Measurement of polydispersity of ultra-narrow polymer fractions by thermal field-flow fractionation

In this paper we demonstrate that the polydispersity µ = M?_w/M?_N of narrow polymer fractions can be readily obtained by measuring band broadening and its velocity dependence in a thermal field–flow fractionation (thermal FFF) system. The thermal FFF method is shown to be more accurate than size exclusion chromatography for the determination of polymer polydispersities due to the simpler band dispersion function and the higher selectivity inherent to the technique. The polydispersities of a series of four narrow polystyrene samples prepared by anionic polymerization were consequently determined by thermal FFF and found to be much smaller (1.003–1.006) than the ceiling values (1.06) suggested by the suppliers. As part of this investigation, an experimental study of band dispersion in thermal FFF is used to examine current theory. The data show nonequilibrium to be the dominant factor, whereas relaxation effects are insignificant at lower flow rates and can be subdued at higher flow rates. A high correlation between nonequilibrium theory and experiment allows for the estimation of diffusion coefficients from plate height–velocity data.     

Influence of Wall-Retarded Transport on Retention and Plate Height in Field-Flow Fractionation

Abstract

The retarded motion of spherical particles in the vicinity of an FFF channel wall is accounted for in theories for the flow FFF retention ratio and the generalized nonequilibrium plate height. These theories do not quantitatively explain select anomalies reported in the FFF literature.     

Exact Analysis of Field-Flow Fractionation

Abstract

A rigorous convective diffusion theory is formulated for the predictive modeling of field-flow fractionation (FFF) columns used for the separation of colloidal mixtures. The theory is developed for simulating the behavior of a colloid introduced into fluid in time-dependent flow in a parallel plate channel across which a transverse field is applied. The methodology of generalized dispersion theory is used to solve the model equations. The theoretical results show that the cross-sectional average concentration of the colloid satisfies a dispersion equation with time-dependent coefficients. The results of this work, in principle, are valid for all values of time since the introduction of the colloid. It is shown that these results asymptotically approach those of the nonequilibrium theory formulated by Giddings for large values of time.

Illustrative numerical results are obtained for the case of steady laminar flow and a uniform initial distribution. The behavior of the coefficients in the dispersion equation is explained on physical grounds. Of particular interest is the fact that at large values of the transverse Peclet number P, Taylor dispersion in the FFF column is very small. Under these conditions, axial molecular diffusion as well as Taylor dispersion in the connecting tubing could make a substantial contribution to the axial dispersion observed in practical FFF columns.

The theoretical predictions are compared with the experimental data of Caldwell et al. and Kesner et al. on electrical FFF columns. The comparisons indicate that the theory has potential in predicting the performance of such systems.     

Hyperlayer Field-Flow Fractionation

Abstract

Hyperlayer field-flow fractionation is proposed as a method designed to overcome some of the limitations of conventional field-flow fractionation (FFF). In hyperlayer FFF, steady-state particle layers are formed above the channel wall by the combination of a primary field (e.g., sedimentation or electrical) and a secondary gradient (such as density of pH). Such zones could be separated along the flow axis in FFF even if they strongly overlap in the field or lateral direction. An approximate theory is derived for sedimentation hyperlayer FFF, showing both the rate of zone migration and the extent of peak broadening. Calculations are presented which show that the system should be highly effective for the separation of particles in the vicinity of μm in diameter or larger.     

A General Nonequilibrium Multicomponent Adsorption Model: Numerical Solution

Abstract

A comprehensive mathematical model has been developed to describe the process of multicomponent adsorption from a well-stirred bath. Both internal and external diffusional resistances were included in the physical model. A nonlinear Fritz-Schluender isotherm was used to describe the adsorption equilibrium. An infinite bath, one-component, non-equilibrium model was compared with an equilibrium model. A numerical solution for a binary system in an infinite bath was obtained. The numerical solution for a two-component model in a stirred finite bath was shown to satisfactorily match previously published experimental data. Its extension to an n-component system was shown. It was shown that the solution of nonequilibrium model is easier and more efficient than that of the equilibrium model. The nonequilibrium model is especially advantageous for a large number of solutes.     

Non-Newtonian Flow for Retention Control in Field-Flow Fractionation

Abstract

Retention in field-flow fractionation (FFF) can be altered and controlled by the introduction of different kinds of velocity profiles in the FFF channel. Here we propose the use of non-Newtonian fluid flow to manipulate retention in FFF. The flexible, three parameter Ellis equation, describing non-Newtonian behavior, is used to derive the dependence of retention ratio R on the dimensionless mean solute layer thickness λ. Numerical calculations show the way in which changes in the parameters of the Ellis equation change the velocity profile in the channel and therefore the shape of the R versus λ functions.     

Reversible redox behaviour of two electroactive polymethacrylates

Summary The radical melt polymerization of 2-[4-(6-methacryloyloxyhexa-1,6-diyloxy)phenylazo]-anthraquinone is described yielding the homopolymer p _m with the number average molecular weight (M _n ) of M _n =74kg/mol determined by gel permeation chromatography (GPC) using polystyrene (PS) calibration. The redox properties of a thin film of p _m were investigated by cyclic voltammetry. Two reversible redox waves were found at all applied sweep rates indicating two reversible electron (E) transfer processes of the anthraquinone units according the EE-mechanism. A thin film of the randomlike copolymethacrylate cp _r with the molar mass of M _n =73kg/mol was investigated, too. The sidegroups of cp _r are substituted by 77mol% with benzyl, by 22mol% with phenylazoanthraquinone and by 1mol% with COOH groups. The redox properties of cp _r depend on the timescale of the cyclovoltammetric experiment. At high sweep rates two reversible redox waves are observable corresponding to the EE-mechanism. At low sweep rates an additional reversible redox wave appears, which is essentially smaller than the other two. The third wave is explained to be a result of hydrogen bonding between the COOH groups and anthraquinone mono- and dianions. The most anthraquinone units are reduced according the EE-mechanism without hydrogen bonding due to statistical reasons. The reversible redox properties of p _m and cp _r are closely connected to their molar masses (M _n ≈75kg/mol), because both polymers have been previously obtained by radical solution polymerization yielding low molecular products with molar masses of M _n ≈10kg/mol. The low molecular polymers have shown an irreversible redox behaviour. Therefore, it could be demonstrated that the molar mass of an electroactive polymer significantly affects its redox properties. Received: 13 November 1998/Revised version: 30 March 1999/Accepted: 20 April 1999     

Peak Capacity in Field-Flow Fractionation

Abstract

Field-flow fractionation (FFF) peak capacity values have been computed with only two major assumptions: first, the plate height is supposed the sum of only two contributions, axial molecular diffusion and transversal nonequilibrium, and second, the steric effect has been neglected in the equations of retention and peak broadening.

Several reduced parameters have been defined to generalize the equations and limit the number of variable parameters. It appears that among the already implemented FFF subtechniques for which the elution spectrum is an explicit function of the principal dimension, or mass, of the retained sample (which excludes electrical FFF), sedimentation FFF has some peculiar characteristics due to the fact that the field-induced velocity depends on a particular sample, while in thermal and flow FFF it is the same for all samples of a given type under fixed experimental conditions. For example, in sedimentation FFF, the axial diffusion contribution to the plate height persists at a much larger reduced eluant velocity than for the other techniques.

The effect on the peak capacity of the retention volume, the channel length, the eluant velocity as well as the influence of detection limit and analysis time have been studied. Simple relationships between peak capacity and these parameters are established in the high retention and negligible axial diffusion limits which previal in most experimental situations, and deviations from these limits are discussed. It is shown that for all three     

A Pinched Inlet System for Reduced Relaxation Effects and Stopless Flow Injection in Field-Flow Fractionation

Abstract

The concept of a pinched inlet system for field-flow fractionation (FFF), in which the channel thickness at the inlet end is reduced to hasten relaxation, is introduced and its advantages in simplifying FFF operation and increasing analysis speed are noted. Three forms of FFF operation are described for taking advantage of the split inlet: stopless flow injection, slow flow injection, and stopflow injection. Stopless flow operation is the simplest because flow is neither stopped nor changed to accommodate relaxation. However, stopless flow operation causes band broadening. It is found that the time-based variance of band broadening for many FFF systems is proportional to the fourth power of channel thickness w. Therefore, by reducing w at the inlet end where relaxation occurs, this band broadening can be controlled. The implementation of this concept is discussed for different forms of FFF.     

Feasibility Study of Dielectrical Field-Flow Fractionation

Abstract

The possible use of dielectrophoretic forces for the development of a new subtechnique of field-flow fractionation (FFF) termed dielectrical FFF is examined. Dielectrical FFF is based on the dielectrophoresis of neutral particles in the nonuniform electric field of an annular channel (or charged coaxial capacitor). The feasibility of the subtechnique is assessed by estimating the magnitudes of retention ratio R predicted from theory for select species representative of several classes of particle/fluid mixtures. Minimum attainable R values are calculated using estimates of the maximum electric field strengths applicable to the mixtures. Calculations show that. the dielectrophoretic force is strong enough to retain and separate ultrahigh-molecular-weight polymers and submicron-diameter particles dissolved or suspended in organic liquids of high dielectric constant Evidence suggests that pearl-chain formation may impose a fundamental limitation on particle retention at the inner cylinder of the annular channel, especially in aqueous suspensions.     

Diffraction Studies on Concentrated Aqueous Hydrochloric Acid Solutions

X-ray diffraction and neutron diffraction experiments with H/D isotopically substituted aqueous 21 mol% hydrochloric acid solutions were carried out in order to obtain detailed features concerning the intermolecular hydrogen-bonded structure in highly concentrated aqueous acidic solutions. Structure parameters, namely, intermolecular distance, root-mean-square amplitude, and coordination number, for the nearest neighbor H₃O⁺···H₂O interaction were determined from the least-squares-fitting analysis of the observed X-ray interference term. These were, respectively, r(H₃O⁺···H₂O) = 2.45(1) Å; l(H₃O⁺···H₂O) = 0.11(1) Å; and n(H₃O⁺···H₂O) = 1.8(1). The intermolecular nearest neighbor distances, r(H···H) = 2.02(5) Å and r(O···H) = 1.69(2) Å, were determined from the least-squares fit to partial structure factors, a_ij (Q), derived from the observed neutron intermolecular interference terms for sample solutions with different H/D isotopic ratios. The present values of intermolecular distances are significantly shorter than those for pure liquid water, implying that extremely strong hydrogen bonds exist in concentrated aqueous acidic solutions.     

Different Hemi-Salen/Salan Ligand Containing Binuclear Boron-Fluoride Complexes: Synthesis,Spectroscopy, Fluorescence Properties,and Catalysis

A family of hemi-salen (L₁H–L₆H) and hemi-salan (L_1aH–L_2aH) ligands-based N,O-chelated binuclear boron-fluoride [L_n(BF₂)₂] (n = L₁–L₆ or L_1a–L_2a) complexes have been prepared and characterized by a variety of spectroscopic techniques (¹H, ¹³C and ¹⁹F NMR, FT-IR, UV-Vis, LC-MS, and fluorescence spectra) and elemental analysis. All of the binuclear boron-fluoride complexes exhibit strong absorption bands due to S₀→S₁ transitions and strong fluorescence properties were observed at room temperature in the solution. The binuclear boron complexes containing two naphthyl groups are significantly red-shifted in comparison with the other binuclear boron-fluoride complexes. After the structures are characterized, these hemi-salen and salan ligand-based N, O-chelated binuclear boron-fluoride complexes were utilized to the transfer hydrogenation of the different acetophenone derivatives conversion to 1-phenylethanol derivatives as catalysts.     

The thermodynamic properties of liquids,including solutions. XIV. Solutions of normal alkanes: Models for oligomer solutions

From published H^E data for 10 n-alkane solutions in benzene at 25°C, the three parameters of the author's solution theory have been calculated. The values obtained agree quite well with εΔ = 3068 J/mole, K = 1, and r_σ = 0.2 + 0.2 n_c = 0.1 n_H. The problems involved in the extension of these results to higher oligomers of polymethylene and to other solutions of chain molecules are briefly discussed.     

Thermogravitational Field-Flow Fractionation: An Elution Thermogravitational Column

Abstract

The major operating characteristics of thermal field-flow fractionation (thermal FFF) and of thermogravitational columns are compared, and it is shown that the two approaches can be advantageously combined in a method we call thermogravitational FFF. The theory of this technique is developed, with primary attention given to a change in the velocity profile under different flow conditions and its effect on component retention, column efficiency, resolution, and selectivity. Experimental results are shown to be in good overall accord with theory. It is shown that the potential of thermogravitational FFF lies in the fractionation of low molecular weight polymers or of other species having weak thermal diffusion.     

Solvothermal Synthesis and Crystal Structure of a Novel 3D Triorganotin Polymer Containing Polyfunctional Ligand 5-mercapto-1(H)-tetrazoleacetic acid

A novel 3D tri-n-butyltin complex [(n-Bu₃Sn)₂(C₂H₂N₄SCO₂)]_n (1) has been solvothermally synthesized and structurally characterized by elemental analysis, FT-IR, NMR (¹H, ¹³C, and ¹¹⁹Sn) spectra and X-ray crystallography. X-ray data of complex 1 reveals that it is a 3D tri-n-butyltin coordination polymer with a metal-organic framework (MOF) structure , significant N → Sn interactions plays an important role in the construction of this structure.     

Generation of Oxygen-Containing Radicals in the Aqueous Media of Mechanical Pulping

Mechanical treatments of veratrylglycerol-β-syringaldehyde ether (M) were conducted with a ceramic ball mill or a vibration ball mill in the presence of water and n-paraffin alcohols which were used as ·OH scavengers. Addition of 1% each of the alcohols to the milling process of Compound (M) greatly decreased the yields of the products, e.g. veratryl alcohol 2, vanillin 3, syringaldehyde 4, 3,5-dimethoxy-p-benzoquinone 5, 3,5-dimethoxy-p-hydroquinone 6 and others. Another addition of n-paraffin alcohols to aqueous media during the millings also significantly reduced the concentration of H₂O₂. When phthalic hydrazide (P) was treated in the mills in the aqueous media, triacetoxyphthalazine (1A), 3-acetoxyphthalic acid (2A) and other products were separated from the acetates of the reaction mixtures. Results mentioned above disclosed the generation of ·O₂H, ·OH, and ·H in the aqueous media during the mechanical treatments.     

Shear Field-Flow Fractionation: Theoretical Basis of a New,Highly Selective Technique

Abstract

Shear field-flow fractionation (shear FFF) is described as an FFF system in which shear forces are responsible for migration perpendicular to flow. It is shown that a desirable configuration for shear FFF is a concentric cylinder system with one cylinder rotating. After providing the relevant theoretical framework of FFF, the equations of Shafer et al. describing shear migration are simplified and applied to the limiting case of very thin annular spaces to get tractable retention expressions. On this basis the maximum selectivity is predicted to be 3 or greater, a value considerably higher than that for any other macromolecular separation technique. This high selectivity is confirmed using an alternate shear migration theory developed by Tirrell et al. However, it is shown that shear FFF is only applicable to macromolecules of high molecular weight, perhaps ～10⁷ and above. It may also be applicable to globular particles.     

From Overcrowded Polycyclic Aromatic Enes to Semifullerenes

Bi-9H-fluoren-9-ylidene (2) and bi-4H-cyclopenta[def]phenanthren-4-ylidene (5) are potential starting materials for the preparation of bowl-shaped fragments of fullerenes. Semiempirical MNDO-PM3 calculations of C₂₆H_n and C₃₀H_n (n = 12, 14, 16) species 2-12 are used to analyze energetic effects on the dehydrocyclization and isomerization reactions of these species. Oxidative photocyclizations on Z-2,2′-bridged derivatives of 2 and 5 are briefly outlined.     

Diffusion Coefficients and Molecular Weight Distributions of Humic and Fulvic Acids Determined by Flow Field-Flow Fractionation

Abstract

The ability to characterize molecules whose physical and chemical properties are intimately linked to their diffusion coefficients and molecular weight is important to further understanding of chemical transport in the environment. Flow field-flow fractionation (flow FFF) was used to obtain separations of water-soluble macromolecules of varying molecular weight, including polystyrene sulfonates and humic substances. The separation occurs due to differing diffusion rates for chemical species of differing molecular weight in aqueous solution. Flow FFF uses fluid flow as the mechanism of separation. A model that yields liquid phase diffusion coefficients as a function of molecular weight was utilized to determine molecular weights from degree of separation. Separations of polystyrene sulfonates, a humic acid, and two fulvic acids of known molecular weight were accomplished using flow FFF. The separations obtained were used to develop a relationship between flow FFF separation and species molecular weight. Separations were obtained for humic and fulvic acids of unknown molecular weight.     

Synthesis of Diorganotin Esters of 5-Bromonicotinic Acid: X-ray Crystal Structure of Polymeric 5-Bromonicotinatodiorganotin

Two types of diorganotins [R₂Sn(OCOC₅H₃N-3-Br-5)₂] _n and {[R₂Sn(OH₂)(OCOC₅H₃N-3-Br-5)₂]₂} _n (R= Me, n-Bu, Ph, n-Oc), are prepared from 5-Br-omonicotinic acid and diorganotin oxides. All the compounds, 1–8, are characterized by elemental analysis as well as IR and ¹H-NMR spectroscopy. The crystal structures of [R₂Sn(OCOC₅H₃N-3-Br-5)₂] _n (2) and {[R₂Sn(OH₂)(OCOC₅H₃N-3-Br-5)₂]₂} _n (8) were determined by single crystal X-ray diffraction. In compound 2, each carboxylate moiety of 5-Br-omonicotinic acid is involved in coordination to one Sn atom via two O-atoms, and the N-atom of one pyridine-ring coordinates to the neighboring Sn atom which leads to a polymeric chain. And the N-atom of the other pyridine-ring is dissociative. In compound 8, the compound proves to be dinuclear macrocyclic compounds with 5-Br-omonicotinic acid bridging the adjacent tin atoms with a 12-member ring. The hydrogen bonds ( ) are observed in the compound 8. These intermolecular hydrogen bonds form another ring, and lead to a polymeric chain in the lattice at the same time. An erratum to this article can be found at