Single Transition Point Research Articles

THE MECHANISM OF COPOLYMER RETENTION IN INTERACTIVE POLYMER CHROMATOGRAPHY. II. GRADIENT SEPARATION

The molecular-statistical theory of polymer solutions in confined media is applied to the conventional chromatographic theory of gradient elution. This approach leads to the prediction of the special mode of interactive polymer chromatography: gradient elution at critical point of adsorption. We demonstrate theoretically and experimentally that under appropriate conditions elution of each compositionally homogeneous fraction of copolymer occurs at the critical mobile phase composition. This critical mobile phase composition depends only on the local structure of the copolymer chain and is independent of its molecular weight. As a consequence, gradient elution produces the chemical composition distribution of the copolymer. The theory provides the quantitative conditions for statistical copolymer chains to have a single transition point. Equations describing relationships between the critical eluent composition and the chemical composition and microstructure of macromolecules are developed. The experimental verification of the theory was performed by the normal phase isocratic and gradient elution of chlorinated polyethylene with various chemical compositions (chlorine content) and molecular weights. To the best of our knowledge, these experiments, for the first time, demonstrate the existence of the adsorption-desorption transition point for statistical copolymers. The gradient separation at the critical point of adsorption can be applied also to other complex polymers containing various types of molecular heterogeneity.

THE MECHANISM OF COPOLYMER RETENTION IN INTERACTIVE POLYMER CHROMATOGRAPHY. I. CRITICAL POINT OF ADSORPTION FOR STATISTICAL COPOLYMERS

A comprehensive analysis of interactive polymer chromatography is presented. Isocratic liquid chromatography of polymers at the critical eluent composition (the transition point where size-exclusion and adsorption interactions completely compensate each other) is currently used to separate functional oligomers and block copolymers. We have extended the concept of this critical elution chromatography to the cases of statistical copolymers as well as porous stationary phases with heterogeneous surfaces (viz., surfaces with both inert and active groups). The theory provides the quantitative condition for statistical copolymer chains to have a single adsorption-desorption transition point. The random copolymers with narrow chemical composition distribution (CCD) always posses such a point. For non-random copolymers this condition includes the comparison between the mean length of chain segments connecting the attractive walls of the pore and the chemical correlation segment characterizing the randomness of the copolymer microstructure or the surface of this pore. If the critical transition point exists, then the copolymer chains behave as hypothetical homopolymer chains with a single energy of interaction between the effective monomer units and the active groups at the surface. The relationship between this energy and the microstructure of copolymer chains has been also analyzed. If copolymer has a broad CCD, each compositionally homogeneous fraction has its own adsorption-desorption threshold. The partial transition points have been established for the copolymers with blocky or alternating microstructure. Only a portion of the copolymer chain effectively behaves as a homopolymer chain at these points. This property was used in the past for the separation of block copolymers according to the length of blocks comprised of the monomer units of a specific type.

Phase micro-heterogeneity in bisphenol-A polycarbonate/poly(methyl methacrylate) blends

The controversial equilibrium phase behaviour in the blend system of poly(methyl methacrylate) and bisphenol-A polycarbonate was re-examined by using differential scanning calorimetry, optical and scanning electron microscopy. This study has shown that the ‘transparent’ blends of PC/PMMA actually displayed micro-heterogeneity, with domain sizes of ca. 100–300Å. The micro-heterogeneous domains were so small that the blends exhibited a single glass transition point ( T g) and appeared transparent. Upon heating above the T g of the matrix components of the blends, the original micro-phase domains suddenly expanded at 180°C, increasing rapidly to about 1–3 μm in size, with increased cloudiness. This present study has also shown that the ‘transparent’ blends when heated above 240°C also displayed micro-phase separation. Consequently, the phase behaviour in the PC/PMMA blends are re-interpreted from kinetic point of view.

Critical behaviour of self-avoiding walks: that cross a square

Consider the set of all self-avoiding walks in the square lattice which start at (0, 0), end at (L, L), and are entirely contained in the square (0, L)*(0, L). Associate a fugacity x with each step of the walk. Whittington and Guttmann (1990) showed that the dominant walks have O(L) steps when x is small and O(L2) steps when x is large, and they conjectured that there is a single transition point at x= mu -1 where mu is the inverse of the connective constant for (unconstrained) self-avoiding walks. We present a rigorous proof of this conjecture (and its analogue in higher dimensions). We also discuss what can be said rigorously about two scaling exponents associated with this phase transition, and compare this with analogous results that have been obtained exactly (and rigorously) on the discrete Sierpinski gasket by Hattori, Hattori and Kusuoka (1990).

Response of Tulip Scale Mitochondria to Temperature in Relation to Cold Treatment of the Bulbs

A uniform batch of tulip bulbs were kept in the dark either at 2 °C or 18 °C. Sample bulbs were withdrawn at intervals from both treatments and mitochondria were isolated from the scale tissue. Arrhenius plots of succinate and NADH oxidation by the mitochondria were made. Within the range 0-36 °C, mitochondria from uncooled bulbs showed a single transition point at about 16 °C, as did mitochondria from freshly formed daughter bulbs. In contrast, mitochondria from bulbs kept for 8 weeks or longer at 2 °C showed strong indications of two discontinuities in the Arrhenius diagrams within a similar temperature range, one about 10 °C below the other. The results suggest that tulip bulbs are chilling-sensitive, and that alterations in the activation energies of certain oxidative enzymes in response to accumulated cold treatment are necessary for metabolism to be directed towards the growth of normal flowers.

Deductions from some artificial refractive index profiles based on the elementary functions

AbstractThe familiar W.K.B.J. method expresses in terms of elementary functions approximate solutions of second order differential equations in normal form that otherwise have no analytical solutions expressible in terms of the standard elementary or transcendental functions. Proofs of the connexion formulae required to trace these approximate solutions across transition points are usually derived by comparison with known functions such as the Airy integral or Bessel functions, or by an appeal to the Stokes phenomenon in the complex plane. A new device is developed for the synthesis of refractive index profiles with transition points, and yet yielding solutions in terms of the elementary functions. These are then used to derive the W.K.B.J. connexion formula by means of a novel limiting process based on solutions considered only along the real z-axis. The method is obviously more complicated than the more usual approach, but contains special features throwing new light on the connexion formula across a single transition point.

Collisional ionization and elastic scattering in alkali–halogen atom collisions

Close-coupling (two-state) computations for collisional ionization and elastic scattering in Na+I and Li+I collisions have been made, using realistic model potentials, at a large range of postthreshold energies. At the higher energies a generalized JWKB procedure was employed which yields a very accurate scattering matrix when compared to a fully quantal solution. The computed elastic and inelastic total and differential cross sections are discussed and compared to the predictions of more approximate methods. The rainbow angles in the angular distribution are compared to those predicted by the classical deflection function obtained from the trajectories along adiabatic or diabatic potential curves (based on the assumption of a single transition point). It is found that at all energies considered these rainbow positions agree best for trajectories computed via the adiabatic representation rather than the diabatic representation. The double rainbow pattern noted in the elastic ionic channel can be interpreted only within the adiabatic representation. Landau–Zener–Stueckelberg (LZS) computations for the energy dependence of the collisional ionization cross section have also been made. The LZS curve jumping mechanism is in better agreement with the quantal results when the transition is taken to occur at the adiabatic coupling point (Rp) rather than the diabatic crossing point (Rx). Moreover, depending on the nature of the potentials, there may also be an additional transition region at small internuclear distances, which is not present in the LZX scheme but may be the source of oscillations found in the post maximum energy dependence of the collisional ionization cross section. The systematics of the collisional ionization cross sections for all alkali metal–halogen atom (M+X) collisions are discussed and the energy dependence of the cross section is computed using realistic potentials. In terms of the reduced velocity (at the crossing point) v/Kp, it is noted that only Li+I and Na+I are in the strong coupling region. For all other systems the cross section is found to decrease with increasing collision energy.

Liquid boiling in a thin film

Liquid boiling has been studied experimentally in a thin film formed over a limited surface area by supplying liquid through a spray nozzle. Water, ethanol, carbon tetrachloride and benzene were used in these experiments. Pressure ranged within 0·08-1 bar. In this study some new correlations have been obtained such as higher critical fluxes in comparison with pool boiling, a single transition point on the boiling curve, q vs. Δ T different behaviour of the dependence of α vs. q and other observations which are discussed in the work.