Generalized Universal Molecular Weight Calibration Parameter in GPC

Abstract

In this report we show by experimental and theoretical investigations that the commonly used GPC universal calibration parameter, the intrinsic viscosity multiplied by the weight average molecular weight ([η] M^w) is incorrect. The error which can arise by using [η] M to calculate the molecular weight across the GPC chromatogram for nonuniformly branched polymers [poly(vinyl acetate) and low density polyethylene] and copolymers with compositional drift, could be very large. We also show conclusively that the number average molecular weight M_n is the correct average to use for the universal calibration parameter. We therefore recommend that our general universal Calibration parameter [η] M_n be used for calculating the molecular weight across the chromatogram for all polymer systems (linear and branched homopolymers, copolymers with or without compositional drift and for polymer blends).     

Polymerization of vinyl chloride with organolithium compounds. V. Fractionation and solution properties of high molecular weight poly(vinyl chloride)

A sample of high molecular weight poly(vinyl chloride) (PVC) was fractionated by classical precipitation fractionation and gel-permeation chromatography (GPC) on a preparative scale. The fractions thus obtained were characterized by light scattering, viscometry, and by the GPC method. The measured weight-average molecular weights M?_w, intrinsic viscosity [η], and polydispersity index M?_w/M?_n values were used for the determination of the Mark-Houwink equation, [η] = KM^a, for PVC in cyclohexanone (CHX) at 25°C valid for molecular weights from 100,000 to 625,000.     

Development of gel permeation chromatography for polymer characterization. II. Universal calibration

GPC appearance volumes have been determined for a series of linear polyethylene, polystyrene, and polybutadiene fractions (M_w/M_n < 1.1) in trichlorobenzene at 130°C. and for the latter two series in tetrahydrofuran at 23°C. A polymer-type independent relationship between appearance volumes and the equivalent hydrodynamic radii of the polymer molecules has been demonstrated. The equivalent hydrodynamic radius is calculated from intrinsic viscosity data. It is proposed that this relationship can be used to construct a universal GPC calibration curve for polymers that assume a spherical conformation in solution. Methods for applying the universal curve to the determination of molecular weight averages and molecular weight distribution are described. In addition, a method is outlined by which the universal calibration curve can be empolyed for determining number-average Mark-Houwink constants from polydisperse samples.     

Determination of molecular weight distribution of cellulose by conversion into tricarbanilate and fractionation

Two samples of cellulose (molecular weight 2.97 × 10⁵ and 1.25 × 10⁵) were transformed into carbanilates (CTC) which were then fractionated by the elution method at a constant composition of the acetone-water elution mixture with the column temperature gradually increasing from ?30°C to 30°C, and by the GPC method in acetone and tetrahydrofuran. Tetrahydrofuran appeared to be a more suitable solvent. The molecular weights of fractions obtained by the elution fractionation were determined by the light-scattering method in tetrahydrofuran. The width of fractions was determined by the GPC method (average M _w/M _n = 1.37); the [η] values and the Mark-Houwink constants (K = 5.3 × 10^-3, a = 0.84) for tetrahydrofuran at 25°C were determined. The calibration curve for the GP method was constructed by means of the fractions thus obtained; it was demonstrated that the universal calibration curve according to Benoit can also be used. It was demonstrated that the molecular weight distribution of cellulose can be conveniently determined by conversion into CTC followed either by the elution fractionation (for preparative purposes) or by fractionation by the GPC method (for analytical purposes).     

Poly(2,6-diphenyl-1,4-phenyl oxide): Characterization by gel-permeation chromatography,light scattering,and solution viscosity

Ten unfractionated poly(2,6-diphenyl-1,4-phenylene oxide) samples were examined by gel permeation chromatography (GPC) and intrinsic viscosity [η] at 50°C in benzene, by intrinsic viscosity at 25°C in chloroform, and by light scattering at 30°C in chloroform. The GPC column was calibrated with ten narrow-distribution polystyrenes and styrene monomer to yield a “universal” relation of log ([η]M) versus elution volume. GPC-average molecular weights, defined as M?gpc = \documentclass{article}\pagestyle{empty}\begin{document}$\Sigma w_i [\eta ]_i M_i /\Sigma w_i [\eta ]_i$\end{document}, w_i denoting the weight fraction of polymer of molecular weight M_i, were computed from the GPC and [η] data on the polyethers. The M?GPC were then compared with the weight-average M?_w from light scattering. The intrinsic viscosity (dl/g) versus molecular weight relations for the unfractionated poly(2,6-diphenyl-1,4-phenylene oxides) determined over the molecular weight range 14,000 ≤ M?_w ≤ 1,145,000 are log [η] = ?3.494 + 0.609 log M?_w (chloroform, 25°C) and log [η] = ?3.705 + 0.638 log M?_w (benzene, 50°C). The M?_w(GPC)/M?_n(GPC) ratios for the polymers in the molecular weight range 14,000 ≤ M?_w ≤ 123,000 approximate 1.5 according to computer integrations of the GPC curves with the use of the “universal” calibration and the measured log [η] versus log M?_w relation. The higher molecular weight polymers (326,000 ≤ M?_w ≤ 1,145,000) show slightly broadened distributions.     

Crystallizable Polyphenylacetylene-Preparation and Solution Properties

The molecular weight distribution (MWD) of crystallizable polyphenylacetylene prepared near room temperature in the presence of ferric acetylacetonate and triethylaluminum was determined through use of fractions characterized by vapor pressure osmometry and gel permeation chromatography (GPC). The number- and weight-average molecular weights (M _n and M _w) are both less than the molecular weight corresponding to the maximum of the weight distribution function, which lacks a high molecular weight tail. M _wandM _n is less than is consistent with models allowing for chain termination characteristic of vinyl polymers. GPC elution volumes are much less than those characteristic of polystyrene of similar molecular weight, and the Mark-Houwink exponent is high (2.4 for M _v 4800 to 6800). These data indicate more rodlike behavior than for polystyrene of equivalent molecular weight. The MWD and other data suggest intramolecular chain termination, possibly associated with the molecule's tendency to form paramagnetic defect states.     

Universal calibration in GPC

The M[η]-elution volume calibration curve for gel-permeation chromatography (GPC) is based on the implicit assumption that the hydrodynamic volume of a solvated polymer species in the GPC columns is that which pertains at infinite dilution. This is not true of highly solvated high molecular weight fractions and results in apparent failure of this calibration in some instances. A model is presented to estimate hydrodynamic volumes of polymers at finite concentrations. The parameters required are polymer concentration, molecular weight, amorphous density, and the Mark-Houwink constants for the particular polymer–solvent combination. The calculated log (hydrodynamic volume)–elution volume relation provides a universal GPC calibration. The model accounts for the occasional shortcomings of the infinite dilution calibration and is essentially equivalent to it in noncritical cases. The use of the proposed calibration method is illustrated.     

Polymerization of 1-octene and determination of markhouwink constants of poly(1-octene)

The polymerization of 1-octene initiated by methylalumoxane（MAO）-activated Ni（Ⅱ）-based-α-diimine complexes[（2,6-i-Pr）₂C₆H₃-DAB（An）]NiBr₂ was investigated.Using this catalyst,poly（1-octene）s with molecular weight between 100×10³ and 400×10³ and polydispersity（M_w/M_n） between 1.3 and 1.5 were synthesized successfully by varying reaction time at room temperature.The poly（1-octene）s were amorphous polymers and could be well soluble in tetrahydrofuran（THF）.After fractional precipitation,poly（1-octene）s with narrow molecular weight distributions（M_w/M_n≤1.12） were obtained.Their weight-average molecular weights were measured by gel permeation chromatography（GPC） in conjunction with online model BI-MwA multiangle laser light scattering（MALLS）,and their intrinsic viscosities were measured by Maron’s single-point method.The k and a values in Mark-Houwink equation[η]= KM^αin THF at 40℃were 0.089 mL/g and 0.61 respectively.     

Chromatographic mass of a polymer and its use for determining the molecular mass characteristics

The method has been proposed for determining the molecular characteristics of flexible-chain polymers that obey the universal calibration principle and for which there are available experimental data on the intrinsic viscosity. This method is based on studying the dependence of the hydrodynamic volume M _n[η], M _w[η], M _z[η], and M _η[η] on parameter a in the Mark-Kuhn-Houwink equation. It has been found that, for parameter a varying in the range from 0.5 to 0.8, the weight-average hydrodynamic volume M _w[η] remains almost unchanged. This allows estimation of M _w based on a single intrinsic viscosity value. The notion of the chromatographic mass of a polymer is advanced and is employed for determining other molecular mass parameters.     

Characterization of Copolymers and Polymer Mixtures by Gel Permeation Chromatography

Abstract

Estimation of molecular weights from GPC data is complicated when the polymer sample consists of a mixture of homopolymers or of statistical copolymers with nonuniform compositions. This is because sizes of solvated polymer coils depend on solvent interaction with both the homo-and hetero-units of the copolymers and because the extent of solvation of different homopolymers can differ. The overall degree of solvation may change effectively with composition and use of a single “average” set of Mark-Houwink constants in calibration procedures will then produce false molecular weight data from the GPC data. A new molecular weight average, M _x, is defined to overcome this problem. This average can be determined from the GPC chromatogram and intrinsic viscosity of the sample in the GPC solvent. Mark-Houwink coefficients are not needed. M _x lies between M _w and M _z.     

On-line viscometry combined with gel permeation chromatography. I. Instrumental calibration and testing with linear polymers

Gel permeation chromatography (GPC) was combined with flow time measurements on the eluent to provide both the distribution of hydrodynamic volumes and the distribution of intrinsic viscosities in linear polymers. Standard polystyrene samples were used to establish a universal hydrodynamic volume calibration as well as the zone spreading and viscometer transfer line tailing parameters. Viscometry data are particularly helpful in establishing the zone spreading parameters and the calibration curve at very high molecular weights. The results were applied to measurements on samples of linear polybutadiene and polyvinyl acetate. Agreement between values of M _w from GPC with those obtained by light scattering confirmed the universal calibration principle.     

Universal calibration in GPC: A study of polystyrene,poly-α-methylstyrene,and polypropylene

The theoretical justification for using M[_η], or a similar quantity, as a universal calibration parameter in GPC is reviewed. The equation based on this parameter is applied to transform the primary calibration curve, obtained by means of polystyrene samples, into calibration curves for poly-α-methylstyrene, polypropylene, and linear polyethylene. The Mark–Houwink equations for these polymers, as they are used in the transformation, are discussed. The resulting GPC calibration curves are compared with molecular weights and peak elution volumes of fractionated poly-α-methylstyrene and polypropylene. The same comparison is made with samples of polypropylene and polyethylene having very broad molecular weight distributions. The agreement lies within experimental error.     

Characterization of Branched Poly (vinyl Acetate) by GPC and Low Angle Laser Light Scattering Photometry

Abstract

Poly (vinyl acetate), PVAC, synthesized by bulk polymerization over a range of initiator concentrations ([AIBN] = 10^?5 to 4 × 10^?3 g-mole/1), temperatures (50°C, 60°C, 70°C, and 80°C) and conversion levels (3 to > 90%) were characterized using low angle laser light scattering (LALLS) photometry to measure M_w of the whole polymers. A number of these samples were characterized using GPC with a differential refractive index (DRI) and LALLS detector to measure the molecular weight distribution (weight fraction versus M_w). M_w for PVAC samples synthesized at suitably low initiator levels at various conversions were found to agree with classical light scattering measurements after Graessley.

An electronic device and a technique which optimizes the sensitivity and the signal-to-noise ratio of the LALLS photometer throughout the molecular weight distribution (MWD) of the GPC chromatogram were devised. These considerably simplify the operation of the LALLS for both offline and online operation with GPC.

Most importantly it was unambiguously shown that the commonly used universal calibration parameter (UCP) with GPC, [n]M_w, is incorrect for polymers with molecules having the same hydrodynamic volume but different molecular weights, i. e., those with only chain branching (LCB), copolymers with compositional drift, and polymer blends. The correct UCP was found to     

Analysis of Low Molecular Weight Polymers with Gel Permeation Chromatography

Intrinsic viscosities and gel permeation chromatography (GPC) elution times were determined in toluene on commercially available standards of polystyrene (PSTY) and polymethyl methacrylate (PMMA) having M_n in the range of 10³ to 10⁵ and 10⁴ to 10⁶, respectively. In addition, elution times were determined on the discrete GPC peaks of dimer, trimer, tetramer, etc. as seen in lower molecular weight PSTY and PMMA. Intrinsic viscosities of oligomers were estimated by extrapolation of the Mark-Houwind-Sakurada equations determined from our data, and the results were used to establish a universal calibration curve over a wide range of molecular weights. A similar approach was taken by using literature data for the intrinsic viscosities of PSTY and PMMA in tetra-hydrofuran. It was verified by proton NMR that the universal calibration curve so constructed is useful at M_n, values as low as 300. No correction was necessary for chain length dependence of the detector response.     

Some applications of gel-permeation chromatography in investigations of structure and the solution properties of radical-initiated poly(vinyl chloride)

The applicability of the published universal calibration parameters for gel-permeation chromatography on polystyrene standards and poly(vinyl chloride) samples with a defined structure has been compared. It was shown experimentally that of several theoretically possible molecular weight averages attributed to the elution volume at the position of the peak maximum, the root mean-square average molecular weight M _Rms = (M _wM _n)^0.5 shows the best accordance. The molecular weights obtained by gel-permeation chromatography were compared with those determined by viscometry, osmometry, and the light-scattering method. The reproducibility of gel-permeation chromatography measurements is 3%, and the average variance of the results as compared with results obtained by the above methods is about 8%. It was also found that the gel-permeation chromatography does not involve any anomalies interfering with results obtained by other methods.     

Aromatic poly(amic acids): Fundamental structural studies

Aromatic poly(amic acids) derived from pyromellitic dianhydride and 4,4′,-diaminodiphenyl ether were characterized by dilute solution techniques. Number-average molecular weights M?_n of 13 samples ranged from 13,000 to 55,000 (DP 31–131). Weight-average molecular weights M?_w of 21 samples ranged from 9,900 to 266,000. The ratio M?_w/M?_n was between 2.2 and 4.8. Heterogeneous polymerization yielded higher molecular weight polymer than homogeneous polymerization. The molecular weight could be varied systematically by control of stoichiometric imbalance. Use of very pure monomers and solvent gave polymers of relatively high number-average molecular weight (～50, 000) and the most probable molecular weight distribution M?_w/M?_n = 2. Impure monomers and/or solvent resulted in lower number-average molecular weight (M?_n ? 20,000–30,000) and wider distributions (M?_w/M?_n = 3–5). The Mark-Houwink relation obtained was [η] = 1.85 × 10^?4M?_w^0.80 The exponent is characteristic of moderately extended solvated coils. The unperturbed chain dimensions (r₀² /M)^1/2 were 0.848 A., and the steric factor σ was 1.24 which is close to the limiting value of unity for an equivalent chain with free internal rotations. The sedimentation constant–molecular weight relation was S₀ = 2.70 × 10^?2M?_w^0.39. This exponent is consistent with the Mark-Houwink exponent.     

SOLUTION PROPERTIES OF LADDER-LIKE POLYMER POLYPHENYLSILSESQUIOXANES

Solution properties of ladder-like polymer polyphenylsilsesquioxane (PPS) were studied by measurement of intrinsic viscosity, small angle laser light scattering and gel permeation chromatography. It was found that PPS can be modeled with a wormlike continuous cylinder rather than a wormlike coil. A plot of (M~2/[η])~(1/3) vs. M~(1/2) was employed in obtaining the persistence length (2λ)~(-1) and effective hydrodynamic diameter. When MW≤5×10~5, Mark-Houwink equation is adequate in describing the relationship between MW and [η] with αabout unity. This implies that PPS chain is semi-stiff. For GPC experiments, it was shown that universal calibration can be applied in PPS. When molecular weights of PPS are sufficiently high, their molecular weight distributions are often very broad.     

Synthesis and Characterization of Styrene-Isoprene Diblock Copolymers

A simple reusable apparatus for the synthesis of up to 40 g quantities of poly(styrene-b-isoprene) diblock copolymers of reasonably low (1.2 to 1.5) polydispersity has been described. The diblock copolymers synthesized were characterized by gel permeation chromatography (GPC), membrane osmometry, viscosimetry, and nuclear magnetic resonance (NMR) spectroscopy. Number-average molecular weights (M _n) calculated from the raw GPC chromatographs of the diblock copolymers using the summation method and M versus elution volume plots for polystyrene and polyisoprene standards agree well with those measured experimentally with osmometry. It is suggested that for polydisperse block copolymers this method is simpler than the use of a universal calibration curve. Mark-Houwink constants K ans a for polyisoprene having 18% (1,2-), 66% (3,4-), and 16% (1,4-) microstructure were found to be 3.2 × 10^?4 dL/g and 0.67, respectively, in THF at 25°C. In toluene at 30°C, K = 2.0 × 10^?4 dL/g and α = 0.7 were obtained. The diblock copolymers had 26% (1,2-), 60% (3,4-), and 14% (1,4-) microstructure in the isoprene segments, and the values of K and a for these copolymers (PS > 50%, M 20.0 × 10³) in THF at 25°C were 9.0 × 10^?5 dL/g and 0.75. For M < 20.0 × 10³ the value of α was 0.5. The experimental values of [η] were found to be lower than those calculated theoretically, presumably due to the polydisperse nature and the biellipsoidal configuration of the diblock copolymers.     

Determination of the Molecular Weight Distribution of Polyethylene Terephthalate by Gel Permeation Chromatography

Abstract

The determination of the molecular weight distribution of polyethylene terephthalate by GPC at room temperature is described. The solvent used is o-chlorophenol-chloroform (1:9) and pure chloroform is used as eluent. K and alpha of the Mark-Houwink equation of polyethylene terephthalate and of polystyrene in this solvent system were obtained. It was shown that the universal calibration can be applied.     

Intrinsic viscosity of polymers of low molecular weight

Experimental evidence concerning the dependence of the intrinsic viscosity [η] on molecular weight M in the low molecular weight range (from oligomers to M = 5 × 10⁴) has been collected in a variety of solvents for about ten polymers, i.e., polyethylene, poly(ethylene oxide), poly(propylene oxide), polydimethylsiloxane, polyisobutylene, poly(vinylacetate), poly(methyl methacrylate), polystyrene, poly-α-methylstyrene, and some cellulose derivatives. In theta solvents, the constancy of the ratio [η]Θ/M^0.5 extends down to values of M much lower than those predicted by current hydrodynamic theories. In good solvents, and on decreasing M, the polymers examined, with the exception of polyethylene and some cellulose derivatives, show a decrease in the exponent a of the Mark-Houwink equation [η] = KM^a. This upward curvature gives rise to the existence of a more or less extended linear region where the equation [η] = K₀M^0.5 is obeyed. Below the linear range, i.e., for even shorter chains, the exponent a can increase, i.e., polydimethylsiloxane, or decrease below 0.5, i.e., poly(ethylene oxide), depending on the particular chain properties. These different dependences have been discussed in terms of: (a) variations of thermodynamic interactions with molecular weight; (b) variations of conformational characteristics (as for instance the ratio) 〈r0²/nl²〉, where 〈r0²〉 is the unperturbed mean square end-to-end distance and n is the number of bonds each of length l; (c) hydrodynamic properties of short chains.