Phase transitions herringbone

S. Chains in the S phase are also oriented normal to the surface, yet the unit cell is rectangular possibly because of restricted rotation. This structure is characterized as the smectic E or herringbone phase. Schofield and Rice [204] applied a lattice density functional theory to describe the second-order rotator (LS)-heiTingbone (S) phase transition. 

LB films of 1,4,8,11,15,18-hexaoctyl-22,25-bis-(carboxypropyl)-phthalocyanine (2), an asymmetrically substituted phthalocyanine, were stable monolayers formed at the water—air interface that could be transferred onto hydrophilic siUca substrates (32—34). When a monolayer film of the phthalocyanine derivative was heated, there was a remarkable change in the optical spectmm. This, by comparison to the spectmm of the bulk material, indicated a phase transition from the low temperature herringbone packing, to a high temperature hexagonal packing. 

Phase transitions in two-dimensional layers often have very interesting and surprising features. The phase diagram of the multicomponent Widom-Rowhnson model with purely repulsive interactions contains a nontrivial phase where only one of the sublattices is preferentially occupied. Fluids and molecules adsorbed on substrate surfaces often have phase transitions at low temperatures where quantum effects have to be considered. Examples are molecular layers of H2, D2, N2 and CO molecules on graphite substrates. We review the path integral Monte Carlo (PIMC) approach to such phenomena, clarify certain experimentally observed anomalies in H2 and D2 layers, and give predictions for the order of the N2 herringbone transition. Dynamical quantum phenomena in fluids are analyzed via PIMC as well. Comparisons with the results of approximate analytical theories demonstrate the importance of the PIMC approach to phase transitions where quantum effects play a role. 

Linear N2 molecules adsorbed on graphite show a transition from a high-temperature phase with orientational disorder to a low-temperature phase with herringbone ordering of the orientational degrees of freedom (see Sec. lie and Fig. 11). 

Furthermore, one can infer quantitatively from the data in Fig. 13 that the quantum system cannot reach the maximum herringbone ordering even at extremely low temperatures the quantum hbrations depress the saturation value by 10%. In Fig. 13, the order parameter and total energy as obtained from the full quantum simulation are compared with standard approximate theories valid for low and high temperatures. One can clearly see how the quasi classical Feynman-Hibbs curve matches the exact quantum data above 30 K. However, just below the phase transition, this second-order approximation in the quantum fluctuations fails and yields uncontrolled estimates just below the point of failure it gives classical values for the order parameter and the herringbone ordering even vanishes below... 

It is concluded [217] that an interpretation of the ideal herringbone transition within the anisotropic-planar-rotor model (2.5) as a weak first-order transition seems most probable, especially since previous assignments [56, 244] can be rationalized. This phase transition is fluctuation-driven in the sense of the Landau theory because the mean-field theory [141] yields a second-order transition. Assuming that defects of the -v/3 lattice and additional fluctuations due to full rotations and translations in three dimensions are not relevant and only renormalize the nonuniversal quantities, these assignments should be correct for other reasonable models and also for experiment [217]. 

Figure 29. Distribution function of the cosine of the relative angle between two N2 molecules i and j in the (->/3 X J3)R30° commensurate phase on graphite obtained from Monte Carlo simulations for either first, second, and third nearest-neighbor pairs (y). Solid line is for pairs ( ) ) which belong to the same sublattice, and dashed line is for the intersublattice pairs. The herringbone transition is located in this model at around 25 K. (Adapted from Fig. 4 of Ref. 183.)...

The main outcome of the study [244] was that the herringbone transition within this model is of first order and occurs at = 25.575 K, or at T = 0.775 when reduced by the appropriate numerical value = 33 K of the coupling parameter in (2.5) based on the gas-phase quadrupole moment for N2. Though the system sizes L x L were already quite large (with linear dimensions of L = 20, 40, 80, and 100), the statistical effort (500-5000... 

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