Composition determination of binary polymer mixtures by size exclusion chromatography with light scattering detection

<正>Base on the principle of absolute quantification of size exclusion chromatography(SEC),a light scattering(LS) detector coupled with a concentration detector(refractive index detector) is utilized to determine the compositions of complicated binary mixtures.A theoretical analysis predicts that the response factors for both LS and RI detectors are linear functions with the composition of any specified polymer mixtures in the binary polymer mixtures.Two pairs of complicated binary mixtures were used to test the theory mentioned in the present paper,and the experimental results show an excellent accordance with the theory.     

Inclusion–exclusion principle for belief functions

The inclusion–exclusion principle is a well-known property in probability theory, and is instrumental in some computational problems such as the evaluation of system reliability or the calculation of the probability of a Boolean formula in diagnosis. However, in the setting of uncertainty theories more general than probability theory, this principle no longer holds in general. It is therefore useful to know for which families of events it continues to hold. This paper investigates this question in the setting of belief functions. After exhibiting original sufficient and necessary conditions for the principle to hold, we illustrate its use on the uncertainty analysis of Boolean and non-Boolean systems in reliability.     

Transformation of macromonomers into ring‐opening polymerization macroinitiators: A detailed initiation efficiency study

In the present study, n‐butyl acrylate macromonomer (BAMM) (M_n = 1900 g mol^?1; PDI = 1.96) has been synthesized via a high‐temperature polymerization process. Subsequently, the olefinic termini of the BAMM have been transformed into a diol via a dihydroxylation process using KMnO₄ as an oxidizing agent. The OH‐terminated macroinitiator pBA(OH)₂ has subsequently been employed for the ring‐opening polymerization (ROP) of ε‐caprolactone via various catalytic systems, that is, organo‐(1,5,7‐triazabicyclo[4.4.0]dec‐5‐ene), metal (tin(II) 2‐ethylhexanoate), and enzymatic catalysis (Novozym® 435). The obtained pBA‐b‐pCL block copolymers and the initiation efficiency of the BAMM macroinitiator have been investigated via size exclusion chromatography (SEC), electrospray ionization–mass spectrometry (ESI‐MS) hyphenated with SEC and liquid chromatography at the critical conditions of both poly(ε‐caprolactone) (pCL) and pBA. The in vitro enzyme catalysis (eROP) approach proved to be the most efficient catalysis system due to minor transesterification side reactions during the polymerization process. However, side reactions such as transesterifications occur in each catalytic system and—while they cannot be suppressed—they can be minimized. The species generated during the eROP process include the desired block copolymer pBA‐b‐pCL as main species as well as pCL homopolymer and residual macroinitiator pBA(OH)₂. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Finite-dimensional representations of a shock algebra

Abstruct The algebra describing a shock measure in the asymmetric simple exclusion model, seen from a second class particle, has finite-dimensional representations if and only if the asymmetry parameterp of the model and the left and right asymptotic densitiesp _± of the shock satisfy [(1−p)/p] ^r =p ₋(1−p ₊)/p ₊(1−p ₋) for some integerr≥1; the minimal dimension of the representation is then 2r. These representations can be used to calculate correlation functions in the model.     

The Asymmetric Exclusion Process: Comparison of Update Procedures

The asymmetric exclusion process (ASEP) has attracted a lot of interest not only because of its many applications, e.g., in the context of the kinetics of biopolymerization and traffic flow theory, but also because it is a paradigmatic model for nonequilibrium systems. Here we study the ASEP for different types of updates, namely random-sequential, sequential, sublattice-parallel, and parallel. In order to compare the effects of the different update procedures on the properties of the stationary state, we use large-scale Monte Carlo simulations and analytical methods, especially the so-called matrix-product Ansatz (MPA). We present in detail the exact solution for the model with sublattice-parallel and sequential updates using the MPA. For the case of parallel update, which is important for applications like traffic flow theory, we determine the phase diagram, the current, and density profiles based on Monte Carlo simulations. We furthermore suggest an MPA for that case and derive the corresponding matrix algebra.     

Size exclusion chromatography with dual-beam refractive index gradient detection of polystyrene samples

Non-aqueous size exclusion chromatography (SEC) of polystyrenes (as model analytes) is examined using the microscale molar mass sensor (μ-MMS) for detection. The μ-MMS is combined with SEC to demonstrate this simultaneously universal and molar mass selective detection method for polymer characterization. The μ-MMS is based on measuring the refractive index gradient (RIG) at two positions (upstream and downstream) within a T-shaped microfluidic channel. The RIG is produced from a sample stream (eluting analytes in the mobile phase) merging with a mobile phase stream (mobile phase only). The magnitude of the RIG is measured as a probe beam deflection angle and is related to analyte diffusion coefficient, the time allowed for analyte diffusion from the sample stream toward the mobile phase stream, and the bulk phase analyte refractive index difference relative to the mobile phase. Thus, two deflection angles are measured simultaneously, the upstream angle and the downstream angle. An angle ratio is calculated by dividing the downstream angle by the upstream angle. The μ-MMS was found to extend the useful molar mass calibration range of the SEC system (nominally limited by the total exclusion and total permeation regions from ∼100,000 g/mol to ∼800 g/mol), to a range of 3,114,000-162 g/mol. The injected concentration LOD (based on 3 s statistics) was 2 ppm for the upstream detection position. The point-by-point time-dependent ratio, termed a ‘ratiogram’, is demonstrated for resolved and overlapped peaks. Within detector band broadening produces some anomalies in the ratiogram shapes, but with highly overlapped distributions of peaks this problem is diminished. Ratiogram plots are converted to molar mass as a function of time, demonstrating the utility of SEC/μ-MMS to examine a complex polymer mixture.     

Molecular weight control of polyacrylamide with sodium formate as a chain‐transfer agent: Characterization via size exclusion chromatography/multi‐angle laser light scattering and determination of chain‐transfer constant

We discuss the synthesis and characterization of polyacrylamide (PAM) homopolymers with carefully controlled molecular weights (MWs). PAM was synthesized via free‐radical solution polymerization under conditions that yield highly linear polymer with minimal levels of hydrolysis. The MW of the PAM homopolymers was controlled by the addition of sodium formate (NaOOCH) to the polymerization medium as a conventional chain‐transfer agent. MWs and polydispersity indices (PDIs) were determined via size exclusion chromatography/multi‐angle laser light scattering analysis; for polymerizations carried out to high conversion, PAM MWs ranged from 0.23 to 6.19 × 10⁶ g/mol, with most samples having PDI ≈2.0. Zero‐shear intrinsic viscosities of the polymers were determined via low‐shear viscometry in 0.514 M NaCl at 25 °C. Data derived from the polymer characterization were used to determine the chain‐transfer constant to NaOOCH under the given polymerization conditions and to calculate Mark–Houwink–Sakurada K and a values for PAM in 0.514 M NaCl at 25 °C. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 560–568, 2003     

Elution Behaviour of Monocarboxylic Acids on a Cation-exchange Resin Column

The retention mechanism of monocarboxylic acids on a cation-exchange resin column was investigated. It was assumed that both Donnan membrane equilibrium and adsorption equilibrium were involved in the chromatographic process. On the basis of the proposed mechanism, an equation was derived for correlating distribution coefficient, Kd, dissociation constant, Aa, and adsorption equilibrium constant, K, of the analyzed acid. By this approach, retention data for some aliphatic acids under different operating conditions were predicted. Results are reasonably in agreement with experiment.     

Advanced analytical methods for the structure elucidation of polystyrene-b-poly(n-butyl acrylate) block copolymers prepared by reverse iodine transfer polymerisation

Reverse iodine transfer polymerisation (RITP) is a living radical polymerisation technique that has shown to be feasible in synthesising segmented styrene-acrylate copolymers. Polymers synthesised via RITP are typically only described regarding their bulk properties using nuclear magnetic resonance spectroscopy and size exclusion chromatography. To fully understand the complex composition of the polymerisation products and the RITP reaction mechanism, however, it is necessary to use a combination of advanced analytical methods. In the present RITP procedure, polystyrene was synthesised first and then used as a macroinitiator to synthesise polystyrene-block-poly(n-butyl acrylate) (PS-b-PBA) block copolymers. For the first time, these PS-b-PBA block copolymers were analysed by a combination of SEC, in situ¹H NMR and HPLC. ¹H NMR was used to determine the copolymer composition and the end group functionality of the samples, while SEC and HPLC were used to confirm the formation of block copolymers. Detailed information on the living character of the RITP process was obtained.     

Separation and quantification of quantum dots and dissolved metal cations by size exclusion chromatography–ICP-MS

The prevalence of engineered metallic nanoparticles within electronic products has evoked a need to assess their occurrence and fate within environmental systems upon potential release of these nanoparticles. Quantum dots (QDs) are mixed-metal nanocrystals with the smallest of particle sizes (2–10 nm) that readily leach heavy metal cations in water, potentially creating a co-occurrence of nanoparticulate and dissolved metal pollutants. In this report, we develop a size exclusion chromatography–inductively coupled plasma–mass spectrometry method (SEC-ICP-MS) for the rapid separation and quantification of ~5-nm-sized CdSe/ZnS QDs and dissolved Cd²⁺ and Zn²⁺ cations in water. The SEC-ICP-MS method provided a wide chromatographic separation of CdSe/ZnS QDs and dissolved Cd²⁺ and Zn²⁺ cations only when using the smallest SEC column pore size available and an eluent composition that prevented loss of metals to column polymer surfaces by using a surfactant to ensure elution of QDs (ammonium lauryl sulfate) and a complexing ligand to ensure elution of metal cations (ethylenediaminetetraacetate). Detection limits were between 0.2 and 2 µg L^–1 for Cd²⁺ and Zn²⁺ among dissolved cation and QD phases, and ranges of linearity covered two to three orders of magnitude. Gold nanoparticles of sizes 5, 10, 20 and 50 nm were also effectively separated from dissolved Au³⁺ cations, illustrating the method applicability to a wide range of nanoparticle sizes and compositions. QD and dissolved metal concentrations measured by SEC-ICP-MS were comparable to those measured using the more conventional method of centrifuge ultrafiltration on split samples for dissolved and total metals. The applicability of the SEC-ICP-MS method to environmental systems was verified by measuring QDs and dissolved metals added to samples of natural waters. The method was also applied to monitoring CdSe/ZnS dissolution kinetics in an urban river water. The SEC-ICP-MS developed here may offer improved automation for characterising heterogeneous suspensions containing >1 µg L^–1 heavy metals.