Comparison of mechanical and molecular measures of mobility during constant strain rate deformation of a PMMA glass

We performed constant strain rate deformation and stress relaxation on a poly(methyl methacrylate) glass at T_g – 19 K, utilizing three strain rates and initiating the stress relaxation over a large range of strain values. Following previous workers, we interpret the initial rate of decay of the stress during the relaxation experiment as a purely mechanical measure of mobility for the system. In our experiments, the mechanical mobility obtained in this manner changes by less than a factor of 3 prior to yield. During these mechanical experiments, we also performed an optical measurement of segmental mobility based on the reorientation of a molecular probe; we observe that the probe mobility increases up to a factor of 100 prior to yield. In the post‐yield regime, in contrast, the mobilities determined mechanically and by probe reorientation are quite similar and show a similar dependence on the strain rate. Dynamic heterogeneity is found to initially decrease during constant strain rate deformation and then remain constant in the post‐yield regime. These combined observations of mechanical mobility, probe mobility, and dynamic heterogeneity present a challenge for theoretical modeling of polymer glass deformation. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1957–1967     

Alternating copolymerization of carbon dioxide and propylene oxide catalyzed by (R,R)‐SalenCoIII‐ (2,4‐dinitrophenoxy) and Lewis‐basic cocatalyst

A binary catalyst system of a chiral (R,R)‐SalenCo^III(2,4‐dinitrophenoxy) (salen = N,N‐bis(3,5‐di‐tert‐butylsalicylidene)‐1,2‐diphenylethylenediimine) in conjunction with (4‐dimethylamino)pyridine (DMAP) was developed to generate the copolymerization of carbon dioxide (CO₂) and racemic propylene oxide (rac‐PO). The influence of the molar ratio of catalyst components, the operating temperature, and reaction pressure on the yield as well as the molecular weight of polycarbonate were systematically investigated. High yield of turnover frequency (TOF) 501.2 h^?1 and high molecular weight of 70,400 were achieved at an appropriate combination of all variables. The structures of as‐prepared products were characterized by the IR, ¹H NMR, ¹³C NMR measurements. The linear carbonate linkage, highly regionselectivity and almost 100% carbonate content of the resulting polycarbonate were obtained with the help of these effective catalyst systems under facile conditions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5050–5056, 2007     

Deformation induced evolution of mobility in PMMA

The stress relaxation response in the glassy state just below T_g was measured for poly(methylmethacrylate) following application of constant strain rate uniaxial tensile deformation at various locations on the stress–strain curve, including the yield and post‐yield region. The macroscopic mobility was determined from analysis of the relaxation response. Up to a factor of 3 decrease in relaxation time was observed with the fastest relaxation occurring in the post‐yield softening region. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Effect of molecular entanglements on craze microstructure in glassy polymers

Thin films of ten glassy polymers are bonded to copper grids and strained in tension to produce crazes, which are then examined in the transmission electron microscope. The average craze fibril extension ratio λ for each polymer is determined from microdensitometer measurements of the mass thickness contrast of the crazes. The extension ratio λ is found to increase approximately linearly with the chain contour length l_e between entanglements, as determined from melt elasticity measurements of the entanglement molecular weight of these polymers. These results are analyzed by comparing them with λ_max, the maximum extension ratio of an entanglement network in which polymer chains neither break nor reptate (i.e., permanent entanglement crosslinks are assumed). The values of λ_max are given by l_e/d where d, the entanglement mesh spacing in the unoriented glass, is computed from d = k(M_e)^1/2 with k determined either from small-angle neutron scattering results on isolated chains in the glass or from coil size measurements in dilute solutions of a θ solvent. The craze extension ratios fall somewhat below λ_max at low λ but increase to well above λ_max for polymers with high l_e. This comparison suggests a significant contribution due to chain breakage (or reptation) in the higher-λ crazes of large-l_e polymers, which may arise from the higher true stresses in the craze fibrils (which for a given applied stress increase proportionally to λ). The results also imply that a useful way to increase the “brittle” fracture stress and decrease the ductile-to-brittle transition temperature of a glassy polymer is to decrease its entanglement contour length l_e.     

Effect of finite extensibility on the viscoelastic properties of a styrene–butadiene rubber vulcanizate in simple tensile deformations up to rupture

Stress–strain and rupture data were determined on an unfilled styrene–butadiene vulcanizate at temperatures from ?45 to 35°C and at extension rates from 0.0096 to 9.6 min^?1. The data were represented by four functions: (1) the well-known temperature function (shift factor) a_T; (2) the constant strain rate modulus, F(t,T), reduced to temperature T₀ and time t/a_T, i.e., T₀F(t/a_T)/T; (3) the time-dependent maximum extensibility, λ_m(t/a_T); and (4) a function Ω(χ) where χ = (λ ? 1)λ_m⁰/λ_m, in which λ is the extension ratio and λ_m⁰ is the maximum extensibility under equilibrium conditions. The constant strain rate modulus characterizes the stress–time response to a constant extension rate at small strains, within the range of linear response; λ_m is a material parameter needed to represent the response at large λ; and Ω(χ) represents the stress–strain curve of the material in a reference state of unit modulus and λ_m = λ_m. The shift factor a_T was found to be sensibly independent of extension. At all values of t/a_T for which the maximum extensibility is time-independent, the relaxation rate was also found to be independent of λ. These observations indicate that the monomeric friction coefficient is strain-independent over the ranges of T and λ covered in the present study. It was found that λ_m⁰ = 8.6 and that the largest extension ratio at break, (λ_b)_max, is 7.3. Thus, rupture always occurs before the network is fully extended.     

Effect of aging time on properties of acrylic impact modifier modified bisphenol A polycarbonate

Polycarbonate (PC) was blended with acrylic impact modifiers (AIMs). The effects of modifiers weight fraction on the Izod impact strength and yield strength of PC/AIM blends were investigated. The samples with 4% modifiers were aged under the T_g of PC in an air‐circulating oven, and the effects of aging time on impact strength, yield strength, modulus, elongation at break, post yield stress drop (PYSD) values, and morphology of fracture surface were investigated. The effects of aging time on the shape of stress–strain curve were also investigated. The aged samples were heat‐treated over the T_g of PC to erase the effects of physical aging. It was found that the drop of impact strength caused by physical aging can be recovered, the increment of yield strength and PYSD value caused by physical aging can only be partly recovered, and the heat‐treatment over the T_g of PC caused further increment of modulus. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2715–2724, 2005     

Basic gel permeation chromatography studies. III. Mathematical analysis of peak spreading

Peak spreading in gel permeation chromatography has been studied with a range of gels including those whose permeation limit corresponded to about 10³, 10⁶, 10⁸, and 10⁹ molecular weight polystyrene. Peak spreading conformed to the equation Y_V ² = Y_M ² + Y_A ² + Y_I ² + Y_D ² + Y_S ², where Y_V is the peak width of a normal chromatogram, Y_M is the contribution due to the true molecular weight of the sample, Y_A is due to peak spreading in the apparatus, Y_I is spreading in the interstitial volume, Y_D is diffusional spreading due to time spent in the gel, and Y_S is due to sorption. Evaluating the appropriate parts of the equation leads to measures of the true molecular weight distribution and the contribution due to diffusion into and out of the gel. The data also allowed estimates as to the diffusional spreading with small molecules. With polystyrene having 100 000 molecular weight, diffusional spreading accounts for 80% of Y_V ,² but with small molecules the contribution due to diffusion was not detected.     

Stress overshoot of polymer solutions at high rates of shear; Polystyrene with bimodal molecular weight distribution

Overshoot of shear stress, σ, and the first normal stress difference, N₁, in shear flow was investigated for dilute solutions of polystyrene with very high molecular weight in concentrated solution of low M PS. In the case that the matrix was a nonentangled system, behavior of overshoot was similar to that of dilute solution of high M PS in pure solvent. The magnitudes of shear, γ_σm and γ_Nm, corresponding to the peaks of σ and N₁ lay on the universal functions of γ˙τ_R, respectively, proposed for dilute solutions in pure solvent. Here τ_R is the Rouse relaxation time for high M PS in the blend evaluated from dynamic modulus at high frequencies. In the case that the matrix was an entangled system, an additional σ peak was observed at high rates of shear at times corresponding to γ_σm = 2–3. This peak can be assigned to the motion of low M chains in entanglement network. When the matrix was entangled, stress overshoot was observed even at relatively low rates of shear, say γ˙τ_R < 10⁻². This is probably due to the motion of high M chains in entanglement of all the chains. In this case the γ_σm and γ_Nm values were higher than those expected for entangled chains of monodisperse polymer in pure solvent. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2043–2050, 2000     

Relationship between fracture toughness and intrinsic deformation parameters in isotropic and flow‐oriented linear low‐density polyethylene

The fracture toughness of isotropic and flow‐oriented linear low‐density polyethylene (LLDPE) is evaluated by the Essential Work of Fracture (EWF) concept, with a special setup of CCD camera to monitor the process of deformation. Allowing for the molecular orientation, flow‐oriented sample, prepared via melt extrusion drawing, is stretched parallel (oriented‐0°) and perpendicular (oriented‐90°) to its original melt extrusion drawing direction, respectively. The obtained values of specific EFW w_e are 34.6, 10.2, and 4.2 N/mm for the oriented‐0°, isotropic and oriented‐90° sample, respectively. With knowledge of intrinsic deformation parameters deduced from uniaxial tensile tests, moreover, a relationship between specific EFW w_e the ratio of true yield stress to strain hardening modulus σ_ty/G is well established. It means that the fracture toughness of polyethylene is determined by both crystalline and amorphous parts, rather than by one of them. Moreover, the true yield stress seems to be nondecisive factors determining the fracture toughness of polyethylene. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2880–2887, 2006     

Synthesis and Reactions of the Novel Diphosphine,iPrN = C[CH2P(NiPr2)2]2

Abstract

The aldimine nBuN=CHiPr and phosphorus trichloride react to give phosphorus(III) amides in a 1:1 and 2:1 molar ratio. An imine-enamine tautomerism is proposed. In a [4+1] cycloaddition reaction diacetyl-(N-n-butyl)diimine and λ³σ³P-species, RPCl₂ or EtOPCl₂, form 1,2,3λ⁵σ⁴ -diazaphospholenes¹. The same diimine and (Et₂N)₂ PCl is furnishing annellated azaphospholenes¹. A 1,3,4λ⁵ σ⁴ -diazaphospholanium is formed from a λ³σ³ -phosphenium and iPrN=CMe₂ ². Phosphorus(III) amides P(NR₂)₃ (R= Me, Et) and O-trimethylsilylated diacetyldioxime give rise to yield the first monocyclic pentaazaphosphoranes.     

Tunable microstructures and mechanical deformation in transparent poly(urethane urea)s

Transparent poly(urethane urea) (TPUU) materials offer an avenue to enable material designs with potential to achieve simultaneous enhancements in both physical and mechanical properties. To optimize the performance required for each application, the molecular features that influence the microstructure, the glass transition temperature (T_g), the deformation mechanisms, and the mechanical deformation behavior must be understood and exploited. In this work, a comprehensive materials characterization of select model PUUs with tunable microstructures is addressed. Increasing the hard segment (HS) content increases the stiffness and flow stress levels, whereas altering the soft segment (SS) molecular weight from 2000 to 1000 g/mol leads to an enhanced phase mixing with a SS T_g shifted ～17 °K toward higher temperatures as well as broadening of the SS relaxation closer to room temperature. As a result, the 1K TPUU materials display greater rate‐dependent stiffening and strain hardening on mechanical deformation over the broad range of strain rates covered in this work (10^?3 to 10⁴ s^?1). In such case of similar urea‐based HS content, the molar content of the urethane linkages, per stoichiometric requirements, is much higher in the 1K TPUUs than the 2K TPUUs. These additional urethane moieties lead to an increase in the extent of intermolecular interactions, via hydrogen bonding between the HS and the SS, providing not only further phase mixing and stronger rate sensitivity but also provide 1K TPUUs with drastically improved barrier properties. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Polymerization of styrene oxide catalyzed by a diethylzinc/α-pinene oxide system

Styrene oxide (SO) was polymerized with a diethylzinc/α-pinene oxide (ZnEt₂/α-PiO) catalyst system under various conditions. Polystyrene oxide (PSO) thus obtained had a regular head-to-tail and isotactic structure. The number-average molecular weight reached 4.07 × 10⁴, and the molecular weight distribution was 5.7 (M_w/M_n). The glass-transition temperature of PSO was about 47 to 50 °C, depending on the molecular weight. The molar ratio of ZnEt₂ to α-PiO, 2 : 1, led to a high molecular weight of PSO in an 89.2% yield within 72 h. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 4640–4645, 1999     

Orientation of cylindrical microdomains of triblock copolymers by in situ stress–strain‐ birefringence measurements

The orientation behavior of polystyrene‐block‐hydrogenated polyisoprene‐block‐polystyrene (SEPS) with cylindrical microdomains of polystyrene (PS) dispersed in the rubbery segments was investigated by simultaneous measurements of stress and birefringence during uniaxial stretching. The stress increased sharply with strain below the yield strain and then it gradually increased. In contrast, the birefringence changed little below the yield strain, increased sharply with strain above the yield strain up to a strain of 0.5, and then gradually increased. The characteristic birefringence behavior is attributed to the form birefringence induced by the orientation and the parallel arrangement of the cylindrical microdomains associated with the orientation of the rubbery segments. The orientation function of the cylindrical microdomains f evaluated by analyzing the form birefringence agrees well with that obtained from the SAXS result. The f was almost zero below the yield strain and it increased sharply with strain up to a strain of 0.5 and then was constant above a strain of 0.5. These results suggest that the orientation of the cylindrical microdomains occur above the yield strain up to a strain of 0.5 and that the orientation does not increase above a strain of 0.5 in spite of the continuous orientation of the rubbery ethylene–propylene segments. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 715–723, 2009     

Low-angle electron diffraction from high temperature polystyrene crazes

Low-angle electron diffraction (LAED) was used to study the microstructure of crazes produced at different temperatures T and strain rates in thin films of monodisperse polystyrene (PS). At a slow strain rate of 4.1 × 10^?6 s^?1 both the fibril diameter D and the fibril spacing D₀ of crazes in 1800k molecular weight PS remained constant with temperature up to T ≈ 70°C and then sharply increased as T approaches T_g. At a higher strain rate of ～ 10^?2 s^?1, both D and D₀ increase only slightly with T. The values of D and D₀ over a range of temperature are in very good agreement with those values obtained in bulk samples using small-angle x-ray scattering. The crazing stress was measured as a function of temperature in the thin films of the 1800k molecular weight PS strained at the same slow strain rate used for the LAED measurements. These measurements were analyzed using a simple model of craze growth to reveal the temperature and strain rate dependence of the craze surface energy Γ. At room temperature Γ ≈ 0.076 J/m² (versus Γ ≈ 0.087 J/m² predicted) and was observed to remain constant up to T ≈ 70°C and then decrease by approximately a factor of two at T = 90°C. This decrease in Γ is believed to result from chain disentanglement to form fibril surfaces at sufficiently high temperatures and occurs in the same temperature range in which the craze fibril extension ratio λ was observed to increase.     

Brush‐First ROMP of poly(ethylene oxide) macromonomers of varied length: impact of polymer architecture on thermal behavior and Li+ conductivity

The properties of polymeric materials are dictated not only by their composition but also by their molecular architecture. Here, by employing brush‐first ring‐opening metathesis polymerization (ROMP), norbornene‐terminated poly(ethylene oxide) (PEO) macromonomers ( MM‐n , linear architecture), bottlebrush polymers ( Brush‐n , comb architecture), and brush‐arm star polymers ( BASP‐n , star architecture), where n indicates the average degree of polymerization (DP) of PEO, are synthesized. The impact of architecture on the thermal properties and Li⁺ conductivities for this series of PEO architectures is investigated. Notably, in polymers bearing PEO with the highest degree of polymerization, irrespective of differences in architecture and molecular weight (~100‐fold differences), electrolytes with lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) as an Li⁺ source exhibit normalized ionic conductivities (σ_n) within only 4.9 times difference (σ_n = 29.8 × 10^?5 S cm^?1 for MM‐45 and σ_n = 6.07 × 10^?5 S cm^?1 for BASP‐45 ) at a concentration of Li⁺ r = [Li⁺]/[EO] = 1/12 at 50 °C. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 448–455     

Morphological change of poly (ε‐caprolactone) with a wide range of molecular weight via formation of inclusion complex with α‐cyclodextrin

The effect of molecular weight of poly(ε‐caprolactone) (PCL) on the formation and stability of inclusion complexes (ICs) between α‐cyclodextrin (α‐CD) and PCL was investigated by FTIR, WAXD, and DSC measurements. ICs between α‐CD and PCLs with a wide range of number‐average molecular weight, M_n = 1.21 × 10⁴ – 1.79 × 10⁵, were prepared by mixing the aqueous solution of CD and acetone solution of PCL followed by stirring at 60 °C for 1h and at the room temperature for 1 day. FTIR, WAXD, and DSC measurement showed the PCL chains were included into the α‐CD cavity, and the crystallization of PCL was suppressed in the α‐CD cavity. Stoichiometry and yield of each IC varied with the molecular weight of guest PCL, and the effect of IC formation on the crystallization behaviour of guest polymer decreased with the increase of molecular weight of guest polymer. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1433–1440, 2005     

Melt drawing of ultra‐high molecular weight polyethylene: Comparison of Ziegler‐ and metallocene‐catalyzed reactor powders

The drawing behavior of the ultra‐high molecular weight polyethylene (UHMW‐PE) melts has been studied by comparing the stress/strain curves for two types of samples as polymerized using conventional Ziegler and newer metallocene catalyst systems. Two UHMW‐PE samples, having the same viscosity average molecular weight of 3.3 × 10⁶, but different molecular weight distribution, have been drawn from melt at special conditions. The sample films for drawing were prepared by compression molding of reactor powders at 180°C in the melt. Differences in the structural changes during drawing and resultant properties, ascribable to their broad or narrow molecular weight distribution, were estimated from tensile tests, SEM observations, X‐ray measurements and thermal analyses. The metallocene‐catalyzed sample having narrower molecular weight distribution, could be effectively drawn from the melt up to a maximum draw ratio (DR) of 20, significantly lower than that obtained for the Ziegler‐catalyzed sample, ∼ 50. The stress/strain curves on drawing were remarkably influenced by draw conditions, including draw temperature and rate. However, the most effective draw for both was achieved at 150°C and a strain rate of 5 min⁻¹, independent of sample molecular weight distribution. The efficiency of drawing, as evaluated by the resultant tensile properties as a function of DR, was higher for the metallocene‐catalyzed sample having narrower molecular weight distribution. Nevertheless, the maximum achieved tensile modulus and strength for the Ziegler sample, 50–55 and 0.90 GPa, respectively, were significantly higher than those for the metallocene sample, 20 and 0.65 GPa, respectively, reflecting the markedly higher drawability for the former than the latter. The stress/strain behavior indicated that the origin of differences during drawing from the melt could be attributed to the ease of chain relaxation for the lower molecular weight chains in the melt. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1921–1930, 1999     

High molecular weight poly(ethylene‐2,5‐furanoate); critical aspects in synthesis and mechanical property determination

Furan‐2,5‐dicarboxylic acid (FDCA) is a widely advocated renewable substitute for terephthalic acid (TA). Preparation of high molecular weight FDCA based polyesters by an industrially common combination of melt polymerization and subsequent solid state post condensation is described. Ultimately, poly(ethylene 2,5‐furanoate) (PEF) with absolute M_n = 83,000 g mol^?1 is obtained, determined by triple detection Size Exclusion Chromatography. The bulk polymer properties of FDCA based polyesters, necessary to evaluate their industrial potential were determined the Young's modulus of PEF is determined to be 2450 ± 220 MPa and the maximum stress 35 ± 8 MPa. The influence of crystallinity on the mechanical properties as function of temperature was determined by dynamic mechanical thermal analysis. A detailed differential scanning calorimetry study on the crystallization behavior of high molecular weight PEF allowed to calculate the equilibrium melting temperature (T_m⁰) of 239.3 and 239.7 °C for the first and second melting peak, respectively. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4191–4199     

Experimental determination of the relationships among various measures of fluid elasticity

The viscoelastic properties of a 4% solution of monodisperse polystyrene (molecular weight 394,000) in Aroclor 1260 were determined by the following techniques: creep recovery, stress relaxation upon cessation of steady flow, dynamic measurements, and normal stress difference and shear stress measurements in steady flow. All measurements were carried out with cone and plate geometry in a Weissenberg rheogoniometer. The modification of this instrument to perform creep and creep recovery experiments by use of an air-bearing suspension and an air-turbine drive is described. A broad range of shear rates and frequencies encompassing both linear and nonlinear behavior was employed. The elastic behavior is described in terms of the recoverable shear strain s or the steady-state compliance J_e°. The first three techniques gave identical results for J_e° in the range of linear viscoelasticity for which it is defined. The normal stress difference measurements confirmed Lodge's relation s = (P₁₁ ? P₂₂)/2σ₂₁. Reasons for previous experimental disagreement with this result are discussed.