Herringbone ordering phase transition order

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. 

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]. 

To test the theoretically predicted thermal properties [37,38] related to the two-dimensional liquid-hexatic transition critically, we have carefully characterized the hexatic B phase in compound 54COOBC [30] and found that it does not display herringbone order. To make a clear distinction between these two cases, we propose to use hexatic B to denote the phase found in 54COOBC and use SmB for the phase found in the nmOBC compounds which has a clear indication of some degree of herringbone order. 

A plausible (but as yet unsubstantiated) explanation for the distinction between N/M and P type behavior lies in terms of the effective cross sections of the columns in the two cases (Fig. 9). For conventional N/M behavior, the colunms in the M phase are pictured as being blade-like and lying in a herringbone pattern. The transition from N to M therefore involves the loss of both lateral positional order and orientational order. In contrast, the P phase columns are pictured as being more or less circular and the N-M transition need only involve the loss of positional order. 

---