Thermodynamic molecular switch in sequence‐specific hydrophobic interactions

This communication will demonstrate the existence of a thermodynamic molecular switch in the pairwise, sequence‐specific hydrophobic interaction of Ile–Ile, Leu–Ile, Val–Leu, or Ala–Leu over the temperature range of 273–333 K reported by Nemethy and Scheraga in 1962. Based on Chun's development of the Planck–Benzinger methodology, the change in inherent chemical bond energy at 0 K, ΔH°(T₀), is 3.0 kcal mol^?1 for Ile–Ile, 2.4 for Leu–Ile, 1.8 for Val–Leu, and 1.2 kcal mol^?1 for Ala–Leu. The value of ΔH°(T₀) decreases as the length of the hydrophobic side chain decreases. It is clear that the strength and stability of the hydrophobic interaction is determined by the packing density of the side chains, with Ala–Leu being the most stable. At 〈T_m〉, the thermal agitation energy, $\int^{T}_{0}\Delta Cp^{\circ}(T)\,dT$, is about five times greater than ΔH°(T₀) in each case. Additionally, the thermal agitation energy for the same series, evaluated at 〈T_m〉, decreases in the same order, that is, as the length of the side chain decreases. This pairwise, sequence‐specific hydrophobic interaction is highly similar in its thermodynamic behavior to that of other biological systems, except that the negative Gibbs free energy change minimum at 〈T_s〉 occurs at a considerably higher temperature, 355 K compared to about 300 K. The melting temperature, 〈T_m〉, is also high, 470 K compared to 343 K in a biological system. The implication is that the negative Gibbs free energy minimum at a well‐defined 〈T_s〉 has it origin in the hydrophobic interactions, which are highly dependent on details of molecular structure. In addition to the four specific dipeptide interactions described, we have shown in our unpublished work the existence of a thermodynamic molecular switch in the interactions of 32 dipeptides wherein a change of sign in ΔCp°(T)_reaction leads to a true negative minimum in the Gibbs free energy of reaction, and hence, a maximum in the related K_eq. Indeed, all interacting biological systems that we have thus far examined using the Planck–Benzinger approach point to the universality of thermodynamic molecular switches. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Dilute solution properties of a polybenzimidazole

Light scattering and viscometric studies have been carried out on dilute solutions of a polybenzimidazole in N,N-dimethylacetamide. The data, which span the molecular weight range 2.9 ≦ 10^?4M_w ≦ 23.3, and the temperature range 290 ≦ T/K ≦343, yield the dependence of the mean-square radius of gyration 〈s²〉_LS, the second virial coefficient A₂, and the intrinsic viscosity [η] on molecular weight M_w and temperature. The unperturbed mean-square radius 〈s〉_LS was calculated using experimental values of 〈s²〉_LS and A₂. It was found that excluded volume effects on 〈s²〉_LS are very small. The unperturbed hydrodynamic chain dimension 〈s〉_η was estimated by considering draining effects. A small value of the draining parameter was obtained. Analysis of the temperature dependence of A₂ and [eta;] leads to the conclusion that this system approaches a lower theta temperature with increasing temperature. The steric factor σ = 〈s〉/〈s〉f, based on the value of 〈s〉_f calculated for the polymer chain with free rotation, is nearly unity. Most of these properties can be interpreted in terms of long rotational units within the main chain.     

Influence of short-range interactions on the shape of an unperturbed polymer chain: polyethylene

The average instantaneous shape of an unperturbed polyethylene chain is studied with a Monte Carlo technique. Different short-range interactions in the polyethylene chain are considered. The shape is evaluated as the ratio 〈L〉:〈L〉:〈L〉, where L₁≤L₂≤L₃ are the orthogonal components in the system of principal axes of gyration. Differences are found for different interactions in short- and medium-length chains, while for long chains all ratios converge to a common limit, which is about 1:2.7:12.0 for polyethylene chains.     

Studies on the composition and kinetics of chromium(III)-alanine system

Kinetics of the complex formation of chromium(III) with alanine in aqueous medium has been studied at 45, 50, and 55°C, pH 3.3–4.4, and μ = 1 M (KNO₃). Under pseudo first-order conditions the observed rate constant (k_obs) was found to follow the rate equation: Values of the rate parameters (k_an, k, K_IP, and K) were calculated. Activation parameters for anation rate constants, ΔH^≠(k_an) = 25 ± 1 kJ mol^?1, ΔH^≠(k) = 91 ± 3 kJ mol^?1, and ΔS^≠(k_an) = ?244 ± 3 JK^?1 mol^?1, ΔS^≠(k) = ?30 ± 10 JK^?1 mol^?1 are indicative of an (I_a) mechanism for k_an and (I_d) mechanism for k routes (‥substrate Cr(H₂O) is involved in the k route whereas Cr(H₂O)₅OH²⁺ is involved in k′ route). Thermodynamic parameters for ion-pair formation constants are found to be ΔH°(K_IP) = 12 ± 1 kJ mol^?1, ΔH°(K) = ?13 ± 3 kJ mol^?1 and ΔS°(K_IP) = 47 ± 2 JK^?1 mol^?1, and ΔS°(K) = 20 ± 9 JK^?1 mol^?1.     

Absorption line shape of two coupled oscillators decaying in two different mediums

The linear response theory is used to study the line shape of two coupled oscillators, decaying in two different baths, when one of the oscillators is coupled to the radiation field. The baths are considered to be thermally excited. The analysis is based on the computation of the correlation functions 〈a (t)a_i (0)〉 and 〈a_i (t)a(0)〉 of each oscillator, taking the coefficients associated with the operators a and a_i in the Heisenbemg representation as the starting point of the calculation. The line shape in different cases is also discussed.     

The Influence of the Ligands Cp*(η5‐C5Me5) and Cp(η5‐C5H5) on the Stability and Reactivity of Titanocene and Zirconocene Complexes: Reactions of the Bis(trimethylsilyl)acetylene Permethylmetallocene Complexes (η5‐C5Me5)2M(η2‐Me3SiC2SiMe3), M = Ti,Zr, with H2O and CO2

The reactions of the bis(trimethylsilyl)acetylene permethylmetallocene complexes CpM(η²‐Me₃SiC₂SiMe₃) (M = Ti ( 1 ), M = Zr ( 2 )) with H₂O and CO₂ were studied and compared to those of the corresponding metallocene complexes Cp₂M(L)(η²‐Me₃SiC₂SiMe₃) (M = Ti ( 3 ), L = – ; M = Zr, L = THF ( 4 )) to understand the influence of the ligands Cp(η⁵‐C₅H₅) and Cp*(η⁵‐C₅Me₅) as well as the metals titanium and zirconium on the reaction pathways and the obtained products. In the reaction of the permethyltitanocene complex 1 with water the dihydroxy complex CpTi(OH)₂ ( 5 ) was formed. This product differs from the well‐known titanoxane Cp₂TiOTiCp₂ which was obtained by the reaction of the corresponding titanocene complex 3 with water. The reaction of the permethylzirconocene complex 2 with water gives the mononuclear alkenyl zirconocene hydroxide 6 . An analogous product was assumed as the first step in the reaction of the corresponding zirconocene complex 4 with water which ends up in a dinuclear zirconoxane. In the conversion of the permethylzirconocene complex 2 with carbon dioxide the mononuclear insertion product 7 was formed by coupling of carbon dioxide and the acetylene. In contrast, the corresponding zirconocene complex 4 affords, by an analogous reaction, a dinuclear complex. In additional experiments the known complex CpZr(η²‐PhC₂SiMe₃) ( 8 ) was prepared, starting from CpZrCl₂ and Mg in the presence of PhC≡CSiMe₃. This complex reacts with carbon dioxide resulting in a mixture of the regioisomeric zirconafuranones 9 a and 9 b . From these in the complex 9 a , having the SiMe₃ group in β‐position to the metal, the Zr–C bond was quickly hydrolyzed by water to give the complex CpZr(OH)OC(=O)–C(SiMe₃)=CHPh ( 10 a ) compared to complex ( 9 b ) which gives slowly the complex CpZr(OH)OC(=O)–CPh=CH(SiMe₃) ( 10 b ).     

Melt‐state polymer chain dimensions as a function of temperature

The unperturbed chain dimensions (〈R²〉_o/M) of cis/trans‐1,4‐polyisoprene, a near‐atactic poly(methyl methacrylate), and atactic polyolefins were measured as a function of temperature in the melt state via small‐angle neutron scattering (SANS). The polyolefinic materials were derived from polydienes or polystyrene via hydrogenation or deuteration and represent structures not encountered commercially. The parent polymers were prepared via lithium‐based anionic polymerizations in cyclohexane with, in some cases, a polymer microstructure modifier present. The polyolefins retained the near‐monodisperse molecular weight distributions exhibited by the precursor materials. The melt SANS‐based chain dimension data allowed the evaluation of the temperature coefficients [dln 〈R²〉_o/dT(κ)] for these polymers. The evaluated polymers obeyed the packing length (p)‐based expressions of the plateau modulus, G = kT/np³ (MPa), and the entanglement molecular weight, M_e = ρN_anp³ (g mol^?1), where n_t denotes the number (～21) of entanglement strands in a cube with the dimensions of the reptation tube diameter (d_t) and ρ is the chain density. The product np³ is the displaced volume (V_e) of an entanglement that is also expressible as pd or kT/G. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1768–1776, 2002     

Specific volume of polysulfone as a function of temperature and pressure

The pressure–volume–temperature (PVT) properties of a commercial polysulfone derived from bisphenol A and 4,4′-dichlorodiphenylsulfone are studied experimentally and theoretically in the temperature range 30–370°C and for pressures to 2000 kg/cm². PVT surfaces are determined for an annealed glass, formed under zero pressure, and for the melt. Two glass-transition lines must be distinguished: T(P) which is the intersection of the glass and melt PVT surfaces, and T_g(P), which is obtained by pressurizing the melt isothermally. The application of Ehrenfest-type equations to these transitions are discussed. The Prigogine–Defay ratio r = Δ_kΔC_p/TV(Δα)² at P = 0 is found to be equal to 0.95 (±20%), using ΔC_p data determined on identical samples. The melt data is compared with the Simha–Somcynski hole theory, using the reducing parameters V^* = 0.788 cm³/g, T^* = 12,560°K, P^* = 10,875 bar. The hole fraction appearing in the theory is found to be constant along T(P), but the glass PVT relationship cannot be reproduced by using the Simha–Somcynsky theory together with the assumption that the hole fraction remains constant in the glass. At P = 0 the hole fraction must be allowed to decrease with decreasing temperature, but at a slower rate than in the melt.     

Kinetics of the solvolysis of [Co(3Rpy)4Cl2]+ ions (R = Me or Et) in water and in water + methanol mixtures

Rates of solvolysis of ions [Co(3Rpy)₄Cl₂]⁺ with R = Me and Et have been measured over a range of temperatures for a series of water-rich water + methanol mixtures to investigate the effect of changes in solvent structure on the solvolysis of complexes presenting a largely hydrophobic surface to the solvent. The variation of the enthalpies and entropies of activation with solvent composition has been determined. A free energy cycle relating the free energy of activation in water to that in water + methanol is applied using free energies of transfer of individual ionic species from water into water + methanol. Data for the free energy of transfer of chloride ions ΔG(Cl^?) from both the spectrophotometric solvent sorting method and the TATB method for separating ΔG(salt) into ΔG(i) for individual ions are used: irrespective of the source of ΔG(Cl^?), in general, ?ΔG(Co(Rpy)₄Cl²⁺) > ?ΔG(Co(Rpy)₄Cl₂⁺), where Rpy = py, 4Mepy, 4Etpy, 3Etpy, and 3Mepy, showing that changes in solvent structure in water-rich water + methanol mixtures generally stabilize the cation in the transition state more than the cation in the initial state for this type of complex ion. A similar result is found when the free energy cycle is applied to the solvolysis of the dichloro (2,2′,2″-triaminotriethylamine)cobalt(III) ion. The introduction of a Me or Et group on the pyridine ring in [Co(Rpy)₄Cl₂]⁺ has little influence on the difference {ΔG(Co(Rpy)₄Cl²⁺)?ΔG(Co(Rpy)₄Cl₂⁺)} in water + methanol with the mol fraction of methanol < 0.20.     

Ethylene polymerization with homogeneous Ziegler-Natta catalysts: theoretical study on the role of ion pairs in the polymerization mechanism

The thermodynamics of the reaction of an ethylene molecule with the Cp₂TiCH₃Cl/Al(CH₃)₂Cl system (Cp = η₅-C₅H₅), as a model for olefin polymerization with homogeneous Ziegler-Natta catalysts, was investigated via quantum mechanical DFT calculations. The comparison of the calculated energies for three possible titanium-olefin coordinated intermediates, the ionic complex Cp₂TiCH₃(C₂H₄)⁺/Al(CH₃)₂Cl, the bimetallic complex Cp₂TiCH₃(C₂H₄)^δ+ · Al(CH₃)₂Cl and the olefin-separated ion pair Cp₂TiCH/C₂H₄/Al(CH₃)₂Cl, shows that the most feasible polymerization mechanism occurs via olefin-separated ion pair.     

Simulation studies of branched polymer molecules

Monte Carlo simulation results are presented for lattice models of uniform stars (one branch point of functionality f = 3), combs (two branch points, ? = 3,3) and brushes (two branch points ? = 3,4 and ? = 3,5). We estimate the critical exponent γ(?), the ratio g(?) = 〈S(?)〉/〈S(1)〉 (where 〈S(?)〉 is the mean-square radius of gyration of a structure having ? branches and N monomers), and the meansquare end-to-end branch lengths, as a function of the number and arrangement of branches. Comparisons with theoretical predictions and experimental data are made where possible, leading to a test of some predictions, and a suggestion concerning future experiments.     

Kinetics and equilibria of the reaction between bromine and ethyl ether. The C?H bond dissociation energy in ethyl ether

The kinetics and equilibria of the reaction: have been studied in the temperature range 298–333 K by using the very low pressure reactor (VLPR) technique. Combining the estimated entropy change of reaction (1), ΔS = 8.1 ± 1.0 eu, with the measured ΔG, we find ΔH = 4.2 ± 0.4 kcal/mol; ΔH(CH₃CHOC₂H₅) = ?20.2 kcal/mol, and DH° [Et OCH(Me)-H] = 91.7 ± 0.4 kcal/mol. We find: where θ = 2.3 RT in kcal/mol. It has been shown that the reaction proceeds via a loose transition state and the “contact TS” model calculation gives a very good agreement with the observed value.     

Iodine catalyzed pyrolysis of dimethyl sulfide. Heats of formation of CH3SCH2I,the CH3SCH2 radical,and the pibond energy in CH2S

A kinetic study has been made of the gas phase, I₂-catalyzed decomposition of (CH₃)₂S at 630–650 K. Some I₂ is consumed initially, reaching a steady-state concentration. The initial major products are CH₄ and CH₂S together with small amounts of CH₃SCH₂I, CH₃I, HI, and CS₂. The initial reaction corresponds to a pseudo-equilibrium: accompanied by: and which brings (I₂) into steady state and a final complex reaction: From the initial rate of I₂ loss it is possible to obtain Arrhenius parameters for the iodination: We measure k₁, (644 K) = 150 L/mol s and from both the Arrhenius plot and independent estimates A₁ (644 K) = 10^{11.2 ± 0.3} L/mol s. Thus, E₁ = 26.7 ± 1 kcal/mol. From the steady-state I₂ concentration, an assumed mechanism and the known rate parameters for the CH₃I/HI system. It is possible to deduce K_A (644) = 3.8 × 10^?2 with an uncertainty of a factor of 2. Using an estimated ΔS (644) = 4.2 ± 1.0 e.u. we find ΔH_A (644) = 7.0 ± 1.1 kcal. With 〈ΔC_PA〉644 = 1.2 this becomes: ΔH_A(298) = 6.6 ± 1.1 kcal/mol. Then ΔH (CH₃SCH₂I) = 6.3 ± 1 kcal/mol. Making the assumption that E_?1 = 1.0 ± 0.5 kcal/mol we find ΔH (644) = 25.7 ± 0.7 kcal/mol and with 〈ΔC_PI〉 = 1.2; ΔH = 25.3 ± 0.8 kcal/mol. This gives ΔH (CH₃S?H₂) = 35.6 ± 1.0 kcal/mol and DH (CH₃SCH₂? H) = 96.6 ± 1.0 kcal/mol. This then yields E_π(CH₂S) = 52 ± 3 kcal. From the observed rate of pressure increase in the system and the preceding data k₃, is calculated for the step CH₃SCH₂ → CH₃ + CH₂S. From an estimated A-factor E₃ is deduced and from the overall thermochemistry values for k_?3 and E_?3. A detailed mechanism is proposed for the I-atom catalyzed conversion of CH₂S to CS₂ + CH₄.     

Stability of Complex Metal Bromides in the gas phase and in toluene

The equilibrium constants of the reactions MBr₂(s) + Al₂Br₆(sln) ? MAl₂Br₈(sln) M = Cr, Mn, Co, Ni, Zn, Cd have been measured at 298 K in toluene. Ni: 0.017 ± 0.0024, Co: 0.54 ± 0.07, Zn: 1.5 ± 0.2, Mn: 2.1 ± 0, 7, Cr: 2.2 ± 1, Cd: 7 ± 5. They are compared with literature values of the equilibrium constants of analogous reactions in the gas phase MX₂(s) + Al₂X₆(g) ? MAl₂X₈(g), X = Cl, Br. For CoAl₂Br₈(sln) the temperature dependence of the equilibrium constant yielded Δ_fH = ?9.4 ± 1 kJ mol^?1 and Δ_fS = ?39.5 ± 3 J mol^?1 K^?1 while literature values for CoAl₂Br₈(g) are Δ_fH = 42.4 ± 2 kJ mol^?1 and Δ_fS = 42.9 ± 2 J mol^?1 K^?1. The solubility of Al₂Br₆ in toluene as well as its enthalpy of dissolution have been measured in order to evaluate ΔH° and ΔS° of the solvation of Al₂Br₆(g) and CoAl₂Br₈(g) in toluene by a thermodynamic cycle. Solvation of Al₂Br₆(g): ΔH = ?72.7 ± 1 kJ mol^?1, ΔS = ?139.6 ± 4 J mol^?1 K^?1, solvation of CoAl₂Br₈(g): ΔH = ?124.5 ± 4kJ mol^?1, ΔS = ?222 ± 9J mol^?1 K^?1. Thus, CoAl₂Br₈ interacts more strongly with the solvent toluene than Al₂Br₆ does.     

Thermochemistry and kinetics of the reaction of methyl mercaptan with iodine

The gas-phase reaction CH₃SH + I₂ has been studied spectrophotometrically over the temperature range of 476–604 K. It was found that the reaction undergoes H abstraction by I at ≤575 K, leading to the formation of MeSI and followed by a secondary reaction which leads to the formation of MeSSMe: Taking into consideration the effect of reaction (2), the equilibrium constant K₁ (554 K) has been evaluated to be 0.025 ± 0.004. This value was combined with the estimated values S (CH₃SI, g) = 73.7 ± 1.0 eu and 〈ΔC〉 = 0.87 ± 0.3 eu to obtain ΔH = 4.03 ± 0.73 kcal/mol. This yields ΔH (CH₃SI, g) = 7.16 ± 0.73 kcal/mol when combined with known thermochemical values for CH₃SH, HI, and I₂. A kinetic study was vitiated by the concurrent heterogeneous reaction of MeSH and I₂ at lower temperatures and the rather complicated chemistry occurring at elevated temperatures. However, attempts at measuring rate constants at 554 K lead to a lower limit of ΔH (CH₃S·, g) ≥ 29.5 ± 2 kcal/mol when an estimated value of A = 10^{10.8 ± 0.2} L/mol·s for the reactionc is used. DH (CH₃S–I) is estimated to be 49.3 ± 1.7 kcal/mol. The bond strengths of some divalent sulfurs and the reaction mechanisms are discussed. A crude estimate of DH⁰(H–CH₂SH) = 96 ± 1 kcal has been obtained from the kinetic data.     

The heats of formation of NO3− and NO3− association complexes with HNO3 and HBr

The equilibrium constant for the reaction has been determined between 331 and 480°K using a variable-temperature flowing afterglow. These data give ΔH°(1) = -1.03 ± 0.21 kcal/mol and ΔS°(1) = —4.6 ± 1.0 cal/mol°K. When combined with the known thermochemical values for HBr, Br^?, and HNO₃, this yields ΔH(NO₃^?) = -74.81 ± 0.54 kcal/mol and S(NO₃^?) = 59.4 cal/mol·°K. In addition ΔH_n-1,n and ΔS_n-1,nfor the gas-phase reactions were determined for n = 2 and 3. The implications of these measurements to gas-phase negative ion chemistry are discussed.     

Variation of the polarizability of the hydrogen molecule ion and the hydrogen molecule with internuclear separation

The variation of the polarizability of H and H₂ with internuclear separation R = 1.6 – R = 2.4 a.u. for H and R = 1.0 – R = 2.0 a.u. for H₂ is determined using a variational method suggested by Das and Bersohn. From these data, values of 〈α〉_0,J for which nuclear motion due to zero point vibration and centrifugal stretching is taken into account, are calculated at 300°K. The relative percent increases of the motion averaged values compared to the equilibrium values are as follows: 10.50% for H and 6.52% for H₂.     

Crystal thickness distributions from melting homopolymers or random copolymers

Differential scanning calorimetry (DSC) can be used to infer the distribution of lamellar crystal thickness l. For homopolymers, the relation between melting temperature T and thickness is described by the Gibbs relation. In this case the weight distribution function of thickness g(l) ∝ P(T)(T − T)², where P(T) is DSC power and T is the melting temperature of an infinitely thick crystal. Copolymer melting is affected by the concentration of noncrystallizable comonomer in the melt as well as lamellar thickness. Unknown melt composition in copolymers with nonequilibrium crystallinity makes determination of the correct distribution g(l) from DSC impossible. An approximate distribution g₂(l) ∝ P(T)(T − T)² is proposed, where T is based on Flory's equilibrium crystallization theory. This approximate distribution is most accurate when crystallinity is small, that is, near the upper end of the melting range. Results are reported for polyethylene homopolymer and model ethylene–butene random copolymers. Corrections were not made for distortion of the DSC endotherms by thermal lag or by melting and recrystallization; these experiments are primarily to illustrate the effect of analysis in terms of an incorrect g₃(l) ∝ P(T). Average crystal thicknesses are about 20 nm for polyethylene and 5 nm for the copolymers. Distributions are characterized by l_w /l_n ≤ 1.1 in all cases. Width of the melting range is not a reliable indicator of the breadth of the thickness distribution. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3131–3140, 1999     

Some thermodynamic parameters for hydroxy amino acids: Bicine and tricine

pK values of N,N-dihydroxyethylglycine (bicine) and N-[tris(hydroxymethyl)methyl]-glycine (tricine) have been determined by the Irving-Rossotti method in an aqueous medium at 25, 30, 35, 40, 45, and 50°C and at different ionic strengths (I = 0.1, 0.5, and 1.0). Plots between pK_a(NH) and 1/T for various ionic strengths have been obtained and the values of slopes have been used to calculate the ΔH, ΔS, and ΔG for the dissociation reactions of bicine and tricine. The ΔH, ΔS, and ΔG values for bicine were found to be 10.6 ± 0.6 kcal mol^?1, ?1.9 ± 1.8 e.u., and 11.1 ± 0.06 kcal mol^?1, respectively, and for tricine 11.2 ± 0.6 kcal mol^?1, 1.6 ± 1.6 e.u., and 10.7 ± 0.06 kcal mol^?1, respectively. The pK_a(NH) values decrease with rise in temperature but the influence of ionic strength is not significant.     

Theoretical studies of diamagnetic properties of the hydrogen molecule ion II. Effect of varying internuclear separation

The diamagnetic susceptibility χ and magnetic shielding σ for H are investigated in the range of internuclear separations R = 1.6 a.u. to R = 2.4 a.u. according to a previously reported technique. From this data values of 〈χ〉 and 〈σ〉, for which nuclear motion due to zero-point vibration and centrifugal stretching is taken into account, are calculated at 300°K. These averages are 〈χ〉 = ?0.3902 α²a and 〈σ〉 = 1.096 × 10^?5 c.g.s. units which are approximately 3.1% and 1.4% respectively, smaller than the equilibrium values.