Narrow Distribution Polystyrene Research Articles

Fine‐tuning in‐plane interdomain spacing of polystyrene‐b‐poly(ethene‐co‐butadiene)‐b‐polystyrene triblock copolymer adding monodisperse polystyrene

The influence of adding narrow molar mass distribution polystyrene (PS) homopolymer on the morphology and/or dewetting processing of polystyrene‐b‐poly(ethene‐co‐butadiene)‐b‐polystyrene triblock copolymer (SEBS) thin films was investigated. The addition of the homopolymer caused a transition from non‐straight ribbons (with regularly spaced necks) to a spherical microdomain structure for an amount of 75 vol% PS (SEBS/PS 1:3), which also shows an interdomain distance increase of three times with respect to the neat SEBS. This spacing and interdomain distance control coincides with the amount of homopolymer added in the blend. The blending with PS demonstrates an approach to fine‐tuning the block copolymer structure and tailoring in‐plane microdomain spacing. Smaller or higher amounts of PS changed the spontaneous patterned structure originally observed for the neat triblock copolymer, resulting in a non‐ordered microphase separation. © 2023 Society of Industrial Chemistry.

Stress relaxation following uniaxial extension of polystyrene melt and oligomer dilutions

The filament stretching rheometer has been used to measure the stress relaxation following the startup of uniaxial extensional flow, on a narrow molar mass distribution (NMMD) polystyrene melt and styrene oligomer dilutions thereof. All samples used here were characterized in molecular weight, mechanical spectroscopy, and constant strain rate uniaxial extension in the work of Huang et al. [Macromolecules 46, 5026–5035 (2013); ACS Macro Lett. 2, 741–744 (2013)]. The stress relaxation following the steady extensional stress was measured on a 285 kg/mole NMMD polystyrene and two 1.92 kg/mole styrene oligomer dilutions thereof {PS-285k, PS-285k/2k-72, and PS-285k/2k-44 in the work of Huang et al. [Macromolecules 46, 5026–5035 (2013)]}. The two dilutions contained 28 and 56 wt. % oligomer, respectively. Further, the stress relaxation on a 545 kg/mole NMMD polystyrene diluted with 48 wt. % 0.972 kg/mole styrene oligomer {PS-545k/1k-52 in the work of Huang et al. [ACS Macro Lett. 2, 741–744 (2013)]} was measured as well. All the terminal relaxations could be predicted by a Doi and Edwards, e.g., pure configurational, type of model. At smaller time scales, agreement with a molecular stress function type of constitutive representation was observed for all measured relaxations.

Stress relaxation of narrow molar mass distribution polystyrene following uniaxial extension

The stress in the startup of uniaxial elongational flow until steady state, followed by stress relaxation, has been measured for a narrow molar mass distribution polystyrene melt with a molecular weight of 145kg∕mol. The experiments are conducted on a filament stretching rheometer, where a closed loop control of the midfilament diameter ensures controlled uniaxial extension. The closed loop control algorithm is extended to apply to the stress relaxation part of the experiment. It ensures a constant midfilament diameter, by controlling the motion of the end plates. By dividing the measured stress with the theoretically predicted stress from the Doi and Edwards model during relaxation, the stretch factors corresponding to each imposed stretch rate are obtained. These stretch factors converge to a unique envelope and eventually converge to unity for long times for all measured elongational rates.

Quantitative prediction of transient and steady-state elongational viscosity of nearly monodisperse polystyrene melts

Elongational behavior of four narrow molar mass distribution polystyrene melts of masses 50 000, 100 000, 200 000, and 390 000, g∕mol, respectively was investigated up to Hencky strains of 5. All melts show strain hardening behavior. For the two highest molar mass polystyrenes, strain hardening starts at elongation rates larger than the inverse reptation time, and the steady-state elongational viscosities decrease with increasing elongation rate according to a power law with a power-law index of approximately −1∕2 instead of −1 as predicted by the original Doi–Edwards tube model. Marrucci and Ianniruberto [Macromolecules 37, 3934 (2004)] have introduced an interchain pressure term arising from lateral forces between the chain and the tube wall into the Doi–Edwards model to account for the latter effect. Based on the molecular stress function theory allowing for a strain-dependent tube diameter, we show that the transient and steady-state elongational viscosities of the nearly monodisperse polystyrene melts can be modeled quantitatively by assuming affine chain deformation balanced by the interchain pressure term of Marrucci and Ianniruberto. The interchain pressure is governed by a tube diameter relaxation time τa, which is found to be larger than the Rouse time τR of the chain, and which is the only parameter of the model. For monodisperse polystyrene melts of sufficient low molar mass, τa is larger than the reptation time, and a maximum in the steady-state elongational viscosity is predicted.

An equation of state for melts of linear homopolymers

We analyze the capability of the continuous Gaussian chain model to describe melts of linear homopolymer chains. We derive the equation of state of a system of n interacting chains by including long chain correlations by means of the one loop diagrams. These correlations which give rise to two combinations of the molecular parameters are found to be necessary for the proper quantification of pressure–volume–temperature ( PVT) behaviour of the melts. The adjustment of the value of the prefactor of the small density term which is in accord with the liquid character of polymeric melts lead to a complete agreement between the experimental results and the outcomes of the theory. The proper dependence on the molecular weight is also predicted and isotherms of narrow distribution polystyrenes of three different molecular weights are used for the evaluation of the molecular parameters.

A 2D model for tube orientation and tube squeezing in fast flows of polymer melts

Motivated by recent data of Hassager and coworkers [A. Bach, K. Almdal, H.K. Rasmussen, O. Hassager, Elongational viscosity of narrow molar mass distribution polystyrene, Macromolecules, 36 (2003) 5174–5179], we develop a new tube model describing the non-linear behaviour of entangled monodisperse linear polymers. Within the context of well established tube theories, the model accounts for the effect of flow on tube diameter, thus somehow picking up a long standing suggestion by Wagner and Schaeffer [M.H. Wagner, J. Schaeffer, Non-linear strain measures for general biaxial extension of polymer melts, J. Rheol., 32 (1992) 1–26] among others. Since tubes with a deformation dependent cross section are rather difficult to deal with, we here limit model development to an artificial two-dimensional situation. The simple 2D model has the advantage of illustrating the new physical assumptions more transparently, and it already proves to correctly predict most qualitative features typically shown by shear and elongational data in the non-linear range.

Prediction of molecular weight distribution of cellulose by using the rheological method

AbstractIn this article, a rheological method that can predict the molecular weight distribution (MWD) of polymer was introduced. Using this method, the MWDs of four cellulose samples were compared from rheological data of the cellulose / N‐methyl morpholine N‐oxide (NMMO) / H2O solutions. The MWDs of cellulose also were determined by gel permeation chromatography (GPC) calibrated with narrow distribution polystyrene standards, using 0.5% lithium chloride (LiCl) in N,N‐dimethylacetamide (DMAc) as the eluent. Comparison of the results from rheology and GPC showed that the MW and MWD of cellulose could be roughly inferred from their rheological data. Although the differential MWD obtained from the rheological method was bell shaped and can not reflect the fine characteristics of cellulose as GPC, it may be feasible to compare the MWDs of cellulose by using the rheological method. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 94: 598–603, 2004

Elongational Viscosity of Narrow Molar Mass Distribution Polystyrene

Transient and steady elongational viscosity has been measured for two narrow molar mass distribution polystyrene melts of molar masses 200 000 and 390 000 by means of a filament stretching rheometer. Total Hencky strains of about five have been obtained. The transient elongational viscosity rises above the linear viscoelastic prediction at intermediate strains, indicating strain hardening. The steady elongational viscosities are monotone decreasing functions of elongation rate. At elongation rates larger than the inverse reptation time, the steady elongational viscosity scales linearly with molar mass at fixed elongation rate.

New bifunctional initiator for use in anionic polymerizations

AbstractThe synthesis is described of narrow distribution polystyrenes initiated by the 2,7‐dimethyl‐3,6‐diphenyl‐octane dianion (DDO2−). DDO2− was synthesized via electron transfer from lithium or potassium metal to 3‐methyl‐2‐phenyl‐1‐butene (MPB) in tetrahydrofuran at temperatures between −78 and −100 °C. In contrast to the analogous α‐methyl styrene, there was no evidence of MPB polymerization. The structure of DDO2− was demonstrated by 1H and 13C NMR, as well as gas chromatography/mass spectrometry characterization of the DDO2− protonation and methylation products. In addition, kinetic studies were performed by ultraviolet–visible spectrophotometry for the determination of the stability of this anion in comparison with other similar species. The initiation of styrene by DDO2− led to narrow molecular weight polymers, as shown by size exclusion chromatography. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2108–2115, 2002

Evaluation of high-performance liquid chromatography column retentivity using macromolecular probes I

The application of macromolecular probes is proposed for evaluation of HPLC column retentivity. The idea is tested with a set of different commercial silica C 18 reversed-phases. For comparison, porous glass C 18 and polystyrene/divinylbenzene column packings are also included. Polar, mainly silanophilic interactions are evaluated. The retention volumes of a series of narrow molar mass distribution polystyrenes (PS) and poly(methyl methacrylate)s (PMMA) in toluene eluent are compared. Toluene is a weak mobile phase concerning silica gel surface and it promotes adsorption of PMMA on silanols, while PS is not adsorbed from toluene. Simultaneously, toluene is a thermodynamically good solvent for both polymers so that extensive partition in favour of stationary phase is not probable. Differences in retention behaviour of PS and PMMA indicate presence of abundant free silanols on the surface of some reversed-phases. These silanols are accessible even for large macromolecules of PMMA. Pore diameter and pore volume of the column packing can be semiquantitatively evaluated from the elution data of PS in toluene in the course of retentivity tests.

Intrinsic Viscosity Variation in Different Solvents for Dendrimers and Their Hybrid Copolymers with Linear Polymers

The intrinsic viscosity of narrow molecular mass distribution polystyrene standards, poly(benzyl) ether dendrimers, and their hybrid block copolymers was measured in a variety of solvents. The relative change in the intrinsic viscosity for all these polymers was almost equivalent, indicating that poly(benzyl ether) dendrimers expand and contract quite readily with a change in solvent. The intrinsic viscosity maximum for all polymers was found to occur at essentially the same solvent solubility parameter demonstrating that the thermodynamic interaction with the selected range of solvents was also equivalent. The intrinsic viscosity for hybrid copolymers in a good solvent for both components was found to fall well below the intrinsic viscosity for neat polystyrene at intermediate molecular masses. Below and above this mass range the intrinsic viscosity was quite similar to polystyrene. Yet, the transition for intermediate to high molecular mass behavior was quite sharp as seen through a rapid intrinsic visc...

NIST-Sponsored Interlaboratory Comparison of Polystyrene Molecular Mass Distribution Obtained by Matrix-Assisted Laser Desorption/Ionization Time-of-Flight Mass Spectrometry: Statistical Analysis

The method of preparation and methods of analysis of a narrow distribution polystyrene of ∼7 ku used in an interlaboratory comparison of matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS) of synthetic polymers is described. Size exclusion chromatography was used to measure the polystyrene sample variability. Fourier transform infrared spectroscopy and MALDI-TOF-MS were used to analyze end groups on the polymer. The polystyrene was analyzed by MALDI-TOF-MS and classical methods of polymer characterization. The number (Mn) and mass (Mw) average of the molecular mass distribution (MMD) determined by the classical methods (light scattering and NMR) were compared with those obtained by MALDI-TOF-MS. Agreement between classical methods to obtain the moments of the MMD and the MALDI is found to be good overall. However, all the experimental values obtained by MALDI fell below the classical values. A discussion of why these values are lower is included. We discuss the statistical analysis of the data from the interlaboratory comparison conducted by NIST, which includes data from 23 different laboratories. Analysis of variance is used to examine the influences of the independent parameters (laboratory, matrix, instrument manufacturer, instrument mode) on the data. The parameters, laboratory and instrument manufacturer, were determined to have an influence on the MMD, where matrix and instrument mode were found not to have a significant influence.

Sliding plate rheometer studies of concentrated polystyrene solutions: Nonlinear viscoelasticity and wall slip of two high molecular weight polymers in tricresyl phosphate

Two high molecular weight, narrow distribution polystyrenes dissolved in tricresyl phosphate were studied using a sliding plate rheometer. Shear stress and birefringence measurements in step strain allowed the determination of N3 for both solutions. Start-up of steady simple shear and large amplitude oscillatory shear measurements revealed that the critical shear stress for slip for both solutions is around 2500 Pa and that slip is dynamic in nature, allowing rheological measurements above the critical stress to be made at sufficiently high frequencies. The critical stress value was used in conjunction with data from the literature to develop a relationship between critical stress and concentration. Large-amplitude oscillatory shear stress measurements revealed that the solutions exhibit a limiting behavior at high strain rate amplitudes in the intermediate frequency range when the dependence on strain rate amplitude becomes small. Birefringence measurements showed that at high frequencies, where the time scale of the deformation is short, the oscillatory component of N3 vanished. This was found to occur at lower frequencies for the lower molecular weight solution. In contrast, the average value of the third normal stress difference, reflected in the zeroth harmonic, was found to vary little between the two solutions.

Measurement of narrow-distribution polydispersity using multiangle light scattering

Molecular radius information obtained with multi-angle laser light scattering combined with gel permeation chromatography was used to obtain an upper limit for the polydispersity − M w/− M n of a narrow-distribution polystyrene standard dissolved in toluene. The radius obtained by light scattering is independent of any other detector and so is not affected by interdetector delay volumes or interdetector broadening. The value obtained for − M w/− M n was 1.00096 ± 0.00004. much closer to unity than previously reported. Column broadening was found to be responsible for nearly all the observed peak width.

Modeling the dynamic properties of monodisperse linear polymer melts with wedge spectra

A mathematical model of the spectrum of relaxation times for molten linear monodisperse homopolymers has been developed which is the sum of two variations of the well-known wedge spectrum. Adjusting the six parameters of the model allows fitting the storage and loss moduli within experimental error over a range of 10–12 logarithmic decades of frequency which encompass the flow, plateau, transition, and glassy zones of viscoelastic behavior. Model parameters are easily determined with a desktop microcomputer using standard nonlinear least-squares fitting procedures. All six model parameters correspond directly to prominent features of experimental data. The plateau modulus, viscosity, steady-state shear compliance, and the frequency at which the storage and loss moduli cross can all be easily calculated from the model parameters. The limiting low- and high-frequency behaviors of the storage and loss moduli predicted by the model are consistent with experiment and with linear viscoelastic theory. For the transition zone, the model can closely mimic the dynamic behavior predicted by normal-coordinate molecular theories. The model is applied to experimental data for five narrow-distribution polystyrenes having molecular weights in the range of 60 000–540 000.

GPC Calibration for the Molecular Weight Measurement of Butyl Rubbers

Abstract Size Exclusion Chromatography (SEC) or Gel Permeation Chromatography [GPC] was used to determine the molecular weight and molecular weight distribution of butyl rubbers. Quantitative data were obtained by viscometry, and by the use of narrow distribution polyisobutylene (PIB) standards for calibration. The application of the Universal Calibration Principle, which uses readily available narrow distribution polystyrene (PS) standards, relies on the knowledge of the Mark-Houwink-Sakurada constants, K and α, for PIB or butyl rubber (the copolymer of isobutylene and isoprene containing 1–3 mol% of the latter). Comparison of narrow PIB and narrow PS calibrations led us to the selection of KPIB=2×10−4 dl/g and α=0.67, the constants published by the American Standards Corporation for PIB in tetrahydrofuran (THF) at 30°C, as best fit values. The weight average molecular weight [Mw] of various samples of commercially produced butyl rubber determined by using the Universal Calibration Principle with the selected constants, agreed well with those measured by viscometry. Other published K and α values yielded a poorer agreement.

Polymer molecular weight distribution from terminal zone of storage modulus-considering the shift factor

Abstract A numeric method for calculating the molecular weight (MW) and molecular weight distribution (MWD) from the terminal zone of viscoelasticity of narrow distribution linear polymers had been developed by one of the authors in previous work. In this work a modification of our previous method, by considering the shift factor, for calculating the polymer molecular weight and molecular weight distribution from the terminal zone of the storage modulus G' (ω) of a broad molecular weight distribution linear polymer is presented. Two narrow distribution polystyrene and one broad distribution polystyrene samples were used as a demonstration to calculate the molecular weight distribution. Good agreement between the results calculated from our method and those obtained from GPC measurements was found.

Dimerization of polystyrene during static SIMS measurements

AbstractIn this work we report on the results of some static time‐of‐flight secondary ion mass spectrometry (TOF‐SIMS) experiments performed on low‐molecular‐weight narrow distribution polystyrene. Evidence of cross‐linking during analysis is found, as indicated by the presence of peaks corresponding to molecules formed by linking of two initial polymer chains. The effect, which can be easily taken into account, does not appreciably affect the molecular weight distribution parameters obtained. However, the observed phenomenon gives the indication that, at least in the case of particularly sensitive systems, ion beam‐induced modification can occur also in static SIMS experiments. In addition, the observed phenomenon can be of relevance in modelling the sputtering of large molecules.

Analytical ultracentrifugation with the new Optima XL-A and its digital u.v./vis. detector: determination of molar mass distribution of polymers from sedimentation velocity

The determination of average molar masses and molar mass distributions (MMDs) of polymers and polyelectrolytes is demonstrated with the new analytical ultracentrifuge Optima XL-A and its very sensitive digital u.v./vis. detector (180–800 nm continuously) from Beckman Instruments, Inc. The machine was tested with the narrow distribution polystyrenes PS 106 000 and 300 000 (and a 50:50 mixture), sodium poly(styrene sulfonate) NaPSS 100 000 and the broad distribution polystyrene NBS 706. Full details of the calculation of average molar masses and MMDs of the polymers from the experimental values are given. The results show that the new absorption optics enable the above-mentioned quantities to be determined as the absorption optics are able to measure at very low concentrations, which allows either a precise extrapolation to zero concentration or averaging of the data. Owing to the fact that a sedimentation run is a real fractionation process (with a higher resolution than size exclusion chromatography) one measures the real MMD. There is no need to presume a special model MMD to analyse the measurement data. The data from the Optima XL-A are accessible as ASCII-files. As the original Beckman computer programs are not suitable for our purposes, we have developed own programs, which are available on request.

Flow birefringence studies of a concentrated polystyrene solution in a two‐roll mill. I. Steady flow and start‐up of steady flow

AbstractWe have studied a 4.8 volume percent solution of a narrow distribution polystyrene with molecular weight 3.84 × 106 in flows generated by a co‐rotating two‐roll mill. These flows have a stagnation point at the midpoint between the roller axes. Further, they are linear, two‐dimensional, and the magnitudes of the strain‐rates are greater than the vorticity. The overall objective of our studies is to explore the dynamics of concentrated polymer solutions which are in the highly deformed state that is generated in the two‐roll mill. Birefringence data are presented for both steady flow and start‐up of steady flow in the two‐roll mill. The steady and transient data are used to analyze the linear and nonlinear viscoelastic regions of material behavior. In the nonlinear regime, the birefringence upon start‐up shows an initial overshoot followed by a strong undershoot that is enhanced as the ratio of elongation to rotation is increased (i.e., the flow becomes increasingly extensional in character.) We attribute this undershoot, which does not seem to appear in simple shear flows, or flows close to simple shear flow, to polymer segment stretching following an initial period of segment reorientation. Model studies are currently underway to test this notion. © 1992 John Wiley & Sons, Inc.