Local forms of molecular mobility in copolymethacrylates containing side‐chain nonlinear optical chromophores

Local forms of molecular mobility of comb‐like random copolymethacrylates, containing side‐chain nonlinear optical chromophores and amyl‐ or octafluoroamyl‐groups, are studied. In the glassy state, two relaxation processes are found, which are due to reorientation of terminal polar groups (γ₂‐process) and rotation of chromophore groups about their long axes (β‐process). For octafluoroamyl‐containing copolymers, the γ₂‐process is superposition of the two molecular motions due to reorientation of terminal chromophore groups and ? CF₂H groups. The intensity and relaxation times in the range of the γ₂‐process depend on the chemical structure and concentration of chromophores in a copolymer. For the β‐process, the molecular mobility weakly depends on the chromophore structure, being mainly determined by the relative lengths of the rigid chromophore and flexible side chains. On the global spectrum of depolarization current it was observed the γ₁‐process due to reorientation of (CH₂)_n spacers between chromophore groups and copolymer backbone. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1488–1496, 2008     

Segmental and secondary dynamics in hydrogen‐bonded poly(4‐vinylphenol)/poly(methyl methacrylate) blends

Broadband dielectric spectroscopy was used to study the segmental (α) and secondary (β) relaxations in hydrogen‐bonded poly(4‐vinylphenol)/poly(methyl methacrylate) (PVPh/PMMA) blends with PVPh concentrations of 20–80% and at temperatures from ?30 to approximately glass‐transition temperature (T_g) + 80 °C. Miscible blends were obtained by solution casting from methyl ethyl ketone solution, as confirmed by single differential scanning calorimetry T_g and single segmental relaxation process for each blend. The β relaxation of PMMA maintains similar characteristics in blends with PVPh, compared with neat PMMA. Its relaxation time and activation energy are nearly the same in all blends. Furthermore, the dielectric relaxation strength of PMMA β process in the blends is proportional to the concentration of PMMA, suggesting that blending and intermolecular hydrogen bonding do not modify the local intramolecular motion. The α process, however, represents the segmental motions of both components and becomes slower with increasing PVPh concentration because of the higher T_g. This leads to well‐defined α and β relaxations in the blends above the corresponding T_g, which cannot be reliably resolved in neat PMMA without ambiguous curve deconvolution. The PMMA β process still follows an Arrhenius temperature dependence above T_g, but with an activation energy larger than that observed below T_g because of increased relaxation amplitude. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3405–3415, 2004     

Indentation of poly(methyl methacrylate) under high‐pressure gases

The variation of the indentation hardness of a high molecular weight poly(methyl methacrylate) (PMMA) subjected to CO₂ and Ar at high pressure was measured in situ. The samples were subjected to gas exposure for 3 h at 40 °C before a conical indenter of an included angle at 105 °, with a fixed load of 0.237 kg, was applied for a loading time of 60 s. The data show that both CO₂ and Ar reduce the hardness of PMMA to a comparable extent at low pressures. The hardness of PMMA subjected to Ar indicates a minimum at about 4 MPa and then increases. CO₂ produced a monotone decreasing trend in hardness in the pressure range studied, and the glass‐transition temperature (T_g) was achieved at about 6.0 MPa. The change in hardness is attributed to plasticization of the polymer matrix that is more extensive for CO₂. The relationship between the change in hardness for this PMMA subjected to high‐pressure CO₂, the corresponding change in the T_g, and the associated swelling of the polymer is discussed. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 3020–3028, 2001     

A new technique for measuring retrograde vitrification in polymer–gas systems and for making ultramicrocellular foams from the retrograde phase

A stepwise temperature‐ and pressure‐scanning thermal analysis method was developed to measure glass‐transition temperature T_g in the two‐phase polymer–gas systems as a function of gas pressure p, and was used to confirm recent theoretical predictions that certain polymer–gas systems exhibit retrograde vitrification, that is, they undergo rubber‐to‐glass transition on heating. A complete T_g‐p profile delineating the glass–rubber phase envelope was established for the PMMA‐CO₂ system. The retrograde vitrification behavior observed, where at certain gas pressures the polymer exists in the rubbery state at low and high temperatures and in the glassy state at intermediate temperatures, was similar to that reported previously based on the creep‐compliance measurements. The existence of the rubbery state at low temperatures was used to generate foams by saturating the polymer with CO₂ at 34 atm and at temperatures in the range −0.2 to 24 °C followed by foaming at temperatures in the range 24 to 90 °C. Foams with very fine cell structure never reported before could be prepared by this technique. For example, PMMA foams with average cell size of 0.35 μm and cell density of 4.4 × 10¹³ cells/g were prepared by processing the low temperature rubbery phase. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 716–725, 2000     

Raman spectroscopic study of CO2 sorption process in poly methyl methacrylate

Raman spectra of poly methyl methacrylate (PMMA) in contact with compressed CO₂ were measured, to investigate effects of CO₂ sorption on structure of the PMMA chain. The solubility and diffusivity of CO₂ in PMMA were estimated from temporal variations of intensities of CO₂ peaks. The PMMA structure was analyzed from temporal variations of vibrational energies of PMMA peaks. The results show that the vibration energies of C H stretching modes of PMMA increase with CO₂ sorption, whereas those for skeletal vibration modes decrease. These energy shifts are attributed to elongational deformation of PMMA. The PMMA structure is deformed with stretching of the chains as a bundle. From energy shifts of the CO₂ peaks, the size of the CO₂ accommodated space between the bundles is estimated to be 1.6–1.9 nm. Furthermore, it was observed that the vibrational energies of the PMMA modes in foamed glassy PMMA differ from the values in glassy PMMA without foams. This result suggests that the local structure of the PMMA chain changes with the process of the CO₂ sorption and/or foaming. The local structure of the PMMA chain might be one of the dominant factors governing the properties of cellular materials. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 831–842, 2008     

Comparative study of the mechanical relaxation behavior of polymethacrylates containing different bulky side groups

The syntheses of poly(1,3‐dioxan‐5‐yl methacrylate), poly(cis‐2‐phenyl‐1,3‐dioxan‐5‐yl methacrylate), poly(trans‐2‐phenyl‐1,3‐dioxan‐5‐yl methacrylate), poly(cis‐2‐cyclohexyl‐1,3‐dioxan‐5‐yl methacrylate), and poly(trans‐2‐cyclohexyl‐1,3‐dioxan‐5‐yl methacrylate) are reported. The mechanical relaxation spectrum of the simplest polymer, poly(1,3‐dioxan‐5‐yl methacrylate), exhibits a prominent β relaxation centered at ?98 °C, at 1 Hz, followed in increasing order of temperature by an ostensible glass–rubber relaxation process. In addition to the β relaxation, the loss curves of poly(trans‐2‐phenyl‐1,3‐dioxan‐5‐yl methacrylate) and poly(trans‐2‐cyclohexyl‐1,3‐dioxan‐5‐yl methacrylate) display in the glassy state a high activation energy relaxation, named the β* process, that seems to be a precursor of the glass–rubber relaxation of these polymers. The mechanical spectra of poly(trans‐2‐cyclohexyl‐1,3‐dioxan‐5‐yl methacrylate) and poly(cis‐2‐cyclohexyl‐1,3‐dioxan‐5‐yl methacrylate) exhibit a low activation energy process in the low‐temperature side of the spectra, which is absent in the other polymers. The molecular origin of the mechanical activity of these polymers in the glassy state is discussed in qualitative terms. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1154–1162, 2002     

Viscoelastic properties of poly(methyl methacrylate) with high glass transition temperature by lithium salt addition

The effect of ion‐dipole interaction between lithium cations and oxygen atoms in poly(methyl methacrylate) (PMMA), which leads to the great enhancement of glass transition temperature (T_g), on the linear viscoelastic properties is studied using binary blends of PMMA and lithium trifluoromethanesulfonate (LiCF₃SO₃). The strong interaction at low temperature leads to the high modulus in the glassy region even near T_g. The interaction becomes weak as increasing the temperature. Consequently, the rheological terminal region is clearly detected without a marked enhancement of steady‐state compliance, although the zero‐shear viscosity increases by the LiCF₃SO₃ addition. The result indicates that the crosslinking due to the ion‐dipole interaction has a lifetime that decides the longest relaxation time. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2388–2394     

Chromatographic investigation of the effect of dissolved carbon dioxide on the glass transition temperature of a polymer and the solubility of a third component (additive)

The effect of dissolved carbon dioxide on the glass transition temperature of a polymer, PMMA, has been investigated using molecular probe chromatography. The probe solute was iso-octane, and the specific retention volumes of this solute in pure PMMA and mixtures of PMMA with CO₂ were measured over a temperature range of 0 to 180°C and CO₂ pressures from 1 to 75 atm. The amount of CO₂ dissolved in the polymer was calculated from a model fit to previously published solubility data determined chromatographically. Classical van't Hoff-type plots were used to determine the glass transition temperature of CO₂-impregnated PMMA from low pressure up to 46 atm of CO₂. Solvent-induced plasticization was observed with the glass transition temperature decreasing by about 40°C. At some pressures, glass transitions at low temperatures could not be determined from the van't Hoff plots because of the proximity of the polymer glass transition temperature to the gas–liquid transition temperature for CO₂. For these pressures, a new method was developed to determine the glass transition composition. The glass transition pressure was then calculated from the measured composition and temperature using an isotherm model. In every case, the glass transition temperature decreased linearly with increasing concentration of CO₂ in the polymer. However, at higher compositions, the glass transition pressure decreased with increasing composition and decreasing temperature. The observed retention volume of iso-octane with PMMA in a glassy state was correlated with an adsorption model developed from a theory for liquid–solid chromatography derived by Martire. This model accurately described the observed decrease in retention of iso-octane by adsorption on the surface of glassy PMMA with increasing concentration of CO₂ dissolved in the polymer. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2537–2549, 1998     

Viscoelastic properties and phase behavior of 12‐tert‐butyl ester dendrimer/poly(methyl methacrylate) blends

This study used refractometry, ultraviolet–visible spectroscopy, Fourier transform infrared spectroscopy, differential scanning calorimetry, and dielectric analysis to assess the viscoelastic properties and phase behavior of blends containing 0–20% (w/w) 12‐tert‐butyl ester dendrimer in poly(methyl methacrylate) (PMMA). Dendritic blends were miscible up through 12%, exhibiting an intermediate glass‐transition temperature (T_g; α) between those of the two pure components. Interactions of PMMA C?O groups and dendrimer N? H groups contributed to miscibility. T_g decreased with increasing dendrimer content before phase separation. The dendrimer exhibited phase separation at 15%, as revealed by Rayleigh scattering in ultraviolet–visible spectra and the emergence of a second T_g in dielectric studies. Before phase separation, clear, secondary β relaxations for PMMA were observed at low frequencies via dielectric analysis. Apparent activation energies were obtained through Arrhenius characterization. A merged αβ process for PMMA occurred at higher frequencies and temperatures in the blends. Dielectric data for the phase‐separated dendrimer relaxation (α_D) in the 20% blend conformed to Williams–Landel–Ferry behavior, which allowed the calculation of the apparent activation energy. The α_D relaxation data, analyzed both before and after treatment with the electric modulus, compared well with neat dendrimer data, which confirmed that this relaxation was due to an isolated dendrimer phase. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1381–1393, 2001     

Slow ester side‐group flips in glassy poly(alkyl methacrylate)s characterized by centerband‐only detection of exchange nuclear magnetic resonance

Slow side‐group dynamics in a series of five poly(alkyl methacrylate)s with various side‐group sizes [poly(methacrylic acid) (PMAA), poly(methyl methacrylate) (PMMA), poly(ethyl methacrylate) (PEMA), poly(isobutyl methacrylate) (PiBMA), and poly(cyclohexyl methacrylate), with ? H, ? CH₃, ? CH₂CH₃, ? CH₂CH(CH₃)₂, and ? cyclohexyl alkyl substituents (CODEX), respectively] were studied quantitatively by centerband‐only detection of exchange nuclear magnetic resonance (NMR). Flips and small‐angle motions of the ester groups associated with the β relaxation were observed distinctly in the CODEX NMR data, and the fraction of slowly flipping groups was measured with a precision of 3%. In PMMA, 34% of the side groups flipped on a 1‐s timescale, whereas the fraction was 31% in PEMA at 25 °C. Even the large isobutylether and cyclohexylester side groups flipped in the glassy state, although the flipping fraction was reduced to 22 and about 10%, respectively. In PMAA, no slow side‐group flips were detected on the 1‐s timescale. A striking difference in the temperature dependence of the flipping fraction in PMMA versus PEMA and PiBMA was observed. In PMMA, the flipping fraction was temperature‐independent between 25 and 80 °C, whereas in PEMA, it increased continuously from 31 to 60% between 25 and 60 °C. A similar doubling was also observed in PiBMA. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2444–2453, 2001     

Electron paramagnetic resonance spin probe study of carbon dioxide‐induced polymer plasticization

Steady‐state electron paramagnetic resonance (EPR) spectroscopy using nitroxide spin probes has been used to investigate the plasticization of poly(vinyl acetate) and poly(ethyl methacrylate) by carbon dioxide. By varying the CO₂ pressure at constant ambient temperature, the glass transition for each polymer could be depressed to 25 °C. This effect has been quantified by a parameter P_50G, obtained by plotting the EPR spectral width as a function of CO₂ pressure. Certain spin probes showed free volume distribution effects, manifested in the EPR spectra as “double peaks.” Possible reasons for this phenomenon are presented and discussed, and the efficacy of CO₂ as a plasticizer is clearly demonstrated by direct comparison with di‐n‐butyl phthalate. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2097–2108, 2005     

Relaxation behavior,intramolecular interactions,and local motions on monosubstituted esters of poly(itaconic acid)

The mechanical relaxation spectrum of poly(monocyclohexylmethylene itaconate) (PMCMI) exhibits two well-developed absorptions in the glassy state that in increasing temperature order are named γ and β absorptions. Owing to the restricted conformational versatility of the backbone, the polymer presents a weak glass-rubber relaxation whose intensity is significantly lower than that of the γ absorption. Comparison of the mechanical spectrum of this polymer with that of poly(dicyclohexylmethylene itaconate) (PDCMI) allows the conclusion that the β relaxation is produced by motions in which the ? COOCH₂C₆H₁₁ side groups are involved. The location of the mechanical γ peak suggests that this absorption is produced by flipping conformational transitions in the cyclohexyl residue. Three dielectric absorptions are observed in the glassy state of PMCMI which in increasing temperature order are called δ, γ, and β relaxations. Both the location and the activation energy of the dielectric and mechanical β absorptions suggest that both relaxations are caused by the same molecular motions. Dipolar interactions in the liquid and glassy state are calculated and the results compared with those experimentally evaluated. © 1994 John Wiley & Sons, Inc.     

Effect of sub-Tg relaxations on chromophore reorientation in corona-poled polymers

Activation volumes for chromophore reorientation were measured for a series of guest–host polymeric materials, indicating a significant coupling between chromophore motion and the glassy α and β relaxation dynamics of the polymer host. The specific systems studied were formed by individually dissolving N,N-dimethyl-p-nitroaniline (DpNA), 4-(dimethylamino)-4′-nitrotolane (DMANT), 4-(diethylamino)-4′-nitrotolane (DEANT), and 1-((4-(dimethylamino)phenyl)ethynyl)-4-((4-nitrophenyl)ethynyl)benzene (DMAPEANT) in poly(methyl methacrylate) (PMMA), poly(ethyl methacrylate) (PEMA), and poly(isobutyl methacrylate) (PiBMA). In each of these systems, the isothermal, sub-T_g decay of the second-order optical susceptibility χ⁽²⁾ was monitored as a function of pressure using second harmonic generation. In each system, the observed decay of χ⁽²⁾ was represented by a stretched exponential equation from which the decay time τ₀ and decay distribution width β_KWW were determined. For each dopant molecule, the decrease in activation volume with the increasing size of the polymer host's alkyl side group and the pressure dependence of β_KWW were indicative of partial coupling between chromophore rotation and the glassy β relaxation dynamics of the polymer host. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1013–1024, 1998     

Preparation of CO2‐switchable latexes using N‐[3‐(dimethylamino)propyl]‐methacrylamide (DMAPMAm)

CO₂‐switchable polystyrene (PS), poly(methyl methacrylate) (PMMA), and poly(butyl methacrylate) (PBMA) latexes were prepared via surfactant‐free emulsion polymerization (SFEP) under a CO₂ atmosphere, employing N‐[3‐(dimethylamino)propyl]methacrylamide (DMAPMAm) as a CO₂‐switchable, water‐soluble, and hydrolytically stable comonomer. The conversion of the SFEP of styrene reaches >95% in less than 5 h. The resulting latexes have near monodisperse particles (PDI ≤ 0.05), as confirmed by DLS and TEM. The latexes could be destabilized by bubbling nitrogen (N₂) and heating at 65 °C for 30 min, and easily redispersed by only bubbling CO₂ for a short time without using sonication. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 1059–1066     

Micromechanical fast quasi‐static detection of α and β relaxations with nanograms of polymer

Micromechanical string resonators are used as a highly sensitive tool for the detection of glass transition (T_g or α relaxation) and sub‐T_g (β relaxation) temperatures of polystyrene (PS) and poly (methyl methacrylate) (PMMA). The characterization technique allows for a fast detection of mechanical relaxations of polymers with only few nanograms of sample in a quasi‐static condition. The polymers are spray coated on one side of silicon nitride (SiN) microstrings. These are pre‐stressed suspended structures clamped on both ends to a silicon frame. The resonance frequency of the microstrings is then monitored as a function of increasing temperature. α and β relaxations in the polymer affect the net static tensile stress of the microstring and result in measureable local frequency slope maxima. T_g of PS and PMMA is detected at 91 ±2°C and 114 ±2°C, respectively. The results match well with the glass transition values of 93.6°C and 114.5°C obtained from differential scanning calorimetry of PS and PMMA, respectively. The β relaxation temperatures are detected at 30 ± 2°C and 33 ± 2°C for PS and PMMA which is in accordance with values reported in literature. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1035–1039     

Specific ionic conduction in poly[oligo (oxyethylene glycol) methacrylate] (PMEO)–Li salt complexes under high‐pressure CO2

We measured the ionic conductivity of amorphous poly[oligo (oxyethylene glycol) methacrylate] (PMEO)–lithium salt complexes under a CO₂ pressure varying from 0.1 to 20 MPa. The pressure dependence of the conductivity was positive, and the conductivity was higher than that under an inert gas such as N₂. The ion‐conductive behavior has been modeled using both the Vogel–Tammann–Fulcher (VTF) equation and activation volume theory. The calculated parameters of the VTF equation show that CO₂ that had permeated into the PMEO matrix acts as solvent molecules to dissolve ions and lower the glass transition temperature at high pressures. The ionic conduction in PMEO complexes under high‐pressure CO₂ was scarcely related to the VTF parameters and activation volume equations. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3151–3158, 2005     

Polymer nanoparticles with a sensitive CO2‐responsive hydrophilic/hydrophobic surface

Poly(methyl methacrylate) (PMMA) nanoparticles with a sensitive CO₂‐responsive hydrophilic/hydrophobic surface that confers controlled dispersion and aggregation in water were prepared by emulsion polymerization at 50 °C under CO₂ bubbling using amphiphilic diblock copolymers of 2‐dimethylaminoethyl methacrylate (DMAEMA) and N‐isopropyl acrylamide (NIPAAm) as an emulsifier. The amphiphilicity of the hydrophobic–hydrophilic diblock copolymer at 50 °C was triggered by CO₂ bubbling in water and enabled the copolymer to serve as an emulsifier. The resulting PMMA nanoparticles were spherical, approximately 100 nm in diameter and exhibited sensitive CO₂/N₂‐responsive dispersion/aggregation in water. Using copolymers with a longer PNIPAAm block length as an emulsifier resulted in smaller particles. A higher concentration of copolymer emulsifier led to particles with a stickier surface. Given its simple preparation and reversible CO₂‐triggered amphiphilic behavior, this newly developed block copolymer emulsifier offers a highly efficient route toward the fabrication of sensitive CO₂‐stimuli responsive polymeric nanoparticle dispersions. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 2149–2156     

Photoviscoelastic behavior of amorphous polymers during transition from the glassy to rubbery state

Tensile stress‐relaxation experiments with simultaneous measurements of Young's relaxation modulus, E, and the strain‐optical coefficient, C_?, were performed on two amorphous polymers—polystyrene (PS) and polycarbonate (PC)—over a wide range of temperatures and times. Master curves of these material functions were obtained via the time‐temperature superposition principle. The value of C_? of PS is positive in the glassy state at low temperature and time; then it relaxes and becomes negative and passes through a minimum in the transition zone from the glassy to rubbery state at an intermediate temperature and time and then monotonically increases with time, approaching zero at a large time. The stress‐optical coefficient of PS is calculated from the value of C_?. It is positive at low temperature and time, decreases, passes through zero, becomes negative with increasing temperature and time in the transition zone from the glassy to rubbery state, and finally reaches a constant large negative value in the rubbery state. In contrast, the value of C_? of PC is always positive being a constant in the glassy state and continuously relaxes to zero at high temperature and time. The value of C_σ of PC is also positive being a constant in the glassy state and increases to a constant value in the rubbery state. The obtained information on the photoelastic behavior of PS and PC is useful for calculating the residual birefringence and stresses in plastic products. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2252–2262, 2001     

Polarized light‐induced photoisomerization in glassy poly(methyl methacrylate) and local relaxation processes of the polymer matrix

Photoisomerization kinetics of trans 4‐methoxystilbene induced by irradiation with linearly polarized light was investigated in the glassy state of poly(methyl methacrylate)(PMMA). The reaction was strongly selected by linearly polarized light as revealed by a large dichroic absorption generated upon irradiation. The optical anisotropy increases with increasing irradiation time and passes through a maximum before approaching an equilibrium value, which strongly depends on the experimental temperatures. From the decay of the total absorbance of the trans‐isomer observed upon irradiation with 313 nm UV light, it was found that the rates of the photoisomerization trans → cis were not significantly changed within the temperature range of the experiments. On the other hand, the reorientational relaxation times of the stilbene, which were directly measured by the annealing‐after‐irradiation techniques, depend strongly on temperature. These relaxation data were compared to the previous results obtained with dopants of the size larger than the stilbene and were discussed in conjunction with the local relaxation processes of the PMMA matrix. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 682–690, 2000     

Unusual relaxation process in polybutadiene: Resolving the controversy

We report the observation of an unusual relaxation process in depolarized light scattering spectra of polybutadiene (PBD) with two different vinyl contents. The process showed up in the gigahertz frequency range with relatively mild temperature dependence and was similar to a secondary relaxation process. The most surprising observation was that the process exists even at high temperatures and does not merge with the segmental relaxation up to a temperature of 400 K (T > 2T_g). Possible mechanisms of this particular relaxation in PBD are discussed. The process is compared to the so‐called E process, double‐bond hopping process, and dielectric β process. We emphasize that this process differs from the dielectric β process, is unique for 1,4‐PBD, and has not been observed in other polymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 994–999, 2004