A general formalism of deriving the pair potential of polymer chains for arbitrary interaction potentials between isolated chain segments at and close to the theta-point

A formalism has been worked out which allows to transform any non-punctiform segment-segment potential of isolated polymer segments ε of fairly short-ranged character into the pair-potentialU operating between linear polymer chains with a certain reference to the arguments as they have been originally put forward byFlory andKrigbaum. Although no restrictions are made in the derivation as to the repulsive or attractive contribution of the segment-segment potential ε because of some known general deficiencies of theFlory-Krigbaum treatment for exclusively repulsive interaction, the resulting equations are primarily intended to describe the thermodynamic situation at and close to the θ-point where repulsion and attraction—though working at different ranges of segment separation—cancel. As the equation derived is somewhat complicated two different approximate forms have been developed: The first one is based on aTaylor series expansion retaining terms up to the fourth order which allows to characterizeU by the second and the fourth moment of the pair segment-segment distribution function, β and γ (β being the so-called binary cluster integral of segment-segment interaction, which is considered to be zero for θ-conditions). In this caseU may be represented by an expression of the general form $$U/kT = A(1 - BR^2 )\exp \{ - bR^2 \} .$$ The second method is based on a separate integration over the repulsive and attractive ranges of ε giving the repulsive (U ₊) and the attractive (U _?) part ofU finally after some approximations leading to an equation of the general form $$U/kT = (U_ + + U_ - )/kT = A_1 \exp \{ - b_1 R^2 \} - A_2 \exp \{ - b_2 R^2 \} .$$ In both cases the knowledge of the exact form of ε is dispensable, only β and γ—or for the second case their repulsive (β₊ and γ₊) and attractive (β_? and γ_?) parts have to be known. It is shown that the approximations are in excellent accordance with the exact form so that they may be conveniently used to describe pair potentials of polymer chains and to analyze pair potentials of segment-segment interactions under the limitations and conditions indicated.     

Influence of solid surface on equilibria in polymer mixtures

The influence of solid disperse particles (aerosil) on phase equilibria in ternary (polymer-polymer-solvent) and binary (polymer-polymer) systems has been investigated using adsorption and gas chromatography techniques. The change in position and shape of the binodal for the ternary systems has been established. The region of thermodynamic compatibility of two polymers in a common solvent is broadened due to the selective adsorption of high molecular weight fraction of one of the polymers, this effect being dependent on the amount of solid particles introduced into the system. For binary systems, the thermodynamic interaction parameters χ₂₃ have been determined and increasing thermodynamic stability of the mixture in the presence of the solid phase has been discovered. The complicated dependences of the interaction parameters on mixture composition are connected with differences in selectivity of adsorption for various compositions. It is supposed that increased thermodynamic stability of a mixture of two incompatible polymers in the presence of solid is due to the transition of both polymers into adsorption and border layers.     

Phase separation behavior of aqueous solutions of a thermoresponsive polymer

Cloud‐point and binodal curves of the LCST type were obtained for aqueous solutions of a thermoresponsive polymer, poly [2‐(2‐ethoxy)ethoxyethyl vinyl ether], poly(EOEOVE). The cloud‐point curve obtained was very flat except in a dilute region, that is the cloud‐point temperature was insensitive to the polymer concentration, resembling the cloud‐point curve for aqueous solutions of poly(N‐isopropylacrylamide). On the other hand, the binodal curve obtained was parabolic, and located within the two‐phase region of the cloud‐point curve. Accompanied with the phase separation, a sharp endothermic peak was observed in a region including the cloud‐point and binodal temperatures. The reciprocal of the osmotic compressibility ?Π/?c obtained by sedimentation equilibrium indicated that water changes from a good to poor solvent for poly(EOEOVE) with increasing temperature. Analyzing the ?Π/?c data by a thermodynamic perturbation theory, we determined the interchain interaction parameters, the hard‐core diameter d and the depth ε of the square‐well potential. Theoretical binodal and endothermic curves calculated by the perturbation theory using the estimated interaction parameters reproduced experimental ones semiquantitatively, but the theoretical binodal disagreed with the experimental flat cloud‐point curve. The disagreement at high concentrations was in the opposite direction to that expected from the sample polydispersity in the molecular weight. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2937–2949, 2005     

Hydration of Fe+: A Monte Carlo simulation of water clusters and of a dilute aqueous solution

Monte Carlo statistical thermodynamic computer simulations are reported for several clusters Fe⁺ (H₂O)_n at different temperatures and for a dilute aqueous solution of Fe⁺ at 298 K. The energy of each configuration has been calculated in the pairwise additivity approximation using the MCY potential for the water–water interaction and an ab initio analytical potential built by us for the Fe⁺–H₂O interaction. Energy and structural analysis of the generated configurations lead to the prediction of a coordination number of six for the first hydration shell of the Fe⁺ ion, both in clusters and in dilute solution. Finally, the variation in the distance to the Fe⁺ ion of the energy and orientation of water molecules in the solution are discussed.     

A spectroscopic/thermodynamic study of the rhodamine B lactone ⇌ zwitterion equilibrium

Temperature dependences of the visible absorption spectra of rhodamine B (RB) in water and 18 alcohol solvents have been examined and utilized to estimate thermodynamic parameters (ΔG°, ΔH°, ΔS°) for the RB lactone ⇌ zwitterion (L ⇌ Z) equilibria in these sol From the L ⇌ Z equilibrium in the strong hydrogen-bonding solvent trifluoroethanol an intrinsic RB zwitterion molar absorptivity of ε = 1.30 × 1O⁵ dm³/mol·cm is estimated. The thermodynamic results suggest that the position of the RB L ⇌ Z equilibrium is strongly influence by self-association of the solvent. The position of the equilibrium in aliphatic alcohols can be predicted from simple features of the solvent molecules. Consequences of the results regarding calculation of the natural radiative lifetime of the fluorescent state from the absorption spectrum are discussed.     

Melting point depression in poly (ethylene oxide)-poly (methyl methacrylate) blends

Thermo-optical analysis of solution cast mixtures of poly (ethylene oxide) (POE) and poly (methyl methacrylate) (PMMA) has been carried out. Melting point depression was observed for increasing proportion of PMMA in the mixture. An analytical expression appropriate to the crystallineamorphous polymer pair has been applied to explain the melting point depression in terms of thermodynamic quantities. From this expression, the interaction parameter for the mixture has been evaluated. The influence of $\text{M}$_w of POE on the binary interaction parameter has been studied.     

Conformational structures and thermodynamic properties of compact polymer chains confined between two parallel plane boundaries

In this paper, the authors investigated the adsorption phenomenon of compact chains confined between two parallel plane boundaries using a pruned‐enriched Rosenbluth method. The authors considered three cases with different adsorption energies of ε = 0, ?1, and ?3 (in units of k_BT) for the confined compact chains of different chain lengths N, respectively. Several parameters were employed to describe the size and shape of compact chain, and some special behaviors in the conformational structures were investigated for the first time. For example, the size and shape of confined compact chains undergo distinct changes in the adsorption cases of ε = ?1 and ?3, and pass through the maximum values at the characteristic distances D_c. The authors found that this characteristic distance D_c could be scaled as D_c～ (N + 1)^ν (ν = 0.56 ± 0.01) in the case of ε = ?3. In addition, the microstructures of chains were investigated, and several significant results were obtained by analyzing the segment density distribution and the mean fractions of segment in tails, trains, bridges, and loops structures. On the other hand, the thermodynamic properties were also investigated for the confined compact chains, such as average energy per bond, Helmholtz free energy per bond, and elastic force per bond. Results show that elastic forces f have different behaviors in three cases, indicating that it is not necessary to exert an external force on the boundaries in the nonadsorption case. At the same time, the average contact energy of compact chain obviously changes when the distance between the two parallel boundaries D increases, which is similar to those of the size and shape parameters. The authors also conclude that these thermodynamic properties of compact chains depend strongly on not only the adsorption energies but also the chain lengths and the confined condition. In addition, several results of the conformational and thermodynamic parameters, such as the segment density distribution and free energy, were compared with the results from the self‐consistent field theory. These investigations may help us to deepen the knowledge about the adsorption phenomenon of confined compact chains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2888–2901, 2006     

Integrated absorption coefficient of adsorbed CO

The integrated absorption coefficient ε has been measured for the stretching band of CO adsorbed on a series of oxides and zeolites. From the temperature dependences of the spectra, ε has been estimated for CO molecules whose stretching frequency is lowered due to their bonding to cationic sites of the zeolite through the oxygen atom. In accordance with the predictions of the electrostatic model, ε decreases as the vibrational frequency of CO increases.     

Experimental determination of the potential for Na(32P)+ Ar from differential scattering cross sections

We have measured the total differential cross section for the interaction of laser excited Na(3²P) interacting with Ar at thermal energies. From these data, which show a well resolved oscillatory pattern, the respective interaction potentials have been determined. The best fit to the experimental data is found with ε = 2.55 × 10^?3 au, r_m = 5.75 au for the well depth parameter of the ²II_{$\text{1}\text{2}$} potentials.     

A study of the relationship between the thermodynamic quality of mobile phases and their strength for the critical conditions of liquid chromatography of polystyrenes

The relationship between the thermodynamic quality of mobile phases and their strength ε was studied for the critical conditions of liquid chromatography. The chromatography of reference polystyrene samples was carried out in the adsorption and exclusion modes, and also under critical conditions, with binary mobile phases and a silica gel column used. The thermodynamic quality of solvent mixtures with respect to one another was evaluated by the intrinsic viscosity [η].     

Transport Coefficients of High Temperature SF6–He Mixtures Used in Switching Applications as an Alternative to Pure SF6

Sulfur hexafluoride (SF₆) gas has a quite high global warming potential and hence it is required that applying any substitute for SF₆ gas. Much interest in the use of a mixture of helium and SF₆ as arc quenching medium were investigated indicating a high performance of arc interruption. The calculated values of transport coefficients of mixtures of SF₆–He mixtures, at high temperatures are presented in this paper: to the knowledge of the authors, related data have not been reported in the literature. The species composition and thermodynamic properties are determined by the method of Gibbs free energy minimization, using standard thermodynamic tables. The transport properties including electron diffusion coefficients, viscosity, thermal conductivity and electrical conductivity, are evaluated by using the Chapman–Enskog method expanded up to the third-order approximation (second-order for viscosity). Particular attention is paid to the collision integral database by the use of the most accurate and recent cross-sections or interaction potentials available in the literature. The calculations, which assume local thermodynamic equilibrium, are performed in the temperature range from 300 to 30,000 K for different pressures between 0.1 and 16 atm. An evaluation of the current interruption performance by adding He into SF₆ is discussed from a microscopic point of view. The properties with regard to SF₆–He mixtures calculated here are expected to be reliable because of the improved collision integrals employed.     

Enthalpimetric measurements in solid—solid reactions. The formation of intermolecular charge-transfer complexes

The possibility of obtaining thermodynamic parameters from solid—solid interaction reactions in the formation of charge-transfer (CT) complexes has been studied carrying out the syntheses directly in a DSC apparatus. The interactions between the donor p-bromophenol and the acceptors p-benzoquinone, chloranyl and bromanyl have been considered. It was observed that the solid—solid interaction occurs only for the system p-bromophenol:p-benzoquinone; for the system p-bromophenol:bromanyl the reaction occurs in the molten donor; the acceptor chloranyl does not react.     

Evaluation of ε for p-dinitrobenzene—aniline complexes by the Scott equation. Failure of the Benesi—Hildebrand equation

The Scott equation has been employed to determine ε for p-dinitrobenzene charge transfer complexes with anilines. It is seen that the Benesi—Hildebrand plots show a random scatter, whereas the Scott plots are satisfactory straight lines.     

Adsorption of bromide at the Ag(100) electrode surface

The adsorption and phase formation of bromide on Ag(100) has been studied by chronocoulometry and surface X-ray scattering (SXS). With increasing electrode potential, bromide undergoes a phase transition from a lattice gas to an ordered c(2×2) structure (θ=0.5). The degree of lateral disorder was estimated by comparing the SXS- and the electrochemical measurements. Based on chronocoulometric experiments, a thermodynamic analysis of charge density data was performed to describe the bromide adsorption at the Ag(100) electrode. The Gibbs surfaces excess, electrosorption valencies, Esin–Markov coefficients, and the Gibbs energy of adsorption, lateral interaction energies as well as surface dipole moments have been estimated. The experimental θ versus E- isotherms are modeled employing (i) a quasi-chemical approximation as well as (ii) the results of a recent Monte Carlo simulation. An attempt is made to discuss the structure data and thermodynamic quantities of bromide adsorption on Ag(100) on the basis of the Grahame–Parsons model of the Helmholtz layer.     

Development of a Modified Bromley's Methodology for the estimation of ionic media effects on solution equilibria: Part 4. The chemical model of Fe(III) with the halide ligands in aqueous solution at 25°C

The Modified Bromley's Methodology (MBM) has been used to construct the basic chemical model between Fe(III) and OH⁻ and the halide ligands Cl⁻, Br⁻ and F⁻ in NaClO₄ medium at 25°C, obtaining the thermodynamic constants and the corresponding interaction parameters for each equilibrium. This basic model has been extended to KNO₃, HCl, and KCl media obtaining the corresponding interaction parameters. The applicability of the model is also discussed.     

Theoretical analysis of sorption of a binary solvent in a polymer phase. I. Occurrence and character of inversion in preferential sorption

Osmotic and sorption equilibria in the system polymer–binary solvent can be represented with advantage in coordinates (u₁, v₃), where v₃ is the volume fraction of the polymer and u₁ gives the composition (volume fraction) of the binary solvent in the polymer phase. The coexistence lines and osmotic isobars are plotted; the former are used to read the preferential sorption ε of one of the solvent components in the polymer. The newly formulated equilibrium condition for the preferential sorption is applied to the Flory–Huggins theory extended by the ternary interaction parameter χ_T. This is used as a starting point for analyzing the conditions under which inversion of preferential sorption takes place, i.e., the sign of ε changes. The existence of inversion and the course of the inversion line in the v₃ versus u₁ plot are affected in a decisive manner by the extent to which the effect of the mutual interaction of solvent components prevails over the effect of the relative difference between their molar volumes and of the difference in strength of their interaction with the polymer. The effect of the ratio of molar volumes upon the preferential sorption increases with the concentration of the polymer, so that for v₃ not too far from unity the component having the smaller molecule is necessarily sorbed preferentially. If, therefore, both types of small molecules are not of the same size, the inversion vanishes for large v₃ even in systems where it actually occurs if v₃ is small. On the contrary, the same effect can in other cases have as its consequence an inversion at moderate values of v₃, even if it does not appear as v₃ approaches zero; a similar effect can also be produced by a nonzero value of the interaction parameter χ_T. The neighborhood of the inversion line can have a “divergent” or a “convergent” character, depending on whether the component being preferentially sorbed is that present in excess. The former case is observed with negative and the latter for the positive values of the binary solvent–solvent interaction parameter χ₁₂. The inversion with the divergent neighborhood has not yet been confirmed experimentally, owing to the small number of systems investigated.     

Utilization of Phyllanthus emblica fruit stone as a Potential Biomaterial for Sustainable Remediation of Lead and Cadmium Ions from Aqueous Solutions

In the present work, an effort has been made to utilize Phyllanthus emblica (PE) fruit stone as a potential biomaterial for the sustainable remediation of noxious heavy metals viz. Pb(II) and Cd(II) from the aqueous solution using adsorption methodology. Further, to elucidate the adsorption potential of Phyllanthus emblica fruit stone (PEFS), effective parameters, such as contact time, initial metal concentration, temperature, etc., were investigated and optimized using a simple batch adsorption method. It was observed that 80% removal for both the heavy metal ions was carried out within 60 min of contact time at an optimized pH 6. Moreover, the thermodynamic parameters results indicated that the adsorption process in the present study was endothermic, spontaneous, and feasible in nature. The positive value of entropy further reflects the high adsorbent–adsorbate interaction. Thus, based on the findings obtained, it can be concluded that the biosorbent may be considered a potential material for the remediation of these noxious impurities and can further be applied or extrapolated to other impurities.     

Viscometry in the study of molecular complexes

Viscometric method has been used to study the interaction between the weak interacting systems such as benzene-CCl₄-cyclohexane, toluene-CCl₄-cyclohexane ando- xylene-CCl₄-cyclohexane. The equilibrium constants and other thermodynamic parameters have been reported and compared with literature data.     

HPLC Characterization of the Gramicidin A Dimer-Monomer Conformational Equilibrium in Ethanol and Study of the Effect of Calcium Ion

Abstract

The usefulness of size-exclusion high-performance liquid chromatography for the study of gramicidin A (GA) dimer-monomer conformational equilibrium in polar organic solvents is demonstrated for the first time. The monome-rization process of GA in ethanol has been analyzed using an Ultrastyragel 1000 Å column isocratically equilibrated with tetrahydrofuran, which has allowed the determination of kinetic and thermodynamic constants. Furthermore, the kinetics of interaction of Ca²⁺ with GA in ethanol has been followed using this methodology, and the binding mechanism has been investigated in terms of the poly-peptide dimer-monomer conformational equilibrium.     

Solvent effects on charge-transfer intensities and heats of formation of chloranil complexes with aromatic hydrocarbons

The spectrophotometric and thermodynamic properties of the charge-transfer complexes of chloranil with aromatic hydrocarbons such as benzene, toluene, xylenes (o-, m- and p-) and mesitylene have been studied in n-heptane solvent to make a correlation between the charge-transfer intensities and the heats of formation of the complexes. The results disagree with Mulliken's prediction—the charge-transfer intensities decrease with increase of heats of formation. An attempt has been made to calculate the thermodynamic as well as spectrophotometric properties of these complexes free from the influence of chloranil—solvent interaction and the results thus obtained show a good correlation between the charge-transfer intensities and the heats of formation of the complexes.