the intermolecular interactions [54, 55]. Much of the related upsurge of interest
into the statics and dynamics of single macromolecules at surfaces has been spurred
by the use of atomic force microscopy [56, 57] (AFM) and optical/magnetic
tweezers [58], which allow one to manipulate single polymer chains. There is a
close analogy between the forced detachment of an adsorbed polymer chain (such
as polyvinylamine and polyacrylic acid) adhering to a solid surface (such as mica or
a self-assembled monolayer) when the chain is pulled by the end monomer and the
unzipping of homogeneous double-stranded DNA [59].
In our investigations [31, 60, 61] along with computer experiments we use the
grand canonical ensemble (GCE) approach of Kafri et al. [59] in order to treat the
detachment of a single chain from a sticky substrate when the chain end is pulled
by external force (cf. Fig. 13a). A central result is the overall phase diagram
of the force-induced desorption transition for a linear self-avoiding polymer chain
(cf. Fig. 13b). We demonstrate its reentrant character when plotted in terms of
detachment force f D against system temperature T [31, 60]. We find that, despite
being of first order, the force-induced phase transition of polymer desorption is
dichotomic in its nature, that is, no phase coexistence and no metastable states exist!
This unusual feature of the phase transformation is unambiguously supported by
our simulation data, e.g., through the comparison of the order parameter probability
distributions in the immediate vicinity on both sides of the detachment line,
whereby no double-peaked structure is detected.
We obtained these results by studying the various conformational building
blocks, characterizing the structure of an adsorbed linear polymer chain, subject
to a pulling force of fixed strength. The GC partition function of the adsorbed chain
of length N at fugacity z, Ξ(z) ¼ ∑
∞
N ¼ 0 Ξ N z
N ¼ V 0 (z)Q(z)[1 À V(z)U(z)]
À 1 , is
AFM
0
0 . 2
0 . 4
0 . 6
T
0
0.5
1
f
0
2
4
6
ε/k B T
0
2
4
6
8
fa/k
B
T
Theory
MC
1
1 0
ε − ε c
1
10
f D
a
b
Fig. 13 (a) Snapshot of an adsorbed polymer chain with length N ¼ 128, partially detached from
the plane by external force f M ¼ 6.13 that keeps the end monomer at height h ¼ 25σ. Reprinted
with permission from [31]. Copyright 2009, American Chemical Society. (b) Critical detachment
force f D ¼ fσ/k B T versus surface potential E/k B T. Triangles and circles denote MC and theoretical
results, respectively. Inset shows a double-logarithmic plot of f D against E À E c with E c ¼ 1.67k B T,
yielding a slope of 0.97 Æ 0.02, in agreement with the prediction f D / (E À E c )
ν/ϕ
. The shaded
area shows the same phase diagram but derived in units of f (right axis) versus temperature
T (top axis). It appears reentrant. Reprinted with permission from [60]
18
R. Berger et al.
into the statics and dynamics of single macromolecules at surfaces has been spurred
by the use of atomic force microscopy [56, 57] (AFM) and optical/magnetic
tweezers [58], which allow one to manipulate single polymer chains. There is a
close analogy between the forced detachment of an adsorbed polymer chain (such
as polyvinylamine and polyacrylic acid) adhering to a solid surface (such as mica or
a self-assembled monolayer) when the chain is pulled by the end monomer and the
unzipping of homogeneous double-stranded DNA [59].
In our investigations [31, 60, 61] along with computer experiments we use the
grand canonical ensemble (GCE) approach of Kafri et al. [59] in order to treat the
detachment of a single chain from a sticky substrate when the chain end is pulled
by external force (cf. Fig. 13a). A central result is the overall phase diagram
of the force-induced desorption transition for a linear self-avoiding polymer chain
(cf. Fig. 13b). We demonstrate its reentrant character when plotted in terms of
detachment force f D against system temperature T [31, 60]. We find that, despite
being of first order, the force-induced phase transition of polymer desorption is
dichotomic in its nature, that is, no phase coexistence and no metastable states exist!
This unusual feature of the phase transformation is unambiguously supported by
our simulation data, e.g., through the comparison of the order parameter probability
distributions in the immediate vicinity on both sides of the detachment line,
whereby no double-peaked structure is detected.
We obtained these results by studying the various conformational building
blocks, characterizing the structure of an adsorbed linear polymer chain, subject
to a pulling force of fixed strength. The GC partition function of the adsorbed chain
of length N at fugacity z, Ξ(z) ¼ ∑
∞
N ¼ 0 Ξ N z
N ¼ V 0 (z)Q(z)[1 À V(z)U(z)]
À 1 , is
AFM
0
0 . 2
0 . 4
0 . 6
T
0
0.5
1
f
0
2
4
6
ε/k B T
0
2
4
6
8
fa/k
B
T
Theory
MC
1
1 0
ε − ε c
1
10
f D
a
b
Fig. 13 (a) Snapshot of an adsorbed polymer chain with length N ¼ 128, partially detached from
the plane by external force f M ¼ 6.13 that keeps the end monomer at height h ¼ 25σ. Reprinted
with permission from [31]. Copyright 2009, American Chemical Society. (b) Critical detachment
force f D ¼ fσ/k B T versus surface potential E/k B T. Triangles and circles denote MC and theoretical
results, respectively. Inset shows a double-logarithmic plot of f D against E À E c with E c ¼ 1.67k B T,
yielding a slope of 0.97 Æ 0.02, in agreement with the prediction f D / (E À E c )
ν/ϕ
. The shaded
area shows the same phase diagram but derived in units of f (right axis) versus temperature
T (top axis). It appears reentrant. Reprinted with permission from [60]
18
R. Berger et al.