Excess free energy,enthalpy and entropy of surfactant-surfactant mixed micelle formation

Enthalpies of dilution and osmotic coefficients of sodium decylsulfate (NaDeS)-dodecyldimethylamine oxide (DDAO) mixtures in water were determined at 298 and 310 K, respectively. From the enthalpies of dilution, the apparent and then the partial molar relative enthalpies of the surfactant mixtures were calculated. From the osmotic coefficients, calculated at 298 K, the non-ideal free energies were derived. The latter were combined with the partial molar relative enthalpies to obtain the non-ideal entropies. From the apparent molar properties, using a previously reported approach, the excess thermodynamic properties for the surfactant-surfactant mixed micelle formation in water were evaluated as functions of the mixture composition at some total micellized concentration. In the whole range of the mixture composition, the excess free energy is negative, indicating that the mixed micelle formation is favoured with respect to that of pure micelles. This process is governed by the enthalpy and/or the entropy, depending on the mixture composition. The effect of the alkyl chain length was also studied by comparing the present results to those of the sodium dodecylsulfate-DDAO mixture.     

The free energy,enthalpy and entropy changes of the dissociation of diprotonated diamines

The ΔG, ΔH and ΔS values of the dissociation of a number of diprotonated diamines were determinated by potentiometric and calorimetric methods, in 1M KNO₃, at 25°C. The results are discussed in terms of solvent effects, the theory of Kirkwood and Westheimer, and microscopic constants.     

气流床粉煤气化的Gibbs自由能最小化模拟

用Gibbs自由能最小化方法对粉煤气化过程进行了热力学平衡分析。对一混合煤种,在3.0 MPa和气化温度限制在1 200 ℃～1 450 ℃时,研究了氧-煤比、蒸气-煤比对气化炉出口气体组成、温度和有效气产率的影响,并由此确定了可行的操作域是氧-煤比545m3/t～605 m3/t、蒸气-煤比为152.64 kg/t～313.92 kg/t及其对应的工艺指标。从操作域中选择有代表性的工艺条件为氧-煤比578 m3/t、蒸气-煤比为187 kg/t,对应的气化炉出口温度1 358 ℃,CO+H2干基体积分数为91.5%,有效气产率为2.123(CO+H2)m3/kg。同时,研究了碳转化率和热损失对气化工艺指标的影响,其影响是显著的。     

Computer simulation of the distribution of hexane in a lipid bilayer: spatially resolved free energy, entropy, and enthalpy profiles

The partitioning behavior of small molecules in lipid bilayers is important in a variety of areas including membrane protein folding and pharmacology. However, the inhomogeneous nature of lipid bilayers on a nanometer length scale complicates experimental studies of membrane partitioning. To gain more insight in the partitioning of a small molecule into the lipid bilayer, we have carried out atomistic computer simulations of hexane in a dioleoyl phosphatidylcholine model membrane. We have been able to obtain spatially resolved free energy, entropy, enthalpy, and heat capacity profiles based on umbrella sampling calculations at three different temperatures. In agreement with experiment, hexane partitions preferentially to the center of the bilayer. This process is driven almost entirely by a favorable entropy change, consistent with the hydrophobic effect. In contrast, partitioning to the densest region of the acyl chains is dominated by a favorable enthalpy change with a small entropy change, which is consistent with the "nonclassical" hydrophobic effect or "bilayer" effect. We explain the features of the entropy and enthalpy profiles in terms of density and free volume in the system.     

Thermodynamics of associated solutions: New expressions for the excess Gibbs free energy and excess enthalpy of mixing of alcohol-solvent systems

This article presents new equations based on a continuous linear association model used by Kretschmer and Wiebe. The new equations are used to reduce experimental vapor-liquid equilibrium and excess enthalpy of mixing data for solutions of alcohols and active solvents. The new equations give an excellent representation of the experimental results and are able to predict equilibrium data for ternary alcohol-solvent systems with good accuracy.     

Comparison of Ca2+ and Mg2+ binding to calmodulin. An enthalpy,entropy, and gibbs free energy analysis

A consistent set of G _B , H _B , and S _B parameters have been determined from ion specific electrode, calorimetric, and spectrophotometric studies for the binding of Ca²⁺ and Mg²⁺ to bovine calmodulin at pH=7.0 and an ionic strength I of 0.113M. A non-linear least squares analysis of calcium specific ion electrode data yields, on a molar basis, four calcium dissociation constants: 10^–7 for the first site, 10^–5 for the fourth site, and two constants between these values. Both calorimetric experiments and an indicator method provide evidence that Mg²⁺ binds to calmodulin, probably at the same sites as Ca²⁺, but with affinities about 100 times smaller: 4×10^–5 for the first site and 2×10^–3 for the fourth. Calorimetric titrations on Ca²⁺ binding to calmodulin in three buffers are consistent with 0.46 protons released upon binding at all four sites and yield an average H _B per site of 5.6 and 7.9 kJ-mol^–1 for Ca²⁺ and Mg²⁺, respectively. The entropy of the system increases by 524 and 361 J-K^–1-mol^–1 when Ca²⁺ and Mg²⁺, respectively, bind to four sites on calmodulin, i.e., the selectivity of calmodulin for Ca²⁺ is primarily derived from entropy effects. Further analysis based on elimination of the entropy term for the metal ions demonstrates that calmodulin bound to Ca²⁺ has a larger entropy than the unbound calmodulin; the opposite is true for calmodulin bound to Mg²⁺. These analyses are consistent with the hypothesis that Ca²⁺ forms tight complexes at all sites on calmodulin and that release of waters of hydration upon binding is the source of the increase of entropy in the system.     

Gibbs free energy of formation of calcium rhodite

The Gibbs free energy of formation of CaRh₂O₄(s) has been determined using two techniques viz., quadrupole mass spectrometer coupled to a Knudsen cell and solid-state cell incorporating CaF₂(s) as the solid electrolyte. In the former method, equilibrium O₂(g) pressures were measured over the phase field Rh(s)+Rh₂O₃(s), in the temperature range 793.7-909.1 K and over the three phase mixture CaRh₂O₄(s)+Rh(s)+CaO(s) was measured from 862.1 to 1022.7 K.The Gibbs free energy of formation of Rh₂O₃(s) from elements in their standard state can be given by

     

Binding free energy, energy and entropy calculations using simple model systems

Free energy differences are calculated for a set of two model host molecules, binding acetone and methanol. Two active sites of different characteristics were constructed based on an artificially extended C60 fullerene molecule, possibly functionalised to include polar interactions in an otherwise apolar, spherical cavity. The model host systems minimise the necessary sampling of conformational space while still capturing key aspects of ligand binding. The estimates of the free energies are split up into energetic and entropic contributions, using three different approaches investigating the convergence behaviour. For these systems, a direct calculation of the total energy and entropy is more efficient than calculating the entropy from the temperature dependence of the free energy or from a direct thermodynamic integration formulation. Furthermore, the compensating surrounding–surrounding energies and entropies are split off by calculating reduced ligand-surrounding energies and entropies. These converge much more readily and lead to properties that are more straightforwardly interpreted in terms of molecular interactions and configurations. Even though not experimentally accessible, the reduced thermodynamic properties may prove highly relevant for computational drug design, as they may give direct insights into possibilities to further optimise ligand binding while optimisation in the surrounding–surrounding energy or entropy will exactly cancel and not lead to improved affinity.     

Thermodynamics of specific interactions of pyridines in aliphatic alcohols: Gibbs energy, entropy, and degree of binding

The activity coefficients at infinite dilution (T = 298.15 K) and Gibbs energy of solvation of pyridines in aliphatic alcohols were determined. The thermodynamic functions of specific interactions in these systems were calculated.     

Gibbs free energy of liquid drops on conical fibers

Small drops can move spontaneously on conical fibers. As a drop moves along the cone, it must change shape to maintain a constant volume, and thus, it must change its surface energy. Simultaneously, the exposed surface area of the underlying cone must also change. The associated surface energies should balance each other, and the drop should stop moving when it reaches a location where the free energy is a minimum. In this paper, a minimum Gibbs free energy analysis has been performed to predict where a drop will stop on a conical fiber. To obtain the Gibbs free energies of a drop at different locations of a conical fiber, the theoretical expressions for the shape of a droplet on a conical fiber are derived by extending Carroll's equations for a drop on a cylindrical fiber. The predicted Gibbs free energy exhibits a minimum along the length of the cone. For a constant cone angle, as the contact angle between the liquid and the cone increases, the drop will move toward the apex of the cone. Likewise, for a constant contact angle, as the cone angle increases, the drop moves toward the apex. Experiments in which water and dodecane were placed on glass cones verify these dependencies. Thus, the final location of a drop on a conical fiber can be predicted on the basis of the geometry and surface energy of the cone, the surface tension and volume of the liquid, and the original location where the drop was deposited.     

Thermodynamic properties (enthalpy, bond energy, entropy, and heat capacity) and internal rotor potentials of vinyl alcohol, methyl vinyl ether, and their corresponding radicals

Vinyl alcohols (enols) have been discovered as important intermediates and products in the oxidation and combustion of hydrocarbons, while methyl vinyl ethers are also thought to occur as important combustion intermediates. Vinyl alcohol has been detected in interstellar media, while poly(vinyl alcohol) and poly(methyl vinyl ether) are common polymers. The thermochemical property data on these vinyl alcohols and methyl vinyl ethers is important for understanding their stability, reaction paths, and kinetics in atmospheric and thermal hydrocarbon-oxygen systems. Enthalpies , entropies , and heat capacities (C(p)()(T)) are determined for CH(2)=CHOH, C(*)H=CHOH, CH(2)=C(*)OH, CH(2)=CHOCH(3), C(*)H=CHOCH(3), CH(2)=C(*)OCH(3), and CH(2)=CHOC(*)H(2). Molecular structures, vibrational frequencies, , and C(p)(T) are calculated at the B3LYP/6-31G(d,p) density functional calculation level. Enthalpies are also determined using the composite CBS-Q, CBS-APNO, and G3 methods using isodesmic work reactions to minimize calculation errors. Potential barriers for internal rotors are calculated at the B3LYP/6-31G(d,p) level and used to determine the hindered internal rotational contributions to entropy and heat capacity. The recommended ideal gas phase values calculated in this study are the following (in kcal mol(-1)): -30.0, -28.9 (syn, anti) for CH(2)=CHOH; -25.6, -23.9 for CH(2)=CHOCH(3); 31.3, 33.5 for C(*)H=CHOH; 27.1 for anti-CH(2)=C(*)OH; 35.6, 39.3 for C(*)H=CHOCH(3); 33.5, 32.2 for CH(2)=C(*)OCH(3); 21.3, 22.0 for CH(2)=CHOC(*)H(2). Bond dissociation energies (BDEs) and group additivity contributions are also determined. The BDEs reveal that the O-H, O-CH(3), C-OH, and C-OCH(3) bonds in vinyl alcohol and methyl vinyl ether are similar in energy to those in the aromatic molecules phenol and methyl phenyl ether, being on average around 3 kcal mol(-1) weaker in the vinyl systems. The keto-enol tautomerization enthalpy for the interconversion of vinyl alcohol to acetaldehyde is determined to be -9.7 kcal mol(-1), while the activation energy for this reaction is calculated as 55.9 kcal mol(-1); this is the simplest keto-enol tautomerization and is thought to be important in the reactions of vinyl alcohol. Formation of the formyl methyl radical (vinoxy radical/vinyloxy radical) from both vinyl alcohol and methyl vinyl ether is also shown to be important, and its reactions are discussed briefly.     

Calculation of the entropy and free energy by the hypothetical scanning Monte Carlo method: application to peptides

A new approach, the hypothetical scanning Monte Carlo (HSMC), for calculating the absolute entropy, S, and free energy, F, has been introduced recently and applied first to fluids (argon and water) and later to peptides. In this paper the method is further developed for peptide chains in vacuum. S is calculated from a given MC sample by reconstructing each sample conformation i step-by-step, i.e., calculating transition probabilities (TPs) for the dihedral and bond angles and fixing the related atoms at their positions. At step k of the process the chain's coordinates that have already been determined are kept fixed (the "frozen past") and TP(k) is obtained from a MC simulation of the "future" part of the chain whose TPs as yet have not been determined; when the process is completed the contribution of conformation i to the entropy is, S(i) approximately -ln Pi(k) TP(k). In a recent paper we studied polyglycine chains, modeled by the AMBER force field with constant bond lengths and bond angles (the rigid model). Decaglycine [(Gly)(10)] was studied in the helical, extended, and hairpin microstates, while (Gly)(16) was treated only in the first two microstates. In this paper the samples are increased and restudied, (Gly)(16) is also investigated in the hairpin microstate, and for (Gly)(10) approximations are tested where only part of the future is considered for calculating the TPs. We calculate upper and lower bounds for F and demonstrate that like for fluids, F can be obtained from multiple reconstructions of a single conformation. We also test a more realistic model of (Gly)(10) where the bond angles are allowed to move (the flexible model). Very accurate results for S and F are obtained which are compared to results obtained by the quasiharmonic approximation and the local states method. Thus, differences in entropy and free energy between the three microstates are obtained within errors of 0.1-0.3 kcal/mol. The HSMC method can be applied to a macromolecule with any degree of flexibility, ranging from local fluctuations to a random coil. The present results demonstrate that the difference in stability, DeltaF(mn)=F(m)-F(n) between significantly different microstates m and n, can be obtained from two simulations only without the need to resort to thermodynamic integration. Our long-term goal is to extend this method to any peptide and apply it to a peptide immersed in a box with explicit water.     

Listening to PS II: enthalpy, entropy, and volume changes

Photosystem II, located in the thylakoid membranes of green plants, algae, and cyanobacteria, uses sunlight to split water into protons, electrons, and a dioxygen molecule. The mechanism of its electron transfers and oxygen evolution including the structure of the protein and rates of the S-state cycle has been extensively investigated. Substantial progress has been made; however, the thermodynamics of PS II electron transfer and of the oxygen cycle are poorly understood. Recent progress in thermodynamic measurements in photosynthesis provides novel insights on the enthalpic and entropic contribution to electron transfer in proteins. In this review the thermodynamic parameters including quantum yield, enthalpy, entropy, and volume changes of PS II photochemistry determined by photoacoustics and other laser techniques are summarized and evaluated. Light-driven volume changes via electrostriction are directly related to the photoreaction in PS II and thus can be a useful measurement of PS II activity and function. The enthalpy changes of the reactions observed can be directly measured by photoacoustics. The apparent reaction entropy can also be estimated when the free energy is known. Dissecting the free energy of a photoreaction into enthalpic and entropic components provides critical information about mechanisms of PS II function. Potential limitations and future direction of the study of the thermodynamics of PS II electron transfer and oxygen evolution are presented.     

Heat capacity,enthalpy and entropy of calcium niobates

Heat capacity and enthalpy increments of calcium niobates CaNb₂O₆ and Ca₂Nb₂O₇ were measured by the relaxation time method (2–300 K), DSC (260–360 K) and drop calorimetry (669–1421 K). Temperature dependencies of the molar heat capacity in the form C _pm=200.4+0.03432T−3.450·10⁶/T ² J K⁻¹ mol⁻¹ for CaNb₂O₆ and C _pm=257.2+0.03621T−4.435·10⁶/T ² J K⁻¹ mol⁻¹ for Ca₂Nb₂O₇ were derived by the least-squares method from the experimental data. The molar entropies at 298.15 K, S _m⁰(CaNb₂O₆, 298.15 K)=167.3±0.9 J K⁻¹ mol⁻¹ and S _m⁰(Ca₂Nb₂O₇, 298.15 K)=212.4±1.2 J K⁻¹ mol⁻¹, were evaluated from the low temperature heat capacity measurements. Standard enthalpies of formation at 298.15 K were derived using published values of Gibbs energy of formation and presented heat capacity and entropy data: Δ_f H ⁰(CaNb₂O₆, 298.15 K)= −2664.52 kJ mol^t-1 and Δ_f H ⁰(Ca₂Nb₂O₇, 298.15 K)= −3346.91 kJ mol⁻¹.     

Thermodynamic behavior of short oligonucleotides in microarray hybridizations can be described using Gibbs free energy in a nearest-neighbor model

While designing oligonucleotide-based microarrays, cross-hybridization between surface-bound oligos and non-intended labeled targets is probably the most difficult parameter to predict. Although literature describes rules-of-thumb concerning oligo length, overall similarity, and continuous stretches, the final behavior is difficult to predict. The aim of this study was to investigate the effect of well-defined mismatches on hybridization specificity using CodeLink Activated Slides and to study quantitatively the relation between hybridization intensity and Gibbs free energy (DeltaG), taking the mismatches into account. Our data clearly showed a correlation between the hybridization intensity and DeltaG of the oligos over 3 orders of magnitude for the hybridization intensity, which could be described by the Langmuir model. As DeltaG was calculated according to the nearest-neighbor model, using values related to DNA hybridizations in solution, this study clearly shows that target-probe hybridizations on microarrays with a three-dimensional coating are in quantitative agreement with the corresponding reaction in solution. These results can be interesting for some practical applications. The correlation between intensity and DeltaG can be used in quality control of microarray hybridizations by designing probes and corresponding RNA spikes with a range of DeltaG values. Furthermore, this correlation might be of use to fine-tune oligonucleotide design algorithms in a way to improve the prediction of the influence of mismatching targets on microarray hybridizations.     

A Gibbs free energy correlation for automated docking of carbohydrates

Thermodynamic information can be inferred from static atomic configurations. To model the thermodynamics of carbohydrate binding to proteins accurately, a large binding data set has been assembled from the literature. The data set contains information from 262 unique protein-carbohydrate crystal structures for which experimental binding information is known. Hydrogen atoms were added to the structures and training conformations were generated with the automated docking program AutoDock 3.06, resulting in a training set of 225,920 all-atom conformations. In all, 288 formulations of the AutoDock 3.0 free energy model were trained against the data set, testing each of four alternate methods of computing the van der Waals, solvation, and hydrogen-bonding energetic components. The van der Waals parameters from AutoDock 1 produced the lowest errors, and an entropic model derived from statistical mechanics produced the only models with five physically and statistically significant coefficients. Eight models predict the Gibbs free energy of binding with an error of less than 40% of the error of any similar models previously published.     

Hydration of dimethyldodecylamine-N-oxide: enthalpy and entropy driven processes

Dimethyldodecylamine-N-oxide (DDAO) has only one polar atom that is able to interact with water. Still, this surfactant shows very hydrophilic properties: in mixtures with water, it forms normal liquid crystalline phases and micelles. Moreover, there is data in the literature indicating that the hydration of this surfactant is driven by enthalpy while other studies show that hydration of surfactants and lipids typically is driven by entropy. Sorption calorimetry allows resolving enthalpic and entropic contributions to the free energy of hydration at constant temperature and thus directly determines the driving forces of hydration. The results of the present sorption calorimetric study show that the hydration of liquid crystalline phases of DDAO is driven by entropy, except for the hydration of the liquid crystalline lamellar phase which is co-driven by enthalpy. The exothermic heat effect of the hydration of the lamellar phase arises from formation of strong hydrogen bonds between DDAO and water. Another issue is the driving forces of the phase transitions caused by the hydration. The sorption calorimetric results show that the transitions from the lamellar to cubic and from the cubic to the hexagonal phase are driven by enthalpy. Transitions from solid phases to the liquid crystalline lamellar phase are entropically driven, while the formation of the monohydrate from the dry surfactant is driven by enthalpy. The driving forces of the transition from the hexagonal phase to the isotropic solution are close to zero. These sorption calorimetric results are in good agreement with the analysis of the binary phase diagram based on the van der Waals differential equation. The phase diagram of the DDAO-water system determined using DSC and sorption calorimetry is presented.