Gel-permeation chromatography: A procedure that corrects for imperfect resolution

Gel-permeation chromatography is an excellent tool for obtaining polymer fractionation data. Inasmuch as chromatograms are functions of instrument operating conditions, an interpretation procedure must be employed to yield correct molecular distributions of macromolecular materials. A procedure is described that corrects for imperfect resolution. Extensive experimental testing of polymeric materials with kinetically known molecular distributions demonstrates its validity in regions where poor resolution is experienced. Applications will allow one to utilize equipment with inherently poor resolution or to operate instruments with high resolution in regions of poor resolution (e.g., rapid analysis).     

Gel permeation chromatography: calibration procedures for chains containing p-phenylene units

Experimental gel permeation chromatography calibrations have been obtained for polystyrene standards, polysulphone fractions, and polycarbonate fractions in chloroform at 30°. Chloroform is a good solvent for all three polymers which have similar polymer solvent interactions. The fractions have narrow molecular weight distributions, so that viscosity average molecular weight can be taken as the peak molecular weight of a chromatogram. The experimental polysulphone and polycarbonate calibrations are compared with curves calculated from the polystyrene calibration using equations which assume that the unperturbed mean-square end-to-end distance and hydrodynamic volume are universal calibration parameters. For molecular weights between 20,000 and 100,000 both universal calibration procedures were found to be acceptable. For polycarbonate extended chain length was also found to be satisfactory for universal calibration. For polycarbonate molecular weights below 20,000, the predicted molecular weight calibration deviated from the experimental data. Possible reasons for this difference are discussed.     

Poly(vinylacetate): reference materials and universal calibration in gel permeation chromatography

Well-characterized fractions of linear poly(vinylacetate) have been used to establish the validity of universal calibration for that polymer in gel permeation chromatography. Viscosity parameters have been determined and comparisons made with earlier work.     

Applicability of the modified universal calibration of gel permeation chromatography on proteins

The modified universal calibration of gel permeation chromatography (GPC) has been applied in the case of native proteins. Plotting log([eta]M/Phi) versus elution volume, instead of log[eta]M versus elution volume used till now, we obtain unique curves with different proteins and non-proteonic polymers ([eta]: intrinsic viscosity, M: molecular mass, Phi: Flory's parameter). The values of Flory's parameter Phi are calculated for each protein using an indirect method based on GPC.     

Gel permeation chromatography and cellulose. II. Application of universal calibration

In previously reported work concerning the chain-length distributions obtained by gel permeation chromatography (GPC) in celluloses, degrees of polymerization (DP) of unusually high magnitude were reported. Later work in GPC has shown that the concept of relating extended nolecular chain length of different polymers to elution volume for obtaining molecular weight is not theoretically sound. Correlation of molecular hydrodynamic volume (indicated by the product of intrinsic viscosity and molecular weight) with elution volume has been found to place polymers of vastly different natures on a single curve, such is now designated universal calibration. Application of universal calibration to the determination of DP distributions in celluloses required a different method of converting counts to DP. This new procedure is described in detail. Weight-average DP's given by the procedure for samples of cellulose I, II, III, and IV were 5190, 4520, 4795, and 3390, respectively. These are decreases of 74–75% from the results obtained by the extended-chain procedure. The results compare favorably with the viscosity-DP's of the samples. Number-average DP's were 1580, 1040, 1140, and 490 for the four samples, respectively, these being decreases of 87–93% from the values formerly reported. The polymolecularity ratios for the samples are now unusually large, being 3.4, 4.7, 4.2, and 7.1, respectively.     

Modification of the universal calibration of gel permeation chromatography to include macromolecules presenting a draining effect

A new universal calibration for gel permeation chromatography is proposed in which the hydrodynamic volume of the macromolecular chains is expressed by the quantity [η]M/Φ instead of the commonly used quantity [η]M (where [η] is the intrinsic viscosity, M is the molecular mass, and Φ is Flory's parameter). Introducing Φ into the hydrodynamic volume is necessary because its value changes from one polymer to another when the polymers present a certain draining effect. The proposed procedure also allows the determination of Φ of any wormlike polymer. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 707–710, 2003     

Quantitative nanotribology by AFM: a novel universal calibration platform

The quantitative determination of friction forces by atomic force microscopy (AFM) in nanotribology requires the conversion of the output voltage signal of the sector area-sensitive photodiode to force using (a) the torsional spring constant of the cantilever and (b) the lateral sensitivity of the photodiode. Many existing methods provide calibration factors with large errors and suffer from poor reproducibility. We report on the fabrication, validation, and application of a new, universally applicable standard specimen that enables one to accurately calibrate all types of AFM cantilevers and tips for quantitative friction force measurements. The Si(100) calibration standard, which exhibits 30 and 50 mum wide notches with tilt angles theta between 20 degrees and 35 degrees with respect to the wafer surface, was fabricated by focused ion beam (FIB) milling. The quantification of friction forces obtained on this universal standard specimen using a direct method (the improved wedge calibration method, as introduced by Ogletree, Carpick, and Salmeron Rev. Sci. Instrum. 1996, 67, 3298-3306), which yields (a) and (b) simultaneously, was critically tested for various types of Si3N4 integrated cantilever-tip assemblies. The error in the calibration factors obtained was found to be ca. 5%, which is a significant improvement compared to errors of 30-50% observed for the often applied two-step calibration procedures of cantilever lateral force constant and photodiode sensitivity. As demonstrated for oxidized Si(100), thin films of poly(methyl methacrylate) (PMMA), and micropatterned self-assembled monolayers (SAMs) on gold, the calibration of various V-shaped and single beam cantilevers based on the application of the new universal standard in conjunction with the direct wedge method proposed allows one to conveniently perform quantitative nanotribological measurements for a wide range of materials and applications.     

Determination of the viscometric constants for chitosan and the application of universal calibration procedure in its gel permeation chromatography

The viscometric constantsa andK in the Mark-Houwink equation were determined in 0.5 M acetic acid-0.5 M.sodium acetate solution for chitosan fractionated by gel filtration. The weight-average molecular weight of each fraction was measured by the light-scattering method. The values obtained area=0.59 andK=0.119 cm³ g^–1.The molecular weightsMw andMn for fractionated chitosan were measured by GPC. The value ofMw by GPC was much different from that by light scattering and, therefore, a universal calibration procedure was applied to the data by GPC. It was concluded that, also in the case of a cationic polysaccharide such as chitosan, the universal calibration procedure is effective for obtaining the reliable molecular weight by GPC.     

Swelling of a polymer brush by a poor solvent

The addition of a small amount of a poor solvent impurity (methanol) to a theta solvent (cyclohexane) is found to cause appreciable swelling (≈30% increase of the average brush height) in a model end‐grafted polystyrene (PS) brush layer. This unusual type of swelling is not observed if octadecyltrichlorosilane (OTS) is first grafted to the portion of the silicon substrate uncovered by the grafting end‐groups of the PS chains. Brush swelling in the absence of OTS surface protection is interpreted as arising from a segregation of methanol to the solid substrate and the resulting modification of the polymer–surface interaction. We also observe that the addition of a small amount of methanol to an adsorbed PS layer exposed to cyclohexane causes rapid film delamination from the silicon substrate. Together these observations imply a strong influence of surface active impurities on the structure and adhesive stability of polymer layers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4126–4131, 2004     

Choice of procedures for preparative chromatography

Quantitative criteria, necessary and sufficient, were developed basing on the analysis of asymtotic solutions of border equations in elution sorption dynamics for realization of selectivity inversion for components in a chromatographic system due to the effect of kinetic selectivity. Analysis is suggested for experiments, where the new approach to realization of chromatographic processes using effect of kinetic selectivity allows optimization of preparative separation of biologically active substances. The approach suggested implies shortening of the experiment duration for separation processes, which can be crucial in most systems where components to be isolated are labile, or the process economics suffers considerably due to mobile phase, or energy consumption.     

Gel-permeation chromatography. IX. Instrumental design and computer interfacing of a GPC molecular weight detector system

The detailed design and computer interfacing of a GPC molecular weight detector based on a real time viscometer are described. The working drawings presented will permit one to fabricate and duplicate the viscometer and the complete GPC molecular weight detector system. The uses and advantages of a laboratory automation system in analyzing GPC results are also described.     

Evaluation of measurement uncertainty for analytical procedures using a linear calibration function

In the EURACHEM/CITAC draft ”Quantifying uncertainty in analytical measurement” estimations of measurement uncertainty in analytical results for linear calibration are given. In this work these estimations are compared, i.e. the uncertainty deduced from repeated observations of the sample vs. the uncertainty deduced from the standard residual deviation of the regression. As a result of this study it is shown that an uncertainty estimation based on repeated observations can give more realistic values if the condition of variance homogeneity is not correctly fulfilled in the calibration range. The complete calculation of measurement uncertainty including assessment of trueness is represented by an example concerning the determination of zinc in sediment samples using ICP-atomic emission spectrometry. Received: 9 February 2002 Accepted: 17 April 2002     

Kinetically frozen structures in polymer gels immersed in a poor solvent

Non‐equilibrium kinetically frozen structures were observed in weakly charged polyacrylamide gels immersed in a poor‐solvent. These structures are due to the vitrification of polymer‐rich regions inside the gel which appear during the gel collapse. The paper presents the main results of the study of these structures by electron microscopy, SAXS and mechanical measurements.     

An evaluation of two calibration procedures using thermal desorption-gas chromatography in the analysis of odorous volatile compounds

In this study, the relative performance of gas chromatography (GC) was investigated with respect to the differences in two types of calibration approaches with a thermal desorption (TD) method: the fixed standard concentration approach (FSC: the comparison of different sample volumes for a given standard) was compared with the fixed standard volume approach (FSV: the comparison of different concentration standards at a fixed loading volume). Gaseous working standards of seven odorants, including methyl ethyl ketone (MEK), butyl acetate, methyl isobutyl ketone, isobutyl alcohol, toluene, xylene, and a reference component, benzene, were prepared at four concentration levels (10-100 ppb). They were then analyzed by controlling the TD-loading volumes at six levels (40-1200 mL). The results derived by these contrasting calibration approaches showed moderate changes in the GC sensitivity, either with an increasing concentration (i.e., FSC), or with an increasing sample loading volume (i.e., FSV). Despite an eccentric trend of MEK, the TD-based analysis was fairly predictable and can be recommended for the analysis of the selected odorants.     

Phase transitions of a single polyelectrolyte in a poor solvent with explicit counterions

Conformational properties of a single flexible polyelectrolyte chain in a poor solvent are studied using constant temperature molecular dynamics simulation. The effects of counterions are explicitly taken in to account. Structural properties of various phases and the transition between these phases are studied by tracking the values of asphericity, radius of gyration, fraction of condensed counterions, number of non-bonded neighbours, and Coulomb interaction energies. From our simulations, we find strong evidence for a first-order phase transition from extended to collapsed phase consistent with earlier theoretical predictions. We also identify a continuous phase transition associated with the condensation of counterions and estimate the critical exponents associated with the transition. Finally, we argue that previous suggestions of existence of an independent intermediate phase between extended and collapsed phases is only a finite size effect.     

Second-order multivariate calibration procedures applied to high-performance liquid chromatography coupled to fast-scanning fluorescence detection for the determination of fluoroquinolones

Different second-order multivariate calibration algorithms, namely parallel factor analysis (PARAFAC), N-dimensional partial least-squares (N-PLS) and multivariate curve resolution-alternating least-squares (MCR-ALS) have been compared for the analysis of four fluoroquinolones in aqueous solutions, including some human urine samples (additional four fluoroquinolones were simultaneously determined by univariate calibration). Data were measured in a short time with a chromatographic system operating in the isocratic mode. The detection system consisted of a fast-scanning spectrofluorimeter, which allows one to obtain second-order data matrices containing the fluorescence intensity as a function of retention time and emission wavelength. The developed approach enabled us to determine eight analytes, some of them with overlapped profiles, without the necessity of applying an elution gradient, and thus significantly reducing both the experimental time and complexity. The study was employed for the discussion of the scopes of the applied second-order chemometric tools. The quality of the proposed technique coupled to each of the evaluated algorithms was assessed on the basis of the figures of merit for the determination of fluoroquinolones in the analyzed water and urine samples. Univariate calibration of four analytes led to limits of detection in the range 20–40 ng mL⁻¹ and root mean square errors for the validation samples in the range 30–60 ng mL⁻¹ (corresponding to relative prediction errors of 3–8%). The ranges for second-order multivariate calibration (using PARAFAC and N-PLS) of the remaining four analytes were: limit of detection, 2–8 ng mL⁻¹, root mean square errors, 3–50 ng mL⁻¹ and relative prediction errors, 1–5%.     

Phase diagram for microphase separation transition in poor solvent polymer solutions

In the present paper, we consider the possibility of microphase separation transition in poor solvent polymer solutions. It is shown that this phenomenon can take place if the following two conditions are fulfilled: i) there is a large entropic contribution to the entropy of polymer/solvent mixing, i.e., solvent acts like a plastisizer; ii) this entropic contribution is nonlocal. Both conditions are met below the glass transition temperature for the pure polymer near the so-called Berghmans point when the glass transition curve intersects the liquid-liquid phase separation curve for polymer solutions. The phase diagram for the microphase separation transition is calculated within the framework of weak segregation approximation first proposed by Leibler for block-copolymer systems. The regions of stability of different microdomain structures (lamellar, triangular, body-centered-cubic) are obtained. It is shown that under certain conditions the phase diagram can have two critical points related to the macro- and microphase separation respectively.This paper is dedicated to Prof. E. W. Fischer on the occasion of his 65th Birthday.This work was done in the course of the Humboldt Research Award stay of A.R. Khokhlov at the Max-Planck-Institute for Polymer Research in Mainz. During this stay A.R.K. greatly benefited from numerous discussions with Professor E.W. Fischer who introduced him to the fascinating field of glass transition in polymer systems and formulated several new directions for future research.