Static wetting behaviour of diblock copolymers

~ Thin liquid films of ordered dihlock copolymers deposited on a solid substrate form a multilayer stacking parallel to the solid surface. A multilayer with a finite extend can he stable, metastable, or unstable, depending on thc relative values of the surface ener&ics of the various interfaces. The spreading parameter and chemical potential of a n-layer are derived, and used for classifying all possible situations. It is shown that only monoand hilayers can be siahle, and that non-wetting multilayers are subjected to a long-time piling up instability, leading in practice to the formation of characteristic riggourat-like Structures. A diblock copolymer is made of two polymer chains with different chemical compositions A and B linked together end to end. Depending on the temperature, these materials are found in two different states. For T > To,, A and I3 are mixed and form a homogeneous melt. On the other hand, for T < Too, A and B species phase-separate and form miccrodomains with one dimension at least comparable to the chain sire. To, is called the microphase separation temperature or the order-disorder transition temperature [ I ] . In the case of symmetric diblock copolymers, which have almost equal volume fractions of A and B, the microphase structure is lamellar. In thin films of these materials deposited on a solid substrate, these layers orient parallel to the substrate. In the present paper, we examine the wetting properties of these copolymer melts. The wetting behaviour of a simple liquid A on a solid surface is controled by the spreading parameter [Z], defined by where ysv , yLs and ypv are the surface tensions associated with the solid-vapour, liquid-solid and liquid-vapour interfaces, respectively. If S,\ is positive, the liquid spreads on the solid surface. Otherwise i t does not wet the surface and forms a drop with a well-defined contact angle 8 , given by the Young relation (2) A Yfv cos H,, = YS" YLS . Equations (1) and (2) hold good for any homogeneous liquid including polymer melts 1486 JOURNAL DE PHYSIQUE I1 N' 10 1. Spreading parameter of a monolayer. Consider a monolayer of a symmetric diblock copolymer lying on a solid substrate, as illustrated in figure 1 . The free energy per chain in such a film can be written as 131 F , = (312) a k B T(8/ROI2 + ( N u ' ~ P ) ( Y ~ B + Y;V + 7;s) ( 3 ) where l' is the monolayer thickness, a a numerical factor of the order of 1, k B the Boltzmann constant, N the monomer index of the polymer, a the typical monomer size and R, = UN This phenomenological expression is found to be able to describe most of the observed properties of the lamellar phase of copolymers in the strong segregation limit, i.e. far from the order disorder transition. In the following we assume the above expression to be valid for a wide range of values of P . Fig. 1. Schematic cross-section of a finite monolayer AB on a solid substrate. The equilibrium thickness PO is obtained for a balance of the different surface tensions, which can be viewed as forces per unit length of the edge. The free energy of the system is therefore given by F , = mF, + rsv(A, A p ) (4) where A, is the total surface area of the solid, A , the area covered by the copolymer and m the total number of polymer chains in the melt. Taking the energy of the bare solid as the reference, one can replace F by A F l = F , y ~ ~ A s . Since A, = n2Nu311', one gets A F l = m((312) u k , T(P/Ro)2 Sl Nu3/!)