Interaction between polymers: Dispersion energy of two infinite linear chains

Using the newly developed discrete variant of the k · p perturbation theory for linear chains an expression is derived for the dispersion interaction between two infinite chains valid for both insulating and metallic polymers. It is shown that the formally divergent dispersion energy is also finite for metallic systems, but it may be considerably enhanced in polymers with partly filled bands as compared with insulting ones. The accuracy of the proposed k · p expansion is investigated on model chains through comparisons with direct ab initio Hartree–Fock crystal orbital calculations. Applying second order perturbation theory an explicit formula in terms of band parameters is given for the numerical calculation of the dispersion energy.     

Kinetics and linear free energy relationship of wittig reaction between substituted benzaldehydes and substituted benzylidenetriphenylphosphorane

Kinetics and linear free energy relationship (LFER) of Wittig reaction of ylides of intermediary stability have been investigated. Evidences are presented which indicate that under such cases the reaction follows a second order rate law, first order in phosphorane and aldehyde respectively, and furthermore that electron withdrawing substituents on both benzaldehyde and benzylidenetriphenylphosphorane impose rate enhancement effect upon the reaction. The mechanism of the reaction is discussed on the basis of the experimental findings.     

Confinement free energy and chain conformations of homopolymers confined between two repulsive walls

Lattice Monte Carlo simulations of polymer solutions confined between two parallel plates were performed. The confinement free energy Deltamicro(conf) per chain and the radius of gyrations of the chains parallel and perpendicular to the plates were obtained. When the concentration of the confined solution is above the overlap concentration, Deltamicro(conf) is found to scale with Na/D in a power law, betaDeltamicro(conf) approximately (Na/D)(m), with an exponent m=1.10+/-0.02 for athermal walls where N is the number of monomers in a chain, D is the slit width, and a is the lattice spacing. The presence of a weak attractive polymer/wall interaction epsilon(w) does not change the scaling variable, but the exponent m increases slightly. Extrapolating the results to melt would suggest that the predictions made by de Gennes [C. R. Acad. Sci. Paris II 305, 1181 (1987)] about the confinement free energy cost per chain in polymer melt is correct as far as the scaling variable is concerned, but is incorrect about the exponent m observed. The implication of this result on the predicted force between plates immersed in polymer melt is discussed. The parallel dimensions of the confined chain is expanded when the slit width D is narrow, however, the expansion is reduced at high concentration. It is conceivable that in melt the chain is not expanded when confined in a repulsive slit.     

A new concept for the application of linear free energy relationships in catalysis

Linear free energy relationships (LFERs) have been used in heterogeneous catalysis for a long time. Their application to heterogeneous catalytic systems have been based on the original substituent concept introduced by Hammett [K.J. Laidler, Chemical Kinetics, Harper Collins Publishers, New York, 1987, pp. 246–251.]. This work deals with the idea of validating a new concept for the application of LFER in heterogeneous catalysis. Following this idea, the considered reactions center is the active site on the catalyst surface, rather than that of the reacting molecule. The confirmation of a successful application to HDS and hydrogenation reaction will be shown as a preliminary example of the potential of the new approach. The implications for catalyst design will be discussed.     

Numerical comparison of HCCI combustion mode between a free piston linear engine and traditional crankshaft engine

Journal of Thermal Analysis and Calorimetry - The free piston linear engine (FPLE) eliminates the crankshaft components and supports variable compression ratio operation. This characteristic makes...     

Extension of linear free energy relationships to multiple ionizations

The linear additivity of free energies of ionization of substituted acids relative to the unsubstituted parent acid is described in terms of the Hammett relationship and as the weighted sums of microscopic free energies for benzenetricarboxylic acids.     

Correlations between two sets of angular relation equations

It is shown here that the angular relation equations between direct and reciprocal vectors are very similar to the angular relation equations in Euler’s theorem. These two sets of equations are usually treated separately as unrelated equations in different fields. In this careful study, the connection between the two sets of angular equations is revealed by considering the cosine rule for the spherical triangle. It is found that understanding of the correlation is hindered by the facts that the same variables are defined differently and different symbols are used to represent them in the two fields. Understanding the connection between different concepts is not only stimulating and beneficial, but also a fundamental tool in innovation and research, and has historical significance. The background of the work presented here contains elements of many scientific disciplines. This work illustrates the common ground of two theories usually considered separately and is therefore of benefit not only for its own sake but also to illustrate a general principle that a theory relevant to one discipline can often be used in another. The paper works with chemistry related concepts using mathematical methodologies unfamiliar to the usual audience of mainstream experimental and theoretical chemists.     

A structure registry condition for the interaction energy between two solids

The interaction energy between two periodic crystals obeys a structure registry condition. When the 2D periodic structures in the atomic planes parallel to the surfaces of the two crystals are not coincident, the energy contribution which accounts for the discrete characteristics of the solids along these planes vanishes. The remaining continuum potential is then unable to discriminate between the atomic distribution of surface atoms when one crystal is laterally translated with respect to the other. This registry condition leads to drastic changes in the interaction energy between two ionic crystals and can be responsible for the disappearance of specific structural properties in solids.     

Characterization of cyclofructan-based chiral stationary phases by linear free energy relationship

Cyclofructans (CFs), a new class of chiral selectors, have been recently introduced for application in liquid chromatography and capillary electrophoresis. So far, derivatized CFs have performed interesting separation possibilities for a variety of compounds. The current work is focused on characterization of three different CF-based chiral stationary phases (CF-based CSPs), i.e. isopropyl carbamate cyclofructan 6 (IP-CF6), R-naphthylethyl carbamate cyclofructan 6 (RN-CF6) and dimethylphenyl carbamate cyclofructan 7 (DMP-CF7). The linear free energy relationship (LFER) model was used to reveal the dominant interactions participating in the complex retention mechanism. A set of 44 different test solutes, with known solvation parameters, was used to determine the regression coefficients of the LFER equation under two mobile-phase compositions in normal separation mode. The LFER results showed that hydrogen bond acidity, hydrophobicity and dipolarity/polarizibility mostly affect the retention and separation process on the CF-based columns in the studied separation systems.     

A recipe for the computation of the free energy barrier and the lowest free energy path of concerted reactions

The recently introduced hills method (Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12562) is a powerful tool to compute the multidimensional free energy surface of intrinsically concerted reactions. We have extended this method by focusing our attention on localizing the lowest free energy path that connects the stable reactant and product states. This path represents the most probable reaction mechanism, similar to the zero temperature intrinsic reaction coordinate, but also includes finite temperature effects. The transformation of the multidimensional problem to a one-dimensional reaction coordinate allows for accurate convergence of the free energy profile along the lowest free energy path using standard free energy methods. Here we apply the hills method, our lowest free energy path search algorithm, and umbrella sampling to the prototype S(N)2 reaction. The hills method replaces the in many cases difficult problem of finding a good reaction coordinate with choosing relatively simple collective variables, such as the bond lengths of the broken and formed chemical bonds. The second part of the paper presents a guide to using the hills method, in which we test and fine-tune the method for optimal accuracy and efficiency using the umbrella sampling results as a reference.     

Microhardness and surface free energy in linear polyethylene: The role of entanglements

The microhardness of a series of melt crystallized samples of linear polyehtylene was investigated in a wide range of molecular weights. The x-ray long period was analyzed to study the variation of the hardness-derived constantb as a function of molecular weight (M ). It is pointed out thatb offers a measure of the hardness depression due to the finite thickness of the lamellar crystals. The data obtained show that the increase and final leveling-off (forM 200 000) ofb withM parallels the concurrent increase of the surface free energy, as derived from DSC experiments. Results are discussed using the concept og chain folded lamellae as thermodynamically stable non-homogeneous microphases. Comparison of experimental and calculated data supports the view that the number of molecular entanglements, segregated onto the defective surface boundary of the heterogeneous crystals influence the shearing mechanism within the mesocrystals and thereby control the yield behavior of the material.     

A general formula for the rate of resonant transfer of energy between two electric multipole moments of arbitrary order using molecular quantum electrodynamics

A general expression is derived for the matrix element for the resonant transfer of energy between an initially excited donor species and an acceptor moiety in the ground state, with each entity possessing an electric multipole moment of arbitrary order. In the quantum electrodynamical framework employed, the coupling between the pair is mediated by the exchange of a single virtual photon. The probability amplitude found from second-order perturbation theory is a product of the electric moments located at each center and the resonant multipole-multipole interaction tensor. Using the Fermi golden rule, a general formula for the rate of energy transfer is obtained. As an illustration of the efficacy of the theory developed, rates of excitation energy exchange are calculated for systems interacting through dipole-quadrupole, dipole-octupole, quadrupole-quadrupole, and the familiar dipole-dipole coupling. For each of the cases examined, the near- and far-zone limits of the migration rate are calculated from the result valid for all donor-acceptor separations beyond wave function overlap. Expression of the octupole contribution to the transfer rate in terms of its irreducible components of weights 1 and 3 leads to new features. The octupole weight-1 term is found to contribute only when the interaction is retarded, while the dipole-octupole weight-1 contribution appears as a higher-order correction term to the dipole-dipole rate. Order of magnitude estimates are given for the contributions of dipole-quadrupole and dipole-octupole terms relative to the leading dipole-dipole rate for near-, intermediate-, and far-zone separations to further understand the role played by higher multipole moments in the transfer of excitation and the mechanism dominating the process.