Temperature and pressure dependence of the free volume in the perfluorinated polymer glass CYTOP: A positron lifetime and pressure‐volume‐temperature study

The microstructure of the free volume was studied for an amorphous perfluorinated polymer (T_g = 378 K). To this aim we employed pressure–volume–temperature experiments (PVT) and positron annihilation lifetime spectroscopy (PALS). Using the Simha‐Somcynsky equation of state the hole free volume fraction h and the specific free and occupied volumes, V_f = hV and V_occ = (1 ? h)V, were determined. Their expansivities and compressibilities were calculated from fits of the Tait equation to the volume data. It was found that in the glass V_occ has a particular high compressibility, while the compressibility of V_f is rather low, although h (300 K) = 0.108 is large. In the rubbery state the free volume dominates the total compressibility. From the PALS spectra the hole size distribution, its mean, 〈v_h〉, and mean dispersion, σ_h, were calculated. From a comparison of 〈v_h〉 with V_f a constant hole density of N_h′ = 0.25 × 10²¹ g^?1 was estimated. The volume of the smallest representative freely fluctuating subsystem, 〈V_SV〉 ∝ 1/σ_h², is unusually small. This was explained by an inherent topologic disorder of this polymer. 〈v_h〉 and σ_h show an exponential‐like decrease with increasing pressure P at 298 K. The hole density, calculated from N_h′ = V_f/〈v_h〉, seems to show an increase with P which is unexpected. This was explained by the compression of holes in the glass in two, rather than three, dimensions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2519–2534, 2007     

Equations of state for polyamide‐6 and its nanocomposites. II. Effects of clay

The pressure‐volume‐temperature (PVT) dependencies of polyamide‐6 and its nanocomposites (polymeric nanocomposites) were measured at temperatures T = 300–600 K and pressures P = 0.1–190 MPa, thus spanning the range of molten and “solid” phases. The Simha‐Somcynsky (S‐S) cell‐hole equation of state (EOS) was used for describing the molten region. At T_g(P) ≤ T ≤ T_m(P), the “solid” phase is a mixture of the liquid polyamide‐6 with dispersion of crystals. Accordingly, the PVT behavior in this region was described as a combination of the S‐S EOS for the liquid phase and the Midha‐Nanda‐Simha‐Jain (MNSJ) EOS for the crystalline one. These two theories based on different models yielded two sets of the characteristic reducing parameters, P^*, T^*, V^* and the segmental molecular weight, M_s. Incorporation of 2 and 5 wt % clay increased P^* and reduced T^* and V^*, but the effects were small. Fitting the combination of S‐S and MNSJ EOS' to isobaric “solid” phase data yielded the total crystallinity, X_cryst, and the correcting excess specific volume, ΔV_m,c. Both parameters were sensitive to pressure, P, and the clay content, w—the former increased with P and w, whereas the latter decreased. The raw PVT data were numerically differentiated to obtain the thermal expansion and compressibility coefficients, α and κ, respectively. At T < T_m, addition of clay reduced their relative magnitude, whereas at T > T_m, the opposite effect was observed, most likely owing to the excess of intercalant in the polymeric nanocomposites samples. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 966–980, 2009     

Free volume,glass transition,and degree of branching in metallocene‐based propylene/α‐olefin copolymers: Positron lifetime,density, and differential scanning calorimetric studies

Positron annihilation lifetime spectroscopy (PALS), density, and differential scanning calorimetric (DSC) measurements were used to study systematically the variation of the glass‐transition temperature (T_g) and the size v and number density N_h of local free volumes in n‐alkyl‐branched polypropylenes. The samples were metallocene‐catalyzed propylene copolymers with different α‐olefins (from C₄ to C₁₆) and a different α‐olefin content (between 0 and 20 mol %). From the total specific volume and crystallinity the specific volume of the amorphous phase V_a was estimated and used to calculate the fractional free (hole) volume h and value of N_h. The variations of T_g, v, V_a, h, and N_h were related to the degree (number and length) of branching. T_g decreases and v increases linearly with the number and length of n‐alkyl branches. This behavior was attributed to an increased segmental mobility caused by branching. Both values, T_g and v, follow linear master curves as a function of the degree of branching (DB) if this is defined as the number of all side‐chain carbons with respect to a total of 1000 (main‐chain and side‐chain) carbons. Only propylene/1‐butene copolymers deviated from these relations. A linear relation between v and T_g was also found. The number density of holes was estimated to be N_h = 0.49(±0.07) nm^?3 and N_h′ = 0.58(±0.11) × 10²¹ g^?1, respectively. It shows a slight variation with the DB, which is also seen in the behavior of the specific volume V_a. This variation was explained by the appearance of sterical hindrances resulting from short‐chain branches that may prevent an efficient packing of the chains. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 434–453, 2002; DOI 10.1002/polb.10108     

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.     

Experimental free volume aspects of the polymer rheology as obtained by positron annihilation lifetime spectroscopy

The ortho‐positronium (o‐Ps) annihilation parameters, i.e. the mean o‐Ps lifetime, τ₃, and the o‐Ps relative intensity, I₃, in cis‐1,4‐polybutadiene (cis‐1,4‐PBD) and polyisobutylene (PIB) over a wide temperature range including the glass‐liquid transition have been measured by means of positron annihilation lifetime Spectroscopy (PALS). From them the free volume microstructural characteristics, i.e. the mean free volume hole size, V_h, and the free volume hole fraction, f_h, have been determined via a semiempirical quantum‐mechanical model of o‐Ps in a spherical hole or a phenomenological model of volumetric and free volume hole properties, respectively. Consequently, the literature rheological data for both the above‐mentioned polymers have been related to the free volume hole fractions via the WLF‐Doolittle type equation. It has been found that i) in the case of PIB this equation holds over 130K above the glass transition temperature T_g and ii) in the case of cis‐PBD the WLF‐Doolitle equation is valid in the temperature range over 60K above 1.3T_g, but below 1.3T_g down to T_g the modified WLF‐Doolittle‐Macedo‐Litovitz equation with the additional activation‐energy term describes the shift factor data better.     

Study of free volume in high-vinyl polybutadiene/cis-polyisoprene blends using positron annihilation spectroscopy

High-Vinyl Polybutadiene (HVBD)/cis-Polyisoprene (CPI) blends were characterized by Differential Scanning Calorimetry (DSC) and Positron Annihilation Lifetime Spectroscopy (PALS). A single DSC glass transition temperature T_g is observed, whose composition dependence strongly deviates from additivity, and shows an apparent cusp when the weight fraction of HVBD ≈ 0.75. The free-volume hole size, V_h, and the scaled fractional free volume, h_ps/C, = I₃V_h were determined by PALS from the orthopositronium (o-Ps) intensities, I₃, and lifetimes, τ₃, over a temperature range encompassing T_g and the temperature at which “positronium bubble” formation occurs. In the glass, V_h and h_ps/C are smaller for CPI than for HVBD, but the thermal expansion coefficient for hole volume, α_f, is larger in the melt for CPI than for HVBD; thus, an iso-hole volume temperature occurs in these blends at T_iso ≈ −34°C. Above and below T_iso, V_h and h_ps/C each show a negative departure from additivity. A quantitative interpretation of the cusp in the composition dependence of T_g can be obtained, via a modified analysis of Kovacs, using free-volume quantities from PALS, with the ratio of scaling constants C_CPI/C_HVBD as an adjustable parameter. At high temperatures, the positron bubble size is smaller in CPI than in HVBD. This agrees with the observation that the thermal expansivity of hole volume, and, hence the internal pressure are larger in the equilibrium melt of CPI. The effect of e⁺-irradiation on the o-Ps intensity was investigated. I₃ decreases more rapidly in the melt as T → T_g, and then more slowly in the glass, suggesting that the effect is due to trapping of radical or ionic species which inhibit o-Ps formation. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 861–871, 1998     

Pressure–volume–temperature of molten and glassy polymers

The pressure–volume–temperature (PVT) dependencies of several amorphous polymers (PS, PC, PPE, and PPE/PS 1:1 blend) in the glassy and molten state were studied. The Simha–Somcynsky (S–S) lattice‐hole equation of state (EOS) was used. Fitting the PVT data in the molten state to the EOS yielded the free volume quantity, h = h(T, P), and the characteristic reducing parameters, P*, V*, and T*. The data within the glassy region were interpreted assuming that the latter parameters are valid in the molten and vitreous state, than calculating h = h(T, P) from the experimental values of V = V(T, P). Next, the frozen free volume fraction in the glass was computed as FF = FF(P). The FF values of polystyrene (PS) resins at ambient pressure showed little scattering (FF_P=1 = 0.691 ± 0.008), while their P‐dependencies varied, reflecting the thermodynamic history of the glass formation as well as the PVT measurements protocol. The pressure gradient of T_g was compared with the Ehrenfest relation for the second‐order transition; here also agreement depended on the method of vitrification. The experimental values of FF at ambient pressure decreased with increasing values of the characteristic temperature reducing parameter, T*. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 270–285, 2007.     

Free volume of molten and glassy polystyrene and its nanocomposites

The Pressure-Volume-Temperature (PVT) dependencies of polystyrene-based clay-containing nanocomposites (CPNC) were determined in the glassy and molten state. The PVT data in the melt were fitted to the Simha-Somcynsky (S-S) lattice-hole equation-of-state (eos), yielding the free volume quantity, h = h(T, P), and the characteristic reducing parameters, P*, V*, T*. The data within the glassy region were interpreted considering that the latter parameters are valid in the whole range of independent variables, than calculating h = h(T, P) from the experimental values of V = V(T, P). Next, the frozen free volume fraction in the glass was computed as FF = FF(P). In the molten state the maximum reduction of free volume was observed at w_solid ≈ 3.6–wt % clay, amount sufficient to adsorb all PS into solidified layer around organoclay stacks. In the vitreous state FF increased with clay content from 0.6 to 1.6—this is the first time FF ≫ 1 has been observed. The highest value was determined for CPNC with the highest clay content, w = 17.1 wt %, thus well above w_solid. The derivative properties, compressibility, κ, and the thermal expansion coefficient, α, depend on T, P, and w. Plots of κ versus T indicate the presence of two secondary transitions, one at T_β/T_g ≈ 0.9 ± 0.1 and other at T_T/T_g = 1.2 ± 0.1. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2504–2518, 2008     

Selenophene‐Flanked Diketopyrrolopyrrole Based Conjugated Polymers for Ambipolar Field‐Effect Transistors

The development of selenophene‐flanked DPP (SeDPP) based copolymers, especially for the ambipolar ones, lags behind other aromatic group flanked DPP‐based polymers. Herein, we report two new ambipolar SeDPP‐based conjugated polymers. One is the alternating polymer PSeDPPFT with normal SeDPP and 3,4‐difluorothiophene units. The other is PSeFDFT , in which the electron acceptor unit is replaced by a new SeDPP derivative, referred as to half‐fused SeDPP. The more planar structure of half‐fused SeDPP endows the backbone of PSeFDFT with good rigidity and planarity. Both polymers exhibit ambipolar transporting properties in air. The PSeFDFT based field‐effect transistors (FETs) display higher and more balanced ambipolar properties with μ_h^ave of 0.27 cm²·V^–1·s^–1, μ_e^ave of 0.18 cm²·V^–1·s^–1, and μ_h^ave/μ_e^ave of 1.5 than those of PSeDPPFT (μ_h^ave = 0.11 cm²·V^–1·s^–1, μ_e^ave = 0.042 cm²·V^–1·s^–1, and μ_h/μ_e = 2.6). This is attributed to the more planar structure, lower LUMO level, higher HOMO level, and better interchain packing orientations of PSeFDFT by comparing with PSeDPPFT . Therefore, a new molecular design strategy to modulate the hole and electron transporting properties is proposed for conjugated D‐A polymers.     

Algebraic solutions for point groups: Cubic groups G in the group chain G⊃T⊃D2⊃C2

Concise algebraic expressions of the symmetry‐adapted functions (SAFs) for both single‐valued and double‐valued representations are derived for the group chain O⊃T⊃D₂⊃C₂ and O⊃D₄⊃D₂⊃C₂, which are functions of only the quantum numbers of the respective group chain without involving any irreducible matrix elements. It is shown that the SAFs of the cubic groups G=O,T_d,T_h,O_h can be expressed in a simple way in terms of the SAFs of the group T. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 585–599, 2000     

Free‐volume variation in polyethylenes of different crystallinities: Positron lifetime,density, and X‐ray studies

High‐quality positron lifetime measurements (70 million total counts) are reported for polyethylenes (PEs) of different crystallinities (X_c = 3–82%). The specific volumes of the crystalline and amorphous phases (V_c and V_a, respectively) were estimated from density and wide‐angle X‐ray scattering (WAXS) experiments. Some samples (those with low values of X_c) were branched PEs, and those with high values of X_c were linear PEs for which X_c was varied with changes in the crystallization temperature. Both V_c and V_a increase with decreasing X_c in the range 0% ≤ X_c ≤ 56% (the branched PEs) but are constant for X_c ≥ 56% (the linear PEs). The lifetime spectra were analyzed with the MELT and LIFSPECFIT routines. Artifacts that can appear in the spectrum analysis were checked via an analysis of computer‐generated spectra. Four lifetime components appeared in all of the PEs; the two long‐lived ones are attributed to pick‐off annihilation of ortho‐positronium (o‐Ps) in crystalline regions (τ₃) and in holes of the amorphous phase (τ₄). With increasing X_c, τ₃ decreases from about 1.2 to 1 ns, τ₄ decreases from 3.0 to 2.5 ns, and the intensity I₄ decreases from 29 to 0%. An increase in I₃ from 6 to 12% was observed. A comparison with simulations shows that the true I₃ value approaches 0 for X_c → 0%. The decrease in I₄ is weaker than the increase in X_c; this leads to the conclusion that the apparent specific o‐Ps yield in the amorphous phase I₄^Xc increases with X_c. Possible reasons for this surprising results are discussed. The fractional free hole volume [h = (V_a ? V_occ)/V_a, where V_occ is the crystalline occupied volume] was estimated from density and WAXS results. Between X_c = 0 and 56%, h decreases from 0.151 to 0.090, but it does not change further above X_c = 56%. The mean size (v) of the local free volumes (holes) estimated from τ₄ decreases from 200 to 150 ų. The number density of holes (N_h) calculated from these values (N_h = h/v) also decreases from 0.8 to 0.6 nm^?3 in the range 0% ≤ X_c ≤ 56%. The values of V_a, V_c, h, and N_h increase with an increasing degree of branching but do not vary for linear PEs. The possible influence of a crystalline–amorphous interfacial phase (three‐phase model) on the observed lifetime parameters is also discussed. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 65–81, 2002     

Electronic quantum motions in hydrogen molecule ion

The hydrogen molecule ion is a two‐center force system expressed under the prolate spheroidal coordinates, whose quantum motions and quantum trajectories have never been addressed in the literature before. The momentum operators in this coordinate system are derived for the first time from the Hamilton equations of motion and used to construct the Hamiltonian operator. The resulting Hamiltonian comprises a kinetic energy T and a total potential V_Total consisting of the Coulomb potential and a quantum potential. It is shown that the participation of the quantum potential and the accompanied quantum forces in the force interaction within H₂⁺ is essential to develop an electronic motion consistent with the prediction of the probability density function |Ψ|². The motion of the electron in H₂⁺ can be either described by the Hamilton equations derived from the Hamiltonian H = T_K + V_Total or by the Lagrange equations derived from the Lagrangian H = T_K ? V_Total. Solving the equations of motion with different initial positions, we show that the solutions yield an assembly of electronic quantum trajectories whose distribution and concentration reconstruct the σ and π molecular orbitals in H₂⁺. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

A study of the pressure-volume-temperature relationships of four related amorphous polymers: Polycarbonate,polyarylate, phenoxy,and polysulfone

The pressure-volume-temperature (PVT) relationships of bisphenol-A polycarbonate, polyarylate, and phenoxy were studied at pressures to 1800 kg/cm² and in both the glassy and melt states. Earlier data on polysulfone are included in the analysis and discussion of the results. All four polymers contain the bisphenol-A residue in their repeat unit, together with a moiety of varying complexity, and are therefore somewhat related. At the glass transition, equations of the Ehrenfest type hold, provided the pressure dependence of the glass transition temperature is defined from the line obtained by intersecting the quasiequilibrium PVT relationship of the glass with the equilibrium PVT surface of the melt. The Prigogine-Defay ratio r = Δ_κΔC_p/T_gV_g(Δα)² at P = O is unity within experimental error for all four polymers. The melt data were fitted successfully to the Simha-Somcynsky theory. Molecular parameters deduced from the reducing parameters vary in a reasonable manner among these four related polymers, lending support to the foundations of the theory.     

Adiabatic compressibility and structural features of non-electrolyte aqueous solutions

Structural characteristics of the hydration complexes of non-electrolytes such as the hydration numbers h, molar adiabatic compressibility of hydration complexes β _h V _h , the molar volume of water in the hydration sphere V _1h , the solute molar volume without hydration environments V _2h and others are determined using the data on the ultrasonic velocity, the density and heat capacity of aqueous solutions of urea, urotropine, acetonitrile, and a number of amides of N-acetyl amino acids. A theoretical model of solvation is also applied. A comparison of the environments of hydrated urotropine molecules with those of urea and acetonitrile molecules in an aqueous medium shows a considerable hydrophobic interaction of urotropine with a solvent.     

Acoustic Study of Solvent Coordination in the Hydration Shells of Potassium Iodide

The isentropic compressibilities of aqueous solutions of potassium iodide, from dilute to almost saturated, were determined at 288 to 308 K based on precise measurements of the speed of ultrasound. Using proper correlations, the hydration numbers (h) were calculated as well as the molar volume and compressibility parameters of the hydrated complexes (V _h , β _h V _h ) of water in the hydration shell (V _1h , β_1h V _1h), and of the cavity containing stochiometric mixtures of K⁺ and I⁻ ions (V _2h, β_2h V _2h). It is revealed that under the studied conditions, the obtained values of h and β _h V _h are independent of temperature whereas the molar compressibility of the hydration shell β _h V _h) is independent of concentration. The electrostatic field of the ions is shown to influence the temperature dependence of the molar volume of water in the hydration shell more substantially than a change of pressure alone influences the temperature dependence of the molar volume of pure water.     

Electrical Conductance and Volumetric Studies in Aqueous Solutions of DL-Pyroglutamic Acid

Conductivity measurements of DL-pyroglutamic acid and sodium pyroglutamate in dilute aqueous solutions were performed in the 288.15–323.15 K temperature range. The limiting molar conductances of pyroglutamate anion, λ^o(pGlu⁻, T) and the dissociation constants of pyroglutamic acid, K(T) were derived from the Onsager, and the Quint and Viallard conductivity equations. Densities of aqueous solutions with molalities lower than 0.5 mol-kg⁻¹ were determined at 5 K intervals from T = 288.15 K to 333.15 K. Densities served to evaluate the apparent molar volumes, V_2,φ(m, T), the cubic expansion coefficients, α (m,T) and the changes of the isobaric heat capacities with respect to pressure, (∂ C_P/∂ P)_T,m. They were correlated qualitatively with the changes in the structure of water when pyroglumatic acid is dissolved in it.     

两个Fe(II)配合物的合成、结构、磁性和穆斯堡尔谱 —— 配合物[Fe(dpq)(Mepy)2(NCS)2]的室温自旋交叉行为

设计制备了两个新的配合物[Fe(dpq)(Mepy)2(NCS)2](1)和[Fe(Medpq)(Mepy)2 (NCS)2](2)。室温下X衍射结果表明配合物（2）为正交晶系,晶胞参数为a = 15.057(3) Å, b = 14.569(3) Å, c = 13.180(3) Å, a = 90.00°, b=90.00°, g = 90.00°。[FeN6] 变型八面体构型中,两个NCS-与其顺式配位,其余四个氮分别来自Medpq和两个Mepy。变温磁化率和穆斯堡尔谱学的研究表明配合物（1）（2）存在自旋交叉,配合物（1）的自旋转换温度为 T1/2 =340K,而配合物（2）在低温条件下的转换是不完全的。     

The Spin Probe Dynamics and the Free Volume in a Series of Amorphous Polymer Glass-Formers

We report the results of a combined study of the local structure and the reorientation dynamics in a series of five amorphous polymers of different fragility: cis-trans-1,4-poly(butadiene) (c-t-1,4-PBD), cis-1,4-poly(isoprene) (cis-1,4-PIP), poly(isobutylene) (PIB), poly(vinyl methylether)(PVME) and poly (propylene glycol) (PPG) by using two different probe methods. The reorientation dynamics of the molecular spin probe 2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPO) from electron spin resonance (ESR) is related to the annihilation behaviour of the atomic ortho-positronium (o-Ps) one as obtained by positron annihilation lifetime spectroscopy (PALS). It was found that a slow to fast transition in the spin probe rotation mobility at the operationally defined spectral temperature parameter, T_50G, is connected with the mean o-Ps lifetime, τ₃ (T_50G) = (2.04 ± 0.26) ns. Consequently, using the free-volume concept of the o-Ps annihilation in terms of a quantum-mechanical model of o-Ps lifetime this transition can be connected with the occurrence of the mean free volume hole, V_h (T_50G) = (102 ± 17) ų, nearly independent of the chemical composition and the basic structural relaxation parameters of the amorphous polymers investigated. Finally, the free volume hole distribution aspect of the slow to fast transition indicates the presence of a sufficient free volume fluctuation at T_50G for both typical fragile PVME and strong PIB polymer and emphasizes the essential role of free volume in the spin probe dynamics.     

The size and number of local free volumes in polypropylenes: A positron lifetime and PVT study

The temperature dependence of the mean size of local free volumes in an amorphous atactic (aPP) and a semicrystalline syndiotactic polypropylene (sPP), and an amorphous ethylene‐propylene copolymer (E‐co‐P48) has been studied. Pressure‐volume‐temperature (PVT) experiments were performed for aPP, from which the hole fraction h of the Simha‐Somcynsky theory and the number density of holes were estimated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3089–3093, 2003