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We consider a wormlike polymer confined between two flat surfaces separated by a distance W. Using a wormlike chain formalism that couples the orientational and positional degrees of freedom, for a wormlike chain much longer than the persistence length 𝓁p, we calculate the free energy per segment as a function of W and compare it with the two scaling behaviors valid in the large and small W/𝓁p limits.

The contact angle between a liquid film and a solid substrate is treated in the van der Waals model used previously by the author to discuss gas adsorption on solid surfaces. The model accounts for the occurrence of three types of wetting behavior, i.e., complete wetting, partial wetting, and nonwetting, as well as for transitions between these different regimes. According to this model, the contact angle depends on two parameters, namely the reduced temperature T/Tc, where Tc is the critical temperature of the liquid, and εw/kTc, where εw is the minimum in the liquid–solid interaction potential. For high-energy surfaces, corresponding to large εw/kTc, the contact angle decreases on increasing temperature; the opposite behavior is predicted to occur on sufficiently low-energy surfaces. With some hypotheses on how εw depends on the nature of the solid and liquid phases present, one can calculate the variation in contact angle with liquid species for a given solid at fixed temperature. The theory is compared with contact-angle results for n-alkanes on teflon surfaces; qualitative agreement is found. The contrasts between the present model and previous theories for the contact angle, in particular those of Good and Girafalco, Navascués and Berry, and Cahn, are discussed. Whereas Cahn predicts that the transition between different wetting classes is first-order in nature, we find that it is actually of second order.

We present a self-consistent field theory (SCFT) of semiflexible (wormlike) diblock copolymers, each consisting of a rigid and a flexible part. The segments of the polymers are otherwise identical, in particular with regard to their interactions, which are taken to be of an Onsager excludedvolume type. The theory is developed in a general three-dimensional form, as well as in a simpler one-dimensional version. Using the latter, we demonstrate that the theory predicts the formation of a partial-bilayer smectic-A phase in this system, as shown by profiles of the local density and orientational distribution functions. The phase diagram of the system, which includes the isotropic and nematic phases, is obtained in terms of the mean density and rigid-rod fraction of each molecule. The nematic-smectic transition is found to be second order. Since the smectic phase is induced solely by the difference in the rigidities, the onset of smectic ordering is shown to be an entropic effect and therefore does not have to rely on additional Flory-Huggins-type repulsive interactions between unlike chain segments. These findings are compared with other recent SCFT studies of similar copolymer models and with computer simulations of several molecular models.

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