Τc Values Research Articles

Interaction between Na+ and polymer in aqueous solution of sodium salts of poly(2‐hydroxyethyl methacrylate‐co‐methacrylic acid) studied by 23Na‐NMR

AbstractThe interaction between Na+ and polymer was studied by 23Na‐NMR for the aqueous solution of P(HEMA‐co‐MAANa), sodium salt of poly(2‐hydroxyethyl methacrylate‐co‐methacrylic acid), as a function of the polymer concentration, charge density of the polymer chain, and temperature. The NMR line width of 23Na‐NMR in 1% (w/v) aqueous solution of the P(HEMA‐co‐MAANa) narrowed with increasing temperature due to the rapid exchange of Na+ between free and polymer‐bound states with a rate of exchange exceeding the quadrupolar relaxation rate in the latter state. At high concentrations of the polymer above 1.0% (w/v) at 298 K, the 23Na‐NMR relaxation fits for a single Lorentzian due to the rapid exchange between two Na+ states. However, it follows a biexponential decay of magnetization in dilute solutions of polymer. The biexponential decay character of relaxation increased with the increase of the fraction of the MAANa monomer unit on the polymer chain. This feature of 23Na‐NMR relaxation was used to deduce the correlation time (τc), the degree of binding (pB), and the quadrupole coupling constants (X) of the polymer‐bound counterion. The χ and τc values show that the mobilities of the polymer chain are correlated with the motion of Na+ in aqueous solution of the polymer and there is a small degree of the specific binding between COO− and Na+. No evidence in support of the intramolecular conformational change by the charge density variation in P(HEMA‐co‐MAANa) was obtained. © 1993 John Wiley & Sons, Inc.

Application of 1H NMR selective and biselective relaxation times. III—conformational analysis of quinidine in solution

AbstractA relaxation method was applied to quinidine (1) where cross‐relaxations (σij) were obtained by 1H selective and biselective T1 measurements and correlation times for molecular reorientation (τc) were evaluated from the frequency dependence of the non‐selective T1. The interproton distances (rij) were estimated using these σij and τc values, and the conformation of 1 was determined by comparing the estimated rij values with those calculated from the molecular model. The resulting proposed conformation had the following dihedral angles: ∠ C‐11C‐10C‐3–C‐4 = 150°, ∠ C‐4′C‐9C‐8C‐7 = 50° and ∠ C‐9′C‐4′C‐9C‐8 = 70°. The conformation of the side‐chain (∠ C‐11C‐10C‐3C‐4) is different from the results for the crystal by x‐ray analyses.

Nuclear magnetic resonance studies of the methylammonium hexahalotellurates

A 2H and 14N NMR study of the solid methylammonium hexahalotellurates, (MA)2TeX6 (MA = CH3ND3+ or CD3NH3+, X = Cl, Br, and I), has been undertaken to characterize the dynamics of the methylammonium (MA) ion as a function of temperature. At room temperature, the MA ion in the hexachlorotellurate (solid II) is confined to C3 jumps about the C—N axis while a small angle libration of the C—N axis is occurring. In the room temperature phase, solid I, of (MA)2TeBr6 and (MA)2TeI6 the MA ions are performing overall reorientations on the ps time scale, averaging the 2H nuclear quadrupolar interactions to zero. Variable temperature 2H NMR spin-lattice relaxation times, T1, indicate an activation energy, EA, for "isotropic" reorientations of the CH3ND3+ ion of 5.2 ± 0.5 and 2.6 ± 0.3 kJ mol−1 for X = Br and I, respectively. Deuterium T1 values for C-deuterated MA ion in the hexaiodotellurate indicate an EA for whole-ion reorientation of 3.1 ± 0.3 kJ mol−1. At any given temperature, the correlation time, τc, derived from the T1 results was found to be the same for the two deuterium-labelled hexaiodotellurates. The similarity of both the EA and the τc values implies correlated motion of the methyl and ammonium groups. The 14N T1 results for solid I of (MA)2TeI6 indicate that C—N axis motions, with an EA = 5.6 ± 0.6 kJ mol−1, are more hindered than N—D or C—D bond dynamics. The 2H NMR spectra for (MA)2TeI6 (solid II) and (MA)2TeBr6 (solids II, III, and IV) are characterized by a Pake doublet line shape. The measured peak-to-peak splittings are less than what is predicted by C3 motion about the molecular symmetry axis. It is possible to model these line shapes by postulating that C3 rotations of the methyl and ammonium groups occur as the C—N axis librates in an effective cone about the position of the static molecular axis. For (CH3ND3)2TeBr6 and (CD3NH3)3TeBr6 the peak-to-peak splittings in the 2H NMR spectra were measured as a function of temperature in solid phases II, III, and IV and were found to be similar. Finally, the 2H NMR line shape relaxation for (MA)2TeBr6 (solid III) displays an orientation dependence indicating that rotations about the C—N axis are discrete rather than diffusive in nature. For solid phase II of (MA)2TeCl6, the line shape is observed to relax isotropically, implying that continuous C3 rotations are taking place. Keywords: 2H and 14N NMR, methylammonium hexahalotellurates, molecular motion.

Carbon‐13 NMR relaxation study of the overall and internal motions in compounds containing n‐octyl chains

AbstractThe 13C nuclear relaxation behaviour of n‐alkyl chains in a variety of compounds can be described in terms of two relaxation times, one for tumbling (τc) and one for each carbon nucleus for the internal motions (τc). Relaxation data for the quaternary carbon nuclei of n‐octylbenzene and n‐octyl cyanide have been used to determine τc) and their activation energies [Ea(τc)]. These values have enabled τe and their associated activation energies [Ea(τe)] to be calculated for each carbon in the alkyl chains of the two compounds. In these compounds the values for C‐6 appear to be invariant with τe(298) = 15 ± 2 ps and Ea(τc) = 15 ± 1 kJ mol−1. Assuming that these are universal values for all n‐octyl chains, we have used them to calculate τe and Ea(τe) for other simple n‐octyl compounds, thus allowing τc and E.a(τc) to be determined. It was found that Ea(τc) values correlate well with those for Ea(n/T) obtained from viscosity measurements. Di‐n‐octyl ether shows motional properties similar to those of the straightchain compounds.Simultaneous fitting of relaxation rate and NOE enhancement data measured over a range of radiofrequencies and temperatures permits a wealth of motional properties to be discerned when there is a suitable frequency dispersion. Both tri‐n‐octylamine and polydecene tumble sufficiently slowly to allow both relaxation rate and NOE data to be used to evaluate τc and τe and their activation energies without making any assumptions about C‐6. The values of τc(298) and Ea(τc) obtained from C‐6 for tri‐n‐octylamine are 314 ± 12 ps and 18.5 ± 0.4 kJ mol−1, respectively, and the corresponding values for polydecene are 576 ± 41 ps and 16.1 ± 1.3 kJ mol−1, respectively.

13C NMR studies of the polymerization mechanism and the dynamics of poly(alkyl methacrylate) grafted onto silk fibers

Abstract13C NMR was extensively used to determine the tacticity of poly(methyl methacrylate) (PMMA), poly(ethyl methacrylate) (PEMA), and poly(butyl methacrylate) (PBMA) grafted onto silk fibers using radiation‐induced graft copolymerization. All polymers are predominantly syndiotactic and the tacticity is virtually independent of the degree of grafting. The value of PΣ (= Pm/r + Pr/m) was calculated from the triad distribution and was found to be approximately one. This indicates that all the above polymer chains grafted onto silk fibers are syndiotactic and obey Bernoullian statistics. The number‐average sequence length of either meso or racemic additions was determined using the triad distribution. The 13C NMR relaxation parameters, spin‐lattice relaxation time, T1, and nuclear Overhauser effect, NOE, were observed and then the value of the correlation time for average segmental motion, τc, and the width parameter, p, were determined by assuming a log χ2 distribution for the correlation time. A relatively small value of p was obtained, indicating that the distribution of the correlation time is large. Taking into account the τc values of different poly(alkyl methacrylate) chains grafted onto silk fibers, the following order of segmental motion was furnished: PMMA > PEMA > PBMA.

Threshold relations for the transport of sediment by overland flow on desert hillslopes

AbstractAlthough the Shields relation was developed for rivers, it has been applied to sediment transport by overland flow. According to the Shields relation, where the critical boundary Reynolds number Re*c exceeds 40, the critical Shields number F*c is independent of both Re*c and the ratio of the critical flow depth to particle diameter dc/D. Analyses of data collected from runoff plots in southern Arizona reveal that F*c is positively correlated with both Re*c and dc/D. Thus the Shields relation does not apply to overland flow on debris‐covered desert hillslopes.Multiple regression analysis is employed to develop alternative threshold relations in which critical boundary shear stress τc is related to D and dc/D (R2 = 0.782) and to D and Sc (critical gradient) (R2 = 0.625). The computed R2 values derive in large part from the spurious correlations of dc/D and Sc with τc. Nevertheless, the relations may be utilized to predict τc. In this regard, the latter relation is likely to prove more useful than the former because Sc is generally known, whereas dc is not.An investigation of the functional relation between τc and D reveals that τc varies approximately with D2 for overland flow on the desert hillslopes under study, whereas the Shields relation predicts a linear relation (i.e. a D exponent of 1). This result is consistent with Cheng's data which show that F*c varies with (dc/D)−1 where 0.4 < dc/D < 2 and may be explained in terms of increased energy dissipation both in separation zones downslope of particles and in distortion of the water surface as dc/D decreases. Consequently, larger values of τc, and hence F*c, are required to initiate the transport of particles of a given size D as dc decreases.

Solvent dependence of 13C relaxation times and reorientational dynamics in tribromobenzene

AbstractThe 13C spin–lattice relaxation times and nuclear Overhauser enhancements of protonated carbons in 1, 3, 5‐tribromobenzene were measured in a number of solvents of widely varying viscosity, Derived reorientational correlation times were found to increase approximately linearly with solution viscosity, as predicted by hydrodynamic theories of rotational diffusion.Rotational correlation times calculated from the perrin stick model were two to three times longer than the measured τc values. Similarly, correlation times predicted by the Hu–Zwanzig slip model were too small by a factor of two. On the other hand, application of the newer Hynes–Kapral–Weinberg theory furnished reorientational correlation times that were in virtually quantitative agreement with the experimental results.

NMR of carboxylic‐17O in amino acids

Abstract17O NMR studies were conducted on the α‐COOH groups of the amino acids Val, Leu, Ile, His and Pro and on the γ‐COOH group of Glu. Limit chemical shifts, downfield from external water, were 249‐257 ppm in aqueous solution at low pH, and 234–243 ppm in HSO3F. The relative nuclear screening order for α‐COOH 17O between pH ‐1 and 13 and in HSO3F was usually Pro>Leu>His>Val>Ile, reflecting on interactions with the side chain. Concomitant with ionization in aqueous solution, the α‐ and γ‐COOH resonances were displaced to lower field, by 13–18 aid 24 ppm, respectively, presumably owing to overriding effects of the bond order‐charge density term in the paramagnetic contribution toward nuclear shielding. Titration with alkali above neutrality resulted in 2–4 ppm upfield shifts related to deprotonation of the α‐NH3+ group. T2 relaxation times were inversely related to the molecular weight. Line widths of amino acid 17O‐COOH resonances near neutrality were between 280 and 525 Hz, corresponding to T2 relaxation times between 0.6 and 1.1 ms. Titration from acidic to neutral pH increased T2 by up to 1.7‐fold. T1 measured for 17O‐Gly and γ‐17O‐Glu changed in parallel with T2. This was attributed to decreasing rotational correlation times, τc, in line with expected changes in the nuclear quadrupole coupling constant. τc values calculated from 17O relaxation in solutions near neutrality (zwitterion predominant) were in good agreement with τη, expected from solution properties and with the assumption of isotropic rotation. T2 decreased when the pH was increased above neutrality, partly owing to increasing solution viscosity.

Poly(O-acyl-hydroxy-L-proline) IV. Studies of Molecular Motions in Poly(O-acetyl, butyryl, hexanoyl, dodecanoyl, and benzoyl-hydroxy-L-proline) Films by the Spin Probe Technique

The molecular motion in poly(O-acetyl (Ac), butyryl (But), hexanoyl (Cap), dodecanoyl (Lau), and benzoyl (Bz)-hydroxy-L-proline (Hyp)) films was investigated by ESR measurements with 2,2,6,6-tetramethyl-4-hydroxypiperidine-1-oxyl (TEMPO) as the spin probe. As the length of acyl side chains increased, the temperature at which the separation of the outer extrema of ESR spectra reached 50 gausses (T50) decreased. The rotational correlation times (τc) obtained from the ESR spectra at −70°C for series of polymers were nearly the same. The values of τc at 130°C decreased with an increase in the acyl side chain length until the number of carbon atoms in the acyl chains reached 6. The activation energies of TEMPO in the polymers were less than 3 kcal mol−1 at low temperatures. At high temperatures, the activation energies of poly(O-Ac-Hyp) and poly(O-Bz-Hyp) differed scarcely from those at low temperatures. The activation energies of poly(O-But-Hyp), poly(O-Cap-Hyp), and poly(O-Lau-Hyp) were enhanced and particularly that of poly(O-Cap-Hyp), exceeding 10 kcal mol−1.

Multinuclear magnetic relaxation determination of nuclear quadrupole coupling constants for adamantane and hexamethylenetetramine in solution

Deuterium and 14N nuclear quadrupole coupling constants for adamantane and hexamethylenetetramine (HMTA) have been determined in carbon tetrachloride and chloroform solutions. The single rotational correlation time, τc, of these globular molecules has been obtained by distinct measurements derived from 1H and 13C nuclear magnetic relaxation. It is shown that molecular geometries optimized by a molecular-mechanics method (MM2) yield consistent τc values extracted from these two spin-½ relaxation rates. These values in turn make it possible to determine the 2H or 14N nuclear quadrupole coupling constant with an accuracy of ±3%. The 2H quadrupole coupling constants of adamantane (182 kHz, independent of the position of the deuterium) and of HMTA (169 kHz) appear to be independent of the solvent. The 14N quadrupole coupling constant of HMTA in carbon tetrachloride (4.17 MHz) is lower than the solid-state value. It is shown that rapid hydrogen bonding between HMTA and chloroform modulates 14N relaxation.

Total‐moment spectra of fourteen large earthquakes

Total‐moment spectra MT(ω) = ‖M(ω)‖/ , where M is the moment rate tensor, are computed for 14 large earthquakes recorded by the International Deployment of Accelerometers (IDA) network using the scalar‐moment retrieval method proposed by Silver and Jordan [1982]. For each event we obtain estimates of MT averaged over the 10 disjunct, 1‐mHz intervals in the low frequency band 1–11 mHz; typical IDA record sets from events with MT ≳ 0.2 A (1 A = 1027 dyne · cm) yield standard errors on the 1‐mHz averages that are generally less than 20%. Our multiple‐band estimates of MT are usually consistent with comparable single‐band values found by other investigators. From the total‐moment spectra we derive the zero‐frequency (static) moment ≡ MT(0) and the characteristic source duration τc ≡ 2 (Var [f(t)])½, where f(t) is the time function of the moment rate tensor, assumed to be the same for all components. The parameter τC formally depends on the second‐degree temporal, spatial, and mixed spatial‐temporal moments of an extended source, but calculations with realistic source geometries indicate that the interpretation of TC strictly in terms of the second temporal moment leads to very little error. A plot of τc against shows considerable scatter; some events lie significantly above the empirical scaling curve of Kanamori and Given [1981] (‘slow earthquakes’) and some below (‘fast earthquakes’). Examples of the former include all three deep‐focus events analyzed here as well as the 1970 Colombia and 1963 Peru‐Bolivia deep‐focus earthquakes, whose total‐moment spectra are calculated from the moment tensor solutions of Gilbert and Dziewonski [1975]. An example of the latter is the great Sumbawa earthquake of August 9, 1977 ( = 24±3 A), which is inferred to have a relatively shallow spatial centroid (< 20 km) and a nearly flat moment spectrum, suggesting that the faulting was confined to the upper, more brittle portion of the oceanic lithosphere. Three other large earthquakes—Tonga (June 22, 1977; = 23±2 A), Kuril Islands (December 6, 1978; = 3.6±0.2 A), and Tumaco (December 12, 1979; = 25±2 A)—exhibit moment spectra which significantly decrease toward higher frequencies, indicating larger values of τc. The aftershocks of both the Tonga and Kuril Islands events are distributed over a considerable range of depths, consistent with rupture into the lower, more ductile portions of the oceanic lithosphere. We speculate that the characteristic source duration may be causally related to the depth of coseismic rupturing within the lithosphere.

Determination of hob offset required to generate nonstandard spur gears with teeth of equal strength

A method has been developed for determining the hob offset e 1 of the pinion from the value of e 1 + e 2 for a pair of spur gears designed to operate at a nonstandard center distance. This method is based on adjusting e 1 and e 2 so that the static stress in the pinion teeth is approximately equal to that in the gear teeth. Charts were plotted so that the ratio of e 1/( e 1 + e 2) could be determined for various velocity ratios and for several changes in center distance. The results of calculating static tooth stresses by the method developed in this paper are compared with those using the Lewis equation and those following the AGMA Standards. Curves were also plotted so that tooth stresses in the form of stress factors could be determined for various values of τC, diametral pitch, and the ratio N 2/( N 1 + N 2).

AMPLITUDE-DEPENDENT SOUND ATTENUATION IN bcc 3He CRYSTALS WITH 4He IMPURITIES

The attenuation of longitudinal sound wave at 10 MHz was investigated in bcc 3He crystals with 4He impurities at a molar volume of 24.4 cm3/mole. The attenuation became amplitude-dependent after the crystals were cooled below the phase separation temperature. Namely, the amplitude dependence appeared at 86 mK and 98 mK for 4He concentrations x4 = 480 ppm and 1600 ppm, respectively, and disappeared at 350 mK irrespective of x4. The critical amplitude above which the attenuation increased was independent of x4 and T. It is proposed that screw dislocations which were multiplied in the course of the phase separation were responsible for the effect. The critical resolved shear stress is estimated to be τc = 5x10-5µ from the critical amplitude, where µ is the shear modulus. The value of τc is considerably lower than the Peierls stress so that the dislocations possibly tunnel the Peierls barrier.

Conformation and dynamic structure of poly(inosinic acid) in neutral aqueous solution by 1 H-, 2 H-, 13 C-, and 31 P-NMR spectroscopy.

The conformation and dynamic structure of single-stranded poly(inosinic acid), poly(I), in aqueous solution at neutral pH have been investigated by nmr of four nuclei at different frequencies: 1 H (90 and 250 MHz), 2 H (13.8 MHz), 13 C (75.4 MHz), and 31 P (36.4 and 111.6 MHz). Measurements of the proton-proton coupling constants and of the 1 H and 13 C chemical shifts versus temperature show that the ribose is flexible and that base-base stacking is not very significant for concentrations varying from 0.04 to 0.10M in the monomer unit. On the other hand, the proton T1 ratios between the sugar protons, T1 (H1 ')/T1 (H3 '), indicate a predominance of the anti orientation of the base around the glycosidic bond. The local motions of the ribose and the base were studied at different temperatures by measurements of nuclear Overhauser enhancement (NOE) of protonated carbons, the ratio of the proton relaxation times measured at two frequencies (90 and 250 MHz), and the deuterium quadrupolar transverse relaxation time T2 . For a given temperature between 22 and 62°C, the 13 C-{1 H} NOE value is practically the same for seven protonated carbons (C2 , C8 , C1' , C2' , C3' , C4' , C5' ). This is also true for the T1 ratio of the corresponding protons. Thus, the motion of the ribose-base unit can be considered as isotropic and characterized by a single correlation time, τc , for all protons and carbons. The τc values determined from either the 13 C-{1 H} NOE or proton T1 ratios, T1 (90 MHz)/T1 (250 MHz), and/or deuterium transverse relaxation time T2 agree well. The molecular motion of the sugar-phosphate backbone (O-P-O) and the chemical-shift anisotropy (CSA) were deduced from T1 (31 P) and 31 P-{1 H} NOE measurements at two frequencies. The CSA contribution to the phosphorus relaxation is about 12% at 36.4 MHz and 72% at 111.6 MHz, corresponding to a value of 118 ppm for the CSA (σ = σ∥ - σ⟂). Activation energies of 2-6 kcal/mol for the motion of the ribose-base unit and the sugarphosphate backbone were evaluated from the proton and phosphorus relaxation data.

Extrudate distortion studies of polystyrene using an extrusion rheometer

Uncorrected and corrected logarithmic flow-curves for a general purpose polystyrene (MW=261000 and MW/MN=4.4) obtained using a Davenport Extrusion Rheometer are shown for the range 160 to 200° C. The uncorrected flow curves show a change in slope, but at the lower extrusion temperatures this change occurs after the appearance of distorted extrudates. The onset of extrudate distortion obtained from observation does not coincide with the change in slope of the graph. The corrected logarithmic flow curves show no change in slope. Values of $$\dot \gamma _c$$ and η c from both sets of graphs show that $$\dot \gamma _c$$ is inversely proportional to η c, and for the higher melt temperatures the corrected τ c values increase with temperature. The high value of critical wall stress at 160° C is attributed to the increase in melt elasticity with decreasing temperature being a greater effect than the decrease in elasticity due to a decrease in $$\dot \gamma _c$$ .

The nature of the NADP complex with manganese(II) ions as studied by proton and phosphorus magnetic resonance

Proton and phosphorus magnetic resonance techniques have been applied to study the conformation of the complex formed between Mn(II) ions and nicotinamide adenine dinucleotide phosphate (NADP) in aqueous solutions at a pH of 7.5 and 20 °C. The dipolar correlation time (τc) for the Mn(II)–NADP complex at 20 °C was calculated to be 1.7 × 10−10 s, based on the measurement of proton longitudinal relaxation time ratios and a literature value of τc for nicotinamide adenine dinucleotide (NAD). The τc, as well as the 1H and 31P relaxation data together with the measured stability constant for this complex, were used to calculate the distances from the 1H and 31P nuclei to the Mn(II) ion. These distances are 3.8 Å to A8, 5.0 Å to A2, 4.5 Å to A1′, 5.3 Å to N2, 5.4 Å to N6, 5.5 Å to N5, 5.8 Å to N1′, and 6.3 Å to N4. The distances to the linkage 31P nuclei are 3.7 Å, and 3.3 Å to the adenosine ribose 2′-phosphate. Based on these distances, a model is proposed for the Mn(II)–NADP complex. In this complex, the Mn(II) ion is bonded to the oxygens of all three phosphates, and the adenine and nicotinamide bases are 7–8 Å apart and parallel. Hence the Mn(II) ion is located between and to one side of the two bases but is distinctly closer to the adenine base. The adenine base is in the anti conformation, whereas the nicotinamide moiety can be either syn or anti. Hence there is little or no close stacking of the two bases in the complex. The addition of Mg(II) ions to a solution of free NADP caused no observable shift of the aromatic proton peaks, indicating no differences in shielding effects. Hence the rings are probably similarly oriented in both free NADP and the metal–NADP complex. Effects on the transverse relaxation rates due to the paramagnetic metal ion (T2p−1) were also measured from the 31P linewidths as a function of temperature. The lifetime of the metal ion in the complex is 4.0 ± 0.5 × 10−6 s and ΔH≠ for the exchange process is 13.7 ± 0.5 kcal/mol.

A nuclear magnetic resonance study of pyridoxal phosphate – metal ion interactions. II. Binding of manganese(II)

The line width and spin–lattice relaxation rates of phosphorus and proton nuclei in PLP have been measured as a function of temperature in the presence of Mn(II) using pulsed nmr methods. The T1M of 31P in PLP-Mn(II) is very close to the T1M values of β- and γ-phosphorus atoms in ATP–Mn(II) at ∼40 °C. The T1 data of 31P and 1H have been interpreted in terms of the dipolar interaction between the electron and nuclear spins. With the assumption that the Mn(II) interacts directly with the phosphate of PLP the rotational correlation time τc at 38 °C was calculated to be 7.6 × 10−10 s from phosphorus T1 data. This τc value was subsequently used to calculate metal–proton distances from proton T1 and T2 data. The results lead to the conclusion that the phosphate-bound metal interacts directly with the aldehyde oxygen in a 1:1 PLP–Mn(II) complex. The linewidth of the 13C resonances of PLP in the presence of Mn(II) supports this conclusion. The structure assigned for PLP–Mn(II) complex is in conformity with the structure for PLP-Co(II) complex.

Molecular motions in liquid. II. Deuteron relaxation study of the rotation of highly symmetrical molecules in solutions

The deuteron spin–lattice relaxation times (T1) of adamantane-d16, tris(3-deutero-2,4-pentadionato) aluminum, α,α-dideuterotetraethylammonium iodide, and α,α-dideuterotetrabutylammonium iodide in several solvents are studied as functions of temperature. The rotational correlation times (τc) for the solute molecules were obtained from the T1 data. The results were analyzed in terms of a dimensionless parameter κ, which is the ratio between experimental τc and the value of τc calculated from the Debye–BPP equation. It seems that for molecules with small κ (slip boundary condition), the value of κ increases with the increase of temperature and for molecules with κ closer to one (stick boundary condition), the value of κ decreases with the increase of temperature.

A method for finding critical stresses of dislocation movement

A method is presented which makes possible the determination of the critical resolved shear stress, τc, for dislocation movement in a crystal. The method is based on the analysis of dislocation rosettes which are generated either by microindentation, or by precipitates of a second phase. The method does not require a knowledge of the indentation (or precipitate) stress field; it requires only information on the positions of a set of leading dislocation loops. At once one can also obtain the effective indentation stress field and, for the first time, the precipitate stress field. For illustration, the method is applied to the determination of τc in silicon, using both indentation and precipitate dislocation rosettes. The value of τc thus obtained varies from a low of 3×107 dyn/cm2 in oxygen-free samples to a high of 5.5×108 dyn/cm2 in a sample containing ∼2×1018 atoms/cm3 of oxygen with clustering. The SiO2 precipitate stress field in the present case was found to vary as x−1, suggesting that the precipitate is probably a thin plate.

Quantitative chemically induced dynamic nuclear polarization (CIDNP) study of the photolysis of benzaldehyde in solution

Qualitative studies of the polarizations in the CIDNP spectra observed from benzaldehyde in a series of solvents are reported and the reaction mechanism which leads to polarized products in hexane solution is established. The time-evolution of two signals which results from isolated protons in single products has been observed in hexane solution under conditions of low overall conversion to products. The results have been analysed using a kinetic model of the reaction and the diffusion description of CIDNP. The quantitative results are entirely consistent with the model, and values of the diffusional correlation time τc= 2.6 ± 0.3 × 10–12 s and the rate constant for hydrogen transfer between the ketyl radical and ground-state benzaldehyde, k3= 1 × 106 mol–1 dm3 s–1, are reported. A feature of the theoretical treatment is the use of intensity ratios to overcome problems of absolute intensities of lines observed in the products of radical reactions.