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     

On the scaling law of the evolution of lap-shear strength with healing temperature at amorphous polymer−polymer interfaces and surface glass transition

The evolution of lap-shear strength (σ) with healing temperature T _h at symmetric and asymmetric amorphous polymer−polymer interfaces formed of the samples with vitrified bulk has been investigated. It has been found that the square root of the lap-shear strength behaves with respect to healing temperature as σ ^1/2 ~ T _h both at symmetric and asymmetric interfaces. Basing on this scaling law between σ and T _h, the values of the surface glass transition temperature ( T_g^surface ) \left( {T_{\rm{g}}^{\rm{surface}}} \right) have been estimated for a number of amorphous polymers by the extrapolation of the experimental curves σ ^1/2 ~ T _h for symmetric polymer−polymer interfaces and, in some cases, for asymmetric, both compatible and incompatible, polymer−polymer interfaces, to zero strength. A significant reduction in surface glass transition temperature T_g^surface T_{\rm{g}}^{\rm{surface}} with respect to the glass transition temperature of the polymer bulk ( T_g^bulk ) \left( {T_{\rm{g}}^{\rm{bulk}}} \right) , reported earlier, has been confirmed by the use of the new proposed approach. The quasi-equilibrium surface glass transition temperature T_g^surface T_{\rm{g}}^{\rm{surface}} of amorphous polystyrene (PS) has been predicted in the framework of an Arrhenius approach using the plot “logarithm of healing time − reciprocal surface glass transition temperature T_g^surface￠￠ T_{\rm{g}}^{\rm{surface}}\prime \prime and the activation energy of the surface alpha-relaxation of PS has been calculated.     

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.     

Glass temperature depression of polymer by use of mixed solvents: A colligative property

The entropy theory of glasses is used to determine the glass temperature depression by a multicomponent low molecular weight plasticizer (diluent). The glass temperature, T_g, is calculated as a function of pressure, P, the mole fractions, m_i, of the plasticizers, and the degree of polymerization p. One finds, provided there is no phase separation, that to a good approximation, the initial glass temperature depression is a function of the total mole fraction of plasticizer. Moreover, the glass temperature depression for small plasticizer molecules is found to be nearly a universal function of the plasticizer mole fraction (it depends on no other plasticizer variable), and to vary inversely as the number of flexible bonds per monomer unit of the polymer. A useful approximation is found, γdT_g/dm₁ = −3T_g, where m₁ is the total mole fraction of diluent on a per monomer of polymer basis, and γ is the number of flexible bonds per monomer. Although these results agree with experimental data in the literature, a more definitive experimental test is needed. © 1996 John Wiley & Sons, Inc.     

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     

Influence of local chain dynamics on diffusion of gases in polymers as determined by pulsed field gradient NMR

Diffusion of gases in polymers below the glass transition temperature, T_g, is strongly modulated by local chain dynamics. For this reason, an analysis of pulsed field gradient (PFG) nuclear magnetic resonance (NMR) diffusion measurements considering the viscoelastic behavior of polymers is proposed. Carbon‐13 PFG NMR measurements of [¹³C]O₂ diffusion in polymer films at 298 K are performed. Data obtained in polymers with T_g above (polycarbonate) and below (polyethylene) the temperature set for diffusion measurements are analyzed with a stretched exponential. The results show that the distribution of diffusion coefficients in amorphous phases below T_g is wider than that above it. Moreover, from a PFG NMR perspective, full randomization of the dynamic processes in polymers below T_g requires long diffusion times, which suggests fluctuations of local chain density on a macroscopic scale may occur. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 231–235, 2010     

Equation of state and the thermodynamic properties of liquid polymers: Application of the Hirai-Eyring model

It is shown that the Hirai-Eyring model for the liquid state is capable of accurately describing the p, V, T behavior of liquid polymers in the temperature range over which measurements are now made, and below. Once the parameter choices necessary to accomplish the fit are made for a particular polymer, the excess thermodynamic functions (differences in properties, liquid less solid) are determined by the same parameters. Above the glass transition temperature T_g the volume, excess enthalpy, and square of the excess entropy are predicted by the model to be essentially linear with temperature, in agreement with experiment. Below T_g, these functions do not remain linear (as is usually assumed in extrapolating the equilibrium behavior to low temperatures), but instead they rapidly approach zero in a continuous way as the temperature is lowered. These remarks apply to glass-forming materials composed of small molecules, as well as to polymers. The “paradox” raised by Kauzmann is thus resolved, and the Gibbs-DiMarzio second-order transition appears to be unnecessary.     

A novel temperature‐step method to determine the glass transition temperature of ultrathin polymer films by liquid dewetting

A novel temperature‐step experimental method that extends the Bodiguel‐Fretigny liquid dewetting method of investigating polymer thin films is described and results presented from an investigation of thickness effects on the glass transition temperature (T_g) of ultrathin polystyrene (PS) films. Unlike most other methods of thin film investigation, this procedure promises a rapid screening tool to determine the overall profile of T_g versus film thickness for ultrathin polymer films using a limited number of samples. Similar to our prior observations and other literature data, with this new method obvious T_g depression was observed for PS thin films dewetting on both glycerol and an ionic liquid. The results for PS dewetting on the two different liquids are similar indicating only modest effects of the substrate on the T_g‐film thickness relationship. In both instances, the T_g depression is somewhat less than for similar PSs supported on silicon substrates reported in the literature. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013 , 51, 1343–1349     

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     

Influence of matrix glass transition temperature on the memory effect of polymer‐dispersed liquid crystals

In this article, macroinitiators with different glass transition temperature (T_g) were synthesized by reversible additional‐fragmental chain transfer polymerization, and used to prepare polymer‐dispersed liquid crystals (PDLCs) with methyl acrylate. The memory effect of these PDLCs was investigated. The results showed that remarkable memory effect exhibit only in PDLCs with high and low T_g block chain. The possible mechanism responsible for the behavior is sketched. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 729–732, 2010     

Liquid dewetting of ultrathin polystyrene films: Is there a molecular architecture effect?

We have used a liquid dewetting method to investigate the glass transition temperature T_g of high molecular weight linear, long branched 3-arm star, and short branched 8-arm star polystyrene (PS) in the form of ultrathin films. The results of these dewetting experiments are consistent with prior studies of dewetting of linear PS films and show that, independent of molecular architecture, the glass transition temperature T_g reductions with decreasing film thickness, while important below about 20 nm, are weaker than those observed for linear PS supported on a rigid substrate and as well as those observed in freely standing films. The lack of a strong molecular architecture effect on the T_g-reductions is consistent with the T_g reductions for the dewetting from a liquid substrate reflects changes in segmental dynamics upon confinement rather than chain effects. This contrasts with changes, including increases seen in dewetting from a rigid substrate, for different molecular architectures reported in the literature.     

Analysis of packing factors of crystalline polymers in terms of the glass transition to melting temperature radio

An expression for the ratio of the glass transition temperature to the melting temperature, T _g/T _m, was derived with allowance for fluctuations of the packing factor in the amorphous state. This relationship made it possible to describe the actual range of variation in T _g/T _m depending on a change in the packing factor in the crystalline state k _{o, cr}. The proposed approach forms the basis for the method of determination of increments in the packing ratio k _{o, cr} and formulation of the principles of selection of experimental data for calculations. The glass transition temperatures in polyethylene depending on the type of unit cell were calculated.     

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.     

Temperature dependence of the dynamic mechanical properties of filled polymers

A theory has been developed to explain the jump in the relative modulus of filled polymers near the glass transition temperature T_g and the subsequent decrease in relative modulus at temperatures above the glass transition temperature. The theory is based upon the concept that there are some particle–particle contacts in doublets and in agglomerates containing a larger number of particles. Below T_g motion of particles at the contact points is possible because of the high modulus of the polymer. At T_g particle–particle motion mostly ceases because of the low modulus of the polymer. At higher temperatures, the mismatch in the coefficients of expansion allows some motion to occur at points of contact and slippage may occur at the polymer–particle interfaces, so the modulus decreases. It is shown theoretically and experimentally that both the elastic modulus and the mechanical damping depend upon the nature of the surface of the particles.     

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     

Pressure dependence of dielectric properties of chlorinated polyethylene vulcanizate. III. β relaxation

The effects of temperature and pressure on the shift factor and the dielectric increment of the β relaxation process were measured for vulcanized chlorinated polyethylene. The isobaric and isochoric activation enthalpies, H^*_P and H^*_V, the activation volume V^*, the pressure dependence of the glass–glass transition temperature, T_gβ/dP, and the apparent extinction temperature T_0β were obtained. The pressure dependences of both V^* and the dielectric increment would reach very small values near the liquid–glass transition temperature T_g, and the β process seems to be affected by the transition near T_g. The value of H^*v/H^*p for the β process is larger than that for the α process, and it is suggested that the molecular motions pertaining to the β process are more strongly restricted than those pertaining to the α process. The ratio T_0β/T₀, where T₀ is the characteristic temperature in the Vogel–Fulcher–Tammann–Hesse equation for the α process, follows the empirical relation of Matsuoka and Ishida, T_gβ/T_g ～0.75. The value of dT_gβ/dP estimated from T_g and T_0β/T₀ is consistent with the experimental value.     

Thermal stability and crystallization kinetics of Pb and Bi borate-based glasses

Glasses with compositions 60B₂O₃–40PbO, 60B₂O₃–40Bi₂O₃, and 60B₂O₃–30Bi₂O₃–10PbO have been prepared and studied by differential thermal analysis. The crystallization kinetics of the glasses was investigated under non-isothermal conditions. From dependence of the glass transition temperature (T _g) on the heating rate, the activation energy for the glass transition was derived. Similarly the activation energy of the crystallization process was determined. Thermal stability of these glasses were achieved in terms of the characteristic temperatures, such as the glass transition temperature, T _g, the onset temperature of crystallization, T _in , the temperature corresponding to the maximum crystallization rate, T _p, beside the kinetic parameters, K(T _g) and K(T _p). The results revealed that the 60B₂O₃–40PbO is more stable than the others. The crystallization mechanism is characterized for glasses. The phases at which the glass crystallizes after the thermal process have been identified by X-ray diffraction.     

The volume structural relaxation theory for amorphous polymers

An interpolation model of density fluctuations in amorphous bulk polymers is suggested for the explanation of some peculiarities of structural relaxation of amorphous polymers volume. The main peculiarities of the model are (i) its account of the influence of fluctuations in the region where the WLF theory is true (the region of large fluctuations); (ii) its account of small fluctuations in the region where the dissipation mechanism appears to be considerably different from that in the region of large fluctuations; and (iii) its joining of the solutions of the resulting kinetic equations in the crossover region. On the basis of the suggested model we have obtained an equation of the Fokker-Plank type for the distribution function for density fluctuations with nontrivial boundary conditions for large fluctuations, and a quasistatic solution for small ones. These equations are analyzed and numerically solved in the isothermal regime. The results show that the theory corresponds to the WLF theory at temperatures much higher than T_g and that memory effects are found in the T_g region. In addition, preliminary estimates show that near T_g an extreme form of temperature dependence on activation energy is observed. All these facts agree qualitatively with experiment.     

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     

Fluorescence spectroscopy of C60 in toluene solutions at 5 K

We have recorded the dispersed fluorescence and the fluorescence excitation spectra of C₆₀ in toluene matrices at 5 K. Upon excitation with the green Ar⁺ laser line (λ=514 nm) we obtained for the first time in this matrix well resolved visible fluorescence spectra which we have compared with those observed in other low temperature matrices. Our spectra were interpreted and assigned using theoretical assessments of vibronic activities of transitions between the three lowest excited electronic states ¹T_1g, ¹T_2g, ¹G_g and the totally symmetric ground state, and on the basis of a single 0⁰ level which has pseudo-Jahn–Teller (JT) components of the three near-degenerate excited states. The fluorescence spectra exhibit prominent JT induced h_g(1) progressions, Herzberg–Teller-induced h_u and other ungerade mode vibrations, including a very active t_1u(4) mode. Excitation wavelength independent bands are assigned to the fluorescence of C₆₀ molecules in toluene microcrystals embedded in the toluene glass whereas excitation wavelength dependent features are interpreted as originating from C₆₀ molecules isolated in the toluene glass itself. These interpretations are supported by the results of spectrally selective detected fluorescence excitation spectra.