The structure of the electric double layer: Atomistic versus continuum approaches

This article reviews recent forays in theoretical modeling of the double layer structure at electrode/electrolyte interfaces by current atomistic and continuum approaches. We will briefly discuss progress in both approaches and present a perspective on how to better describe the electric double layer by combining the unique advantages of each method. First-principles atomistic approaches provide the most detailed insights into the electronic and geometric structure of electrode/electrolyte interfaces. However, they are numerically too demanding to allow for a systematic investigation of the electric double layers over a wide range of electrochemical conditions. Yet, they can provide valuable input for continuum approaches that can capture the influence of the electrochemical environment on a larger length and time scale due to their numerical efficiency. However, continuum approaches rely on reliable input parameters. Conversely, continuum methods can provide a preselection of interface structures and conditions to be further studied on the atomistic level.     

Study of the order-disorder transitions in methoxy-functionalized polyalkylthiophenes

This article describes the solvatochromic properties of two polyalkylthiophene (PAT) samples functionalized at the end of the hexamethylenic side-chains with a methoxy group, which is able to strongly enhance the solubility, workability and filmability of this kind of polymers. The latter are obtained using either a regioselective or a regiospecific polymerization procedure, thus leading to a different configurational order in the final polymer. The optical features of the synthesized samples—which are very interesting for chemosensor and electrooptical applications—are observed in many solvent/non-solvent systems and derive from the conformational modification of the conjugated backbone induced by side-chain order-disorder transitions. These transitions strongly depend on the content of HT dyads; a fact which undeniably shows the importance of the polymer configuration, directly deriving from the adopted polymerization method, on the final electrical and electronic properties of the obtained material. The low sensitivity of the regioregular sample towards the temperature changes together with its higher tendency to give thick, semicrystalline and self-consisting films makes it very promising for the obtainment of organic semiconductors for electronic devices subjected to high temperature variations.     

An order-disorder transition in the conjugated polymer MEH-PPV

The poly(p-phenylene vinylene) derivative MEH-PPV is known to exist as two morphologically distinct species, referred to as red phase and blue phase. We show here that the transition from the blue phase to the red phase is a critical phenomenon that can be quantitatively described as a second order phase transition with a critical temperature T(c) of 204 K. The criticality is associated with the trade-off between the gain in the electronic stabilization energy when the π-system of a planarized chain can delocalize and the concomitant loss of entropy. We studied this transition by measuring the absorption and fluorescence in methyltetrahydrofuran (MeTHF) in two different concentrations as a function of temperature. The spectra were analyzed based upon the Kuhn exciton model to extract effective conjugation lengths. At room temperature, the chains have effective conjugation lengths of about five repeat units in the ground state (the blue phase), consistent with a disordered defect cylinder conformation. Upon cooling below the critical temperature T(c), the red phase with increased effective conjugation lengths of about 10 repeat units forms, implying a more extended and better ordered conformation. Whereas aggregation is required for the creation of the red phase, its electronic states have a predominant intrachain character.     

Protein secondary structure preferencs

This paper addresses the question to what extent steric properties of sequence neighbors effect the preferences of an amino acid residue to assume the-helical or some other secondary structure conformation. We find that an amino acid has increased tendency to be in-helical conformation when its sequence neighbors are bulky. This result is an outcome of our automated method for finding conformational preferences as functions of physical parameters important for protein folding. The steric environment for a given residue in a protein is defined as an average of water-accessible surface areas of its primary structure neighbors in extended conformation for model tripeptides. For all amino acids, including non-helix formers like glycine and arginine, the preference for the helical structure increases if their primary structure neighbors form a larger steric environment.     

Surface order-disorder phase transitions and percolation

In the present paper, the connection between surface order-disorder phase transitions and the percolating properties of the adsorbed phase has been studied. For this purpose, four lattice-gas models in the presence of repulsive interactions have been considered. Namely, monomers on honeycomb, square, and triangular lattices, and dimers (particles occupying two adjacent adsorption sites) on square substrates. By using Monte Carlo simulation and finite-size scaling analysis, we obtain the percolation threshold theta(c) of the adlayer, which presents an interesting dependence with w/k(B)T (w, k(B), and T being the lateral interaction energy, the Boltzmann constant, and the temperature, respectively). For each geometry and adsorbate size, a phase diagram separating a percolating and a nonpercolating region is determined.     

Protein structure prediction using basin-hopping

Associative memory Hamiltonian structure prediction potentials are not overly rugged, thereby suggesting their landscapes are like those of actual proteins. In the present contribution we show how basin-hopping global optimization can identify low-lying minima for the corresponding mildly frustrated energy landscapes. For small systems the basin-hopping algorithm succeeds in locating both lower minima and conformations closer to the experimental structure than does molecular dynamics with simulated annealing. For large systems the efficiency of basin-hopping decreases for our initial implementation, where the steps consist of random perturbations to the Cartesian coordinates. We implemented umbrella sampling using basin-hopping to further confirm when the global minima are reached. We have also improved the energy surface by employing bioinformatic techniques for reducing the roughness or variance of the energy surface. Finally, the basin-hopping calculations have guided improvements in the excluded volume of the Hamiltonian, producing better structures. These results suggest a novel and transferable optimization scheme for future energy function development.     

Statistical mechanics of order-disorder in the thiourea + cyclohexane adduct

An order-disorder model for the transition at 128.8 K in the adduct of c-C₆H₁₂ with thiourea is evaluated by statistical mechanics. It is assumed that each c-C₆H₁₂ molecule can occupy any of six positions and that it interacts with the “host” lattice and also with nearest-neighbour c-C₆H₁₂ molecules both in its own channel and in neighbouring channels. A “mean field” approximation is applied to the latter type of interaction. With values of the interaction parameters computed by summing atom-atom potentials the predicted curve for heat capacity against temperature is too broad and has its maximum at a temperature which is too low. The effects of modification of the parameters are examined.     

The classification of order-disorder transitions on surfaces

Order-disorder transitions occur in adsorbed systems of great diversity.However, the transitions themselves can be shown to fall into just a few classes which are characterized by differing critical properties. The particular class to which a given transition belongs is determined directly from the nature of the ordered state and substrate. The critical behavior of some of these classes is of great interest currently, and the observations of such transitions provide a test of the modern theory of critical phenomena. The simple but powerful ideas of Landau and Lifshitz which underlie the above classification are elucidated in the context of order-disorder transitions on surfaces. The “Landau rules” are derived, applied, and yield the several universality classes which can be observed in surface transitions. Specific applications are made to recent experiments, and some areas which call for experimental investigations are noted.     

Protein aggregate structure under high pressure

We show that casein protein micelles--a complex protein/inorganic phosphate structure--can be subjected to high pressures (up to 350 MPa) while making in situ structural measurements using (ultra-)small angle neutron scattering, to give insight to the protein structure, aggregation and stability under pressure.     

Protein secondary structure prediction with SPARROW

A first step toward predicting the structure of a protein is to determine its secondary structure. The secondary structure information is generally used as starting point to solve protein crystal structures. In the present study, a machine learning approach based on a complete set of two-class scoring functions was used. Such functions discriminate between two specific structural classes or between a single specific class and the rest. The approach uses a hierarchical scheme of scoring functions and a neural network. The parameters are determined by optimizing the recall of learning data. Quality control is performed by predicting separate independent test data. A first set of scoring functions is trained to correlate the secondary structures of residues with profiles of sequence windows of width 15, centered at these residues. The sequence profiles are obtained by multiple sequence alignment with PSI-BLAST. A second set of scoring functions is trained to correlate the secondary structures of the center residues with the secondary structures of all other residues in the sequence windows used in the first step. Finally, a neural network is trained using the results from the second set of scoring functions as input to make a decision on the secondary structure class of the residue in the center of the sequence window. Here, we consider the three-class problem of helix, strand, and other secondary structures. The corresponding prediction scheme "SPARROW" was trained with the ASTRAL40 database, which contains protein domain structures with less than 40% sequence identity. The secondary structures were determined with DSSP. In a loose assignment, the helix class contains all DSSP helix types (α, 3-10, π), the strand class contains β-strand and β-bridge, and the third class contains the other structures. In a tight assignment, the helix and strand classes contain only α-helix and β-strand classes, respectively. A 10-fold cross validation showed less than 0.8% deviation in the fraction of correct structure assignments between true prediction and recall of data used for training. Using sequences of 140,000 residues as a test data set, 80.46% ± 0.35% of secondary structures are predicted correctly in the loose assignment, a prediction performance, which is very close to the best results in the field. Most applications are done with the loose assignment. However, the tight assignment yields 2.25% better prediction performance. With each individual prediction, we also provide a confidence measure providing the probability that the prediction is correct. The SPARROW software can be used and downloaded on the Web page http://agknapp.chemie.fu-berlin.de/sparrow/ .     

Effects of confinement on the order-disorder transition of diblock copolymer melts

The effects of confinement on the order-disorder transition of diblock copolymer melts are studied theoretically. Confinements are realized by restricting diblock copolymers in finite spaces with different geometries (slabs, cylinders, and spheres). Within the random phase approximation, the correlation functions are calculated using the eigenvalues and eigenfunctions of the Laplacian operator inverted Delta(2) in the appropriate geometries. This leads to a size-dependent scattering function, and the minimum of the inverse scattering function determines the spinodal point of the homogeneous phase. For diblock copolymers confined in a slab or in a cylindrical nanopore, the spinodal point of the homogeneous phase (chiN)(s) is found to be independent of the confinement. On the other hand, for diblock copolymers confined in a spherical nanopore, (chiN)(s) depends on the confinement and it oscillates as a function of the radius of the sphere. Further understanding of the finite-size effects is provided by examining the fluctuation modes using the Landau-Brazovskii model.     

Effect of correlations in the interaction along polymer chain on the globule structure

A special potential for interaction between polymer chain units, whose energy decreases with increasing distance s between the units as s ^–1, was introduced for the first time. According to Monte Carlo simulation, interactions of this type result in the formation of a globule with an equilibrium packing of domains in space. The radius of gyration of a chain segment in these globules varies with segment length according to the scaling law typical of crumpled globules.     

A new statistical thermodynamic theory for substoichiometric fluorite structure compounds and its application: I. An order-disorder model theory for the thermodynamic functions of substoichiometric fluorite structure compounds

In this work an attempt is made of constructing the (G, T, x) curves for the case of substoichiometric oxides of the fluorite structure on the basis of a statistical model. Considering the fluorite structure as a repitition of oxygen ions tetrahedrically coordinated, the hypothesis is made of a local bond between the reduced cations and the oxygen vacancy in the tetrahedron (“tetrahedral defect”).This “tetrahedral defect” constitutes the building block of the low temperature sub-phases often encountered in these systems; at higher temperatures its packing in the lattice gives rise to “residual structures”.One can express all thermodynamic functions, at given oxygen/metal ratio, as a function of an “ordering parameter” p, representing larger and larger packings of the tetrahedral defects, in such a way making this model a typical order-disorder treatment.Introducing the formalism of chemical equilibria in the equilibria between the various defect species it is also possible to obtain thermodynamic functions by the solution of a system of pseudo-chemical equilibrium equations, when probability functions f are employed in place of the activities of the defects species.     

BeP2: A tetrahedral structure of type order-disorder which obeys a coordination rule for short-range order

Single-crystal studies on BeP₂ indicate that this compound possesses an OD structure. The substructure has a tetragonal unit cell with: a = 3.546 Å, c = 15.01 Å, Z = 4, space group: $\text{I4}{}_1\text{amd}$. The final R factor has a value of 0.033. The atom sites in this substructure correspond to the sites of diamond if the latter is described with a tetragonal cell, where $\text{a = (}\text{2}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{2}\text{)a}{}_{\mathrm{<mtext>diamond</mtext>}}$ and c = 3a_diamond. A short-range order governs the occupation of these sites with Be and P atoms. Each Be has four tetrahedral P neighbors and every P has two Be and two P neighbors. Consideration of the maxima on the diffuse streaks between the sharp reflections of the substructure leads to an intermediate unit cell with a = 7.09 Å and c = 30.02 Å. Coordination considerations allow a structure proposal to be formulated for this intermediate structure which is triclinic but pseudotetragonal. The true unit cell is also pseudotetragonal with a = 7.09 Å and c = N · 15.01 Å, where N is a large integer.     

Free energy of the solid C60 fullerene orientational order-disorder transition

The free energies of the orientationally ordered crystal phase of C60 at low temperatures and the disordered crystal phase at high temperatures are calculated to an accuracy of +/-0.05 kJ/mol using the expanded ensemble Monte Carlo method with the potential model of Sprik et al. [J. Phys. Chem. 96, 2027 (1992)]. The order-disorder transition temperature at zero pressure is determined directly from these free energies, and is found to be consistent with the abrupt changes in configurational energy and unit cell size also found in simulation. A modification of the potential results in predictions of the transition temperature of 257 K and the entropy change of 18.1 J/mol K at this transition, which are in good agreement with the experimental values of 260 K and 19 J/mol K, respectively. The orientational distinguishability in the ordered phase and the indistinguishability in the disordered phase lead to a contribution to the entropy difference of k ln 60, with 60 being the symmetry number of C60. This quantum mechanical correction is important for the accurate prediction of the phase transition properties of the C60 crystals.     

Protein structure prediction by tempering spatial constraints

Summary The probability to predict correctly a protein structure can be enhanced through introduction of spatial constraints – either from NMR experiments or from homologous structures. However, the additional constraints lead often to new local energy minima and worse sampling efficiency in simulations. In this work, we present a new parallel tempering variant that alleviates the energy barriers resulting from spatial constraints and therefore yields to an enhanced sampling in structure prediction simulations.     

The order-disorder state of diaminoalkanes in Cu-based metal-organic materials

Two novel metal-organic compounds, [NH₃(CH₂)_nNH₃][Cu₂(HCOO)₄Cl₂], where n = 3,4, have been investigated by X-ray diffraction and spectroscopic methods to determine the interactions in the crystal and their influence on the molecular arrangement. The disorder found in the n = 3 crystal is of static nature as it has been confirmed by IR and Raman spectroscopy. It has also been suggested that the copper paddle-wheel pyramids can accommodate the conformation of the 1,3-diaminopropane cations through rotary motion.