Repulsive Intermolecular Forces Research Articles

The effect of pressure on the Raman spectra of solids. VII. The internal Raman bands in solid and coordinated pyridine

The pressure dependences of the internal Raman-active modes of solid pyridine and pyridine-d5 in both the crystalline and glassy modifications as well as of the complexes Zn(py)2Cl2, Ni(py)2Cl2, and Ni(py)4Cl2 are reported. When pyridine is frozen by the application of pressure, some ring modes as well as those involving the hydrogen atoms reflect this transformation. Upon the coordination of pyridine to metal ions, the ring vibrations show appreciable blue shifts. The pressure dependences of ν1, the C–C stretching mode, and ν12, the in-plane ring bending mode of the pyridine rings, are discussed in detail. The unusually high d5–h5 isotopic ratio of ν12 and its contrasting pressure dependences in the liquid and condensed phases of pyridine-d5 are explained. The association of pyridine molecules in the condensed phase does not occur through hydrogen bonds and the C–H stretching modes, in particular, show that repulsive intermolecular forces become very significant at higher pressures. The ratio of the intensities Iν12/Iν1 varies linearly with the strength of the M–N bonds in a series of pyridine complexes and a correlation also exists between Iν12/Iν1 and ∂ν12/∂p. The vibrations ν1 and ν2 are coupled through Fermi resonance in pyridine and its complexes and the pressure dependence of the Fermi resonance constant W is calculated for Zn(py)2Cl2. The C–H stretching modes reflect the presence of more than one distinct pyridine group in the lattice and are of much lower intensity than in complexes where only one distinct pyridine group is found.

Adsorption of CO on Rh(100) studied by infrared reflection–absorption spectroscopy

The interaction of CO with a Rh(100) surface at 90 and 300 K has been investigated with infrared reflection–absorption spectroscopy (IRAS). Absorption bands due to the C–O stretch are found in both the linear and bridging regions at all coverages for both adsorption temperatures. For adsorption at 300 K, an ordered CO layer is formed at ∼0.4 monolayers (ML) as evidenced by a sharp, highly symmetrical, linear-CO band. At θCO>0.45 ML, the reduction in intermolecular separation and increasing intermolecular repulsive forces in the CO adlayer are evidenced by the increased broadness of both the linear- and the bridged-CO bands. CO adsorption at 90 K yields a nonuniform adlayer dominated by island formation at θCO<0.5 as indicated by peak splitting of the linear-CO band and the presence of a broad bridged-CO band. At θCO∼0.5, a highly ordered CO adlayer is suggested by the appearance of a highly symmetrical linear-CO band as well as the formation of a sharp c(2×2) LEED pattern. The presence of multiple components in the linear-CO band along with the drastic variations in the relative absorption intensities for both CO bands at coverages between 0.5 and 0.7 ML imply that the CO adlayer undergoes a phase transition within this coverage regime. These IRAS data are in agreement with the observed transition of a sharp c(2×2) pattern at θCO=0.5 to an ordered LEED pattern with a p(4×4)R45° coincidence structure at θCO=0.7. From a series of temperature-dependent IRAS measurement, it has been determined that the difference in binding energy of linear and bridged sites at θCO=0.2–0.5 ranges from ∼0.1 to ∼0.4 kcal/mol with the bridged-bound CO being the more stable species.

Condensation of DNA by trivalent cations. 1. Effects of DNA length and topology on the size and shape of condensed particles

In vitro condensation of DNA by multivalent cations can provide useful insights into the physical factors governing folding and packaging of DNA in vivo. We have made a detailed study of hexammine cobalt (III) induced condensation of 2700 and 1350 base pair (bp) fragments of plasmid pUC12 DNA by electron microscopy and laser light scattering. The condensed DNA takes the form of toroids and rods. Both are present in all condensates, but the proportion of toroids is higher with the larger fragments. The intact, closed circular plasmid produces smaller particles than the linear fragments. The size of a particle is independent of DNA fragment length. Two hours after adding the condensing agent, a typical toroid is about 800 A in diameter; the outer radius (R1) is approximately 400 A, and the inner radius (R2) is approximately 140 A for both sets of fragments. These dimensions are relatively stable, but there is sufficient change in both R1 and R2 to produce approximately 50% increase in volume from 2 to 24 h. A typical rod at 2 h is about 1800 A long and 300 A wide. The distribution of rod lengths is similar to that of mean toroid circumferences pi (R1 + R2), and the distribution of rod widths is similar to that of toroidal widths (R1-R2). The 2700-bp fragments show a significantly higher ratio of toroids to rods than the 1350-bp fragments. Both types of particle are multimolecular. The average number of molecules/particle, calculated from the above dimensions, assuming hexagonally packed B-form DNA with a center-to-center spacing of 27 A, is 13 +/- 4 for condensates of 2700-bp fragments and 26 +/- 11 for those of 1350-bp fragments. Monomolecular condensates of much larger DNAs have similar dimensions, suggesting that size is governed primarily by the balance of attractive and repulsive intermolecular forces rather than by the entropic factors associated with incorporation of a number of small particles into a larger one. The similar dimensions and volumes of toroids and rods indicate that the free energy cost of continual bending in toroids, minus that gained by extra net attraction in a cyclic particle, is comparable to that of abrupt bending or kinking in rods. Although the condensed particles are multimeric, their distinct toroidal or rodlike shapes distinguish them from the random aggregates that would be generally expected from the multimolecular association of large, flexible polymers.

Molecular interactions and interface properties of nematic liquid crystals

Molecular perturbation methods are used to derive an approximate free-energy functional for nonuniform nematic liquids with anisotropic repulsive and attractive intermolecular forces. The free energy is simplified to a Landau–de Gennes form, providing expressions for the elastic constants and surface fields of the latter in terms of microscopic interactions. These expressions are evaluated using the Gay–Berne model potential (GB) between rigid rod-like molecules. Short-range attractive and repulsive components of that potential are found to give similar contributions to the Landau–de Gennes parameters, but these are strongly counterbalanced by long-range attractive contributions. The theory is applied to orientational alignment and nematic wetting at the free liquid–vapor interface. The preferred nematic alignment is predicted to be perpendicular to the interface, due to a weak dominance by repulsive and short-range attractive forces. It is found that wetting by the nematic phase changes from complete to incomplete as the molecular elongation increases.

Der Einfluß der Nahordnungsstruktur auf die chemischen Verschiebungen der Aromatenprotonen in flüssigen Mischungen von Acetonitril mit 5 aromatischen Lösungsmitteln

AbstractThe proton chemical shifts of benzene, thiophene, pyridine, pyridazine and pyrimidine were measured at 298 K as a function of concentration in acetonitrile. The susceptibility values that are needed to correct the chemical shifts were evaluated according to a nmr method. The local structure of the mixtures were interpreted by using the model of hard convex bodies, assuming the predominance intermolecular repulsive forces at high densities. So it was possible to calculate the contact values of the pairdistribution function. The derivatives of these contact values were compared with the derivatives of the chemical shifts as a function of concentration. — This allows to identify different local structurs around the protons of the aromatic molecule.

Statistical Theory of Surface Tension and Molecular Orientations in Nematic Liquid Crystals.II. The Nematic-Isotropic Interface

The surface tension of the nematic-isotropic ( N - I ) interface is calculated in a mean field approximation for the system of rod-like molecules interacting via attraction as well as hard-core repulsion. It is found that the excluded volume effect favors the planar orientation of molecules at the N - I interface in contrast with the case of the nematic free surface at which the effect favors the normal alignment. Experimental behavior of nematogens such as 4- n -pentyl-4'-cyanobiphenyl (5CB) and 4-methoxybenzylidene-4'-butylaniline (MBBA) are analysed. Orientations of a molecule at the N - I interface and at the nematic free surface are explained consistently as effects of a counterbalance between the repulsive and attractive intermolecular forces.

The Local Structure in Liquid Mixtures of Acetonitrile with 6 Aromatic Solvents

AbstractThe chemical shifts of the methyl protons of acetonitrile were measured at 298 K as a function of concentration in 6 aromatic solvents. The local structure of the solutions are interpreted by using the model of hard convex bodies, assuming anisotropic aromatic shielding terms and intermolecular repulsive forces. So the angels α can be determined, which show the intermolecular orientation between the acetonitrile and the aromatic molecules. This way it is possible to calculate the angles β of the orientation between the aromatic molecules. Two different kinds of aromatic solvents could be identified: benzene, furane, thiophene‐ with intermolecular plane to plane angle β ≈ 60° pyridazine, pyridine, pyrimidin‐ with intermolecular plane to plane angle β ≈ 30°.

Statistical Theory of Surface Tension and Molecular Orientations at the Free Surface in Nematic Liquid Crystals

The surface tension γ is calculated in the mean field approximation in the system of rod-like molecules interacting via attraction as well as hard-core repulsion. It is found that the excluded volume effect favours the normal alignment of molecules at the free surface. The molecular orientations observed at the free surface are explained as an effect of counterbalance between the repulsive and attractive intermolecular forces as in the following: (1) normal to the surface (8CB, 5CB), (2) tilt against the surface, (3) transition between the normal and tilt orientations at a certain temperature T 0 lower than the nematic-isotropic transition temperature T c (MBBA, EBBA). The jump of γ at T c obtained in this work agrees with the experimental results.

ChemInform Abstract: VIBRATIONAL PHASE RELAXATION IN ETHANE AT MODERATE DENSITIES, INCLUDING THE CRITICAL REGION

The bandwidth of the isotropic component and the frequency of the ν3 (C–C stretch) Raman band of ethane have been measured for a range of densities at constants temperature, and for a range of temperatures at the critical density. No critical anomaly is observed. The rotation‐vibration coupling contribution to the bandwidth is calculated. The remaining contribution to the bandwidth increases with increasing density in a manner consistent with current theories that take into account both the repulsive and attractive intermolecular forces. However, the attractive force contribution cannot be related in a simple fashion to the macroscopic compressibility. Data taken over a wider range of density and temperature will be required to quantitatively determine the separate repulsive and attractive contributions to the width.

Molecular Structure and Mesomorphic Properties of Thermotropic Liquid Crystals — I

The influence of molecular structure on the mesomorphic properties of thermotropic liquid crystals is discussed. The role of intermolecular attractive and repulsive (steric) forces in determining the packing and consequently the mesomorphic behaviour of the molecules is described. A correlation between the geometry of the rigid core of the molecules and the mesomorphic properties is found. The intermolecular separation strongly influences the thermodynamic stability of the mesophase. Alkyl chains do not only fill in spaces but also take part in the molecular interactions and affect the packing

Van der Waals Picture of Liquids, Solids, and Phase Transformations

The van der Waals picture focuses on the differing roles of the strong short-ranged repulsive intermolecular forces and the longer ranged attractions in determining the structure and dynamics of dense fluids and solids. According to this physical picture, the attractive interactions help fix the volume of the system, but the arrangements and motions of molecules within that volume are determined primarily by the local packing and steric effects produced by the repulsive forces. This very useful approach, its limitations, and its successful application to a wide variety of static and dynamic phenomena in condensed matter systems are reviewed.

Vibrational phase relaxation in ethane at moderate densities, including the critical region

The bandwidth of the isotropic component and the frequency of the ν3 (C–C stretch) Raman band of ethane have been measured for a range of densities at constants temperature, and for a range of temperatures at the critical density. No critical anomaly is observed. The rotation-vibration coupling contribution to the bandwidth is calculated. The remaining contribution to the bandwidth increases with increasing density in a manner consistent with current theories that take into account both the repulsive and attractive intermolecular forces. However, the attractive force contribution cannot be related in a simple fashion to the macroscopic compressibility. Data taken over a wider range of density and temperature will be required to quantitatively determine the separate repulsive and attractive contributions to the width.

Chiral discrimination in the liquid state a hard-core model for the role of repulsive forces

We report a study of the rōle of repulsive intermolecular forces in chiral discrimination. A realistic model based on hard-core repulsive potentials, the RISM formalism, and a superposition approximation is used to compare the interaction between the same (dextro—dextro) and opposite (dextro—laevo) enantiomers of chlorofluoroacetonitrile in the liquid phase, at room temperature. Chiral discrimination arises through differences in pairwise packing in the two types of pair. Calculations are made also for the gas phase. The excess volume of mixing (−0.1 to −0.2 cm 3 mol 1̄), derived predominantly from nearest-neighbour contact distances, shows more efficent (d, l) contact packing. The excess enthalpy ( = 12 J mol −1, obtained by using an isotropic Lennard-Jones interaction, weights larger intermolecular distances and is endothermic. These results emphasize the need to consider the dependence of intermolecular orientational correlations on intermolecular separation in the interpretation of experimental data on chiral discrimination in liquids. Experimental results are not available for the system studied here, however the results are compatible with measured values for other systems.

The Raman spectrum of solid carbon dioxide at high pressure

Raman spectra of carbon dioxide were measured as functions of molar volume and temperature in the region 0 to 200 cm−1. In crystals constrained to remain at constant volume, the frequencies of the Raman active libron modes were found to shift much less with temperature than expected by comparison with solid nitrogen. In fact, when the slight expansion of the alloy steel cell is taken into account the frequency vs temperature plots show a slight positive temperature dependence as opposed to the fairly large negative shift observed in the nitrogen case. From these measurements, the value of the mode Gruneisen parameters (defined by γj=−d lnωj/d lnV) were determined to be 2.3±0.2, almost 3 times that predicted by the quadrupole–quadrupole model but in fairly good agreement with recent calculations by Gibbons and Klein, and Kobashi and Kihara. These are based on models which include short ranged intermolecular repulsive forces. Linewidths were measured and indicate that in carbon dioxide four phonon processes dominate the decay of the Eg mode, in contrast with nitrogen in which three phonon processes dominate.

Theory of Transport Coefficients for Moderately Dense Gases

A general introduction to and bibliography for transport phenomena in gases is provided. Methods for obtaining density expansions of transport coefficients from time-correlation functions in a moderately dense gas with short-range repulsive intermolecular forces are considered. A unified treatment of the two methods appearing in the literature (the $t$ method due to Cohen, Dorfman, and Ernst and the $\ensuremath{\epsilon}$ method due to Zwanzig) is given. Both of these methods lead to integral equations from which the first two terms in the density expansion of transport coefficients can be computed. However, because of many-body effects in the gas, both methods diverge when used to compute terms beyond the first two in these density expansions. Because of this divergence, it is necessary to prove that the $t$ and $\ensuremath{\epsilon}$ methods give the same results for the first two terms in the density expansion of transport coefficients. The required proof is provided, and we conclude that either the $t$ or $\ensuremath{\epsilon}$ method can be used to compute the first two terms in the density expansion of transport coefficients provided one assumes that the remaining (divergent) terms, which are neglected, do not contribute to the first two terms.

Application of the Mayer Method to the Melting Problem

The antiferromagnetic Ising model can also describe a gas with purely repulsive intermolecular forces, and a comparison of the two is made, the transition of such a `gas' to a solid-like structure being the analogue of the appearance of an antiferromagnetic structure. Three simple lemmas enable the asymptotic behaviour of the Mayer cluster sums to be related to other combinatorial problems on the lattice, such as that studied by Hammersley and Broadbent (1957). Some information on these problems is already available, but a detailed discussion is reserved to another paper. The Mayer formalism can be generalized to deal with the antiferromagnetic problem, with the conclusion that the transition is probably first-order and associated with a singularity of the Mayer b-series on the positive real axis of the z variable, but that there is a closer one on the negative real axis. The Mayer β-series can probably be extended beyond the transition and corresponds to a metastable liquid. Its divergence probably represents the absolute limit of the metastable state. The symmetry of the particular model used implies a second transition at a still higher density which may be likened to a change of crystal structure. (The gas of completely rigid molecules is a limiting case, and has only one transition, the transition curve then being a linear relation between P and T.) These considerations agree well with other work on the antiferromagnetic Ising model. A `solid-gas' critical temperature seems most unlikely for any realistic interaction, through it could occur for a sufficiently `soft' one.

Equations of state, physical properties and thermodynamic transformation. Intermolecular repulsive forces

The first page of this article is displayed as the abstract.

The replusive forces between isotopic molecules

It is usually assumed that the forces of attraction and repulsion between two molecules depend only on their electronic structures and are independent of the nuclear masses. While this assumption is undoubtedly true to a first approximation it fails to take into account the zero-point energy associated with the nuclear vibrations, which will modify the charge distribution both of the nuclei and of the electronic shells. Since the zero-point energy depends upon the nuclear mass, this may lead to differences between the behaviour of a pair of isotopic molecules such as H 2 and D 2 . If the restoring force of the nuclear vibration is not directly proportional to the displacement of the nuclei from their mean position, then the mean internuclear distance will be different for the two isotopes. The magnitude of this anharmonic effect can be calculated from spectrum data, and it is found that for H 2 and D 2 the difference is less than 10 -11 cm., and hence negligible. However, the energy of interaction of two molecules will not be a linear function of the inter­ nuclear distance within the molecules, so that even for harmonic oscillations the observed interaction will depend upon the magnitude of the zero-point energy. Both the attractive and the repulsive intermolecular forces will be affected in this way, but it is difficult to treat the former owing to the absence of any exact treatment of exchange forces between molecules. The problem is more easily attacked in the case of the Coulomb forces (which have a net repulsive effect), and the present paper constitutes an attempt to estimate the isotope effect for this type of force. It will be necessary to neglect the mutual deformation of the charge distributions caused by the approach of the two molecules. This assumption is usually made in dealing with Coulomb forces, and it is unlikely to introduce serious error in calculating the isotopic difference. The total Coulomb interaction between two molecules can then be written as G = G n + G n c + G e (1) where G n is the interaction between the nuclei of the two molecules, G ne the interaction between the nuclei of one molecule and the electron shell of the other, and G e the interaction between the two electron shells. The principles involved are most easily seen by considering G n for two diatomic molecules.