Specific volume of polysulfone as a function of temperature and pressure

The pressure–volume–temperature (PVT) properties of a commercial polysulfone derived from bisphenol A and 4,4′-dichlorodiphenylsulfone are studied experimentally and theoretically in the temperature range 30–370°C and for pressures to 2000 kg/cm². PVT surfaces are determined for an annealed glass, formed under zero pressure, and for the melt. Two glass-transition lines must be distinguished: T(P) which is the intersection of the glass and melt PVT surfaces, and T_g(P), which is obtained by pressurizing the melt isothermally. The application of Ehrenfest-type equations to these transitions are discussed. The Prigogine–Defay ratio r = Δ_kΔC_p/TV(Δα)² at P = 0 is found to be equal to 0.95 (±20%), using ΔC_p data determined on identical samples. The melt data is compared with the Simha–Somcynski hole theory, using the reducing parameters V^* = 0.788 cm³/g, T^* = 12,560°K, P^* = 10,875 bar. The hole fraction appearing in the theory is found to be constant along T(P), but the glass PVT relationship cannot be reproduced by using the Simha–Somcynsky theory together with the assumption that the hole fraction remains constant in the glass. At P = 0 the hole fraction must be allowed to decrease with decreasing temperature, but at a slower rate than in the melt.     

Synthesis,characterization, and properties of linear poly(ether sulfone)s with dendritic terminal groups

Hybrid linear‐dendritic ABA polymers, where A and B are dendritic and linear polymers, respectively, were synthesized in a single step via step‐growth polymerization of 4,4′‐difluorodiphenylsulfone and bisphenol A using arylether ketone dendrons of first and second generations (G1‐OH and G2‐OH) as monofunctional end‐cappers. These G1 and G2‐terminated poly(ether sulfone)s (G1‐PESs and G2‐PESs) were characterized by ¹H NMR, SEC, DSC, TGA, melt rheology, and tensile tests. The comparison of the glass transition temperatures (T_gs) of these polymers with those of t‐butylphenoxy‐terminated polysulfones reveal that the G1‐ and G2‐PESs have lower T_gs at all molecular weights investigated. However, a plot of T_g versus 1/M_n shows that the difference between the three series becomes negligible at infinite molecular weight and agrees to the chain end free volume theory. The melt viscosities of G1‐PES and G2‐PES with high molecular weights do not show a Newtonian region and, in the high frequency region, their viscosities are lower than that of the control while the stress–strain properties are comparable to those of the control, suggesting that it is possible to reduce the high shear melt viscosity of a PES without affecting the stress–strain properties by introducing bulky dendritic terminal groups. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 958–969, 2008     

The glass transition in polymer melts

This paper presents some results of a Monte Carlo simulation for the glass transition in two- and three-dimensional polymer melts. The melt was simulated by the bond-fluctuation model on a d-dimensional cubic lattice which was combined with a two-level hamiltonian favouring long bonds in order to generate a competition between the energetic and topological constraints in the system. This competition prevents crystallization and makes the melt freeze in an amorphous structure as soon as the internal relaxation times match the observation time of the simulation set by the cooling rate. The freezing point of the melt, i.e the glass transition temperature T_g, thus depends upon the cooling rate and additionally upon the chain length of the polymers. The dependence of the glass transition temperature on the cooling rate was closely analysed in three and that on the chain length in both two and three dimensions, resulting in a non-linear relationship between T_g and the logarithm of the cooling rate and a linear relationship between T_g and the inverse chain length, respectively. In addition to this behaviour of the melt during the cooling process an example for the relaxational properties of the three-dimensional model is provided by a quantitative analysis of the incoherent intermediate scattering function in the framework of the idealized mode coupling theory.     

The equation of state of solid and molten poly (butylene terephthalate) to 300°C and 200 MPa

The volumetric behavior of poly (butylene terephthalate) (PBT) was studied from 30 to 303°C and pressures from atmospheric to 200 MPa. The pressure-volume-tempreature (PVT) data show behavior typical of other semicrystalline materials. The empirical Tait equation was used to fit the measured volumes in the solid and melt regions. The maximum deviations between the Tait fits and the measured volumes were 0.001 and 0.002 cm³/g in the semicrystalline and melt regions, respectively. The theoretical equation of Simha-Somcynsky was used to represent the PVT behavior of this material in the equilibrium melt. Fitting the theory to the data involves a determination of the reducing parameters of the theory. We find P* = 1139 MPa, V* = 0.7838 cm³/g, and T* = 11133 K. From these parameters we calculate that the chemical repeat unit of PBT has 6.37 external degrees of freedom, in comparison with 4.97 degrees of freedom to the closely related poly(ethylene terephthalate), with two less (? CH₂? ) units in the backbone. The difference of 1.4 degrees of freedom may be compared with the 0.88 degrees of freedom of the polyethylene (? C₂H₄? ) repeat unit itself.     

Miscible blends containing a crystallizable component: poly(vinyl alcohol)/poly(ethyleneimine)

Blends of poly(vinyl alcohol) (PVAI) with poly(ethyleneimine) (PEI) were prepared by casting from a common solvent. All blends show a single, composition dependent glass transition temperature (T_g), indicating that the blends are miscible in the amorphous state and in the melt. The overall crystallization rate of PVAI in the blend decreases with increasing PEI content. The crystallinity index of PVAI in the blend does not decrease greatly with PEI content up to a composition of 70/30 PVAI/PEI, since the T_g of the crystallizable component PVAI is larger than that of the non-crystallizable component PEI. The T_g of the system PVAI/PEI decreases with increasing PEI content. The interaction parameter B of the two polymers in the melt was found to be −24 J/cm³.     

高聚物玻璃化转变温度和分子参数的关系 Ⅰ.高聚物链柔性与Tg的关系

 本文采用晶格模型,以动力学链段长度作为统计单元大小,推导了高聚物玻璃化温度T_8和链静态刚性因子σ²(T₈),链动态刚性因子β(T₈)以及聚合度DP等分子参数之间的关系。具体讨论了链柔性对T₈的影响。理论预测和几十种聚合物的实验数据能较好吻合,分析结果表明T₈值基本上取决于高聚物链σ(T₈)大小。     

Probe rotation near and below the glass transition temperature: Relationship to viscoelasticity and physical aging

Reorientation times ť_c for two probes in several amorphous polymers near the glass transition temperature T_g are reported. T_g for these polymers ranges from 205 to 459 K. Probe reorientation was measured in the time window from 10⁻² to 10⁴ s with a recently developed photobleaching method. ť_c for a given probe at the T_gs of the different polymers varies more than three decades. Viscoelastic relaxation times characteristic of the Rouse modes of the matrix polymers are closely related to probe rotation times and thus also not constant at T_g. The characteristic length scale of motions responsible for the glass transition varies significantly for the three polymers studied. Preliminary physical aging results indicate that probe reorientation in polystyrene ages slightly faster than the volume.     

Challenge and Solution of Characterizing Glass Transition Temperature for Conjugated Polymers by Differential Scanning Calorimetry

Thermomechanical properties of polymers highly depend on their glass transition temperature (T _g). Differential scanning calorimetry (DSC) is commonly used to measure T _g of polymers. However, many conjugated polymers (CPs), especially donor–acceptor CPs (D–A CPs), do not show a clear glass transition when measured by conventional DSC using simple heat and cool scan. In this work, we discuss the origin of the difficulty for measuring T _g in such type of polymers. The changes in specific heat capacity (Δc _p) at T _g were accurately probed for a series of CPs by DSC. The results showed a significant decrease in Δc _p from flexible polymer (0.28 J g^?1 K^?1 for polystyrene) to rigid CPs (10^?3 J g^?1 K^?1 for a naphthalene diimide‐based D–A CP). When a conjugation breaker unit (flexible unit) is added to the D–A CPs, we observed restoration of the Δc _p at T _g by a factor of 10, confirming that backbone rigidity reduces the Δc _p. Additionally, an increase in the crystalline fraction of the CPs further reduces Δc _p. We conclude that the difficulties of determining T _g for CPs using DSC are mainly due to rigid backbone and semicrystalline nature. We also demonstrate that physical aging can be used on DSC to help locate and confirm the glass transition for D‐A CPs with weak transition signals. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1635–1644     

Positron annihilation lifetime studies of changes in free volume on cross-linking cis-polyisoprene,high-vinyl polybutadiene,and their miscible blends

Measurements of average free volume hole sizes, 〈v_f〉, and the fractional free volumes, f_ps, in vulcanized cis-polyisoprene (CPI), high-vinyl polybutadiene (HVBD), and their 50 : 50 blend were made via determination of orthopositronium annihilation lifetimes. The results are compared to corresponding data on the uncured materials. On crosslinking, 〈v_f〉 decreases in the rubbery state but remains essentially unchanged in the glass. This is consistent with the expectation that the crosslinks greatly restrict the thermal expansion of the chains above the glass transition temperature (T_g) but have less influence on the packing density in the glass. Scaling relationships between 〈v_f〉, f_ps, the thermal expansion coefficient α_f = df_ps/dt, and T_g are examined. We find that 〈v_f〉_g, the hole volume at T_g, and f_ps,g, the fractional free volume at T_g, each increase significantly with increasing T_g. This behavior is consistent with previous observations reported in the literature and has been interpreted as a manifestation of the kinetic character of the glass transition. High-T_g polymers need a larger free volume to pass into the liquid state. The change in expansion coefficient on passing from the glass to the liquid, Δα_f = α_f,l − α_f,g, increases slowly with T_g, as predicted by free volume theory. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2754–2770, 1999     

Thermoanalytical evaluation of readily available reference polymers

A commercial set of polymers has been characterized by TG-DTA, DSC, TMA, FTIR spectroscopy and X-ray diffraction analysis (XRD). Thermal and mechanical stability, as well as the polymer glass transition temperature,T _g, and melt temperature,T _m, have been documented. There is a good correlation between measuredT _g andT _m values and published data. The degree of polymer crystallinity for polyethylene has been verified by XRD. The credibility and stability of these reference polymers is based on a comparison of their thermal properties, over a wide range of temperatures from two versions of a reference set, published in 1979 (A) and 1994 (B). The thermal properties and crystallinity of these polymers have stood the test of time and are reliable, readily available and consistent.     

Thermophysical properties of azomethine ether main-chain liquid crystalline polymers at pressures to 200 MPa

This article reports on an experimental investigation of the equation of state and the transition behavior of main-chain thermotropic liquid crystalline polymers over a wide temperature range, and at pressures to 200 MPa. The materials studied were a series of azomethine ether polymers. A varying number n (= 4, 7, 8, 9, 10 and 11) of methylene spacer units in the backbone provided systematic variation of the structure. Experimental techniques used included high-pressure dilatometry (PVT measurements) to 200 MPa, high-pressure differential thermal analysis, also to 200 MPa, and conventional (atmospheric-pressure) differential scanning calorimetry (DSC). The equation of state of the materials can be well represented by the Tait equation in distinct regions, separated by a glass transition, T_g(P), a first-order transition to a nematic state, T_k-n(P), and a first-order transition to an isotropic melt state T_c(P). The atmospheric pressure values of T_k-n and T_c decreased with increasing number of spacer units and showed a clear odd-even effect. T_g and T_k-n both increased with pressure. The pressure dependence of T_c could not be observed due to the onset of degradation in the same temperature region. On isobaric cooling at 3°C/min, the crystallization from the nematic state occurred a few tens of degrees below T_k-n. This supercooling was independent of pressure for some materials, while for others it increased with increasing pressure. The values of the enthalpy and entropy associated with the first-order transition into the nematic state were lower than those of typical isotropic polymers at their melting transitions. The transition enthalpy did not have any systematic variation with increasing number of spacer units. Values of the transition enthalpy calculated from the Ciapeyron equation did not always agree with the values measured by DSC. This may be due to the two-phase nature of the low-temperature state. At the transition to the isotropic state, the transition enthalpy at P = 0 decreased with n and showed an odd-even effect. © 1994 John Wiley & Sons, Inc.     

Synthesis,characterization, and thermal and dielectric properties of three different methacrylate polymers with zwitterionic pendant groups

The synthesis, characterization, thermal, and dielectric properties of three different zwitterionic methacrylates of the sulfobetaine type are presented. Diethylamine-ethyl-, 2-(diethylaminoethoxy)-ethyl-, and 2-(2-diethylaminoethoxy) ethoxy-ethyl-methacrylates were made to react with butanosultone to prepare monomers with variable flexibility. The flexibility of the lateral chain of the polymethacrylates decreased the glass transition temperature (T_g down to 300 K) of the polymers. A linear relationship between T_g and the number of carbon atoms was shown for these materials. X-ray diffraction and DSC experiments showed the formation of new ordered phases in these polymers, which inhibited their dipole conductivity. On heating, these phases were destroyed and values of conductivity of 10⁻⁷–10⁻³ S cm⁻¹ were obtained in the studied range of temperature. Variation of conductivity with temperature was established according to the Arrhenius equation. Dielectric properties exhibited a small deviation of the Debye type behavior, and β parameters of the Cole–Cole equations were calculated for the synthesized polymers. © 1997 John Wiley & Sons, Inc.     

Positronium annihilation in amine-cured epoxy polymers

Positronium annihilation spectroscopy (PAS) has been used to study the microstructural properties of amine-cured epoxy polymers. We have determined the free-volume “hole” sizes in these polymers by comparing the observed ortho-positronium lifetimes with the known lifetime–free volume correlation for low-molecular-weight systems. The free volumes for four epoxies with different crosslink densities are found to vary significantly over the temperature range between ?78° and 250°C. The free-volume holes for these polymers are found to range from 0.025 to 0.220 nm³. Two important transition temperatures were found: one corresponds to the glass transition temperature T_g determined by differential scanning calorimetry (DSC), and the other occurs about 80–130°C below T_g. The sub-T_g transition temperature is interpreted tentatively as being where hole size reaches dimensions adequate for positronium trapping or else the onset temperature for local mode or side-chain motions. These two transition temperatures plus two additional onset temperatures are found to be correlated with crosslink densities calculated from stoichiometry.     

高聚物玻璃化转变温度和分子参数的关系 Ⅱ.分子量对玻璃化转变温度的影响

 根据前文提出的理论模型,本文推导出下述表征高聚物数均分子量(M_n)与玻璃化转变温度T₈关系的理论公式: T_g=T_g∞-K_g/M_n K_g=T_g∞·σ²(T_g)·M_u十几种高聚物的K_g理论计算位能较好地和实验值吻合。应用理论关系式具体计算了聚苯乙烯、聚氯乙烯、聚二甲基硅氧烷和聚α-甲基苯乙烯的T_g随分子量的变化,其结果是令人满意的。     

Synthesis and characterization of 4-cyanobiphenyl-4′-yloxy-functionalized poly(7-oxanorbornene-5,6-exo-dicarboximide)s via ring opening metathesis polymerization (ROMP)

N-[n-(4-cyanobiphenyl-4′-yloxy)alkyl]-7-oxanorbornene-5,6-exo-dicarboximide ( CBON ₂– CBON ₈) with increasing number of methylene groups in the alkyl part (n = 2–8) were synthesized by Mitsunobu condensation between the appropriate alcohols ( CBA ₂– CBA ₈) and 7-oxanorbornene-5,6-exo-dicarboximide ( ON ). The conditions for the ring opening metathesis polymerization of CBON _n giving acceptable molecular weights and molecular distributions were established. Characterization of the resulting polymers ( P ₂– P ₈) by ¹H- and ¹³C-NMR has shown a high trans content. Differential scanning calorimetry and optical microscopy analysis have shown that the alcohols CBA _n are thermotropic with some variations between the first and second heating-cooling cycles, the monomers CBON _n melt with no evidence of any mesomorphic state, the polymers P _n show only the glass transition, and the glass transition temperature (T_g) decreases with increases in the spacer length. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 2807–2821, 1998     

Synthesis and Characterization of Novel Poly(Arylene Ether)s from 4,4′‐Thiodiphenol

Four novel perfluoroalkylated poly(arylene ether)s have been synthesized successfully using four perfluoroalkyl‐activated bisfluoro monomers. These polymers are synthesized through nucleophilic displacement of the fluorine atoms on the benzene ring with 4,4′‐thiodiphenol and are named as 1a, 1b, 1c and 1d, respectively. The polymers obtained by displacement of the fluorine atoms exhibit weight‐average molar masses up to 3.9×10⁴ g · mol^?1 in Gel permeation chromatography. These poly(arylene ether)s showed very high thermal stability up to 548°C for 10% weight loss in TGA under nitrogen and high glass transition temperature (T_g) up to 178°C in DSC depending on the repeat unit structures. The glass transition temperatures taken as peak in tan δ in DMA measurements are in good agreement with the DSC T_g values. All the polymers synthesized are soluble in a wide range of organic solvent such as CHCl₃, CHCl₂, THF, NMP, DMF and toluene. Transparent thin films of these polymers cast from THF exhibited tensile strengths up to 72 MPa, modulus up to 1.69 GPa with low elongation at break depending on their exact repeating unit structures. Rheological properties showed ease of processability of these polymers with no change in melt viscosity with temperature.     

Glass Transition Temperature and Value of the Relaxation Time at Tg in Vitreous Polymers

Summary: Many works focused on glassy polymers determine values of glass transition temperature (T_g) and an overview of the literature shows that depending on the method used, values of T_g are found different for the same material. In this paper, a review of data collected on different materials are used and interpreted in term of molecular mobility characterized by relaxation time functions. By using three independent experimental procedures (dielectric, thermally depolarized current and calorimetric), we show that the value of the glass transition and the value of the relaxation time at T_g can be correctly determined. It is also shown that the assumption: τ _(Tg) = 100 s is constant, is not correct. The protocol proposed also allows the determination of the value of the fragility index “m” of the glass forming liquid with a great accuracy.     

Study of glass transition kinetics of selenium matrix alloyed with up to 10% indium

Glassy selenium matrix alloyed with up to 10% indium, namely Se_0.95In_0.05 and Se_0.9In_0.1, was prepared by the melt quenching technique. Differential thermal analysis (DTA) has been used to study the glass transition kinetics of the two binary Se–In alloys in comparison with that of pure Se. DTA scans were recorded at different constant heating rates (β = 1:20 °/min). The glass transition temperature (T _g) is found to be shifting to a higher value with increasing of both β and In-content. Such a configurationally response is related to the observed increase of the stability parameters accompanied with the introduction of In into the Se matrix. The activation energy of glass transition (E _g) has been determined using two different non-isothermal models (Moynihan and Kissinger) where a good coincidence is obtained. The compositional dependence (0:10% In) of all considered parameters is discussed in terms of the introduced structural matrix.     

Free volume microstructure of amorphous polymers at glass transition temperatures from positron annihilation spectroscopy data

The analysis of annihilation characteristics of ortho-positronium at conventional calorimetric glass transition temperatures for a series of amorphous polymers reveals empirical correlations of average lifetime of o-Ps , and of its product with a relative intensityI _3g with appropriateT _g ^DSC values. These trends in terms of free volume mean that both the average size of free volume hole entityv _hg and the fractional free volume grow with increasingT _g ^DSC . The results are discussed considering the chemical microstructure as well as possible mechanisms acting in glass transition. A relation is indicated between geometric and flexibility characteristics of chains and thev _hg andf _g parameters of free volume microstructure on the one side and potential motional processes responsible for solidification of the amorphous system on the other side.