Average Ring Size Research Articles

Probability distribution functions as descriptors for long range randomness in non-crystalline solids

Probability distribution functions (PDF) can be useful descriptors for the random structure of non-crystalline solids. The lognormal PDF has provided a good description of the distribution of interstitial site sizes in non-crystalline solids, both metallic and nonmetallic. The utility of this descriptor to characterize the ring statistics of vitreous silica under a wide range of pressures has been evaluated. In fact, the normal (Gaussian) PDF is a better descriptor for ring statistics for pressures up to 23 GPa. Although the average ring size is largely unchanged (slightly less than 6.0) over the entire pressure range, the standard deviation of the ring size distribution rises sharply at 9 GPa serving as a sensitive indicator of the onset of plastic deformation.

The acoustic properties of borosilicate glass affected by oxide of rare earth gadolinium

SiO 2–Na 2O–B 2O 3 glasses doped with different mol% content of Gd 2O 3 have been prepared by rapid-quenching method. Longitudinal and transverse ultrasonic wave velocities have been measured using the pulse-echo method at 4 MHz frequency at room temperature. Elastic moduli, Debye temperature, softening temperature and Poisson’s ratio have been obtained as a function of Gd 2O 3 modifier content and are found to be rather sensitive to the glass composition. Information about the structure of the glass can be deduced after calculating the average stretching force constant and the average ring size. A comparison between the experimental elastic moduli data obtained in this study and those calculated theoretically by other models has been discussed.

Structural Analysis of Some Alkali Diborate Glasses

This manuscript presents a theoretical analysis of the correlation between the computed bulk modulus and the structure of a series of multicomponent sodium diborate based glasses in terms of the bond compression model. The main parameters in the analysis were the computed elastic moduli, the average stretching force constant and the average atomic ring size. These parameters were calculated for every glass series and for every glass composition. The results showed that the average force constant and the elastic moduli of these glasses are sensitive to the decrease in the sodium diborate content. This behaviour was attributed to the increase in the molar volume, and to the role of the dierent modifiers.

Optical and acoustic properties of TeO2/WO3 glasses with small amount of additive ZrO2

The optical and acoustic properties of tellurite glasses in the system TeO 2 /ZrO 2 /WO 3 have been investigated. The refractive index at different wavelengths and the optical spectra of the glasses have been measured. From the refractive index and absorption edge studies for prepared glasses, the optical parameter viz; optical band gap ( E opt ), Urbach energy, (Δ E ), dispersion energy, E d , and the average oscillator energy, E 0 , have been calculated. Sound velocities were measured by pulse echo technique. From these velocities and densities values, various elastic moduli were calculated. The variations in the refractive index, optical energy gap and elastic moduli with WO 3 content have been discussed in terms of the glass structure. Quantitatively, we used the bond compression model for analyzing the room temperature elastic moduli data. By calculating the number of bonds per unit volume, the average stretching force constant, and the average ring size we can extract valuable information about the structure of the present glasses.

Molecular dynamics simulations of calcium aluminate glasses

Molecular dynamics simulations of a series of calcium aluminate glasses have been carried out using empirical potentials with a covalent term. The simulations closely reproduce the total neutron correlation function of glasses with 30 and 38 mol% Al 2O 3 and physical properties such as elastic constants. For compositions close to the eutectic 37 mol% Al 2O 3, aluminum is tetrahedrally coordinated by oxygen, but the proportion of five-fold and six-fold coordination and also edge-sharing tetrahedra gradually increases with increasing Al 2O 3 content. The coordination number for oxygen around calcium atoms is close to 6 and this involves a larger coordination at a shorter, well-defined distance, followed by a smaller coordination with a broader range of distances. When the Al 2O 3 content decreases, the calcium aluminate structure becomes depolymerised and the average ring size increases. Also reported is an X-ray photoelectron spectroscopy measurement on a glass sample with 38 mol% Al 2O 3, which shows that 38.6 ± 0.9% of the oxygens are non-bridging, in excellent agreement with the simulations.

Ultrasonic studies of (TeO 2) 50–(V 2O 5) 50− x(TiO 2) x glasses

New ternary tellurite glasses in the form (TeO 2) 50–(V 2O 5) 50− x (TiO 2) x have been prepared. Both longitudinal and shear ultrasonic velocities were measured in different compositions of the glass system by using the pulse-echo method at 5 MHz frequency and at room temperature. The elastic properties of ternary telluirte glasses (TeO 2) 50–(V 2O 5) 50− x (TiO 2) x were measured as a function of composition. The ultrasonic velocity data, the density, the calculated elastic moduli, micro-hardness, softening temperature, and Debye temperature depend on the glass composition. By calculating the number of network bonds per unit volume, the average stretching force constant, and the average ring size, information about the structure of the glass can be deduced. Comparison between the calculated and the experimental elastic moduli and Poisson's ratio have been carried out.

Structural interpretations of aluminosilicate glasses

This manuscript presents a theoretical analysis of the correlation between the bulk moduli and the structure of a series of multicomponent aluminosilicate glasses in terms of the bond compression model. The main parameters in the analysis were the computed elastic moduli, the average stretching-force constant and the average atomic ring size. These parameters were calculated for every glass series and for every glass composition. The results showed that the average force constant of these glasses increases and the elastic moduli decrease with the increase in the SiO 2 content (pure covalent bonds). This behaviour was attributed to the decrease in the molar volume, and the role of both CaO and Al 2O 3. The average atomic ring size of the studied glasses are about two-thirds of pure SiO 2, whilst the elastic moduli of pure SiO 2 glass are about two thirds of these glasses.

Nature of Residual Liquid Holdup in Packed Beds of Spherical Particles

The theoretical prediction of the residual liquid holdup in beds packed with nonporous spherical particles is tested by microscopic imaging of a bed of glass spheres wetted by water. The commonly used Young−Laplace equation accurately predicts the meniscus shapes of the pendular rings (Saez, A. E.; Carbonell, R. G. J. Colloid Interface Sci. 1990, 140, 408). The ring sizes are measured directly, and the minimum internal energy (Mao et al. Chem. Eng. Sci. 1993, 48, 2697) and critical percolation (Kramer, G. J. Chem. Eng. Sci. 1998, 53, 2985) boundary conditions proposed in the literature are shown to overpredict the average ring size. The summation of ring volumes over the bed yields a residual holdup smaller than that obtained through weighing. It is concluded that additional liquid is trapped through capillary action at locations where two or more particles are in close proximity. Photographic evidence of the existence of such liquid “globules” is presented.

Ultrasonic study and physical properties of some borate glasses

The structure of the glass system (75− x)B 2O 3– xBi 2O 3–25Li 2O, where x=5, 10, 15, and 20 mol% was investigated by using pulse-echo technique. Elastic properties of the glass system have been calculated together with Poisson’s ratio and Debye temperature from the measured densities as well as longitudinal and shear ultrasonic velocities at room temperature. Ultrasonic velocity measurements were taken at 4 MHz. Estimated parameters based on Makishima–Mackenzie theory and bond compression model were calculated in order to analyse the experimental elastic moduli. Addition effect of Bi 2O 3 on the elastic moduli was investigated in terms of the number of network bonds and the mean cross-link density of the glass systems. The average atomic ring size of the network was also calculated and it was found that it depends on the concentration of the modifiers. Composition dependence of the elastic moduli and Poisson’s ratio from one hand and the trend of both the ring diameter and the packing density from the other hand showed structural change at x=15 mol%.

“Secondary” descriptor development for zeolite framework design: an informatics approach

An analytical foundation for statistically identifying key crystallographic descriptors for zeolite frameworks is presented in this paper. A new set of descriptor formulations containing various aspects of information about zeolite crystal structure is introduced. Selected crystallographic structure data for all known zeolite structure types were analyzed using principal components (PC) and partial least squares in order to understand the statistical distribution and hence help design new zeolites. Critical crystallographic ratios and transformed variables with good correlations to average ring size were calculated. The principal components of the framework descriptors were used to identify the important linear combinations of critical descriptors and to identify statistical outliers. Partial least squares was used to predict the average ring size based on these descriptors. These new secondary descriptors were tested against experimental findings of zeolite analogue structures demonstrating the value of these secondary descriptors as a guide for future combinatorial experiments.

Effect of irradiation on some optical properties and density of lithium borate glass

Borates and silicate glasses containing boron oxide have been widely used for optical lenses with high refractive index and low dispersion characteristics. Alkali borate glasses are of great technological interest especially lithium borates as solid electrolytes because of their fast ionic conduction. In this study the optical properties including infrared and refractive index and density of lithium borate glass as a base glass were studied. The effect of the presence of either aluminum or lead oxide, or the presence of one of the following transition metal, Fe 2O 3, TiO 2 or V 2O 5 was investigated. The effect of exposing the glass to either gamma, or fast neutron irradiation on the last properties was also studied. The results showed that three main bands appeared due to bending vibration or stretching of either, tetrahedral or triagonal borate units. The addition of alkalies causes only a shift of the bands either to higher or lower wavelength. Glass containing lead oxide had the highest refractive index and density, also the presence of any of the transition metal oxide lowering the average coordination number of oxygen which causes a compaction of the structure hence an increase in the values of density and refractive index. Since irradiation of glass causes compaction of B 2O 3 by breaking the bonds between triagonal elements, the average ring size becomes smaller which leads to an increase in density and refractive index too.

Ultrasonic velocity and elastic moduli of heavy metal tellurite glasses

Longitudinal and transverse ultrasonic waves velocities in lead tungsten tellurite glasses have been measured using the pulse-echo method at 5MHz frequency and at room temperature (300K). The elastic properties; longitudinal modulus, shear modulus, Young’s modulus, bulk modulus and Poisson’s ratio together with the microhardness, softening temperature, and Debye temperature are found to be rather sensitive to the glass composition. Information about the structure of the glass can be deduced after calculating the average stretching force constant and the average ring size. A comparison between the experimental elastic moduli data obtained in this study and those calculated theoretically by other models has been discussed.

Mechanistic Study on the Plastic Phenomena of Coal

Highly coking coal, Goonyella coal, and slightly coking coal, Witbank coal, were submitted to ruthenium ion catalyzed oxidation (RICO) reaction to clarify the structural features of the two coals. Expected structural differences between the two coking coals were meager but interesting: Witbank coal has a little bit larger amount of longer methylene bridges (C15−C25) and longer alkyl chains (C15−C30) than Goonyella coal. Combined use of 13C NMR and 1H NMR spectra gave valuable information of the average aromatic ring size: Goonyella coal has larger aromatic rings than Witbank coal on average. To obtain the information about the evolution of volatile materials during heating which are supposed to be significant for the appearance of coal plasticity, two steps of heat treatment of the coals were performed: the first step is heating to the softening temperature, and the second step is heating the resulting sample to resolidification temperature. Witbank coal gave a relatively larger amount of tar in the first step of the heating than in the case of Goonyella coal, while Goonyella coal gave a larger amount of tar in the second step of the heating compared with the corresponding fraction of Witbank coal. These strongly suggest that a larger amount of metaplast, which is indispensable for the appearance of fluidity, could be produced during the plastic range (the temperature range from the softening temperature to the resolidification temperature) in the case of Goonyella coal, this leading to its higher Gieseler maximum fluidity. We previously reported that these two coking coals have almost the same amount of transferable hydrogen. Therefore, Witbank coal is supposed to consume relatively large amounts of transferable hydrogen for the formation of tar during the heating to softening temperature, probably via oxygen functional group related reactions and carbon−carbon bond breaking reactions. Due to a lower amount of transferable hydrogen in the char, subsequent bond cleavage reactions at the plastic range lead to recombination to show a very low value of its Gieseler maximum fluidity, although the three-dimensional structure framework of Witbank coal collapses to a small extent.

Ultrasonic studies on ternary TeO 2–V 2O 5–Sm 2O 3 glasses

Longitudinal and shear wave velocities were measured in different compositions of the ternary glass system; 65TeO 2–(35 − x)V 2O 5– xSm 2O 3 at room temperature and at 4 MHz frequency using pulse echo technique. The densities of the glasses were measured by the displacement method using toluene as immersion liquid. The elastic moduli, Debye temperature, softening temperature, and micro-hardness were then calculated and have been used to obtain quantitative details about the structure of these glasses. The effect of adding Sm 2O 3, on the expense of V 2O 5, was investigated in terms of the number of network bonds of the glass. The average atomic ring size of the network was also calculated and it was found that it depends on the concentration of the modifier. The results obtained showed that these glasses become more stable and compact when modified with the rare earth oxide Sm 2O 3. This in turn increases the number of network bonds per unit volume and decrease the average atomic ring size of the network and consequently increases the elastic properties of these glasses.

A Raman spectroscopic study of shock-wave densification of anorthite (CaAl 2 Si 2 O 8 ) glass

Structural modifications induced by shock-wave compression up to 40 GPa in anorthite glass are investigated by Raman spectroscopy. In the first investigation, densification increases with increasing shock pressure. A maximum densification of 2.2% is obtained for a shock pressure of 24 GPa. This densification is attributed to a decrease of the average ring size, favoring three-membered rings. The densification is much lower than in silica glass subject to shock at similar pressures (11%), because the T-O-T bond angle decrease is impeded in anorthite glass. For higher shock pressures, the decrease of the recovered densification is attributed to partial annealing of the samples due to high after-shock residual temperatures. The study of the annealing process of the most densified glass by in-situ high temperature Raman spectroscopy confirms that relaxation of the three-membered rings occurs above about 900 K.

A Raman spectroscopic study of shock-wave densification of vitreous silica

The densification processes in SiO2 glass induced by shock-wave compression up to 43.4 GPa are investigated by Raman spectroscopy. At first, densification increases with increasing shock pressure. A maximum densification of 11% is obtained for a shock pressure of 26.3 GPa. This densification is attributed to the reduction of the average Si−O−Si angle, which occurs first by the collapse of the largest ring cavities, then by further reduction of the average ring size. For higher shock pressures, a different structural modification is observed, resulting in decreasing densification with increasing shock pressure. Indeed, the recovered densification becomes very small, with values of 1.8 and 0.5% at 32 and 43.4 GPa, respectively. This is attributed to partial annealing of the samples due to high after shock residual temperatures. The study of the annealing process of the most densified glass by in situ high temperature Raman spectroscopy confirms that relaxation of the Si−O−Si angle starts at a lower temperature (about 800 K) than that of the siloxane rings (about 1000 K), thus explaining the high intensity of the siloxane defect bands in the samples schocked at compressions of 32 and 43.4 GPa. The large intensity of the siloxane bands in the nearly undensified samples shocked by compressions above 30 GPa may be explained by the relaxation during decompression of five- and six-fold coordinated silicon species formed at high pressure and high temperature during the shock event.

Macrocycles IV. Macrocyclic polylactones as bifunctional monomers for polycondensations

Tin containing macrocyclic polylactones were prepared by di-n-butyl-2-stanna-1,3-dioxepane-initiated polymerizations of ε-caprolactone in bulk. The average ring size was varied from 10 to 100 monomer units via the monomer/initiator (M/I) ratio. Addition of terephthaloyl or sebacoyl chloride to the in situ prepared macrocycles yielded polycondensates under elimination of di-n-butyl tin dichloride. The molecular weights increased with the reaction temperature (e.g., 80–140°C) and with the size of the macrocycles. Number-average molecular weights (Mns) up to 90,000 and polydispersities between 1.65 and 2.0 were obtained. Further polycondensations were conducted with isophthaloyl chloride, 4,4′-biphenyldicarbonylchloride and 4,4′-phenylenebisacryloylchloride. Several polycondensations were performed with macrocyclic poly (δ-valerolactone) and poly (β-D,L-butyrolactone). In those cases the increase of the molecular weight was lower. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 1373–1378, 1998

Extended structural integrity in network glasses and liquids

Brillouin scattering measurements of B 2O 3, GeO 2 and SiO 2 glasses and liquids, to temperatures ≤ 1550°C, reveal anomalous thermo-mechanical behavior. Transverse acoustic waves are supported by the liquids of all three oxides. In all systems, the longitudinal and shear elastic moduli increase with increasing temperature below, and again far above the glass transition. This apparent strengthening of the glassy network below T g is less pronounced, the more fragile the glass former, while in the molten state the opposite seems to be the case. This positive temperature dependence of the elastic properties can be explained by localized structural reorganizations which do not require the breaking of network bonds. The decrease in elastic moduli immediately above T g, characteristic of fragile systems, is due to the increase of the average network ring size, achieved through a low-activation energy neighbor exchange mechanism. The ability of these liquids to support shear stresses at very high temperatures indicates a persistent network structure.

Lyotropic Behavior of “3,4-(42-Crown-14)benzyl Dodecyl Ether” in Toluene in the Presence of Water

The lyotropic behavior of an amphiphilic macrocrown ether (MC-12) with an average ring size of 42 atoms attached to a hydrophobic 12-carbon tail was studied in 70 wt % toluene in the presence of small amounts of water by a combination of polarized optical microscopy, 1H-NMR, X-ray diffraction, and 13C-NMR relaxation studies and by comparison to the lyotropic behavior of the corresponding solutions of Igepal-CO-720 [oligo(oxyethylene) nonylphenyl ether]. Igepal-CO-720 is a classic linear surfactant with a distribution of oligo(oxyethylene) lengths. MC-12 is a macrocyclic surfactant with a distribution of ring sizes. Since it was synthesized from poly(ethylene glycol) 600, 3,4-(42-crown-14)benzyl dodecyl ether is the predominant structure. Similar to Igepal-CO-720, MC-12 in 70 wt % toluene organizes into a lyotropic lamellar (Lα) mesophase, in which the macrocrown ethers are relatively flexible, when [H2O]:[EO] ≤ 2.2. When [H2O]:[EO] > 2.7, the solutions macroscopically phase separate into an isotropic tolu...

Amphiphilic Approach for Preparing Homopolyrotaxanes of Poly(ethylene oxide)

A new concept was introduced for preparing homopolyrotaxanes that lack an enthalpic driving force for threading, and which are therefore truly a physical entrapment of non-interacting cyclic molecules and linear polymer chains. It is based on the ability of amphiphiles to form lamellae and columnar micelles in solvents that selectively solvate one of its components. An amphiphilic macrocrown ether (MC-12) with an average ring size of 42 atoms attached to a hydrophobic 12-carbon tail was prepared by formation of the macrocycle in the presence of multiple potassium template ions under pseudo-high dilution conditions. MC-12 is almost insoluble in aliphatic hydrocarbon solvents, but forms micelles in benzene and toluene in the presence of water. The micellar solutions of MC-12 macroscopically phase separate if water-soluble threads are added, but remain intact and solubilize less-water-soluble poly(ethylene glycol) (PEG) derivatives. PEG3350−bis(amine) threads do not react, or react incompletely, with tert-butyltrityl end-capping agents functionalized with benzaldehyde and acid chloride groups, respectively. The optimum end-capping reaction for PEG−bis(amine) threads in the water-induced micellar solutions of MC-12 is the addition reaction with 2-p-[tris(p-tert-butylphenyl)methyl]phenoxymethyl-4,4-dimethylazlactone.