holds, the location U c (W ) of the transition will depend on W, but not the critical
exponents. Klushin et al. [32] showed that indeed all exponents are independent of
the parameter W, but for the crossover exponent there occurs a correction term
(/N
À 1/2
), whose amplitude (which is not expected to be universal) strongly
depends on W. However, if we introduce a blob picture such that N ¼ ng, where
g is the number of monomers per blob, n is the number of blobs, and the blob
diameter (g
ν ) is chosen equal to W, one finds that all systems behave rather similarly
(Fig. 6) [32]. It also is evident that for smaller values of N the effective crossover
exponent is distinctly larger than 0.5, whereas for N ! ∞ the Grassberger [30]
estimate ϕ % 0.48 is confirmed. The conclusion that ϕ is universal is also
confirmed by a study of the loop length distribution function at U ¼ U c (W ),
which is found to satisfy a universal power law (in the limit N ! ∞).
Another interesting question is the effect of chain stiffness on polymer
adsorption. It has been found [34] that increase of ‘ p ! 1 causes a crossover in
the character of the adsorption transition from second order (for finite ‘ p ) to first
order as ‘ p diverges. This finding is compatible with mean field theories [35].
However, a complication that has not been analyzed before is the finding that the
persistence length ‘ p is not only dependent on the bending potential, but also
depends on the distance from the adsorption transition [34].
1.4 Adsorption of Single Chains
1.4.1 Copolymer Localization on Selective Liquid–Liquid Interfaces
The behavior of hydrophobic–polar (amphiphilic) copolymers (HP-copolymers) at
a selective interface (the interface that divides two immiscible liquids, say, water
and oil, each liquid being a good solvent for one type of monomer and bad for the
other) is of great importance in the chemical physics of polymers. HP-copolymers
are readily localized at such an interface because, under a sufficiently large degree
of selectivity, the hydrophobic (H) and polar (P, hydrophilic) parts of a copolymer
chain try to stay on different sides of the interface due to the interplay between the
entropy loss in the vicinity of the interface and the energy gain in the proper solvent
(cf. Fig. 7). Not surprisingly, during the last two decades the problem has attracted
a lot of attention and has been looked at experimentally [37–39], theoretically
[40, 41], and in computer experiments [42]. In earlier studies, attention was mostly
focused on diblock copolymers [37, 38] due to their relatively simple structure, but
the scientific interest shifted later to random HP-copolymers at penetrable interfaces [41, 43, 44]. In contrast, our investigations have focused mainly on
unexplored aspects such as the impact of block size M on the static properties and
on the localization kinetics of regular multiblock copolymers at the phase boundary
between the two immiscible solvents. We showed that these are well described
by a simple scaling theory [36, 45, 46] in terms of the total copolymer length
10
R. Berger et al.
exponents. Klushin et al. [32] showed that indeed all exponents are independent of
the parameter W, but for the crossover exponent there occurs a correction term
(/N
À 1/2
), whose amplitude (which is not expected to be universal) strongly
depends on W. However, if we introduce a blob picture such that N ¼ ng, where
g is the number of monomers per blob, n is the number of blobs, and the blob
diameter (g
ν ) is chosen equal to W, one finds that all systems behave rather similarly
(Fig. 6) [32]. It also is evident that for smaller values of N the effective crossover
exponent is distinctly larger than 0.5, whereas for N ! ∞ the Grassberger [30]
estimate ϕ % 0.48 is confirmed. The conclusion that ϕ is universal is also
confirmed by a study of the loop length distribution function at U ¼ U c (W ),
which is found to satisfy a universal power law (in the limit N ! ∞).
Another interesting question is the effect of chain stiffness on polymer
adsorption. It has been found [34] that increase of ‘ p ! 1 causes a crossover in
the character of the adsorption transition from second order (for finite ‘ p ) to first
order as ‘ p diverges. This finding is compatible with mean field theories [35].
However, a complication that has not been analyzed before is the finding that the
persistence length ‘ p is not only dependent on the bending potential, but also
depends on the distance from the adsorption transition [34].
1.4 Adsorption of Single Chains
1.4.1 Copolymer Localization on Selective Liquid–Liquid Interfaces
The behavior of hydrophobic–polar (amphiphilic) copolymers (HP-copolymers) at
a selective interface (the interface that divides two immiscible liquids, say, water
and oil, each liquid being a good solvent for one type of monomer and bad for the
other) is of great importance in the chemical physics of polymers. HP-copolymers
are readily localized at such an interface because, under a sufficiently large degree
of selectivity, the hydrophobic (H) and polar (P, hydrophilic) parts of a copolymer
chain try to stay on different sides of the interface due to the interplay between the
entropy loss in the vicinity of the interface and the energy gain in the proper solvent
(cf. Fig. 7). Not surprisingly, during the last two decades the problem has attracted
a lot of attention and has been looked at experimentally [37–39], theoretically
[40, 41], and in computer experiments [42]. In earlier studies, attention was mostly
focused on diblock copolymers [37, 38] due to their relatively simple structure, but
the scientific interest shifted later to random HP-copolymers at penetrable interfaces [41, 43, 44]. In contrast, our investigations have focused mainly on
unexplored aspects such as the impact of block size M on the static properties and
on the localization kinetics of regular multiblock copolymers at the phase boundary
between the two immiscible solvents. We showed that these are well described
by a simple scaling theory [36, 45, 46] in terms of the total copolymer length
10
R. Berger et al.