Polymer Physics

membrane translocation, and bio-compatibility. When a single polymer coil is
forced to form too many contacts with a flat substrate, the coil will be deformed,
which causes a loss of conformational entropy, as illustrated in Fig.4.16. At the
same time, in order to minimize the entropy loss, the mass center of the coil tries to
keep a certain distance from the substrate, leading to a “depletion layer” at the
contacting surface (Joanny et al. 1979 ). The depletion zone becomes significant
near a mainly repulsive substrate surface.
A mainly attractive substrate with a contact-energy gainewill draw a polymer
chain closer to the surface, and such a condensation process causes a loss of
entropy. Therefore, there exists an equilibrium thicknessdfor the coil absorbed
onto the substrate surface (De Gennes 1976 ). The blob model can be used again to
estimate the chain length dependence ofdfor the absorbed single chain. Assuming
each blob has the sizedand containsgmonomers, then

dbgn (4.96)

where the value of the exponentndepends upon solvent quality:n¼3/5 in a good
solvent;n¼1/2 in a theta solvent. In each blob, the entropy loss due to confinement
is balanced by the thermal fluctuation energykT, thus the total entropy loss of the
absorbed single chain is

EelkT

n

g

kTnð

b

d

Þ^1 =n (4.97)

On the other hand, only the first contacting layer of the monomers contains the
adsorption energy, and the number of contacting monomers isnb/d(here supposing
very weak adsorption for the monomers homogeneously distributed over the thick-
nessd). Therefore, the total adsorption energy of the single chain is

Eadsenð

b

d

Þ (4.98)

Fig. 4.16 Illustration of the
entropy loss (left side, leading
to an elastic bounce for the
formation of “depletion
layer”) and the absorbing
conformation (right side) for
a single polymer chain near a
flat solid substrate

70 4 Scaling Analysis of Real-Chain Conformations