Randomly branched styrene/divinylbenzene copolymers. I. Preparation,molecular weight characterization,and GPC analysis

A series of randomly branched copolymers of styrene and divinylbenzene were prepared using a benzoyl peroxide-initiated free-radical bulk polymerization at 78°C. DVB contents were varied from 0.01% to 2%. Two samples were polymerized with 0.4% DVB to different conversions: series 9A at 6% conversion and series 9B at 15% conversion (just short of the gelation point). Both samples were fractionated and the fractions characterized by ultracentrifugation, light scattering, osmometry, viscometry, and gel permeation chromatography. The data indicated that the fractions were not of narrow MWD and that the breadth of the MWD of the fractions from series 9B were greater than those of 9A. GPC calibration curves of M, [η], and M [η] were generated for both 9A and 9B fractions by employing curve-fitting techniques to the GPC data. For all of the fractions 9B, the molecular weight calibration provided accurate values of M?_z, M?_w, and M?_n, suggesting that no serious peak spreading had occurred in the GPC experiments. The universal calibration parameter M[η] for the 9A fractions agreed with that of linear polystyrene, while that of the high-conversion series 9B did not. It will be shown in a later paper that series 9B is highly branched, while 9A is lightly branched. Consequently, it is recommended that any GPC analysis of branching units make an allowance for the deviation of highly branched polymers from the linear M[η] calibration curve.     

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.     

Mark–Houwink equation and GPC calibration for linear short-chain branched polyolefines,including polypropylene and ethylene–propylene copolymers

The reduction in molecular dimensions due to the presence of short side chains in otherwise linear polyolefins can very simply by calculated by assuming that the configuration of the main chain is not influenced by the side chains. This enables us to express the intrinsic viscosity–molar mass relationship as a function of the mass fraction of side chains (S): [η] = (1 ? S)^α+1K_PEM_ν^α and, with use of the universal calibration principle, to convert the GPC calibration for purely linear polymers samples into the calibration for short-chain branched polymers: M^* = (1 ? S)M. Experimental data from literature on short-chain branched poly-ethylenes, and our own data on ethylene–propylene copolymers are used to verify the above assumption. It appears that the experimentally found relations between [η], M_w and M^*_w (GPC) within the usual accuracy justify this approach.     

Polystyrene-equivalent molecular weight versus true molecular weight in size-exclusion chromatography

The evaluation of the size-exclusion chromatography (SEC) concentration elution curves by means of a calibration dependence obtained in a given SEC set for a polymer different from the polymer to be analyzed results in an error in the determination of both molecular weight and molecular-weight distribution (MWD). The problem is analyzed assuming the validity of the universal-calibration concept. The differences between the true and apparent values of molecular weight, MWD and M_w/M_n depend on and are expressed in terms of the parameters of the Mark-Houwink-Kuhn-Sakurada equation, describing the molecular-weight dependence of intrinsic viscosity, for the polymer to be analyzed and the polymer used for calibration. The differences in molecular weight and the M_w/M_n ratio are typically tens of percent and, in extreme cases, can amount up to a factor of three for molecular weight and a factor of two for the M_w/M_n ratio.     

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.     

Evaluation of different branching functions used in the determination of random branching by GPC

Three branching functions are evaluated for use in the measurement of random branching by GPC. Initial evaluations of the functions g^1/2, g^3/2, and h³ were made by computer simulations of GPC experiments using published data of lightly and highly randomly branched polymers. Actual GPC experiments were then performed on characterized samples of lightly and highly branched styrene–divinylbenzene copolymers. The results indicate that h³ adequately predicts branching and molecular weight at all branching densities, whileg^1/2 is accurate only for lightly branched polymers and g^3/2 is accurate only for highly branched polymers. A means for predicting the M–[η] curve for branched polymers from the M–[η] calibration curve for linear polymer is proposed.     

Universal calibration assessment in aqueous gel permeation chromatography

It was the objective of this paper to assess the applicability of the universal calibration method to aqueous GPC/SEC with nonionic and anionic polymers using the Viscotek differential viscosity detector. Three water-soluble polymers—polyacrylic acid, dextran, and polyethylene oxide—were chromatographed using four Ultrahydrogel^TM columns with 0.3 M NaCl and 0.1M KH₂PO₄ as the mobile phase adjusted to pH 7. Three distinct calibration curves were obtained. Upon addition of 10% methanol, a reasonably good universal calibration curve was obtained. However, quantitative analysis of the data exhibited about 5% deviation in average M_w and M_n for sodium polyacrylate as calculated from the single curve as opposed to about 40% when calculated from the composite curve. The applicability of three theoretical models for the universal calibration method was assessed, and a recommendation was made for future work. © 1993 John Wiley & Sons, Inc.     

pH‐responsive polyzwitterions: A comparative study of acrylamide‐based polyampholyte terpolymers and polybetaine copolymers

A comparative study of pH‐responsive polyzwitterions (PZs) with polyampholyte or polybetaine architectures was conducted with well‐defined model polymer systems. Low‐charge‐density PZs, including ampholytic terpolymers composed of acrylamide (AM), sodium 3‐acrylamido‐3‐methylbutanoate, and (3‐acrylamidopropyl)trimethylammonium chloride and carboxybetaine copolymers composed of AM and 3‐(3‐acrylamidopropyldimethylammonio)propionate, were prepared via free‐radical polymerization in 0.5M NaCl to yield ter‐ and copolymers with random termonomer and comonomer distributions. Sodium formate was used as a chain‐transfer agent during the polymerizations to eliminate the effects of the monomer feed composition on the degree of polymerization (DP) and to suppress gel effects and broadening of the molecular weight distributions. The polymer compositions were determined via ¹³C‐NMR spectroscopy, and the residual counterion content was determined via elemental analysis for Na⁺ and Cl^?. The molecular weights (MWs) and polydispersity indices (PDIs) were determined via size exclusion chromatography/multi‐angle laser light scattering (SEC–MALLS); the polymer MWs ranged from 1.4 to 1.5 × 10⁶ g/mol, corresponding to DPs of 1.6–1.9 × 10⁴ repeat units, with all the polymers exhibiting PDIs less than or equal to 2.1. The intrinsic viscosities determined from SEC–MALLS data and the Flory–Fox relationship agreed with the intrinsic viscosities determined via low‐shear dilute‐solution viscometry. Data from the SEC–MALLS analysis were used to analyze the radius of gyration/molecular weight (R_g–M) relationships and the Mark–Houwink–Sakurada intrinsic viscosity/molecular weight ([η]–M) relationships for the PZs. The R_g–M and [η]–M relationships and viscometric data revealed that under size exclusion chromatography conditions, the poly[acrylamide‐co‐3‐(3‐acrylamidopropyldimethylammonio)propionate] betaine copolymers had more open, random‐coil conformations and greater polymer–solvent interactions than the ampholytic poly[acrylamide‐co‐sodium 3‐acrylamido‐3‐methylbutanoate‐co‐(3‐acrylamidopropyl)trimethylammonium chloride] terpolymers. The pH‐ and salt‐responsive dilute‐solution viscosity behavior of the PZs was examined to assess the effects of the polymer structure and composition on the solution properties. The polyampholyte terpolymers had greater solution viscosities and more pronounced stimuli‐responsiveness than the polybetaine copolymers because of their stronger intramolecular interactions and increased chain stiffness. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 24–39, 2004     

Molar mass distribution by size exclusion chromatography: Comparison of multi-angle light scattering and universal calibration

Series of polymers of various molar mass, chemical composition, and molecular architecture was analyzed by size exclusion chromatography (SEC) coupled with a multi-angle light scattering (MALS) photometer and an online viscometer. The molar mass averages were determined from the signal of MALS or calculated from the intrinsic viscosity and universal calibration. The comparison of the obtained results showed significant differences between the two methods. The MALS detection was shown to be more accurate for the determination of the weight-average molar mass and less vulnerable to the spreading of polymer peak by band broadening. The universal calibration can yield more accurate estimation of the number-average molar mass of branched polymers. It is also significantly more accurate for the characterization of fluorescent polymers than MALS with a regular laser of 660 nm. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47561.     

Calibration of GPC with polydisperse standards

An iteration method has been developed to prepare a calibration curve for gel permeation chromatography (GPC). It requires a number of samples of the same polymer which may have broad molecular weight distributions (MWD) of which two molecular weight averages must be known previously. The method has been applied to dextran standards with known M _w and M _n. Modifications involving the use of branched polymers are discussed.     

Intrinsic viscosity–number average molecular weight relationship for poly(1,4‐butylene adipate) diol

The relationship between number average molecular weight (M_n) and intrinsic viscosity ([η]) was studied for poly(1,4‐butylene adipate) diol (PBAD) in tetrahydrofuran, toluene, and ethyl acetate at 25°C. Thus, a series of PBAD samples were prepared by polymerization between 1,6‐adipic acid and 1,4‐butanediol. The values of M_n for the samples were determined by end‐group analysis as well as by ebulliometry, and the average difference of M_n between the two analysis ways was about 2.69%. The Mark–Houwink–Sakurada equations for PBAD were obtained to relate [η] with M_n in the range of 1900–10,000. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Rheology of polymeric solutions I. Zero shear conditions

Based on kinetic considerations, the following equation, connecting the zero‐shear viscosity of polymeric solutions with temperature and the molecular weight and concentration of the polymer was derived: RTln η_R = KBφMⁿ /(1 + BφMⁿ), where η_R is relative viscosity (i.e., the ratio of the solution viscosity to the solvent viscosity); K represents a change in enthalpy of viscous flow from a pure solvent to a pure polymer at the same temperature or from a polymer of low molecular weight (M) to one of higher molecular weight, and has the dimensions of energy (e.g., J/mol) because the ratio BφMⁿ/(1 + BφMⁿ) is dimensionless; φ is the volume or molar fraction of a polymer in solution (concentration units can be used in dilute solutions); B is a constant related to the stiffness of the chains of the polymer in a given solvent; and at BφMⁿ >> 1, ln η_R = K/RT. The equation describes published data on the zero‐shear viscosity of four polar and nonpolar polymers in nine solvents with R² > 0.98. This approach allows the use of solutions of moderate concentrations for the characterization of polymers and opens a way for a single‐point degree of polymerization (DP) determination of polymers at moderate concentrations if constants K, B, and n of the equation are known. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2064–2073, 2002     

Determination of Polymer Branching with Gel Permeation Chromatography. Abstract of a Review

Abstract

The effect of long- and short-chain branching in polymer molecules on GPC separation is reviewed (1–4). The calculation of branched GPC curves is developed from the uiiiversal calibration techniques, which is based on the concept of hydrodynamic volume (M [η]) and previously established relationships for the effect of branching on molecular dimensions. Typical calibration curves are shown for different branching models and degrees of branching. As the branching level increases, the curves arc shown to approach a limiting value. Methods of characterizing branching level3 and molecular-weight distributions of fractions and whole polymers from GPC and intrinsic viscosity data arc prcsentecl. An iterative computer program is described which was written to calculate the degree of branching in whole polymers. Long-chain branching in beveral low-density polyethylene samples was determined, using both the fraction and the whole polymer methods. Effects of various experimental errors and branching models were investigated. For polyethylene, the data show that the effect of branching in intrinsic viscosity is best described by the relationship (g ₃) _w = [η]_br/[η] whre (g _s is the Zimin-Stockmeyer expression for trifunctional branch points in a polydisperse sample.     

Number-average molecular weight and functionality of poly(tetramethylene glycol) by multidetector SEC

Multidetector size exclusion chromatography (SEC) is used to simultaneously determine molecular weight and number of reactive end groups per chain (functionality) of poly(tetramethylene glycol)s. Hydroxyl groups are first quantitatively derivatized with phenyl isocyanate, providing an end-group-selective UV-absorbing tag. The number of end groups per chain is then determined from the SEC chromatogram using a UV detector. Molecular weight at each retention volume and the number-average molecular weight of the whole polymer are calculated by four methods involving (1) a concentration detector and a narrow standard log M calibration curve, (2) the UV detector and a narrow standard log M calibration, (3) a viscometry detector and a universal calibration curve, and (4) combined differential viscometry and concentration detectors using a universal calibration curve. The multidetector experiment provides a unique opportunity to assess the accuracy and limitations of each approach on low-molecular-weight polymers. In particular, the effect of end groups on the concentration detector response and the application of universal calibration principles at small molecular sizes are important factors. It is shown that the concentration response can be corrected by a simple relationship between detector response and reciprocal molecular weight. Also, the quality of calibration curves is critical to the calculation of accurate molecular weight. In general, log M calibration curves provide superior results to universal calibration methods. © 1995 John Wiley & Sons, Inc.     

Molecular weight and chain conformation of amylopectin from rice starch

By using laser light scattering (LS) and size exclusion chromatography combined LS, we have investigated the molecular weight and chain conformation of amylopectin from rice of India (II‐b), japonica (IJ‐b), and glutinous (IG‐b) in dimethyl sulfoxide (DMSO) solution. The weight‐average molecular weight (M_w) and radius of gyration (〈S²〉^½) of amylopectin were determined to be 4.06 × 10⁷ and 128.5 nm for India rice, 7.41 × 10⁷ and 169.6 nm for japonica rice, 2.72 × 10⁸ and 252.3 nm for glutinous rice, respectively. The 〈S²〉^½ values were much lower than that of normal polymers, indicating a small molecular volume of amylopectin, as a result of highly branched structure. Ignoring the difference of degree of branching, approximated dependences of 〈S²〉^½ and intrinsic viscosity ([η]) on M_w for amylopectin in DMSO at 25°C were estimated to be 〈S²〉^½ = 0.30M_w^0.35 (nm) and [η] = 0.331M_w^0.41 (mL g^?1) in the M_w range studied. Moreover, from the 〈S²〉^½ values of numberless fractions obtained from many experimental points in the SEC chromatogram detected with LS, the dependence of 〈S²〉^½ on M_w for the II‐b sample was estimated also to be 〈S²〉^½ = 0.34 M_w^0.347, coinciding with the above results. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Viscosity/molecular‐weight relationship for γ‐(2,3‐dihydroxypropoxy)propyl‐terminated poly(dimethylsiloxane)s

A series of γ‐(2,3‐dihydroxypropoxy)propyl‐terminated poly(dimethylsiloxane) (DHT‐PDMS) samples with different molecular weights were prepared through the acid‐catalyzed equilibrium copolymerization of octamethylcyclotetrasiloxane and 1,3‐bis[γ‐(2,3‐dihydroxypropoxy)propyl]tetramethyldisiloxane. The intrinsic viscosity in toluene ([η]_toluene) and the number‐average molecular weight (M_n) were determined with an Ubbelohde viscometer and ¹H‐NMR spectra, respectively. In this way, the relationship between [η]_toluene and M_n was established. For 2.0 × 10⁴ < M_n < 4.0 × 10⁴, [η]_{toluene,25°C} was 1.874M_n ^0.323. The solution behavior of DHT‐PDMS was also investigated. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 1759–1762, 2004     

Molecular architectures of four‐arm star‐shaped styrene‐butadiene copolymer

To understand the molecular architectures of styrene‐butadiene four‐arm star (SBS) copolymers, a size exclusion chromatography combined with laser light scattering (SEC‐LLS) has been used to determine their weight‐average molecular weight (M_w) and radius of gyration (〈S²〉^1/2), and a new method for the establishment of the Mark‐Houwink equation from one sample has been developed. Based on the Flory viscosity theory, we successfully have reduced the 〈S²〉^1/2 values of numberless fractions estimated from many experimental points in the SEC chromatogram to intrinsic viscosities ([η]). For the first time, the dependences of 〈S²〉^1/2 and [η] on M_w for the four‐arm star SBS in tetrahydrofuran at 25°C were found, respectively, to be 〈S²〉^1/2 = 2.62 × 10^?2 M (nm) and [η] = 3.68 × 10^?2 M (mL/g) in the M_w range from 1.4 × 10⁵ to 3.0 × 10⁵. From data of [η] and 〈S²〉^1/2 for linear and star SBS, we have obtained the information about the branching, namely, the ratios (g and g′) of 〈S²〉 and [η] for star SBS to that of the linear SBS of the same molecular weight, which agree with theoretical predictions. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 961–965, 2005     

Polyether polyols as GPC calibration standards for determination of molecular weight distribution of polyether polyols

Average molecular weights (M_n, M_w and M_p) are important characteristics of oligomers and polymers, and therefore there is a need to have a precise and reliable determination method. A gel permeation chromatography (GPC) coupled with a single refractive index detector was used to determine the molecular weight distributions of commercial polyether polyols calibrated against a series of polyether polyols with known molecular weights and low polydispersity. Results of these GPC analyses were compared to the ones calibrated against the commercially available polystyrene (PS) standards. The number‐average molecular weights (M_n) obtained with GPC using polyether polyols calibration were closer to the theoretical values than the M_n obtained using PS as calibration standards. Hence, these GPC analyses using polyether polyols as calibration standards can provide reliable determination of molecular weight distribution of polyether polyols and can be potentially applied to natural oil‐based polyols, including palm oil‐based polyols. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42698.     

Studies on the preparation of branched polymers from styrene and divinylbenzene

The self‐condensing vinyl polymerization of styrene and an inimer formed in situ by atom transfer radical addition from divinylbenzene and 2‐bromoisobutyl‐tert‐butyrate using atom transfer radical polymerization technique was studied. To study the polymerization mechanism and achieve high molecular weight polymer in a high polymer yield, the polymerization was carried out in bulk at 80°C. Proton nuclear magnetic resonance (¹H‐NMR) spectroscopy and gel permeation chromatography (GPC) coupled with multiangle laser light scattering (MALLS) were used to monitor the polymerization process and characterize the solid polymers. It is proved that the polymerization shows a “living” polymerization behavior and the crosslinking reaction has been restrained effectively due to the introduction of styrene. Polymers with high molecular weight (M_w.MALLS > 10⁵) can be prepared in high yield (near 80%). Comparison of the apparent molecular weights measured by GPC with the absolute values measured by MALLS indicates the existence of branched structures in the prepared polymers. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007