Coil‐stretch transition in deformation flows

We present a novel Monte‐Carlo lattice model for the study of the coil‐stretch transition for polymer chains in deformation flows. Our results indicate that elongational flows are much more effective than shear flows in stretching polymer chains, in full agreement with experimental observation. Our model data also show that the ε˙_c∼M^−1.5 powerlaw observed experimentally for the dependence of critical flow rate on polymer molecular weight can be fully explained through a nonuniform stretching of the chain by the flow. A higher powerlaw exponent is predicted in more affine deformation cases. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2422–2428, 2000     

Gamma radiation-initiated polymerization of styrene at high pressure. II. Chain termination

The pressure dependence of the termination rate constant k_t for the free radical polymerization of monomers such as styrene is a function of polymer chain length, chain stiffness, and monomer viscosity, all of which influence the rate of segmental diffusion of an active radical chain end out of the coiled polymer chain to a position in which it can react with a proximate radical. Although k_t is not sensitive to changes in chain length, the large increase in molecular weight is responsible for a significant reduction in k_t at high pressures. For most of the common vinyl polymers, which exhibit some degree of chain stiffness, k_t is inversely proportional to a fractional power of the monomer viscosity because it depends in part on the resistance of chain segments to movement and in part on the influence of viscosity in controlling diffusion of the chain ends. The fractional exponent appears to increase with pressure and this is interpreted as evidence that the polymer chains become more flexible in a more viscous solvent. Because the fractional exponent is higher for more flexible chains, the value of the activation volume for chain termination is an indication of the degree of flexibility of the polymer chains, provided that the monomer is a good solvent for the polymer and that chain transfer is negligible.     

Free‐Radical Termination Kinetics Studied Using a Novel SP‐PLP‐ESR Technique

Summary: A novel method for measuring termination rate coefficients, k_t, in free‐radical polymerization is presented. A single laser pulse is used to instantaneously produce photoinitiator‐derived radicals. During subsequent polymerization, radical concentration is monitored by time‐resolved electron spin resonance (ESR) spectroscopy. The size of the free radicals, which exhibits a narrow distribution increases linearly with time t, which allows the chain‐length dependence of k_t to be deduced. The method will be illustrated using dodecyl methacrylate polymerization as an example.

Two straight lines provide a very satisfactory representation of the chain‐length dependence of k_t over the entire chain‐length region (c_R = radical concentration).     

Chain length‐dependent termination in pulsed‐laser polymerization. VIII. The temperature dependence of the rate coefficient of bimolecular termination in the bulk polymerization of styrene

The photosensitized polymerization of styrene in bulk was investigated in the temperature range of 25–70°C with respect to the average rate coefficient of bimolecular chain termination k̄_t, especially its chain length dependence at low conversions, by means of pulsed laser polymerization (PLP). Three methods were applied: two of them were based on equations originally derived for chain length independent termination taking the quantity k_t contained therein as an average k̄_t, while the third one consisted in a nonlinear fit of the experimental chain length distribution (CLD) obtained at very low pulse frequencies (LF‐PLP) to a theoretical equation. The exponent b characterizing the extent of chain length dependence was unanimously found to decrease from about 0.17–0.20 at 25°C to 0.08–0.11 at 70°C, slightly depending on which of the three methods was chosen. This trend toward more “ideal” polymerization kinetics with rise of polymerization temperature is tentatively ascribed to a quite general type of polymer solution behavior that consists in a (slow) approach to a lower critical solution temperature (LCST), which is associated with a decrease of the solvent quality of the monomer toward the polymer, an effect that should be accompanied with a decrease of the parameter b. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 697–705, 2000     

Microstructure and rheological properties of polybutadienes

The viscosities, rubbery deformations, densities, and their dependence on temperature have been measured for several series of polybutadienes with molecular weights ranging from 5,000 to 400,000 and differing in proportions of cis and trans structures (cis content from 40 to 95%). On the basis of the viscosity measurements the critical molecular weight M_c has been determined, corresponding to a sharp change in the nature of the viscosity versus molecular weight dependence. Rubbery deformations are displayed pronouncedly in specimens with M > M_c and are closely related to the appearance of non-Newtonian flow. The value of M_c depends on the relative content of cis and trans forms. When M > M_c, the initial viscosity is a parameter sensitive to the microstructure of polybutadienes, so that with at a single molecular weight, depending on the ratio of cis and trans units, the viscosity may vary over a more than tenfold range. The glass transition temperature and activation energy of viscous flow rise regularly with increasing trans content in the polymer chain, these parameters becoming independent of the molecular weight for specimens with M > M_c within a series of polybutadienes of equal microtacticity. Thermomechanical investigations of polybutadienes also made it possible to define more accurately the boundaries of the crystallization region and the dependence of the melting point on the microtacticity. The results obtained are discussed on the basis of modern ideas of polymer structure.     

The Influence of Chain Length‐Dependent Propagation on the Evaluation of the Chain Length Dependence of the Rate Coefficient of Bimolecular Termination, 1. PLP–SEC Methods

Chain length distributions have been calculated for polymers prepared by pulsed laser polymerization (PLP) under the condition that not only chain termination but also chain propagation is subject to chain length dependence. The interplay between these two features is analyzed with the chain length dependence of the rate coefficient of termination k_t introduced in the form of a power law and that of propagation k_p modeled by a Langmuir‐type decrease from an initial value for zero chain length to a constant value for infinite chain lengths. The rather complex situation is governed by two important factors: the first is the extent of the decay of radical concentration [R] during one period under pseudostationary conditions, while the second is that termination events are governed by [R]² while the propagation goes directly with [R]. As a consequence there is no general recommendation possible as to which experimental value of k_p is best taken as a substitute for the correct average of k_p characterizing a specific experiment. The second point, however, is apparently responsible for the pleasant effect that the methods used so far for the determination of k_t and its chain length dependence (i.e., plotting some average of k_t versus the mean chain‐length of terminating radicals on a double‐logarithmic scale) are only subtly wrong with regard to a realistic chain length dependence. This is especially so for the quantity k_t* (the average rate coefficient of termination derived from the rate of polymerization in a PLP system) and its chain length dependence.     

Neutral polymer slow mode and its rheological correlate

Quasi‐elastic light scattering spectroscopy intensity–intensity autocorrelation functions [S(k,t)] and static light scattering intensities of 1 MDa hydroxypropylcellulose in aqueous solutions were measured. With increasing polymer concentration, over a narrow concentration range, S(k,t) gained a slow relaxation. The transition concentration for the appearance of the slow mode (c^t) was also the transition concentration for the solution‐like/melt‐like rheological transition (c⁺) at which the solution shear viscosity [η_p(c)] passed over from a stretched exponential to a power‐law concentration dependence. To a good approximation, we found c^t[η] ≈ c⁺[η] ≈ 4, [η] being the intrinsic viscosity. The appearance of the slow mode did not change the light scattering intensity (I): from a concentration lower than c^t to a concentration greater than c^t, I/c fell uniformly with increasing concentration. The slow mode thus did not arise from the formation of compact aggregates of polymer chains. If the polymer slow mode arose from long‐lived structures that were not concentration fluctuations, the structures involved much of the dissolved polymer. At 25 °C, the mean relaxation rate of the slow mode approximately matched the relaxation rate for the diffusion of 0.2‐μm‐diameter optical probes observed with the same scattering vector. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 323–333, 2005     

Syndiotactic and isotactic poly(tert-butylethylene oxide)

The rate of polymerization of t-BuEO by t-BuOK in DMSO is about one-tenth that of propylene oxide. The slow rate of propagation was accompanied by considerable chain transfer. In the absence of solvent, the polymer obtained was crystalline, different from the isotactic form and therefore must be syndiotactic. The NMR spectra indicate the isotactic polymer exists in solution preferentially in the skew₁ form, while syndiotactic is about 60% skew₁, 40% skew₂. Amorphous polymer accompanying isotactic exists about 50% in the trans conformer, by NMR data.     

Correlations between chemical structure and chain packing in two- and three-dimensional systems

Phosphatidylcholines (PCs) containing a branched chain fatty acid at the sn-1 position of the glycerol backbone were characterized by calorimetric and X-ray diffraction studies with bilayers as well as by thermodynamic studies with monolayers. Branching leads to altered thermal properties which are connected with a modified structural polymorphism. Gel phases with interdigitated chains or nonbilayer liquid-crystalline phases could be found in dependence on the length of the side branches. The pressure-area isotherms of the monobranched PCs were measured over a wide range of temperature. The critical temperatures T_c of the transition between the liquid-expanded and condensed films were estimated and compared with the main transition temperatures T_m of the bulk phase. T_c was found to be either lower or higher or equal to T_m. The correlations between T_c and T_m are discussed in terms of chain packing in the two- and threedimensional systems.     

Modeling Termination Kinetics of Non‐Stationary Free‐Radical Polymerizations

Pulsed‐laser induced polymerization is modeled via an approach presented in a previous paper.^[1] An equation for the time dependence of free‐radical concentration is derived. It is shown that the termination rate coefficient may vary significantly as a function of time after applying the laser pulse despite of the fact that the change in monomer concentration during one experiment is negligible. For the limiting case of t ≫ c^–1 (k_pM)^–1, where c is a dimensionless chain‐transfer constant, k_p the propagation rate coefficient and M the monomer concentration, an analytical expression for k_t is derived. It is also shown that time‐resolved single pulse‐laser polymerization (SP–PLP) experiments can yield the parameters that allow the modeling of k_t in quasi‐stationary polymerization. The influence of inhibitors is also considered. The conditions are analyzed under which M (t) curves recorded at different extents of laser‐induced photo‐initiator decomposition intersect. It is shown that such type of behavior is associated with a chain‐length dependence of k_t.     

Model for the fracture energy of glassy polymer–polymer interfaces

The increase in the interfacial fracture energy (G_c) with increasing interfacial width (a_i) goes through a transition at a critical value of a_i that is unique to each polymer–polymer system. This transition point does not scale with the bulk entanglement spacing (d_t) for different systems, implying that the role of chain friction in reinforcing these interfaces is more important than previously thought. A theoretical model has been developed to calculate G_c as a function of the interfacial stress transfer due to individual polymer chains. When including the effects of chain friction only, the model reproduces the nonuniversal behavior of G_c with respect to a_i/d_t but yields poor fits for a_i/d_t > 1. The effects of entanglements are then added by calculating the fraction of entangled chains as a function of a_i/d_t. This contribution, although not material specific, matches the qualitative behavior of G_c for large values of a_i/d_t. When both contributions are included in the model, excellent fits are obtained for all data sets. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2377–2386, 2002     

Elementary Steps of Initiation and Termination Processes in Radical Polymerization

Investigations into the kinetics of primary radicals produced in photochemically and thermally induced decomposition of peroxides of type R₁C(O)O-OR₂ are presented. The correlation of peroxide structure with decomposition rate and with initiator efficiency in radical polymerizations is discussed. Termination rate coefficients, k_t, as a function of temperature, pressure, polymer content, and of chain length may be deduced from two types of time-resolved experiments in which, after applying an excimer laser pulse, either monomer conversion is measured via near-infrared spectroscopy or the decay in radical concentration is monitored via electron spin resonance.     

Linear Chain Termination in the Kinetics of Postpolymerization of Dimethacrylates

The kinetics of postpolymerization (after turning off UV irradiation) of various dimethacrylates differing in their nature and molecular weight was studied over a wide range of temperatures. For each temperature, a series of kinetic curves, varying in the initial conversion during a dark period, was obtained. The proposed kinetic model is based on the following assumptions. The process in the interphase layer at the liquid monomer-solid polymer boundary has the most significant contribution to the kinetics of postpolymerization. Chain termination in the interphase layer occurs by the unimolecular reaction, is controlled by the chain growth rate, and presents the act of self-burying of an active radical in a conformational trap. A wide spectrum of characteristic times is inherent in unimolecular chain termination, and the relaxation function is described by the Kohlraush' stretched exponential law. The rate law obtained agrees well with experimental data. This fact made it possible to estimate the rate constants (k _t) and the activation energies of chain termination and to establish the scale dependence of k _t on the molar concentration [M₀] of the monomer in a block. It is suggested that both the stretched exponential law and the scale k _t-[M₀] dependence are due to a wide spectrum of characteristic times of relaxation exhibiting the properties of a fractal set.     

Stress relaxation under large step equibiaxial elongation for low‐density polyethylene

The stress relaxation under large step equibiaxial elongation for low‐density polyethylene with long‐chain branches revealed that the time‐strain separability holds in relaxation modulus G_B(t, ε_B), and damping function h_B(ε_B) exhibits weaker equibiaxial elongational strain ε_B dependence than that predicted by the Doi–Edwards theory without the independent alignment approximation. Dependencies of damping function h(γ) for step shear deformation and h_B(ε_B) on stretch ratio α of polymer contour length and orientation of a polymer chain in direction of the maximum orientation were evaluated, and it was found that the α dependencies of h(γ) and h_B(ε_B) are different, whereas dependencies of h(γ) and h_B(ε_B) on the orientation coincide fairly well. These results indicate that the damping is dominated by the chain orientation rather than α. This implies that withdrawal of long‐chain branches into tube of a backbone chain occurs when the orientation of the long‐chain branches is large and friction force against the branch point withdrawal is small. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1275–1284, 2009     

Rheological properties of linear and crosslinked polymer blends: Relation between crosslink density and enhancement of elongational viscosity

Strain‐hardening behavior in the elongational viscosity of binary blends composed of a linear polymer and a crosslinked polymer, in which the molecular chains of the linear polymer were incorporated into the network chains of the crosslinked polymer, was studied. Blending the crosslinked polymer characterized as the gel just beyond the sol–gel transition point greatly enhanced the strain‐hardening behavior in the elongational viscosity, even though the amount of the crosslinked polymer was only 0.3 wt %. However, the crosslinked polymer, which was far beyond or below the sol–gel transition point, had little influence on the elongational viscosity as well as the shear viscosity. The stretching of the chain sections between the crosslink points was responsible for the strain‐hardening behavior. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 228–235, 2001     

Modeling termination kinetics in free‐radical polymerization using a reduced number of parameters

An approach for modeling chain‐length dependent termination rate coefficients is presented. The method is based on the assumption that free‐radical chain length may be considered as a continuous variable. As compared to discrete numerical methods, in continuous modeling the number of independent dimensionless parameters can be significantly reduced. As a consequence, for a wide variety of monomers the conversion dependence of k_t can be predicted without extensive numerical calculations. The method may also be used to determine polymerization conditions under which simpler models of k_t (which neglect effects arising from the dependence of k_t on chain length) may be applied. Calculations for methyl methacrylate, styrene, and butyl acrylate bulk polymerizations up to high degrees of monomer conversion show that the impact of chain length on termination varies with conversion and strongly depends on the type of monomer.     

The glass transition in polymer melts

This paper presents some results of a Monte Carlo simulation for the glass transition in two- and three-dimensional polymer melts. The melt was simulated by the bond-fluctuation model on a d-dimensional cubic lattice which was combined with a two-level hamiltonian favouring long bonds in order to generate a competition between the energetic and topological constraints in the system. This competition prevents crystallization and makes the melt freeze in an amorphous structure as soon as the internal relaxation times match the observation time of the simulation set by the cooling rate. The freezing point of the melt, i.e the glass transition temperature T_g, thus depends upon the cooling rate and additionally upon the chain length of the polymers. The dependence of the glass transition temperature on the cooling rate was closely analysed in three and that on the chain length in both two and three dimensions, resulting in a non-linear relationship between T_g and the logarithm of the cooling rate and a linear relationship between T_g and the inverse chain length, respectively. In addition to this behaviour of the melt during the cooling process an example for the relaxational properties of the three-dimensional model is provided by a quantitative analysis of the incoherent intermediate scattering function in the framework of the idealized mode coupling theory.     

Kinetics of emulsion polymerization of methyl methacrylate

The kinetics of the emulsion polymerization of methyl methacrylate at 50°C have been studied in seeded systems using both chemical initiation and γ-radiolysis initiation. Both steady-state rates and (for γ-radiolysis) the relaxation from the steady state were observed. The average number of free radicals per particle was quite high (e.g., ～0.7 for 10^?3 mol dm^?3 S₂O²₈ initiator). The data are quantitatively interpreted using a generalized Smith–Ewart–Harkins model, allowing for free radical entry, exit, biomolecular termination within the latex particles, and aqueous phase hetero-termination and re-entry. From this treatment, there results (i) the dependence of the termination rate coefficient (k_t) on the weight fraction of polymer (w_p), (ii) lower bounds for the dependence of the entry rate coefficient on initiator concentration, and (iii) the conclusion that most exited free radicals undergo subsequent re-entry into particles rather than hetero-termination. The results for k_t(w_p) are consistent with diffusion control at temperatures below the glass transition point. Comparisons are presented of the behavior of methyl methacrylate, butyl methacrylate, and styrene in emulsion polymerization systems.     

On the (im)possibility of evaluating correct individual rate constants of chain propagation kp and chain termination kt by combining kp2/kt and kp/kt data for chain‐length dependent termination

On the basis of simulated data two ways of evaluating individual rate constants by combining k_p²/k_t and k_p /k_t (k_p , k_t = rate constants of chain propagation and termination, respectively) were checked considering the chain‐length dependence of k_t. The first way tried to make use of the fact that pseudostationary polymerization yields data for k_p²/k_t as well as for k_p /k_t referring to the very same experiment, in the second way k_p²/k_t (from steady state experiments) and k_p/k_t data referring to the same mean length of the terminating radical chains were compared. In the first case no meaningful data at all could be obtained because different averages of k_t are operative in the expressions for k_p /k_t and k_p²/k_t. In spite of the comparatively small difference between these two averages (≈15% only) this makes the method collapse. The second way, which can be regarded as an intelligent modification of the “classical” method of determining individual rate constants, at least succeeded in reproducing the correct order of magnitude of the individual rate constants. However, although stationary and pseudostationary experiments independently could be shown to return the same k_t for the same average chain‐length of terminating radicals within extremely narrow limits no reasonable chain‐length dependence of k_t could be derived in this way. The reason is an extreme sensitivity of the pair of equations for k_p/k_t and k_p²/k_t towards small errors and inconsistencies which renders the method unsuccessful even for the high quality simulation data and most probably makes it even collapse for real data. This casts a characteristic light on the unsatisfactory situation with respect to individual rate constants determined in the classical way, regardless of a chain‐length dependence of termination. As a consequence, all efforts of establishing the chain‐length dependence of k_t are recommended to avoid this way and should rather resort to methods based on inserting a directly determined k_p into the equations characteristic of k_p²/k_t or k_p/k_t, properly considering the chain‐length dependent character of k_t.     

三代碳硅烷光致变色液晶树状物的光化学研究——端基含108个4-丁氧基偶氮苯介晶基元

报道了新化合物含108个丁氧基偶氮基元端基的三代(D3)碳硅烷光致变色液晶树状物在各溶液中的反-顺光异构化(光致变色)反应速率常数k_p, 光化学回复异构化正/逆反应速率常数k_t和k_c, 热回复异构化反应速率常数k_H, 光化学回复异构化反应平衡常数k_t/k_c, 活化能E, 异构化转换率及热回复异构化反应中的反-顺异构体组分比. D3的光致变色反应速率常数为10^－1 s^－1, 而含偶氮基元的光致变色液晶聚硅氧烷的光致变色反应速率常数为10^－8 s^－1, 因此, D3的光响应速度比后者快10⁷倍.