Nonequilibrium Theory for Field-Flow Fractionation in Annular Channels

Abstract

The principles of field-flow fractionation (FFF) and reasons for extending the FFF methodology from parallel-plate channels to annular channels (ANNCs) are briefly reviewed. A theory for the nonequilibrium plate height H of FFF zones in ANNCs is developed by extending the nonequilibrium theory of FFF to polar coordinates. The principal assumption in the theory is that component zones are localized near the ANNC walls by the general force F = A/rⁿ , where A and n are constants and r is the radial coordinate. Equations for H are developed as functions of n, the inner-to-outer radius ratio of the ANNC, and the fundamental FFF parameter, γ. A closed-form analytical solution to H is obtained when n = 1; the n ≠ 1 solution must generally be expressed as a ratio of the integrals involved. These integrals can be approximated analytically, however, when γ ? 1. The functions for H are compared to their parallel-plate counterpart, and differences are rationalized.     

Synthesis and characterization of BDSDA/APB polyimide

A novel linear aromatic polyphenylene ethersulfideimide (BDSDA/APB) has been synthesized. Its physical, mechanical, thermal, and flow properties and its resistance to some of the more commonly used solvents were determined. The results of these property evaluations indicate this polymer system can be processed via conventional thermoplastic techniques. It has been molded, used as a resin, and cast into thin films and, accordingly, may have a wide variety of applications. Its molecular weight was varied by endcapping with phthalic anhydride. Over the M?_n range 14,000–45,000 the apparent viscosities and G_Ic values varied only slightly. However, a change in M?_n from 14,000 to 8700 resulted in a dramatic decrease in the apparent viscosity at both 250°C and 280°C. The G_Ic values for these same molecular weight materials decreased in a like manner as the M?_n decreased, indicating tradeoffs can be made between process optimization and final mechanical properties when polymer systems are developed.     

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.     

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.     

Size-exclusion chromatography with two-angle laser light-scattering (SEC-TALLS) of high molecular weight and branched polymers

The accuracy and precision of results obtained from light-scattering detection at two angles (TALLS) for size-exclusion chromatography (SEC) are examined for linear narrow molecular weight distribution polystyrenes between 1,290,000 and 20,000,000 MW and for branched polyesters. The ratio of light-scattering intensities at 15° and 90° is used to calculate weight-average molecular weight, M?_w, and an average root-mean-square radius, r?_gu, equivalent to the z-average radius. A shape for the polymer molecule is assumed and an analytical relationship for the particle-scattering function is required. It is shown that analysis of the data using the particle-scattering function for a random coil is valid for both high molecular weight, linear polystyrenes and long-chain branched polyesters. The radius, r?_gu, is determined with high precision by using the ratio of light-scattering signals, which is insensitive to errors in sample concentration and changes in the eluent flow rate. The correct average radius for the whole polymer is obtained despite using low-efficiency, large-particle diameter SEC columns; however, axial dispersion significantly affects molecular weights and radii calculated at each retention volume that can limit the utility of plots used to deduce polymer conformation. © 1995 John Wiley & Sons, Inc.     

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     

Thermal analysis of styrene–alkyl methacrylate polymers. II. Thermogravimetric kinetics

The thermal stability and degradation kinetics of several polystyrenes and styrene–alkyl methacrylate copolymers and terpolymers with a number-average molecular weight (M?_n) of 6000–250,000 g/mole have been studied using dynamic thermogravimetry (TG). The degradation kinetics of each polymer sample have been successfully attributed to a sample first-order reaction expression. The results indicate that the thermal stability and degradation kinetics of the polymers are independent of the size of the molecules within the molecular weight range investigated. The steric hindrance effects of the pendent groups appear to be responsible for the improved thermal stability and resistance of C? C bond scission in the styrene–alkyl methacrylate copolymers and terpolymers.     

Conducting ferromagnetic copolymer of aniline and 3,4‐ethylenedioxythiophene containing nanocrystalline barium ferrite particles

This article reports the synthesis of conducting ferromagnetic complex of 3,4‐ethylenedioxythiophene (EDOT) and aniline (An) containing M‐type hexagonal barium ferrite (BaFe₁₂O₁₉) particles using in situ emulsion polymerization and electrochemical oxidative polymerization. Magnetic and conductivity studies reveal that the conducting ferromagnetic complex possesses high‐saturation magnetization (M_s) value of 29.2 emu/g and conductivity of the order of 0.256 S/cm determined through vibrating sample magnetometer and four‐probe method. Microwave measurement has shown the reflection loss (R_L) of ?12.1 dB in Ku‐band that can be used as a microwave absorbing material. The polymer complex was further characterized by techniques like X‐ray diffraction, Fourier transform infrared, UV–visible, cyclic voltammetry, and thermal analysis with thermogravimetric analysis. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci 2008     

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.     

Siloxane surfactant‐modified clay and its effect in reinforcing the laminate of polymethylsilsesquioxane

To achieve good compatibility between clay layers and siloxane polymer, polymethylsilsesquioxane (PMSQ), montmorillonite was modified by a novel siloxane surfactant with M?_w = 1900 and then environmentally friendly solution‐compounded with PMSQ to prepare glass fiber laminates. Transmission electronic microscope shows the orderly, exfoliated structure of the modified clay in PMSQ matrix; scanning electronic microscope demonstrates the fine dispersion of the clay layers in the matrix because of the good compatibility between the grafted surfactant and the matrix. Both the modified clay and its nanocomposite indicate much improved thermal stability. By incorporation of merely 0.3 wt % of the clay, the flexural modulus and strengths of fiber/PMSQ laminate are increased by 21 and 62%, respectively. This study illuminates the importance of the compatibility of the grafted siloxane surfactant with the matrix polymer in achieving both exfoliation and dispersion of clay as well as ideal mechanical properties for silicone‐based polymers. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 3974–3980, 2006     

Influence of molecular weight and molecular weight distribution on the tensile properties of amorphous polymers

Tensile property data for polystyrene samples of varying polydispersity are correlated with various parametric measures of molecular weight. Traditional measures of molecular weight, such as M?_n, M?_w, and M?_z, are shown to be unable to account for the variation of tensile properties with molecular weight. However, a new molecular weight parameter, termed the failure property parameter, is able to provide a single relationship between tensile strength and the parameter for both the broad and narrow distribution polymers. The form of this parameter is consistent with its having origins in the view that it is the entanglement network in an amorphous polymer that provides the observed strength properties. Specifically for polystyrene, the failure property parameter results indicate that material below 60,000 molecular weight does not contribute to polymer strength. Although the results of this investigation are specifically for polystyrene, the arguments used to develop the failure property parameter are not dependent on polymer chemical structure. Consequently, we believe that both the concepts and definition of this new parameter are applicable to all amorphous polymers.     

Estimation on thermal conductivities of filled polymers

A new thermal conduction model is proposed for filled polymer with particles, and predicted values by the new model are compared with experimental data. The model is fundamentally based on a generalization of parallel and series conduction models of composite, and further modified in taking into account that a random dispersion system is isotropic in thermal conduction. The following equation is derived from the new model; log λ = V · C₂ · log λ₂ + (1 ? V) · log(C₁ · λ₁). Therefore, when thermal conductivities of polymer and particles (λ₁, λ₂) are known, thermal conductivity of the filled polymer (λ) can be estimated by the equation, with any volume content of particles (V). The new model was proved by experimental data for filled polyethylene, polystyrene and polyamide with graphite, copper, or Al₂O₃.     

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.     

Influence of chemical functionalization of carbon nanotubes on their dispersibility in alkyl methacrylate polymer matrix

Nanocomposites based on poly(methyl methacrylate) (PMMA) and poly(methyl methacrylate‐co‐octadecyl methacrylate) (M/O) matrices and four different types of multiwall carbon nanotubes: pristine, oxidized (MWCNT–COOH), methyl ester (MWCNT–COOCH₃), and dodecyl ester (MWCNT–COOC₁₂H₂₅) functionalized, were prepared in situ by radical (co)polymerization. The effectiveness of preparation of nanocomposites regarding dispersion and distribution of various MWCNT in polymer matrices was sized by Scanning electron microscopy. In case of PMMA matrix, the best dispersion and distribution were accomplished for MWCNT–COOCH₃ due to their chemical resemblance with polymer matrix. After the introduction of 10 mol % of octadecyl methacrylate in polymer matrix a fairly good dispersion and distribution of MWCNT–COOCH₃ were retained. The addition of 1 wt % of MWCNTs caused a significant reduction in the degree of polymerization of the PMMA matrix. But at the same time, the present MWCNTs increased storage modulus of PMMA nanocomposites except for dodecyl ester functionalized MWCNT. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 46113.     

Preparation of ultrahigh molecular weight polyacrylonitrile and its terpolymers

The synthesis of high molecular weight (in excess of 10⁶ million Daltons) poly(acrylonitrile) and poly(acrylonitrile-co-methylacrylate-co-itaconic acid) is described. An inverse emulsion polymerization formulation with AIBN as the initiator was used. However, polymer precipitation occurred early in the polymerization. In each case, the molecular weight distribution was surprisingly narrow (M?_w/M?_n ～ 1.5). Conversion vs. time plots with monomers containing the inhibitor had the “S” shape typical of emulsion polymerizations. The terpolymer composition and molecular weight were quite uniform throughout the polymerization. With inhibitor-free monomers, the initial molecular weights were very high (～ 3 × 10⁶ Daltons), but gelation occurred at ca. 50% conversion. There was an inverse relationship between the monomer inhibitor content and the polymer molecular weight. It is suggested that the growing polymer radicals are occluded in the precipitated polymer particles and are terminated by inhibitor diffusing into the particles, accounting for the narrow molecular weight distribution. © 1995 John Wiley & Sons, Inc.     

Low-density polyethylene depth profile analysis by photoacoustic spectroscopy

Near-infrared photoacoustic spectra of polyethylene (1 mm slab) were taken in the modulation range 10–240 Hz, which corresponds to thermal diffusion layers in the 56?11 μm range. Thick-layer spectra are very similar to polyethylene film transmission spectra, but large differences are observed between the spectra taken at various modulation frequencies. From 10 to 80 Hz, all the spectral band intensities decrease linearly with ω^?a where ω is the light modulation frequency and a varies from 0.48 to 1.00 for different constituent groups. The analysis of spectral intensity as a function of modulation frequency shows that peak intensity ratios of ? CH₃, ?CH₂, and ? OH groups, relative to that of methylene groups, increase as thinner, closer-to-surface polymer layers are sampled. From this we conclude that near-to-surface layers of solid polyethylene are richer in ? CH₃, ?CH₂ and ? OH groups than the polymer bulk.     

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.     

Characterization of low-density polybutadiene latexes by sedimentation field–flow fractionation

A procedure based on sedimentation field–flow fractionation for physical characterization of polydisperse latexes is presented. The particle density, dimensions, polydispersity, size distribution and aggregation can be determined for both narrow and wide polydispersities. The procedure is applied to the sample case of polybutadiene latexes with density lower than water. The results are compared with independent measurements obtained by electron microscopy. The relevance of significant steps of the procedure, such as the nonequilibrium corrections, are discussed.     

Fluorene‐based copolymers with donor–acceptor units on the side chain and main chain: Synthesis and application in polymer solar cells

Two narrow band gap fluorene‐based copolymers with donor–acceptor (D–A) structure on the polymer side chain and/or main chain are synthesized by Pd‐catalyzed Stille coupling reactions. The two copolymers have excellent thermal stability. The effects of D–A structure on the main and side chains on the absorption and electrochemical properties are studied. The copolymer PF‐BTh‐DBT with D–A structure both on the main and side chains has broader and stronger absorption and narrower band gap than the copolymer PF‐BTh with only a pendent D–A structure. The power conversion efficiency of the assembled solar cell using PF‐BTh‐DBT as donor and PC₇₁BM as acceptor is 1.6% with open‐circuit voltage (V_oc) 0.84 V under simulated AM 1.5 G solar irradiation (100 mW/cm²). © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 3276–3281, 2013     

Optical,electrochemical, and photovoltaic properties of conjugated polymers with dithiafulvalene as side chains

Three conjugated polymers, P1–P3, with dithiafulvalene (DTF) as side chains have been synthesized. All polymers have good thermal stabilities. The DTF unit could be oxidized to DTF?⁺ which was observed from cyclic voltammetry and ultraviolet–visible (UV–vis) spectra, and the oxidation process was independent of the conjugated backbone of the polymer. The strong π–π* transition absorbing band of the three polymers decreases gradually as increasing oxidation, and the resulting DTF?⁺ species give rise to an additional band at 750–1100 nm, which can be assigned to a distinguishing feature of the cation radical species. Photovoltaic device based on the blend of P2 and [6,6]‐phenyl‐C61‐butyric acid methyl ester (PC₆₁BM) showed the power conversion efficiency of 1.05% with a fill factor of 42.8%. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41508.