Phase diagram smectic

Let us enter the world of liquid crystals built by the purely entropic forces present in hard body systems. The phase diagram of hard spherocylinders (HSC) shows a rich variety of liquid crystalline phases [71,72]. It includes the isotropic, nematic, smectic A, plastic, and solid phases [73]. In a plastic crystal the particle centers lie on lattice sites, but the orientations of the... 

Fig. 11 Binary phase diagram between phthalic acid and decyloxystilbazole. (Crc and Cra are the crystal phase of the complex and the acid, respectively E is the crystal smectic E phase). Adapted from [35]...

Figure 7.1 Illustration of different aggregation states obtained (from left to right) by increasing temperature crystal (K), smectic C (SmC), nematic (N) and isotropic (I). Row a shows macroscopic appearance of samples in row b, short-range microscopic ordering is represented (each bar represents a molecule) thermotropic phase diagram of row c illustrates relevant transition temperatures (Tm melting temperature Tsmc-N transition temperature between SmC and N Tc clearing temperature) row d shows different texture of different states as seen through polarizing microscope (with crossed polars, isotropic phase appears black).

Note 3 Two TGBA structures are possible in one, the number of blocks corresponding to a rotation of the layer normal by 2ti is an integer, while in the other, it is a non-integer. Note 4 A TGBA is found in a phase diagram between smectic A and chiral nematic mesophases or between a smectic A mesophase and an isotropic phase. 

Early work predicted smectic (or lamellar) ordering in rod-coil copolymers (Semenov 1991 Semenov and Vasilenko 1986). In liquid crystals, a smectic A phase is a lamellar phase where the molecules are, on average, parallel to the layer normal. In a smectic C phase, the molecules are tilted with respect to this direction. The imbalance in interfacial area per chain for a rod or coil can lead to tilting of chains to maintain uniform density. Semenov (1991) constructed a phase diagram for rod-coil copolymers in which second-order phase transitions... 

Fig. 3.3 Phase diagram of diacylphosphatidylcholines as suggested by X-ray, optical birefringence, and electron microscopy. Lj corresponds to the smectic A state and tp, Lf, Pp to the smectic B phase of thermotropic liquid crystals. The shaded area is a region of coexistence. (Reprinted from Fig. 2 of ref. 15 with permission from Wiley-VCH.)...

Fig. 9-6. Phase diagram of ferrocenes 11. Melting point nematic/isotropic liquid transition smectic A/isotropic liquid transition A isotropic liquid/smectic A transition O isotropic liquid/nematic transition.

Fig. 9-13. Phase diagram of ferrocenes 15. Melting point clearing point smectic C/nematic transition A nematic/smectic C transition.

Figure 10.38 Temperature-shear-rate phase diagram for 8CB in the vicinity of the transition temperature Tan = 33.58°C from the nematic to the smectic A phase. At temperatures more than 5.5°C above Tan, 8CB is a flow-aligning nematic, and it orients close to the flow direction in orientation b. As the temperature is lowered, the nematic becomes a tumbler, preferring the a orientation, mixed with either b or c. The a orientation prevails even in the smectic-A state at temperatures within a degree of Tan, especially at high shear rates. At lower temperatures, the orientation is a mixture of a and c. The globes show the ranges of orientations obtained in each of the states ac, a, a i, and b inferred from x-ray scattering. (From Safinya et al. 1991, reprinted with permission from the American Physical Society.)...

Figure 21. Phase diagram of the complexes of 8 with lithium triflate (g = glassy, k = crystalline, S = smectic A, cub = cubic, col = columnar, i = isotropic).

However, a most significant observation is in the comparison between the two phase diagrams where it is seen that the smectic phases present in the triflate complexes are retained with dodecylsulphate as the anion. This is unusual if the alkylsulphate is considered as a lateral alkyl chain, where it would normally be the case that smectic phases were suppressed. Further, the phase diagram of the dodecylsulphate complexes shows, for seven homologues, a cubic phase between the Sc and Sa phase. Both of these points deserve comment. 

The re-entrant or Tammann loop-shape phase diagram as observed in proteins is also found in other systems and has been connected to exothermic disordering [88]. In this particular case, nematic - smectic A transitions in liquid crystals and the phase behaviour of a crystalline polymer, poly(4-methyl-pentene-l), the phase behaviour can be understood by... 

As the concentration increases, the amphiphilic molecules form micelles and then form columns. The columns are arranged into a hexatic array. As the concentration further increases, the system forms a laminar structure, i.e., a smectic liquid crystal phase. Sometimes, a cubic phase may appear between the micelle and hexatic phases. In fact, the micelles are packed to form a cubic phase. The three phases are all liquid crystal phases hexatic phase, laminar phase and cubic phase. As seen in the figure, the phase diagram of amphiphilic molecules actually depends on the temperature as well. Tk in Figure 1.15 is the Kraft temperature, below which the system is phase separated into crystal and water. 

Figure 8. Phase diagram of the Gay-Berne model with the original and the most-studied parameterization (k = 3, k = 5, fi = 2, v = 1) in the density-temperature plane as obtained from computer simulations. Filled diamonds mark simulation results the phase boundaries away from these points are drawn as a guide only. The domains of the thermodynamic stability of the isotropic (/), nematic (N), and smectic (SB) phases are shown. The liquid-vapor critical point is denoted by C. Two-phase regions are shaded. (Reproduced from Ref. 104.)...

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