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1.
Measurements of average free volume hole sizes, 〈vf〉, and the fractional free volumes, fps, 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, 〈vf〉 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 (Tg) but have less influence on the packing density in the glass. Scaling relationships between 〈vf〉, fps, the thermal expansion coefficient αf = dfps/dt, and Tg are examined. We find that 〈vfg, the hole volume at Tg, and fps,g, the fractional free volume at Tg, each increase significantly with increasing Tg. 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-Tg 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, Δαf = αf,l − αf,g, increases slowly with Tg, as predicted by free volume theory. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2754–2770, 1999  相似文献   

2.
The microstructure of the free volume was studied for an amorphous perfluorinated polymer (Tg = 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, Vf = hV and Vocc = (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 Vocc has a particular high compressibility, while the compressibility of Vf 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, 〈vh〉, and mean dispersion, σh, were calculated. From a comparison of 〈vh〉 with Vf a constant hole density of Nh′ = 0.25 × 1021 g?1 was estimated. The volume of the smallest representative freely fluctuating subsystem, 〈VSV〉 ∝ 1/σh2, is unusually small. This was explained by an inherent topologic disorder of this polymer. 〈vh〉 and σh show an exponential‐like decrease with increasing pressure P at 298 K. The hole density, calculated from Nh′ = Vf/〈vh〉, 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  相似文献   

3.
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.  相似文献   

4.
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, Tgβ/dP, and the apparent extinction temperature T were obtained. The pressure dependences of both V* and the dielectric increment would reach very small values near the liquid–glass transition temperature Tg, and the β process seems to be affected by the transition near Tg. 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/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, Tgβ/Tg ~0.75. The value of dTgβ/dP estimated from Tg and T/T0 is consistent with the experimental value.  相似文献   

5.
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.  相似文献   

6.
The melt viscosity, the glass transition, and the effect of pressure on these are analyzed for polystyrene on the basis of the Tammann-Hesse viscosity equation: log η = log A + B/(T ? T0). Evidence that the glass transition is an isoviscosity state (log ηg ? 13) for lower molecular weight fractions (M < Mc) is reviewed. For a polystyrene fraction of intermediate molecular weight (M ? 19,000; tg = 89°C.), it is shown that B is independent of the pvT state of the polymer liquid and that dT0/dP = dTg/dP. This is consistent with the postulate that B is determined by the internal barriers to rotation in the isolated polymer chain. Relationships are derived for flow “activation energies” at constant pressure and at constant volume, and for the “activation volume.” Values for polystyrene along the zero-pressure isobar and along the constant viscosity, glasstransition line are reported. For the latter, ΔVg* is constant and corresponds to about 10 styrene units. The “free volume” viscosity equation: log η = log A + b/2.3?, is reexamined. For polystyrene and polyisobutylene, ?g/b = 0.03, but ?g and b themselves differ appreciably in these polymers. The parameter b is the product of an equilibrium term Δα and the kinetic term B, and none of these is a “universal” constant for different polymers. The physical significance of the free volume parameter ?, particularly with regard to the “excess” liquid volume, remains undefined. Two new relationships for dTg/dP, one an exact derivation and the other an empirical correlation, are presented.  相似文献   

7.
A theory of the liquid state, suitably modified for the glass, contains a characteristic structure functionh, which represents a free volume fraction. As shown previously by means of experimental pressure-volume-temperature studies,h retains finite, nonvanishing temperature and pressure coefficients upon passing through the glass transition. These results are now employed to compute the mean-square thermal density fluctuations in poly(vinyl acetate). AboveT g , the result attests again to the satisfactory quantitative performance of the equilibrium theory. BelowT g , two glasses formed at low and elevated pressures, respectively, are considered under quasi-equilibrium conditions. The results show the anticipated initial accord with the approximation proposed by Fischer and Wendorff, involving the isothermal compressibility of the liquid atT g . The theory delineates the increasing departures with decreasing temperature observed in the literature. We comment finally on the trend of the fluctuations on approaching absolute zero. Explicit low temperature calculations remain to be undertaken.Dedicated to Professor Dr. F. H. Müller.  相似文献   

8.
Positron annihilation lifetime spectroscopy (PALS), density, and differential scanning calorimetric (DSC) measurements were used to study systematically the variation of the glass‐transition temperature (Tg) and the size v and number density Nh 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 Va was estimated and used to calculate the fractional free (hole) volume h and value of Nh. The variations of Tg, v, Va, h, and Nh were related to the degree (number and length) of branching. Tg 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, Tg 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 Tg was also found. The number density of holes was estimated to be Nh = 0.49(±0.07) nm?3 and Nh′ = 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 Va. 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  相似文献   

9.
The conductivity, κ, in a suspension of polystyrene sulfonic latex without supporting electrolyte showed a linear dependence on the volume fraction, vf, of the latex for vf<0.03 with a finite intercept. In contrast, this deviated upward from the linear line for vf>0.03. These variations were qualitatively consistent with the dependence of the voltammetric reduction current of H+ on vf without supporting electrolyte. The current values were only a few percent of the theoretical diffusion-controlled current that could be observed in the suspension with supporting electrolyte. This fact indicates the electrostatic immobilization of the hydrogen ions by sulfonic latex particles. A plot of the current against κ at common values of vf showed that the current for vf>0.07 was smaller than the value predicted from the conductivity. This can be explained in terms of a combination of the increase in electrostatically unbounded H+ estimated by conductance measurements and electric migration in which the electrochemical depletion of [H+] also causes the depletion of the latex.  相似文献   

10.
The adiabatic compressibility βS of nitroethane/isooctane is measured from 18 to 900 Hz at reduced temperatures ? ranging from 5 × 10-5 to 5 × 10-2. The zero-frequency compressibility extrapolated from the data is related with the specific heat at constant pressure cp through the theory of Ferrell and Bhattacharjee (FB). The coupling constant g is evaluated from this relation as 0.38, which agrees with that from the thermodynamic definition of g. βS at 900 Hz is observed for nitroethane/3-methylpentane at ? 5 × 10-5-6 × 10-2. A linear plot of the critical part of βS against 1n? gives g = 0.34, which agrees with g from the thermodynamic definition and also with that from ultrasonic absorption. Numerical values of the critical and background components of βS, the isothermal compressibility βT, cp, the specific heat at constant volume cv, and the thermal expansion coefficient αp are calculated for the two mixtures. The expression of βS from Anisimov's theory is found to be consistent with that from the FB theory.  相似文献   

11.
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,vf〉, 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 (Tg - 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.  相似文献   

12.
A diffusive gas-transport isotope effect is used to estimate the size of the free volume element above and below the glass transition for poly(ethyl methacrylate) and poly(vinyl fluoride). The cavity size, as measured by the hydrogen probe molecule, is apparently larger in the glassy region for both polymers than it is above Tg. It is postulated that the number of free volume elements essentially decreases below Tg, so that the total free volume, which is the sum of all such elements, is smaller below the glass transition, in accord with density measurements on bulk polymers.  相似文献   

13.
It was found that the tribosorption of methyl iodide from the gas phase of a closed reactor onto a matrix of KI is described by the rate equation for a reversible first-order reaction v gv , g = mv ts * exp(–td D sp), where v g and v , g are, respectively, the current and equilibrium amounts of methyl iodide in the gas phase; v ts * is the equilibrium amount of methyl iodide tribosorbed per gram of salt; m is the mass of potassium iodide; td is a constant, which characterizes the efficiency of tribodesorption (td = 0.011 ± 0.005 g/J); and D sp is the specific dose of mechanical energy absorbed by the KI powder. The value of v ts * monotonically increased with increasing equilibrium partial pressure of methyl iodide and reached a maximum value of 25 mol/g. The lower limit of the constant td, which characterizes the efficiency of tribosorption, was estimated at 0.1 g/J.  相似文献   

14.
Measurements of the emission of purposely entrained volatiles (Ar and D2O) during the loading and unloading of a bisphenol-A polycarbonate in vacuum are made by quadrupole mass spectrometry. Transient loading events are accompanied by dramatic increases in emission, reflecting a similar rise in the diffusion constant of the measured species. We attribute this change to an increase in size of molecular voids in the polymer network, which accompany the increase in sample volume under load. The results are interpreted in terms of the Dolittle relation in which the diffusion constant depends exponentially upon v*/vf0, the ratio between an activation volume for diffusion and the average size of the relevant voids in the polymer network. Our data suggests that v*/vf0 is unusually low in the D2O-polycarbonate system, which we attribute to a relatively large value of vf0; this would be consistent with the relatively long distance between flexible links in the polycarbonate structure. © 1994 John Wiley & Sons, Inc.  相似文献   

15.
The catalytic activity of the complexes prepared by the reaction of Grignard reagents with ketones, esters, and an epoxide as polymerization catalysts of methyl and ethyl α-chloroacrylates was investigated. The modifiers which gave isotactic polymers were α,β-unsaturated ketones such as benzalacetophenone, benzalacetone, dibenzalacetone, mesityl oxide, and methyl vinyl ketone, and α,β-unsaturated esters such as ethyl cinnamate, ethyl crotonate, and methyl acrylate. Catalysts with butyl ethyl ketone, propiophenone, and propylene oxide as modifiers produced atactic polymers but no isotactic polymers. It was revealed that the complex catalysts having a structure ? C?C? O? MgX (X is halogen) gave isotactic polymers. The mechanism of isotactic polymerization was discussed. In addition, for radical polymerization of ethyl α-chloroacrylate, enthalpy and entropy differences between isotactic and syndiotactic additions were calculated to give ΔHi* ? ΔHs* = 910 cal/mole and ΔSi* ? ΔSs* = 0.82 eu.  相似文献   

16.
Summary Concerning the relation between the experimental heat of fusion H* and the specific volumev of PETP a considerable uncertainty exists in literature. For PBTP obviously no data have been reported. The present paper reports H* andv measurements for undrawn PETP and PBTP samples which have been crystallized from the glassy state or from the melt at different temperatures for different periods of time.For PETP a linear relation is obtained: H* = 1411–1886v (Jg–1). Published values for the specific volumev c of the PETP crystal range from 0.660 to 0.687 cm3g–1. Ifv c = 0.660 cm3g–1 is accepted, a heat of fusion M m = 166 Jg–1 is obtained for the PETP crystal.For PBTP also a linear relation is found: H* = 1296–1628v (Jg–1). Withv c = 0.71 cm3g–1 one obtains H M = 140 Jg–1 as the heat of fusion of the PBTP crystal. The specific volumev a of amorphous PBTP (H* = 0) is 0.796 cm3g–1 which is much higher than the hitherto used values of 0.781–0.782 cm3g–1. The reason for this difference is thatv a cannot directly be measured, because the low quasi-static glass temperature of 15 °C enables quenched PBTP to undergo cold crystallization at 20 °C.
Zusammenfassung Hinsichtlich des Zusammenhangs zwischen experimenteller Schmelzwärme H* und spezifischem Volumenv von PETP bestehen in der Literatur beträchtliche Diskrepanzen. Für PBTP wurden bislang offensichtlich keine Ergebnisse veröffentlicht. In der vorliegenden Arbeit werden Messungen von H* undv für unverstreckte PETP- und PBTP-Proben mitgeteilt, die unterschiedlich lange bei ver-schiedenen Temperaturen aus dem Glaszustand oder aus der Schmelze kristallisiert wurden.Für PETP ergibt sich die lineare Beziehung: H* = 1411–1886v (Jg–1). Literaturwerte für das spezifische Volumenv c des PETP-Kristalls schwanken zwischen 0.660 und 0.687 cm3g–1. Nimmt manv c = 0.660 cm3g–1 als richtig an, so erhält man als Schmelzwärme des PETP-Kristalls H M = 166 Jg–1 = 32 kJ mole–1.Auch für PBTP erhält man eine lineare Abhängigkeit: H* = 1296–1628v. Mitv c = 0.71 cm3g–1 ergibt sich als Schmelzwärme des PBTP-Kristalls H M = 140 Jg–1 = 31 kJ mole–1. Das spezifische Volumen des amorphen PBTP beträgt a = 0.796 cm3g–1 und ist erheblich größer als der bisher angenommene Wert von 0.781 cm3g–1. Die Ursache fÜr diese Diskrepanz liegt darin begündet, daßv a nicht direkt gemessen werden kann, weil wegen der niedrigen quasi-statischen Glastemperatur von 15°C bei abgeschrecktem PBTP die Kaltkristallisation bei 20°C bereits einsetzt.


With 7 figures and 3 tables

Dedicated to Professor Dr. Matthias Seefelder on the occasion of his 60th birthday  相似文献   

17.
This paper reports physical aging results for PMMA, PMMA/PEO blends, PS, PC, PVC and PET (semicrystalline). Also included in this study is amorphous selenium. Temperature down-jumps from equilibrium above Tg to a temperature below Tg were carried out. Relaxed enthalpy, Δh and volume contraction, Δv, were measured. From the aging records, the constant ratio Δhv = Ka was evaluated. For the polymeric samples Ka values of about 2 GPa were observed, thus similar to the inverse value of the isothermal compressibility close to Tg. Similarly for Se the Ka value obtained from Δh and Δv was in fair agreement with its isothermal compressibility.  相似文献   

18.
Chain‐end free volume theory is extended for studying the glass‐transition temperature (Tg) as a function of conversion in hyperbranched polymers. Tg is found to have a non‐linear inverse relationship to the molecular weight for polymers obtained by self‐condensing vinyl polymerization (SCVP). During the monomer conversion process, Tg decreases with the increase in molecular weight (P) in the low conversion range, then levels off in the high conversion range.  相似文献   

19.
Numerical calculations were performed for the viscoelastic properties of dilute solutions of branched star polymers with equal branch lengths as formulated in terms of a bead-spring model by Zimm and Kilb without using the integrodifferential equation approximation method to calculate the eigenvalues. The complex modulus and complex viscosity were calculated as functions of frequency for various combinations of the number of branches f (4, 8, and 13), the number of beads in one branch Nb (= N/f; 20 to 100, where N + 1 is the total number of beads, N the number of springs in the molecule) and the reduced hydrodynamic interaction parameter h* (= h/N1/2 0.05 to 0.3, where h is the hydrodynamic interaction parameter of Zimm and Kilb). The frequency dependence of the complex modulus in the low-frequency range depends mainly on h* and not on Nb if Nb is large enough, and it is very close to that calculated from the eigenvalues for h→∞ obtained by Zimm and Kilb, if h* is about 0.25. As h* decreases from 0.25, the frequency dependence gradually approaches that of the free-draining cash (h→0). Calculations may be carried out for h* values somewhat larger than 0.25 and result in a frequency dependence that is not intermediate to the h → 0 and h → ∞ cases as evaluated by Zimm and Kilb. The physical meaning of such “super-non-free-draining” values of h* is uncertain, however. The intrinsic viscosity ratio g′ = [η]f/[η]lin is an increasing function of h* and changes very slowly with N. For h* = 0.25, g′ is close to the non-free-draining limit for any value of N.  相似文献   

20.
Densities, ρ, viscosities, η, and refractive indices, nD, of glycine (Gly) (0.1 — 0.5 M) in aqueous 1,2‐ethanediol (1,2‐EtD), 1,2‐propanediol (1,2‐PrD), and 1,3‐butanediol (1,3‐BuD) (30% v/v) were measured at 298, 303, 308, and 313 K. Experimental values of ρ and η were used to calculate partial molar volumes, ?0v, partial molar volumes of transfer of Gly from water to aqueous diol solutions, ?0v(tr), Falkenhagen and Jones ‐Dole coefficients, A and B, respectively, free energies of activation of viscous flow, Δμ0*1 and Δμ0*2, per mole of solvent and solute, respectively, enthalpies, ΔH* and entropies, ΔS* of activation of viscous flow. Large positive values of ?0v, and an increasing value of Sv*, for all the three mixtures at each temperature suggest the presence of strong solute‐solvent interaction, and this interaction decreases as the size of alkyl moiety increases from 1,2‐EtD to 1,3‐BuD. Positive ?0v(tr) values tend to decrease with increasing the number of CH2 group, thereby indicating that the electrostriction effect in diols follows the sequence; 1,2‐EtD > 1,2‐PrD > 1,3‐BuD. Small A values, with large values of B, are indicative of weak solute‐solute and strong solute‐solvent interactions that operate in the present systems, and that the magnitudes of B are in the sequence: 1,2‐EtD > 1,2‐PrD > 1,3‐BuD and, thus, the sequence represents the strength of interaction between Gly and diol molecules. Moreover, positive SB/ST values suggest the structure‐breaking nature of Gly in diol + water mixtures. The observed values of Δμ0*2 fall in the sequence: 1,2‐EtD > 1,2‐PrD > 1,3‐BuD which, like ?0v and Sv*, reinforce that Gly‐diol interaction decreases with subsequent addition of CH2 group in diols. The trends in the variation of ΔH* and ΔS* with Gly concentration also reveal the presence of significant solute‐solvent interaction in all three systems. An almost linear increase in RD with an increasing amount of Gly reveals that Gly tends to increase the polarizability of the aqueous‐diol molecules under study. The variation of all these parameters with concentration of Gly and with temperature suggests the presence of strong solute‐solvent interaction, which decreases as the size of alkyl moiety in diols increases from 1,2‐EtD to 1,3‐BuD.  相似文献   

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