Evaluation of light-scattering detectors for size exclusion chromatography. I. Instrument precision and accuracy

A systematic evaluation of two types of light-scattering detectors for size exclusion chromatography (SEC) was completed. The two detectors were the low-angle laser light scattering photometer (LALLS) and the multiangle laser light-scattering photometer (MALLS). Instrument evaluations were performed at both room (30–40°C) and high (135–145°C) temperatures using the polystyrene standard, NBS 706, at room temperature and the polyethylene standard, SRM 1476, at high temperature. Results of the evaluation showed that when experimental uncertainties were taken into account LALLS and MALLS demonstrated equivalent precision and accuracy for molecular weight determination. The main source of inaccuracy found (particularly for SRM 1476) was the sensitivity difference between the light-scattering and the concentration (DRI) detectors; i.e., the DRI detector was unable to measure very low concentrations of very high molecular weight material present in SRM 1476, whereas the light-scattering detectors respond strongly. It was shown that for LALLS the overall weight-average molecular weight (M?_w) for the whole polymer calculated using an equation that did not require the DRI detector output circumvented this sensitivity problem while assuming that the low angle used was sufficiently close to zero. Use of this equation for MALLS is possible by extrapolating data from all angles used to obtain a light-scattering chromatogram at zero angle. However, this possibility was not examined here. A particular advantage of MALLS over LALLS is that MALLS can provide the z-average root mean square radius (commonly referred to here and in other light-scattering literature as the “radius of gyration”) values from the same data as those used to obtain molecular weight values. Although the radius of gyration values at each retention volume were not as precise as the corresponding weight-average molecular weights, at room temperature, precision was better than 2% for a significant portion of the chromatogram. © 1993 John Wiley & Sons, Inc.     

Calibration of size-exclusion chromatography columns with polydisperse polymer standards. II. Applications

New methods for calibrating SEC columns by means of polydisperse polymer samples with known M_n and M_w have been tested with computer-generated chromatograms and with experimental data of high-performance SEC. Calculations with the artificial chromatograms show that accurate calibration dependences can be recovered even when polymers with broad and/or bimodal molecular weight distributions are used as standards. Polystyrene calibration calculated by the proposed method from chromatograms of five polydisperse polystyrenes follows closely the curve obtained in a conventional manner from nine narrow polystyrene standards. The dependence log M vs. ν for PMMA determined from chromatograms of six PMMA samples with moderately broad molecular weight distributions agrees well with the curve obtained by shifting the dependence for polystyrene using the universal calibration concept. The new method is particularly useful when SEC columns are to be calibrated for dextrans in water, where only a few standards having a rather broad molecular weight distribution are available, and can considerably improve the accuracy of molecular weight determination by SEC.     

Size exclusion chromatography with multiple detectors: Solution properties of linear chains of varying flexibility in tetrahydrofuran

Narrow molecular weight distribution polyisoprenes (PI), polybutadienes (PBD), poly(isobuty1enes) (PIB), poly(methylmethacry1ates) (PMMA), polystyrenes (PS), and poly(octadecy1 methacrylates) (PODMA) have been studied by size exclusion chromatography (SEC) in tetrahydrofuran (THF) with light scattering and viscometric detectors. The molecular weight (M) dependence of the intrinsic viscosity, [η], and radius of gyration, R_g, is reported for THF solutions of these polymers, in many instances for the first time. The availability of these data for a series of chains of varying flexibility allows a test of the universal calibration principle in SEC. Furthermore, an apparent dependence of the hydrodynamic parameter in good solvents, Φ, on chain stiffness is observed. All chains appear to exhibit hydrodynamic draining in THF. © 1996 John Wiley & Sons, Inc.     

Number-average molecular weight by size exclusion chromatography

It is now theoretically possible to obtain absolute accurate values of number-average molecular weight of complex polymers (e.g., branched polymers or copolymers) using size exclusion chromatography (SEC) with only a detector that measures the difference between the eluting polymer solution viscosity and the viscosity of the pure mobile phase (a differential viscometer [DV] detector). However, both precision and accuracy of these “DV M?_n” values are of concern. In this work, the precision of NBS 706 polystyrene was found to be two to three times worse for the DV M?_n than for the conventionally calculated M?_n. Also, regarding accuracy, the DV M?_n values were affected by the location of the universal calibration curve along the retention volume axis (a problem intimately associated with the problem of specifying the correct interdetector volume), the sensitivity of the DV detector to low molecular weights present in the sample, and axial dispersion. Each of these sources of error are examined in turn and two methods of calculating M?_n values are proposed. © 1994 John Wiley & Sons, Inc.     

Number‐average molecular weight of branched polymers from SEC with viscosity detection and universal calibration

BACKGROUND: Number‐average molecular weight, M?_n, is an important characteristic of synthetic polymers. One of the very few promising methods for its determination is size‐exclusion chromatography (SEC) using on‐line viscometric detection and assuming the validity of the universal calibration concept. RESULTS: We have examined the applicability of this approach to the characterization of statistically branched polymers using 22 copolymers of styrene and divinylbenzene as well as 3 homopolymers of divinylbenzene with various degrees of branching. SEC with three on‐line detectors, i.e. concentration, light scattering and viscosity, enables us to evaluate experimental data by various computational procedures yielding M?_n and weight‐average molecular weight, M?_w. Analysis of the results has shown that the universal calibration theorem has limited validity, apparently due to the dependence of the Flory viscosity function on the molecular shape, the molecular weight distribution and the expansion of molecules. CONCLUSION: For complex polymers, the universal calibration, i.e. the dependence of the product of intrinsic viscosity and molecular weight, [η]M, on elution volume, can differ in values of [η]M from those obtained for narrow molecular weight standards by 10–15%. The method studied is helpful for the determination of M?_n of polymers, in particular of those with very broad molecular weight distribution, such as statistically highly branched polymers. Copyright © 2008 Society of Chemical Industry     

Determination of molecular weight and size distribution and branching characteristics of PVAc by means of size exclusion chromatography/multi-angle laser light scattering (SEC/MALLS)

SEC/MALLS has been applied for the determination of molecular weight and size distributions and to quantify branching in polyvinyl acetate (PVAc). Linear and branched samples obtained by solution and bulk polymerization were analyzed. The molecular weight distribution of the branched polymer was broader and the mean square radius was found to be smaller, 38.8 nm (with molecular weight of 770?000), than for the linear polymer, 42.3 nm (with molecular weight of 740?000). Branching characteristics could be determined by using Zimm and Stockmayer equations. It has been found that the number of branches for the branched sample increases from about 1 to 9, per molecule, with increasing molecular weight.     

Dilute solution properties of randomly branched poly(methyl methacrylate)

Randomly branched poly(methyl methacrylate) samples were prepared by copolymerization with different amounts of ethylene dimethacrylate. The molecular weight distributions, radius of gyration distributions, and intrinsic viscosity distributions were measured by size exclusion chromatography with refractive index, multiangle light-scattering, and viscosity detectors. The effect of branching on the radius of gyration was compared with the effect on the intrinsic viscosity. It was found that the intrinsic viscosity contraction factor gⁱ scales with the radius of gyration contraction factor g, with the exponent, ϵ, having a value in the range 0.8–1.0. © 1996 John Wiley & Sons, Inc.     

Effects of different molecular weights of polystyrene on the acylation reaction and on the reaction kinetics

In this study, chemical modification reactions of polystyrenes with different molecular weights with maleic and acetic anhydrides in the presence of a catalyst [BF₃ · O(C₂H₅)₂] were examined. The number of polyfunctional groups bound to the polymer structure changed according to the molecular weight of the polymer, and more functional groups were bound to lower molecular weight polystyrenes. The bound functional groups and their amounts were determined with spectral and chemical analysis methods. The effects of the molecular weights of the polystyrenes on the chemical modification kinetics with maleic and acetic anhydrides in the presence of BF₃ · O(C₂H₅)₂ were examined. The kinetic parameters of the reaction and its activation energy were calculated. The higher the molecular weight of polystyrene was, the lower its rate of modification was and the greater its activation energy was; the lower the molecular weight of polystyrene was, the higher its rate of modification was and the lower its activation energy was. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 253–259, 2005     

Photoactive Polyesters Containing o-Nitro Benzyl Ester Functionality for Photodeactivatable Adhesion

The fabrication of modern microelectronic silicon devices mechanically challenges these thin silicon substrates during manufacturing operations. Melt and solution polyesterification enabled the synthesis of polyesters containing photoreactive o-nitro benzyl ester units for use as a potential photocleavable adhesive. Melt transesterification provided a solvent-free method for synthesis of 2-nitro-p-xylylene glycol (NXG)-containing polyesters of controlled molecular weights. ¹H NMR spectroscopy confirmed the chemical composition of the photoactive polyesters. Size exclusion chromatography (SEC) determined the number-average molecular weights (M_n) of the polyesters synthesized in the range of 6000 to 12000 g/mol. ¹H NMR spectroscopy confirmed increasing levels of photocleavage of the o-nitro benzyl ester functionality with increasing exposure to broad wavelength UV irradiation, and exposure levels ranged from 0–187 J/cm² UVA. Photocleaveage of approximately 90% of the o-nitro benzyl ester (ONB) units within the backbone of the polymer occurred at maximum dosage. Wedge fracture testing revealed approximately a two-fold decrease in fracture energy upon UV irradiation, suggesting that these structural adhesives offer potential for commercial “flip bonding” applications.     

Effect of molecular weight on the partial specific volume of polystyrenes in solution

The partial specific volume $\text{v}\text{?}{}_2$ of linear and branched polystyrenes has been measured as a function of molecular weight (1300<M_w<9×10⁶). In the low molecular weight range, the effect of end-groups is predominant. In the high molecular weight range (M_w > about 20 000), we have detected small but significant variations due to the intramolecular segment-segment contacts within the coil. We have proposed an empirical relation between $\text{v}\text{?}{}_2$ and the segment density of the macromolecule; this relation has been confirmed using highly branched polystyrenes. These results relative to dissolved polystyrenes are compared to experimental data obtained by different authors on pure liquid polystyrenes at different temperatures. Starting from simple additivity rules and from the known chemical composition of liquid polymers, we have shown that the variation of specific volume with high molecular weights is due to some phenomenon different from an effect of chain-ends.     

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.     

Improved accuracy and precision in the light-scattering characterization of homo- and copolymers in THF

A one-point method was developed for the estimation of weight-averaged molecular weights from light-scattering data. The method is based on the calculation of the second virial coefficient from theoretical predictions of the dependence of A₂ on the molecular weight. The second virial coefficient is then regressed for a particular polymer—solvent combination from a series of preexisting measurements over a range of molecular weights. The one-point method is found to yield as accurate molecular weight estimates as obtained from a Debye plot using the conventional dilution technique. The variance in the estimation of the Rayleigh factor has also been found to be highly dependent on the measurement concentration. Therefore, the precision in the estimation of molecular weight can be improved by calculating molecular weights at or near the optimal concentration, which is itself molecular weight-dependent. The one-point method is demonstrated for poly(methyl methacrylate)s of various polydispersities in tetrahydrofuran. The molecular weight of polystyrene and polystyrene-co-acrylic acid were also estimated by the one-point method in THF. In the case of the polystyrene-co-acrylic acid, THF becomes a poorer solvent with increasing levels of acrylic acid in the copolymer, and the parameter (A₂M^0.5) is found to vary with the copolymer composition, as is theoretically predicted. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 1303–1316, 1997     

Effects of functional groups on the thermal properties of modified polystyrene

Polystyrene is, after polyolefins, the most widespread polymer in both industry and everyday life, successfully replacing some raw natural materials. In this study, the chemical modification of polystyrenes of different molecular weights was performed with various functional group modifiers (epichlorohydrin, maleic anhydride, and acetic anhydride) in one stage and in the medium of the cationic catalyst BF₃·O(C₂H₅)₂ according to previous studies. The concentration of the functional groups bonded to the aromatic ring of the polymer as a result of the chemical modification of polystyrenes of different molecular weights depended on the molecular weight of the polymer, and more functional groups were bonded to lower molecular weight polystyrene. The effects of the functional groups bonded to the structure of the polymer on the thermal properties of modified polystyrene were investigated. The polystyrene that was modified by maleic anhydride was more stable against thermal destruction at high temperatures. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 2549–2553, 2007     

Synthesis,characterization and biodegradation studies of chain‐coupled polyesters based on tartaric acid

A series of chain‐coupled polyesters based on tartaric acid was synthesized and characterized following a two‐step procedure. In the first step, tartaric acid based hydroxyl terminated polyesters with various alkane diols were prepared and then, in a second step, a chain‐coupling approach using hexamethylene diisocyanate was employed on the synthesized polyesters to prepare a series of chain‐coupled polyesters. The number‐average molecular weights (M_n) of the polyesters were found to vary in the range (4.8 ? 28.1) × 10³ g mol^?1. Thermomechanical studies demonstrate that the storage modulus of the chain‐coupled polyesters decreases with increasing polymethylene chain length which is attributable to enhanced flexibility. The isolation of bacteria on medium containing polymer as the sole source of carbon indicates the ability of the synthesized polyesters to be taken up by microorganisms for growth. © 2013 Society of Chemical Industry     

Low-angle laser light scattering–aqueous size exclusion chromatography of polysaccharides: Molecular weight distribution and polymer branching determination

A low-angle laser light scattering detector (LALLS) used with size exclusion chromatography (SEC/LALLS) has been applied for the determination of molecular weight, molecular weight distribution (MWD), and degree of branching of polysaccharides in 0.5N NaOH aqueous solution. Data from both detectors [differential refractive index (DRI) and LALLS] are used to calculate the absolute molecular weight at each point in a sample chromatogram. The correct average molecular weight and MWD can be obtained without calibration methods used in conventional SEC. As a consequence of this technique, Mark—Houwink coefficients can be predicted from a single broad-distribution, homopolymer without recourse to time-consuming fractionation methods. Moreover, the hydrodynamic volume separation mechanism of SEC can be exploited with the SEC/LALLS method to gain information about polymer branching. In the studies described in this paper, SEC/LALLS has been employed to obtain data about the branching parameters g_v and g_M for samples of amylose, amylopectin, starch, and glycogen. For three homopolymers (amylose, amylopectin, and glycogen), branching frequency (as measured by chemical means), and the branching parameters (g_v and g_M) are inversely related. This trend is consistent with theoretical predictions. For starch, a nonhomogeneous branching distribution is observed as a function of molecular weight.     

Comparison of size distribution data from dynamic light scattering and size-exclusion chromatography

The intensity-defined distribution functions of hydrodynamic radii of equivalent spheres, R_h, obtained from dynamic light-scattering experiments using the CONTIN procedure via the Stokes formula were compared with distributions of gyration radii, R_g, determined by size-exclusion chromatography. The number-, weight-, and intensity- (z)-defined R_g distributions accessible from size-exclusion chromatography experiments were calculated using the Flory-Fox relation. Reliable ratios of average radii, R_g/R_h, for linear polystyrenes having narrow, broad, or bimodal molecular weight distributions were obtained in toluene. Care should be taken to utilize properly averaged experimental quantities. For instance, the CONTIN DLS data evaluation procedure yields the z-average of the inverse of the hydrodynamic radius, 〈1/R_h〉_z^?1. © 1995 John Wiley & Sons, Inc.     

Anionic synthesis and characterization of ω-formyl-functionalized polystyrenes

ω-Formyl-functionalized polystyrenes can be synthesized in quantitative yield by reacting poly(styryl)lithium (M _n = 2 × 10³?8 × 10³ g/mol) in benzene with a 0.1?0.4 molar excess of 4-morpholinecarboxaldehyde followed by methanol termination and precipitation into methanol. Narrow molecular weight distribution ω-formyl-functionalized polystyrenes were characterized by hydroxylamine end-group titration, thin layer chromatography and both ¹H and ¹³C NMR spectroscopy. The mechanism of the functionalization was studied by trapping the tetrahedral α-amino alkoxide intermediate with diphenylphosphinic chloride.     

Synthesis and enzymatic degradation of high molecular weight aliphatic polyesters

The aliphatic polyesters with high molecular weight have been prepared according to two methods. First is the synthesis of the polyesters by polycondensation of dimethyl succinate (DMS) with 1,4‐butanediol (BD) using various metal alkoxides as a catalyst. Among the metal alkoxides used, titanium tetraisopropoxide [Ti(OiPr)₄] gave the best results (highest molecular weight and yield). Thus, we have prepared aliphatic polyesters using a variety combinations of diesters [MeOOC—(CH₂)_x—COOMe, x = 2–8] with BD by the catalysis of Ti(OiPr)₄. The polyesters with high number‐average molecular weight (M_n > 35,000), except dimethyl adipate (DMA, x = 4)/BD polyester (M_n = 26,900), were obtained in high yield. The melting temperatures (T_m) of polyesters were relatively low (43.4–66.8°C) except that (115.6°C) of the DMS/BD polyester. Second is the synthesis of high molecular weight polyesters by chain extension reaction of lower molecular weight (M_n = 15,900–26,000) polyesters using hexamethylene diisocyanate (HDI) as a chain extender. The M_n values of chain‐extended polyesters consequently increased more than two times (M_n = 34,700–56,000). The thermal properties of polyesters hardly changed before and after chain extension. Enzymatic degradations of the polyesters were performed using three different enzymes (cholesterol esterase, lipase B, and Rhizopus delemar lipase) before chain extension. The enzymatic degradability varied depending on both thermal properties of polyesters [melting temperature and heat of fusion (crystallinity)] and the substrate specificity of enzymes, but it was the following order: cholesterol esterase > lipase B > R. delemar lipase. The ¹H‐NMR spectrum of water‐soluble degraded products of the polyester indicated that the polyester was degraded into a condensation product of diol with diester in a monomer form. The enzymatic degradation of chain extended polyesters was slightly smaller than that before chain extension, but proceeded steadily. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 340–347, 2001     

Prediction of the molecular and polymer solution properties of LDPE in a high-pressure tubular reactor using a novel Monte Carlo approach

In the present work, a novel kinetic/topology Monte Carlo algorithm is developed for the prediction of molecular, topological and solution properties of highly branched low-density polyethylene (LDPE), produced in a high-pressure multi-zonal tubular reactor. It is shown that the combined kinetic/topology MC algorithm can provide comprehensive information regarding the distributed molecular and topological properties of LDPE (i.e., molecular weight distribution, short- and long-chain branching distributions, joint molecular weight-long chain branching distribution, branching order distribution, seniority/priority distributions, etc.) The molecular/topological results obtained from the MC algorithm are then introduced into a random-walk molecular simulator to calculate the solution properties of LDPE (i.e., the mean radius of gyration, R_g, and the branching factor, g) in terms of the chain length of the branched polyethylene. The validity of the commonly applied approximation regarding the random scission of highly branched polymer chains is assessed by a direct comparison of the average molecular properties of LDPE (i.e., number and weight average molecular weights), calculated by the combined kinetic/topology MC algorithm, with the respective predictions obtained by the commonly applied method of moments (MOM). Through this comparison it is demonstrated that the ambiguous implementation of the random scission reaction in the MOM formulation can result in erroneous predictions of the weight average molecular weight and MWD of LDPE. Finally, the effects of two key process parameters, namely, the polymerization temperature profile and the solvent concentration, on the molecular, topological and polymer solution properties of LDPE produced in a multi-zonal tubular reactor are investigated.     

Assessment of branching in polymers from small angle X-ray scattering (SAXS): SAXS from model comb-branched polystyrenes

Comb-branched polystyrenes having both fixed backbone length and number of branches but variable branch lengths were prepared anionically. Small angle X-ray scattering of the model polystyrenes from methyl ethyl ketone (MEK) solutions at 25°C was examined and it is shown that the mass per unit length and cross-sectional radius of gyration increase with increasing branch length. A maximum appears in the Kratky plot for the branched polymers. While the linear polymer displays an essentially Gaussian segment distribution in solution, the branched polymers deviate considerably from the behaviour of the linear polymer under the same conditions.