is a function of degree of polymerization, N).
The product χN of a BCP system determines the strength or degree of segregation
of these nanoscale domains. Theoretical calculations of coil-coil BCPs show that if
χN > > 10.5, BCP undergoes microphase separation and forms ordered structures
separated by sharp phase boundaries, and the system is considered to be in the strong
segregation limit (SSL). For χN < < 10.5, entropic factors dominate and the BCP
system is in a state of disorder or in the weak segregation limit (WSL) (Bates and
Fredrickson 1990; Hamley 1998; Muthukumar et al. 1997). While χN determines the
strength of microphase separation, the morphology of the BCP nanostructure is
determined by the volume fraction ( f ) of the combining blocks. 1-dimensional
(1D) structures called lamellar (L) morphology is commonly observed at symmetric
volume fractions ( f A ~ 0.5) in which alternating layers of polymer A and B are
stacked together. Asymmetry in f leads to nonplanar morphologies with curved
interfaces so that the stretching penalty of the majority block is reduced. The degree
of curvature increases with increase in the degree of asymmetry leading to morphologies such as 3D honeycomb-like structure called the double gyroid (G) ( f A ~
0.28–0.34), 2D hexagonally close packed cylinders (C) ( f A ~ 0.17–0.28), and 0D
spheres (S) ( f A < 0.17) of the minority block forming a body-centered cubic (BCC)
lattice in the matrix of the majority block. L, G, C, and S, schematically shown in
Fig. 1 (Grason 2006), are the four traditional BCP morphologies and are shown to be
the only structures that possess a constant mean curvature at the corresponding f and
are hence thermodynamically stable. A periodically ordered BCP phase structure
turns into a disordered melt as a function of temperature. The temperature at which
the order to disorder transition occurs is called order-disorder transition temperature
(ODT), and it varies form system to system.
Numerous research groups have investigated the phase behavior of coil-coil
BCPs using both theoretical calculations and experimental methods. At the ODT,
all the BCP phases (except the S morphology) undergo direct transition into a
disordered state. The BCC S structure transforms into a disordered micellar structure
which ultimately forms a disordered melt at two different temperatures called the
lattice disorder temperature (LDOT) and demicellization temperature (DMT),
respectively (Han et al. 2000). Helfandet al. and Semenov et al. provided the basis
for quantitative analysis of BCP phase behavior in the SSL using a self-consistent
field theory (SCFT) approach based on Meier’s criterion of enthalpic gain and
entropic loss in high M n systems (Helfand and Wasserman 1976; Helfand and
Wasserman 1978; Meier 1969; Semenov 1985). Leibleret al. investigated the
phase behavior of BCPs in the high temperature or WSL regions and in the regions
near ODT (Leibler 1980). Matsenet al. developed a comprehensive theoretical phase
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K. K. Tenneti et al.
a variety of self-assembled ordered nanostructures at much smaller length scales
(typically 10-100 nm). The nanostructure formation process is the cumulative result
of enthalpy gain due to polymer segregation (into domains) and the corresponding
loss in entropy due to chain stretching away from the interface. The chemical bond
between the two blocks becomes the boundary between the two nanodomains. The
dimensions of these nanodomains are a function of the radius of gyration (R g ) of the
polymer chains (which in turn is a function of degree of polymerization, N).
The product χN of a BCP system determines the strength or degree of segregation
of these nanoscale domains. Theoretical calculations of coil-coil BCPs show that if
χN > > 10.5, BCP undergoes microphase separation and forms ordered structures
separated by sharp phase boundaries, and the system is considered to be in the strong
segregation limit (SSL). For χN < < 10.5, entropic factors dominate and the BCP
system is in a state of disorder or in the weak segregation limit (WSL) (Bates and
Fredrickson 1990; Hamley 1998; Muthukumar et al. 1997). While χN determines the
strength of microphase separation, the morphology of the BCP nanostructure is
determined by the volume fraction ( f ) of the combining blocks. 1-dimensional
(1D) structures called lamellar (L) morphology is commonly observed at symmetric
volume fractions ( f A ~ 0.5) in which alternating layers of polymer A and B are
stacked together. Asymmetry in f leads to nonplanar morphologies with curved
interfaces so that the stretching penalty of the majority block is reduced. The degree
of curvature increases with increase in the degree of asymmetry leading to morphologies such as 3D honeycomb-like structure called the double gyroid (G) ( f A ~
0.28–0.34), 2D hexagonally close packed cylinders (C) ( f A ~ 0.17–0.28), and 0D
spheres (S) ( f A < 0.17) of the minority block forming a body-centered cubic (BCC)
lattice in the matrix of the majority block. L, G, C, and S, schematically shown in
Fig. 1 (Grason 2006), are the four traditional BCP morphologies and are shown to be
the only structures that possess a constant mean curvature at the corresponding f and
are hence thermodynamically stable. A periodically ordered BCP phase structure
turns into a disordered melt as a function of temperature. The temperature at which
the order to disorder transition occurs is called order-disorder transition temperature
(ODT), and it varies form system to system.
Numerous research groups have investigated the phase behavior of coil-coil
BCPs using both theoretical calculations and experimental methods. At the ODT,
all the BCP phases (except the S morphology) undergo direct transition into a
disordered state. The BCC S structure transforms into a disordered micellar structure
which ultimately forms a disordered melt at two different temperatures called the
lattice disorder temperature (LDOT) and demicellization temperature (DMT),
respectively (Han et al. 2000). Helfandet al. and Semenov et al. provided the basis
for quantitative analysis of BCP phase behavior in the SSL using a self-consistent
field theory (SCFT) approach based on Meier’s criterion of enthalpic gain and
entropic loss in high M n systems (Helfand and Wasserman 1976; Helfand and
Wasserman 1978; Meier 1969; Semenov 1985). Leibleret al. investigated the
phase behavior of BCPs in the high temperature or WSL regions and in the regions
near ODT (Leibler 1980). Matsenet al. developed a comprehensive theoretical phase
176
K. K. Tenneti et al.