Daniel E. Martire

The effect of quasispherical solutes on the nematic to isotropic transition in liquid crystals

When nonmesomorphic solutes are added to nematic liquid crystals, the nematic–isotropic transition temperature is depressed and a two‐phase region is observed. The slopes, βn and βi, of the nematic and isotropic phase boundary lines in the reduced nematic–isotropic transition temperature (T*) vs solute mole fraction (x) diagrams are reported for binary mixtures of quasispherical solutes with nematic liquid crystals. The systems studied are Me4Sn, Et4C, Et4Sn, Pr4Sn, Bu4Pb, and Bu4Sn (Me = methyl, Et = ethyl, Pr = propyl, and Bu = butyl), mixed with p‐methoxybenzylidene‐p′‐n‐butylaniline (MBBA), and CCl4 mixed with p‐p′‐di‐n‐hexyloxyazoxybenzene (DHAB). Also reported are infinite dilution solute activity coefficients for several mixtures involving Et4C and CCl4. The experimental results are compared with predicted values from statistical–mechanical theories based on (a) a lattice model of hard rectangular parallelepipeds and cubes, (b) a virial expansion treatment of hard spherocylinders and spheres, and (c) a proposed modification of a mean field treatment (Maier–Saupe type) of axially symmetric and spherical molecules. All three models correctly predict the observed trend of increasing βn and βi with increasing solute size and yield predicted slopes which are at least within a factor of 2 of the experimental slopes. The modified mean field approach is found to give the best agreement with the activity coefficient data. A simple experimental method is proposed for estimating the effect of potential impurities (x?0.01) on the nematic–isotropic transition, and possible directions for future research in this area are suggested.When nonmesomorphic solutes are added to nematic liquid crystals, the nematic–isotropic transition temperature is depressed and a two‐phase region is observed. The slopes, βn and βi, of the nematic and isotropic phase boundary lines in the reduced nematic–isotropic transition temperature (T*) vs solute mole fraction (x) diagrams are reported for binary mixtures of quasispherical solutes with nematic liquid crystals. The systems studied are Me4Sn, Et4C, Et4Sn, Pr4Sn, Bu4Pb, and Bu4Sn (Me = methyl, Et = ethyl, Pr = propyl, and Bu = butyl), mixed with p‐methoxybenzylidene‐p′‐n‐butylaniline (MBBA), and CCl4 mixed with p‐p′‐di‐n‐hexyloxyazoxybenzene (DHAB). Also reported are infinite dilution solute activity coefficients for several mixtures involving Et4C and CCl4. The experimental results are compared with predicted values from statistical–mechanical theories based on (a) a lattice model of hard rectangular parallelepipeds and cubes, (b) a virial expansion treatment of hard spherocylinders and spheres, and (...

Molecular Theory of Liquid Adsorption Chromatography

Abstract A statistical-mechanical theory, based on a lattice model, has been developed to address the molecular mechanism of retention and selectivity in both normal-phase and reversedphase liquid adsorption chromatography. The model is a natural “competitive-equilibrium” one, where possible contributions from solvent-solvent and solute-solvent interactions, and, hence, from solution nonideality, are not neglected. Homogeneous and heterogeneous adsorbent surfaces, single-solvent and binary mixed-solvent mobile phases, and solute molecules of different size and shape are treated. Practical applications of the theory are presented to demonstrate its utility and significance. For homogeneous adsorbents and neat solvents, the molecular energetics of retention and selectivity are examined, with special emphasis on the effects of solute size and shape, and, relatedly, the modes of solute adsorption. Separations of geometrical isomers and homologous series in real and simulated chromatographic processes are inve...

Statistical Mechanics of Rodlike Particles. II. A Scaled Particle Investigation of the Aligned→Isotropic Transition in a Fluid of Rigid Spherocylinders

Expressions for the equation of state and the chemical potential are derived as functions of density and temperature for both a perfectly aligned and a completely isotropic fluid of rigid spherocylinders through consideration of the reversible work W(α, λ, ρ) necessary to add a scaled spherocylinder of radius α and cylindrical length λ at an arbitrary fixed point in the fluid. A first‐order aligned→isotropic transition is obtained and the transition densities, free volume fractions, and entropy change determined at various values of the radius and cylindrical length of the spherocylinders. Although the densities of the two phases and the density change at the transition depend on the radius of the particles, the entropy change and the free volume fractions of the two phases at the transition depend only on the length‐to‐breadth ratio x, indicating that the transition results from packing effects alone. The behavior of the expansivity and the compressibility of the system near the transition is also determ...

Generalized treatment of spatial and temporal column parameters, applicable to gas, liquid and supercritical fluid chromatography : I. Theory

Abstract Starting with Darcys law, rearranged and expressed in terms of the local carrier density at a given temperature, general equations are derived for the spatial and temporal density distribution functions, average densities and column profiles of the mobile-phase fluid, and the observed (column-averaged) capacity factor(s) and column profiles of the solute component(s). These more direct, exact and tractable equations are applied to gas, liquid and supercritical fluid chromatography, and the results are discussed.

Plate height theory for compressible mobile phase fluids and its application to gas, liquid and supercritical fluid chromatography

Abstract General expressions for apparent plate height are derived in terms of temporal and spatial average values of local plate height, solute capacity factor and mobile phase density. The general expressions are applied to the appropriate expressions for gas chromatography, liquid chromatography and supercritical fluid chromatography with open tubular and packed columns. For gas chromatography, the equations reduce to the equations presented earlier by Giddings. For liquid chromatography, the equations reduce to those for local plate height. Predicted results for supercritical fluid chromatography are compared to experimental results reported in the literature.

A general model of liquid—solid chroamtography with mixed mobile phases involving concurrent adsorption and partition effects

Abstract Liquid—solid chromatography (LSC) with mixed mobile phases is discussed in terms of classical thermodynamics. It is shown that a rigorous consideration of solute and solvent competitive adsorption in systems with a non-ideal mobile (bulk) phase and a surface-influenced non-ideal stationary phase leads to a new general equation for the distribution coefficient of a solute involving concurrent adsorption and partition effects. For special sets of parameters this equation reduces to familiar limiting expressions describing either adsorption or partition effects. A detailed discussion is presented for LSC systems with binary phases, in which bulk and surface solutions are assumed to be regular ones.

The effect of quasispherical and chainlike solutes on the nematic to isotropic phase transition in liquid crystals

The effects of solute molecular structure (size, shape and flexibility) and solvent molecular structure (length‐to‐breadth ratio and end‐chain flexibility) on nematic phase stability in dilute binary mixtures of nonmesomorphic solutes and nematogenic solvents are examined through experiment and theory. Addition of the perturbing solute to the liquid‐crystalline solvent leads to depression of the nematic–isotropic (NI) transition temperature and formation of a two‐phase region. Directly determined moduli of the slopes, βn and βi, of the nematic and isotropic phase boundary lines in the reduced NI transition temperature (T*) vs solute mole fraction (x2) diagrams are reported for quasispherical and chainlike solutes with two nematogenic solvents. The systems studied are the quasispheres Et4C (tetraethylmethane) and R4Sn (R = CH3, C2H5, n‐C3H7 and n‐C4H9) and the chains n‐C8H18 through n‐C14H30, mixed with p‐methoxybenzylidine‐p′‐n‐butylaniline (MBBA) and p‐n‐pentyl‐p′‐cyanobiphenyl (5CB). Also reported are i...

Meaningful error analysis of thermodynamic measurements by gas-liquid chromatography

Abstract The usefulness of a simplified error analysis procedure for infinite-dilution partition coefficients ( K R as measured by gas—liquid chromatography is established by comparison of calculated with experimental reltive standard deviations. It is shown that the determination of the column liquid-phase volume, V L , is the largest source of random error, other error sources, such as that for retention times, being trivial by comparison. As a result, simple apparatus is found to be adequate for the described measurements. An inter-laboratory comparison of partition coefficients shows, further, that the reproducibility of these data can be as good as ±1%, these finding, in addition, execellent agreement with those determined by a static technique.

Statistical Mechanics of Rodlike Particles. III. A Fluid of Rigid Spherocylinders with Restricted Orientational Freedom

A scaled particle treatment is applied to a fluid of rigid spherocylinders of radius a and cylindrical length l, with cylindrical axes permitted to point in only three mutually perpendicular directions. Singling out one of these, by means of some arbitrary device such as an infinitesimal applied field, and denoting by s the fraction of rods in each of the directions perpendicular to this “preferred” direction in any given configuration of the system, an expression is derived for the configurational Helmholtz free energy Ac as a function of s, and an equation determining s, that value of s which minimizes Ac, is obtained. At densities below some critical value ρc, the only solution to the latter equation is s = 13, but for ρ > ρc, an anisotropic solution is also possible. A first‐order anisotropic–isotropic transition is observed and the transition densities, free volume fractions, and entropy change are determined at two values of a and for ratios l / a from 2 through 18. Thus, that transition which Zwa...

A Quasi-Chemical Lattice Treatment of Rod-like Molecules. Application to the Nematic-lsotropic Transition

Abstract A quasi-chemical treatment is applied to a face-centered cubic lattice system containing N0 holes (or “solute molecules”) and Nx interacting rods of length-to-breadth ratio x. The resulting partition function is then maximized with respect to the numbers of rods in each of the six allowed directions on the lattice. Two stable “phases” are obtained: a completely aligned “phase”, more stable at lower volume fractions of holes ν0, and an isotropic “phase”, more stable at higher ν0s. When alignment is not favored energetically, the relative stabilities of these two “phases” are temperature independent, but when alignment is favored, this is no longer the case and a first-order aligned → isotropic transition is observed. When the dependencies of the transition temperature and enthalpy of transition on the segment interaction energies of the system, on ν0, and on x are determined, it is found that our simple model is able to predict a number of important aspects of the behavior of nematogenic substanc...