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     

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     

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     

Molecular weight-dependence of free volume in polystyrene studied by positron annihilation measurements

Positron annihilation lifetime measurements are reported for four monodisperse polystyrenes with molar mass M = 4,000, 9,200, 25,000, and 400,000. The temperature dependences of orthopositronium (o-Ps) lifetime (τ₃) and intensity (I₃) were measured from 5°C to T_g + 30°C for each sample. From these data, the free volume hole size, 〈v_f(τ₃)〉, and fractional free volume h_ps=CI₃〈v_f(τ₃)〉 were calculated. The temperature dependences of τ₃, 〈v_f(τ₃)〉 and h_ps show a discrete change in slope at an effective glass transition temperature, T_g,ps, which is measurably below the conventional bulk T_g. This suggests that τ₃ is sensitive to large holes which retain their liquid-like mobility in the glassy state. Good agreement was found for T > h_g,ps between h_ps and the theoretical free volume fraction h_th deduced from experimental P-V-T data for polystyrene using the statistical mechanical theory of Simha and Somcynsky. Below T_g,ps, deviations between h_ps and h_th are observed, h_ps falling increasingly below h_th as temperature decreases. Whereas h_ps and h_th depend strongly on M in the melt, each essentially independent of M in the glass. A free volume quantity, computed from the bulk volume, which is in good numerical agreement with the Simha-Somcynsky h-function in the melt, gives improved agreement with h_ps in the glassy state. © 1994 John Wiley & Sons, Inc.     

Free‐volume and crystallinity in low molecular weight poly(ethylene oxide)

Positron annihilation lifetime spectroscopy (PALS), differential scanning calorimetry, X‐ray diffraction, and polarized light optical microscopy were used to study six low molar mass poly(ethylene oxide) samples with average molar masses ranging from 1 × 10³ to 10 × 10³ g mol^?1. Dynamic light scattering was used to determine molar mass and polydispersity rigorously. Polymer samples with 70–95% crystallinity, which is an unusual range in PALS studies, were prepared by molten material quenching. The ortho‐positronium pick‐off lifetime (τ₃) and relative fractional free volume (f_v), determined by the free volume model, correlated well with the average molar mass and crystallinity of the polymers. X‐ray diffraction and polarized light optical data support the interpretation of positron annihilation results. PALS parameter, I₃, which is associated with high cavity content, remained approximately constant at 20–22% for all samples. The cavities are present as crystallite defects in the spherulitic open texture and the amorphous phase for the low crystallinity sample (e.g., for M_w = 1390) and at the interfaces and in interlamellar spherulite regions of the more crystalline materials. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2400–2409, 2007     

Positron annihilation lifetime and differential scanning calorimetric study of immiscible NBR/PE blends

The temperature dependence of the mean size of nanoscale free‐volume holes, 〈V_h〉, in polymer blend system consisting of polar and nonpolar polymers has been investigated. The positron lifetime spectra were measured for a series of polymer blends between polyethylene (PE) and nitrile butadiene rubber (NBR) as a function of temperature from 100 to 300 K. The glass transition temperatures (T_g) for blends were determined from the ortho‐positronium (o‐Ps) lifetime τ₃ and the mean size of free‐volume holes 〈V_h〉 versus temperature as a function of wt % of NBR. The T_gs estimated from the PALS data agree very well with those estimated from DSC in view of different time scales involved in the two measurements. Both DSC and PALS results for the blends showed two clear T_gs of a two‐phase system. Furthermore, from the variation of thermal expansivity of the nanoscale free‐volume holes, the thermal expansion coefficients of glass and amorphous phases were estimated. Variations of the o‐Ps formation probability I₃ versus temperature for pure PE and blends with low wt % of NBR were interpreted on the basis of the spur reaction model of Ps formation with reference to the effects of localized electrons and trapping centers produced by positron irradiation. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 227–238, 2009     

Kinetics of methyl methacrylate and n‐butyl acrylate copolymerization mediated by 2‐cyanoprop‐2‐yl dithiobenzoate as a RAFT agent

The RAFT (co)polymerization kinetics of methyl methacrylate (MMA) and n‐butyl acrylate (BA) mediated by 2‐cyanoprop‐2‐yl dithiobenzoate was studied with various RAFT concentrations and monomer compositions. The homopolymerization of MMA gave the highest rate. Increasing the BA fraction f_BA dramatically decreased the copolymerization rate. The rate reached the lowest point at f_MMA ～ 0.2. This observation is in sharp contrast to the conventional RAFT‐free copolymerization, where BA homopolymerization gave the highest rate and the copolymerization rate decreased monotonously with increasing f_MMA. This peculiar phenomenon can be explained by the RAFT retardation effect. The RAFT copolymerization rate can be described by 〈R_p〉/〈R_p〉₀ = (1 + 2(〈k_c〉/〈k_t〉)〈K〉)[RAFT]₀)^?0.5, where 〈R_p〉₀ is the RAFT‐free copolymerization rate and 〈K〉 is the apparent addition–fragmentation equilibrium coefficient. A theoretical expression of 〈K〉 based on a terminal model of addition and fragmentation reactions was derived and successfully applied to predict the RAFT copolymerization kinetics with the rate parameters obtained from the homopolymerization systems. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3098–3111, 2007     

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.     

Free volumes in simple and polymeric liquids

Values of ε₀ν₀ the vaporization energy and volume in the hypothetical liquid state at 0°K., are derived for some simple polar and nonpolar molecules used as models for vinyl polymers. The following empirical relationship between the free volume fraction, f = (v ? v₀)/v, and the liquid compressibility coefficient β is demonstrated: ?f² ∝? This is applied to several vinyl polymer liquids near their glass transition temperatures, T_g, giving. f_g ? 0.17, if the “hard-core” volume v^* is considered to be independent of pressure and temperature, (i.e., v^* = v₀); or, f_g ?0.12, if the P,T dependence of v^* is considered to be the same as that of the glass. These agree with f_g values derived by Simha and Boyer from thermal expansion coefficients for the two analogous cases. An empirical viscosity-free volume equation of the Doolittle form: η = ATⁿe^b/f is applied to the glass transition, on assuming that this is an isoviscosity state and with the use of reported values for the expansion and compressibility coefficients and dT_g/dP for three polymers: polystyrene, poly(methyl methacrylate), and poly(vinyl acetate). Reasonable values of b/n are thus obtained. This viscosity equation is critically examined in the light of molecular theories of liquid viscosity.     

Partitioning technique,perturbation theory,and rational approximations

Instead of the Schródinger equation ??Ψ = EΨ subject to the boundary condition 〈φ|Ψ〉 = 1, where φ is a normalized reference function in the Hilbert space, one studies the inhomogeneous equation (?? ? ?)Ψ_? = aφ, where ? is a complex variable, with the same boundary condition, which gives a = 〈φ|??|Ψ_?〉 ? ? = ?₁ ? ?. Introducing the projector P = 1 ? |φ〉〈φ| for the complement to O = |φ〉〈φ|, one finds easily the explicit solution Ψ_? = (1 ? P??/?)^?1φ = (1 + T_???)φ, where T_? = (? ? P??)^?1P = P(? ? P??P)^?1P is the reduced resolvent associated with the auxiliary Hamiltonian H? = P??P. The existence of these operators is discussed. It is shown that, if the parameter ? is real in the “discrete part” of the spectrum to ??, then ? and ?₁ = 〈φ|??|Ψ_?〉 = 〈φ|?? + ??T_???|Φ〉 ≡f(?) bracket a true eigenvalue E satisfying the relation E = f(E). The Newton-Raphson solution to the equation F(?) = ? ? f(?) = 0 is related to the variation principle. Putting ?? = ??₀ + V and expanding the inverse (? ? P??₀ ? PV)^?1 in terms of powers of V or (V ? α), one gets various expansions relating to finite-order perturbation theory. Exact expressions for the ordinary wave and reaction operators are obtained. If A is an arbitrary nonsingular operator and h = {h₁,h₂,…,h_n} is a linearly independent set, the inner projection Á_n = | h 〉 〈 h |A^?1| h 〉^?1〈 h | is a “rational approximation” to the operator A which converges toward A when n→∞ and the set h becomes complete. If A is positive (or has a finite negative part) the convergence is from below. Applying this principle to the partitioning technique, one gets rational perturbation approximations instead of the standard power series, similar to the Padé approximants but derived in a different way with the remainder term under control. The method has been used to calculate lower bounds to eigenvalues.     

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     

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.     

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.     

Analytical Representation of Solutions to Lattice‐Hole Theory

The Simha and Somcynsky (S‐S) lattice‐hole theory has been shown to represent accurately the pressure‐volume‐temperature (PVT) surface of chain molecular melts and their mixtures. Proceeding beyond its original intent, it has led to correlations with other properties and extension into the steady state and relaxing glass. The equilibrium results appear as the solutions of two coupled equations, involving the variables of state and the hole fraction, h = h (V, T) – a kind of free volume quantity. These are to be solved numerically. Notwithstanding the theory's quantitative success, its implicit form has on some occasions been a practical limitation. We remedy this situation by fitting the scaled and thus general solutions of the coupled equations to accurate algebraic equations, V = V (T, P) and h = hV, T). In this manner, explicit analytical expressions for configurational thermodynamic functions and their derivatives are now available. The new expressions for V and h are simple to employ; the convergence of the non‐linear least‐squares fit is obtained in seconds. The numerical values of the scaling parameters so derived are nearly identical to those computed from the original coupled equations. Having h and V from the original theory, the cohesive energy density [CED = δ²V, T)] was also considered. The results are again well represented by a simple algebraic expression. An expression for the reduced solubility parameter δ = δ (T, P) is also given. The usefulness of these solutions is further illustrated by an application to the PVT surfaces of polystyrene and polyphenylene ether blends.     

Apparent Molar Volume and Isentropic Compressibility for the Binary Systems {Methyltrioctylammonium Bis(trifluoromethylsulfonyl)imide + Methyl Acetate or Methanol} and (Methanol + Methyl Acetate) at <Emphasis Type="Italic">T</Emphasis>=298.15, 303.15, 308.15 and 313.15 K and Atmospheric Pressure

The densities and speeds of sound for binary mixtures containing the solute ionic liquid (IL) methyltrioctylammonium bis(trifluoromethylsulfonyl)imide ([MOA]⁺[Tf₂N]⁻), solute/solvent methanol, and solvent methyl acetate have been measured at 298.15, 303.15, 308.15 and 313.15 K at atmospheric pressure. The binary mixtures studied are ([MOA]⁺[Tf₂N]⁻ + methyl acetate or methanol), and (methanol + methyl acetate). The apparent molar volume, V _φ and the apparent molar isentropic compressibility, k _φ , have been evaluated from the experimental density and speed of sound data, respectively. The parameters of a Redlich–Mayer type equation were fitted to the apparent molar volume and apparent molar isentropic compressibility data. The apparent molar volume and apparent molar isentropic compressibility at infinite dilution, V_f⁰V_{\phi}^{0} and k_f⁰k_{\phi}^{0}, respectively, of the binary solutions have also been calculated at each temperature. The infinite dilution apparent molar volume indicates that intermolecular interactions for (IL + methyl acetate) mixtures are stronger than for (IL + methanol) mixtures at all temperatures except at 298.15 K, and that V_f⁰V_{\phi}^{0} for the (IL + methyl acetate or methanol) binary systems increases with an increase in temperature. For the (methanol + methyl acetate) system the intermolecular interaction are weaker and V_f⁰V_{\phi}^{0} also increases with an increase in temperature. Values of the infinite dilution apparent molar expansibility, E_f⁰E_{\phi}^{0}, indicate that the interaction between (IL + methyl acetate) is greater than for (IL + methanol) and (methanol + methyl acetate).     

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.     

Measurement of Some Thermodynamic and Acoustic Properties of Binary Solutions of N,N-Dimethylformamide with 1-Alkanols at 30°C and Comparison with Theories

Densities, and ultrasonic velocities, uof binary mixtures of N,N-dimethylformamide (DMF) + methanol, + ethanol, + 1-propanol, + 1-butanol, + 1-pentanol, and + 1-hexanol have been measured at 30°C. The ultrasonic velocities have been compared with values calculated from the free-length theory ( FLT) due to Jacobson and collision-factor theory ( CFT) due to Schaaffs. The measured data are used to compute adiabatic compressibility (k _s), deviation in adiabatic compressibility (k _s), intermolecular free length (L _f), molar volume (V _m), and available volume (V _a). The excess molar volume ( V _m ^E) and excess free length (L _f ^E) are also evaluated. For all systems, these results were satisfactorily correlated by the Redlich–Kister polynomial. These parameters are used to discuss dissociation of the self-associated 1-alkanol molecules and the formation of aggregates between unlike molecules through C=O...H–O hydrogen bonding.     

Initiator efficiency of 2,2′‐azobis(isobutyronitrile) in bulk dodecyl acrylate free‐radical polymerizations over a wide conversion and molecular weight range

An Erratum has been published for this article in J. Polym. Sci. Part A: Polym. Chem. (2004) 42(21) 5559 . The initiator efficiency, f, of 2,2′‐azobis(isobutyronitrile) (AIBN) in dodecyl acrylate (DA) bulk free‐radical polymerizations has been determined over a wide range of monomer conversion in high‐molecular‐weight regimes (M_n ? 10⁶ g mol^?1 [? 4160 units of DA)] with time‐dependent conversion data obtained via online Fourier transform near infrared spectroscopy (FTNIR) at 60 °C. In addition, the required initiator decomposition rate coefficient, k_d, was determined via online UV spectrometry and was found to be 8.4 · 10^?6 s^?1 (±0.5 · 10^?6 s^?1) in dodecane, n‐butyl acetate, and n‐dodecyl acetate at 60 °C. The initiator efficiency at low monomer conversions is relatively low (f = 0.13) and decreases with increasing monomer to polymer conversions. The evolution of f with monomer conversion (in high‐molecular‐weight regimes), x, at 60 °C can be summarized by the following functionality: f^{60 °C} (x) = 0.13–0.22 · x + 0.25 · x² (for x ≤ 0.45). The reported efficiency data are believed to have an error of >50%. The ratio of the initiator efficiency and the average termination rate coefficient, 〈k_t±, (f/〈k_t〉) has been determined at various molecular weights for the generated polydodecyl acrylate (M_n = 1900 g mol^?1 (? 8 units of DA) up to M_n = 36,500 g mol^?1 (? 152 units of DA). The (f/〈k_t〉) data may be indicative of a chain length‐dependent termination rate coefficient decreasing with (average) chain length. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5170–5179, 2004     

Volume and compressibility effects in the formation of metal-EDTA complexes

We used precise measurements of ultrasonic velocity and density to study the complexation of ethylendiaminetetraacetic acid (EDTA) with Mg²⁺, Ca²⁺, Sr²⁺, and Ba²⁺ at 25‡C and pH 12. From these measurements we obtained the changes in the molar concentration increment of the ultrasonic velocity δA, the apparent molar adiabatic compressibility δK_sΦ, and the apparent molar volume δV_Φ of complex formation. The hydration contributions δ(AV_h) to the volume effect of binding range from 39.6 to 46.6 cm³-mol^-1 while the hydration contribution to the adiabatic compressibility change in the binding, δ(δK_h), ranges from 103.9X 10^-4 to 131.1 X 10^-4 cm³-mol^-1-bar^-1. These data are interpreted in terms of dehydration of interacting molecules,i.e., transfer of water molecules from the hydration shells of cations and EDTA into the bulk water. The ratio δ(δV_h)/ δ(δV_h) is in the range 0.35 to 0.38 bar, indicating a dominant contribution from the dehydration of charged atomic groups in the volume and the compressibility effects of complex formation.     

Studies on Acoustic Behavior, Viscosity, and Density of Some Commercial Extractants and Their Molecular Interaction with Diluent, Modifier, and Extractant

Acoustical and viscosity measurements have been made for binary liquid mixtures of commercially available solvent extractants, LIX reagents such as LIX 622 and LIX 860 in benzene, amyl alcohol, and tri-n-butyl phosphate (TBP) at 303.15 K. The measured values of ultrasonic velocity, density, and viscosity have been utilized to compute some acoustic as well as thermodynamic parameters such as intermolecular free length, L _f, isentropic compressibility, _s, molar volume, V, and Gibb's excess free energies of activation of viscous flow, G*^E. These parameters along with the derived values of isentropic compressibility, _s ^E, intermolecular free length, L _f ^E, and molar volume, V ^E, have been utilized for a comparative study of molecular interactions between the components present in different liquid systems. The experimental ultrasonic velocities for aforementioned mixtures have been compared with theoretically estimated velocities using different empirical relations, and the relative merits of these theories and relations have been discussed in terms of percentage variation.