Numerical calculation of the combinatorial entropy of partially ordered ice

Using a one-parameter case as an example, we demonstrate that multicanonical simulations allow for accurate estimates of the residual combinatorial entropy of partially ordered ice. For the considered case, corrections to an (approximate) analytical formula are found to be small, never exceeding 0.5%. The method allows one as well to calculate combinatorial entropies for other systems.     

A reexamination of the ice III/IX hydrogen bond ordering phase transition

Ice III is a hydrogen bond disordered crystal which when cooled 1 K / min or faster transforms to an antiferroelectric hydrogen bond ordered structure, ice IX. Throughout its region of stability, experiments indicate that the H bonds in ice III are, in fact, partially ordered, i.e., some proton arrangements are preferred. In addition, there has been evidence that the structure of ice IX retains some residual disorder after the transition. Diffraction experiments and calorimetry apparently conflict with regard to the degree of ordering at the ice III/IX transition. Mean field statistical mechanical theories have been used to link partial occupations from diffraction data with thermodynamics. In this work, we investigate the ice III/IX proton ordering phase transition using electronic density functional theory calculations for small unit cells, extended to simulate the phase transition in a large unit cell using graph invariants. In agreement with experiment, we observe partial ordering over a wide range of temperatures as ice III transforms to partially disordered ice IX, near 126 K, which becomes fully ordered at lower temperatures. We compare our results from full statistical mechanical simulations with mean field models, finding small errors for the low-temperature ice IX phase and much larger errors for the high-temperature ice III phase. The failure of mean field theories may explain the apparent conflict between diffraction experiments and calorimetry.     

Simulations of proton order and disorder in ice Ih

Computer simulations of ice Ih with different proton orientations are presented. Simulations of proton disordered ice are carried out using a Monte Carlo method which samples over proton degree of freedom, allowing for the calculation of the dielectric constant and for the examination of the degree of proton disorder. Simulations are also presented for two proton ordered structures of ice Ih, the ferroelectric Cmc2(1) structure or ice XI and the antiferroelectric Pna2(1) structure. These simulations indicate that a transition to a proton ordered phase occurs at low temperatures (below 80 K). The symmetry of the ordered phase is found to be dependent on the water potential. The stability of the two proton ordered structures is due to a balance of short-ranged interactions which tend to stabilize the Pna2(1) structure and longer-range interactions which stabilize the Cmc2(1) structure.     

Comparison of the site occupancies determined by combined Rietveld refinement and density functional theory calculations: example of the ternary Mo-Ni-Re σ phase

The site occupancies of the Mo-Ni-Re σ phase have been studied as a function of the composition in the ternary homogeneity domain by both experimental measurements and calculations. Because of the possible simultaneous occupancy of three elements on the five sites of the crystal structure, the experimental determination of the site occupancies was achieved by using combined Rietveld refinement of X-ray and neutron diffraction data, whereas calculation of the site occupancies was carried out by using the density functional theory results of every ordered (i.e., 3(5) = 243) configuration appearing in the ternary system. A comparison of the experimental and calculation results showed good agreement, which suggests that the topologically close-packed phases, such as the σ phase, could be described by the Bragg-Williams approximation (i.e., ignoring the short-range-order contributions). On the other hand, the atomic distribution on different crystallographic sites of the Mo-Ni-Re σ phase was found to be governed by the atomic sizes. Ni, having the smallest atomic size, showed a preference for low-coordination-number (CN) sites, whereas Mo, being the largest in atomic size, preferred occupying high-CN sites. However, the preference of Re, having intermediate atomic size, varied depending on the composition, and a clear reversal in the preference of Re as a function of the composition was evidenced in both the calculated and experimental site-occupancy results.     

A powerful computational crystallography method to study ice polymorphism

Classical molecular dynamics (MD) simulations are employed as a tool to investigate structural properties of ice crystals under several temperature and pressure conditions. All ice crystal phases are analyzed by means of a computational protocol based on a clustering approach following standard MD simulations. The MD simulations are performed by using a recently published classical interaction potential for oxygen and hydrogen in bulk water, derived from neutron scattering data, able to successfully describe complex phenomena such as proton hopping and bond formation/breaking. The present study demonstrates the ability of the interaction potential model to well describe most ice structures found in the phase diagram of water and to estimate the relative stability of 16 known phases through a cluster analysis of simulated powder diagrams of polymorphs obtained from MD simulations. The proposed computational protocol is suited for automated crystal structure identification.     

Prediction of a phase transition to a hydrogen bond ordered form of ice VI

Ice VI is a hydrogen bond disordered crystal over its known region of stability. In this work, we predict that ice VI will transform into a hydrogen bond ordered phase near 108 K, and have identified the likely low-temperature phase as ferroelectric (space group Cc) with an antiferroelectric structure (space group P2(1)2(1)2(1)) close by in energy. Electronic density functional theory calculations provide input to our calculations, which are extended to cells large enough for statistical simulations by using graph invariants. A significant decrease in the configurational entropy is predicted as hydrogen bonds exhibit partial order above the transition, provided that the hydrogen bonds can equilibrate on an experimental time scale. Conversely, partial disorder is predicted at temperatures below the transition. Although some evidence for ordering of ice VI has been observed in experiments, a low-temperature proton ordered phase has not been identified experimentally.     

Nano‐ice on Boron Nitride Nanomesh: Accessing Proton Disorder

Water was investigated on a h‐BN/Rh(111) nanomesh template using variable temperature scanning tunneling microscopy (STM) and density functional theory (DFT) calculations. Below 52 K, two distinct phases self‐assemble within the 3.2 nm unit cell of the nanomesh that consists of “holes” and “wires”. In the 2 nm holes, an ordered phase of nano‐ice crystals with about 40 molecules is found. The ice crystals arrange in a bilayer honeycomb lattice, where hydrogen atoms of the lower layer point to the substrate. The phase on the 1 nm wires is a low density gas phase. Tunneling barrier height dI/dz spectroscopy measurements reveal the dipoles of individual molecules in the nano‐ice clusters and access proton disorder.     

No evidence for large-scale proton ordering in Antarctic ice from powder neutron diffraction

We have examined a sample of 3000 year old Antarctic ice, collected at the Kohnen Station, by time-of-flight powder neutron diffraction to test the hypothesis of Fukazawa et al. [e.g., Ann. Glaciol. 31, 247 (2000)] that such ice may be partially proton ordered. Great care was taken to keep our sample below the proposed ordering temperature (237 K) at all times, but we did not observe any evidence of proton ordering.     

Influence of chemical composition and sequence length on the transport properties of proton exchange membranes

One of the integral parts of the fuel cell is the proton exchange membrane. Our research group has been engaged in the past few years in the synthesis of several sulfonated poly(arylene ether) random copolymers. The copolymers were varied in both the bisphenol structure as well as in the functional groups in the backbone such as sulfone and ketones. To compare the effect of sequence length, multiblock copolymers based on poly(arylene ether sulfone)s were synthesized. This paper aims to describe our investigation of the effect of chemical composition, morphology, and ion exchange capacity (IEC) on the transport properties of proton conducting membranes. The key properties examined were proton conductivity, methanol permeability, and water self diffusion coefficient in the membranes. It was observed that under fully hydrated conditions, proton conductivity for both random and block copolymers was a function of IEC and water uptake. However, under partially hydrated conditions, the block copolymers showed improved proton conductivity over the random copolymers. The proton conductivity for the block copolymer series was found to increase with increasing block lengths under partially hydrated conditions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2226–2239, 2006     

One-Dimensionally Disordered Chiral Sorting by Racemic Tiling in a Surface-Confined Supramolecular Assembly of Achiral Tectons

The aggregation of (pro)chiral/achiral molecules into crystalline structures at interfaces forms conglomerates, racemates, and solid solutions, comparable to known bulk phases. Scanning tunneling microscopy and Monte Carlo simulations were employed to uncover a distinct racemic phase, expressing 1D disordered chiral sorting through random tiling in surface-confined supramolecularly assembled achiral 4,4′′-diethynyl-1,1′:4′,1′′-terphenyl molecules. The configurational entropy of the 1D disordered racemic tiling phase was verified by analytical modeling, and found to lie between that of a perfectly ordered 2D racemate and a racemic solid solution.     

A calorimetric study on the low temperature dynamics of doped ice V and its reversible phase transition to hydrogen ordered ice XIII

Doped ice V samples made from solutions containing 0.01 M HCl (DCl), HF (DF), or KOH (KOD) in H(2)O (D(2)O) were slow-cooled from 250 to 77 K at 0.5 GPa. The effect of the dopant on the hydrogen disorder --> order transition and formation of hydrogen ordered ice XIII was studied by differential scanning calorimetry (DSC) with samples recovered at 77 K. DSC scans of acid-doped samples are consistent with a reversible ice XIII <--> ice V phase transition at ambient pressure, showing an endothermic peak on heating due to the hydrogen ordered ice XIII --> disordered ice V phase transition, and an exothermic peak on subsequent cooling due to the ice V --> ice XIII phase transition. The equilibrium temperature (T(o)) for the ice V <--> ice XIII phase transition is 112 K for both HCl doped H(2)O and DCl doped D(2)O. From the maximal enthalpy change of 250 J mol(-1) on the ice XIII --> ice V phase transition and T(o) of 112 K, the change in configurational entropy for the ice XIII --> ice V transition is calculated as 2.23 J mol(-1) K(-1) which is 66% of the Pauling entropy. For HCl, the most effective dopant, the influence of HCl concentration on the formation of ice XIII was determined: on decreasing the concentration of HCl from 0.01 to 0.001 M, its effectiveness is only slightly lowered. However, further HCl decrease to 0.0001 M drastically lowered its effectiveness. HF (DF) doping is less effective in inducing formation of ice XIII than HCl (DCl) doping. On heating at a rate of 5 K min(-1), kinetic unfreezing starts in pure ice V at approximately 132 K, whereas in acid doped ice XIII it starts at about 105 K due to acceleration of reorientation of water molecules. KOH doping does not lead to formation of hydrogen ordered ice XIII, a result which is consistent with our powder neutron diffraction study (C. G. Salzmann, P. G. Radaelli, A. Hallbrucker, E. Mayer, J. L. Finney, Science, 2006, 311, 1758). We further conjecture whether or not ice XIII has a stable region in the water/ice phase diagram, and on a metastable triple point where ice XIII, ice V and ice II are in equilibrium.     

One‐Dimensionally Disordered Chiral Sorting by Racemic Tiling in a Surface‐Confined Supramolecular Assembly of Achiral Tectons

The aggregation of (pro)chiral/achiral molecules into crystalline structures at interfaces forms conglomerates, racemates, and solid solutions, comparable to known bulk phases. Scanning tunneling microscopy and Monte Carlo simulations were employed to uncover a distinct racemic phase, expressing 1D disordered chiral sorting through random tiling in surface‐confined supramolecularly assembled achiral 4,4′′‐diethynyl‐1,1′:4′,1′′‐terphenyl molecules. The configurational entropy of the 1D disordered racemic tiling phase was verified by analytical modeling, and found to lie between that of a perfectly ordered 2D racemate and a racemic solid solution.     

Thermotropic rigid chain copolymers I. crystallization kinetics and thermodynamic properties

The kinetics of structure formation and the thermal properties of the ordered phase were analyzed calorimetrically for a rigid polymer, characterized by an irregular chemical structure. The transition from the nematic melt to a partially ordered state was found to involve two different processes, a fast and a slow one. The fast one corresponds apparently to a thermally activated nucleation and growth mechanism, whereas the slow one is strongly self delaying. Its transition rate is only weakly dependent on the temperature. The thermal properties of the ordered phase, resulting from this process, vary strongly with the annealing temperature and annealing time. The enthalpy and entropy of fusion, characteristic for the pure ordered phase, are lower by a factor of about 10 in comparison to the corresponding values of flexible chain molecules.     

Thermotropic rigid-chain copolymers: X-ray investigations of the structure

The structure of a rigid rodlike random copolyester, consisting mainly of p-hydroxybenzoic acid, hydroquinone, and carbonyl units, was investigated by means of wide-angle x-ray scattering. The lateral order of the chain molecules was found to be short-range in the nematic melt, in close agreement with the spatial order in the melt of flexible chain molecules. The packing density was found to be surprisingly large in the anisotropic melt. The low-temperature solid state consists of two phases, namely a frozen-in nematic and a three-dimensionally ordered crystal phase. Quenched samples were found to have a degree of crystallinity of about 25%, whereas well-annealed samples may display a degree of crystallinity of up to 70%. The ordered phase apparently displays an orthorhombic unit cell. Its dimensions indicate that a cocrystallization of the comonomers has taken place. On the basis of the observations that the lattice dimensions change continuously as a function of annealing parameters and taking into account the fact that the transition enthalpy, entropy, and volume are smaller by at least one order of magnitude in comparison to those found for crystals of flexible chains, we arrived at the conclusion that the polymer displays a rotationally disordered crystalline state.     

Four phases of amorphous water: Simulations versus experiment

Multiplicity of the liquid-liquid phase transitions in supercooled water, first obtained in computer simulations [Brovchenko et al., J. Chem. Phys. 118, 9473 (2003)], has got strong support from the recent experimental observation of the two phase transitions between amorphous ices [Loerting et al., Phys. Rev. Lett. 96, 025702 (2006)]. These experimental results allow assignment of the four amorphous water phases (I-IV) obtained in simulations to the three kinds of amorphous ices. Water phase I (rho approximately 0.90 gcm(3)) corresponds to the low-density amorphous ice, phase III (rho approximately 1.10 gcm(3)) to the high-density amorphous ice, and phase IV (rho approximately 1.20 gcm(3)) to the very-high-density amorphous ice. Phase II of model water with density rho approximately 1.00 gcm(3) corresponds to the normal-density water. Such assignment is confirmed by the comparison of the structural functions of the amorphous phases of model water and real water. In phases I and II the first and second coordination shells are clearly divided. Phase I consists mainly of the four coordinated tetrahedrally ordered water molecules. Phase II is enriched with molecules, which have tetrahedrally ordered four nearest neighbors and up six molecules in the first coordination shell. Majority of the molecules in phase III still have tetrahedrally ordered four nearest neighbors. Transition from phase III to phase IV is characterized by a noticeable drop of tetrahedral order, and phase IV consists mainly of molecules with highly isotropic angular distribution of the nearest neighbors. Relation between the structures of amorphous water phases, crystalline ices, and liquid water is discussed.     

Exceptional Isotopic‐Substitution Effect: Breakdown of Collective Proton Tunneling in Hexagonal Ice due to Partial Deuteration

Multiple proton transfer controls many chemical reactions in hydrogen‐bonded networks. However, in contrast to well‐understood single proton transfer, the mechanisms of correlated proton transfer and of correlated proton tunneling in particular have remained largely elusive. Herein, fully quantized ab initio simulations are used to investigate H/D isotopic‐substitution effects on the mechanism of the collective tunneling of six protons within proton‐ordered cyclic water hexamers that are contained in proton‐disordered ice, a prototypical hydrogen‐bonded network. At the transition state, isotopic substitution leads to a Zundel‐like complex, [HO???D???OH], which localizes ionic defects and thus inhibits perfectly correlated proton tunneling. These insights into fundamental aspects of collective proton tunneling not only rationalize recent neutron‐scattering experiments, but also stimulate investigations into multiple proton transfer in hydrogen‐bonded networks much beyond ice.     

Raman spectra of proton ordered phase XI of ICE I. Translational vibrations below 350 cm(-1)

Polarized Raman spectra from single crystals of ice XI (proton ordered phase of ice Ih) were measured and assigned for the modes below 350 cm(-1) in the translational vibration region. In contrast to the proton disordered ice Ih, the spectra in ice XI show clear polarization dependence and several new peaks are observed. Most of the vibrational modes were successfully assigned by the simplified point mass model with the symmetry C(2v) (12)(Cmc2(1)) and by the depolarization effect. In particular, LO-TO splitting of the mode near 240 cm(-1) was experimentally confirmed for the first time, which indicates that the long range force effect appears distinctly in ice XI.     

The Raman spectra of the KOH-doped ice polymorphs: V and VI

The effect on the Raman spectra of the proton ordering induced by KOH in the high pressure phases of ice, ice V and VI has been studied. Our previous Raman studies of ice V and ice VI (ref.1) showed spectroscopic evidence of partial proton ordering at low temperatures (below about 130 K) in ice V and a possible phase change in ice VI. These conclusions were made on the measurements of the lattice vibration region. The present results, based on the observation of the bands due to the uncoupled O-D stretching vibrations of KOH-doped ice V and, in particular, ice VI, show that some kind of proton ordering or partial proton ordering may be induced by the presence of KOH dopant in these two ices.A Lorentzian curve fit has been used to separate the main band from the side bands in the relatively complex structured band due to the uncoupled O-D stretching vibration in ice V and ice VI.     

Simulation of multiple ordered phases in C23 n-alkane

Normal alkanes display multiple ordered phases, including an orthorhombic crystal (X) and two partially ordered rotator phases (RI and RII). The rotator phase transitions X-RI and RI-RII are of interest because they are weakly first-order, and because experiments suggest that crystalline polyethylene may nucleate via a metastable rotator phase. We have performed heating and cooling scans of all-atom NσT (isothermal, isostress) simulations of a pure C(23) solid. We find a sequence of phases, transition temperatures, structural and thermodynamic properties, all reasonably consistent with experiment, except that a monoclinic crystal is more stable in our simulations than the experimental orthorhombic structure. We find that the RI phase is well described as an orthorhombic crystal disordered by random ±90° rotations of molecules about their stem axis, and the RII phase can be represented as a loose hexagonal packing of parallel chain stems, which tend to orient with the in-plane projection of C-C bonds pointing between neighbors. To measure local orthorhombic, RI, or RII order, we define Potts- and Ising-like order parameters, from which global order parameters and correlation functions can be computed. We observe modest pretransitional fluctuations of local RI order in the RII phase near T(RI-RII), characteristic of this weakly first-order transition.     

Proton ordering in cubic ice and hexagonal ice; a potential new ice phase--XIc

Ordinary water ice forms under ambient conditions and has two polytypes, hexagonal ice (Ih) and cubic ice (Ic). From a careful comparison of proton ordering arrangements in Ih and Ic using periodic density functional theory (DFT) and diffusion Monte Carlo (DMC) approaches, we find that the most stable arrangement of water molecules in cubic ice is isoenergetic with that of the proton ordered form of hexagonal ice (known as ice XI). We denote this potential new polytype of ice XI as XIc and discuss a possible route for preparing ice XIc.