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.     

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     

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     

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.     

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     

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.     

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     

Free volume quantities and viscoelasticity of polymer glasses

We have investigated, in terms of the Cohen-Turnbull theory, a relationship for polycarbonate (PC) glasses between average stress relaxation times, <to, and average free volume sizes, 〈v_f〉, obtained from positron annihilation lifetime spectroscopy. This examination suggests that the minimum free volume required for stress relaxation, v*, decreases with decreasing temperature and that, near the glass transition temperature, only a subset of extremely large free volume elements contributes to the stress relaxation of PC glasses. This suggestion is consistent with the idea that near the glass transition temperature, the viscoelastic response is dominated by large-scale, main-chain motion, whereas at lower temperature it is controlled by local motion. Moreover, comparison with the v* value estimated from gas diffusivity through various PC species at room temperature shows that the required free volume size for stress relaxation in the glass transition region is much larger than that for gas diffusion. Previously we showed that the Doolittle equation fails to correlate viscoelastic relaxation times of polymer glasses with changing temperature; determining the free volume fraction, h, from theoretical analysis of volume recovery data and theory, the Doolittle equation is shown to be valid in PC above 135°C (T_g - 14°C) irrespective of temperature and physical aging times. This result supports the idea suggested in the previous article that, as glassy polymers approach the transition region, viscoelastic properties increasingly tend to be controlled by free volume. © 1996 John Wiley & Sons, Inc.     

Dynamics of thin polymer films: Recent insights from incoherent neutron scattering

Incoherent neutron scattering is presented as a powerful tool for interpreting changes in molecular dynamics as a function of film thickness for a range of polymers. Motions on approximately nanosecond and faster timescales are quantified in terms of a mean-square atomic displacement (〈u²〉) from the Debye–Waller factor. Thin-film confinement generally leads to a reduction of 〈u²〉 in comparison with the bulk material, and this effect becomes especially pronounced when the film thickness approaches the unperturbed dimensions of the macromolecule. Generally, there is a suppression (never an enhancement) of 〈u²〉 at temperatures T above the bulk calorimetric glass-transition temperature (T_g). Below T_g, the reduction in the magnitude of 〈u²〉 depends on the polymer and the length scales being probed. Polymers with extensive segmental or local mobility in the glass are particularly susceptible to reductions of 〈u²〉 with confinement, especially at the Q vectors probing these longer length scales, whereas materials lacking these sub-T_g motions are relatively insensitive. Moreover, a reduced 〈u²〉 value correlates with reduced mobility at long time and spatial scales, as measured by diffusion in these thin polymer films. Finally, this reduced thin-film mobility is not reliably predicted by thermodynamic assessments of an apparent T_g, as measured by discontinuities or kinks in the T dependence of the thermal expansion, specific volume, index of refraction, specific heat, and so forth. These measurements illustrate that 〈u²〉 is a powerful and predictive tool for understanding dynamic changes in thin polymer films. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3218–3234, 2004     

The temperature dependence of the local free volume in polyethylene and polytetrafluoroethylene: A positron lifetime study

Positron lifetime measurements, performed in the temperature range 80–300 K, are reported for polyethylene (PE) and polytetrafluoroethylene (PTFE). The lifetime spectra have been analyzed using the data processing routines LIFSPECFIT and MELT. Two long-lived components appear, which are attributed to pick-off annihilation of ortho-positronium in crystalline regions and at holes in the amorphous phase. The ortho-positronium lifetimes, τ₃ and τ₄, are used to estimate the crystalline packing density and the size of local free volumes in the crystalline and amorphous phases. The interstitial free volume in the crystals exhibits a weak linear increase with the temperature which is attributed to thermal expansion of the crystal unit cell. In the amorphous phase, the hole volume varies between 0.053 and 0.188 nm³ (PE) and between 0.152 and 0.372 nm³ (PTFE). Its temperature variation may be fitted by two straight lines, the intersection of which is used to estimate a glass transition temperature of T_g = 195 K for both PE and PTFE. The slopes of the free volume in the glassy and crystalline phases with the temperature correlate well with each other. The coefficients of thermal expansion of the hole volume are compared with the macroscopic volume change below and above the glass transition. From this comparison a fractional hole volume at T_g of 4.5 (PE) and 5.7% (PTFE) and a number of 0.73 (PE) and 0.36 (PTFE) × 10²⁷ holes/m³ is estimated. Finally, it is found that the intensity of o-Ps annihilation in crystals shows a different temperature dependence to that in the amorphous phase. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1513–1528, 1998     

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.     

Pressure‐volume‐temperature and glass transition behavior of silica/polystyrene nanocomposite

The pressure‐volume‐temperature (PVT) behavior and glass transition behavior of a 10 wt % silica nanoparticle‐filled polystyrene (PS) nanocomposite sample are measured using a custom‐built pressurizable dilatometer. The PVT data are fitted to the Tait equation in both liquid and glassy states; the coefficient of thermal expansion α, bulk modulus K, and thermal pressure coefficient γ are examined as a function of pressure and compared to the values of neat PS. The glass transition temperature (T_g) is reported as a function of pressure, and the limiting fictive temperature (T_f′) from calorimetric measurements is reported as a function of cooling rate. Comparison with data for neat PS indicates that the nanocomposite has a slightly higher T_g at elevated pressures, higher bulk moduli at all pressures studied, and its relaxation dynamics are more sensitive to volume. The results for the glassy γ values suggest that thermal residual stresses would not be reduced for the nanocomposite sample studied. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1131–1138     

Effect of water sorption on oxygen‐barrier properties of aromatic polyamides

Aromatic polyamides based on poly(m‐xylylene adipamide) (MXD‐based polyamides) and poly(hexamethylene isophthalamide) (HMD‐based polyamides) were examined. Insight into the excellent gas‐barrier properties was obtained by the characterization of the effect of water sorption on the thermal transitions, density, refractive index, free‐volume hole size, and oxygen‐transport properties. Reversing the carbonyl position with respect to the amide nitrogen substantially lowered the oxygen permeability of MXD‐based polyamides in comparison with that of HMD‐based polyamides by facilitating hydrogen‐bond formation. The resulting restriction of conformational changes and segmental motions reduced diffusivity. The primary effect of water sorption was a decrease in the glass‐transition temperature (T_g) attributed to plasticization by bound water. No evidence was found to support the idea that sorbed water filled holes of free volume. When the polymer was in the glassy state, the drop in T_g accounted for hydration‐dependent changes in the density, refractive index, and free‐volume hole size. The correlation of the oxygen solubility with T_g and density confirmed the concept of oxygen sorption as filling holes of excess free volume. In some cases, water sorption produced a glass‐to‐rubber transition. The onset of rubbery behavior was associated with a minimum in the oxygen permeability. The glass‐to‐rubber transition also facilitated the crystallization of MXD‐based polymers, which complicated the interpretation of oxygen‐transport behavior at higher relative humidity. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1365–1381, 2005     

Ortho‐positronium lifetime distribution analyzed with MELT and LT and free volume in poly(ε‐caprolactone) during glass transition,melting, and crystallization

Positron annihilation lifetime spectroscopy (PALS) was used to study the free volume behavior in the temperature range between 100 and 370 K in semicrystalline poly(ε‐caprolactone) (PCL). For the analysis of the spectra we used the well‐known routine MELT as well as the new program LT8.0, which allows both discrete and log‐normal distributed annihilation rates. From experiments, confirmed by the analysis of simulated spectra, we found that MELT returns too large values for the o‐Ps lifetime τ₃ associated with too small intensities I₃. This is due to the underestimation of the width of o‐Ps lifetime distribution in MELT (the spectra analyzed contained 3 million counts). The same effects were observed in the parameters obtained from the discrete term analysis. LT, however, returns, when allowing the o‐Ps lifetime to be distributed, rather accurate values for τ₃, I₃, and the width (standard deviation σ₃) of the o‐Ps lifetime distribution. The effect of the glass transition, melting, and crystallization on the annihilation parameters was observed. These results were compared with differential scanning calorimetry (DSC) and pressure–volume–temperature (PVT) experiments. From this comparison, the number density of holes and the fractional free (hole) volume have been estimated. At a “knee” temperature T_k ≈ 1.5 T_g, a leveling off of the o‐Ps lifetime τ₃ and a distinct decrease in the width, σ₃, of its distribution was observed; the latter effect was detected for the first time. Fast motional processes and/or the disappearance of the dynamic heterogeneity of the glass and the transition to a homogeneous liquid are discussed as possible reasons for these effects. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3077–3088, 2003     

Equations of state for polyamide‐6 and its nanocomposites. 1. Fundamentals and the matrix

The pressure‐volume‐temperature (PVT) surface of polyamide‐6 (PA‐6) was determined in the range of temperature T = 300–600 K and pressure P = 0.1–190 MPa. The data were analyzed separately for the molten and the noncrystalline phase using the Simha‐Somcynsky (S‐S) equation of state (eos) based on the cell‐hole theory. At T_g(P) ≤ T ≤ T_m(P), the “solid” state comprises liquid phase with crystals dispersed in it. The PVT behavior of the latter phase was described using Midha‐Nanda‐Simha‐Jain (MNSJ) eos based on the cell theory. The data fitting to these two theories yielded two sets of the Lennard‐Jones interaction parameters: ε*(S‐S) = 34.0 ± 0.3 and ε*(MNSJ) = 22.8 ± 0.3 kJ/mol, whereas v*(S‐S) = 32.00 ± 0.1 and v*(MNSJ) = 27.9 ± 0.2 mL/mol. The raw PVT data were numerically differentiated to obtain the thermal expansion and compressibility coefficients, α and κ, respectively. At constant P, κ followed the same dependence on both sides of the melting zone near T_m. By contrast, α = α(T) dependencies were dramatically different for the solid and molten phase; at T < T_m, α linearly increased with increasing T, then within the melting zone, its value step‐wise decreased, to slowly increase at higher temperatures. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 299–313, 2009     

Twinkling fractal theory of the glass transition

In this paper we propose a solution to an unsolved problem in solid state physics, namely, the nature and structure of the glass transition in amorphous materials. The development of dynamic percolating fractal structures near T_g is the main element of the Twinkling Fractal Theory (TFT) presented herein and the percolating fractal twinkles with a frequency spectrum F(ω) ∼ ω^df–1 exp −|ΔE|/kT as solid and liquid clusters interchange with frequency ω. The Orbach vibrational density of states for a fractal is g(ω) ∼ ω^df–1, where d_f = 4/3 and the temperature dependent activation energy behaves as ΔE ∼ (T² − T). The key concept of the TFT derives from the Boltzmann population of excited states in the anharmonic intermolecular potential between atoms, coupled with percolating solid fractal structures near T_g. The twinkling fractal spectrum F(ω) at T_g predicts the correct dynamic heterogeneity behavior via the spatio-temporal thermal fluctuation autocorrelation relaxation function C(t). This function behaves as C(t) ∼ t^−1/3 (short times), C(t) ∼ t^−4/3 (long times) and C(t) ∼ t⁻² (ω < ω_c), which were found to be in excellent agreement with published nanoscale AFM dielectric force fluctuation experiments on a glassy polymer near T_g. Using the Morse potential, the TFT predicts that T_g = 2D_o/9k, where D_o is the interatomic bonding energy ∼ 2–5 kcal/mol and is comparable to the heat of fusion ΔH_f. Because anharmonicity controls both the thermal expansion coefficient α_L and T_g, the TFT uniquely predicts that α_L×T_g ≈ 0.03, which is found to be universal for a broad range of glassy materials from Pyrex to polymers to glycerol. Below T_g, the glassy structure attains a frustrated nonequilibrium state by getting constrained on the fractal structure and the thermal expansion in the glass is reduced by the percolation threshold p_c as α_g ≈ p_cα_L. The change in heat capacity ΔC_p = C_pL–C_pg at T_g was found to be related to the change in dimensionality from D_f to 3 in the Debye approximation as the ratio C_pL/C_pg = 3/D_f, where D_f is the fractal dimension of the glass. For polymers, the TFT describes the molecular weight dependence of T_g, the role of crosslinks on T_g, the Flory-Fox rule of mixtures and the WLF relation for the time-temperature shift factor a_T, which are traditionally viewed in terms of Free-Volume theory. The TFT offers new insight into the behavior of nano-confined glassy materials and the dynamics of physical aging. It also predicts the relation between the melting point T_m and T_g as T_m/T_g = 1/[1−p_c] ≈ 2. The TFT is universal to all glass forming liquids. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2765–2778, 2008     

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     

Above,below, and in‐between the two glass transitions of ultrathin free‐standing polystyrene films: Thermal expansion coefficient and physical aging

In previous work we observed two simultaneous transitions in high molecular weight (MW) free‐standing polystyrene films that were interpreted as two thickness‐dependent reduced glass transition temperatures (T_gs). The weaker lower transition agreed well with the MW‐dependent T_g(h) previously reported, while the much stronger upper transition matched the MW‐independent T_g(h) previously observed in low‐MW free‐standing films. Here, we investigate the nature of these two transitions by inspecting the temperature dependence of the films' thermal coefficient of expansion (TCE) and present physical aging measurements using ellipsometry both below and in‐between the two transitions. TCE values indicate approximately 80 to 90% of the film solidifies at the upper transition, while only 10 to 20% remains mobile to lower temperatures, freezing out at the lower transition. Physical aging is observed at a temperature below the upper transition, but above the lower transition, indicative of the upper transition being an actual glass transition associated with the α‐relaxation. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 64–75     

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     

Phase behavior and some calorimetric and physical properties of diurethanes from perfluoropolyether macromonomers

Density and calorimetric measurements have been carried out on copolymeric perfluoropolyethers of molecular weight ranging between 500 and 4700, terminated at both chain ends either with  CH₂OH or ethylurethane groups. Samples of the second series are models for perfluoropolyethers based polyurethanes. Density measurements point out that the terminal alcoholic group brings about a negative excess volume, which increases with decreasing the molecular weight; a lower excess volume is found for urethane‐terminated molecules. Calorimetric traces, T_g, and Δc_p at T_g show that alcoholic‐terminated molecules are amorphous and one phase systems, while urethane‐terminated compounds are crystalline; phase separation is observed for this last series when the molecular weight of the fluorinated segment is larger than 1000. The trend of T_g with molecular weight is discussed for one‐ and two‐phase systems in the light of current theories for the glass transition. The decrease of the melting point with increasing the molecular weight for the urethane series can be described by the Flory equation for random copolymers. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1609–1622, 1999