Influence of torsional stiffness upon temperature response of a polymeric chain

The influence of torsional stiffness upon the temperature dependence of the mean square end-to-end polymer chain distance 〈r〉 was studied parametrically for six different polymer chain models. The equations for 〈r〉, expressed in terms of the torsional potential energy, were differentiated with respect to temperature and the resulting equations were evaluated numerically. The magnitudes and locations of the secondary barrier heights, angular location and magnitudes of the energy minima, angular location of the maximum barrier U₀, spacing of the extrema, and the number of extrema were all found to play a significant role in the value of the predicted thermal expansion coefficients. The coefficients were also found to critically depend upon the relative energy ratio and were usually a highly nonlinear function of this ratio. Transitions between positive and negative values of the thermal expansion coefficients were found to exist and to depend upon the torsional potential shape, energy ratio, and the polymer chain model.     

The role of the torsional potential in relaxation dynamics: a molecular dynamics study of polyethylene

The role of the torsional potential in bulk polymer chain dynamics is investigated via molecular dynamics simulation using polyethylene as a model system. A number of three-fold barrier values, both greater and less than the standard one, were invoked. The one-fold potential that determines the gauche vs trans energy difference was also varied. For each of the selected torsional potentials, the MD volumetric glass transition temperature, T_g, was located. It was found that T_g is quite sensitive to the three-fold barrier magnitude, moving from below 100 K to nearly 400 K as the barrier goes from zero to twice the standard value. However T_g was found to be quite insensitive to the gauche trans energy difference. Details of the conformational dynamics were studied for the case of a zero torsional potential. This included the rate and location of conformational transitions, the decay of the torsional angle autocorrelation function (ACF) and the cooperativity of conformational transitions, all as a function of temperature. The temperature dependence of the conformational transition rate remains Arrhenius at all temperatures. The relaxation time characterizing the torsional angle ACF decay exhibits WLF temperature behavior. The conformational transitions are randomly distributed over the bonds at high temperature, but near T_g they become spatially heterogeneous and localized. The transitions show next-neighbor correlation as well as self-correlated forward-backward transitions. All of these features are similar to those found in previous simulations under the standard torsional potential.     

Maximum Thermodynamic Electrical Efficiency of Fuel Cell System and Results for Hydrogen,Methane, and Propane Fuels

The maximum electrical efficiency of fuel cell system, η_e^max, is important for the understanding and development of the fuel cell technology. Attempt is made to build a theory for η_e^max by considering the energy requirement of heating the fuel and air streams to the fuel cell operating temperature T. A general thermodynamic analysis is performed and the energy balances for the overall operating processes of a fuel cell system are established. Explicit expressions for the determination of η_e^max are deduced. Unlike the Carnot efficiency, η_e^max is found to be fuel specific. Except for hydrogen fuel, chemical equilibrium calculations are necessary to compute η_e^max. Analytical solutions for the chemical equilibrium of alkane fuels are presented. The theoretical model is used to analyze the effects of T and the steam contents of CH₄, C₃H₈, and H₂ on η_e^max for systems with various degrees of waste heat recovery. Contrary to the common perception concerning methane and propane fuels, η_e^max decreases substantially with the increase of T. Moreover, η_e^max of hydrogen fuel can be higher than that of methane and propane fuels for a system with a medium level of waste heat recovery and operated at 700 ℃≤T≤900 ℃.     

Large-Scale Molecular Dynamics Simulations of Energetic Ni Nanocluster Impact onto the Surface

On the atomic scale, Molecular Dynamics (MD) Simulation of Nano Ni cluster impact on Ni (100) substrate surface have been carried out for energies of E _a = 1–5 eV/atom and total energy of E _T = 195 eV (the total energy of cluster is E _T = nE _a, n is the number of cluster atoms) to understand quantitatively the interaction mechanisms between the cluster atoms and the substrate atoms. The many-body Embedded Atom Method (EAM) was used in this simulation. We investigated the maximum substrate temperature T _max and the time t _max within which this temperature is reached as a function of cluster sizes and the total energy E _T. The temperature T _max is linearly proportional to total cluster energy. For the constant energy per atom and for the cluster size increase, the correlated collisions rapidly transfers energy to the substrate, and the time t _max approached a constant value. For constant total energy the temperature T _max and the time t _max versus different cluster sizes was studied. We showed that the cluster implantation and sputtering atoms from the surface are affected by the cluster size and total kinetic energy of the clusters. Finally time dependence of the number N _dis of disordered atoms in the substrate was observed.     

Single-shot measurement of solids and liquids T1 values by a small-angle flip-flop pulse sequence

We propose the small-angle flip-flop (SAFF) pulse sequence as an alternative procedure for the rapid measurement of the ¹H spin–lattice relaxation time in the laboratory frame (T₁) of solid and liquid substances, in a time-domain NMR experiment. Based on the original flip-flop pulse sequence, this technique allows the fast estimation of T₁ values of samples that require minutes to hours of acquisition time if traditional pulse sequences are employed. We have applied SAFF to different substances, with T₁ ranging from microseconds up to seconds, including natural clays, polymers, and organic and inorganic solvents. We also demonstrate the potential of the pulse sequence in the real-time monitoring of dynamic processes, such as the conformational changes of polymeric materials during heating. The results we obtained with SAFF are comparable with those acquired with the inversion-recovery pulse sequence, with the addition of several benefits. This pulse sequence obeys steady-state and magnetization-conserving principles, making it possible to dismiss the need for relaxation delay times of the order of 5T₁. SAFF has shown high sensitivity in the resolution of individual components of T₁ in multiexponential systems and can be easily integrated to well-established pulse sequences, such as Magic Sandwich Echo and Carr–Purcell–Meiboom–Gill, for the single-shot determination of T₁ and T₂ or T_2*.     

Conformational properties of polar polymers. II. Poly(vinylidene chloride)

A recently developed polarization model for representing polar bond effects in conformational energy calculations is applied to poly(vinylidene chloride) (PVDC). The geometries and conformational energies of a number of conformers of 2,2,4,4,6,6-hexachloroheptane were calculated. The geometries were found to be similar to the hydrocarbon analog polyisobutylene (PIB) in that steric crowding results in the usual T, G, G′ states being split into + or ? distortions of the torsional angles away from the traditional values. Only distortions of the same sign occur in the same pair of bonds interior to CCl₂ groups. Distortions of G states towards eclipsed were found to be much more stable than those away. The interior skeletal valence angle is also distorted to an unusually large value, ca. 121°. The calculated dipole moments were used to infer a group moment for CCl₂ of 1.56 D. The calculated conformational energies were fitted by linear combinations of interaction parameters representing the stabilities of G₊, G_? bonds (relative to T₊, T_?) and the interactions between bonds across intervening CCl₂ groups. These parameters were used in statistical mechanical calculations of the characteristic and dipole-moment ratios. In order to make comparison with experiment, the dipole-moment/repeat unit of a 90% (by weight) PVDC copolymer with PVC was measured and found to be 1.42 ± 0.05 D. From this, the dipole-moment ratio for PVDC homopolymer is inferred to be ca. 0.8. The characteristic and dipole-moment ratios calculated from the interaction parameter set were somewhat too high but adjustment of the gauche energies downward brings the calculated ratios into agreement with experiment. The same statistical model along with energy parameters previously calculated also gives agreement with experiment for the characteristic ratio of PIB. The calculated geometries are in agreement with the conformation in the crystal being ? (T₊G′₊T_?G_?)? .     

Structure of acetyl chloride molecule isotopomers CH<Subscript>3</Subscript>COCl and CD<Subscript>3</Subscript>COCl in the ground and lowest excited singlet and triplet electronic states: a quantum mechanical study

The structures of isotopomers of conformationally flexible acetyl chloride molecule, CH₃COCl and CD₃COCl, in the ground (S₀ and lowest excited singlet (S₁) and triplet (T₁) electronic states were calculated by the RHF, MP2, and CASSCF methods. The equilibrium geometric parameters and harmonic vibrational frequencies of the molecules in these electronic states were estimated. According to calculations, electronic excitation causes considerable conformational changes involving rotation of the CH₃ (CD₃) top and a substantial deviation of the CCOCl fragment from planarity. The results of calculations agree with experimental data. Two dimensional torsional inversion sections of the potential energy surface were calculated and analyzed. Vibrational problems for large amplitude vibrations (torsional vibration in the S₀ state and both torsional and inversion vibrations in the T₁ and S₁ states) were solved in one- and two-dimensional approximations.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 62–70, January, 2005.     

Electronic quantum motions in hydrogen molecule ion

The hydrogen molecule ion is a two‐center force system expressed under the prolate spheroidal coordinates, whose quantum motions and quantum trajectories have never been addressed in the literature before. The momentum operators in this coordinate system are derived for the first time from the Hamilton equations of motion and used to construct the Hamiltonian operator. The resulting Hamiltonian comprises a kinetic energy T and a total potential V_Total consisting of the Coulomb potential and a quantum potential. It is shown that the participation of the quantum potential and the accompanied quantum forces in the force interaction within H₂⁺ is essential to develop an electronic motion consistent with the prediction of the probability density function |Ψ|². The motion of the electron in H₂⁺ can be either described by the Hamilton equations derived from the Hamiltonian H = T_K + V_Total or by the Lagrange equations derived from the Lagrangian H = T_K ? V_Total. Solving the equations of motion with different initial positions, we show that the solutions yield an assembly of electronic quantum trajectories whose distribution and concentration reconstruct the σ and π molecular orbitals in H₂⁺. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Spin-free quantum chemistry. XXVI. The Ising,small-bipolaron theory of cuprate superconductivity

The Ising, small-bipolaron (ISB ) theory is a strong-coupling theory of cuprate superconductivity which is based on the negative-U, Hubbard Hamiltonian. Its ground state is composed of (small) bipolarons and (small-bipolaron) holes with a vibronically induced, bipolaron-hole exchange interaction, J_BH, between them. The energy gap, Δ(0), is taken to be equal to the dissociation energy of a small bipolaron and which, since it is defined spectroscopically, is not an order parameter. The application of the Ising mean-field theory to the highly degenerate ground-state yields a second-order phase change with kT_C/2 = J_BH and a real order parameter, Ω(T), which is valid over the entire temperature range from zero to T_C. Near T_C, the Ising free-energy functional takes the same form as does the Landau. In the presence of an electromagnetic field, the Ising functional is a generalization of the Ginzburg-Landau functional which employs a complex order parameter and which is invariant under the electromagnetic gauge transformation. The breaking of the gauge invariance yields the London theory of superconductivity. © 1996 John Wiley & Sons, Inc.     

Formation of Stilbene Azo-Dimer by Direct Irradiation of p-Azidostilbene†

Triplet arylnitrenes may provide direct access to aryl azo-dimers, which have broad commercial applicability. Herein, the photolysis of p-azidostilbene ( 1 ) in argon-saturated methanol yielded stilbene azo-dimer ( 2 ) through the dimerization of triplet p-nitrenostilbene (³ 1N ). The formation of ³ 1N was verified by electron paramagnetic resonance spectroscopy and absorption spectroscopy (λ_max ~ 375 nm) in cryogenic 2-methyltetrahydrofuran matrices. At ambient temperature, laser flash photolysis of 1 in methanol formed ³ 1N (λ_max ~ 370 nm, 2.85 × 10⁷ s⁻¹). On shorter timescales, a transient absorption (λ_max ~ 390 nm) that decayed with a similar rate constant (3.11 × 10⁷ s⁻¹) was assigned to a triplet excited state (T) of 1 . Density functional theory calculations yielded three configurations for T of 1 , with the unpaired electrons on the azido (T_A) or stilbene moiety (T_Tw, twisted and T_Fl, flat). The transient was assigned to T_Tw based on its calculated spectrum. CASPT2 calculations gave a singlet–triplet energy gap of 16.6 kcal mol⁻¹ for 1 N ; thus, intersystem crossing of ¹ 1N to ³ 1N is unlikely at ambient temperature, supporting the formation of ³ 1N from T of 1 . Thus, sustainable synthetic methods for aryl azo-dimers can be developed using the visible-light irradiation of aryl azides to form triplet arylnitrenes.     

Effect of hydration andpH on the thermal stability of proteinase K

The effect of hydration andpH on the thermal stability of proteinase K was studied in the temperature range 310–450 K by differential scanning calorimetry. The dependences of the denaturation temperatureT _d, the specific enthalpy of denaturation H _d and the maximum of excess apparent specific heat capacityC _ex ^max upon the degree of hydrationh and thepH of the buffers used are presented. The relation betweenT _d andh is of the Flory-Garrett's type. By means of Ooi's model, the two components of the denaturation enthalpy arising from hydration and conformational change, respectively, were estimated. The fact that the specific denaturation enthalpy of proteinase K is very low may be attributed to its very low enthalpy of conformational change per heavy atom.Dedicated to Prof. Menachem Steinberg on the occasion of his 65th birthdayThis major project was supported by the National Natural Science Foundation of China.     

Zero-field mobilities in helium: highly accurate values for use in ion mobility spectrometry

The zero-field mobilities of 46 atomic ions in helium are calculated as functions of the gas temperature in an ion mobility spectrometer. The calculations are based on highly accurate, ab initio potential energy curves obtained in the last few years. In general, they start from a small value at low temperature, rise steadily to a maximum at some specific temperature, T _max , and then decline at higher temperatures. The ratio of T _max to the dissociation energy (well depth) of the ion-neutral interaction potential is shown to be approximation the same for all singly-charged ions and a few multiply-charged ions.     

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     

Conformational energy contribution to the heat of solution in polymer–solvent systems. Part I. Theory

The conformational energy contribution (ΔU_conf) to the heat of solution in polymer-solvent systems is presented and discussed in connection with chain conformational properties. In particular, ΔU_conf has been discussed in terms of various possible mechanisms of coil deformation.     

Molecular van der Waals symmetry affecting bulk properties of condensed phases: melting and boiling points

Qualitative analysis of the trends in melting temperatures T _m and boiling temperatures T _b of organic compounds and related substances supports a concept of van der Waals symmetry suggested earlier by the authors. Data for substituted methanes, ethanes, ethylenes, benzenes and cyclohexanes, reveal linear T _b versus M ^α patterns but usually non-uniform T _m versus M ^α patterns (where M is the molecular mass, α varies from 0.5 to 1). In the same set of isomers, T _m and T _b often change in different succession. To explain the observed trends, a local van der Waals field U that acts on a molecule in a solid or liquid phase, was represented by a sum of an averaged long-range field U ₀ from all molecules, and a short-range “contact” term W determined by a molecular shape. Variations of T _m and T _b among closely related substances correspond to different strength of perturbation of U ₀ ^(C) (in a crystal) and U ₀ ^(L) (in a liquid) by W. Higher T _b of isomers with medium-symmetry molecules (like 1,2-disubstituted benzenes and cyclohexanes) reflect the better fitting of their molecules to a local molecular environment in a liquid (that contains vacancies). Highly symmetrical quasispherical molecules (e.g., C₂Cl₆ or C₆F₁₂) produce a stabilised solid and destabilised liquid state, hence their molecular crystals easily sublime rather than melt at ambient pressure. Dedicated in memory of Professor Petr M. Zorky     

Determination of the ionic radii by means of the Kohn–Sham potential: Identification of the chemical potential

Under the Kohn–Sham theory, we examine solutions for the equations δT_S/δρ(r) = 0 and δT_S/δρ(r) = ν_KS(r) that link the chemical potential of the electronic system with the effective Kohn–Sham potential through μ = ν_KS(r) + δT_S/δρ. For single ions, we identify the chemical potential with the eigenvalue of the frontier orbital when the atom is in the limit of full ionization. For the case of cations, the chemical potential is found above ?(I + A)/2 and has the property of grouping ions with the same chemical characteristics. For the anion instead, the chemical potential is fixed at the ionization energy. By solving the above equations numerically, two radial points called r_? and r₊ are obtained and compared with the Shannon–Prewitt ionic radius. Moreover, we found for the halide series, that r_? is numerically equivalent to rm, the radii where the electrostatic potential has its minimum, but shows different behavior upon charge variation. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Conformational stability,barriers to internal rotation,structural parameters,ab initio calculations,and vibrational assignment of cyclopropanecarboxaldehyde

The asymmetric torsional potential function, conformational energy difference, vibrational frequencies, and structural parameters of Cyclopropane-carboxaldehyde have been obtained from ab initio calculations at the 3–21G and/or 6-31G^* baiss set levels. These results have allowed for a reinterpretation or clarification of some of the corresponding results obtained from experiment. The conformations that have the oxygen atom oriented cis and trans to the three-membered ring are observed and calculated to be the most stable and high energy forms in the gaseous phase, respectively. From the ab initio calculations using the 6–31 G^* basis set, the energy difference between the two conformers is 114 cm^–1. For the liquid, the trans conformer is more stable and is the only rotamer present in the annealed solid. Based on a combination of results obtained from ab initio calculations, microwave spectroscopy, and the electron diffraction technique,r _o structural parameters have been obtained for both conformations.     

Soret Coefficients for Aqueous Polyethylene Glycol Solutions and Some Tests of the Segmental Model of Polymer Thermal Diffusion

A thermogravitational cell is used to measure Soret coefficients (s) for dilute binary aqueous solutions of ethylene glycol, diethylene glycol, triethylene glycol, tetraethylene glycol, and polyethylene glycol (PEG) fractions with average molecular weights from 200 to 20,000 g-mol^–1. The cell design allows the top and bottom halves of the solution column to be withdrawn and injected into a high-precision HPLC differential refractometer detector for analysis. Previously reported mutual diffusion coefficients D and the measured Soret coefficients are used to calculate thermal diffusion coefficients D _T. s and D vary with the PEG molecular weight M as M ^+0.53 and M ^–0.52, respectively; hence, D _T = sD is essentially independent of M. The segmental model of polymer thermal diffusion predicts D _T = D_seg U _S/RT ², where D _seg is the segment diffusion coefficient, U _S the solvent activation energy for viscous flow, R the gas constant, and T the temperature. The predicted D _T values, although independent of M, are too large by a factor of five. Additional tests of the segmental model are provided using literature data for polystyrene + toluene, n-alkane + CCl₄, and n-alkane + CHCl₃ solutions. Agreement with experiment is not obtained. In particular, the measured D _T values for the alkane solutions are negative.     

Peptide models XXIII. Conformational model for polar side‐chain containing amino acid residues: A comprehensive analysis of RHF,DFT, and MP2 properties of HCO‐L‐SER‐NH2

Geometric and energetic properties of a diamide of serine, HCO‐NH‐L ‐CH(CH₂OH)CO‐NH₂, are investigated by standard methods of computational quantum chemistry. Similarly to other amino acid residues, conformational properties of HCO‐L ‐Ser‐NH₂ can be derived from the analysis of its E=E(ϕ,ψ;χ₁,χ₂) hypersurface. Reoptimization of 44 RHF/3‐21G conformers at the RHF/6‐311++G** level resulted in 36 minima. For all conformers, geometrical properties, including variation of H‐bond parameters and structural shifts in the torsional space, are thoroughly investigated. Results from further single‐point energy calculations at the RHF, DFT, and MP2 levels, performed on the entire conformational data set, form a database of 224 energy values, perhaps the largest set calculated so far for any single amino acid diamide. A comprehensive analysis of this database reveals significant correlation among energies obtained at six levels of ab initio theory. Regression parameters provide an opportunity for extrapolation in order to predict the energy of a conformer at a high level by doing explicit ab initio computations only for a few selected conformers. The computed conformational and relative energy data are compared with structural and occurrence results derived from a nonhomologous protein database incorporating 1135 proteins. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 626–655, 2000     

Model for Conformational Relaxation of Flexible Conjugated Polymers: Application to p‐Phenylenevinylene Trimers in Nonpolar Solvents

Photoexcitation of flexible conjugated polymers is invariably followed by a fast conformational/torsional relaxation towards a configuration favouring coplanarity of the conjugated segments. In general, the experimental relaxation rate constant (k_CR) depends on the solvent viscosity (η) and temperature (T), and is not proportional to T/η. A theory capable of explaining the observed dependence of k_CR on T and η over a wide range of these variables is not available. This gap is filled here by presenting a stochastic model that includes the participation of the oligomer side chain in storing and dissipating the stresses induced by photoexcitation. The model is able to account for the softening of solute–solvent interactions and its predictions are found to be in excellent agreement with the observed relaxation rate constants of a series of substituted p‐phenylenevinylene trimers [ChemPhysChem 2009 , 10, 448–454] on T, η and the size of the side‐chains.