New aspects of chain-length dependent termination

A survey is given on a selection of recently developed methods for the evaluation of the rate coefficient k_t of termination and its chain-length dependence. In particular these are the time-resolved single-pulse pulsed laser polymerization (TR-SP-PLP), the single pulse pulsed laser polymerization in combination with the analysis of the molecular weight distribution produced (SP-PLP-MWD), the methods yielding an average k_t either from the second moment of the chain-length distribution (CLD) or from the rate of polymerization, and a method focusing on the chain-length dependence of k_t consisting in an analysis of the CLD resulting from PLP experiments carried out at low pulse frequencies (LF-PLP). The results obtained by these methods are compared and discussed. The role of the shielding of the two radical chains by their appendant coils is emphasized.     

Atomic mechanism of fracture of solid polymers

Macromolecular chain scission under mechanical stress has been studied by infrared spectroscopy. The dependence of accumulation of chemical bond scissions on temperature T and uniaxial tensile stress σ has been investigated. The rate constant K for bond dissociation under mechanical stress has been found to obey the modified Arrhenius equation: K = K₀ exp{ ? (E_A ? ασ)/RA}. The quantitative connection between the rate constant for bond dissociation and mechanical lifetime τ has been established. Analysis of the experimental data indicates that the strength and mechanical lifetime of polymers is determined by the kinetics of mechanochemical scission of the main chains of polymer molecules.     

Statistical mechanical model of diffusion of complex penetrants in polymers. I. Theory

A previously developed model of simple penetrant diffusion is extended to encompass complex penetrants of idealized molecular shape, characterized by dimensions of length, width, and thickness. Expressions are obtained for D(0,T), the diffusion coefficient at zero penetrant concentration (c), and the fractional increase in D(0,T) as a function of c and temperature (T). The model predicts that D(0,T) will exhibit Arrhenius behavior at temperatures well above T_g and gives the limiting activation energy as a function of penetrant thickness and the polymer energy/distance constants used previously. For T_g < T ? T_g + 150 K the model requires two new disposable parameters, in addition to the jump-length parameter of the simple penetrant theory. These parameters, however, have precise physical meanings (all are lengths) and together with the penetrant dimensions and polymer constants determine the absolute magnitude of the diffusion coefficient as well as its relative dependence on c and T. For T ? T_g + 40 the relative concentration dependence may be calculated in terms of the penetrant dimensions and polymer constants only.     

The incorporation of side reactions into pseudostationary polymerization, 3. The closed solution of a kinetic scheme for pulsed-laser polymerization comprising concomitant continuous initiation

A procedure is developed that allows the calculation of chain-length distributions of polymers prepared by periodic modulation of the initiation process considering concomitant continuous initiation. For the case of a (pseudostationary) laser-pulse initiated polymerization process a closed solution could be derived for the pseudostationary radical concentration and for the chain-length distribution of dead polymer terminated by disproportionation or stabilized by chain-transfer to monomer or solvent. The analysability of the characteristic peaks appearing in the chain-length distributions of laser-pulse initiated polymers (which is the key for determining the rate constant k_p) is only moderately influenced by continuous thermal radical formation if the extent of this side reaction is not pathologically large, i.e. as long as the amount of primary radicals created by the laser-pulse appreciably exceeds that produced in the dark reaction.     

Osmotic pressure,atomic pressure and the virial equation of state of polymer solutions: Monte Carlo simulations of a bead-spring model

A recently introduced coarse-grained model of polymer chains is studied analyzing various contributions to the pressure as obtained from the virial theorem as a function of chain length N, temperature T and density ϕ. The off-lattice model of the polymer chains has anharmonic springs between the beads, but of finite extensibility, and the Morse-type interaction between beads is repulsive at very short distances and attractive at intermediate distances. Solvent molecules are not explicitly included. It is found that the covalent forces along the chain (modelled by the spring potentials) contribute a negative term to the pressure, irrespective of temperature, which vanishes linearly in ϕ as ϕ → 0. In contrast, both contributions to the pressure due to intrachain nonbonded forces and due to forces between different chains change sign from high temperatures (T ≫ θ, θ the theta-temperature) where they are positive, to low temperature where both parts of the pressure become negative. It is shown that the total pressure has the expected behavior with temperature near the θ-temperature, i.e., Δp ≡ p_tot − k_B · T_p ∼ (T − θ). We study also the concentration and chainlength dependence of the various contributions to the pressure in the good solvent regime and interpret them with scaling predictions.     

Glass transition in poly(propylene glycol) networks

Difficulty in controlling and determining the structural parameters of polymer networks has hindered experimental studies on the glass transition in crosslinked polymers. A series of wellcharacterized networks of poly(propylene glycol) having narrow network chain-length distributions and average molecular weight between crosslinks M _c in the range of 425–3000 has been prepared. The glass transition temperatures T_g of these networks were found to vary linearly with M , consistent with several theoretical treatments. Both the physical crosslinking and the incorporation of crosslinking agent into the system (a “copolymer” effect) are shown to be responsible for increase in T_g upon crosslinking in this system. Varying the network chain-length distribution without changing M _c did not affect the T_g of the system. The chemical nature of the crosslinking agent, however, does affect the T_g of the network, particularly at high crosslink densities.     

Open spaces and molecular motions of polyether-based network polymers probed by positron annihilation

The lifetimes of positrons have been measured for network polymers based on polyethers. From the temperature dependence of the lifetime of ortho-positronium (o-Ps), τ₃, for the network polymer of poly(ethylene oxide-co-propylene oxide) [P(EO/PO)], an onset temperature for limited local motions of molecules, T_γ, and the glass transition temperature, T_g, were determined to be 57 and 201 K, respectively. For the network polymer of poly[EO-co-2-(2-methoxyethoxy)ethyl glycidyl ether] [P(EO/MEEGE)], T_γ and T_g were determined to be 57 and 185 K, respectively. For both specimens, above 270 K, the observed linear temperature dependence of τ₃ was attributed to the thermal expansion of open spaces in a liquid state. In the temperature range between T_γ and 270 K, for the P(EO/MEEGE) network, τ₃ was longer and its intensity was smaller than those for the P(EO/PO) network. These results were attributed to the increase in the size of open spaces for the P(EO/MEEGE) network polymer and the blocking of these regions by motions of side chains and chain ends. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1919–1925, 1998     

Influence of macroinitiator’s glass transition temperature on the response times of polymer dispersed liquid crystals

Glass transition temperature (T_g), an important parameter of polymer, was reported to have great influence on the electro-optical properties of polymer dispersed liquid crystals (PDLCs). In this study, macroinitiators with different T_g were synthesised by reversible addition fragmentation chain transfer polymerisation, and used to prepare PDLCs with different T_g block chains. The effect of different T_g of the block chains on response times was investigated. It was found that rise time decreased and decay time increased with the decrease of the block chain’s T_g. We proposed a possible mechanism by which T_g of the block chains influence response times.     

A molecular approach to the spurt effect in polymer melt flow

The Doi-Edwards theory of polymer melts, extended to include relaxation processes associated with chain-length equilibration, is used to make quantitative predictions of a discontinuity in the flow curve of a monodisperse melt in a capillary. A fluid interface between regions of high and low deformation rates is found to propagate from the former into the latter. Our results for the “spurt” and its hysteresis compare favorably with experiment using a molecular weight dependence of the ratio of “reptation time” (T_d) to “equilibration time” (T_eq) in agreement with that determined from nonlinear stress relaxation.     

Tensile flow and stress–strain behavior over a wide temperature range for poly(butyl methacrylate) with a broad molecular weight distribution

The poly(butyl methacrylate) studied is a polymer with a normal molecular weight distribution and a relatively low molecular weight close to M_c, the critical molecular weight from the viscosity–molecular weight relation. The polymer was subjected to uniaxial extension and shear over a temperature range which included T_g. It was found that in the region of T_g an increase in applied stress is accompanied by a decrease both in the temperature shift factor a_T and in the activation energy for relaxation and rupture of polymer melts. Close attention is given to the long-term durability of the polymer. As is expected in the temperature range below T_g, its dependence on the stress is exponential, whereas at temperatures above T_g a power law fits the data. In the latter case a log-log plot of the long-term durability versus stress can be represented by two intersecting straight lines which can be replotted as a generalized straight line if the long-term durability values are normalized by the viscosity.     

Study of the dissolution process of polystyrene in concentrated cyclohexane solution by MNR relaxation

 ¹³C-NMR relaxation times of polystyrene (PS) chains in its theta solvent, cyclohexane, have been measured at different temperatures. It was found that relaxation of carbon nuclei of the side-chain-phenyl groups and those of main chains have remarkably different temperature-dependent relaxation behaviors in the solvent. A two-step model for the dissolution process is proposed. According to the model, swelling of the polymer below θ temperature corresponds mainly to the gradual dispersion of the side-chain phenyl groups; while the complete dissolution above θ temperature corresponds mainly to the gradual dispersion of the main chains at a molecular level. These dispersions reflect the fact that cohesional interaction among side-chain-phenyl rings or main chains are weakened by solvent molecules, which shows the existence of the cohesional entanglements among polymer chains. The results of T ₁(C) are confirmed by the biexponential dependence of ¹H-NMR spin–spin relaxation on temperature. Received: 2 July 1997 Accepted: 21 October 1997     

Branched polymer via free radical polymerization of chain transfer monomer: A theoretical and experimental investigation

A simple mathematic model for the free radical polymerization of chain transfer monomers containing both polymerizable vinyl groups and telogen groups was proposed. The molecular architecture of the obtained polymer can be prognosticated according to the developed model, which was validated experimentally by homopolymerization of 4‐vinyl benzyl thiol (VBT) and its copolymerization with styrene. The chain transfer constant (C_T) of telogen group in a chain transfer monomer is considered to play an important role to determine the architecture of obtained polymer according to the proposed model, either in homopolymerization or copolymerization. A highly branched polymer will be formed when the C_T value is around unity, while a linear polymer with a certain extent of side chains will be obtained when the C_T value is much bigger or smaller than unity. The C_T of VBT was determined to be around 15 by using the developed model and ¹H NMR monitored experiments. The obtained poly(VBT) and its copolymers were substantiated to be mainly consisted of linear main chain with side branching chains, which is in agreement with the anticipation from the developed model. The glass transition temperature, number average molecular weight, and its distribution of those obtained polymer were primarily investigated. This model is hopefully to be used as a strategy to select appropriate chain transfer monomers for preparing hyperbranched polymers. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 1449–1459, 2008     

Investigation of molecular motions of crosslinked polyepichlorohydrin by nuclear magnetic resonance spectroscopy

The molecular motion of crosslinked polyepichlorohydrin (PECH) is studied qualitatively by NMR techniques. The results of temperature dependence of ¹H T₂ and T₁ indicate that the crosslinking (crosslink density < 3%) restricts molecular motions of the polymer even far above its T_g. The ¹H T₁ minimum, corresponding to the large-scale chain-motion of crosslinked PECH, shifts to higher temperatures with increasing crosslink density. ¹H T₂ data also show that the crosslinking hinders free chain motions of the polymer above its T_g. The ¹³C T₁ relaxation time is sensitive to such motional changes as well. ¹³C linewidths of crosslinked PECHs vary with the crosslink density in both the swollen state and the solid state. The mechanism of ¹³C linewidth broadening of crosslinked polymers is discussed in detail. In the case of PECH, the linewidth broadening is caused by changing molecular environment due to crosslinking (such as presence of various chemical shift structures and freezing effects in conformational environment as chain mobility decreases), rather than increasing correlation times, which shorten the relaxation time (T₂) of polymer chains. © 1994 John Wiley & Sons, Inc.     

Brillouin scattering in amorphous polymeric solids

Brillouin scattering of laser light has been used to study the temperature dependence of phonon velocity in a variety of amorphous polymeric systems, particularly internally and externally plasticized methacrylates. Discontinuities in the temperature coefficient of the hypersound velocities are observed at the glass transition temperatures (T_g). This phenomenon is related to changes in the temperature behavior of the specific volume accompanied by corresponding discontinuities in certain second-order thermodynamic quantities. This method was also used to examine the temperature dependence of the Landau-Placzek ratio. This ratio is relatively large in polymer systems and appears to be independent of temperature in the region of the glass transition, provided that there are no internal strains in the sample at the temperature of measurement. Evidence is presented which suggests that the abrupt changes in this ratio at T_g reported by earlier workers were due to kinetic effects related to the relaxation of internal strains above T_g, and the results of recent studies by other investigators, both corroborating and supplementing the present work, are reviewed.     

Mutual diffusion and thermodynamics in the blends of polystyrene and tetramethylbisphenol-A polycarbonate

A study was made of miscible polymer blends of deuterated polystyrene (d-PS) and tetramethylbisphenol-A polycarbonate (TMPC). The Flory interaction parameter χ was obtained from the relation between mutual and tracer diffusion coefficients, D? and D^*, which were measured by forward recoil spectrometry. The temperature dependence of diffusion at PS weight fractions ω of 0.25 and 0.5, and the composition dependence at temperatures 45°C above the glass transition temperature, T_g, were investigated. A stronger dependence of χ on both temperature (at ω = 0.5) and composition was observed in comparison with other miscible binary polymer blends involving PS. Analysis using the generalized lattice-fluid model of Sanchez and Balazs¹ showed that the incorporation of a significant specific interaction is needed to explain the temperature dependence of χ. The diffusion coefficients obtained in the one-phase region were extrapolated to the two-phase region, and these were compared with the effective diffusion coefficient extracted from phase separation dynamics measured by light scattering.² A significant discrepancy between the extrapolated and effective diffusion coefficients was observed. © 1995 John Wiley & Sons, Inc.     

A MONTE CARLO STUDY OF THE GLASS TRANSITION OF POLYMETHYLENE*

By this Monte Carlo simulation we studied the glass transition of polymethylene using themodified bond-fluctuation model combined with considering the rotational-isomeric state model. Theconfigurational properties in the polymethylene (PM) melts, such as the mean length, the mean energy perbond and the mean square radius of gyration were monitored. We found that the chains cannot be in theequilibrium states after a very long time when the temperature of the dense PM chains decreases to 120 K. Asthe melt vitrifies, these quantities gradually become independent of temperature in a narrow range. The glasstransition temperature T_g depends upon the chain length of PM chains, and extrapolation to (CH_2)_∞givesT_g~∞=212 K. The dynamics in the PM melts was also studied. It was found that the diffusion coefficients canbe described by the Vogel-Fulcher law and the Vogel-Fulcher temperature T_0 is 124 K. This method may beused to investigate the glass transition of other real polymer chains.     

Rebuttal to “comments on ‘some evidence against the existence of the liquid–liquid transition. IV. The temperature dependence of shear viscosity’”

Data on the temperature dependence of viscosity obtained on three different polystyrenes with narrow molecular weight distributions are fitted to the Vogel, Fulcher, Tamman, and Hesse (VTFH) equation as well as to two intersecting Arrhenius lines. Both fits are optimized by means of computer programs. The data were chosen to fit the requirements stated by Boyer. The results of the analyses support the earlier conclusions that temperature-dependent viscosity data do not indicate the presence of any liquid-liquid transition T_LL above the glass temperature T_g. In addition, evidence is presented which indicates that the viscosity at T_g of high-molecular-weight polystyrenes is proportional to the 3.4 power of the molecular weight. Hence T_g is not an isoviscous temperature.     

Statistics of stiff polymer chains near an adsorbing surface

The exact solution of the problem of adsorption of a long ideal polymer chain with variable degree of stiffness on a plane surface is presented. It is shown that the adsorption of stiff polymer chains is a second-order phase transition; in the adsorbed state “train” (i.e. adsorbed) sections are relatively longer and loop sections relatively shorter than for flexible chains. This effect is very pronounced: already for moderately stiff chains the number of Kuhn segment lengths in one “train” section at the temperature T = T_cr/2 (T_cr is the critical temperature for adsorption transition) can reach several thousands, and deviation from the surface occurs only in the form of small “hairpins”. The maximum length of the chain, which at the given conditions would flatten completely on the surface, is estimated.     

Photopolymerization kinetics of oligo(ethylene oxide) and oligo(methylene) oxide dimethacrylates

The influence of temperature on the photopolymerization kinetics of oligo(methylene) oxide and oligo(ethylene oxide) dimethacrylate series has been investigated by isothermal DSC. The DSC curves showed a rapid rise in rate due to the Trommsdorff effect, and then a slow decline. A shoulder, apparent on many of the DSC curves at low conversions, became more prominent when the cure temperature was lowered. The kinetics were relatively insensitive to the dimethacrylate structure in the early stages of the reaction, but became more dependent as the reaction proceeded. A previously derived mathematical model, which allows for the influence of diffusion on the rate constants, was used to predict the kinetics. The dependence of the maximum rate and conversion on the curing temperature were adequately described by the model. The experimentally observed shoulder on the rate curve was also predicated as was the evolution of the rate/time curves with curing temperature. Similar predictions were found when a nonsteady state version of the model was used. The radiation intensity exponent varied from 0.3 to 0.6 possibly due to chain-length effects and pseudo-first order termination, respectively. The final degree of conversion increased with curing temperature (T_cure) and was correlated with the flexibility of the dimethacrylate. These data were fitted to a theoretical expression relating the final conversion to the resin T_g and to the T_cure. © 1993 John Wiley & Sons, Inc.