Some evidence against the existence of the liquid-liquid transition. IV. The temperature dependence of shear viscosity

The viscosity data available for four anionically polymerized polystyrenes ranging in molecular weight from 1100 to 47,000 for the temperature range T_g to T_g + 100°C have been fitted by computer programs to both the Vogel, Fulcher, Tamman, and Hesse (VFTH) equation and to two optimum intersecting Arrhenius equations. The intersection point has been interpreted as a manifestation of a liquid-liquid transition. The fits to the VFTH equation were in every case found to be far superior. Systematic deviations of the residuals were observed for the best Arrhenius fits which indicate the lack of any validity for such a representation of the data.     

Comments on “some evidence against the existence of the liquid-liquid transition. IV. The temperature dependence of shear viscosity”

A formal definition of T_LL as a function of M?ⁿ for polystyrene was prepared with literature T_LL values from torsional braid analysis (TBA), differential scanning calorimetry (DSC), and zero-shear melt viscosity η₀. Data from six authors using anionically prepared PS and blends thereof were involved. The resultant linear least-squares regression line, T_LL(°C) = 148.5 ? 11.487 × 10⁴M? [standard error in T_LL (calculated) 4.056 K, correlation coefficient R² = 0.9534] is considered valid from M?_n = 2000 to the entanglement molecular weight M_c = 35,000. The “best” T_LL values reported by Orbon and Plazek from double Arrhenius plots are well below this line for M?_v = 47,000, 16,400, 3400, and above it for M?_v = 1100. These best T_LL values are artifacts arising from no or insufficient data points above or below T_LL and/or too many data points near T_g. The associated high enthalpies of activation which they report confirm this diagnosis. The fact that these artificial T_LL values tend to disappear when checked by the three-parameter Vogel equation, logη = logA + B exp[(T ? T_∞)^?1], has no relevance to the controversy concerning the existence and meaning of T_LL. The claim by Orbon and Plazek that T_LL values obtained by TBA, DSC, and melt viscosity are all artifacts of the individual methods by which they were obtained is inconsistent with the excellent master plot which they generate. Alternative plotting devices which reveal T_LL > T_g from η₀ vs. T^?1 data, as developed by van Krevelen and Hoftyzer and by Utracki and Simha (not previously considered by either party), are reviewed. A statistical examination of the nature of the Vogel–Fulcher–Tammann–Hesse equation, based on synthetic data, is presented. Evidence for T_LL in atactic polypropylene is offered based on published data by Plazek and Plazek. T_LL is considered to possess both relaxational and quasiequilibrium attributes, just as T_g does.     

Tensile flow and stress–strain behavior over a wide temperature range for poly(butyl methacrylate) with a broad molecular weight distribution

The poly(butyl methacrylate) studied is a polymer with a normal molecular weight distribution and a relatively low molecular weight close to M_c, the critical molecular weight from the viscosity–molecular weight relation. The polymer was subjected to uniaxial extension and shear over a temperature range which included T_g. It was found that in the region of T_g an increase in applied stress is accompanied by a decrease both in the temperature shift factor a_T and in the activation energy for relaxation and rupture of polymer melts. Close attention is given to the long-term durability of the polymer. As is expected in the temperature range below T_g, its dependence on the stress is exponential, whereas at temperatures above T_g a power law fits the data. In the latter case a log-log plot of the long-term durability versus stress can be represented by two intersecting straight lines which can be replotted as a generalized straight line if the long-term durability values are normalized by the viscosity.     

Solvent crazing of “dry” polystyrene and “dry” crazing of plasticized polystyrene

The critical strain ε_c for crazing of polystyrene in each of a variety of organic liquids has been measured along with the degree of swelling of the polymer by the liquid and the attendant reduction in the glass transition temperature T_g of the polymer. The critical strain for the crazing in air and the T_g of each of a set of specimens molded from mixtures of o-dichlorobenzene and polystyrene have also been determined. Correlations of ε_c with T_g in the two cases are identical within experimental error for the first 40°C of T_g reduction; these results imply (1) that organic liquids do not exercise a significant surface energy role in solvent crazing and (2) that their only roles are associated with flow processes. Correlation of solvent crazing ε_c with solubility parameter of the crazing fluid is very poor for several reasons that are discussed.     

Viscoelastic properties of linear polymers in the high-elastic state

The relation between molecular weight, chain rigidity and the length of the high-elasticity plateau is determined from frequency and temperature dependences of the storage modulus for polybutadienes and polystyrenes with M _w/M _n ? 1.1. Use is made of the concept of equivalence of high-elastic states characterized by equal lengths of high-elastic plateaus for linear polymers. The high-elastic states of the linear polymers studied are equivalent if the polymer chains have equal numbers of dynamic segments and if the reference temperature is T₀ = 1.22T_g, where T_g is the glass transition temperature. The viscoelastic properties of the polymers in the high-elastic state are determined unambiguously by T_g and the molecular weight of the dynamic segment. The quantitative relation between thermomechanical characteristics obtained by measuring deformation versus temperature under a constant time regime and dependence of storage modulus versus frequency under isothermal conditions is discussed.     

“Experimentation and modeling for the apparent elongation viscosity of polymer melts with the White–Metzner model”

The measurement of the apparent elongation viscosity (η_e) of several polyolefin melts was conducted in this study by using the isothermal fiber‐spinning method. The White–Metzner (W–M) model was used to analyze the spinning flow of the polymer melts and, thus, the elongation viscosity was predicted at elongation strain rates ranging from 0 to approximately 5 s^?1. The values of the model parameters required in the W–M model were obtained by curve fitting the experimental data obtained from the shear measurements. The elongation viscosity predicted using the W–M model was in good agreement with the experimental results of fiber spinning. In addition, η_e could also be estimated directly from the measured shear viscosity (η_S) with a formulation using the W–M model; the subsequently obtained elongation viscosity and Trouton ratio (T_R) were reasonable within a wide range of strain rates. Based on the experimental and theoretical results, the polyolefin with a high molecular weight was observed to have high elongation viscosity, and the polymer with a broad molecular weight distribution also possessed high η_e. The T_R value of the commercial polypropylene (PP‐1040) began to increase from 3 at a deformation rate of 0.1 s^?1 and grew up asymptotically to 10, whereas the T_R of high‐density polyethylene (HDPE‐606) remained nearly at 3 within the entire range of strain rates. Copyright © 2014 John Wiley & Sons, Ltd.     

Tearing energy study of “oriented and relaxed” polystyrene in the glassy state

To study the effect of processing history, molecular weight/molecular weight distribution, and thermal history on solid state properties (in particular fracture properties and orientation), carefully characterized polydisperse and monodisperse polystyrene samples were drawn above T_g and the orientation frozen in. The objective was to simulate the incidental orientation of polymer chains after processing, molding, and so forth (e.g., injection or compression, blow molding) as a result of melt flow. A series of polystyrene samples was produced by hot drawing at temperatures of 113 and 148 °C, followed by a relaxation period, and then a quench to below T_g. The level of segmental orientation imposed in the samples was determined by birefringence measurements. The tear energy of the sheets was measured at 20 °C by tearing along the draw direction, ultimately giving a value for the fracture energy, G_3C. Samples of high draw ratio and low segmental orientation were unexpectedly found to have highly anisotropic fracture properties despite the low level of optical anisotropy. The fracture properties also depended significantly on whether the samples were drawn with or without lateral constraint. The results are compared with measurements of isotropic samples and the findings of a previous investigation utilizing SANS and birefringence. Modeling the drawing conditions at the chain level using a recent nonlinear tube theory explains how birefringence alone is an inadequate measure of molecular orientation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 377–394, 2007     

Influence of monofunctional reactants on the physical properties of dimer acid‐based polyamides

Dimer acid‐based polyamides were synthesized by condensation polymerization in the absence and presence of monofunctional reactants. Acetic acid, oleic acid and propyl amine were used as monofunctional reactants. The influences of the equivalent percentage (E%) and type of monofunctional reactant on the physical properties of dimer acid‐based polyamides such as glass transition temperature (T_g), melting point (T_m), heat of fusion (ΔH), degree of polymerization (DP), number average molecular weight (M_n), and kinematic viscosity were investigated. The molecular weight and viscosity of dimer acid‐based polyamides decreased with the increase in equivalent percentage of monofunctional reactant. Differential scanning calorimetry (DSC) studies showed that acetic acid and propyl amine had higher effect on the thermal properties of polyamides than that of oleic acid. In the case of polyamides prepared in the presence of acetic acid, the values of T_g, T_m, and ΔH of the polyamides increased remarkably with the increase in acetic acid content. On the contrary, propyl amine had a decreasing effect on the values of T_g, T_m, and ΔH of the polyamides. Incorporation of oleic acid into the polymer structure had no significant effect on the values of T_g and T_m of the dimer acid‐based polyamides. Copyright © 2006 John Wiley & Sons, Ltd.     

Nuclear relaxation in atactic polystyrenes: T1 and T1ρ measurements

Measurements have been made on a series of linear atactic polystyrenes whose molecular weights range from 900 to 1.8 × 10⁶, where M _w/M _n ? 1.2. Spin lattice relaxation times have been measured in the laboratory frame (T₁) and in the rotating frame (T_1ρ) in the temperature range 90–500°K. Two major relaxation minima were observed in both sets of measurements. The high temperature process corresponds to the glass transition (α process), the position of the minimum depending on the chain length. The low temperature process appears to originate from the n-butyl endgroups in the polymer, its position being independent of chain length while its intensity is inversely proportional to molecular weight. No other minima were observed, in contrast to some other observations made by broadline and pulsed NMR techniques. Relaxation was exponential in all cases except in the region of the high temperature T_1ρ minimum and above. This nonexponential behavior is possibly connected with the transition at T > T_g observed by a number of other techniques and which is thought to correspond to a transition between two types of liquid state. A correlation frequency diagram has been drawn for all the processes observed in polystyrene by other techniques, (α, β, αβ, γ, and δ) which shows that the T₁ and T_1ρ minimum positions correlate well with the α process and that there is a possible contribution to the relaxation due to the γ process on the low temperature side of the α process. At these measurement frequencies the α and β processes are merged into an αβ process. There is no evidence for a contribution from the mechanical δ process. The effect of the endgroups is observed to very high molecular weights (4.98 × 10⁵), and it seems that a three-dimensional diffusion model would be more adequate than the one-dimensional model used to interpret similar behavior of paraffins and polyethylenes. Measurements of T₁ in the low-temperature region would constitute a method for a rough measurement of the molecular weight of these polymers.     

α-amidoalkylation of polystyrene

Crystal polystyrene was alkylated with N-methylolacetamide (CH₃CONHCH₂OH), boron trifluoride being used as the catalyst. A linear relationship between degree of N-methyleneacetamide substitution and the glass transition temperature T_g of the polystyrene was observed. The T_g values ranged from 104°C for 0% amidization to 125°C for 20% amidization. The critical strain ε_c of these materials was measured at room temperature in air, hexane, and oil (50–50, a cottonsed oil–oleic acid) and an increase in the ε_c above which crazing occurs was observed as the degree of alkylation increased. Thermogravimetric analysis (TGA) of the amidized polystyrenes in air at 250°C showed these materials to become more stable as the amount of N-methylene substitution increased. Tensile data show that the amidized polystyrene, although stronger than the unsubstituted material, exhibits the same elongation at break and tensile modulus.     

Precise synthesis of a series of poly(4‐n‐alkylstyrene)s and their glass transition temperatures

Poly(4‐n‐alkylstyrene)s with six kinds of n‐alkyl groups such as methyl, ethyl, propyl, butyl, hexyl, and octyl groups covering wide molecular weight range from around 5 k to over 100 k were precisely synthesized by living anionic polymerizations. It was confirmed that all the polymers obtained have narrow molecular weight distribution, that is, M_w/M_n is all less than 1.1, by SEC. T_gs of all the polymers were estimated by DSC measurements and it turned out to be clear that their molecular weight dependence was well described by the Fox–Flory equations. Furthermore, it is evident that T_g monotonically decreases as a number of carbon atoms of n‐alkyl group is increased, though T_g values are all 20 K or more higher than those reported previously for the same polymer series. This is because backbone mobility increases by introducing longer n‐alkyl side groups with high mobility, while T_g difference in between this work and the previous one may due to the experimental conditions and also to the molecular weight range adopted. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 757–763     

Temperature Dependence of the Viscosity and Conductivity of Mildly Functionalized and Non‐Functionalized [Tf2N]− Ionic Liquids

A series of bis(trifluoromethylsulfonyl)imide ionic liquids (ILs) with classical as well as mildly functionalized cations was prepared and their viscosities and conductivities were determined as a function of the temperature. Both were analyzed with respect to Arrhenius, Litovitz and Vogel–Fulcher–Tammann (VFT) behaviors, as well as in the context of their molecular volume (V_m). Their viscosity and conductivity are highly correlated with V_m/T or related expressions (R²≥0.94). With the knowledge of V_m of new cations, these correlations allow the temperature‐dependent prediction of the viscosity and conductivity of hitherto unknown, non‐ or mildly functionalized ILs with low error bars (0.05 and 0.04 log units, respectively). The influence of the cation structure and mild functionalization on the physical properties was studied with systematically altered cations, in which V_m remained similar. The T_o parameter obtained from the VFT fits was compared to the experimental glass temperature (T_g) and the T_g/T_o ratio for each IL was calculated using both experimental values and Angell’s relationship. With Walden plots we investigated the IL ionicity and interpreted it in relation to the cation effects on the physical IL properties. We checked the validity of these V_m/T relations by also including the recently published variable temperature viscosity and conductivity data of the [Al(OR^F)₄]^? ILs with R^F=C(H)(CF₃)₂ (error bars for the prediction: 0.09 and 0.10 log units, respectively).     

Interaction of inorganic salts with polar polymers. I. Physical properties of phenoxy–calcium thiocyanate mixtures

Calcium thiocyanate is appreciably soluble in “Phenoxy” polymer. Solutions of this salt have significantly different physical properties compared to the pure polymer. The glass-transition temperature T_g is increased, and the kinetics of the glass transition are affected. The melt viscosity and its temperature dependence are increased. The viscosity changes are predicted from the changes in T_g and thermal expansion coefficients, in contrast to ionomers, in which clustering or domain formation cause viscosity to increase. Mechanical properties of the glassy polymers are also affected by the presence of dissolved salt. The most striking effect is an increased resistance to stress cracking by polar organic liquids. This may be related to the T_g increase, or to changes in solubility parameter, as indicated by insolubility of the salt solutions in solvents for the pure polymer. Increased water sorption and electrical conductivity are also results of salt incorporation.     

Dynamic birefringence of oligostyrene: A symptom of “polymeric” mode

The dynamic birefringence and the dynamic viscoelasticity of an oligostyrene, A1000, whose molecular weight (M_w = 1050) was comparable to the Kuhn segment size, M_K, were examined near and above the glass‐transition temperature in order to characterize polymeric features of very short chains with M ∼ M_K. The complex shear modulus, G*(ω), was similar to that for supercooled liquids: No polymeric modes such as the Rouse mode were detected at low frequencies of viscoelastic spectrum. On the other hand, the strain‐optical coefficient was found to be negative in the terminal flow zone and positive in the glassy zone. Because the negative birefringence of polystyrene is originated by polymeric modes associated with chain orientation, the present results indicate that polymeric modes exist and become dominant for birefringence in the terminal flow. The data were analyzed using a modified stress‐optical rule: The modulus and the strain‐optical ratio were separated into polymeric (rubbery) and glassy components. The total modulus, G*(ω), was mostly due to the glassy component, G_G*(ω), resulting in the positive birefringence. G_G*(ω) for A1000 agreed with that for high M polystyrenes when compared at a comparable reduced frequency scale. The polymeric component, G_R*(ω), giving rise to the negative birefringence was lower than G_G*(ω) over the whole frequency range but its contribution to the birefringence exceeded that of the glassy component at low frequencies because of the larger optical anisotropy and longer characteristic relaxation time of the former. The limiting modulus of G_R* at high frequencies was about 3 times lower than that for high M polystyrenes, indicating that the main‐chain orientation of the oligostyrene on instantaneous deformation was reduced compared with that of high M polystyrenes. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 954–964, 2000     

Rebuttal to “comments on ‘some evidence against the existence of the liquid–liquid transition. III. The evaluation of the TLL event by differential scanning calorimetry’ ”

It is proposed here that readily observable viscous deformation is the common underlying phenomenon which is reflected in several kinds of evidence advanced for the existence of a liquid–liquid transition T_LL . These include flow temperature T_f measurements, microscope hotstage coalescence, and differential scanning calorimetry (DSC) measurements. A DSC peak observed at T_g in high-molecular-weight bulk-polymerized poly(methyl methacrylate) is discussed in terms of the presence of conformations of low entropy.     

Polar,functionalized diene‐based material. III. Free‐radical polymerization of 2‐[(N,N‐dialkylamino)methyl]‐1,3‐butadienes

The bulk free‐radical polymerization of 2‐[(N,N‐dialkylamino)methyl]‐1,3‐butadiene with methyl, ethyl, and n‐propyl substituents was studied. The monomers were synthesized via substitution reactions of 2‐bromomethyl‐1,3‐butadiene with the corresponding dialkylamines. For each monomer the effects of the polymerization initiator, initiator concentration, and reaction temperature on the final polymer structure, molecular weight, and glass‐transition temperature (T_g) were examined. Using 2,2′‐azobisisobutyronitrile as the initiator at 75 °C, the resulting polymers displayed a majority of 1,4 microstructures. As the temperature was increased to 100 and 125 °C using t‐butylperacetate and t‐butylhydroperoxide, the percentage of the 3,4 microstructure increased. Differential scanning calorimetry indicated that all of the T_g values were lower than room temperature. The T_g values were higher when the majority of the polymer structure was 1,4 and decreased as the percentage of the 3,4 microstructure increased. The Diels–Alder side products found in the polymer samples were characterized using NMR and gas chromatography‐mass spectrometry methods. The polymerization temperature and initiator concentration were identified as the key factors that influenced the Diels–Alder dimer yield. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4070–4080, 2000     

Molten polystyrene structures above the glass transition,T > Tg

The old controversial idea of structures in molten amorphous polymers is being accepted with theoretical and experimental evidence. Wool's twinkling fractal theory of the glass transition and recent atomic force micrographs are convincing proof of the dynamic, solid aggregate presence below and above T_g. This article offers detailed analysis of the experimental data from high‐pressure dilatometry, as well as from the oscillatory shear tests in the glassy and the molten state of polystyrenes. The results indicate the presence of a transient structure at T > T_g; transient as it depends on the structure of the vitreous polymer and the rate of heating it across T_g. Thus, molten polymer is not always at the thermodynamic equilibrium. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1369–1380, 2011     

Glass Transition Temperatures of Poly[(methyl methacrylate)‐co‐(butyl acrylate)]s Synthesized by Atom‐Transfer Radical Polymerization

Glass transition temperatures T_g of methyl methacrylate/butyl acrylate copolymers obtained by means of atom‐transfer radical polymerization are measured using differential scanning calorimetry. Due the nature of this polymerization method an increase in molecular weight is produced as the reaction progresses, which gives rise to an increase in T_g. Simultaneously, a composition gradient with the enrichment of butyl acrylate causes a decrease in T_g. These opposite effects almost compensate each other and, therefore, no influence on the molecular weight at M̄_n < 10000 is found. This fact allows the application of the Johnston's equation and the Mayo‐Lewis terminal model to describe and predict the variation in T_g with copolymer conversion for the copolymers and under the experimental conditions investigated.     

Influence of molecular architecture on fast and segmental dynamics and the glass transition in polybutadiene

Changes in the fast dynamics of polybutadiene (PB) with molecular weight and molecular architecture have been investigated by light and neutron scattering spectroscopy. Differences observed in the fast dynamics of various molecules correlate with differences seen in the value of the glass‐transition temperature (T_g). The segmental and fast dynamics as well as the value of T_g are dependent on the total molecular weight of the molecule but independent of its architecture. In other words, the dynamics of PB depend on the number of segments in the molecule but do not show a significant dependence on how the segments are connected (molecular topology), even for arm molecular weights commensurate with the entanglement molecular weight. Literature data for the T_g's of highly branched, phenolic‐terminated dendritic poly(benzyl ethers) of various core structures exhibit the same trend. There is no explanation for why the segmental motion appears to be sensitive to the total molecular weight of the molecule but is independent of its architecture. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2431–2439, 2002     

Glass‐Transition Temperature as a Function of Conversion in Hyperbranched Polymers Obtained by Self‐Condensing Vinyl Polymerization

Chain‐end free volume theory is extended for studying the glass‐transition temperature (T_g) as a function of conversion in hyperbranched polymers. T_g is found to have a non‐linear inverse relationship to the molecular weight for polymers obtained by self‐condensing vinyl polymerization (SCVP). During the monomer conversion process, T_g decreases with the increase in molecular weight (P) in the low conversion range, then levels off in the high conversion range.