over a larger distance because all the neighbouring lattice sites are occupied (DLL
can also work with vacancies included). Consequently, most of the attempted
displacements finish with the return to the initial position. Only joint attempts
undertaken in groups of beads (at least two-member groups) can be successful, as it
is illustrated in Fig. 8.14. In the considered system, only paths in the form of closed
loops (a sum of displacement vectors for a given loop equals zero) can satisfy this
condition. The algorithm defined by the DLL model starts with a random selection
of unit vectors which are assigned to all beads and represents movement attempts.
An exemplary assignment for simple liquid on the triangular lattice is shown in
Fig. 8.14. All beads which do not contribute to correlated sequences (loops) are
immobilized; the rest is moved by one lattice constant. Many rearrangements can
appear simultaneously in the system as the algorithm is fully parallel [202]. The
introduction of bonds between beads, representing polymer chains, leads to two
additional constraints—movement attempts leading to breaking a bond or violating
bond excluded volume are immobilized. DLL can be implemented on sequential
computers (even PC class). However, full capabilities of DLL model could be
reached only on parallel machines like Analyzer of Real Complex Systems—
ARUZ (built in Lodz in 2016). DLL has been successfully used in simulations of a
variety of problems related to stimuli-responsive polymers, including gelation
processes [204], polymer stars formation [205], polymer network crosslinking
[206], diffusion in complex environments [207].
The complexity of stimuli-responsive systems and difficulties in simulations in a
broad range of time and size scales lead to the limited number of works devoted to
these materials. However, some crucial points were discussed in the literature in the
light of results of computer simulations. These are hydration of polymer chains,
diffusion properties of particular components (polymer chains, water and eventual
additives), changes in polymer conformation. Further discussion is restricted only to
synthetic SRPS in water with the exception of biological systems, such as proteins,
lipids, polysaccharide and others.
The most well-studied thermo-responsive polymer is poly(N-isopropylacrylamide) (PNIPAM) and its co-polymers. It forms hydrogel that exhibits
the volume phase transition in water at 32 °C (305 K) [208]. One of the first MD
simulations of PNIPAM–water system was performed in 2004 by Longhi et al.
[209], who investigated the hydration of PNIPAM monomer and 50-unit oligomer
in dilute aqueous solution at 300 and 310 K. The study of water–polymer hydrogen
bonding showed that the water molecules constituting bound water (called by the
authors’ first hydration shell) were mainly localized in the hydrophilic region of the
monomer. This observation was confirmed also for other polymers such as PVME
[210]. It was also shown that the number of water–water hydrogen bonds in the
region near to the hydrophilic groups of PVME is smaller by 1–1.9 than those in
pure water. Furthermore, this effect was not compensated by polymer–water
hydrogen bonds in case of PVME. This result well corresponds to the correlation
between the water structure and the hydration degree of PVME chain found
experimentally by Pastorczak et al. [162]—see Fig. 8.10. In the region near the
hydrophobic groups, the average number of water–water hydrogen bonds was
250
M. Kozanecki et al.
can also work with vacancies included). Consequently, most of the attempted
displacements finish with the return to the initial position. Only joint attempts
undertaken in groups of beads (at least two-member groups) can be successful, as it
is illustrated in Fig. 8.14. In the considered system, only paths in the form of closed
loops (a sum of displacement vectors for a given loop equals zero) can satisfy this
condition. The algorithm defined by the DLL model starts with a random selection
of unit vectors which are assigned to all beads and represents movement attempts.
An exemplary assignment for simple liquid on the triangular lattice is shown in
Fig. 8.14. All beads which do not contribute to correlated sequences (loops) are
immobilized; the rest is moved by one lattice constant. Many rearrangements can
appear simultaneously in the system as the algorithm is fully parallel [202]. The
introduction of bonds between beads, representing polymer chains, leads to two
additional constraints—movement attempts leading to breaking a bond or violating
bond excluded volume are immobilized. DLL can be implemented on sequential
computers (even PC class). However, full capabilities of DLL model could be
reached only on parallel machines like Analyzer of Real Complex Systems—
ARUZ (built in Lodz in 2016). DLL has been successfully used in simulations of a
variety of problems related to stimuli-responsive polymers, including gelation
processes [204], polymer stars formation [205], polymer network crosslinking
[206], diffusion in complex environments [207].
The complexity of stimuli-responsive systems and difficulties in simulations in a
broad range of time and size scales lead to the limited number of works devoted to
these materials. However, some crucial points were discussed in the literature in the
light of results of computer simulations. These are hydration of polymer chains,
diffusion properties of particular components (polymer chains, water and eventual
additives), changes in polymer conformation. Further discussion is restricted only to
synthetic SRPS in water with the exception of biological systems, such as proteins,
lipids, polysaccharide and others.
The most well-studied thermo-responsive polymer is poly(N-isopropylacrylamide) (PNIPAM) and its co-polymers. It forms hydrogel that exhibits
the volume phase transition in water at 32 °C (305 K) [208]. One of the first MD
simulations of PNIPAM–water system was performed in 2004 by Longhi et al.
[209], who investigated the hydration of PNIPAM monomer and 50-unit oligomer
in dilute aqueous solution at 300 and 310 K. The study of water–polymer hydrogen
bonding showed that the water molecules constituting bound water (called by the
authors’ first hydration shell) were mainly localized in the hydrophilic region of the
monomer. This observation was confirmed also for other polymers such as PVME
[210]. It was also shown that the number of water–water hydrogen bonds in the
region near to the hydrophilic groups of PVME is smaller by 1–1.9 than those in
pure water. Furthermore, this effect was not compensated by polymer–water
hydrogen bonds in case of PVME. This result well corresponds to the correlation
between the water structure and the hydration degree of PVME chain found
experimentally by Pastorczak et al. [162]—see Fig. 8.10. In the region near the
hydrophobic groups, the average number of water–water hydrogen bonds was
250
M. Kozanecki et al.