局限空间中水的相变与动态学研究

在本篇论文中,主要讨论水分子在局限空间中的运动及相变行为,所使用的方法为双量子过滤核磁共振光谱及T₁反转回覆光谱,体系为利用MCM-41吸附不同量的重水. 本研究中所使用的这两种光谱方法各有其独特之处,其中双量子过滤核磁共振光谱是利用被吸附的重水分子中氘核残余四极作用力所产生双量子讯号进行侦测,因此是特别针对表面吸附的水分子进行观测, 而T₁反转回覆光谱则是侦测整体孔洞內水分子的行为,借由两种光谱的谱线分析相互比对,得到在MCM-41內各层水分子对温度变化的完整动态学行为. 在描述表面水分子运动上,采用的是修改过的锥体模型,主要将水分子分成相对其对称轴的摇摆运动及旋转运动,在研究中发现,表面水分子是被MCM-41表面单独的SiOH所吸附,比例上为一个水分子对一个SiOH,而表面分子的运动会受到第二层水分子的形成与否所影响,一但第二层水分子 的量够多时,其平移扩散运动会借由碰撞影响表面水分子的摇摆运动,而且在孔洞中属于非表面吸附的水分子,在随温度变化至240~250 K之间时会有相变发生,相变的温度则会随水量充填在MCM-41內的多寡而改变,当水分子越多时,因为彼此间空间有限,使得氢键网路结构与一般正常在大量水分子体系的结构有些相异,因此使得相变温度会随之下降. 除此之外,本研究中亦提出不同的双量子过滤核磁共振脉冲序列以及不同的模型来讨论.     

Pore size distribution calculation from H NMR signal and N2 adsorption–desorption techniques

The pore size distribution (PSD) of nano-material MCM-41 is determined using two different approaches: N₂ adsorption–desorption and ¹H NMR signal of water confined in silica nano-pores of MCM-41. The first approach is based on the recently modified Kelvin equation [J.V. Rocha, D. Barrera, K. Sapag, Top. Catal. 54(2011) 121–134] which deals with the known underestimation in pore size distribution for the mesoporous materials such as MCM-41 by introducing a correction factor to the classical Kelvin equation. The second method employs the Gibbs–Thompson equation, using NMR, for melting point depression of liquid in confined geometries. The result shows that both approaches give similar pore size distribution to some extent, and also the NMR technique can be considered as an alternative direct method to obtain quantitative results especially for mesoporous materials. The pore diameter estimated for the nano-material used in this study was about 35 and 38 Å for the modified Kelvin and NMR methods respectively. A comparison between these methods and the classical Kelvin equation is also presented.     

2H T2rho relaxation dynamics and double-quantum filtered NMR studies

In this study 2H T2rho DQF NMR spectra of water in MCM-41 were measured. The T2rho double-quantum filtered (DQF) NMR signal is generated by applying a radio frequency (RF) field for various durations and then observed after a monitor RF pulse. It was found that the transfer between different quantum coherences by the couplings during long-duration RF fields (i.e., soft pulses) and that residual quadrupolar interaction dominates the signal decay. Knowledge of coherence transfer during long-RF pulses has special significance for the development of sophisticated multi-quantum NMR experiments especially multi-quantum MRI applications.     

μSR studies of fullerenes and their derivatives

The dynamic properties of pristine C₆₀ and C₇₀ are reviewed, emphasizing the results of the ZF‐ and ALC‐μ⁺SR techniques. In C₆₀, the \mboxfcc\rightarrow\mboxsc transition is accompanied by a change in the dynamics from isotropic reorientational to quasi‐random jump motion between nearly‐degenerate orientations. C₇₀ is frozen on a timescale of 30 ns up to 170 K. At higher temperatures, the motion is found to be complex, consisting of a uniaxial rotation part together with a nutational or jumping motion of the unique axis. Anisotropy on the 30 ns timescale persists to 370 K, well into the fcc phase. The ZF‐μ⁺SR technique has been also employed to study the magnetic properties of fullerides. In the organic salt (TDAE)C₆₀, spontaneous magnetic order is directly observed below a Curie temperature of 16.1 K, higher than any other organic material. In the quasi‐one‐dimensional conductor CsC₆₀, static magnetic order of a random nature is observed to develop in the vicinity of the metal–insulator transition at 30 K with no direct evidence of long range order present. This revised version was published online in August 2006 with corrections to the Cover Date.     

Large angle jumps of small molecules in amorphous matrices analyzed by 2D exchange NMR

The reorientation dynamics of deuterated benzene and hexamethyl benzene as additives to the glass former oligostyrene is studied below the glass transition temperature T_g. By means of 2D ²H NMR, analyzed in the frequency and in the time domain, it is shown that the dynamics of the small molecules is governed by an isotropic large angle reorientation process, which is close to the random jump model. Furthermore, the dynamics is characterized by a broad distribution of correlation times. Even 65 K below T_g, a fraction of small molecules reorients on the timescale of 100 ms. In contrast, small angle reorientation dominates in the neat glass former polystyrene near T_g. As a consequence of the presence of large angle jumps, the 2D spectra can be described by an additive superposition of two sub-spectra—a ridge along the diagonal and a complete exchange pattern—where the weighting factor W(t_m) is directly given by the reorientational correlation function F₂(t_m). Additionally, for a sample with very low benzene concentration (c≈0.5%), the 1D spectra indicate that the same dynamic scenario is present in the single particle limit. Tentatively, we assume that the large angle reorientation of the small molecules is associated with a translational diffusion process of the small molecules within the amorphous matrix.     

Analysis of H NMR spectra of water molecules on the surface of nano-silica material MCM-41: Deconvolution of the signal into a Lorentzian and a powder pattern line shapes

Water ²H NMR signal on the surface of nano-silica material MCM-41 consists of two overlapping resonances. The ²H water spectrum shows a superposition of a Lorentzian line shape and the familiar NMR powder pattern line shape, indicating the existence of two spin components. Exchange occurs between these two groups. Decomposition of the two signals is a crucial starting point to study the exchange process. In this article we have determined these spin component populations along with other important parameters for the ²H water NMR signal over a temperature range between 223 K and 343 K.     

39K NMR study of the low temperature phase transitions in KLiSO4

The³⁹K NMR spectra, spin-spin (T ₂) and spin-lattice (T ₁) relaxation times of KLiSO₄ have been measured in the temperature range from 300 K to 90 K. The temperature dependence of the³⁹K (I=3/2) NMR spectra demonstrates the occurrence of a first order phase transition atT _c1=217 K which occurs without a change in the K⁺ site symmetry and another first order transition atT _c2=190 K which is connected with a lowering of the K⁺ site symmetry and the formation of three kinds of ferroelastic domains. From the angular dependence of the second order quadrupole shifts of the³⁹K NMR 1/2–1/2 transitions the electric-field gradient (EFG) tensors at the potassium sites were determined at 290 K, 204 K and 180 K. The symmetry of the ferroelastic phase is monoclinic and not orthorhombic as the K⁺ EFG tensors are tilted away from thec-axis belowT _c2. TheT ₁ data further show the freezing in of the slow reorientational motion 10^–8 s with decreasing temperature from 300 to 90 K.On leave from: J. Stefan Institute, E. Kardelj University of Ljubljana, Ljubljana, Yugoslavia     

Synthesis and characterization of ionic liquid-functionalized alumino-silicate MCM-41 hybrid mesoporous materials

Ionic liquid-functionalized alumino-silicate MCM-41 hybrid mesoporous materials have been synthesized with two-step approach, by means of in situ skeleton doping with aluminium and post surface grafting with N-methylimidazole ionic liquid groups. The samples were characterized by X-ray diffraction (XRD), high resolution transmission electron microscope (HRTEM), N₂ adsorption-desorption, Fourier transform infrared (FTIR) spectra, ²⁷Al and ¹³C MAS NMR spectra and temperature-programmed desorption (TPD) of NH₃. The results indicated that the bifunctionalized MCM-41 possessed ordered mesostructure. Aluminium was efficiently introduced into the framework of the mesostructure, generating Lewis and Brönsted acid sites. N-methylimidazole ionic liquid groups were covalently grafted onto the surface of mesoporous materials. The as-synthesized bifunctional MCM-41 showed good catalytic performance in the coupling reaction of CO₂ and propylene oxide.     

Reorientation dynamics in liquid alcohols from Raman spectroscopy

Polarized Raman spectroscopy has been employed to study the reorientational, or more specifically the translational relaxation dynamics, of alcohol molecules in pure liquids and aqueous solutions. It is found from the spectral width measurements that alcohol molecules in pure liquids have typically translational relaxation times on the order of picoseconds, following the order methanol < ethanol < i‐propanol < n‐propanol. Temperature‐dependent measurements show that hydrogen‐bonding (HB) and hydrophobic interactions control the translational motion. The hydrophobic interaction reduces the relaxation time more apparently in view of the  CH₃ group than the skeleton motion. For alcohol–water mixtures, the increase of water concentration generally slows down the relaxation process in a non‐monotonic behavior. However, the trend stops at a certain point and the motion of alcohol molecules becomes faster when the alcohol concentration further drops. Different mechanisms have been proposed to interpret these observations, which might be helpful to gain deeper insight into the HB networks of alcohols with water. Our study strongly illustrates that Raman spectroscopy can be applied to the study of fast translational motion of molecules in HB systems. Copyright © 2011 John Wiley & Sons, Ltd.     

Coherence transfer between nuclear spins in paramagnetic systems: effects of nucleus—electron dipole—dipole cross-correlation

In nuclear magnetic resonance of paramagnetic systems, cross-correlations between the fluctuations of a nucleus—nucleus dipole—dipole coupling I^k I^l and a nucleus—electron dipole coupling I^kS induces cross-relaxation and makes it possible to generate bilinear terms in the density matrix of the type 2I^k _xI^l _z from coherence I^k _x that can lead to ‘relaxation-allowed’ coherence transfer between two nuclei I^k and I^l . In this paper these effects are demonstrated in a complex involving a fragment of double-stranded DNA and two chromomycin molecules complexing a paramagnetic cobalt ion. Analytical expressions are given for the cross-correlation rates in particular conditions, while the extension to anisotropic g tensors or zero field splittings are addressed. It is shown that relaxation-allowed coherence transfer leads to characteristic signals in double-quantum filtered correlation spectroscopy (DQF—COSY), but not in total correlation spectroscopy (TOCSY). Analytical expressions are unable to reproduce the observed cross-peak patterns. A careful numerical study reveals that in the high spin Co(II) complex studied here, the cross-correlation dynamic shift contribution is of the same order of magnitude as the cross-correlation rate, a value much larger than what can be computed assuming isotropic Brownian motion and complete separation between the electron spin and the lattice.     

Solid-State NMR Studies on Ionic <Emphasis Type="Italic">closo</Emphasis>-Dodecaborates

Alkali metal dodecahydro-closo-dodecaborates M₂[B₁₂H₁₂] (M = K, Rb, Cs, NH₄, N(CH₃)₄) and the perhalogenated cesium salts Cs₂[B₁₂X₁₂] (X = Cl, Br, I) are studied by solid-state ¹¹B nuclear magnetic resonance (NMR) spectroscopy as well as X-ray diffraction (XRD) and differential scanning calorimetry. The present work addresses the molecular dynamics of the anionic [B₁₂X₁₂]²⁻ icosahedra which is examined by variable-temperature ¹¹B NMR line shape studies between 120 and 370 K. Characteristic line shape effects are observed which strongly depend on the actual substituent X and the counterion M⁺. All alkali metal dodecahydro-closo-dodecaborates M₂ [B₁₂H₁₂] exhibit at elevated temperatures ¹¹B NMR spectra with a single isotropic line which proves the presence of an efficient molecular process, resulting in dynamic (rotational) disorder along with vanishing dipolar and quadrupolar interactions. The positional order of the boron clusters, however, remains unaffected, as shown by the XRD data. At lower temperatures, the underlying motions are frozen on the NMR timescale resulting in characteristic ¹¹B NMR spectra with a dominant homonuclear ¹¹B–¹¹B dipolar splitting. The per-halogenated cesium salts Cs₂[B₁₂X₁₂] behave differently. Hence, from the experimental ¹¹B NMR spectra at room temperature a substantial mobility is only seen for the [B₁₂Cl₁₂]²⁻ anion. Obviously, the degree of anion mobility depends on the size of the substituent X in the [B₁₂X₁₂]²⁻ clusters (X = H, Cl, Br, I). A quantitative analysis of the experimental ¹¹B NMR spectra of the alkali metal dodecahydro-closo-dodecaborates M₂ [B₁₂H₁₂] is achieved by line shape simulations, considering [B₁₂H₁₂]²⁻ ions undergoing reorientational jumps between icosahedral sites. From the motional correlation times the activation energies are derived. It is found that a correlation exists between the activation energies, the motional correlation times and the lattice constant. Hence, the activation energies and correlation times strongly increase with decreasing size of the cation M⁺, which reflects an increasing sterical hindrance due to a decreasing crystallo-graphic lattice constant in the same direction. Authors' address: Klaus Müller, Institut für Physikalische Chemie, Universit?t Stuttgart, Pfaffen-waldring 55, Stuttgart 70569, Germany     

A molecular dynamics study of carbon dioxide in water: diffusion,structure and thermodynamics

Atomistic simulations are reported of a model of CO₂ in water. CO₂ is modelled by partial charges and Lennard-Jones interaction sites on each atom; the SPC/E model for water is used. Good agreement with experiment is found for the translational diffusion constants. The variation of the dynamics with the potential parameter was investigated. As expected, the orientational correlation times increase as the magnitude of the quadrupole moment is increased, but the translational diffusion constants are found to be surprisingly insensitive to the magnitude of the CO₂ quadrupole moment. The translational friction coefficient was resolved into electrostatic, Lennard-Jones and cross-terms; the Lennard-Jones contribution is found to be the largest. Varying the Lennard-Jones size parameter affects both translational and reorientational motion. In order to try to understand these results further, the variation of solvation free energy was investigated and the solvent structure around carbon dioxide was examined as the electrostatic and Lennard-Jones parameters were changed. The temperature dependence of the self-diffusion constant of pure SPC/E water was determined.     

Dynamics of different molecules adsorbed in porous media

We present in this paper a comparative study on the dynamics of benzene, cyclohexane, and methanol molecules, confined in the pores of MCM-41 molecular sieve and HZSM-5 zeolite. The quasi-elastic neutron scattering (QENS) measurements revealed that the physical state of these adsorbed molecules depended not only on the structural characteristics of the host matrix but also on the chemical properties, such as dipole moment, of the guest molecules. Thus, while no motion was observed in the time-scale of 10⁻¹⁰−10⁻¹² s in the case of methanol, the larger size benzene and cyclohexane molecules are found to perform six-fold and three-fold jump rotation, respectively, when adsorbed inside the cages of HZSM-5 at room temperature. At the same time, all the three molecules are found to undergo a translational motion inside the pores of MCM-41 molecular sieves, the value of diffusion constant being the lowest in case of methanol because of its higher polarity. Translationl motion of the guest molecules inside the pores of MCM-41 can be satisfactorily described by Chudley-Eliott fixed jump length diffusion and accordingly the residence time, jump length and diffusion constant are estimated.     

New phase transition in an easy-axis “triangular” antiferromagnet

The NMR of ⁵⁵Mn in the quasi-one-dimensional noncollinear anti-ferromagnet CsMnI₃ is investigated at T=1.3 K in magnetic fields up to ∼80 kOe and angles between the field and C ₆ axis ϕ≈ 0.5° and ϕ=7°. A new reorientational magnetic phase transition is observed in a field H _c1≈39.0 kOe. The magnetic structure for H>H _c1 is determined. The average Mn²⁺ spins of the magnetic sublattices in the new phase are determined from an analysis of the NMR spectrum to be 〈 S _C 〉=1.63 and 〈S _D 〉=1.72. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 12, 988–993 (25 June 1998)     

Nuclear spin–lattice relaxation and complex motion of macromolecules in solution

The NMR spectral densities of a complex motion consisting of a combination of anisotropic overall motion and internal motion have been derived. Two approximations of the equations derived for the cases of slow, J_slow (ω), and fast, J_fast (ω), internal motions are presented. These equations imply that reduction in spectral density of overall motion can be observed if the maxima of internal and overall motions spectral densities versus temperature are well separated, as for fast internal motion. Slow intramolecular motion influences the values of spectral densities of the overall motion if one of the two spins performs a motion, for example a proton in double minimum of the ¹⁵N-H?···?N hydrogen bond. The analysis presented reveals small differences between the temperature dependencies of spectral densities of the isotropic and anisotropic overall motions. The theory is illustrated by the ¹³C protonated carbon spin-lattice relaxation of α-cyclodextrin macromolecule, using the expected motional parameters: D _∥/D _⊥?≈?5 at room temperature and for a fast or slow internal motion.     

DNA Duplex Dynamics: NMR Relaxation Studies of a Decamer with UniformlyC-Labeled Purine Nucleotides

Dynamics in a DNA decamer duplex,d(CATTTGCATC) ·d(GATGCAAATG), were investigated via a detailed¹³C NMR relaxation study. Every 2′-deoxyadenosine and 2′-deoxyguanidine was chemically enriched with 15%¹³C and 98%¹⁵N isotopes. Six nuclear relaxation parameters [R(¹³C_z),R(¹H_z),R(2¹H_z¹³C_z),R(¹³C_x),R(2¹H_z¹³C_x) and steady-state¹³C{¹H} NOE] were measured at 600 MHz and three were measured at 500 MHz (¹H frequency) for the CH spin systems of sugar 1′, 3′, and 4′ as well as base 8 and 2 positions. A dependence of relaxation parameter values on chemical position was clearly observed; however, no sequence-specific variation was readily evident within our experimental error of ∼5–10%, except for 3′ and 5′ termini. It was demonstrated that the random 15%¹³C enrichment effectively suppressed both scalar and dipolar contributions of the neighboring carbons and protons on the relaxation parameters. To analyze dynamics via all observed relaxation parameters, full spectral density mapping (1992, J. W. Peng and G. Wagner,J. Magn. Reson.98, 308) and the “model-free” approach (1982, Lipari and Szabo,J. Am. Chem. Soc.104, 4546) were applied complementarily. A linear correlation between three spectral density values,J(ω_C),J(ω_H− ω_C), andJ(ω_H+ ω_C) was observed in plots containing all measured values, but not for the other spectral density terms includingJ(0). These linear correlations reflect the effect of overall motion and similar internal motions for each CH vector in the decamer. The correlations yielded two correlation times, 3–4 ns and 10–200 ps. One value, 3–4 ns, corresponds to the value of 3.3 ns obtained for the overall isotropic tumbling correlation time determined from analysis of¹³C T1/T2 ratios. The possibility of overall anisotropic tumbling was examined, but statistical analysis showed no advantage over the assumption of simple isotropic tumbling. Lack of correlations entailingJ(0) implies that a relatively slow chemical exchange contributes to yielding of effectiveJ_eff(0) values. Based on spectral density mapping and the T1/T2 ratio analysis, three basic assumptions were initially employed (and subsequently justified) for the model-free calculation: isotropic overall tumbling, one internal motion, and the presence of chemical exchange terms. Except for terminal residues, the order parameterS²and the corresponding fast internal motion correlation time were determined to be about 0.8 ± 0.1 and 20 ± 20 ps, respectively, for the various CH vectors. Only a few differences were observed between or within sugars and bases. The internal motion is very fast (ps–ns time scale) and its amplitude restricted; e.g., assuming a simple wobble-in-a-cone model, the internal motion is restricted to an angular amplitude of ±22.5° for each of the 1′, 3′, 4′, 2, and 8 positions in the purine nucleotides in the entire duplex.     

Effect of the frequency of intramolecular motions on the NMR relaxation in liquid state temperature regime

Equations for the spectral densities of complex motion of a spin pair undergoing internal motion and isotropic/anisotropic overall rotation have been considered. The fluctuations of the interproton distances, caused by internal motion, have been taken into account in the theoretical equations. A method allowing a distinction between the isotropic and the anisotropic overall rotation of molecules has been proposed. The effect of the activation parameters of internal motions (known from the solid state study) on the measured T ₁ relaxation of the ¹³C and ¹H–¹H cross-relaxation rates has been analysed for methyl-β-D-galactopyranoside in DMSO-d6 solution. The conformational trans-gauche jumps of the methylene group are not fast enough to affect the T ₁ value of carbon C6 in the liquid state temperatures regime. Only the methyl group rotation is a very fast internal motion. This motion influences the carbon C7 relaxation and methyl protons–anomeric proton cross-relaxation. The values of interatomic distances between anomeric H(C1) and H(C5) as well as the three methyl protons H(C7) have been calculated from the cross-relaxation rates. The distance H(C1)–H(C7) fluctuates due to the rotation of methyl group. The application of the ‘model-free approach’ to study molecular dynamics in solutions is discussed.     

Detecting columnar deformations in a supermesogenic octapode by proton NMR relaxometry

We used proton ( ¹H nuclear magnetic relaxation (NMR) dispersions to study the molecular dynamics in the isotropic phase and mesophases (nematic and columnar hexagonal) of a supermesogenic octapode formed by laterally connecting calamitic mesogens to an inorganic silsesquioxane cube through flexible spacers. The dispersions of the spin-lattice relaxation time (T₁) are interpreted through relaxation mechanisms used for the study of molecular dynamics in low-molar-mass liquid crystals but adapted to the case of liquid crystalline supermolecules. At high frequencies (above 10MHz) the behaviour of the T₁ with the Larmor frequency is similar for all phases and is ascribed to local reorientations and/or rotations. At intermediate and low frequencies (below 10MHz) our results show notable differences in the T₁ behaviour with respect to the mesophases. The nematic (N) and isotropic (Iso) phases’ low-frequency results are similar and are interpreted for both phases in terms of order director fluctuations (ODF), revealing that even in the isotropic phase local nematic order is detected by proton NMR relaxometry. Local nematic order in the Iso phase is interpreted in terms of the presence of nematic cybotactic clusters induced by the interdigitation of mesogens that is promoted by the silsesquioxane octapode molecular structure. In the columnar hexagonal (Col _h phase, the T₁ dispersions show that elastic columnar deformations (ECD) dominate the nuclear magnetic relaxation below 10MHz. This result shows that the columnar packing of the octapode clearly restricts the collective fluctuations of the mesogenic units inspite of their local nematic order.     

Raman light scattering,infrared absorption and DSC studies of the phase transition and vibrational and reorientational dynamics of H2O ligands and ClO4– anions in [Ba(H2O)3](ClO4)2

[Ba(H₂O)₃](ClO₄)₂ between 90 and 300 K possesses two solid phases. One phase transition of the first‐order type at: = 211.3 K (on heating) and = 204.6 K (on cooling) was determined by differential scanning calorimetry. The entropy change value (ΔS ≈ 15 Jmol^–1 K^–1), associated with the observed phase transition, indicates a moderate degree of molecular dynamical disorder. Both, vibrational and reorientational motions of H₂O ligands and ClO₄^– anions, in the high‐temperature and low‐temperature phases, were investigated by Fourier transform far‐infrared and middle‐infrared and Raman light scattering spectroscopies. The temperature dependences of the full‐width at half‐maximum values of the bands associated with ρ_w(H₂O) mode, in both infrared (~570 cm^–1) and Raman light scattering (~535 cm^–1) spectra, suggest that the observed phase transition is not associated with a sudden change of a speed of the H₂O reorientational motions. Ligands reorient fast, with correlation time of the order of several picoseconds, with a mean activation energy value E_a = 5.1 kJ mol^–1 in both high and low temperature phases. On the other hand, measurements of temperature dependences of full‐width at half‐maximum values of the infrared band at ~460 cm^–1, associated with δ_d(OClO)E mode, and Raman band at ~1105 cm^–1, associated with ν_as(ClO)F₂ mode, revealed the existence of a fast ClO₄^– reorientation in phase I and in phase II, with the E_a(I) and E_a(II) values equal to 8.0 and 6.5 kJ mol^–1, respectively. These reorientational motions of ClO₄^– are slightly distorted at the T_C. Fourier transform far‐infrared and middle‐infrared spectra with decreasing of temperature indicated characteristic changes at the vicinity of PT at T_C, which suggested lowering of the crystal structure symmetry. All these experimental facts suggest that the discovered phase transition is associated with small change of H₂O ligands and somewhat major change of ClO₄^– anions reorientational dynamics, and with insignificant change of the crystal structure, too. Copyright © 2012 John Wiley & Sons, Ltd.     

Molecular-dynamics simulation of methane adsorbed on MgO: Evidence for a Kosterlitz-Thouless transition

A realistic model of a monolayer molecular crystal of methane adsorbed on the (100) surface of MgO has been studied by means of molecular dynamics. The model treates the atomicity of the MgO substrate explicitly. Large corrugations in energy are found for both the translational and rotational motion of methane across the substrate. The preferred configurations of adsorption is over an Mg²⁺ ion in a tripod-down orientation. The orientationally ordered low-energy states of the monolayer have been found. Finite-size-scaling calculations on systems of different sizes indicate, however, that the ordered state exhibits only quasi-long-range order. The disclinations in the ordered phase exist in low concentrations and in bound pairs. Evidence is presented for a Kosterlitz-Thouless-type unbinding transition occurring at T _c ≈ 27 K. No evidence is found for a first-order transition. The specific heat exhibits an anomaly at T ≈ 32 K. The disclination density in the region of the transition is reported; below T _c, this density can be fitted to an Arrhenius-type law, yielding an estimate of the core enegy for a bound vortex-antivortex pair.