Configurational Entropy Effects Research Articles

A dynamic light scattering study of hydrogels with the addition of surfactant: a discussion of mesh size and correlation length

We report a study of the interaction of sodium dodecyl sulfate (SDS) with hydrogels made of hydroxyethylcellulose (HEC) and hydrophobically modified hydroxyethylcellulose (HMHEC) by means of dynamic light scattering. The results reveal that the interaction between the hydrogels and SDS only affects the cooperative diffusion, while the slow relaxation of the hydrogels was not influenced by the interaction. Gel swelling due to the presence of SDS is also examined by measuring the weight change of the gel. The main observation is that when the gel swells due to increasing SDS concentration, the cooperative diffusion becomes faster. As such, we raise the question of whether the correlation length obtained from DLS is still proportional to the mesh size inferred from gel swelling. In the discussion, we attribute the cause to the quantity of bound surfactants. The mutual diffusion of SDS micelles could be detected at high SDS concentrations, and the diffusion coefficient of SDS in the gel matrix was determined. HEC (or HMHEC) gel swells due to increasing SDS concentration, while the cooperative diffusion becomes faster. This indicates that the HEC (or HMHEC) gel can swell until the osmotic pressure equals the modulus when the charge effect dominates over the effect of configurational entropy for uncharged gels interacting with charged surfactants.

Energetic stability and magnetic moment of tri-, tetra-, and octa- ferromagnetic element nitrides predicted by first-principle calculations

Formation energies and magnetic moments of tri-, tetra-, and octa- ferromagnetic element nitrides have been calculated using spin-polarized Perdew–Wang generalized gradient approximations of the density functional theory. From the energetic point of view, Fe4N are more stable compared to Fe and N2 gas. Ni4N may be a metastable phase since mixture of Ni3N and Ni would be more energetically stable. Fe4N may be also a metastable from energetic point of view but effect of configurational entropy caused by N-vacancy and of disregarded random occupation of interstitial sites by N observed in Fe3N must be evaluated so as to make precise evaluation, which is beyond the scope of the present work. Co4N are not stable compared to Co metal with the hcp structure and N2 gas, but more stable in case Co metal with the fcc structure is used as a reference state. Only Fe8N with the α″-Fe16N2 type structure would be stable among octa-metal nitrides with the assumed structure of the α″-Fe16N2 type and the Ni32N4 type structure. All of Fe3N, Co3N, and Ni3N are stable, but Ni3N would be non-magnetic in contrast to ferromagnetism of other tri-metal nitrides.

Uncommon Synergy between Adsorption and Diffusion of Hexane Isomer Mixtures in MFI Zeolite Induced by Configurational Entropy Effects

While n-hexane (nC6) can adsorb at any location within the MFI zeolite pore network, configurational considerations cause the branched isomer 2-methylpentane (2MP) to locate preferentially at the channel intersections. For adsorption of nC6/2MP mixtures, infrared microscopy (IRM) measurements show that the adsorption selectivity favors the linear isomer by about one order of magnitude when the total mixture loading, Θt, exceeds four molecules per unit cell at which all intersection sites are fully occupied. The IRM data are in quantitative agreement with configurational-bias Monte Carlo (CBMC) simulations. IRM monitoring of the transient uptake of nC6/2MP mixtures within crystals of MFI exposed to step increases in the pressures shows that the configurational entropy effect also leaves its imprint on the uptake characteristics. For operating conditions in which Θt > 4, increase in the 2MP partial pressure in the bulk gas phase leads to a reduction in the 2MP uptake; this reduction leads to a concomitant a...

Phase Competition in Bismuth Layered Structure Based on First Principles Thermodynamics

The difficulties of synthesis of pure Aurivillius phases largely impede them from extensive application. In this work, the first principles thermodynamics approach was applied to investigate the phase competition relation of three homologous Aurivillius series CaBi2Nb2O9-nNaNbO(3), Bi4Ti3O12-nSrTiO(3) and Bi4Ti3O12-nCaTiO(3), in order to uncover the thermodynamic mechanism of the phase stability. The competition among different phases was analyzed by the relative Gibbs energy as a function of chemical potential of perovskite unit. The analysis reveals that most phases are able to overcome others to be the most stable ones in a certain range as chemical potential increases, which can be applied to interpret the relevant experimental phenomena including the phase mixture and disordered structures. Temperature dependence of phase competition evolutions are also studied based on the configurational and vibrational entropy effect, the former effect changes the competition relations of different phases, while the latter only increases the stable range of the lower phases.

Prediction of SAMPL3 host-guest affinities with the binding energy distribution analysis method (BEDAM).

BEDAM calculations are described to predict the free energies of binding of a series of anaesthetic drugs to a recently characterized acyclic cucurbituril host. The modeling predictions, conducted as part of the SAMPL3 host-guest affinity blind challenge, are generally in good quantitative agreement with the experimental measurements. The correlation coefficient between computed and measured binding free energies is 70% with high statistical significance. Multiple conformational stereoisomers and protonation states of the guests have been considered. Better agreement is obtained with high statistical confidence under acidic modeling conditions. It is shown that this level of quantitative agreement could have not been reached without taking into account reorganization energy and configurational entropy effects. Extensive conformational variability of the host, the guests and their complexes is observed in the simulations, affecting binding free energy estimates and structural predictions. A conformational reservoir technique is introduced as part of the parallel Hamiltonian replica exchange molecular dynamics BEDAM protocol to fully capture conformational variability. It is shown that these advanced computational strategies lead to converged free energy estimates for these systems, offering the prospect of utilizing host-guest binding free energy data for force field validation and development.

Solvent response of mixed polymer brushes

We have performed classical density functional theory calculations to study the behavior of mixed polymer brushes tethered to a planar surface. We assume no lateral segregation of the polymer at the grafting density studied and consider an implicit solvent. For a binary mixture of short and long athermal polymer chains, the short chain is compressed while the long chain is stretched compared with corresponding pure polymer chains at the same grafting density, which is consistent with simulation. This results from configurational entropy effects. Furthermore, we add a mean-field interaction for each polymer brush to simulate their different response towards a solvent. The long chain is forced to dislike the solvent more than the short chain. Through the interplay between the solvent effects and configurational entropy effects, a switch of the polymer brush surface (or outer) layer is found with increasing chain length of the long chain. The transition chain length (long chain) increases with increasing the solvent selectivity, and decreases with increasing the grafting density of the long chain. These results can provide guidance for the design of smart materials based on mixed polymer brushes.

Configurational entropy and intersection blocking effects in multicomponent systems in MFI-type zeolites studied by IR Microscopy

Configurational entropy and intersection blocking effects in multicomponent systems in MFI-type zeolites studied by IR Microscopy

Systematic Study of Aggregation Structure and Thermal Behavior of a Series of Unique H-Shape Alkane Molecules

The H-shape alkanes of various arm lengths have been synthesized successfully through the Grignard reaction. The detailed investigation of these novel compounds may allow us to widen the topological chemistry field furthermore. The molecular form and molecular packing structure in the crystal lattice have been revealed successfully on the basis of X-ray structure analysis as well as the analysis of Raman longitudinal acoustic modes (LAM) sensitive to the alkyl zigzag chain segments. The molecular conformation in the crystal lattice is deformed markedly from the originally imagined H-shape. In the cases of C3HOH to C6HOH, for example, the molecules are packed in a complicated manner and the OH···O hydrogen bonds govern the whole intermolecular interactions mainly. Since the alkyl segmental length is not very long, the conformational change is not very drastic, i.e., the small configurational entropy. Synergic effect of the hydrogen bonds and the small configurational entropy gives the higher melting point as known from the thermal data. On the other hand, in the cases of C10HOH and C12HOH, one of the long alkyl chain arms is found to be bent by 90° so that all of the alky chain segments of planar-zigzag conformation can be packed as closely as possible, and the intermolecular OH···O hydrogen bonds are also formed effectively without any mistake. As a result, the contribution of nonbonded intra- and intermolecular van der Waals interactions between the trans-zigzag alkyl chain segments become major, and the coupling of this enthalpy effect with the larger configurational entropy effect of the molecular shape results in the decrement of the melting point which approaches gradually that of longer n-alkane compound. In this way a sensitive balance between the nonbonded van der Waals interactions, the OH···O hydrogen bonds, as well as the configurational entropy effect gives the characteristic thermal behavior of the H-shape compounds. The thus-newly synthesized H-shape alkane compounds should give us new insight into the packing topology of complicated molecules, leading to the development of new functionality unexpected for normal linear alkane compounds.

Efficient Incorporation of Protein Flexibility and Dynamics into Molecular Docking Simulations

Flexibility and dynamics are protein characteristics that are essential for the process of molecular recognition. Conformational changes in the protein that are coupled to ligand binding are described by the biophysical models of induced fit and conformational selection. Different concepts that incorporate protein flexibility into protein-ligand docking within the context of these two models are reviewed. Several computational studies that discuss the validity and possible limitations of such approaches will be presented. Finally, different approaches that incorporate protein dynamics, e.g., configurational entropy, and solvation effects into docking will be highlighted.

Isomorphously substituted B-MFI hollow fibre membranes for p-xylene separation from C 8 aromatic mixtures

In this study, Al-MFI and B-MFI (Si/B = 100 and Si/B = 50) hollow fibres with nanocomposite architecture have been prepared on α-alumina by pore-plugging hydrothermal synthesis at 443 K for 89 h using a precursor clear solution with molar composition 1 SiO 2: 0.45 TPAOH: 27.8 H 2O: xH 3BO 3 ( x = 0–0.02). The synthesized materials were characterized by XRD, SEM, ICP-AES and 29Si, 27Al- and 11B-MAS-NMR, revealing the genesis of well-intergrown materials with isomorphously substituted boron in the MFI unit cell. The pure ethylbenzene permeance within these membranes decreased in the order Al-MFI > B-MFI (Si/B = 50) > B-MFI (Si/B = 100). All the MFI materials were selective to p-xylene in the vapour permeation of ternary p-/m-/o-xylene mixtures and quaternary p-/m-/o-xylene/ethylbenzene model mixtures in the temperature range 400–650 K and for total feed vapour pressures lower than 4.5 kPa. The p-/m-xylene separation factor increased in the sense Al-MFI < B-MFI (Si/B = 100) ≈ B-MFI (Si/B = 50). The p-/m-xylene and p-/o-xylene separation factors, as well as p-xylene mixture fluxes, decreased with the ethylbenzene feed concentration, probably due to configurational entropy effects in the mixture adsorption patterns. The membranes showed however slightly preferential p-xylene permeation than ethylbenzene at low total aromatic vapour pressures despite the similar kinetic diameter of both molecules (5.8 vs. 6.0 Å), the B-MFI (Si/B = 50) material achieving a p-xylene/ethylbenzene separation factor as high as 5.

Effect of Counterion and Configurational Entropy on the Surface Tension of Aqueous Solutions of Ionic Surfactant and Electrolyte Mixtures

In order to clarify the adsorption behavior of cationic surfactants on the air/aqueous electrolyte solution surface, we derived the theoretical equation for the surface tension. The equation includes the electrical work required for charging the air/water surface and the work attributable to the configurational entropy in the adsorbed film. By fitting the equation to the experimental data, we determined the binding constant between adsorbed surfactant ion and counterion, and found that the bromide ions, rather than the chloride ions, are preferentially adsorbed by the air/water surface. Furthermore, it was suggested that the contribution of configurational entropy to the surface tension is predominant in the presence of electrolytes because of the increase in the surface density of surfactant molecules associated with decreasing the repulsive interaction between their hydrophilic groups.

Inclusion of Solvation and Entropy in the Knowledge-Based Scoring Function for Protein−Ligand Interactions

The effects of solvation and entropy play a critical role in determining the binding free energy in protein-ligand interactions. Despite the good balance between speed and accuracy, no current knowledge-based scoring functions account for the effects of solvation and configurational entropy explicitly due to the difficulty in deriving the corresponding pair potentials and the resulting double counting problem. In the present work, we have included the solvation effect and configurational entropy in the knowledge-based scoring function by an iterative method. The newly developed scoring function has yielded a success rate of 91% in identifying near-native binding modes with Wang et al.'s benchmark of 100 diverse protein-ligand complexes. The results have been compared with the results of 15 other scoring functions for validation purpose. In binding affinity prediction, our scoring function has yielded a correlation of R(2) = 0.76 between the predicted binding scores and the experimentally measured binding affinities on the PMF validation sets of 77 diverse complexes. The results have been compared with R(2) of four other well-known knowledge-based scoring functions. Finally, our scoring function was also validated on the large PDBbind database of 1299 protein-ligand complexes and yielded a correlation coefficient of 0.474. The present computational model can be applied to other scoring functions to account for solvation and entropic effects.

Tetrahedral occupancy of ferric iron in (Mg,Fe)O: Implications for point defects in the Earth's lower mantle

We investigated the concentration and site occupation of ferric iron (Fe 3+) in (Mg,Fe)O to understand the influence of point defects on transport properties such as atomic diffusion, electrical conductivity and viscosity. We conducted Mössbauer spectroscopy of (Mg 0.8Fe 0.2)O single crystals synthesized at temperatures from 1673 to 2273 K and pressures from 5 to 15 GPa with Re–ReO 2 and Mo–MoO 2 oxygen fugacity buffers. The isomer shift of the Mössbauer spectra suggests that Fe 3+ occupies mostly the tetrahedral site at reduced conditions and both the octahedral and tetrahedral sites at oxidized conditions. We formulate a thermodynamic model of point defect dissolution in (Mg,Fe)O which suggests that unassociated tetrahedral Fe 3+ is more stable than unassociated octahedral Fe 3+ at high-pressure and low oxygen fugacity due to the effect of configurational entropy. The pressure dependence of Fe 3+ concentration indicates a change in the dominant site occupancy of Fe 3+: (1) Fe 3+ in the tetrahedral site, (2) Fe 3+ in the octahedral site, and (3) defect clusters of Fe 3+ and cation vacancy, in the order of increasing oxygen fugacity and decreasing pressure. This is in reasonable agreement with previously reported experiments on Fe 3+ concentration, Mg–Fe interdiffusivity and electrical conductivity. We consider it plausible that (Mg,Fe)O accommodates Fe 3+ in the tetrahedral site down to the lower mantle. Based on our results and available experimental data, we discuss the solubility competition between Fe 3+ and protons (H +), and its implications for transport properties in the lower mantle.

Drastic symmetry breaking in supramolecular organization of enantiomerically unbalanced monolayers at surfaces

There is considerable interest in skewing the transmission of chirality, or 'handedness', from the molecular to the supramolecular level so that single-handed superstructures are created from mixed enantiomer systems. One approach is to flip the chirality of all the molecular building blocks to the same handedness. However, manipulation of molecular chirality is not possible for non-interconvertible enantiomers, and mechanisms that skew such systems are unclear. Here, we track the molecule-to-supramolecular chiral transfer in such systems at the nanoscale by probing molecular monolayers at surfaces. Scanning tunnelling microscopy and theoretical modelling show that enantiomeric imbalances lead to nonlinear symmetry breaking in organization, driven by configurational entropy effects. Thus, the majority enantiomer readily organizes into its superstructure with the minority left fragmented and disorganized, and thus impeded from realizing its superstructure. Such effects promise new strategies in chiral separations and enantioselective processes, and may have contributed to the homochiral evolution of complex matter from prebiotic environments.

First‐principles study of nitridoaluminosilicate CaAlSiN3

AbstractAtomic and electronic structure of nitridoaluminosilicate CaAlSiN3 (Cmc 21, No. 36), a distorted AlN‐based wurtzite superstructure with Al and Si disordered on 8b site and Ca occupying 4a site, has been investigated by first‐principles pseudopotential method based on density functional theory. The random distribution of Al/Si atoms is treated in two ways: (1) virtual crystal approximation (VCA) with a mixed Al/Si pseudopotential, (2) several assumptions of Al/Si distribution order in the primitive unit cell. Geometry optimization based on the aliovalent VCA reproduces the experimental orthorhombic structure as well as the bond lengths. The calculations of Al/Si‐ordered models lead to monoclinic structures that appear sufficiently close to the experimental structure, with the averages of the optimized Al–N/Si–N bond lengths corresponding to the experimental ones. Relative stability among the Al/Si‐ordered models appears consistent with Pauling's second crystal rule. The random Al/Si distribution leading to the experimental determination of the system as Cmc 21 can be explained by crystal symmetry, energetics among the ordered models, and configurational entropy effect. The electronic structure based on the VCA appears similar with those of the Al/Si‐ordered models. All the band structures indicate that the system has indirect band gap. (© 2006 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Monte Carlo Simulation for the Adsorption and Separation of Linear and Branched Alkanes in IRMOF-1

The adsorption and separation of linear and branched alkanes in the isoreticular metal-organic framework IRMOF-1 have been investigated using Monte Carlo simulation. For pure linear alkanes (C1-nC5), the limiting adsorption properties exhibit linear behavior with the alkane carbon number; the long alkane is preferentially adsorbed over the short alkane at low fugacities, whereas the reverse is found at high fugacities. For pure branched alkanes (C5 isomers), the linear isomer adsorbs more than its branched analogue. The adsorbed amounts of pure alkanes in IRMOF-1 are substantially greater than in a carbon nanotube bundle and in silicalite. For a five-component mixture of C1 to nC5 linear alkanes, the long alkane adsorption first increases and then decreases with increasing fugacity, whereas short alkane adsorption continually increases and progressively replaces the long alkane at high fugacity due to the size entropy effect. For a three-component mixture of C5 isomers, the adsorption of each isomer increases with increasing fugacity until saturation, though there is less adsorption of the branched isomer due to the configurational entropy effect. The adsorption selectivity among the alkanes in IRMOF-1 is smaller than in a carbon nanotube bundle and in silicalite.

Pore Size or Geometry: Which Determines the Shape and Inverse-Shape Selective Adsorption of Alkane Isomers?

The adsorption of pure pentane (C(5)) isomers and their ternary mixture is simulated in a series of carbon nanoslits. With decreasing nanoslit pore size, shape selective adsorption first occurs in the order of nC(5) > or = iC(5) > neoC(5) due to the configurational entropy effect, then inverse-shape selective adsorption occurs in the order of nC(5) < iC(5) < or = neoC(5) due to the area entropy effect, and finally no adsorption occurs. The entropy effects lead to a large adsorptive separation among the C(5) isomers from their mixture. Similar behavior has been observed from the simulation of C(5) adsorption in carbon nanotubes with variation in pore size. These results reveal that pore size rather than geometry determines the shape and inverse-shape selective adsorption of alkane isomers in nanopores.

Shape versus inverse-shape selective adsorption of alkane isomers in carbon nanotubes

Simulation results are reported for the adsorption of pure pentane (C5) isomers and their ternary mixture in a series of open-ended armchair-type (m,m) single-walled carbon nanotubes (SWNTs). Inverse-shape selective adsorption occurs in the order of nC5<iC5<neoC5 only in the (7,7) SWNT as a result of the length entropy effect. In the larger (20,20) and (10,10) SWNTs, shape selective adsorption occurs in the order of nC5>or=iC5>neoC5 as a result of the configurational entropy effect. In smaller SWNTs, depending on the diameter, only nC5 adsorbs, or no adsorption at all occurs. The entropy effects are found to lead to a large adsorptive separation among the C5 isomers from their mixture. Using the ideal-adsorbed-solution theory with data on the adsorption of only the pure isomers, we predict mixture adsorption. The agreement between predictions and simulations deteriorates with decreasing diameter of the SWNT.

Adsorption and separation of linear and branched alkanes on carbon nanotube bundles from configurational-bias Monte Carlo simulation

The adsorption and separation of linear $({\mathrm{C}}_{1}\text{\ensuremath{-}}n{\mathrm{C}}_{5})$ and branched (${\mathrm{C}}_{5}$ isomers) alkanes on single-walled carbon nanotube bundles at 300 K have been studied using configurational-bias Monte Carlo simulation. For pure linear alkanes, the limiting adsorption properties at zero coverage exhibit a linear relation with the alkane carbon number; the long alkane is more adsorbed at low pressures, but the reverse is found for the short alkane at high pressures. For pure branched alkanes, the linear isomer adsorbs to a greater extent than its branched counterpart. For a five-component mixture of ${\mathrm{C}}_{1}\text{\ensuremath{-}}n{\mathrm{C}}_{5}$ linear alkanes, the long alkane adsorption first increases and then decreases with increasing pressure, but the short alkane adsorption continues increasing and progressively replaces the long alkane at high pressures due to the size entropy effect. All the linear alkanes adsorb into the internal annular sites with preferred alignment parallel to the nanotube axis on a bundle with a gap of 3.2 \AA{}, and also intercalate the interstitial channels in a bundle with a gap of 4.2 \AA{}. For a three-component mixture of ${\mathrm{C}}_{5}$ isomers, the adsorption of each isomer increases with increasing pressure until saturation, though $n{\mathrm{C}}_{5}$ increases more rapidly with pressure and is preferentially adsorbed due to the configurational entropy effect. All the ${\mathrm{C}}_{5}$ isomers adsorb into the internal annular sites on a bundle with a gap of 3.2 \AA{}, but only $n{\mathrm{C}}_{5}$ also intercalates the interstitial channels on a bundle with a gap of 4.2 \AA{}. This work suggests the possibility of separating alkane mixtures based on differences in either size or configuration, as a consequence of competitive adsorption on the carbon nanotube bundles.

Efficiency of multiple atom doping in wide band gap semiconductors

We present a thermodynamic model calculation for the efficiency of an impurity-atom-complex formation suggested for doping of wide band gap semiconductors, where the complexes with various sizes coexist at local equilibrium as suggested by Van de Walle and Neugebauer [J. Appl. Phys. 95, 3851 (2004)]. When the size of a target complex becomes large, the effect of configurational entropy of smaller complexes shows up in the energetics and may even hamper stabilization of the target. Thus one should design a target complex with the size being as small as possible and the binding energy as large as possible, in order to make the concept of multiple atom doping a real technology.