Simple Statistical Mechanical Theory Research Articles

Formation of a Three-Electron Sulfur-Sulfur Bond as a Probe for Interaction between Side Chains of Methionine Residues.

The mechanism of oxidation processes of l-Met-(Pro)n-l-Met peptides that contain two Met residues located on the N- and C-terminal and separated by a defined number (n = 0-4) of proline residues was investigated in aqueous solutions using pulse radiolysis. The use of such peptides allowed for distance control between the sulfur atoms located in the side chains of the Met residues. The formation of a contact between the side chains of the Met residues was probed by the observation of transients with σ*-type 2c-3e S∴S and S∴O bonds as well as of α-(alkylthio)alkyl radicals (αS). This approach enabled the monitoring, in real time, of the efficiency and kinetics of interactions between methionine side chains. Such knowledge is important, inter alia, for long-distance electron transfer processes because methionine side chains can serve as relay stations and also for many aspects of protein folding when the formation of a contact between two amino acid residues in an unfolded polypeptide chain plays a central role in protein-folding mechanisms. The yields of these transients (measured as G-values) were found to be dependent on the number of Pro residues; however, they were not dependent in a simple way on the average distance ⟨rS-S⟩ between the sulfur atoms in Met residues. A decrease in the yield of the (S∴S)(+) species with an increase in the number of Pro residues in the bridge occurred at the expense of an increase in the yields of the intramolecular three-electron-bonded (S∴O)(+) radical cations and αS radicals. A detailed understanding of these trends in the chemical yields was developed by modeling the underlying chemical kinetics with Langevin dynamical simulations of the various oligoproline peptide chains and combining them with a simple statistical mechanical theory on the end-to-end contact rates for polymer chains. This analysis showed that the formation of a contact between terminal Met residues in the peptides with 0-2 Pro residues was controlled by the activated formation of (S∴S)(+) whereas in the peptides with 3 and 4 Pro residues, by the relative diffusion of the sulfur radical cation and unoxidized sulfur atom. In this picture, the dynamics of the other radical products can be seen to be only indirectly dependent on the length of the proline bridges because their formation is in competition with (S∴S)(+) formation.

Microscopic Structure of NaCd Compound Forming Binary Molten Alloys

A simple statistical mechanical theory based on compound formation model (compound Aμ Bv formed by the preferential arrangement of A and B constituent atoms of the alloy AB, μA + νB ≒ Aμ Bv) has been used to investigate the phenomena of compound formation in NaCd liquid alloys through the study of concentration fluctuation in the long wavelength region [Scc(0)] and chemical short range order parameter (α1). The study explains the observed asymmetry successfully and suggest the existence of Cd2Na complex in the melt. The tendency of compound has been found to be weak. A tendency of inversion from segregation to order although very small, has been observed, in NaCd liquid alloys.

Interionic pair potential and entropy of mixing of Al–Mg compound forming binary molten alloys

The observed asymmetric behaviour of mixing properties of AlMg liquid alloys around equiatomic composition with smaller negative values for excess free energy of mixing (−0.15 kJ mol −1) has aroused our interest to undertake a theoretical investigation of this system. A simple statistical mechanical theory based on compound formation model ( μA + νB ⇌ A μ B ν ) has been used to investigate the energetics of formation of intermetallic compound Al 3Mg 2 in the melt, through the steady of thermodynamic property such as entropy of mixing. Besides, the interionic interactions between component atoms (Al and Mg) of the alloy have been understood through the study of interionic pair potential ϕ ij ( r), calculated from pseudopotential theory in the light of CF model. Our study of ϕ ij ( r) suggests that the effective interaction between Al–Al atom in the pure state is found to be smaller than those obtained in Al 0.425Mg 0.575 and Al 0.625Mg 0.375 alloys. Φ Al–Al in the case of Al 0.625Mg 0.375 alloys lies in between pure state (Al) and Al 0.425Mg 0.575 .The nearest neighbour distance does not change appreciably on alloying, whereas the effective interaction between Mg–Mg atoms increase in the order Al 0.625Mg 0.375 < Al 0.425Mg 0.575 < Mg pure, being minimum in CF alloys. The computed values of S M from pseudopotential theory are positive at all concentrations, but the agreement between theory and experimental is not satisfactory. This might be happening due to parameterization of σ 3 and Ψ compound.

Case study of enthalpy-entropy noncompensation.

Enthalpy-entropy noncompensation characterizes the relative changes in the hydration thermodynamic functions upon "transforming" ethane into fluoromethane, chloromethane, bromomethane, and iodomethane. An analysis grounded on a simple statistical mechanical theory of hydration allows a plausible rationalization of such enthalpy-entropy noncompensation. It is shown that increasing the strength of solute-water attractive interactions modifying the chemical nature of a part of the solute molecule, but not its size, is a largely noncompensating process for the hydration of noncharged and nonhydrogen bonding species, and dominates the compensating contribution coming from the reorganization of water H bonds.

Strongly dipolar fluids at low densities

We propose a simple statistical mechanical theory for a strongly dipolar fluid at low densities, based on the analogy between a system of polydisperse linear chains and the equilibrium structure of these fluids as revealed by computer simulations. At low densities, both steric and dipolar interactions between long chains are weak and thus the dipolar fluid is well described as an ideal gas of polydisperse chains. We have further investigated how the residual dipolar interaction between monomers and/or additional isotropic attractions between the spheres cause the dissociation of the chains and/or the condensation of the dipolar fluid.

Strongly dipolar fluids: a theoretical and computational challenge

We propose a simple statistical mechanical theory for a strongly dipolar fluid at low densities, based on the analogy between a system of polydisperse polymer chains and the equilibrium structure of these fluids as shown by computer simulation. Both steric and dipolar interactions between long chains are weak at low densities and as a result the dipolar fluid, in this regime, is well described as an ideal gas of polydisperse chains. We further investigate how the residual dipolar interaction between monomers and attractive Van der Waals interactions between particles may cause dissociation of the chains and condensation of the dipolar fluid.

Effective potential approach to bulk thermodynamic properties and surface tension of molecular fluids I. Single component n-alkane systems

The aim of this work is to develop spherically symmetric effective potentials allowing bulk thermodynamic properties and surface tension of molecular fluids to be predicted semiempirically by the use of statistical mechanical methods. Application is made to the straight chain alkane fluids from methane to decane. An effective Lennard-Jones potential is generated with temperature-dependent parameters fitted to the critical temperature and pressure and to Pitzer's acentric factor. Insertion of this potential into the generalised van der Waals (GvdW) density functional theory yields bulk properties in good agreement with experiments. The surface tension is overestimated for the longer alkane chains. In order to account for the surface tension, an independently adjustable attractive range of interaction is required and obtained through the use of square-well potentials chosen so as to leave the bulk thermodynamics unaltered while the attractive range is fitted to the surface tension at a single temperature. The GvdW theory, which includes binding energy, entropic and profile shape contributions, then generates surface tension estimates that are of good accuracy over the full range of available experimental data. It appears that, given a sufficiently flexible form, effective potentials combined with simple statistical mechanical theory can reproduce both bulk and non-uniform fluid data of great variety in an insighful and practically useful way.

Intermetallic associations in AlMg liquid alloys

The observed asymmetric behaviour of mixing properties of AlMg liquid alloys around equiatomic composition with smaller negative value for excess free energy of mixing ( G M XS = −0.15 KJ mol −1) has aroused our interest to undertake a theoretical investigation of this system. It will be proper to mention that various factors such as size difference and electronegativity difference are too small to account for the asymmetry in the above system. The existence of an intermetallic compound in the solid phase, which is manifested in the phase diagram, may be one of the factors for the anomalous behaviour of the properties of mixing. A simple statistical mechanical theory based on the complex-formation model (the complex A μ B v is formed by the preferentialarrangement of A and B constituent atoms of the alloy AB; μA + vB⇌A μ B v ) has been used to investigate the phenomenon of compound formation in AlMg liquid alloys through the study of various thermodynamic as well as microscopic functions such as the excess free energy of mixing, heat of mixing, concentration fluctuations at the long-wavelength [ S CC(0)], chemical short-range-order parameter ( α 1), etc. Our study, which explains the observed asymmetry almost successfully suggests that Al 3Mg 2 complexes exist in the liquid phase. But the tendency to form a compound is not so strong. The system exhibits almost ideal behaviour in the Mg-rich end ( C Mg>0.8). This ideal behaviour might be linked with the glass formation. But this aspect to the AlMg system requires investigation. The temperature dependence of energy parameters plays an important role in the mixing in AlMg liquid alloys.

Statistical thermodynamics of single‐chain single crystals

AbstractA simple statistical mechanical theory is developed assuming a chain‐folded crystal. Taking account of the side‐surface energy of the single‐chain single crystal, the partition function and the free energy are calculated. Also, the expressions for equilibrium thickness le and melting temperature Tm, e of the single‐chain single crystal are obtained, and they are similar to that given by a thermodynamic analysis of the single‐chain single crystal. It is shown that le depends on temperature and on the molar mass of the single‐chain single crystal, while Tm, e depends on the molar mass. Furthermore, it is found that the side‐surface and the fold‐surface free energies γ and γe can be explained on a molecular basis.

Dynamic Monte Carlo simulations of globular protein folding/unfolding pathways: I. Six-member, Greek key β-barrel proteins

In the context of a simplified diamond lattice model of a six-member, Greek key β-barrel protein that is closely related in topology to plastocyanin, the nature of the folding and unfolding pathways have been investigated using dynamic Monte Carlo techniques. The mechanism of Greek key assembly is best described as punctuated “on site construction”. Folding typically starts at or near a β-turn, and then the β-strands sequentially form by using existing folded structure as a scaffold onto which subsequent tertiary structure assembles. On average, β-strands tend to zip up from one tight bend to the next. After the four-member, β-barrel assembles, there is a long pause as the random coil portion of the chain containing the long loop thrashes about trying to find the native state. Thus, there is an entropic barrier that must be surmounted. However, while a given piece of the protein may be folding, another section may be unfolding. A competition therefore exists to assemble a fairly stable intermediate before it dissolves. Folding may initiate at any of the tight turns, but the turn closer to the N terminus seems to be preferred due to well-known excluded volume effects. When the protein first starts to fold, there are a multiplicity of folding pathways, but the number of options is reduced as the system gets closer to the native state. In the early stages, the excluded volume effect exerted by the already assembled protein helps subsequent assembly. Then, near the native conformation, the folded parts reduce the accessible conformational space available to the remaining unfolded sections. Unfolding essentially occurs in reverse. Employing a simple statistical mechanical theory, the configurational free energy along the reaction co-ordinate for this model has been constructed. The free energy surface, in agreement with the simulations, provides the following predictions. The transition state is quite near the native state, and consists of five of the six β-strands being fully assembled, with the remaining long loop plus sixth β-strand in place, but only partially assembled. It is separated from the β-barrel intermediate by a free energy barrier of mainly entropic origin and from the native state by a barrier that is primarily energetic in origin. The latter feature is in agreement with the “Cardboard Box” model described by Goldenberg and Creighton but, unlike their model, the transition state is not a high-energy distorted form of the native state. The theory predicts that the rate of folding is less sensitive to changes in folding conditions than is the rate of unfolding, in agreement with experiment. Finally, the simple theory provides a means of assessing the effects of amino acid substitutions that favor native-like turn formation. By stabilizing the intermediate, they enhance the rate of folding to the intermediate from the denatured state and the rate of unfolding out of the native state, and they act to slow down the rate of folding from the intermediate to the native state. But even when every turn residue is modified, the effect is relatively small.

A simple statistical mechanical theory for the mutual solubility of fluid mixtures of water and organic solvents under high pressure

A simple statistical mechanical theory is presented to explain phase diagrams of fluid mixtures with both a lower critical solution temperature and an upper critical solution temperature under pressure. By postulating a temperature dependence for the interaction free energy parameter of the constituent molecules and a pressure dependence for the excess volume, phase diagrams with both lower critical solution temperature, and upper critical solution temperature and their pressure dependence can be reproduced by quadratic surfaces in temperature-concentration-pressure space. The topological aspects of the observed phase diagrams in this space have been related to our theoretical model, and the thermodynamical meaning of the topologies has been interpreted based on our model. Experimental data for the mutual solubility of water and 2-butanol under pressure and that of water and 3-methylpyridine with added salts have been analyzed quantitatively and theoretical parameters are determined.

Temperature dependence of the anchoring strength at a nematic liquid crystal-evaporated SiO interface

The out-of-plane anchoring strength at the interface between 4-n-pentyl-4′-cyanobiphenyl (5CB) and an obliquely evaporated SiO was measured as a function of temperature by applying the ‘‘high-electric-field technique’’ recently developed by Yokoyama and van Sprang [J. Appl. Phys. 57, 4520 (1985)]. The orientational ‘‘extrapolation length’’de for the interface was found to remain virtually constant at about 30 nm up to nearly 1 K below the clearing temperature Tc=308.4 K. At temperatures closer to Tc, however, it was observed to show an apparently critical increase, which approximately follows de∝[(Tc−T)/Tc]−0.45. At 0.043 K below Tc, de=183±3 nm, yielding the anchoring energy of (1.13±0.03)×10−5 J/m2. The implications of the observed temperature dependence are first investigated by extending Gibbs’ surface thermodynamics to a nematic-wall interface, deriving a general relationship between the temperature variation of de and the surface excess entropy. In particular, it is concluded on thermodynamic grounds that the exponent of −0.45 can never be associated with a real critical behavior, but is indicative of the occurrence of crossover to a more singular or noncritical behavior. To draw specific connections between the temperature dependence of de and the orientational order near the interface, we develop a simple statistical mechanical theory of the anchoring strength, based on a van der Waals picture of the nematic-wall interface. We show that the extrapolation length consists of two essentially distinct contributions: one is from the anisotropic interactions at the interface and the other is unconventionally from the interfacial inhomogeneity of the order parameter itself. For the most relevant cases, the van der Waals theory states that a reduction of the anchoring strength should always be accompanied by a depression of the surface order parameter. By comparing the theory with the experiment, the surface order parameters just below and above Tc are found to be 0.04 and 0.01, respectively, in agreement with the estimates from the contact angle and the pretransitional birefringence experiments. It is also argued, based on the present model, that the order parameter inhomogeneity is predominantly responsible for the quasicritical behavior of the anchoring strength.

The segregation of calcium ions at the surface of magnesium oxide: theory and calculation

Atomistic simulation methods have been used to calculate the energetics of substitution and segregation of calcium ions near and at the {001} and {110}¦ surfaces of magnesium oxide at thermal equilibrium. Defect clusters and complete planes of segregating ions have been considered, thereby including impurity-impurity interaction terms. Calculated enthalpies of segregation of −0.42 and −0.78 eV, derived from different interatomic potentials, are in good agreement with the experimental heat of segregation of −0.78±0.22 eV reported recently by Wynblatt and McCune. A simple statistical mechanical theory leads to an Arrhenius expression for large crystals and the deviation from this behaviour expected in microcrystallites.

A simple approach to the equilibrium statistical mechanics of two-dimensional fluids

A simple statistical mechanical theory previously developed for three-dimensional hard spheres is applied to a system of two-dimensional hard disks to obtain analytical equations for activity and pressure. The first order result, based on only the third virial coefficient, fits the molecular dynamics data for fluid disks significantly better than the seven-term virial series, but (unlike the case in three dimensions) not so well as the scaled particle theory. The second order result, involving the fourth virial coefficient, is the equal of the Padé approximant (3,4) with seven correct virial coefficients built in, and is significantly better than the scaled particle theory. The simple theory is surprisingly accurate even for the hard disk crystal. A simple theory of the two-dimensional Lennard-Jones fluid is obtained by incorporation of attractive wells with a hard core of temperature-dependent diameter. Comparison of the theory with the 17 high-density, supercritical pressures obtained by Fehder using molecular dynamics shows deviations averaging only 3 1/2%. Agreement with the high-density, low-temperature data obtained by Tsien and Valleau using Monte Carlo techniques is not so good. Calculations for the Lennard-Jones 6–12 potential are compared with calculations for the 6–12–3 potential, proposed as more suited than the 6–12 for adsorbed gases.

A simple approach to the equilibrium statistical mechanics of Lennard-Jones fluids

A simple statistical mechanical theory previously developed for hard spheres and for two-dimensional fluids is applied to three-dimensional particles interacting through a Lennard-Jones 6–12 potential. The results are compared with the molecular dynamics experiments of Verlet, with surprisingly good agreement. Employing the potential parameters obtained for argon from second virial coefficient data results in pressure isotherms which fit the experimental data of Michels with greater accuracy than the choice of potential warrants.

Entropy of Mixing of Liquid NaCd System

The observed asymmetric behaviour of mixing properties of NaCd liquid alloys, with smaller negative value for excess free energy of mixing (-4.4919KJ) has aroused our interest to undertake a theoretical investigation of this system.The existence of an intermetallic compound in the solid phase, which is manifested in the phase diagram, may be one of the factors for the anomalous behaviour of property of mixing. A simple statistical mechanical theory based on complex formation model (the complex is formed by the preferential arrangement of A and B constituent atoms of the alloy AB ;( μA + νB = Aμ Bν) has been used to investigate the phenomena of compound formation in NaCd liquid alloys through the study of entropy of mixing through out the whole concentration range.Nepal Journal of Science and Technology Volume 10, 2009 December Page: 105-107