Dissipative Particle Dynamics Approaches to Modeling …
91
strength (ISIS) method for the study of the large-scale self-assembly of polyelectrolytes [142, 143]. ISIS-DPD incorporates electrostatic contribution using mean
field approximations into the estimation of the overall repulsive parameter. This
method was proved to be reliable when the solvent ionic strength is relatively high,
approaching the limit of excessive counterions to which the ion-ion correlation would
have to be considered. The ISIS-DPD method is a novel coarse-grained approach
that yields the repulsive parameter between polyelectrolyte monomers by implicitly
applying solvent ion screening. This method uses the repulsion parameter (a ii ) developed by Groot and Warren [100], where a ii is given by 25 for a system of water with
a DPD bead density of ρ = 3 at room temperature, by additionally incorporating an
electrostatic repulsion (a elec ):
a pp = a ii + a elec
(24)
where a pp is the total polyelectrolyte repulsion. For a sufficiently ionized salt solution containing polyelectrolytes, Borisov et al. show that by using the mean-field
approximation, the second virial coefficient (v) can be described as [37]:
v = v A +
α
2
c s
(25)
where v A ≤ 1 is the bare non-electrostatic contribution to v, α is the degree of
ionization, and c S is the solvent ionic strength. By combining the approach provided
by the second virial coefficient [50] and that of Groot and Warren for the repulsion
parameter of water, a ii and a elec can be resolved to provide a polyelectrolyte repulsion
that includes both non-electrostatic and electrostatic contributions. This results in a
polyelectrolyte-polyelectrolyte interaction characterized by an a ii = 25 (when ρ
= 3) and a elec ≈ 1/c S . It is important to notice that as the solution increases ionic
strength, c S increases leading to a pp approaching a ii , i.e. the charge of polyelectrolyte
monomers is screened. Increasing the ionic strength beyond charge saturation of the
polyelectrolyte, to the point at which phenomena such as ion-ion correlation must
be accounted is a limit to this approach.
The ISIS-DPD method was employed to build a morphological phase diagram
predicting the various conformations of polyelectrolyte diblock copolymers and
triblock copolymers as a function of polyelectrolyte block length (N A ) and repulsion
parameter (a pp ) (Fig. 3b) in aqueous solution [142, 144]. In the first case, diblocks had
a short hydrophobic block with a fixed degree of polymerization of 4 and a variable
length of the hydrophilic block where N A ranges from 4 to 90 (Fig. 3b). To validate
predictions, the self-assembly of asymmetric, 54-mer ssDNA amphiphiles was examined using static light scattering and AFM imaging and compared to the results of
the simulations. The polyelectrolyte amphiphiles were synthesized by appending on
average four hydrophobic nucleotides (i.e., F-dUTP) to the 3
termini of hydrophilic
polynucleotides (polyT 50 ) via an enzymatic polymerization (Fig. 3b) [145]. The
dependence of micelle size on solvent ionic strength from DPD simulations matches
very well with experimental measurements. Li et al. then applied the methodology
91
strength (ISIS) method for the study of the large-scale self-assembly of polyelectrolytes [142, 143]. ISIS-DPD incorporates electrostatic contribution using mean
field approximations into the estimation of the overall repulsive parameter. This
method was proved to be reliable when the solvent ionic strength is relatively high,
approaching the limit of excessive counterions to which the ion-ion correlation would
have to be considered. The ISIS-DPD method is a novel coarse-grained approach
that yields the repulsive parameter between polyelectrolyte monomers by implicitly
applying solvent ion screening. This method uses the repulsion parameter (a ii ) developed by Groot and Warren [100], where a ii is given by 25 for a system of water with
a DPD bead density of ρ = 3 at room temperature, by additionally incorporating an
electrostatic repulsion (a elec ):
a pp = a ii + a elec
(24)
where a pp is the total polyelectrolyte repulsion. For a sufficiently ionized salt solution containing polyelectrolytes, Borisov et al. show that by using the mean-field
approximation, the second virial coefficient (v) can be described as [37]:
v = v A +
α
2
c s
(25)
where v A ≤ 1 is the bare non-electrostatic contribution to v, α is the degree of
ionization, and c S is the solvent ionic strength. By combining the approach provided
by the second virial coefficient [50] and that of Groot and Warren for the repulsion
parameter of water, a ii and a elec can be resolved to provide a polyelectrolyte repulsion
that includes both non-electrostatic and electrostatic contributions. This results in a
polyelectrolyte-polyelectrolyte interaction characterized by an a ii = 25 (when ρ
= 3) and a elec ≈ 1/c S . It is important to notice that as the solution increases ionic
strength, c S increases leading to a pp approaching a ii , i.e. the charge of polyelectrolyte
monomers is screened. Increasing the ionic strength beyond charge saturation of the
polyelectrolyte, to the point at which phenomena such as ion-ion correlation must
be accounted is a limit to this approach.
The ISIS-DPD method was employed to build a morphological phase diagram
predicting the various conformations of polyelectrolyte diblock copolymers and
triblock copolymers as a function of polyelectrolyte block length (N A ) and repulsion
parameter (a pp ) (Fig. 3b) in aqueous solution [142, 144]. In the first case, diblocks had
a short hydrophobic block with a fixed degree of polymerization of 4 and a variable
length of the hydrophilic block where N A ranges from 4 to 90 (Fig. 3b). To validate
predictions, the self-assembly of asymmetric, 54-mer ssDNA amphiphiles was examined using static light scattering and AFM imaging and compared to the results of
the simulations. The polyelectrolyte amphiphiles were synthesized by appending on
average four hydrophobic nucleotides (i.e., F-dUTP) to the 3
termini of hydrophilic
polynucleotides (polyT 50 ) via an enzymatic polymerization (Fig. 3b) [145]. The
dependence of micelle size on solvent ionic strength from DPD simulations matches
very well with experimental measurements. Li et al. then applied the methodology