Collapse of polymer brushes grafted onto planar ... - Wageningen UR

COLLAPSE OF POLYMER BRUSHES GRAFTED ONTO PLANAR OR CONVEX SURFACE
V.M. Amoskov, T.M. Birshtein, A.A. Mercurieva
Institute of Macromolecular Compounds, Academy of Science of Russia,
31, Bolshoy pr., V.O., St-Petersburg, 199004, Russia
email: vic@avm.macro.pu.ru
ABSTRACT
The collapse of polymer brushes is investigated. Four types of the polymer systems are considered: (1)
polyelectrolyte brushes in poor solvent, (2) non-ionizable and ionizable brushes in binary solvents, (3)
brushes with n-cluster interactions and (4) thermotropic LC brushes. Both an asymptotic analytical analysis
(for chain length N →∞)
and exact numerical computations (for finite N) are applied for investigating these
systems in a self-consistent field (SCF) framework. The SCF numerical calculations are carried out using the
formalism developed by J.Scheutjens and G.Fleer in their classical works.
For the brushes of planar geometry it has been stated that under suitable external and internal conditions,
collapse in all of these systems can occur as a first order phase transition. The solvent quality (system 1), the
fraction of better solvent (system 2), the energy of isotropic interactions (system 3) and the energy of anisotropic
interaction (system 4) are the parameters that govern corresponding phase transitions. The brushes
grafted onto convex curved surfaces are also investigated. It is found that for the brushes grafted onto
external cylindrical or spherical surfaces (combs, stars, micelles and so on), collapse may also occur as a
first order phase transition.
Though investigated polymer systems differ in the interactions as well as in the grafting type, it is shown
that a number of features are similar for the phase transitions observed in all of them.
At small (or large) enough values of the governing parameter, anyone of the systems under consideration
exists only in a single-phase state, namely, in extended (or collapsed) state. However, there is an intermediate
range of the governing parameter values where the swollen and the collapsed microphases may
coexist, such a state being usually referred as a micro-segregated brush (MSB). It is noteworthy that a more
compact phase is typically located in the neighborhood of the grafting surface, while the swollen phase is at
the periphery. If the brush is in the biphasic state, its chains are never partly collapsed and partly extended:
on the contrary, the chains are strictly divided into two groups that are either fully collapsed or fully extended.
The fraction of the chains responsible for one or another sublayer in the brush depends on the value of the
corresponding governing parameter. Collapsed chains never participate in the formation of the swollen layer,
thus decreasing the effective grafting density for the remaining chains and allowing their existence in the
swollen state. The free end distribution for any brush in MSB state is bimodal. All these effects are
irrespective of the grafting surface type.
At relatively small values of the grafting densities and finite values of the number of segments N in each
chain, the brush collapse takes place in a jump-like manner, that being typical of the first order phase
transitions. The size of nuclei of the collapsed phase is defined as H ~ N δ and grows with the chain length N
slower than the brush size. Hence the first order phase transitions cannot exist at the limit of N →∞.