Surface dynamics during latex film formation

Surface dynamics during latex film formation has been investigated theoretically and experimentally by atomic force microscopy. The peak-to-valley distance, y(t), of the latex particles in the surface plane of the latex film decayed exponentially with time during film formation. A theoretical relationship between y(t) and time, t, is given by y(t)=y(0) exp[−t/τ], where y(0) is the value of y(t) when t is zero. τ is a characteristic constant related to the nature of polymer, the particle radius, the surface diffusion coefficient and the temperature. The relationship between the surface diffusion coefficient, D_s, y(0), the radius of the latex particles, R, temperature, T, and τ is given approximately by D_s=1.2×10⁻²⁰y(0)²[2R−y(0)]²T/τ (cm²/s), where the units are manometers for y(0) and R, kelvin for temperature, and seconds for τ. By measuring the decay of y(t) with time, the surface diffusion coefficient can be obtained. The surface diffusion coefficient for a poly(methyl methacrylate-co-butylacrylate) (50:50) copolymer latex film was found to be A×10⁻¹³ cm²/s, A is temperature-dependent.     

Dilute solution properties of carboxymethylchitins in high ionic-strength solvent

The hydrodynamic characteristics in aqueous solution at ionic strength I=0.2  of carboxymethylchitins of different degrees of chemical substitution have been determined. Experimental values varied over the following ranges: the translational diffusion coefficient (at 25.0°C), 1.1<10⁷×D<2.9 cm² s⁻¹; the sedimentation coefficient, 2.4<s<5.0 S; the Gralen coefficient (sedimentation concentration-dependence parameter), 130<k_s<680 mL g⁻¹; the intrinsic viscosity, 130<[η]<550 mL g⁻¹. Combination of s with D using the Svedberg equation yielded ‘sedimentation–diffusion' molecular weights in the range 40 000<M<240 000 g mol⁻¹. The corresponding Mark–Houwink–Kuhn–Sakurada (MHKS) relationships between the molecular weight and s, D and [η] were: [η]=5.58×10⁻³ M^0.94; D=1.87×10⁻⁴ M^−0.60; s=4.10×10⁻¹⁵ M^0.39. The equilibrium rigidity and hydrodynamic diameter of the carboxymethylchitin polymer chain is also investigated on the basis of wormlike coil theory without excluded volume effects. The significance of the Gralen k_s values for these substances is discussed.     

Variation of the aerosol charge neutralization coefficient in the entire particle size range

The rate at which the mean charge on aerosol particles relaxes to its steady-state value under bipolar charging is characterized by the neutralization rate constant, β (s⁻¹). It is an important parameter for fixing the nt product in charge neutralizers as well as in the theory of charging-induced diffusion. Here we compute the neutralization coefficient, β/n (where n is the mean ion density), as a function of particle size through the use of ion-particle combination coefficients provided by the recent theories. The results indicate that β/n decreases from a continuum limit value of 3.1 × 10⁻⁶ cm³ s⁻¹, to a free molecular limit value of 1.4 × 10⁻⁶ cm³ s⁻¹. The changeover occurs rapidly in the transitional regime (10–100 nm). This clearly indicates that the nt product required to attain steady state is higher for nano particles than for larger ones. The paper also presents the variations of the mean square variance of charge, the coefficients of charging-induced drift and diffusion, as a function of particle size.     

Adsorption of acid dye onto woodmeal by solid diffusional mass transfer

The adsorption of Telon Blue (Acid Blue 25) dye onto wood has been studied using an agitated batch adsorber. The variables studied include agitation, initial dye concentration, wood mass, wood particle size and dye solution temperature. Isotherms were measured and the isotherm parameters were determined.

A mathematical model has been developed using the basis of the model proposed by Mathews and Weber Jr. This model is based on external mass transfer and solid-phase diffusion, and has been used to generate theoretical concentration—time decay curves. The results of the model were adjusted to the experimental data using a ‘best fit’ approach. The external mass transfer coefficient was found to vary with the degree of agitation, and consequently all other variables were considered at a constant agitation speed of 400 rev min⁻¹. A good agreement between the theoretical generated and the experimental concentration—time decay curves was achieved using a constant external mass transfer coefficient, 0.30 × 10⁻³ cm ⁻¹, and a constant solid-phase diffusivity, 0.200 × 10⁻⁸ cm² s⁻¹, for varying initial dye concentrations as well as wood mass. In experiments where the particle diameter was varied, a constant external mass transfer coefficient was sufficient to describe the system, but a decreasing diffusivity was required with increasing particle size. To simulate the effect of varying temperature, both external mass transfer coefficient and diffusivity were varied.     

The ratio of the extinction coefficient to the mass of atmospheric aerosol particles as a function of the relative humidity

The ratio R_K of the extinction coefficient of aerosol particles in cm ¹, at the wavelength of light λ = 0·55 μm, and the mass of atmospheric aerosol particles in gem³ has been computed as function of the relative humidity for six types of continental and maritime aerosols. With the mean value R_K = 10⁴ cm²/g for all aerosol types being assumed to be independent of relative humidity, only the order of magnitude of the aerosol mass can be determined from visibility observation or measurement of the extinction coefficient of the aerosol particles.     

Decolorization of organic dyes on Pilkington Activ™ photocatalytic glass

The air–solid photocatalytic degradation of organic dye films Acid Blue 9 (AB9) and Reactive Black 5 (RBk5) is studied on Pilkington Activ™ glass. The Activ™ glass comprises of a colorless TiO₂ layer deposited on clear glass. The Activ™ glass is characterized using atomic force microscopy (AFM) and X-ray diffraction (XRD). Using AFM, the TiO₂ average agglomerate particle size is 95 nm, with an apparent TiO₂ thickness of 12 nm. The XRD results indicate the anatase phase of TiO₂, with a calculated crystallite size of 18 nm.

Dyes AB9 and RBk5 are deposited in a liquid film and dried on the Activ™ glass to test for photodecolorization in air, using eight UVA blacklight-blue fluorescent lamps with an average UVA irradiance of 1.4 mW/cm². A novel horizontal coat method is used for dye deposition, minimizing the amount of solution used while forming a fairly uniform dye layer. About 35–75 monolayers of dye are placed on the Activ™ glass, with a covered area of 7–10 cm². Dye degradation is observed visually and via UV–vis spectroscopy.

The kinetics of photodecolorization satisfactorily fit a two-step series reaction model, indicating that the dye degrades to a single colored intermediate compound before reaching its final colorless product(s). Each reaction step follows a simple irreversible first-order reaction rate form. The average k₁ is 0.017 and 0.021 min⁻¹ for AB9 and RBk5, respectively, and the corresponding average k₂ is 2.0 × 10⁻³ and 1.5 × 10⁻³ min⁻¹. Variable light intensity experiments reveal a p = 0.44 ± 0.02 exponent dependency of initial decolorization rate on the UV irradiance. Solar experiments are conducted outdoors with an average temperature, water vapor density, and UVA irradiance of 30.8 °C, 6.4 g water/m³ dry air, and 1.5 mW/cm², respectively. For AB9, the average solar k₁ is 0.041 min⁻¹ and k₂ is 5.7 × 10⁻³ min⁻¹.     

Small-angle neutron scattering from branched epoxide resins

Small-angle neutron scattering experiments in the range of q² from 0.01 to 25 nm⁻² have been carried out on branched epoxide resins based on bisphenol-A at the Institute Laue—Langevin (I.L.L) in Grenoble (q=(4π/λ) sin(θ/2)). Measurements were made with six samples in the range of M_W from 1500 to 19 000 and four concentrations between 1.3 and 10% (w/w) in deuterated diglyme. The results are as follows: (i) The mean square radius of gyration follows a relationship S²_z=4.69×10⁻⁴M^1.20_W (nm²). (ii) In all cases fairly large second virial coefficients A₂ are obtained which, however, decrease strongly with molecular weight. Above M_W=2500, the virial coefficient follows the relationship A₂=1.6M^−0.85_W (mol cm³g⁻²). (ii) The reciprocal particle scattering factor as a function of q² exhibits only a slight upturn and otherwise shows the behaviour of a randomly branched polycondensate. The slight upturn is discussed as being caused by the finite volume of the monomeric unit. Possible reasons for the high exponent in the S²_z versus M_W dependence are briefly discussed.     

Thermoelectric characterization of NaxMx/2Ti1−x/2O2 (M=Co, Ni and Fe) polycrystalline materials

Layered -titanate materials, Na_xM_x/2Ti_1−x/2O₂ (M=Co, Ni and Fe, x=0.2–0.4), were synthesized by flux reactions, and electrical properties of polycrystalline products were measured at 300–800 °C. After sintering at 1250 °C in Ar, all products show n-type thermoelectric behavior. The values of both d.c. conductivity and Seebeck coefficient of polycrystalline Na_0.4Ni_0.2Ti_0.8O₂ were ca. 7×10³ S/m and ca. −193 μV/K around 700 °C, respectively. The measured thermal conductivity of layered -titanate materials has lower value than conductive oxide materials. It was ca. 1.5 Wm⁻¹ K⁻¹ at 800 °C. The estimated thermoelectric figure-of-merit, Z, of Na_0.4Ni_0.2Ti_0.8O₂ and Na_0.4Co_0.2Ti_0.8O₂ was about 1.9×10⁻⁴ and 1.2×10⁻⁴ K⁻¹ around 700 °C, respectively.     

Electrodeposition of cesium at mercury electrodes in the tri-1-butylmethylammonium bis((trifluoromethyl)sulfonyl)imide room-temperature ionic liquid

The electrochemistry of cesium was investigated at mercury electrodes in the tri-1-butylmethylammonium bis((trifluoromethyl)sulfonyl)imide (Bu₃MeN⁺Tf₂N⁻) room-temperature ionic liquid (RTIL) by using cyclic staircase voltammetry, rotating disk electrode voltammetry, and chronoamperometry. The reduction of cesium ions at mercury exhibits quasireversible behavior with k⁰ = 9.8 × 10⁻⁵ cm s⁻¹ and = 0.36. The diffusion coefficient of Cs⁺ in this RTIL was 1.04 × 10⁻⁸ cm² s⁻¹ at 303 K. Bulk deposition/stripping experiments conducted at a rotating mercury film electrode gave an average recovery of 97% of the electrodeposited Cs. The density, absolute viscosity, and equivalent conductance of Bu₃MeN⁺Tf₂N⁻ were measured over the range of temperatures from 298 to 353 K. A polynomial equation describing the temperature dependence of the density is presented. Both the viscosity and conductance exhibited the non-Arrhenius temperature dependence typical of glass-forming liquids. The ideal glass transition temperature and the activation energies for viscosity and conductance were obtained by fitting the Vogel–Tammann–Fulcher (VTF) equation to the experimental data for these transport properties.     

High-quality, oriented and mesostructured organosilica monolith as a potential UV sensor

We synthesized high-quality and oriented periodic mesoporous organosilica (PMO) monoliths through a solvent evaporation process using a wide range of mole ratios of the components: 0.17–0.56 1,2-bis(triethoxysilyl)ethane (BTSE): 0.2 cetyltrimethylammonium chloride (CTACl): 0–1.8 × 10⁻³ HCl: 0–80 EtOH: 5–400 H₂O. X-ray diffraction (XRD) patterns and transmission electron microscopy (TEM) images indicated that the mesoporous channels within the monolith samples were oriented parallel to the flat external surface of the PMO monolith and possessed a hexagonal symmetry lattice (p6mm). The PMO monolith synthesized from a reactant composition of 0.35 BTSE: 0.2 CTACl: 1.8 × 10⁻⁶ HCl: 10 EtOH: 10 H₂O had a pore diameter, pore volume, and surface area – obtained from an N₂ sorption isotherm – of 25.0 Å, 0.96 cm³ g⁻¹ and 1231 m² g⁻¹, respectively. After calcination at 280 °C for 2 h in N₂ flow, the PMO monolith retained monolith-shape and mesostructure. Pore diameter and surface area of the calcined PMO monolith sample were 19.8 Å, 0.53 cm³ g⁻¹ and 1368 m² g⁻¹, respectively. We performed ²⁹Si and ¹³C CP MAS NMR spectroscopy experiments to confirm the presence of Si–C bonding within the framework of the PMO monoliths. We investigated the thermal stability of the PMO monoliths through thermogravimetric analysis (TGA). In addition, rare-earth ions (Eu³⁺, Tb³⁺ and Tm³⁺) were doped into the monoliths. Optical properties of those Eu³⁺, Tb³⁺ and Tm³⁺-doped PMO monoliths were investigated by photoluminescence (PL) spectra to evaluate their potential applicability as UV sensors.     

Estimation of the contribution of tube renewal in the terminal relaxation of linear polybutadiene

A set of low-molecular-weight (low-MW) entangled linear polybutadienes with molecular weights between 1.1 × 10⁴ and 2.5 × 10⁵ have been dilutedly embedded in a high-molecular-weight linear polybutadiene (M_w = 7.6 · 10⁵) matrix. The viscoelastic properties of these blends with 9.1% low-MW polymer have been measured. The loss moduli-frequency master curves, G^″ (Щ), contain contributions from both polymers. The contribution of the low-MW polymer is obtained by subtracting the contribution of the matrix. The maximum in G^″, G^″_m, due to the low-MW polymer occurs at a lower frequency (0.3 to 0.5 log units) than in the homopolymer. This result indicates that the longest relaxation time of the entangled linear polymer embedded in a high-molecular-weight matrix is increased by a factor of 2.0 to 3.0 because tube renewal normally operating in the homopolymer is almost completely absent in the matrix. The longest relaxation time of the polymers in the matrix depends on M^3.3₀. This is only slightly less than the dependence found in linear polymer melts (M^3.3₇). This indicates that reptation and chain-end fluctuation together contribute to the relaxation of linear polymers in permanent networks.     

Conformation of isotactic polystyrene (IPS) in the bulk crystallized state as revealed by small-angle neutron scattering

Neutron scattering experiments have been performed on isotactic polystyrene (IPS) samples in the bulk crystallized state (T_{crystallization} = 185°C). The determination of the conformation of tagged chains ranging from 2.5 × 10⁵ to 7 × 10⁵ has been undertaken on two different hydrogenated IPS matrices. A matrix of usual molecular weight (M_w = 4 × 10⁵) leads to results which do not agree with Flory's model. In this case, measurements on radius of gyration R_g show on the one hand an important increase of this parameter (40%) with increasing crystallinity for the highest molecular weight tagged chains and on the other hand a variation with molecular weight like M^0.78. These results are interpreted with a schematic model involving a long crystalline sequence incorporated in the monocrystal along the 110 plane and two amorphous wings. Such an assumption is confirmed by the scattering behaviours in the intermediate range. On the other hand, by using an IPSH matrix of very high molecular weight (M_w = 1.75 × 10⁶), and the same tagged chains previously considered, a very weak variation of R_g with increasing crystallinity is observed. This leads to consider in this case Flory's conformation which is corroborated by data obtained in the intermediate range.     

Photocatalytic degradation kinetics of di- and tri-substituted phenolic compounds in aqueous solution by TiO2/UV

In this study, photocatalytic degradation of 2,4,6-trimethylphenol (TMP), 2,4,6-trichlorophenol (TCP), 2,4,6-tribromophenol (TBP), 2,4-dimethylphenol (DMP), 2,4-dichlorophenol (DCP) and 2,4-dibromophenol (DBP) has been studied by TiO₂/UV. Although degraded phenolic compound concentration increased by increasing initial concentration photocatalytic decomposition rates of di- and tri-substituted phenols at 0.1–0.5 mM initial concentrations decreased when the initial concentration increased. The fastest degradation observed for TCP and the slowest for TMP. Photodegradation kinetics of the compounds has been explained in terms of Langmuir–Hinshelwood kinetics model. Degradation rate constants have been observed to be extremely depended on electronegativity of the substituents on phenolic ring. Degradation rate constant and adsorption equilibrium constant of TCP were calculated as k 0.0083 mM min⁻¹ and K 9.03 mM⁻¹. For TBP and TMP the values of k and K were obtained as 0.0040 mM min⁻¹, 19.20 mM⁻¹, and 0.0017 mM min⁻¹, 51.68 mM⁻¹, respectively. Degradation rate constant of DBP was similar as DCP (0.0029 mM min⁻¹ for DBP and 0.0031 mM min⁻¹ for DCP) whereas adsorption equilibrium constants differed (48.40 mM⁻¹ for DBP and 30.52 mM⁻¹ for DCP). K and k of DMP found as 83.68 mM⁻¹ and 0.0019 mM min⁻¹, respectively. The adsorption equilibrium constants in the dark were ranged between 1.11 and 3.28 mM⁻¹ which are lower than those obtained in kinetics. Adsorption constants have inversely proportion with degradation rate constants for all phenolic compounds studied.     

A new tantalum sulfur compound as electrode material for non-aqueous alkali metal batteries

Polycrystalline (PbS)_1.14(TaS₂)₂, a misfit layer sulfide, was used as cathodic material for lithium secondary battery. One molar LiClO₄ in propylene carbonate (PC) was used as electrolyte. The cell could be galvanostatic discharged down to x = 4.6 [Li_x(PbS)_1.14(TaS₂)₂] when the current density was 65 μA cm⁻² and the cell was cycled more than 100 times between 3.5 and 1.5 V at a current density of 260 μA cm⁻². Lattice expansion increased linearly with lithium content and was less than that reported for the Li/TaS₂ system. Chemical diffusion coefficients were determined by a modified version of the galvanostatic intermittent titration technique and they were fairly constant in the composition range 0.2 < x < 1, and an average value of 8.1 × 10⁻¹¹ cm² s⁻¹ was calculated. Sodium intercalation was also accomplished, but the uptake of this ion resulting in a significant lattice expansion compared with that observed for lithium ions. Moreover, a similar dependence of the sodium chemical diffusion coefficient on the composition was observed with an average value of 1.4 × 10⁻¹⁰ cm² s⁻¹, somewhat higher than that of lithium ion. We believe that differences in lattice expansion may be responsible for the differences found in the chemical diffusivity values.     

FTIR study of the adsorption of single pollutants and mixtures of pollutants onto titanium dioxide in water: oxalic and salicylic acids

The use of ATR–FTIR to probe the adsorption of oxalic and salicylic acids, and of mixtures of both, onto TiO₂ (Degussa P-25) demonstrates the potential of the technique to characterise the evolution of the catalyst with time, including surface poisoning. Under equilibrium dark conditions, three surface species are formed by oxalate, and two by salicylate. Their stabilities, described by conditional Langmuir-type equilibria involving the dissociative, electroneutral adsorption of the acids H₂L, are at pH 3.7, 2.4×10⁶, 3.0×10⁴ and 3.0×10³ mol⁻¹ dm³ for oxalic acid, and 2.9×10⁵ and 9.1×10³ mol⁻¹ dm³ for salicylic acid. The nature of the species is discussed in terms of their spectral features. The displacement of each acid from the surface by addition of the other one was followed also by ATR–FTIR. The results demonstrate that oxalate displaces totally chemisorbed salicylate, whereas salicylate displaces oxalate only partially. These results are explained by assuming competitive chemisorption onto two different surface sites, plus oxalate adsorption onto a site that exhibits negligible affinity for salicylate. Irreversible adsorption by partially oxidised products in the course of photocatalytic processes can therefore be assessed by ATR–FTIR.     

Oxidative conversion of methane to syngas over NiO/MgO solid solution supported on low surface area catalyst carrier

Influence of time-on-stream (0.5–15 h), CH₄/O₂ ratio in feed (1.8–8.0), space velocity (6000–510,000 cm³ g⁻¹ h⁻¹), catalyst particle size (22–70 mesh), and catalyst dilution by inert solid particles (diluent/catalyst weight ratio=4) on the performance at different temperatures (600–900°C) of the NiO/MgO solid solution deposited on SA-5205 [which is a low surface area macroporous silica-alumina catalyst carrier] in the oxidative conversion of methane to syngas (a mixture of CO and H₂) has been investigated. The dependence of conversion and selectivity on the space velocity is strongly influenced by the temperature. Both the conversion and selectivity for H₂ and CO are decreased markedly by increasing the CH₄/O₂ ratio in the feed. The catalyst dilution resulted in a small but significant decrease in both the conversion and selectivity for H₂ and CO. The increase in the catalyst particle size had also a small but significant effect on both the conversion and selectivity in the oxidative conversion process. Both the heat and mass transfer processes seem to play significant roles in the oxidative conversion of methane to syngas at a very low contact time or very high space velocity (5.1×10⁵ cm³ g⁻¹ h⁻¹).     

Particle deposition in the guinea pig respiratory tract

Equations relating particle size of aerosols to deposition by impaction, diffusion and sedimentation are applied to a previously established model of the guinea pig lung using a tidal volume of 4.44 cm³ and a respiratory rate of 60 breath min⁻¹. These calculated deposition values are combined with measured values of nasal deposition to give an estimate of the particle deposition characteristics of the guinea pig respiratory tract. The nasopharyngeal-tracheobronchial (NP-TB) region removes 99% of unit density spherical particle 10 μm or more in diameter. Deposition in this region reaches a minimum of 10% at a particle diameter of 0.8 μm. For particles less than 0.8 μm, deposition increases because of diffusion. Deposition in the pulmonary region is about 17% for particle diameters from 0.08 to 4 μm. For typical polydisperse aerosols with mass median diameters above 1 μm, a greater fraction of the mass than of the count is deposited in the NP-TB region, while a smaller fraction of the mass than of the count is deposited in the pulmonary region. Aerosol clouds with mass median diameters less than 0.1 μm deposit a greater fraction of the count than of the mass in the NP-TB region and a smaller fraction of the count than of the mass in the pulmonary region.     

Interpenetrating polymer networks of poly(dimethylsiloxane): 1. Preparation and characterization

Model networks of ,ω-dihydroxy-poly(dimethylsiloxane) (PDMS) were prepared by tetrafunctional crosslinking agent tetraethyl orthosilicate (TEOS) and the catalyst stannous 2-ethylhexanoate. Hydroxylterminated chains of PDMS having molecular weights 15 × 10³ and 75 × 10³ g mol⁻¹ were used in the crosslinking reaction. Bimodal networks were obtained from a 50% (w/w) mixture of PDMS chains with M_n = 15 × 10³ and 75 × 10³ g mol⁻¹. A sequential interpenetrating network of these PDMS chains was also prepared. Physical properties of the elastomers were determined by stress-strain tests, swelling and extraction experiments, and differential scanning calorimetry measurements.     

Methacryl-terminated macromers by living polymerization as precursors of IPN polymer electrolytes

A new class of polymer electrolytes, based on the interpenetrating polymer network approach, was obtained starting from functionalised macromers, of poly-ether nature, in the presence of a lithium salt (LiBF₄, LiClO₄, LiCF₃SO₃) and propylene carbonate (PC) or tetraethyleneglycol dimethylether (TGME), as plasticizers.

The macromers were synthesised by living polymerisation employing a HI/I₂ system as the initiator. The macromer has a polymerisable end group, which can undergo radical polymerisation, attached to a monodisperse poly-vinylether, containing suitable ethylene oxide groups for ion coordination. Monomers and macromers were characterised by FTi.r., u.v.–vis, ¹H- and ¹³C-n.m.r.

Self-consistent and easily handled membranes were obtained as thin films by a dry procedure using u.v. radiation to polymerise and crosslink the network precursors, directly on suitable substrates, in the presence of the plasticizer and the lithium salt. The electrolytic membranes were studied by complex impedance and their thermal properties determined by differential scanning calorimetry analysis.

Ionic conductivities (σ) were measured for PC and TGME-based membranes at various plasticizer and salt contents as a function of T (60 to −20°C). LiClO₄/PC/PE electrolytes, with 3.8% (w/w) salt and 63% PC, have the highest σ (1.15×10⁻³ and 3.54×10⁻⁴ S cm⁻¹ at 20°C and −20°C, respectively). One order of magnitude lower conductivities are achieved with TGME; samples with 6% (w/w) LiClO₄ and 45% (w/w) TGME exhibit σ values of 2.7×10⁻⁴ and 2.45×10⁻⁵ S cm⁻¹ at 20°C and −20°C.     

The elastic modulus of the poly(phosphonitrilic chloride) crystal

The Young's modulus for a crystal of poly(phosphonitrilic chloride) (poly-dichlorophosphazene) (NPCl₂)_n has been calculated using force constants derived from spectroscopy. Assuming that the molecule is a uniform helix the value of the modulus is 1.38 × 10⁹ dyne cm⁻² [dyne cm⁻² = 0.1 N m⁻²]; the result is 1.66 × 10¹⁰ dyne cm⁻² if a cis-planar structure is assumed for the molecule. Neither value is close to those obtained experimentally (1.8 × 10⁶ to 6.5 × 10⁶ dyne cm⁻²). This is because experimental values relate to the amorphous polymer whereas the calculated values are those for the crystal. There is good agreement between the values calculated for the (NPCl₂)_n crystal and those for other polymer crystals.