Raymond F. Boyer

Dynamics and thermodynamics of the liquid state (T < Tg) of amorphous polymers

Abstract The liquid state behavior of the following atactic polymers has been reviewed: the alkyl and cycloalkyl methacrylates; polyisobutylene; polybutadiene, its random copolymers with styrene and acrylonitrile, and S-B diblocks; polystyrene; and the poly-α-olefins C3, C5, and C6. Just as Tg manifests itself through time-dependent (relaxational) and thermodynamic (transition) effects, so also does a T Tg or Tβ relaxation. With increasing syndiotactic content, PMMAs reveal strengthening Tβ and Tl processes. Relaxation maps plotting log frequency-T−1 are presented for PBD and PIB, showing both Tg and Tl. The latter exhibits non-Arrhenius behavior with an activation enthalpy about half that at T...

Dielectric loss of an oligomeric poly(propylene oxide) in the liquid region above Tg

Abstract Dynamic dielectric studies of oligomeric poly(propylene oxide) (PPO) of M n =3034 , between −10° and 40°C at 0.1, 1, and 10 KHz, reveal a glass transition and a T >Tg liquid-liquid transition. Analysis of d ϵ′ d T in the liquid region of PPO also indicates the presence of T11. The activation enthalpies for the Tg and T11 transitions have been calculated to be 39 and 18 kCal mol−1, respectively. The T11 transition in poly(propylene oxide) has been assigned to the motion of the entire polymer molecule.

Dependence of Tg and T ll on tacticity of PMMA by differential scanning calorimetry

Abstract A differential scanning calorimeter (DSC) investigation (heating rate 10 K/min) is presented on the multiple transition (relaxation) spectra of PMMA: Tβ Tg; and Tlρ > Tll, as a function of tacticity. Specimens are characterized by fractional triad content: isotactic (it-), Xii; syndiotactic (st-), Xss; and atactic (at-), Xis. Values for the seven specimens are it-, 1.0;, at-, 0.495 to 0.750; st-, 0.958. Results on Tβ were inconclusive. Our Tg results clarify some discrepancies in the prior literature. Linear least squares regression analyses give: Tg (°C) = 56.6 + 76.6 Xss (our data) Tg (°C) = 49.1 + 87.3 Xss (our data plus selected literature data) Extrapolated Tg s for Xss = 1 are 133.2°C and 136.1°C, respectively, in contrast to Thompsons extrapolated value of 160°C. Similarly Tg(°C) = 99.5 + 71.6 (1−Xii) for our DSC data. The extrapolated Tll for Xss = 1 is 171.1°C. The intensity of Tll is high for st-and it-, with a broad minimum over the at-region. A second liquid state pr...

Evidence from T ll and Related Phenomena for Local Structure in the Amorphous State of Polymers

We have recently completed what we conceived as a definitive review of T ll and related liquid state transitions (relaxations) in the T>T g region of atactic polymers and the T>T m region of crystalline polymers.1 A table of contents appears on page 233 of that article. In general the subject matter covered definition of terms, history, theories for T ll , experimental techniques, practical significance, and a guide to the literature.

Polymer chain cross-section and the Mooney-Rivlin constants

Abstract We started with a critical examination of published Mooney-Rivlin constants on the common commercial elastomers and some experimental ones. Following a suggestion by Treloar, plots were made of C2/C1 against 2C1 in order to select values of the ratio at constant 2C1 in comparing all elastomers. We found empirically that a log-log plot of C2/C1 against 2C1 seemed to be either linear or slightly concave downwards. This fact facilitated the extrapolation which was necessary in several instances. Cross-sectional areas of elastomer chains in the amorphous state were assumed to be proportional to areas for the same polymers in the crystalline state. (The areas of copolymers were obtained from an averaging process of the areas of the corresponding crystalline homopolymers.) A plot of log C2/C1 against log (area per chain) is linear, as seen in Figure 7, with a slope of about −2. This is, to our knowledge, the first positive correlation of Mooney-Rivlin constants with a specific molecular parameter. It i...

Correlations involving the Mooney—Rivlin C2 constant and the number of chain atoms between physical entanglements, Nc

Abstract We start with two previously calculated semi-empirical equations: (1) C 2 C 1 = K 1 A −2 (for 2 C 1 = 0.2 MPa). K 1 is a constant and A is the area per polymer chain; (2) N c = K 2 A 0.67 where K 2 is another constant. It follows from these two relationships that: C 2 C 1 (at 2 C 1 = 0.2) = K 3 N −3 c . N c , determined for bulk polymers, increases on dilution with a solvent according to N c ( o 2 ) = N c ( o 2 = 1) o − r 2 where o 2 is the volume fraction of elastomer and r is a constant for a given elastomer, usually unity. For vulcanizates prepared in the presence of diluents but tested in the bulk state, one predicts C 2 C 1 = K 4 o 3r 2 if entanglements are the sole source of the C 2 term. Plots of log C 2 C 1 against log o 2 show slopes ranging from 0.5 to 3.0 but more commonly near unity. There is wide discrepancy between different authors. We conclude that chain entanglement cannot be the sole source of the C 2 term but that several factors probably operate. Different theories and ideas about the origin of the C 2 term are briefly reviewed. Excellent linear plots of log C 2 C 1 against log 2 C 1 are presented for trans -polypentenamer and for Hevea rubber. In general, sufficient data for the rigorous testing of the C 2 C 1 —o 3r 2 relationship are not available. A correlation of f e f with area per chain (where f e is the energetic contribution to the total force, f ) increases rapidly at small areas but levels off above ∼ 0.4 nm 2 . All studies reported herein are based on published data.

DSC evidence for Tu > Tm in n-alkanes and polymers

SummaryWe agree with Claudy and Létoffé that oxidation of hydrocarbons can occur in closed DSC pans because of entrapped O2. We do not find oxidation in open pans under flowing N2 unless dissolved O2 is present in the polymer. We report a Tu > Tm in trans polyisoprene by DSC (open pan) and by dynamic mechanical loss. Our work supports the existence of the Tu transition of Krüger and coworkers.

Thermal evidence for a transition above Tm in n-alkanes and crystalline polymers

SummaryA series of n-alkanes, CH3-(CH2)nCH3, including polyethylene, crystalline polymers, and crystalline copolymers have been studied by differential scanning calorimetry at very high sensitivity through and above the melting temperature, Tm. A transition designated Tu after KRÜGER et al. is observed at about 1.2 Tm (K) (range 1.10 to 1.42). In low n-alkanes it appears as an endothermic slope change, shifting to an endothermic step change as n exceeds 100. This step change is also characteristic of polymers. Tu is rate sensitive, increasing as the rate of heating increases. Tu by DSC is higher than values reported by KRÜGER et al. from Brillouin scattering and kinematic viscosity. Tu may correspond to the temperature at which persistent structures (smectic, mesomorphic, hetical, etc.) are destroyed thermally.

Differential Scanning Calorimetry (DSC) Observation of the T ll Transition in Polystyrene

The T ll liquid-liquid transition in atactic polystyrene can now be determined reproducibly on fused films of polymer in standard DSC equipment. Computer analysis of published adiabatic calorimeter data in polyisobutylene showed that the increase in C p above T g does not follow the quadratic usually assumed, but is much better fitted by three straight lines. We identify the first intersection with T ll , a liquid-liquid transition. By analogy, DSC thermograms on fused films of polystyrene should show an endothermic slope change above T g . For anionic polystyrenes T ll increases with increasing molecular weight but levels off asymptotically at a limiting value of around 435 K. This is called T ll (∞). The ratio T ll /T g is essentially constant with a range of 1.15 to 1.17 and an average of 1.16 for six specimens varying in molecular weight from 600 to 2,000,000. It does not change nature at M c , the critical weight for chain entanglement, as it does when measured by torsional braid analysis (TBA) and by DSC on powders. The latter involve melt flow, whereas DSC on fused film does not. The magnitude of the slope change at T ll is found to be dependent on the thermal history of the specimen. The greatest effect is observed when the specimen is annealed for 20 to 60 minutes about 5 to 10 K below T ll . The intensity of the T ll transition was also found to decrease as a function of crosslink density in a series of polystyrenes crosslinked with 0 to 5.5% divinylbenzene.

Dielectric Investigations of Poly(Propylene oxide) in the Liquid Region Above T g

Transitions and relaxations in poly(propylene oxide) (PPO) have been extensively studied by dynamic mechanical1–3 and dielectric4–7 methods. The molecular weight range of poly(propylene oxide) investigated by dynamic mechanical methods is much larger (400–1,000,000) than the range studied by dielectric methods (400–4,000). Both the dynamic mechanical and dielectric data have always been presented as a function of frequency or reduced frequency. Dielectric studies on poly(propylene oxide) oligomers by Baur and Stockmayer7 showed two dispersions in e′ and e″. The high frequency process corresponds to the segmental motion at the glass transition and the low frequency process corresponds to the motion of the entire polymer molecule. The maximum in e″ for the glass transition temperature dispersion is invariant with the molecular weight of PPO, whereas the maximum in e″ corresponding to the “slow process” moves to lower frequencies and becomes more diffuse with increasing molecular weight. Although Yano et al.8 reported the dielectric loss as a function of temperature, they were only interested in the T g loss peak and not the T >T g peak. McCammon and Work5 were also interested only in the T g and T>T g peaks in their dielectric studies. In addition, they used a high molecular weight, partially crystalline PPO in their investigations. Creep, creep recovery, and dynamic mechanical measurements as a function of frequency by Cochrane et al.9 and Barlow and Erginsav10 in the 103–108 Hz region and dielectric data of Alper et al.11 for PPO of nominal molecular weight 4,000, showed the existence of a slow process attributed to the motion of the entire polymer molecule.