The effect of molecular properties on the rheological and fatigue behaviors of solid polystyrene (PS)/polyisoprene (PI) block copolymers was investigated. Linear model systems of PS–PI (SI), PS–PI–PS ...(SIS), and PI–PS–PI (ISI) block copolymers were synthesized via anionic polymerization with well-defined molecular structure variation such as block order, PI content, molecular weight, microstructure, and polydispersity. The different block sequences (SI vs SIS vs ISI) result, for similar PI contents, in different microdomain sizes, which correlate with the phase-separated morphologies as quantified via small-angle X-ray scattering (SAXS). The samples were mechanically characterized in the solid state via strain sweep tests to obtain their storage G′(γ0) and loss G″(γ0) moduli at room temperature as well as their nonlinear properties determined via the Fourier transform (FT) of the stress response. The fatigue behavior was determined via strain-controlled oscillatory torsion tests. First, the effect of strain amplitude on the number of cycles to failure was analyzed via Wöhler curves, specifically strain amplitude vs fatigue lifetime. A significant effect of the block sequence order, the microdomain size, and the chain dynamics on fatigue resistance was found. The fatigue resistance of SI diblock with 30 mol % PI outperforms the SIS or ISI triblock copolymer with a similar composition and, compared to neat PS, increases by a factor of 10 and even 4500, respectively. Second, the time-dependent stress response was analyzed via Fourier transform rheology to better quantify the time-dependent behavior of the nonlinear mechanical parameters and to determine quantitative parameters related to failure onset. Since the fatigue tests were performed under large amplitude oscillatory shear (LAOS), higher harmonics were detected and the time evolution was quantified in the FT spectra. Linear parameters such as the storage (G′) and loss (G″) moduli, as well as the third (I 3) harmonic over the fundamental one (I 1), were analyzed, leading to clear indications related to both brittle or ductile failure mechanisms.
Comb and bottlebrush polymers present a wide range of rheological and mechanical properties that can be controlled through their molecular characteristics, such as the backbone and side chain lengths ...as well as the number of branches per molecule or the grafting density. This review investigates the impact of these characteristics specifically on the zero shear viscosity, strain hardening behavior, and plateau shear modulus. It is shown that for a comb polymer with an entangled backbone and entangled side chains, a maximum in the strain hardening factor and minimum in the zero shear viscosity η0 can be achieved through selection of an optimum number of branches q. Bottlebrush polymers with flexible filaments and extremely low plateau shear moduli relative to linear polymers open the door for a new class of solvent‐free supersoft elastomers, where their network modulus can be controlled through both the degree of polymerization between crosslinks, nx, and the length of the side chains, nsc, with GBB0≈ρkTnx−1(nsc+1)−1.
Comb and bottlebrush polymers exhibit unusual rheological properties compared to their linear analogs due to side‐chain crowding. Investigation of the melt rheology of model branched polymers with controlled grafting density, side chain, and backbone lengths allows correlation of macroscopic flow properties such as zero shear viscosity, plateau modulus, and strain‐hardening behavior to conformational regimes by means of scaling analysis and tube theory.
：Linear and nonlinear rheological properties of model comb polystyrenes (PS) with loosely to densely grafted architectures were measured under small and medium amplitude oscillatory shear (SAOS and ...MAOS) flow. This comb PS set had the same length of backbone and branches but varied in the number of branches from 3 to 120 branches. Linear viscoelastic properties of the comb PS were compared with the hierarchical model predictions. The model underpredicted zero-shear viscosity and backbone plateau modulus of densely branched comb with 60 or 120 branches because the model does not include the effect of side chain crowding. First- and third-harmonic nonlinearities reflected the hierarchy in the relaxation motion of comb structures. Notably, the low-frequency plateau values of first-harmonic MAOS moduli scaled with Mw-2 (total molecular weight), reflecting dynamic tube dilution (DTD) by relaxed branches. Relative intrinsic nonlinearity
exhibited the difference between comb and bottlebrush via no low-frequency
peak of bottlebrush corresponding to backbone relaxation, which is probably related to the stretched backbone conformation in bottlebrush.
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-N br-44, had the same entangled backbone, M w,bb = 290 kg/mol, corresponding to a number of entanglements along the backbone Z bb ≅ 20, and similar branch length, M w,br ≅ 44 kg/mol or Z br ≅ 3, but varied in the number of branches per molecule, N br, from 3 to 190 branches. Consequently, the average number of entanglements between two consecutive branch points along the backbone (branch point spacing), Z s, ranged from well entangled, Z s ≅ 5, to values that were far less than one entanglement, Z s ≅ 0.1. Linear viscoelastic data including the zero-shear rate viscosity, η0, diluted modulus, G N,s 0, and a new diluted modulus extracted from the van Gurp–Palmen plot, |G*| at δ = 60°, were analyzed as a function of the M w of the combs. Scaling of η0 versus M w revealed three different regions for increasing N br or decreasing Z s: (1) loosely grafted combs with Z br < Z s and η0 ∼ exp(M w), (2) densely grafted combs with 1 < Z s < Z br and η0 ∼ M w –3.4 followed by η0 ∼ M w –1 for 0.2 < Z s < 1, and (3) loosely grafted bottlebrushes with Z s < 0.2 and η0 ∼ M w 5. The relative maximum in η0 corresponded to a comb-PS with Z s ≅ Z br, and the relative minimum resulted from a comb-PS with Z s ≅ 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 N br 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.
The effect of the molecular architecture of a series of anionically synthesized linear and comb atactic polystyrenes (PS) on their foam properties including cell size, cell density, and volume ...expansion ratio (V.E.R.) was investigated. The comb-PS had the same molecular weight of the backbone, Mw,bb ≈ 290 kg/mol, Zbb ≈ 20 entanglements, and branches, Mw,br ≈ 44 kg/mol, Zbr ≈ 3 entanglements, but different numbers of branches, 3 ≤ Nbr ≤ 190. Batch foaming of well-purified linear and comb-PS using CO2 resulted in cell densities about 109 and 4 × 109 cell/cm3, respectively, which shows that LCB has no distinct effect on the cell density, whereas a small amount of residual impurity in linear PS reduced the cell density to ~108 cell/cm3. For a comb-PS series with the same entangled backbone, Mw,bb ≈ 290 kg/mol, Zbb ≈ 20 entanglements, and similar branches, Mw,br ≈ 44 kg/mol, Zbr ≈ 3 entanglements, but different numbers of branches, 3 ≤ Nbr ≤ 190, an increase in the Nbr to 120 with densely grafted comb conformation gradually increased the highest achievable V.E.R. close to a theoretical limit given by the CO2 solubility. The further increase of Nbr to 190 with a bottlebrush conformation reduced the V.E.R. of the foam. From a rheological point of view, this optimum Nbr was related to a comb-PS which showed the maximum strain hardening factor (SHF ≈ 200) in uniaxial extension, and simultaneously the minimum in the zero shear viscosity, η0. The optimum Nbr = 120 for this comb-PS series corresponds to an average spacing distance between two neighbor branch points of about Zs ≈ 0.2 entanglements.
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•Long chain branched comb-PS improve foamability at elevated temperatures.•Maximum strain hardening factor is related to highest achievable volume expansion.•Low zero shear viscosity does not affect foamability in case of strain hardening.•Strain hardening in later foaming stage outweighs the effect of low viscosity.•Densely grafted comb conformation achieve 90% foaming efficiency up to V.E.R. = 40.
The effect of the molecular architecture of anionically synthesized linear and comb atactic polystyrenes (PS), as well as lab-scale emulsion polymerized PS and commercial PS on the cell density of ...foam (number of cells per unit volume of neat polymer) was investigated using CO2 as foaming agent in a batch foaming setup. The effects of molecular weight, Mw, dispersity (Ð), low molecular weight components, i.e. oligomers and residual surfactant, and the number of long chain branches per molecule, Nbr, in a series of comb-PS with the same entangled backbone, Mw,bb ≈ 290 kg/mol, Zbb ≈ 20 entanglements, and similar branches, Mw,br ≈ 44 kg/mol, Zbr ≈ 3 entanglements, but different numbers of branches, 3 ≤ Nbr ≤ 190, on the cell density were investigated. Specimens for foaming have been prepared with three different methods, which resulted in non-purified, treated, and purified samples. Well-purified samples produced foams with cell density above 109 cell/cm3, while foams out of the non-purified PS had one to three orders of magnitude lower cell density. However, artificial addition of 6 wt% oligomer PS or 3 wt% surfactant to the purified samples did not reduce the cell density significantly. Treated samples prepared by only dissolving the PS in a solvent followed by removing the solvent, produced a foam with slightly lower cell density, ~5 × 108 cell/cm3, than the purified PS. Lower cell density in non-purified PS was supposed to be related to the formation of a continuous ionic thin film layer (e.g. surfactant) rather than only the presence of low molecular weight components as impurity in the polymer. In the absence of such low molecular weight components, other molecular parameters, i.e. Mw, Ð, and Nbr in these series of comb-PS had surprisingly no distinct effect on the cell density.
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•Low cell density in commercial PS is related to formation of ionic thin film layer.•Presence of low molecular weight components has little effect on cell density.•Treatment and purification of commercial PS results in higher cell density.•Molecular weight and dispersity has no effect on cell density of final foam.•Long chain branching in synthesized model comb PS slightly increases cell density.
The effect of the molecular architecture of anionically synthesized linear and comb atactic polystyrenes (PS), as well as lab-scale emulsion polymerized PS and commercial PS on the cell density of ...foam (number of cells per unit volume of neat polymer) was investigated using CO2 as foaming agent in a batch foaming setup. The effects of molecular weight, Mw, dispersity (Ð), low molecular weight components, i.e. oligomers and residual surfactant, and the number of long chain branches per molecule, Nbr, in a series of comb-PS with the same entangled backbone, Mw,bb ≈ 290 kg/mol, Zbb ≈ 20 entanglements, and similar branches, Mw,br ≈ 44 kg/mol, Zbr ≈ 3 entanglements, but different numbers of branches, 3 ≤ Nbr ≤ 190, on the cell density were investigated. Specimens for foaming have been prepared with three different methods, which resulted in non-purified, treated, and purified samples. Well-purified samples produced foams with cell density above 109 cell/cm3, while foams out of the non-purified PS had one to three orders of magnitude lower cell density. However, artificial addition of 6 wt% oligomer PS or 3 wt% surfactant to the purified samples did not reduce the cell density significantly. Treated samples prepared by only dissolving the PS in a solvent followed by removing the solvent, produced a foam with slightly lower cell density, ~5 × 108 cell/cm3, than the purified PS. Lower cell density in non-purified PS was supposed to be related to the formation of a continuous ionic thin film layer (e.g. surfactant) rather than only the presence of low molecular weight components as impurity in the polymer. In the absence of such low molecular weight components, other molecular parameters, i.e. Mw, Ð, and Nbr in these series of comb-PS had surprisingly no distinct effect on the cell density.
The fatigue behavior of 28 amorphous and semi‐crystalline thermoplastic polymers and elastomers is tested under strain controlled sinusoidal tension‐tension (TT) and torsion (T) at room temperature ...and analyzed via strain‐life (total strain amplitude versus fatigue lifetime) and crack propagation rate versus total strain amplitude curves, analogous to Paris’ law. Investigating fatigue is extremely time‐ and resources consuming, so universal relationships between the exponents of the strain‐life power‐law and material properties are of high importance. For a brittle failure mechanism (I), the strain‐life curves are found to have fixed exponents of BTT,I = −0.27 and BT,I = −0.22, respectively, while the crack propagation versus strain amplitude in TT has an exponent of mda/dN,I = 4. For ductile failure (II), fixed strain‐life curve exponents in TT of BTT,II = −0.35 and in torsion of BT,II = −0.48 with mda/dN,II = 2.8 are obtained. In torsion, most semi‐crystalline polymers show brittle and ductile failure depending on the applied strain amplitude, so the strain‐life curve exponent changes accordingly. The universal exponents for strain‐life and crack growth‐strain amplitude curves offer a significant simplification to rapidly estimate, predict, and simulate the fatigue behavior of polymers.
The fatigue behavior of 28 thermoplastic polymers and elastomers is tested under strain controlled sinusoidal tension‐tension (TT) and torsion (T) and analyzed via strain‐life and crack propagation rate versus total strain amplitude curves. Constant exponents for both curves are found, depending only on brittle or ductile failure, not on the material.
The influence of topology on the strain hardening in uniaxial elongation is investigated using monodisperse comb and dendrigraft model polystyrenes (PS) synthesized via living anionic polymerization. ...A backbone with a molecular weight of Mw,bb = 310 kg mol−1 is used for all materials, while a number of 100 short (SCB, Mw,scb = 15 kg mol−1) or long chain branches (LCB, Mw,lcb = 40 kg mol−1) are grafted onto the backbone. The synthesized LCB comb serves as precursor for the dendrigraft‐type branch‐on‐branch (bob) structures to add a second generation of branches (SCB, Mw,scb ≈ 14 kg mol−1) that is varied in number from 120 to 460. The SCB and LCB combs achieve remarkable strain hardening factors (SHF) of around 200 at strain rates greater than 0.1 s−1. In contrast, the bob PS reach exceptionally high SHF of 1750 at very low strain rates of 0.005 s−1 using a tilted sample placement to extend the maximum Hencky strain from 4 to 6. To the best of the authors’ knowledge, SHF this high have never been reported for polymer melts. Furthermore, the batch foaming with CO2 is investigated and the volume expansions of the resulting polymer foams are correlated to the uniaxial elongational properties.
Anionically synthesized monodisperse model polystyrenes with comb and dendrigraft‐like branch‐on‐branch architectures exhibit tremendously high strain hardening factors in uniaxial elongation in the order of 2–3 decades. Batch foaming is used to investigate the extensional properties under practical aspects. The foam volume expansion ratio is correlated to the strain hardening factor and influential factors governing the processing performance are identified.
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