Monodisperse comb polystyrenes (comb-PS) with loosely to densely grafted architectures up to loosely grafted bottlebrush structures were synthesized via anionic polymerization. This comb-PS series, named PS290-Nbr-44, had the same entangled backbone, Mw,bb = 290 kg/mol, corresponding to a number of entanglements along the backbone Zbb ≅ 20, and similar branch length, Mw,br ≅ 44 kg/mol or Zbr ≅ 3, but varied in the number of branches per molecule, Nbr, from 3 to 190 branches. Consequently, the average number of entanglements between two consecutive branch points along the backbone (branch point spacing), Zs, ranged from well entangled, Zs ≅ 5, to values that were far less than one entanglement, Zs ≅ 0.1. Linear viscoelastic data including the zero-shear rate viscosity, η0, diluted modulus, GN,s0, and a new diluted modulus extracted from the van Gurp–Palmen plot, |G*| at δ = 60°, were analyzed as a function of the Mw of the combs. Scaling of η0 versus Mw revealed three different regions for increasing Nbr or decreasing Zs: (1) loosely grafted combs with Zbr < Zs and η0 ∼ exp(Mw), (2) densely grafted combs with 1 < Zs < Zbr and η0 ∼ Mw–3.4 followed by η0 ∼ Mw–1 for 0.2 < Zs < 1, and (3) loosely grafted bottlebrushes with Zs < 0.2 and η0 ∼ Mw5. The relative maximum in η0 corresponded to a comb-PS with Zs ≅ Zbr, and the relative minimum resulted from a comb-PS with Zs ≅ 0.2, which displayed almost the same η0 as the linear PS290. Strain hardening factors, SHF ≡ ηE,max/ηDE,max, measured in extensional experiments increased with increasing Nbr and reached SHF > 200 for Hencky strains below εH = 4, which is tremendously high and has to the best of our knowledge not been observed yet. Such a high strain hardening is of great fundamental and technical importance in extensional processes, e.g., foaming, film blowing, or fiber spinning.

•A high sensitivity system for capillary rheometry is presented.•It achieves remarkable pressure and time resolutions to detect melt flow instabilities.•It can determine the first normal stress difference via the ‘hole effect’.•The first normal stress difference was estimated for a low and a high density polyethylene.•The presence of the hole influences the onset of instabilities.The development of a high sensitivity polymer melt extrusion flow instability detection die capable of estimating the normal stress differences of polymer melts during capillary rheometry tests via the ’hole effect’ is presented here as proof-of-principle. Two polymer melts, a low density polyethylene (branched topology) and a high density polyethylene (linear topology), were tested in a variety of experimental configurations with the purpose of determining optimal conditions for performing normal stress difference measurements. The data was compared with rotational rheometry oscillatory shear measurements analyzed via the Laun rule. It is shown that it is possible to estimate the first normal stress difference in the capillary die, whereas the second normal stress difference cannot be determined within the experimental errors using the current configuration design. Furthermore, the influence of the induced streamline curvature via the ’hole effect’ on the onset and development of melt flow instabilities is simultaneously assessed. It is shown that the hole depth has a stabilizing influence, i.e. the onset of instabilities occurs at higher shear rates, in the long chain branched polymer tested, whereas for the linear polymer tested it has a destabilizing effect on the stick-slip instability i.e. the onset of stick-slip occurs at lower shear rates.

Linear mono- and polydisperse homopolymer melts have been investigated with Fourier transformation rheology (FT rheology) to quantify their nonlinear behavior under oscillatory shear via mechanical higher harmonics, i.e., I3/1(ω,γ0). Master curves of the zero-strain nonlinearity, 3Q0(ω) ≡ limγ0→0 I3/1/γ02, have been created for these linear homopolymer melts, applying the time–temperature superposition (TTS) principle. The quantity 3Q0(ω) is examined for its dependence on molecular weight, molecular weight distribution, and monomer. The investigated nonlinear master curves of 3Q0(ω) for polymer melts with a polydispersity index (PDI) of about 1.07 or smaller display the expected scaling exponent of 3Q0(ω) ∝ ω2 at low frequencies until a maximum, 3Q0,max, is reached. This maximum 3Q0,max was found to be in the magnitude of the longest relaxation time τ0 and the value of 3Q0,max to be weakly dependent on molecular weight, or the number of entanglements Z, with 3Q0,max ∝ Z0.35. Within the measured experimental window, the initial slope at low frequencies of nonlinear master curves is very sensitive toward the molecular weight distribution, as quantified through the PDI. The slope of 3Q0(ω) decreases until approximately zero as a limiting plateau value is reached at a polydispersity of around PDI ≈ 2. The experimental findings are also compared to 3Q0(ω) predictions from pom-pom and molecular stress function (MSF) constitutive models. Analytical solutions of 3Q(ω,γ0) for diminishing small strain amplitudes (γ0 → 0) are presented for each model, and an asymptotic solution for 3Q0(ω) is derived for low and high frequencies for monodisperse samples. This simplified equation is a function of Deborah number (De = ωτ0) in the general form of 3Q0(De) = aDe2/(1 + bDe2+k). This equation was fitted to our experimental data of monodisperse homopolymer melts. It is shown that under these conditions the parameters a and b are only functions of the number of entanglements Z and are independent of the investigated monomers. Consequently, a and b can be linked to general polymer properties. With this article, the mechanical nonlinear response of linear polymer melts with regard to molecular weight and distribution as well as monomer type is quantified. The here presented results should be of great interest toward constitutive model development and toward computational polymer physics, e.g., molecular dynamic simulations, as our results seem to quantify general features in nonlinear rheology of linear homopolymer melts.

•Well defined polystyrene (PS) combs were synthesized via anionic polymerization.•For the same total Mw, chain branching reduces the solution viscosity.•Comb polymers lead to bead free electrospun fibers at lower solution concentrations.•The electrospun fiber diameter depends on the solution viscosity and is larger for combs than linear PS.The bead to bead-free fibers transition for electrospun filaments was investigated for well-defined linear and comb homopolymers. A series of monodisperse model comb structures with well-defined backbone and side chains was synthesized using anionic polymerization of polystyrene (PS). All model combs had the same backbone and a similar total molecular weight. The length and number of branches was varied, but the total number of monomers in the side chains was nearly constant.Solutions of these polystyrenes in N,N-dimethylformamide (DMF) were electrospun under identical conditions to determine the effect of molecular topology on the morphology of the fibers. The morphology and fiber diameter for all PS model polymers depended on the zero shear viscosity, η0. The comb solutions generally formed fibers at lower η0 and the fibers had larger diameters compared with linear polystyrene. The bead to fiber transition occurred at substantially lower polymer concentrations for combs with fewer, but longer branches.

Polymer materials are becoming more complex and require increasingly sophisticated analysis methods. The development of coupled techniques, especially SEC and molecular spectroscopy, is one approach to meet this need. In this report, the technical realization of a new FTIR spectroscopy and SEC coupling, where the FTIR serves as a true online detector is described. The basic idea is to measure FTIR spectra online with the highest possible sensitivity and then use a mathematical approach to subtract the solvent signals, reduce drifts and minimize noise. This publication describes in detail how this method was optimized including the most important demands on the spectrometer and other required equipment, e.g. the custom designed flow cells. The applied data treatment, which is called “solvent suppression”, and a guide to interpretation of the data are explained in detail. Several application examples demonstrate not only the potential of the method, but also clarify the current limits. It is shown that FTIR spectroscopy can successfully be used as an online detection method for SEC to provide detailed chemical information as a function of the elution volume, respectively molecular weight, for basically any polymer in any isocratic solvent. It is also shown that minor components down to ca. 5 mol% can be detected.

This work presents an experimental study of the network structure of swollen, charged hydrogels. We provide an in-depth comparison of two proton low-field NMR methods, i.e., transverse relaxation and double-quantum spectroscopy, that are both sensitive to residual orientation correlations of the network chain segments. The results are in both cases analyzed by help of integral inversion techniques, and both methods are demonstrated to provide comparable results despite the more qualitative nature of the transverse relaxation. We investigate model samples that are similar to commercial superabsorber materials based on partly neutralized and chemically cross-linked poly(acrylic acid) as prepared by free radical polymerization. The degree of cross-linking and the monomer concentration are varied during synthesis. Both parameters are found to affect the network structure and the amount of elastically inactive defects in a systematic way, and a comparison with commercial samples with homogeneous or purposely inhomogeneous core–shell structures proves that the cross-linking bimodality of the latter is readily revealed despite the rather large intrinsic inhomogeneity of the swollen gels.

In this article, a new way to characterize the percolation threshold of polymer nanocomposites made of polyethylene (PE) with single and multi walled carbon nanotubes (SWCNTs and MWCNTs) is presented. Small and large oscillatory shear (SAOS and LAOS) experiments were performed to characterize the degree of dispersion and percolation threshold. The analysis of the stress response in the LAOS regime as a function of the applied deformation amplitude and frequency was performed using Fourier Transform (FT)-Rheology. The zero strain intrinsic nonlinear parameter, Q0(ω), was calculated by extrapolation of I3/1(γ0, ω) and was, used to quantify the nonlinearity measured by FT-Rheology. Interestingly, a drop in Q0 as a function of the CNT weight fraction at a fixed frequency was found that was below the percolation threshold. This was followed by, a steep rise in Q0 above the percolation threshold. Therefore, the new method based on this observation that is proposed and described with this article has the potential to lead to a better understanding of structure-property relationships in polymer nanocomposites.

Strain-controlled large amplitude oscillatory shear (LAOStrain) experiments on a polyisoprene melt and a polyisobutylene solution were conducted on four different rheometers. The results are compared using nonlinear quantities such as the normalized intensity of the third harmonic (I3/1) and the intrinsic nonlinearity in order to assess the reproducibility of the experiments. Two of the investigated instruments were strain-controlled rheometers, another two, were advanced stress-controlled rheometers. Since the stress-controlled rheometers are able to conduct strain-controlled tests when employing an active deformation control loop, the two different rheometer types could be compared. Experimental details like the gain of the deformation control loop, and the method of temperature control have been shown to play crucial roles in achieving reasonable reproducibility across the different instruments. Furthermore, deviations from the quadratic scaling of I3/1 with the strain amplitude and the influence of instrument inertia on nonlinear quantities were observed for one of the stress-controlled instruments. The standard deviation of the intrinsic nonlinearity Q0(ω0) at a specific angular frequency as determined by measurements on the same instrument was found to be 8 % or lower. The relative deviations of Q0 across different instruments were instead up to 12 % in the investigated frequency range with an exception for a specific instrument and one of the samples, where the deviation was considerably larger.

•Loss modulus and nonlinearity parameter show different time dependencies during LAOS for PS–PLLA.•Lamellar PS–PLLA can be oriented parallel to a shear field using LAOS.•Self-assembly of the PS–PLLA block copolymer has a decelerating effect on the crystallization kinetics.•The crystallization under soft confinement conditions lead to an increase in the domain spacing and a loss of periodicity.The rheological behavior of a poly(styrene)–poly(l-lactide) (PS–PLLA) block copolymer was investigated in the viscoelastic linear and nonlinear regime. Large amplitude oscillatory shear (LAOS) experiments in the nonlinear regime led to an exponential decay of the G moduli and the nonlinearity parameter I3/1. During LAOS, the lamellar microstructure of a low molecular weight PS–PLLA copolymer was orientated parallel to the shear field to achieve a macroscopically ordered material. The degree of orientation was analyzed via small angle X-ray scattering (SAXS) measurements. The crystallization kinetics could be accurately described by the Avrami equation as determined by DSC and rheology. These experiments revealed that the crystallization process was slower for the PS–PLLA copolymers than for the PLLA homopolymers. SAXS was also used to monitor the crystallization of the PS–PLLA copolymers. When the temperature of the crystallization experiments, Tc  , was lower than the glass transition temperature of the amorphous PS block, Tga (hard confinement), the lamellar microstructure of the low molecular weight PS–PLLA was maintained apart from a small increase in the domain spacing. When Tc   was higher than Tga of PS (soft confinement), the block copolymer also retained its lamellar structure, but the increase in the domain spacing was unexpectedly increased compared to what occurred for crystallization under hard confinement conditions. In addition, two-dimensional (2-D) SAXS diffractograms indicated a loss of the structure periodicity during crystallization under soft confinement.Graphical abstract

Although controlled/living radical polymerization processes have significantly facilitated the synthesis of well-defined low polydispersity polymers with specific functionalities, a detailed and systematic knowledge of the thermal stability of the products–highly important for most industrial processes–is not available. Linear polystyrene (PS) carrying a trithiocarbonate mid-chain functionality (thus emulating the structure of the Z-group approach via reversible addition–fragmentation chain transfer (RAFT) based macromolecular architectures) with various chain lengths (20 kDa ≤ Mn,SEC ≤ 150 kDa, 1.27 ≤ Đ = Mw/Mn ≤ 1.72) and chain-end functionality were synthesized via RAFT polymerization. The thermal stability behavior of the polymers was studied at temperatures ranging from 100 to 200 °C for up to 504 h (3 weeks). The thermally treated polymers were analyzed via size exclusion chromatography (SEC) to obtain the dependence of the polymer molecular weight distribution on time at a specific temperature under air or inert atmospheres. Cleavage rate coefficients of the mid-chain functional polymers in inert atmosphere were deduced as a function of temperature, resulting in activation parameters for two disparate Mn starting materials (Ea = 115 ± 4 kJ·mol–1, A = 0.85 × 109 ± 1 × 109 s–1, Mn,SEC = 21 kDa and Ea = 116 ± 4 kJ·mol–1, A = 6.24 × 109 ± 1 × 109 s–1, Mn,SEC = 102 kDa). Interestingly, the degradation proceeds significantly faster with increasing chain length, an observation possibly associated with entropic effects. The degradation mechanism was explored in detail via SEC–ESI–MS for acrylate based polymers and theoretical calculations suggesting a Chugaev-type cleavage process. Processing of the RAFT polymers via small scale extrusion as well as a rheological assessment at variable temperatures allowed a correlation of the processing conditions with the thermal degradation properties of the polystyrenes and polyacrylates in the melt.

Well-defined, monodisperse homopolymer comb architectures with varied number and length of the branches under linear and nonlinear deformation were synthesized and examined to determine the effect of branching on different rheological properties. The correlation of the rheological properties with the comb topology is of special interest for the determination of the degree of branching. Therefore, well-defined polystyrene-based comb polymers with systematically varied number and molecular weight of the branches, narrow polydispersities, and a controlled, but low, number of branches (typically 0.1–1 mol % branches per backbone) were synthesized and compared with data from polystyrene combs of the Roovers series that have a higher number of branches (>1 mol % branches per backbone). To investigate the rheological properties in detail, various linear and nonlinear techniques were applied. Within the linear regime, the reduced van Gurp–Palmen plot (δ vs |G*|/GN0) was used to identify critical points that illustrated the influence of the branch molecular weight and number of branches on the resulting rheological properties. In the nonlinear regime large amplitude oscillatory shear (LAOS) measurements were performed to obtain the nonlinear parameter Q0(ω) via a quadratic scaling law from FT-rheology. An intrinsic nonlinear master curve based on the Q0(ω) parameter reflected the relaxation hierarchy and was shown to be a sensitive method to extract information on the different relaxation time scales. The nonlinear shear measurements were complemented by uniaxial extensional measurements to quantify the strain hardening effect and how the strain hardening was affected by branch relaxation. The results obtained from the uniaxial extensional measurements could be correlated to relaxation times obtained from the intrinsic nonlinear master curve Q0(ω). Pom-pom constitutive model predictions were performed for the comparison with experimental data for extensional rheology with focus on the strain hardening behavior and for LAOS with focus on the nonlinear parameter Q0(ω) as a function of increasing number and molecular weight of the branches in the pom-pom molecule. A comparison of the applied rheological methods—(1) small amplitude oscillatory shear (SAOS) in the linear regime, (2) LAOS in combination with FT-rheology, and (3) extensional rheology in the nonlinear regime—illustrated the detection limits as well as the advantages and disadvantages of each technique toward the investigation of rare, but entangled branched comb polymer topologies.

A highly sensitive rheodielectric experimental setup was used to investigate the macroscopic alignment of symmetric poly(styrene-b-1,4-isoprene) (SI) diblock copolymers under large-amplitude oscillatory shear (LAOS). The dielectric normal-mode of the 1,4-cis-polyisoprene chains in the diblock copolymer was chosen to probe in situ the macroscopic orientation process. It was shown that the development of the overall orientation of the lamellar microstructure can be followed in situ using the time progression of the dielectric loss modulus ε″(t). The dielectric loss ε″(t) correlates directly with the nonlinear mechanical response I3/1(t) of the sample as determined via Fourier transform rheology (FT-rheology). In addition to these two dynamic methods, small-angle X-ray scattering was used to ascertain the degree and type of the macroscopic orientation as a function of the applied shear conditions. Evidence presented here showed that a decrease in ε″(t) relative to the initial value of ε″(t = 0 s) for a macroscopically isotropic sample melt was indicative of a macroscopic parallel orientation while an increase in ε″(t) corresponded to an overall perpendicular alignment. These phenomena are explained on a molecular level by the anisotropic diffusion of the confined polymer chains, resulting in a higher mobility of the dielectrically active end-to-end vector parallel to the interface, which can be detected via dielectric spectroscopy.

A new apparatus for the measurement of magnetorheological properties of magnetic fluids in a commercial strain-controlled rheometer is proposed. The new setup makes use of the concept of the Halbach cylinder to generate a homogeneous dipolar magnetic field, using only permanent magnets. Two of these Halbach cylinders are combined, allowing the magnetic field to be varied by simply rotating the cylinders relatively to one another. The magnetic field achieved in the middle of the cylinders varies from nearly zero to about 0.6 T without a significant variation on the high homogeneity (ΔB/B < 2 × 10 − 2) of the resulting field. To perform the rheological experiments inside a strong magnetic field, measurement geometries (concentric cylinders and a four-bladed vane) were constructed from a non-magnetic material (polyoxymethylene). For the first experiments with the new setup, a commercial magnetic suspension of carbonyl iron particles in hydrocarbon oil was investigated. Stress growth experiments at varying shear rates in the steady shear regime, as well as strain sweep experiments at constant frequency in the dynamic oscillatory regime, were performed. The results show a shift of the linear (elastic) regime in oscillatory shear to higher strain values for increasing magnetic field. The steady shear viscosity increases with increasing magnetic field. The behaviour of the magnetic suspension was understood in the context of the ratio from the viscous to the polarisation forces, the so-called Mason number.