of the block size. Moreover, in our considerations we have largely ignored the
possible effects of hydrodynamic interactions, even though the case of Zimm
dynamics was accounted for in our scaling approach [47]. Also, the penetrable
interface has been considered in the simplest approximation of zero thickness
although the existence of some intrinsic width, capillary waves, etc. might add
additional facets to the overall picture. Thus, a variety of details are relegated
to further studies and the reported results should be seen as a first step into a
fascinating field of phenomena that might offer a broad perspective for application
and development.
1.4.2 Single Chain Adsorption: Statics and Kinetics
Adsorption of polymers on surfaces plays a key role in numerous technological
applications and is also relevant to many biological processes. During the last three
decades it has been constantly a focus of research interest. The theoretical studies
of the behavior of polymers interacting with solid substrate have been based
predominantly on both scaling analysis [49] as well as on the self-consistent field
(SCF) approach [50]. The close relationship between theory and computer experiments in this field [27, 51] has proved especially fruitful. Most investigations focus
on the determination of the critical adsorption point (CAP) location and on the
scaling behavior of a variety of quantities below, above, and at the CAP.
The investigations mentioned above have been devoted exclusively to homopolymers, but the adsorption of copolymers (e.g., multiblocks or random copolymers) is
still much less understood. Thus, for instance, the CAP dependence on block size
M at fixed concentration of the sticking A-mers is still unknown, as are the scaling
properties of regular AB-multiblock copolymers in the vicinity of the CAP. The main
focus of our investigations [52] has been aimed at the adsorption transition of random
and regular multiblock AB-copolymers on a rigid substrate. We have used two
different models to establish an unambiguous picture of the adsorption transition
and to test scaling predictions at criticality. The first model is an off-lattice coarsegrained bead-spring model of polymer chains that interact with a structureless surface
by means of a contact potential, once an A-monomer comes close enough to be
captured by the adsorption potential. The second model is the pruned-enriched
Rosenbluth method (PERM) on a cubic lattice, which is very efficient, especially
for very long polymer chains, and provides high accuracy of the simulation results
at criticality. Notwithstanding their basic difference, both methods suggest a consistent picture of the adsorption of copolymers on a rigid substrate and confirm the
theoretical predictions, even though the particular numeric values of the CAP are
model-specific and differ considerably.
As one of the central results of our studies, one should point out the phase
diagram of regular multiblock adsorption, which gives the increase in the critical
adsorption potential E c (M ) with decreasing length M of the adsorbing blocks
(cf. Fig. 11a). For very large block length, M
À1
! 0, we find that the CAP
systematically approaches that of a homogeneous polymer. We demonstrate also
Mechanical Properties of Single Molecules and Polymer Aggregates
15
possible effects of hydrodynamic interactions, even though the case of Zimm
dynamics was accounted for in our scaling approach [47]. Also, the penetrable
interface has been considered in the simplest approximation of zero thickness
although the existence of some intrinsic width, capillary waves, etc. might add
additional facets to the overall picture. Thus, a variety of details are relegated
to further studies and the reported results should be seen as a first step into a
fascinating field of phenomena that might offer a broad perspective for application
and development.
1.4.2 Single Chain Adsorption: Statics and Kinetics
Adsorption of polymers on surfaces plays a key role in numerous technological
applications and is also relevant to many biological processes. During the last three
decades it has been constantly a focus of research interest. The theoretical studies
of the behavior of polymers interacting with solid substrate have been based
predominantly on both scaling analysis [49] as well as on the self-consistent field
(SCF) approach [50]. The close relationship between theory and computer experiments in this field [27, 51] has proved especially fruitful. Most investigations focus
on the determination of the critical adsorption point (CAP) location and on the
scaling behavior of a variety of quantities below, above, and at the CAP.
The investigations mentioned above have been devoted exclusively to homopolymers, but the adsorption of copolymers (e.g., multiblocks or random copolymers) is
still much less understood. Thus, for instance, the CAP dependence on block size
M at fixed concentration of the sticking A-mers is still unknown, as are the scaling
properties of regular AB-multiblock copolymers in the vicinity of the CAP. The main
focus of our investigations [52] has been aimed at the adsorption transition of random
and regular multiblock AB-copolymers on a rigid substrate. We have used two
different models to establish an unambiguous picture of the adsorption transition
and to test scaling predictions at criticality. The first model is an off-lattice coarsegrained bead-spring model of polymer chains that interact with a structureless surface
by means of a contact potential, once an A-monomer comes close enough to be
captured by the adsorption potential. The second model is the pruned-enriched
Rosenbluth method (PERM) on a cubic lattice, which is very efficient, especially
for very long polymer chains, and provides high accuracy of the simulation results
at criticality. Notwithstanding their basic difference, both methods suggest a consistent picture of the adsorption of copolymers on a rigid substrate and confirm the
theoretical predictions, even though the particular numeric values of the CAP are
model-specific and differ considerably.
As one of the central results of our studies, one should point out the phase
diagram of regular multiblock adsorption, which gives the increase in the critical
adsorption potential E c (M ) with decreasing length M of the adsorbing blocks
(cf. Fig. 11a). For very large block length, M
À1
! 0, we find that the CAP
systematically approaches that of a homogeneous polymer. We demonstrate also
Mechanical Properties of Single Molecules and Polymer Aggregates
15