A continuum theory of dislocations is applied to three different problems: edge profiles in thin diblock copolymer films deposited on a solid substrate, equilibrium location of the edge dislocation in lamellar systems near free surfaces, and nematic-smectic phase transition in thin freely suspended liquid crystal films. Because of the surface tension the edge profile at the air/diblock copolymer surface in thin films is very broad. In semi-infinite lamellar systems with small surface tension the dislocation is stabilized at a finite distance from the surface. In smectic films of thickness D the temperature of the unbinding transition for dislocation loops, $T_{N-A}$(D), is proportional to 1/ √D .

We derive the equation for the single-chain correlation function in polymer blends. The chains in the incompressible blend have a radius of gyration smaller than the radius of gyration for ideal chains. The chains shrink progressively as we approach the critical temperature $T_c$. The correction responsible for shrinking is proportional to 1/ √N , where N is the polymerization index. At T=$T_c$ and for N=1000, the size of the chain has been estimated to be 10% smaller than the size of the ideal coil. The estimate relies on the appropriate cutoff. In the limit of N→∞ the chains approach the random walk limit. Additionally, we propose in this paper a self-consistent determination of the radius of gyration and the upper wave-vector cutoff. Our model is free from any divergences such as were encountered in the previous mean-field studies; we make an estimate of the chain size at the true critical temperature and not the mean-field one.

We study in the framework of the continuum theory of dislocations the structure of the interface between an AB diblock copolymer lamellar film deposited on a solid substrate and an A‐homopolymer melt. The dislocation inside the lamellar phase induces steps at the interface. The shape of the profile at the edge of a step (edge profile) depends on the distance of the dislocation from the interface. The profile and the equilibrium location of the dislocations are both studied as a function of the film thickness, D. For large D, the dislocation is stabilized at a finite distance, h_eq, from the interface, due to the small surface tension and large surface bending elastic constant, K_s. For zero surface tension, h_eq ≈ K_s/(2K), where K is the bulk bending elastic constant. For small D, h_eq is mainly determined by the proximity of the solid substrate. The edge profile along the interface is a monotonic function of the distance along the interface for large D of the film and becomes nonmonotonic for small D. Also the dislocation energy strongly depends on D for small D. The theory is discussed in connection to recent experimental studies of diblock copolymer films deposited on a solid substrate.

The distortions induced by dislocation loops are studied in finite systems. The influence of finite size, D, of the system, surface tension, and surface-bending elastic constant on the nematic-smectic (NA) phase transition is discussed. In thin freely suspended smectic liquid-crystal films the nematic-smectic transition temperature, $T_{\mathrm{NA}}$(D), is proportional to 1/ √D , providing the transition is initiated by the unbinding of the dislocation loops. The smectic phase is stabilized in films, i.e., $T_{\mathrm{NA}}$(D)>$T_{\mathrm{NA}}$(∞). The loop-unbinding mechanism for the NA transition is completely suppressed in films sandwiched between solid boundaries, because the distortion energy in this case is proportional to the area of the loop, while the loop configurational entropy is proportional to its length. For temperatures T≥$T_{\mathrm{NA}}$(∞) the equilibrium size of the loop, $R_{\mathrm{eq}}$, is proportional to the distance between solid boundaries, D. It could grow to infinity only for D→∞ and T≥$T_{\mathrm{NA}}$(∞).

The elastic interactions between dislocations in a finite lamellar system of N layers are calculated as a function of the size of the system, surface tension and lamellar elastic constants. For large surface tension the in-plane interactions are repulsive for like dislocations and attractive for opposite ones, decaying exponentially with the decay length proportional to √N. Their strength is inversely proportional to √N. For small surface tension the elastic interactions are attractive at large distances for like dislocations and repulsive for opposite ones. In thin films with small surface tension like dislocations are stabilized at finite separations (~ √N), while in thick films they unbind due to Helfrich forces. The unbinding transition is extremely sensitive to the surface tension and surface bending elastic constant.

We thoroughly discuss the layer deformations in smectic-A liquid crystals. The invariant elastic free energy is presented in terms of the derivatives of the vector field normal to layers and the change of the distance between the layers. We compare our results with the previous works of de Gennes and of Grinstein and Pelcovits. It is pointed out that anharmonic terms in the elastic free energy might be responsible for the change of the average layer spacing, layer spacing profile and in particular for the tilt profiles in finite smectic systems.

The correlation function for the layer displacement in a finite smectic system is calculated using the continuous model. The results are compared with the predictions of the discrete model of layer fluctuations and a difference of only a few percent is found. Additionally, the fluctuation-induced deformations of the smectic film are discussed. The fluctuations increase the average layer spacing by about 3%. Consequently, the areal density in the smectic layer and also the temperature of the Kosterlitz-Thouless phase transition decrease.

We use the field‐theoretical methods to derive the self‐consistent one‐loop equations (Hartree approximation) for the location of the critical point in binary mixtures of polymers. The small parameter in the loop expansion is the inverse of the square root of the number of segments (monomers) in a polymer chain 1/√N. Both the ideal chain conformation and fluctuation corrections to the Flory–Huggins mean field result are taken into account. For symmetric mixtures, the critical temperature T_c is shown to deviate from its mean field value (∼N) as √N, while the critical concentration remains unchanged in comparison to its mean field value φ̄_c=1/2. Since the fluctuations tend to disorder the system, the real value of the critical temperature is lower than its mean field value. For asymmetric A,B mixture (N_A≳N_B), the critical concentration of A monomers φ̄_c is shown to be larger than its mean field value. In the limit of N_A→∞, the critical temperature attains its mean field value, even for finite N_B. However, we estimate that for N_A=N_B∼10⁴, the correction to the Flory–Huggins parameter at the critical point may still be of the order of 10%, although it depends on the details of the system. The explicit formulas for T_c and φ̄_c as functions of N_A and N_B are given. The role of the upper wave vector cutoff in these formulas is emphasized and its proper estimate is given. The loop expansion, viewed as an expansion in a small parameter, is correct as long as both N_A and N_B are much larger than unity and breaks down when any of these quantities becomes of the order of unity. The calculation of the Ginzburg region in the temperature‐concentration plane is also given. It is based on the analysis of the scattering intensity. The comparison with the earlier estimates of the Ginzburg criterion (for temperature) is made.

We consider three systems containing rigid and/or flexible main‐chain nematogenic polymers: mixtures of a rigid and a flexible polymer, mixtures of two different rigid polymers, and a system of diblocks of rigid and flexible pieces. The flexible components are modeled as chains with freely rotating bonds, while the rigid components are modeled as rods of negligible thickness. The Landau–de Gennes expansion of the free energy is derived, and the form of the phase diagrams is examined. Conditions for the existence of generic diagrams is given in terms of the Flory–Huggins and Maier–Saupe interaction parameters. The location of the azeotrope in the rigid–rigid mixture is calculated analytically. The nematic–isotropic phase transition in the rigid–flexible diblock (in general, n‐block) copolymer system is also studied. In particular, the change in the transition temperature with the number of monomers in a rigid block is determined.

We study the behavior of the contact angle of a middle-phase pendant drop at an oil-water interface in an amphiphilic system. A Landau theory with a one-component order parameter is employed. We find that as a weak amphiphilic system departs from its balanced state, the contact angle decreases monotonically to zero at a wetting transition as a critical end point is approached. In a stronger system, the angle initially increases with this departure before ultimately falling to zero. For a very strong system, the angle can increase to 180° before falling to zero. In such a case, three wetting transitions would be encountered

The low-frequency vibrations of freely suspended smectic liquid-crystal films are analyzed. The characteristic frequencies for very thin films can be used for the determination of the smectic-liquid-crystal–vapor surface tension. In thick films one can also determine from the vibrational frequencies the compressional elastic constant B for smectic liquid crystals.

It is argued that an enhancement of the surface hexatic in-plane ordering is due to the quench of the out-of-plane surface-layer fluctuations. It is shown that the layer-by-layer freezing (liquid-hexatic phase transition) in freely suspended liquid-crystal films can be induced by the layer fluctuation profile. The obtained results relating transition temperatures to the bend elasticity and the surface tension can be also applied to monolayers undergoing liquid-hexatic phase transition on liquid or liquid-crystal surfaces.

Recent experiments on oil, water, and surfactant mixtures indicate that these systems can be brought close to a Lifshitz tricritical point. We investigate the interfacial properties of a system in the vicinity of such a point, based on a single-order-parameter Ginzburg-Landau model. We find that the microemulsion does not wet the oil-water interface all the way to the Lifshitz tricritical point. In addition, the scattering intensity shows a characteristic scaling form. The interfacial behavior near Lifshitz critical end points is also examined.