Shock tube and modeling study of propene pyrolysis

The thermal decomposition of propene behind reflected shock waves with 1200 < T₅ < 1800 K and 1.6 × 10^?5 < ρ₅ < 2.7 × 10^?5 mol/cm³ was studied by IR laser kinetic absorption spectroscopy and gas-chromatographic analysis of reaction products. The present data together with earlier shock tube data were satisfactorily modeled with a 51-reaction mechanism. As the initial step of the reaction, three channels, C₃H₆ = CH₃ + C₂H₃ (1), C₃H₆ = H + AC₃H₅ (2), and C₃H₆ = CH₄ + C₂H₂ (3), were necessary to interpret all the experimental data. © John Wiley & Sons, Inc.     

A detailed chemical kinetic model for high temperature ethanol oxidation

A detailed chemical kinetic model for ethanol oxidation has been developed and validated against a variety of experimental data sets. Laminar flame speed data (obtained from a constant volume bomb and counterflow twin‐flame), ignition delay data behind a reflected shock wave, and ethanol oxidation product profiles from a jet‐stirred and turbulent flow reactor were used in this computational study. Good agreement was found in modeling of the data sets obtained from the five different experimental systems. The computational results show that high temperature ethanol oxidation exhibits strong sensitivity to the fall‐off kinetics of ethanol decomposition, branching ratio selection for C₂H₅OH + OH ↔ Products, and reactions involving the hydroperoxyl (HO₂) radical. The multichanneled ethanol decomposition process is analyzed by RRKM/Master Equation theory, and the results are compared with those obtained from earlier studies. The ten‐parameter Troe form is used to define the C₂H₅OH(+M) ↔ CH₃ + CH₂OH(+M) rate expression as k^∞ = 5.94E23 T^−1.68 exp(−45880 K/T) (s⁻¹) k^o = 2.88E85 T^−18.9 exp(−55317 K/T) (cm³/mol/sec) F_cent = 0.5 exp(−T/200 K) + 0.5 exp(−T/890 K) + exp(−4600 K/T) and the C₂H₅OH(+M) ↔ C₂H₄ + H₂O(+M) rate expression as k^∞ = 2.79E13 T^0.09 exp(−33284 K/T) (s⁻¹) k^o = 2.57E83 T^−18.85 exp(−43509 K/T) (cm³/mol/sec) F _cent = 0.3 exp(−T/350 K) + 0.7 exp(−T/800 K) + exp(−3800 K/T) with an applied energy transfer per collision value of <ΔE_down> = 500 cm⁻¹. An empirical branching ratio estimation procedure is presented which determines the temperature dependent branching ratios of the three distinct sites of hydrogen abstraction from ethanol. The calculated branching ratios for C₂H₅OH + OH, C₂H₅OH + O, C₂H₅OH + H, and C₂H₅OH + CH₃ are compared to experimental data. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 183–220, 1999     

Specific spectral properties of a photochromic ferromagnetic (C25H23N3O3Cl)CrMn(C2O4)3·H2O

A molecular magnetic (C₂₅H₂₃N₃O₃Cl)CrMn(C₂O₄)₃·H₂O whose spiropyran cation contains a quaternized pyridine fragment in the side aliphatic chain was synthesized for the first time. The compound possesses the properties of a ferromagnetic with T _c = 5.2 K and photochromic properties in the crystalline state. The photochemical properties of the hybrid compound were studied by electronic and IR spectroscopies. Photochromic transformations of the spiropyran cation are accompanied by the appearance of a broad absorption band in the region 400–600 nm in the electronic spectra and by reduction of intensity of the ν(C_spiro-O) IR band at 942 cm⁻¹. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1055–1061, June, 2007.     

An experimental and modeling study of ethanol oxidation kinetics in an atmospheric pressure flow reactor

Experimental profiles of stable species concentrations and temperature are reported for the flow reactor oxidation of ethanol at atmospheric pressure, initial temperatures near 1100 K and equivalence ratios of 0.61–1.24. Acetaldehyde, ethene, and methane appear in roughly equal concentrations as major intermediate species under these conditions. A detailed chemical mechanism is validated by comparison with the experimental species profiles. The importance of including all three isomeric forms of the C₂H₅O radical in such a mechanism is demonstrated. The primary source of ethene in ethanol oxidation is verified to be the decomposition of the C₂H₄OH radical. The agreement between the model and experiment at 1100 K is optimized when the branching ratio of the reactions of C₂H₅OH with OH and H is defined by (30% C₂H₄OH + 50% CH₃CHOH + 20% CH₃CH₂O) + XH. As in methanol oxidation, HO₂ chemistry is very important, while the H + O₂ chain branching reaction plays only a minor role until late in fuel decay, even at temperatures above 1100 K.     

Kinetics of isopropanol decomposition and reaction with H atoms from shock tube experiments and rate constant optimization using the method of uncertainty minimization using polynomial chaos expansions (MUM‐PCE)

We have used the single‐pulse shock tube technique with postshock GC/MS product analysis to investigate the mechanism and kinetics of the unimolecular decomposition of isopropanol, a potential biofuel, and of its reaction with H atoms at 918‐1212 K and 183‐484 kPa. Experiments employed dilute mixtures in argon of isopropanol, a radical scavenger, and, for H‐atom studies, two different thermal precursors of H. Without an added H source, isopropanol decomposes in our studies predominantly by molecular dehydration. Added H atoms significantly augment decomposition, mainly by abstraction of the tertiary and primary hydrogens, reactions that, respectively, lead to acetone and propene as stable organic products. Traces of acetaldehyde were observed in some experiments above ≈ 1100 K and establish branching limits for minor decomposition pathways. To quantitatively account for secondary chemistry and optimize rate constants of interest, we employed the method of uncertainty minimization using polynomial chaos expansions (MUM‐PCE) to carry out a unified analysis of all datasets using a chemical model–based originally on JetSurF 2.0. We find: k(isopropanol → propene + H₂O) = 10^{(13.87 ± 0.69)} exp(?(33 099 ± 979) K/ T) s^?1 at 979‐1212 K and 286‐484 kPa, with a factor of two uncertainty (2σ), including systematic errors. For H atom reactions, optimization yields: k(H + isopropanol → H₂ + p‐C₃H₆OH) = 10^{(6.25 ± 0.42)} T^2.54 exp(?(3993 ± 1028) K /T) cm³ mol^?1 s^?1 and k(H + isopropanol → H₂ + t‐C₃H₆OH) = 10^{(5.83 ± 0.37)} T^2.40 exp(?(1507 ± 957) K /T) cm³ mol^?1 s^?1 at 918‐1142 K and 183‐323 kPa. We compare our measured rate constants with estimates used in current combustion models and discuss how hydrocarbon functionalization with an OH group affects H abstraction rates.     

The high temperature pyrolysis of 1,3-butadiene: heat of formation and rate of dissociation of vinyl radical

The high temperature pyrolysi of 1,3-butadiene has been investigated in the shock tube with two time-resolved diagnostic techniques: laser schlieren measurements of density gradient with 1, 2, 4, and 5% C₄H₆ in Ar or Kr, 0.26 < P₂ < 0.66 atm, over 1550–2200 K, and time-of-flight mass spectra for 3% C₄H₆–Ne, P₅ ～ 0.4 atm, 1400–2000 K. When combined with a recent single-pulse shock tube product analysis covering 1050–2050 K, these measurements permit a complete modeling of major species in C₄H₆ pyrolysis. Extrapolated density gradients and product analyses show initiation is dominated by C₄H₆ → 2C₂H₃., significant falloff and Arrhenius curvature being seen in the derived rates. A restricted rotor, Gorin model RRKM fit to these rates with reasonable parameters generates The derived barrier, ΔH${}_{\text{0}}^{\text{º}}$ = 99 ± 4 kcal/mol, translates to ΔH${}_{\text{f}}^{\text{º}}$ _,298 = 63.4 ± 2 kcal/mol for the heat of formation of vinyl radical. A mechanism for the formation of all products detected in the above experiments is given, together with a successful but semiquantitative kinetic model for major products. The measurements require the rate of vinyl radical dissociation, C₂H₃ + M → C₂H₂ + H + M, to be extremely low, k < 10⁹ cm³/mol s for 1600 K, so that the dominant chain carrier in C₄H₆ pyrolysis is vinyl radical.     

Chain photohalogenation of ethylene at liquid helium temperatures

Photolysis of a halogen in solid 1:1 molecular complexes of ethylene with chlorine (1) and bromine (2) at 18–70 K led to the formation oftrans-1,2-dihaloethanes by a chain mechanism (with quantum yields of 25–30 for 1 and 10–12 for 2 atT45 K) but molecular addition occurred above 90 K to give thegauche isomer. The rate constant for chain growth is independent of temperature atT45 K, but is described by the Arrhenius equation atT50 K (E ₀ 1 kcal/mole). It is proposed that chain growth occurs by a tunneling reaction of the C₂H₄Hal radical with an Hal₂ molecule at a neighboring lattice site.Institute of Chemical Physics, Russian Academy of Sciences, 142432 Chernogolovka. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 10, pp. 2268–2277, October, 1992.     

Rate constant and RRKM product study for the reaction between CH3 and C2H3 at T = 298 K

The total rate constant k₁ has been determined at P = 1 Torr nominal pressure (He) and at T = 298 K for the vinyl‐methyl cross‐radical reaction: (1) CH₃ + C₂H₃ → Products. The measurements were performed in a discharge flow system coupled with collision‐free sampling to a mass spectrometer operated at low electron energies. Vinyl and methyl radicals were generated by the reactions of F with C₂H₄ and CH₄, respectively. The kinetic studies were performed by monitoring the decay of C₂H₃ with methyl in excess, 6 < [CH₃]₀/ [C₂H₃]₀ < 21. The overall rate coefficient was determined to be k₁(298 K) = (1.02 ± 0.53) × 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹ with the quoted uncertainty representing total errors. Numerical modeling was required to correct for secondary vinyl consumption by reactions such as C₂H₃ + H and C₂H₃ + C₂H₃. The present result for k₁ at T = 298 K is compared to two previous studies at high pressure (100–300 Torr He) and to a very recent study at low pressure (0.9–3.7 Torr He). Comparison is also made with the rate constant for the similar reaction CH₃ + C₂H₅ and with a value for k₁ estimated by the geometric mean rule employing values for k(CH₃ + CH₃) and k(C₂H₃ + C₂H₃). Qualitative product studies at T = 298 K and 200 K indicated formation of C₃H₆, C₂H₂, and C₃H₅ as products of the combination‐stabilization, disproportionation, and combination‐decomposition channels, respectively, of the CH₃ + C₂H₃ reaction. We also observed the secondary C₄H₈ product of the subsequent reaction of C₃H₅ with excess CH₃; this observation provides convincing evidence for the combination‐decomposition channel yielding C₃H₅ + H. RRKM calculations with helium as the deactivator support the present and very recent experimental observations that allylic C‐H bond rupture is an important path in the combination reaction. The pressure and temperature dependencies of the branching fractions are also predicted. © 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 304–316, 2000     

Behavior of ethylene and ethane within single-walled carbon nanotubes. 1-Adsorption and equilibrium properties

Endohedral adsorption properties of ethylene and ethane onto single-walled carbon nanotubes were investigated using a united atom (2CLJQ) and a fully atomistic (AA-OPLS) force fields, by Grand Canonical Monte Carlo and Molecular Dynamics techniques. Pure fluids were studied at room temperature, T=300 K, and in the pressure ranges 4×10⁻⁴<p<47.1 bar (C₂H₄) and 4×10⁻⁴<p<37.9 bar (C₂H₆). In the low pressure region, isotherms differ quantitatively depending on the intermolecular potential used, but show the same qualitative features. Both potentials predict that ethane is preferentially adsorbed at low pressures, and the opposite behavior was observed at high loadings. Isosteric heats of adsorption and estimates of low pressure Henry’s constants, confirmed that ethane adsorption is the thermodynamically favored process at low pressures. Binary mixtures of C₂H₄/C₂H₆ were studied under several (p,T) conditions and the corresponding selectivities towards ethane, S, were evaluated. Small values of S<4 were found in all cases studied. Nanotube geometry plays a minor role on the adsorption properties, which seem to be driven at lower pressures primarily by the larger affinity of the alkane towards the carbon surface and at higher pressures by molecular volume and packing effects. The fact that the selectivity towards ethane is similar to that found earlier on carbon slit pores and larger diameter nanotubes points to the fact that the peculiar 1-D geometry of the nanotubes provides no particular incentive for the adsorption of either species.     

Novel determination of the dimerization mechanism for thermal polymerization of α-methylstyrene

This study discussed the phenomena on thermal polymerization of α-methylstyrene (AMS). A curve scanned by temperature-programmed technique was performed by differential scanning calorimetry (DSC). Heat of polymerization (ΔH) and onset temperature of exothermic (T₀) behavior were determined to be 280±10 J g^-1 and about 138±1°C, respectively. A dimer formation mechanism was proposed for initiation of the propagating chain. Spectroscopic identification of dimer structure was conducted by infrared (IR) spectroscopy in the wavenumber from 650 to 1100 cm^-1associated with molecular fingerprint characteristics. The mechanism of thermal polymerization on α-methylstyrene proposed in this study was similar to that of styrene suggested by Mayo.     

Polymer-Supported Lewis Acid Catalysts. II. Cationic Polymerization of α-Methylstyrene with Polystyrene-Gallium Trichloride Complex as Initiator

The polymerization of α-methylstyrene catalyzed by a polymer-supported Lewis acid catalyst, polystyrene-gallium trichloride complex, is described. The kinetic equation of the cationic polymerization is R_p = k˙C_ms˙C_cat , and the apparent activation energy is 20.9 kJ/mol. The effect of different solvents on the polymerization rate is quite pronounced; for example, the polymerization rate decreased in the following order in the three solvents: CH₂ ClCH₂ Cl < CH₂ Cl₂ < CCl₄. High molecular weight poly(α-methylstyrene) (T_g = 185°C) could be obtained at room temperature. The mechanism of the polymerization is also discussed.     

Chain transfer to solvent in the radical polymerization of N‐isopropylacrylamide

Chain transfer to solvent has been investigated in the conventional radical polymerization and nitroxide‐mediated radical polymerization (NMP) of N‐isopropylacrylamide (NIPAM) in N,N‐dimethylformamide (DMF) at 120 °C. The extent of chain transfer to DMF can significantly impact the maximum attainable molecular weight in both systems. Based on a theoretical treatment, it has been shown that the same value of chain transfer to solvent constant, C_tr,S, in DMF at 120 °C (within experimental error) can account for experimental molecular weight data for both conventional radical polymerization and NMP under conditions where chain transfer to solvent is a significant end‐forming event. In NMP (and other controlled/living radical polymerization systems), chain transfer to solvent is manifested as the number‐average molecular weight (M_n) going through a maximum value with increasing monomer conversion. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Thermal decomposition of ethane

The decomposition of C₂H₆ in Ar was studied by laser-absorption and laser-schlieren measurements of the reaction rate behind incident shock waves with 1300 < T < 2500°K and 1.1 < ρ < 4.4 × 10^?6 mol/cm³. The experimental profiles were parameterized by suitable measures of reaction progress. Computer simulations using a 14-reaction mechanism were used to compare assumptions about rate constant expressions with the experimental parameters and to investigate the sensitivity of computed parameters to these assumptions. A rate constant expression k(cm³/mol˙sec) = 2 × 10¹¹¹ T^?25.26 exp(?80 320/T) was found for the primary dissociation step C₂H₆ + M ? CH₃ + CH₃ + M under the conditions studied; no difference in rate was discernable between M ? Ar and M ? C₂H₆. Rate constant expressions found to be suitable for the remaining reactions of the mechanism, to some of which the computed parameters were sensitive, were in accord with previous proposals. Our results and results from earlier investigations of the primary decomposition reaction, in both forward and reverse directions, were extrapolated, using RRK methods, to obtain low-pressure limiting rate constants and found to be concordant.     

Microemulsion polymerization of styrene stabilized by sodium dodecyl sulfate and short‐chain alcohols

Styrene microemulsion polymerizations with different short‐chain alcohols [n‐C_iH_2i+1OH (C_iOH), where i = 4, 5, or 6] as the cosurfactant were investigated. Sodium dodecyl sulfate and sodium persulfate (SPS) were used as the surfactant and initiator, respectively. The desorption of free radicals out of latex particles played an important role in the polymerization kinetics. An Arrhenius expression for the radical desorption rate coefficient was obtained from the polymerizations at temperatures of 50–70 °C. The polymerization kinetics were not very sensitive to the alkyl chain length of alcohols compared with the temperature effect. The maximal polymerization rate in decreasing order was C₆OH > C₄OH > C₅OH. This was related to the differences in the water solubility of C_iOH and the structure of the oil–water interface. The feasibility of using a water‐insoluble dye to study the particle nucleation mechanisms was also evaluated. The parameters chosen for the study of the particle nucleation mechanisms include the cosurfactant type (C_iOH), the SPS concentration, and the initiator type (oil‐soluble 2,2′‐azobisisobutyronitrile versus water‐soluble SPS). © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3199–3210, 2001     

Rubidium and lithium butanoates binary phase diagram

The temperature and enthalpy vs. composition diagrams of the binary system [xC₃H₇CO₂Li+(1–x)C₃H₇CO₂Rb], where x=mole fraction, were determined by differential scanning calorimetry (DSC). This binary systems displays the formation of two mixed salts with a composition 1:1 and 1:2, which melt incongruently at T _fus=590.5 K, with Δ_fus H _m=11.6 kJ mol^–1, and congruently at T _fus=614.5 K, with Δ_fus H _m=20.2 kJ mol^–1, respectively. The phase diagram also presents an ionic liquid-crystalline phase in a wide temperature range: 95 K.     

Radical sensitization of acetylene pyrolysis

The kinetics of acetylene polymerization initiated by neopentane (Np) or acetone (Ac) decompositions has been investigated in a static reactor dynamically coupled to a modulated beam mass spectrometer between 850–950 K. Overall rates follow the expression: R = ?d[C₂H₂]/dt = k_s[X]^1/2[C₂H₂] + k_u[C₂H₂]² (I), where X represents Np or Ac and k_s, k_u the rate constants of the sensitized and unsensitized reactions, respectively. The rate law of the sensitized reaction clearly suggests a chain polymerization mechanism with k_s = k_p(k_i/k_t)^1/2 (i, t, and p stand for initiation, termination, and propagation, respectively). Remarkably, the derived values of k_p are nearly independent of the sensitizer, although Ac acts as a source of methyl radicals whereas Np also produces hydrogen atoms, and fall in the expected range for the addition of vinylic radicals to acetylene. It is shown that a chain transfer process involving the fast [1,5] intramolecular hydrogen atom shift in 4-methyl-buta-1,3-dien-1-yl radicals (CH₃? CH ? CH? CH ??H) followed by further addition to C₂H₂ and aromatization, transforms methyl radicals into hydrogen atoms and is able to account for the presence of toluene among the products of the sensitized reactions. Based on current thermochemical data for the but-1-en-3-yn-2-yl radical (CH₂??? C?CH) and present rates of propagation it is argued that if the unsensitized polymerization of acetylene also proceeded by a vinyl radical chain, then even the most favorable self-initiation reaction: 2C₂H₂ = C₄H₃ + H (a), would be far too slow. Finally, present results also show that acetone at impurity levels (? 0.1%) can not provide fast enough spurious initiation rates in chain mechanisms for the “unsensitized” acetylene pyrolysis at pressures above 10 torr.     

Kinetics of the microemulsion polymerization of styrene with short‐chain alcohols as the cosurfactant

The kinetics of styrene microemulsion polymerization stabilized by sodium dodecyl sulfate (SDS) and a series of short‐chain alcohols (n‐C_iH_2i+1OH, abbreviated as C_iOH, where i = 4, 5, or 6) at 60 °C was investigated. Sodium persulfate was used as the initiator. The microemulsion polymerization process can be divided into two intervals: the polymerization rate (R_p) first increases to a maximum at about a 20% conversion (interval I) and thereafter continues to decrease toward the end of the polymerization (interval II). For all the SDS/C_iOH‐stabilized polymerization systems, R_p increases when the initiator or monomer concentration increases. The average number of free radicals per particle is smaller than 0.5. The molecular weight of the polymer produced is primarily controlled by the chain‐transfer reaction. In general, the reaction kinetics for the polymerization system with C₄OH as the cosurfactant behaves quite differently from the kinetics of the C₅OH and C₆OH counterparts. This is closely related to the different water solubilities of these short‐chain alcohols and the different concentrations of the cosurfactants used in the preparation of the microemulsion. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 898–912, 2001     

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     

Kinetics of C6H5 radical reactions with 2‐methylpropane, 2,3‐dimethylbutane and 2,3,4‐trimethylpentane

The absolute bimolecular rate constants for the reactions of C₆H₅ with 2‐methylpropane, 2,3‐dimethylbutane and 2,3,4‐trimethylpentane have been measured by cavity ringdown spectrometry at temperatures between 290 and 500 K. For 2‐methylpropane, additional measurements were performed with the pulsed laser photolysis/mass spectrometry, extending the temperature range to 972 K. The reactions were found to be dominated by the abstraction of a tertiary C H bond from the molecular reactant, resulting in the production of a tertiary alkyl radical: C₆H₅ + CH(CH₃)₃ → C₆H₆ + t‐C₄H₉ (1) (1) C₆H₅ + (CH₃)₂CHCH(CH₃)₂ → C₆H₆ + t‐C₆H₁₃ (2) (2) C₆H₅ + (CH₃)₂CHCH(CH₃)CH(CH₃)₂ → C₆H₆ + t‐C₈H₁₇ (3) (3) with the following rate constants given in units of cm³ mol⁻¹ s⁻¹: k₁ = 10^{(11.45 ± 0.18)} e^{−(1512 ± 44)/T} k₂ = 10^{(11.72 ± 0.15)} e^{−(1007 ± 124)/T} k₃ = 10^{(11.83 ± 0.13)} e^{−(428 ± 108)/T} © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 645–653, 1999     

Calorimetric relaxation and glass transition in poly(propylene glycols) and its monomer

The glass transition temperature T_g of propylene glycol (PG) and poly(propylene glycols) (PPGs) of molecular weight up to 4000 has been measured by differential scanning calorimetry, and the activation energy and change in heat capacity ΔC_p have been determined in the glass transition range. The activation energy increases with an increase in the molecular weight of the polymer, and ΔC_p measured at a fixed heating rate decreases. The increase in T_g with molecular weight is remarkably more rapid for poly(propylene glycols) than for other polymers, and a limiting value of T_g is reached for a chain containing 20 monomer units. These results are discussed in terms of the Fox-Flory and the entropy theories. The calorimetric relaxation times are comparable with the extrapolated dielectric relaxation times. The initial increase of ΔC_p from PG to PPG 200 is attributed to the decrease of H-bonding sites from 12 in 3 monomers to 4 on polymerization to PPG 200 and further decrease with increase in molecular weight to an increasingly large amplitude of the β-process at T < T_g.