Effect of soft segment molecular weight on tensile properties of poly(propylene oxide) based polyurethaneureas

Influence of soft segment molecular weight and hard segment content on the morphology, thermomechanical and tensile properties of homologous polyurethaneurea copolymers based on narrow molecular weight poly(propylene oxide)glycol (PPG) oligomers were investigated. A series of polyurethaneureas with hard segment contents of 12–45% by weight and PPG number average molecular weights <M_n> of 2000 to 11,800 g/mol were synthesized and characterized structurally by SAXS and mechanically by DMA and stress strain analysis. Bis(4-isocyanatocyclohexyl)methane and 2-methyl-1,5-diaminopentane were used as the diisocyanate and the chain extender respectively. All copolymers displayed microphase separation by SAXS and DMA. The critical entanglement molecular weight (M_e) of PPG is reported to be around 7700 g/mol. Our mechanical results suggest that when copolymers possess similar hard segment contents and are compared to those based on soft segments with number average molecular weights (M_n) greater than M_e, they generally displayed higher tensile strengths and particularly lower hysteresis and creep than those having soft segment molecular weights below M_e. These results imply that soft segment entanglements in thermoplastic polyurethaneureas may provide a critical contribution to the tensile properties of these copolymers – particularly in the range where the soft segment content is dominant.     

Polymer Network Mobility and Environmental Stress Cracking Resistance of High Density Polyethylene

Zero shear viscosity and molecular weight between entanglements (M _e ) are determined from dynamic oscillatory shear experiments. Lower M _e value means higher number of entanglements in the system and is associated with increasing strain hardening stiffness. With the understanding that strain hardening is related to environmental stress cracking resistance (ESCR) of high density polyethylene (HDPE), M _e is then related to the ESCR of several resins in this study. The inversely proportional relationship between M _e and ESCR indicates that low network mobility due to an increasing number of chain entanglements increases the ESCR of HDPE.     

Craze microstructure and molecular entanglements in polystyrene-poly(phenylene oxide) blends

Polystyrene and poly(phenylene oxide) are miscible over the entire range of compositions. Thin films of five blends of high molecular weight polystyrene (PS) with high molecular weight poly(phenylene oxide) (PPO), and four blends of low molecular weight PS (whose molecular weight lies below its entanglement molecular weight M_e) with the same PPO have been prepared. Following bonding of these films to copper grids, crazes were grown by uniaxial straining in air. Suitable crazes were then observed by transmission electron microscopy. From microdensitometry of the image plates it is possible to measure the extension ratio λ_craze within crazes in the nine blends. These measured values are compared with predicted values of λ_max, computed from λ_max = I_ed, where I_e is the chain contour length between entanglements and d is the root mean square end-to-end distance for a chain of molecular weight M_e. For the high molecular weight PS blends λ_max depends on the entanglement properties of both PS and PPO chains. For the low molecular weight PS blends, the PS chains cannot form part of the entanglement network and the correct value of λ_max is obtained from appropriate scaling of the pure PPO value. Comparison of λ_craze and λ_max for both types of blends shows excellent agreement, demonstrating the importance of the entanglement network in determining craze parameters and hence the toughness of a given polymer.     

Variation of periodic crazing based on polymer blends of an ultra‐high and a low molecular weight poly(methyl methacrylate)

Periodic crazes are caused in a polymer film by the unique mechanical method using bending. Generation of a craze depends on entanglements of the molecular chains of a polymer. Therefore, control of composite morphology of periodic crazes was attempted by varying the entanglements of molecular chains. An effective entanglement network became sparse by polymer blends of an ultra‐high molecular weight polymethylmethacrylate (PMMA) and a low molecular weight PMMA. Consequently, the composite morphology of periodic crazes caused in the blend film varied. In other words, the periodic craze can be used for the evaluation of the effective entanglements. In addition, it was figured out that PMMA of which the number‐average molecular weight (M_n) is less than twice of the effective entanglement molecular weight (M_e^*) works as a plasticizer in the blend film. And also, it was revealed that the mechanical properties of the blend film decreased dramatically at M_n ≒ 6M_e^*. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 44332.     

A model for the zero shear viscosity

An empirical equation for the number of entanglements per molecule has been proposed, which applies over all the molecular weight range. On this ground a simple equation for the zero shear viscosity of monodisperse polymer melts, η₀, has been worked out that appears able to properly take into account the sharp transition of viscosity between the monomeric and the entanglement regimes. The molecular parameters appearing in the new viscosity equation are: the monomeric molecular weight m₀, the monomeric friction factor ζ₀, the molecular weight M, the average molecular weight between entanglements M_e, and the entanglement friction factor ζ_e^3.4. This last parameter was evaluated for a number of monodisperse polymers.     

Dependence of zero-shear viscosity and steady-state compliance on molecular weight between entanglements for ethylene-cycloolefin copolymers

Dynamic viscoelastic properties of a series of cyclic olefin copolymers have been investigated. The specimens differ in total molecular weight as well as molecular weight between entanglements. The angular frequency (ω) dependence curves of dynamic storage and loss moduli (G′ and G″, respectively) of the specimens have shown that G′ ∝ ω² and G″ ∝ ω in the terminal region, and a plateau region at high ω. On the basis of the experimental results, the dependence of total molecular weight as well as molecular weight between entanglements has been examined for zero-shear viscosity (η₀) and steady-state compliance (J_e). It is shown that for the melts of the copolymers in the entangled regime, M_w being the weight-average molecular weight and M_e the molecular weight between entanglements. The steady-state compliance J_e for the melts scales with M_e and M_w as .     

Linear viscoelastic relaxation modulus of polydisperse poly(dimethylsiloxane) melts containing unentangled chains

This work analyzes the relationship between the shear relaxation modulus of entangled, linear and flexible homopolymer blends and its molecular weight distribution (MWD) when a fraction of the sample contains chains with molecular weight M lower than the effective critical molecular weight between entanglements Mc_eff. This effective critical parameter is defined in terms of the critical molecular weight between entanglements M_c of the bulk polymer that forms the physical network and the effective mass fraction Wc_eff of the unentangled chains. In the terminal zone of the linear viscoelastic response, the double reptation mixing rule for blended entangled chains and a modified law for the relaxation time of chains in a polydisperse matrix are considered, where the effect of chains with M<Mc_eff is included. Although chain reptation with contour length fluctuations and tube constraint release are still the relevant mechanisms of chain relaxation in the terminal zone when the polydispersity is high, it is found that the presence of a fraction of molecules with M<Mc_eff modifies substantially the tube constrain release mode of chain relaxation. In this sense, a modified relaxation law for polymer chains in a polydisperse entangled melt that includes the effect of the MWD of unentangled chains is proposed. This law is validated with rheometric data of linear viscoelasticity for well-characterized polydimethylsiloxane (PDMS) blends and their MWD obtained from size exclusion chromatography. The short time response of PDMS, which involves the glassy modes of relaxation, is modeled by considering Rouse diffusion between entanglement points of chains with M>Mc_eff. This mechanism is independent from the MWD. The unentangled chains with M<Mc_eff occluded in the polymer network also follow Rouse modes of relaxation although they exhibit dependence on the MWD.     

Role of chain entanglements on fiber formation during electrospinning of polymer solutions: good solvent, non-specific polymer-polymer interaction limit

Chain entanglements are one of many parameters that can significantly influence fiber formation during polymer electrospinning. While the importance of chain entanglements has been acknowledged, there is no clear understanding of how many entanglements are required to affect/stabilize fiber formation. In this paper, polymer solution rheology arguments have been extrapolated to formulate a semi-empirical analysis to explain the transition from electrospraying to electrospinning in the good solvent, non-specific polymer-polymer interaction limit. Utilizing entanglement and weight average molecular weights (M_e, M_w), the requisite polymer concentration for fiber formation may be determined a priori, eliminating the laborious trial-and-error methodology typically employed to produce electrospun fibers. Incipient, incomplete fiber formation is correctly predicted for a variety of polymer/solvent systems at one entanglement per chain. Complete, stable fiber formation occurs at ≥2.5 entanglements per chain.     

The Effect of the Density and Nature of Spatial Network in Elastomers on Their Viscoelastic Characteristics

Abstract

We have studied the effect of the density of the networks formed by fluctuating entanglements and chemical crosslinking on the relationships between the circular frequency ω and the storage and loss moduli, G' and G”, for polybutadienes of narrow and wide molecular weight distributions (the ratio M_w/M_n varied from 1.1 to 3.35) and different microstructure. Polybutadienes were crosslinked by thermal, radiation, and sulphur vulcanization. With increasing density v of a network of chemical crosslinks, which is characterized by the average molecular weight of a chain length (M_e ), pseudo-equilibrium plateau extends to the side of low frequencies with a certain small increase of its level. This increase becomes noticeable when M_e is approximately equal to the average molecular weight M_e of the chain length between the fluctuating entanglements of an uncrosslinked elastomer. At the same time the maxima on the curves of G”(ω) are smoothed out and the losses reduce to negligibly small values with decreasing frequency.     

Glass transition elevation by polymer entanglements

For some polymers a plot of glass transition temperature, T_g, versus reciprocal molecular weight can be taken to define two lines which intersect at a molecular weight which is designated as M_g. The value of M_g agrees, within a factor of two, with critical values of molecular weight reported for other properties which are generally attributed to incipient formation of a network of entanglements. Therefore, it is suggested that an increased elevation of T_g at molecular weights greater than M_g is due to an increasing concentration of entanglements.A more detailed analysis was made by extending the Fox-Flory theory of the glass transition to include negative contributions to the free volume from entanglements. This extension leads to revised estimates of the free volume per chain end which are much smaller (6–19 ų near T_g) than previous estimates which took no account of entanglements. These smaller values are interpreted to mean that the jump units are correspondingly small at T_g, such as envisaged in the Gibbs-diMarzio theory of the glass transition.     

The dispersion of magnetic nanorods in poly(2‐vinylpyridine)

The dispersion of magnetic nanorods in poly(2‐vinylpyridine) (PVP) as a function of rod length, particle loading and molecular weight of PVP was investigated. The nanorods were organized into small spherical clusters at low particle loading. Further increasing the particle concentration caused an increase in the size of the aggregates. Additionally, the internal structure of the nanorods developed into a raft‐like structure, forming rectangular clusters. The incorporation of longer nanorods in the PVP amplified the magnetic interaction energy, which created conditions to induce extensive aggregation. The entanglement of the polymer also played an important role in the arrangement of the nanorods. This behavior could be categorized into two regimes, M_PVP > M_e and M_PVP < M_e, where M_PVP and M_e are the number‐average molecular weight and entanglement molecular weight of PVP, respectively: for M_PVP > M_e, PVP formed entanglements that prevented nanorods from extensive aggregation; for M_PVP < M_e, PVP could not form entanglements, and nanorods could move freely in the PVP, and thus significant rod aggregation occurred. Simple calculations to assess the contribution of the magnetic interaction, the van der Waals interaction and the free energy of mixing of the system to the arrangement of magnetic nanorods in the homopolymer are discussed. © 2013 Society of Chemical Industry     

Linear viscoelastic properties of mixtures of 3- and 4-arm polybutadiene stars

The viscoelastic properties of a three-arm and a four-arm star polybutadiene with the same arm molecular weight (M_a) were studied. The zero-shear recoverable compliance (J⁰_e) and plateau modulus (G⁰_N) for these stars are the same. The zero-shear viscosity (η₀) of the three-arm star is 20% lower than that of the four-arm star. Mixtures of the stars had J⁰_e and G⁰_N unchanged. A $\text{50}\text{50}$ mixture of the three- and four-arm star was diluted with a low molecular weight linear polybutadiene. G⁰_N∝ø²; J⁰_e∝ø^?1 and M_e∝ø^?1, as expected for dilution with a θ-solvent.     

Concentration dependence of the primitive path step length

Recent experiments by Donald and Kramer have measured the extension ratio, λ_craze, for polymers in crazes under tensile strain. In this paper it is shown that $\text{λ}{}_{\mathrm{<mtext>craze</mtext>}}\text{∝I}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}_{\mathrm{<mtext>e</mtext>}}\text{i}$ where I_e is the average contour length between entanglements in glassy, and not permanently crosslinked polymers and is obtained from melt elasticity experiments. It is also shown that I, the Rouse chain step length for a molten polymer, is independent of monomer density and that the average distance between entanglements, d ∝ ?^?α, where ? is the number of monomers per unit volume with $\text{1}\text{4}\text{? α ?}\text{1}\text{2}$. Finally these results are shown to provide confirmation for the configurational assumptions of the primitive path for reptation in which α appears as the determining factor for the concentration dependence of the relaxation modulus, the steady state viscosity and terminal relaxation time.     

Radiation induced embrittlement of PTFE

The radiochemical degradation of polytetrafluoroethylene (PTFE) samples has been studied in air at dose rate 100 Gy/h for doses up to 5000 Gy, at ambient temperature. The polymer degradation has been monitored by DSC, tensile testing and Essential Work of Fracture (EWF) testing. Some fractured samples have been observed by scanning electron microscopy. The polymer undergoes a fast chain scission, its number average molar mass is divided by about 20 for a dose of 1000 Gy and tends towards a pseudo asymptotic value of ∼20 kg mol⁻¹ (against 6200 kg mol⁻¹ initial value). The modulus and yield characteristics seem to be almost unaffected whereas ultimate properties undergo strong variations. The ultimate elongation ε_R and the EWF plastic work characteristic βw_p first increase and then decrease. The ultimate stress decreases and tends towards a pseudo asymptotic value. The mechanisms of radiation induced ultimate property changes are discussed. The first stage could be due to the destruction of non-extended tie molecules (due to the presence of very long chains) responsible for interfibrillar bridging during fracture. The (more classical) second stage is a progressive embrittlement due to the destruction of the entanglement network. The critical molar mass M′_c for embrittlement is such as M′_c∼50M_e, M_e being the molar mass between entanglements in the melt. This relationship could be a general characteristic of high crystallinity non-polar polymers.     

Entanglement network of chitin and chitosan in ionic liquid solutions

Concentrated solutions of a chitin from squid pens and of two commercial samples of chitosan were successfully prepared by using an ionic liquid 1‐butyl‐3‐methylimidazolium acetate as a solvent. The dynamic viscoelasticity data for the solutions exhibited rubbery plateaus, indicating the existence of entanglement network of chitin and chitosan in the solutions. To characterize the network, the values of the molecular weight between entanglements (M_e) for chitin and chitosan in the solutions were determined from the plateau moduli. Then the values of M_e in the molten state (M_e,melt), a material constant reflecting the inherent nature of polymer species, for chitin and chitosan were estimated to be 1.7 × 10³ and 3.0 × 10³, respectively. It was found that there was a significant difference in M_e,melt between chitin and chitosan. Compared with other polysaccharides such as cellulose and agarose in terms of the number of monosaccharide units between entanglements (N_unit), chitin had significantly smaller N_unit of 8, while chitosan had equivalent N_unit of 19. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 2439–2443, 2013     

Synthesis of linear isotactic-rich poly(p-methylstyrene) via cationic polymerization coinitiated with AlCl3

Cationic polymerizations of p-methylstyrene (pMS) with H₂O/AlCl₃/triphenylamine (TPA) or triethylamine (TEA) initiating system were carried out in mixed solvents of n-hexane and dichloromethane at ?80 ～ ?50 °C. The effects of TPA or TEA concentration, solvent polarity, polymerization temperature and time on monomer conversion, number-average molecular weight (M_n), molecular weight distribution (MWD, M_w/M_n), stereoregulatity and crystallinity of poly(p-methylstyrene) (PpMS) were investigated. The stereospecific cationic polymerization of p-methylstyrene could be achieved and high molecular weight (M_n = 116,000 ～ 436,000 g mol^?1) polymers with isotactic-rich segments (more than 75% of meso dyad) along macromolecular chains could be successfully synthesized. A possible mechanism for stereospecific cationic polymerization of pMS was proposed. The propagation proceeded via the dominant back-side attack and insertion of monomer from the growing ion paired species. The steric course of propagation was mainly determined by the tightness of the growing ion paired species and steric hindrance in counteranion. The resulting isotactic-rich PpMS could form crystal morphology with 10 ～ 30 μm in size by flow-induced crystallization under pressure at 180 °C. A possible model for the aligning mechanism was sketched to describe crystallization and to explain the multi-melting peaks and lower glass transition temperatures of PpMS. This is the first example of stereospecific cationic polymerization of p-methylstyrene to get crystallizable polymers with such high molecular weights and isotacticity.     

Molecular weight dependence of the fracture toughness of glassy polymers arising from crack propagation through a craze

We investigate criteria for craze failure at a crack tip and the dependence of craze failure on the molecular weight of the polymer. Our micromechanics model is based on the presence of cross-tie fibrils in the craze microstructure. These cross-tie fibrils give the craze some small lateral load bearing capacity so that they can transfer stress between the main fibrils. This load transfer mechanism allows the normal stress on the fibrils directly ahead of the crack tip in the center of the craze to reach the breaking stress of the polymer chains. We solve for stress field near the crack trip and use it to relate craze failure to the external loading and microstructural quantities such as the craze widening (drawing) stress, the fibril spacing, the molecular weight, and the force to break a single polymer chain. The relationship between energy flow to the crack tip due to external loading and the work of local fracture by fibril breakdown is also obtained. Our analysis shows that the normal stress acting on the fibrils at the crack tip increases linearly as the square root of the craze thickness, assuming that the normal stress distribution is uniform and is equal to the drawing stress acting on the craze-bulk interface. The critical crack opening displacement, and hence the fracture toghness is shown to be proportional to [1–(M_e/qM_n)]², where M_e is the entanglement molecular weight, M_n is the number average molecular weight of polymer before crazing, and q is the fraction of entangled strands that do not undergo chain scission in forming the craze.     

Stress softening of multigraft copolymers

The hysteresis behaviour of multigraft (MG) copolymers, with a polyisoprene backbone and polystyrene (PS) side chains, was investigated by applying a modified softening model proposed by Elías-Zúñiga, which uses an approach of Ogden and Roxburgh. The model was combined with the non-affine tube model of rubber elasticity of Kaliske and Heinrich. Four parameters are obtained: chemical and physical cross-link moduli (G_c, G_e), the number of statistical segments between two successive entanglements (n_e/T_e) and a softening parameter (b). The model was proven to be valid by a comparison with other methods evaluating hysteresis behaviour. The characterization of the multigraft copolymers revealed a branch point and molecular architecture dependence of the softening parameter. b was low for tetrafunctional MG copolymers with cylindrical microdomains, and it was further reduced for a spherical morphology and for more complex molecular architectures. The magnitude of b also depends on the PS arm molecular weight for hexa- and tetrafunctional multigraft copolymers.     

Rheological properties of concentrated solutions of agarose in ionic liquid

The rheological properties of agarose solutions were examined under the effect of entanglement coupling between agarose chains. Agarose solutions were prepared by using an ionic liquid 1‐butyl‐3‐methylimidazolium chloride as a solvent. The concentration of agarose was varied from 1.1 × 10¹–2.1 × 10² kg m^?3. The master curves of the angular frequency (ω) dependence of the storage modulus (G′) and the loss modulus (G″) showed a rubbery region in the middle ω region and a flow region at low ω region, respectively. The molecular weight between entanglements (M_e) for agarose was calculated from the plateau modulus. Moreover, M_e for agarose melt was determined to be 2.3 × 10³ from the concentration dependence curve of M_e. By using well‐known empirical relations in polymer rheology, information on molecular characteristics of sample agarose was derived. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Molecular weight scaling of the spherulite growth rate in isothermally melt crystallized polyethylene nanocomposites

The spherulite growth rate, G_II, was measured for three monodisperse linear polyethylenes filled with up to 4 vol. % of SiO₂ nanoparticles in the crystallization regime II of small undercooling, ΔT. The fumed SiO₂ used did not exhibit any measurable nucleation activity. The G_II scaled with the number average molecular weight, M_n, as M_n^ν with the scaling exponent, ν, equal to (2.2 ± 0.1). This corresponds to the reptation controlled surface self-diffusion of loop-train adsorbed chains with the contour length fluctuation (CLF) and the chain constraint release (CR) contributions. In order to verify the hypothesis of the chain reptation as the molecular mechanism responsible for the chain transport, logG_II was plotted against the logarithm of the number of effective entanglements per chain, logN_eff. The N_eff was the sum of the number of “true” entanglements in the neat resin of a given M_n and the number of apparent “temporary” entanglements due to adsorption/desorption of segments of PE chains onto SiO₂ nanoparticles with their inter-particle distance equal or shorter than the average entanglement length. Adding 2 vol % and 4 vol. % SiO₂, respectively, resulted in an increase of the N_eff by 40% and 80% of apparent “temporary” entanglements, respectively. When plotted against logN_eff, all the experimental logG_II data for a given undercooling, ΔT, collapsed to a single line. The slope of the logG_II vs. logN_eff dependence was independent of ΔT and varied from −2.13 to −2.24, similarly to the slope of the logG_II vs. logM_n dependence. This supported the conclusion that the effects of increasing the M_n and/or adding the non-nucleating nanometer sized SiO₂ on the spherulite growth rate were additive in nature and their effect can be superimposed. The retarded reptation of the chains to the growing crystal front was identified as the primary molecular mechanism of chain transport controlling the reduction of the spherulite growth rate in the model PE/SiO₂ nanocomposites investigated.