Dissipative Particle Dynamics Approaches to Modeling …
77
concentration [49–51]. The ability of ionic BCPs to bind with charged molecules
make it favorable for use in drug carriers for gene delivery [52] and to prepare nanolithography templates or thin films for next-generation transistors and photovoltaics
[53]. Experimental studies have indicated that the variation in the morphologies
of the ionic BCP material is not only dependent on the block length, molecular
weight and polymer concentration, but also on the polymer charge density, pH, salt
concentration and possible applied external electrical field [54–57]. For example,
if the charged solvophilic block of the ionic BCP contains a relatively high charge
density then only spherical aggregates will form. This is due to the morphologically
prohibitive electrostatic repulsion within the charged corona. However, continuous
increase of the solvent ionic strength brings concomitant screening effect and triggers the regrowth of the micellar core size, ultimately changing the morphology
of the aggregates. The interplay between the factors controlling the morphology as
well as the micellization kinetics of the ionic aggregates is complex [38, 39]. With
the growing demand of ionic aggregates with select properties for various applications, computational studies can obtain a deeper understanding of the processes and
mechanism underlying the self-assembly of ionic BCPs.
In this chapter, we first provide a general overview of the theories governing
the self-assembly of BCPs (Sect. 2) for both neutral (Sect. 2.1) and polyelectrolyte
or ionic BCP (Sect. 2.2). We start with providing a summary of scaling relations
associated with micellization theories. We then transition to discuss the advantages
and limitations of the mesoscale modeling technique, Dissipative Particle Dynamics
(DPD), that is most widely used for understanding of the dynamic self-assembly of
neutral and ionic BCPs in diluted and semi-diluted regimes (Sect. 3). We would like
to note that this chapter primarily focuses on the morphology and self-assembly of
neutral/ionic BCPs in solution. Prediction of phase behavior of block-copolymers in
the bulk is not included in this review.
2 Theory: Micellization of Block Copolymers
In the classical description, the morphology of the aggregates formed is determined
by the size of the solvophobic blocks, which is directly related to the curvature of
the solvophobic and solvophilic interface [58]. The dimensionless packing or characteristic morphological parameter for the aggregates, p, is related to the curvature
of the solvophobic-solvophilic interface, the mean curvature H and the Gaussian
curvature, K through the following relation [59]:
p =
V
al
= 1 + Hl +
K l
2
3
(1)
where V is the solvophobic volume of the amphiphile, a is the interfacial area of this
volume, l is the chain length normal to the interface. Generally, spherical micelles,
cylindrical micelles and bilayer structures, including membranes and vesicles, are
77
concentration [49–51]. The ability of ionic BCPs to bind with charged molecules
make it favorable for use in drug carriers for gene delivery [52] and to prepare nanolithography templates or thin films for next-generation transistors and photovoltaics
[53]. Experimental studies have indicated that the variation in the morphologies
of the ionic BCP material is not only dependent on the block length, molecular
weight and polymer concentration, but also on the polymer charge density, pH, salt
concentration and possible applied external electrical field [54–57]. For example,
if the charged solvophilic block of the ionic BCP contains a relatively high charge
density then only spherical aggregates will form. This is due to the morphologically
prohibitive electrostatic repulsion within the charged corona. However, continuous
increase of the solvent ionic strength brings concomitant screening effect and triggers the regrowth of the micellar core size, ultimately changing the morphology
of the aggregates. The interplay between the factors controlling the morphology as
well as the micellization kinetics of the ionic aggregates is complex [38, 39]. With
the growing demand of ionic aggregates with select properties for various applications, computational studies can obtain a deeper understanding of the processes and
mechanism underlying the self-assembly of ionic BCPs.
In this chapter, we first provide a general overview of the theories governing
the self-assembly of BCPs (Sect. 2) for both neutral (Sect. 2.1) and polyelectrolyte
or ionic BCP (Sect. 2.2). We start with providing a summary of scaling relations
associated with micellization theories. We then transition to discuss the advantages
and limitations of the mesoscale modeling technique, Dissipative Particle Dynamics
(DPD), that is most widely used for understanding of the dynamic self-assembly of
neutral and ionic BCPs in diluted and semi-diluted regimes (Sect. 3). We would like
to note that this chapter primarily focuses on the morphology and self-assembly of
neutral/ionic BCPs in solution. Prediction of phase behavior of block-copolymers in
the bulk is not included in this review.
2 Theory: Micellization of Block Copolymers
In the classical description, the morphology of the aggregates formed is determined
by the size of the solvophobic blocks, which is directly related to the curvature of
the solvophobic and solvophilic interface [58]. The dimensionless packing or characteristic morphological parameter for the aggregates, p, is related to the curvature
of the solvophobic-solvophilic interface, the mean curvature H and the Gaussian
curvature, K through the following relation [59]:
p =
V
al
= 1 + Hl +
K l
2
3
(1)
where V is the solvophobic volume of the amphiphile, a is the interfacial area of this
volume, l is the chain length normal to the interface. Generally, spherical micelles,
cylindrical micelles and bilayer structures, including membranes and vesicles, are