Thermodynamics of polymeric fluids – effect of volume on the configurational entropy of chain molecules

Various conformation‐dependent properties of chain molecules have been successfully treated within the rotational isomeric state approximation. The conformation entropy is one of such properties which can be readily defined by the partition function, the sum of all possible configurations of the chain. Flexible polymers often exhibit crystallization and in some cases liquid‐crystallization as well. In these first‐order transitions, changes in the spatial arrangement of polymer chains are considered to be a major factor involved. In order to explicitly determine the conformational contribution to the melting entropy, the latent entropy observed under the isobaric condition must be corrected for the volume change. The entropy separation involves a hypothetical assumption that the volume of the isotropic fluid may be compressed to that of the solid state without affecting the configurational part of the entropy of molecules. Finally thermodynamic significance of the conformation entropy in these transitions is emphasized on the basis of the critical studies of the entropy‐volume relation of chain molecules in the liquid state.     

Two-particle entropy and structural ordering in liquid water

Entropies of simple point charge (SPC) water were calculated over the temperature range 278-363 K using the two-particle correlation function approximation. Then, the total two-particle contribution to the entropy of the system was divided into three parts, which we call translational, configurational, and orientational. The configurational term describes the contribution to entropy, which originates from spatial distribution of surrounding water molecules (treated as points, represented by the center of mass) around the central one. It has been shown that this term can serve as the metric of the overall orientational ordering in liquid water. Analyzing each of these three terms as a function of intermolecular distance, r, we also find a rational definition of the hydration shell around the water molecule; the estimated radii of the first and second hydration shells are 0.35 nm and 0.58 nm, respectively. We find, moreover, that the first hydration shell around the water molecule participates roughly in 70% of the total orientational entropy of water, and this rate is roughly temperature independent.     

Using bulk convection in a microtensiometer to approach kinetic-limited surfactant dynamics at fluid-fluid interfaces

The effects of carbon chain length and temperature were investigated on adsorption kinetics and surface tension of a group of slightly volatile, short carbon chain molecules: 1-octanol, 1-hexanol, and 1-butanol. Experiments were performed in a closed chamber where simultaneous adsorption from both sides of the vapor/liquid interface was considered. The dynamic (time dependent) and steady-state surface tensions were found to decrease with temperature ranging from 10 °C to 35 °C. It was shown that, at the final steady-state, the effect of adsorption from the vapor phase was much more important than that from the liquid phase especially for short carbon chain molecules (e.g., 1-butanol). The modified Langmuir equation of state and modified kinetic transfer equation, which account for adsorption from both sides of a vapor/liquid interface, were used to model the experimental data of the steady-state and dynamic surface tension, respectively. Modeling results showed that the equilibrium constants and adsorption rate constants were increased with temperature and carbon chain length. The maximum surface concentration showed a decrease with temperature and an increase with carbon chain length. Some variations in the fitting parameters were observed in the dynamic modeling. These variations may be due to the experimental errors or the limitations of the proposed model.     

On the inverse temperature transition and development of an entropic elastomeric force of the elastin mimetic peptide [LGGVG](3, 7)

We report on a molecular dynamics simulation based study of the thermal and mechanical properties of the elastin mimetic peptide [LGGVG](n) (n = 3, 7). Our findings indicate that this peptide undergoes an inverse temperature transition as the temperature is raised from ~20 °C to 42 °C. The thermal behavior is similar to what has been observed in other well studied short mimetic peptides of elastin. Both [LGGVG](n) (n = 3, 7) peptides exhibit an increase in the number of side chain contacts and peptide-peptide hydrogen bonds when the temperature is raised from ~20 °C to 42 °C. These observations are accompanied by a decrease in the number of proximal water molecules and number of peptide-water hydrogen bonds. This work also reports on a comparison of the thermal and mechanical properties of [LGGVG](3) and [VPGVG](3) and quantifies the interaction with surrounding waters of hydration under mechanically strained conditions. It is demonstrated, via a quasi-harmonic approach, that both model peptides exhibit a reduction in the population of low-frequency modes and an increase in population of high-frequency modes upon elongation. The shift in population of frequency modes causes the peptide entropy to decrease upon elongation and is responsible for the development of an entropic force that gives rise to elasticity. These observations are in disagreement with a previously published notion that model elastin peptides, such as [VPGVG](18), increase in entropy upon elongation.     

A rationale for the contrasting activity (towards globular proteins) of tert-butyl alcohol and trimethylamine N-oxide

tert-Butyl alcohol, TBA, and trimethylamine N-oxide, TMAO, even though they are isosteric molecules, have contrasting activity towards globular proteins: the former destabilizes the native state, whereas the latter stabilizes it. TBA addition to water causes a density decrease and it tends to form self-aggregates; TMAO addition to water causes a density increase and it does not show any tendency to form self-aggregates. By inserting such experimental information in the framework of the statistical thermodynamic model devised to rationalize the conformational stability of globular proteins [G. Graziano, Phys. Chem. Chem. Phys., 2010, 12, 14245-14252], it emerges that: (a) TBA is a destabilizing agent because its addition to water causes a significant decrease in the magnitude of the contribution due to the solvent-excluded volume decrease associated with protein folding; (b) TMAO is a stabilizing agent because its addition to water causes a significant increase in the magnitude of the contribution due to the solvent-excluded volume decrease associated with protein folding.     

Solvation and pairwise association in a 2D fluid

It is shown that it is possible: (a) to derive the 2D scaled particle theory formula of the reversible work of cavity creation using a geometric approach; (b) to obtain the solvation Gibbs energy in a 2D Lennard-Jones fluid; (c) to calculate the solvent contribution to the solvophobic interaction of two Lennard-Jones disks on the basis of geometric arguments. The solvent-excluded surface area associated with cavity creation decreases significantly upon pairwise association, leading to a marked increase in the configurational/translational entropy of solvent disks.     

Environmental swap energy and role of configurational entropy in transfer of small molecules from water into alkanes

We studied the effect of segmented solvent molecules on the free energy of transfer of small molecules from water into alkanes (hexane, heptane, octane, decane, dodecane, tetradecane, and hexadecane). For these alkanes we measured partition coefficients of benzene, 3-methylindole (3MI), 2,3,4,6-tetrachlorophenol (TeCP), and 2,4,6-tribromophenol (TriBP) at 3, 11, 20, 33 [corrected], and 47 degrees C. For 3MI, TeCP, and TriBP the dependence of free energy of transfer on length of alkane chains was found to be very different from that for benzene. In contrast to benzene, the energy of transfer for 3MI, TeCP, and TriBP was independent of the number of carbons in alkanes. To interpret data, we used the classic Flory-Huggins (FH) theory of concentrated polymer solutions for the alkane phase. For benzene, the measured dependence of energy of transfer on the number of carbons in alkanes agreed well with predictions based on FH model in which the size of alkane segments was obtained from the ratio of molar volumes of alkanes and the solute. We show that for benzene, the energy of transfer can be divided into two components, one called environmental swap energy (ESE), and one representing the contribution of configurational entropy of alkane chains. For 3MI, TeCP, and TriBP the contribution of configurational entropy was not measurable even though the magnitude of the effect predicted from the FH model for short chain alkanes was as much as 20 times greater than experimental uncertainties. From the temperature dependence of ESE we obtained enthalpy and entropy of transfer for benzene, 3MI, TeCP, and TriBP. Experimental results are discussed in terms of a thermodynamic cycle considering creation of cavity, insertion of solute, and activation of solute-medium attractive interactions. Our results suggest that correcting experimental free energy of transfer by Flory-Huggins configurational entropy term is not generally appropriate and cannot be applied indiscriminately.     

Oscillating repulsive force between macroscopic surfaces as a consequence of the fluctuation of the density in the gap region

We try to explain the short-range repulsive force between surfaces as a consequence of a decrease in the configurational entropy of liquid molecules in the gap region as the width of the gap decreases. A simple model shows that the density has an oscillating variation when the surfaces are pushed towards each other. As a consequence, an oscillating repulsive force appears between the macroscopic surfaces, which is the result of a loss of configurational freedom of the liquid molecules because of their orientation in the gap. Received: 14 August 2000 Accepted: 30 January 2001     

Solubility and Solution Structure of Cellulose Derivatives

Strongly interacting solvents are needed to dissolve cellulose; therefore, in the past the interpretation of the uncommon solution behavior of cellulose and its derivatives was based mainly on energetic (enthalpic) considerations, for example, hydrogen bonding. These attempts have not been very successful. The present paper demonstrates that entropic effects influence the solution behavior much stronger than hitherto supposed. In the well-known Flory–Huggins theory the driving force for dissolution of flexible chains is the configurational entropy of mixing. This large entropy is strongly reduced by the chain stiffness of the cellulose backbone and by the strictly regular primary structure of this polysaccharide. It strongly reduces the driving force for dissolution. The entropy of mixing becomes largely increased again by the attachment of long side chains and causes solubility with surprising efficiency (hairy rod principle). This effect is demonstrated with several examples. Among others, the surprising insolubility of short, regular-selectively substituted cellulose chains is explained, although long chains of the same substitution pattern are soluble. The striking behavior of cellulose ethers in water is based on the hydrophobic effect, which causes an increased order of the polymer surrounding water molecules. The induced order results in a very pronounced decrease of entropy of mixing that overcompensates the positive configurational entropy of mixing. Common rules of basic thermodynamics now predict phase separation on heating, contrary to the Flory–Huggins theory, which can only predict phase separation on cooling.     

Thermodynamic functions of water and ice confined to 2 nm radius pores

The heat capacity C(p) of the liquid state of water confined to 2 nm radius pores in Vycor glass was measured by temperature modulation calorimetry in the temperature range of 253-360 K, with an accuracy of 0.5%. On nanoconfinement, C(p) of water increases, and the broad minimum in the C(p) against T plot shifts to higher temperature. The increase in the C(p) of water is attributed to an increase in the phonon and configurational contributions. The apparent heat capacity of the liquid and partially frozen state of confined water was measured by temperature scanning calorimetry in the range of 240-280 K with an accuracy of 2%, both on cooling or heating at 6 K h(-1) rate. The enthalpy, entropy, and free energy of nanoconfined liquid water have been determined. The apparent heat capacity remains higher than that of bulk ice at 240 K and it is concluded that freezing is incomplete at 240 K. This is attributed to the intergranular-water-ice equilibrium in the pores. The nanoconfined sample melts over a 240-268 K range. For 9.6 wt % nanoconfined water concentration ( approximately 50% of the maximum filling) at 280 K, the enthalpy of water is 81.6% of the bulk water value and the entropy is 88.5%. For 21.1 wt % (100% filling) the corresponding values are 90.7% and 95.0%. The enthalpy decrease on nanoconfinement is a reflection of the change in the H-bonded structure of water. The use of the Gibbs-Thomson equation for analyzing the data has been discussed and it is found that a distribution of pore size does not entirely explain our results.     

Unravelling the specific site preference in doping of calcium hydroxyapatite with strontium from ab initio investigations and Rietveld analyses

Strontium can be substituted into the calcium sublattice of hydroxyapatite without a solubility limit. However, recent ab initio simulations carried out at 0 K report endothermic nature of this process. There is also striking discrepancy between experimentally observed preference of Sr doping at Ca-II sites and the first principles calculations, which indicate that a Ca-I site is preferred energetically for the Sr substitution. In this paper we combine insights from Density Functional Theory simulations and regular configurational entropy calculations to determine the site preference of Sr doping in the range of 0-100 at% at finite temperatures. In addition, samples of Sr-HA are synthesized and refinement of the relevant structural information provides benchmark information on the experimental unit cell parameters of Sr-HA. We find that the contribution of the entropy of mixing can efficiently overcome the endothermic excess energy at a temperature typical of the calcining step in the synthesis route of hydroxyapatite (700-950 °C). We observe that the most preferential substitution pattern is mixed substitution of Sr regardless of the concentration. For a wet chemical method, carried out at a moderate temperature (90 °C), the mixed doping is still slightly favourable at higher Sr-concentrations, except the range at 20% Sr, where Site II substitution is not restricted energetically and equally possible as the mixed doping. We observe a close correspondence between our theoretical results and available experimental data. Hence it should be possible to apply this theory to other divalent dopants in HA, such as Zn(2+), Mg(2+), Pb(2+), Cu(2+), Ba(2+), Cd(2+) etc.     

Comparing landscape calculations with calorimetric data on ortho-terphenyl, and the question of the configurational fraction of the excess entropy

Mossa et al. [Phys. Rev. E 65, 041205 (2002)] have calculated the total and configurational entropies of supercooled ortho-terphenyl liquid using the potential-energy landscape formalism and a simplified model of the intermolecular potential. I show here that the agreement of their calculated configurational entropy with the experimental data depends on what is assumed about the configurational fraction of the excess entropy and its temperature dependence. In particular, if the configurational fraction is taken as 0.70 and independent of temperature the agreement is excellent; if a marked temperature dependence of that fraction inferred from calorimetric data is assumed the agreement is only fair at best. This marked temperature dependence of the configurational fraction also implies some implausible behavior of contributions to the excess entropy at the Kauzmann temperature, but no obvious reason for disregarding it presents itself.     

Ionic liquid crystalline phases in 3-hexadecylimidazolium bromide and binary mixtures with 1-decanol

3-Hexadecylimidazolium bromide was synthesized and characterized showing formation of thermotropic smectic liquid crystals at temperatures above its melting point from 48.5 to 150.9°C. With decreasing temperature, the peak intensities in XRD patterns increase and full widths at half-maximum decrease, suggesting structural order increases with decreasing temperature. Compared with 1,2-dimethyl-3-hexadecyl-imidazolium bromide and hexafluorophosphate, the IL shows a lower melting point and less degree of chain interdigitation. The main reason is due to a more symmetrical structure and denser assembly of the IL molecules, which results in more steric resistance for the alkyl chain to interdigitate. The self-assembly behavior of the hydrophobic IL in an organic solvent was investigated showing SmA(2) lyotropic liquid crystalline phases. The first-order scattering peak shifts to lower q values with increasing IL content, which is opposite to the shift directions of the binary mixtures of the soluble imidazolium IL and water, indicating a different packing behavior of the hydrophobic IL in 1-decanol.     

Configurational entropy of polyethylene and other linear polymers

The configurational entropy of the polyethylene chain at the melting points calculated in two ways. In both calculations, tetrahedral angles and discrete trans and gauche arrangements of all bonds are assumed, and trans bonds are assumed more stable than gauche by energy U₁. First, calculations are made on chains of up to N = 18 bonds, disallowing all configurations having overlapping atoms, and the result is extrapolated to large N. Second, a calculation is made directly for long chains, with overlaps excluded only over every short chain segment. The results are in almost exact agreement, suggesting that the second method can be safely used with other molecules. The calculated configurational entropy is in line with that suggested by the entropy of fusion, assuming the chains to acquire a configurational freedom in the melt which approaches that of independent chains.     

On similarity of hydrogen-bonded networks in liquid formamide and water as revealed in the static dielectric studies

The paper presents the experimental verification of the result obtained with the molecular dynamics simulation which revealed the differences in the topology of the hydrogen-bonded networks in liquid formamide and water, namely, the differences in their intermolecular cyclization process (I. Bakó, et al. J. Chem. Phys. 2010, 132, 014506). It is shown in our paper that the difference in the (simulated) size distribution of the hydrogen-bonded molecular rings in water (a relatively sharp maximum at about 6 molecules) and formamide (a broad maximum at about 11 molecules) strongly manifests itself in the experimental values of the Kirkwood correlation factor of the compounds. A much larger number of molecules included in the cyclic species (of more or less compensated dipole moment) leads to significant decrease of the Kirkwood correlation factor of formamide in comparison to that of water. Besides, as a consequence of an enhancement in formation of the cyclic multimers of formamide, one observes an essential reduction of the orientational entropy increment of that liquid, in comparison to the entropy effect related to liquid amides where the chain multimers are formed.     

Generating Excess Protons in Microsolvated Acid Clusters under Ambient Conditions: An Issue of Configurational Entropy versus Internal Energy

Acid dissociation, and thus liberation of excess protons in small water droplets, impacts on diverse fields such as interstellar, atmospheric or environmental chemistry. At cryogenic temperatures below 1 K, it is now well established that as few as four water molecules suffice to dissociate the generic strong acid HCl, yet temperature-driven recombination sets in simply upon heating that cluster. Here, the fundamental question is posed of how many more water molecules are required to stabilize a hydrated excess proton at room temperature. Ab initio path integral simulations disclose that not five, but six water molecules are needed at 300 K to allow for HCl dissociation independently from nuclear quantum effects. In order to provide the molecular underpinnings of these observations, the classical and quantum free energy profiles were decomposed along the dissociation coordinate in terms of the corresponding internal energy and entropy profiles. What decides in the end about acid dissociation, and thus ion pair formation, in a specific microsolvated water cluster at room temperature is found to be a fierce competition between classical configurational entropy and internal energy, where the former stabilizes the undissociated state whereas the latter favors dissociation. It is expected that these are generic findings with broad implications on acid–base chemistry depending on temperature in small water assemblies.     

Adsorption of 1-Monoglycerides at the Hexane/Water Interface: II. 1-Monolaurin

The interfacial tension of a hexane solution of 1-monolaurin against water was measured as a function of temperature and concentration under atmospheric pressure. The thermodynamic quantity changes associated with the adsorption of 1-monolaurin were evaluated and compared with those of the previously reported 1-monomyristin. The decrease of two carbon atoms in the hydrocarbon chain results in a slight expansion of the 1-monolaurin adsorbed film and in a slight decrease in entropy and energy changes compared with those of the 1-monomyristin system. The large negative value of the entropy change at a high concentration is related to the restricted orientation of the polar head group of 1-monolaurin at the hexane/water interface due to the strong interaction between the large hydrophilic group of 1-monolaurin and the water molecules, as in the 1-monomyristin system. The origin of the distinction in the entropy change behavior between the adsorption from the hexane phase and water phase was discussed. The usefulness of an easier calculation process for the partial molar entropy change is verified by comparison with the usual reliable value and with the entropy of adsorption.     

Entropy change on the cooling and heating paths between liquid and glass and the residual entropy

We analyze the C(p)-T data for the glassy state of eight materials of varied molecular interactions and structures to investigate how the use of the C(p)d ln T integral in the time-dependent (nonreversible) thermodynamic path between a liquid and glass affects our estimates of the entropy. Since the change in entropy on such a path cannot be determined, we estimate the upper and lower values of the change, Δσ, from the C(p)d ln T integral. For the same rates of cooling and heating and without annealing, Δσ on the cooling path is negligibly different from that on the heating path. The difference is ～1∕60th-1∕25th of the lowest known value of the residual entropy and even less than the configurational entropy of the supercooled liquid at its kinetic freezing temperature. Thus use of the C(p)d ln T integral in the nonreversible path does not introduce significant errors in estimating the residual entropy. Dynamic C(p) data cannot be used to infer that configurational entropy decreases on glass formation. Time dependence of the C(p)-T path has little consequence for reality of the residual entropy.     

The contribution of hydrogen bonds to the surface tension of water

The surface energy, the surface free energy and the surface entropy of liquid water are calculated from the decrease in the number of hydrogen bonds in the surface layer, estimated on the bash of a simplified aater structure scheme. In the calculations of the free energy density function only the hydrogen-bond interactions between molecules are taken into consideration. The resulting surface free energy of water is ≈43 mN/m at 25°C. The calculated temperature dependence is consistent with that observed.     

Adsorption of 1-Monoglycerides at the Hexane/Water Interface

The interfacial tension of a hexane solution of 1-monolaurin against water was measured as a function of temperature and concentration under atmospheric pressure. The thermodynamic quantity changes associated with the adsorption of 1-monolaurin were evaluated and compared with those of the previously reported 1-monomyristin. The decrease of two carbon atoms in the hydrocarbon chain results in a slight expansion of the 1-monolaurin adsorbed film and in a slight decrease in entropy and energy changes compared with those of the 1-monomyristin system. The large negative value of the entropy change at a high concentration is related to the restricted orientation of the polar head group of 1-monolaurin at the hexane/water interface due to the strong interaction between the large hydrophilic group of 1-monolaurin and the water molecules, as in the 1-monomyristin system. The origin of the distinction in the entropy change behavior between the adsorption from the hexane phase and water phase was discussed. The usefulness of an easier calculation process for the partial molar entropy change is verified by comparison with the usual reliable value and with the entropy of adsorption. Copyright 1999 Academic Press.