Dielectric relaxation due to the heterogeneous structure of wood charcoal

Delignified hinoki wood and cellulose as well as hinoki and lauan woods were carbonized at 590°C for 1 h. The dielectric properties of these specimens were measured at 20°C in a frequency range of 20 Hz to 1 MHz. Inflection points in the dielectric constant (ε′) versus the logarithm of frequency (log f) curves as well as in the logarithm of the electric conductivity (log σ) versus log f curves for all specimens prepared were recognized. Peaks in the dielectric loss and the imaginary part of the complex conductivity versus the log f curves were detected in the frequency location corresponding to the inflection point in the ε′ and log σ versus log f curves. It was considered that this relaxation was responsible for the interfacial polarization observed in heterogeneous materials because no permanent dipoles existed in the specimens carbonized above 500°C. The Cole–Cole circular arc law was applied to account for this relaxation. Similar average relaxation times were obtained for all specimens. These results suggested that the observed relaxation was ascribed to interfacial polarization at microscopic levels in the cell walls.     

Dynamic viscoelastic properties of wood acetylated with acetic anhydride solution of glucose pentaacetate

 Spruce wood specimens were acetylated with acetic anhydride (AA) solutions of glucose pentaacetate (GPA), and their viscoelastic properties along the radial direction were compared to those of the untreated and the normally acetylated specimens at various relative humidities and temperatures. Higher concentrations of the GPA/AA solution resulted in more swelling of wood when GPA was introducted into the wood cell wall. At room temperature the dynamic Young's modulus (E′) of the acetylated wood was enhanced by 10% with the introduction of GPA, whereas its mechanical loss tangent (tan δ) remained almost unchanged. These changes were interpreted to be an antiplasticizing effect of the bulky GPA molecules in the wood cell wall. On heating in the absence of moisture, the GPA-acetylated wood exhibited a marked drop in E′ and a clear tan δ peak above 150°C, whereas the E′ and tan δ of the untreated wood were relatively stable up to 200°C. The tan δ peak of the GPA-acetylated wood shifted to lower temperatures with increasing GPA content, and there was no tan δ peak due to the melting of GPA itself. Thus the marked thermal softening of the GPA-acetylated wood was attributed to the softening of wood components plasticized with GPA. Received: March 29, 2002 / Accepted: May 21, 2002 Correspondence to:E. Obataya     

Initial shapes of stress-strain curve of wood specimen subjected to repeated combined compression and vibration stresses and the piezoelectric behavior

This study investigated the relationship between the initial shape of the stress (σ)-strain (ε) curve of a Chamaecyparis obtusa wood specimen subjected to repeated combined compression and vibration stresses at various angles between the fiber direction and load direction and the piezoelectric behavior. The main findings of the study are: (1) the σ-ε curve became convex initially, and then the stress was proportional to the strain. The σ-ε curve had almost the same shape during both loading and unloading. (2) The σ-piezoelectric voltage (P) curve was nonlinear, with a maximal point or cusp on the curve, which had almost the same shape during both loading and unloading, as was also observed for the σ-ε curve. (3) The plot of the first derivative of the stress [dσ/dε (= σ′)] against ε was nonlinear. The σ′-ε and P-ε curves at various angles were fairly similar. (4) The stress at the maximal point (or cusp) of the σ-P curve decreased with an increase in the angle between the fiber direction and load direction. The tendency of the stresses was very similar to that of Young’s modulus and compression strength calculated from Hook’s law and Hankinson’s law, respectively.     

Radial variations of vibrational properties of three tropical woods

The radial trends of vibrational properties, represented by the specific dynamic modulus (E′/ρ) and damping coefficient (tan δ), were investigated for three tropical rainforest hardwood species (Simarouba amara, Carapa procera, and Symphonia globulifera) using free-free flexural vibration tests. The microfibril angle (MFA) was estimated using X-ray diffraction. Consistent patterns of radial variations were observed for all studied properties. E′/ρ was found to decrease from pith to bark, which was strongly related to the increasing pith-bark trend of MFA. The variation of tan δ along the radius could be partly explained by MFA and partly by the gradient of extractives due to heartwood formation. The coupling effect of MFA and extractives could be separated through analysis of the log(tan δ) versus log(E′/ρ) diagram. For the species studied, the extractive content putatively associated with heartwood formation generally tends to decrease the wood damping coefficient. However, this weakening effect of extractives was not observed for the inner part of the heartwood, suggesting that the mechanical action of extractives was reduced during their chemical ageing.     

Dielectric properties of silicon dioxide/wood composite

For a better understanding of the binding between silicon dioxide and wood as well as the dielectric properties of silicon dioxide/wood composite, dielectric relaxation was measured for untreated wood [Cunninghamia lanceolata (Lamb.) Hook] and for silicon dioxide/wood composite with different weight percentage gain (WPG). Cole–Cole’s circular arc law, distribution spectrum of relaxation time and relation model were applied to the results of relaxation due to motions of the methylol groups. The results were as follows. The generalized relaxation time and ε _s − ε _∞ decreased with increasing WPG. The distribution spectrum of relaxation time decreased more and more and broadened with increasing WPG. The methylol group in the amorphous region of the wood cell wall participated in hydrolysis reaction and condensation reaction caused by tetraethylorthosilicate (TEOS), and there is a cross-link between silicon dioxide and wood. The value of apparent activation energy (ΔE) increased for silicon dioxide/wood composite, and increased with increasing WPG. Activation enthalpy (ΔH) and activation entropy (ΔS) increased, while activation free energy (ΔG) decreased with increasing WPG. The number of hydroxyl groups cut in dielectric relaxation increased with increasing WPG.     

Identification of anisotropic vibrational properties of Padauk wood with interlocked grain

Grain deviations and high extractives content are common features of many tropical woods. This study aimed at clarifying their respective impact on vibrational properties, referring to African Padauk (Pterocarpus soyauxii Taub.), a species selected for its interlocked grain, high extractives content and uses in xylophones. Specimens were cut parallel to the trunk axis (L), and local variations in grain angle (GA), microfibril angle (MFA), specific Young’s modulus (E′ _L /ρ, where ρ stands for the density) and damping coefficient (tanδ_L) were measured. GA dependence was analysed by a mechanical model which allowed to identify the specific Young’s modulus (E′₃/ρ) and shear modulus (G′/ρ) along the grain (3) as well as their corresponding damping coefficients (tanδ₃, tanδ_G). This analysis was done for native and then for extracted wood. Interlocked grain resulted in 0–25° GA and in variations of a factor 2 in E′_L/ρ and tanδ_L. Along the grain, Padauk wood was characterized, when compared to typical hardwoods, by a somewhat lower E′₃/ρ and elastic anisotropy (E′/G′), due to a wide microfibril angle plus a small weight effect of extracts, and a very low tanδ₃ and moderate damping anisotropy (tanδ_G/tanδ₃). Extraction affected mechanical parameters in the order: tanδ₃ ≈ tanδ_G > G′/ρ > > E′₃/ρ. That is, extractives’ effects were nearly isotropic on damping but clearly anisotropic on storage moduli.     

A mathematical verification of the reinforced-matrix hypothesis using the Mori-Tanaka theory

This article presents a theoretical verification of the reinforced-matrix hypothesis derived from tensor equations, σ ^W = σ ^f + σ ^m and ε ^W = ε ^f = ε ^m (Wood Sci Technol 32:171–182, 1998; Wood Sci Technol 33:311–325, 1999; J Biomech Eng 124:432–440, 2002), using classical Mori-Tanaka theory on the micromechanics of fiber-reinforced materials (Acta Metall 21:571–574, 1973; Micromechanics — dislcation and inclusions (in Japanese), pp 141–147, 1976). The Mori-Tanaka theory was applied to a small fragment of the cell wall undergoing changes in its physical state, such as those arising from sorption of moisture, maturation of wall components, or action of an external force, to obtain 〈σ ^A〉_D = ϕ·〈σ ^F〉_I + (1−ϕ)·〈σ ^M〉_D−I. When the constitutive equation of each constituent material was applied to the equation 〈σ ^A〉_D = ϕ·〈σ ^F〉_I + (1−ϕ)·〈σ ^M〉_D−I, the equations σ ^W = σ ^f + σ ^m and ε ^W = ε ^f = ε ^m were derived to lend support to the concept that two main phases, the reinforcing cellulose microfibril and the lignin-hemicellulose matrix, coexist in the same domain. The constitutive equations for the cell wall fragment were obtained without recourse to additional parameters such as Eshelby’s tensor S and Hill’s averaged concentration tensors A^F and A^M. In our previous articles, the coexistence of two main phases and σ ^W = σ ^f + σ ^m and ε ^W = ε ^f =ε ^m had been taken as our starting point to formulate the behavior of wood fiber with multilayered cell walls. The present article provides a rational explanation for both concepts.     

The effect of lignin on the bending properties and fixation by cooling of wood

To clarify the effects of lignin on the fixation of bending deformation by cooling, cooling set for delignified woods with various lignin residues were investigated to compare with mechanical and dynamic viscoelastic properties. Bending tests showed that steep reductions occurred in the modulus of elasticity and modulus of rupture with delignification during the initial stage of delignification. The dynamic viscoelastic measurements revealed that the peak temperature of tan δ due to micro-Brownian motion of lignin was reduced with delignification, and the peak disappeared in the temperature range of 5°–100°C for the specimens that had lost more than 21% of their weight. On the other hand, no clear change in residual set was found in the range of 0%–15% of weight loss in spite of a marked reduction in lignin content. Subsequently, set decreased steeply for the specimens delignified beyond 15% of weight loss. It was suggested that cooling set is not determined solely by lignin content but is influenced by changes in the quality of lignin due to delignification. Lignin quality affects the balance of the elastic potential to recover from deformation and its viscosity, which is an indication of resistance against flow. Part of this report was presented at the 57th Annual Meeting of the Japan Wood Research Society, Hiroshima, August 2007     

Effects of temperature on mechano-sorptive creep of delignified wood

The effects of temperature on mechano-sorptive (MS) creep of delignified hinoki wood (Chamaecyparis obtusa Endl.) were investigated using longitudinal (L) and radial (R) specimens during adsorption and desorption over the temperature range of 20°–80°C. The results were compared with those of stepwise delignified specimens tested at a constant temperature of 20°C. It was found that the effects of temperature on the MS creep of delignified specimens are more remarkable than for untreated specimens. The tendencies of increasing MS creep with temperature, delignification, and their combination were observed. The increase in MS creep for L specimens was relatively small and almost equal in both adsorption and desorption processes, while for R specimens the MS creep was small in desorption, but significantly different in adsorption. In addition, good correlation was observed between the MS coefficient (K) and instantaneous compliance (J ₀). The increase in MS creep occurs as a result of temperature increase or decrease in lignin content, or their interacting effects. However, in the case of desorption for R specimens, the increase of MS creep was unexpectedly small due to a remarkably increased J ₀. Part of this report was presented at the 15th Annual Meeting of the Chubu Branch of the Japan Wood Research Society in Fukui, October 2005     

Dielectric properties of copper-ethanolamine treated Chinese fir (Cunninghamia lanceolata Hook.)

In order to clarify the interaction between copper and wood substances in wood treated with copper containing water-borne wood preservatives, the dielectric constant ε′ and dielectric loss factor ε″ of untreated wood and wood treated with four concentration levels of copper-ethanolamine (Cu-EA) solutions were determined within a temperature range from –100 to 40°C and a frequency range from 100 to 1 MHz. Three dielectric relaxation processes were observed in the ε″ spectrum; among them R-I is based on the reorientation of methylol groups in the amorphous region of wood cell walls and R-II is related to wood extractives. R-III appeared in Cu-EA treated wood, and its magnitude decreases with the concentration of Cu-EA solutions used in this experiment. This relaxation process was considered to be based on the reorientation of copper-ethanolamine-wood complexes in wood cell walls. At low copper retention, the hydrogen in the complex can form hydrogen bonding with adjacent hydroxyl groups, which results in a strong bonding state between copper and wood; at high copper retention, the numerous copper-ethanolamine complexes not only hinder them from forming hydrogen bonding with adjacent wood molecules due to steric hindrance, but also weaken the interaction between wood molecules themselves, which corresponds to reducing ε″ values of both R-I and R-III processes. The results explain the fact of in-creasing copper leaching in wood treated with high concentration copper-based water-borne preservatives.     

Anisotropy of wood vibrational properties: dependence on grain angle and review of literature data

The anisotropy of vibrational properties influences the acoustic behaviour of wooden pieces and their dependence on grain angle (GA). As most pieces of wood include some GA, either for technological reasons or due to grain deviations inside trunks, predicting its repercussions would be useful. This paper aims at evaluating the variability in the anisotropy of wood vibrational properties and analysing resulting trends as a function of orientation. GA dependence is described by a model based on transformation formulas applied to complex compliances, and literature data on anisotropic vibrational properties are reviewed. Ranges of variability, as well as representative sets of viscoelastic anisotropic parameters, are defined for mean hardwoods and softwoods and for contrasted wood types. GA-dependence calculations are in close agreement with published experimental results and allow comparing the sensitivity of different woods to GA. Calculated trends in damping coefficient (tanδ) and in specific modulus of elasticity (E′/ρ) allow reconstructing the general tanδ-E′/ρ statistical relationships previously reported. Trends for woods with different mechanical parameters merge into a single curve if anisotropic ratios (both elastic and of damping) are correlated between them, and with axial properties, as is indicated by the collected data. On the other hand, varying damping coefficient independently results in parallel curves, which coincide with observations on chemically modified woods, either “artificially”, or by natural extractives.     

Dynamic viscoelastic behavior of wood under drying conditions

In this study heartwood from a Chinese fir [Cunninghamia lanceolata (Lamb.) Hook] plantation was treated using a high-temperature drying (HTD) method at 115°C, a low-temperature drying (LTD) method at 65°C, and freeze vacuum drying (FVD), respectively. The dynamic viscoelastic properties of dried wood specimens were investigated. The measurements were carried out at a temperature range of −120 to 250°C at four different frequencies (1, 2, 5, and 10 Hz) using dynamic mechanical analysis (DMA). We have drawn the following conclusions: 1) the storage modulus E′ and loss modulus E″ are the highest for HTD wood and the lowest for FVD wood; 2) three relaxation processes were detected in HTD and LTD wood, attributed to the micro-Brownian motion of cell wall polymers in the non-crystalline region, the oscillations of the torso of cell wall polymers, and the motions of the methyl groups of cell wall polymers in the non-crystalline region in a decreasing order of temperatures at which they occurred; and 3) in FVD wood, four relaxation processes were observed. A newly added relaxation is attributed to the micro-Brownian motions of lignin molecules. This study suggests that both the HTD and the LTD methods restrict the micro-Brownian motion of lignin molecules somewhat by the cross-linking of chains due to their heating history. __________ Translated from Journal of Beijing Forestry University, 2008, 30(3): 96–100 [译自: 北京林业大学学报]     

Changes in structural and chemical components of wood delignified by fungi

Summary Cerrena unicolor, Ganoderma applanatum, Ischnoderma resinosum and Poria medulla-panis were associated with birch wood that had been selectively delignified in the forest. Preferential lignin degradation was not uniformly distributed throughout the decayed wood. A typical white rot causing a simultaneous removal of all cell wall components was also present. In the delignified wood, 95 to 98% of the lignin was removed as well as substantial amounts of hemicelluloses. Scanning and transmission electron microscopy were used to identify the micromorphological and ultrastructural changes that occurred in the cells during degradation. In delignified areas the compound middle lamella was extensively degraded causing a defibration of cells. The secondary wall, especially the S₂ layer, remained relatively unaltered. In simultaneously white-rotted wood all cell wall layers were progressively removed from the lumen toward the middle lamella causing erosion troughs or holes to form. Large voids filled with fungal mycelia resulted from a coalition of degraded areas. Birch wood decayed in laboratory soil-block tests was also intermittently delignified. Selective delignification, sparsely distributed throughout the wood, and a simultaneous rot resulting in the removal of all cell wall components were evident. Scanning electron microscopy appears to be an efficient technique for examining decayed wood for fungi with the capacity to selectively delignify wood.The authors would like to thank Kathy Zuzek for technical assistance and Dr. M. Larsen, Forest Prod. Lab., Madison, for identifying the sporophores of Poria medulla-panis. This research was founded in part by a grant from the USDA Forest Service, Forest Products Laboratory and from the Graduate School, University of Minnesota     

Interaction of lignin and polysaccharides in beech wood (Fagus sylvatica) during drying processes

Summary ¹³C CP MAS NMR spectroscopy was used to characterize the structural changes of cell wall polymers in beech wood Fagus sylvatica during drying processes. The analysis of five wood samples, namely, untreated, untreated dried, pre-treated by steam and/or NaOH subjected to drying showed partial depolymerization of lignin component as well as the change of the ratio of the crystalline and of the amorphous parts of cellulose as the consequence of wood pre-treatment. In addition, T_1ρ(¹H) relaxation times were determined in beech wood sample pre-treated with steam at 135 °C and the lignin isolated from this sample. The magnitudes of the relaxation times were found comparable in both samples as well as in the lignin-cellulose model compound. These unique T_1ρ (¹H) values indicate that spin diffusion is complete and homogeneous due to spatial proximity of spins and confirmed the formation of lignin-cellulose complex during thermal treatment of wood. Received 30 June 1997     

Effect of extractives on vibrational properties of African Padauk (<Emphasis Type="Italic">Pterocarpus soyauxii</Emphasis> Taub.)

Extractives can affect the vibrational properties tanδ (damping coefficient) and E′/ρ (specific Young’s modulus), but this is highly dependent on species, compounds, and cellular locations. This paper investigates such effects for African Padauk (Pterocarpus soyauxii Taub.), a tropical hardwood with high extractives content and a preferred material for xylophones. Five groups of 26 heartwood specimens with large, yet comparable, ranges in vibrational properties were extracted in different solvents. Changes in vibrational properties were set against yields of extracts and evaluation of their cellular location. Methanol (ME) reached most of the compounds (13%), located about half in lumen and half in cell-wall. Water solubility was extremely low. tanδ and E′/ρ were very strongly related (R ² ≥ 0.93), but native wood had abnormally low values of tanδ, while extraction shifted this relation towards higher tanδ values. ME extracted heartwood became in agreement with the average of many species, and close to sapwood. Extractions increased tanδ as much as 60%, irrespective of minute moisture changes or initial properties. Apparent E′/ρ was barely changed (+2% to −4%) but, after correcting the mass contribution of extracts, it was in fact slightly reduced (down to −10% for high E′/ρ), and increasingly so for specimens with low initial values of E′/ρ.     

Working mechanism of adsorbed water on the vibrational properties of wood impregnated with extractives of pernambuco (Guilandina echinata Spreng.)

To clarify the lowering mechanism of loss tangen (tan) of sitka spruce (Picea sitchensis Carr.) wood impregnated with extractives of pernambuco (Guilandina echinata Spreng. synCaesalpinia echinata Lam.), we examined the vibrational properties of the impregnated wood in relation to the adsorbed water. The results obtained were as follows: (1) The equilibrium moisture content (EMC) of impregnated sitka spruce decreased to some extent compared with untreated wood. (2) Frequency dependencies of tan a about 400–8000Hz showed that impregnated wood has much lower tan than untreated wood at around 9% mois ture content (MC), except for the high-frequency region. At high relative humidity, impregnated wood has a minimum tan (at around 4000Hz); and at other frequency ranges the tan of impregnated wood did not differ considerably from that of untreated wood. (3) The apparent activation energy of the mechanical relaxation process (E) concerned with adsorbed water molecules was higher for impregnated specimens than for untreated ones at moderately high relative humidity, whereas at high relative humidity the difference was not observed. Based on these results, it is thought that the tan of impregnated wood decreased at low rela tive humidity because of the formation of direct hydrogen bonds between impregnated extractives and wood components. However, when the specimen is at higher relativePart of this work was presented at the 48th annual meeting of the Japan Wood Research Society, Shizuoka, April 1998 humidity, the formation of direct hydrogen bonds are disturbed by the existence of a large number of water molecules, and some extractives act as a plasticizer.     

Influence of heating and drying history on micropores in dry wood

To investigate the influence of heating and drying history on the microstructure of dry wood, in addition to the dynamic viscoelastic properties, CO₂ adsorption onto dry wood at ice.water temperature (273 K) was measured, and the micropore size distribution was obtained using the Horvath-Kawazoe (HK) method. Micropores smaller than 0.6 nm exist in the microstructures of dry wood, and they decreased with elevating out-gassing temperature and increased again after rewetting and drying. Dry wood subjected to higher temperatures showed larger dynamic elastic modulus (E′) and smaller loss modulus (E″). This is interpreted as the result of the modification at higher temperature of the instability caused by drying. Drying history influenced the number of micropores smaller than 0.6 nm in dry wood not subjected to high temperature, although the difference in the number of micropores resulting from the drying history decreased with increasing out-gassing temperature. A larger number of micropores smaller than 0.6 nm exist in the microstructure of dry wood in more unstable states, corresponding to smaller E′ and larger E″ than in the stable state. Consequently, unstable states are considered to result from the existence of temporary micropores in the microstructures of dry wood, probably in lignin. Part of this report was presented at the 55th Annual Meeting of the Japan Wood Research Society, Kyoto, March 2005, and at the 56th Annual Meeting of the Japan Wood Research Society, Akita, August 2006     

Effects of high temperature kiln drying on the practical performances of Japanese cedar wood (Cryptomeria japonica) II: Changes in mechanical properties due to heating

Japanese cedar wood specimens were steamed at 80°, 100°, and 120°C over 14 days, and their equilibrium moisture content (M) at 20°C and 60% relative humidity, longitudinal dynamic Young’s modulus (E), bending strength (σ _max), and breaking strain (ε _max) were compared with those of unheated specimens. Steaming for a longer duration at a higher temperature resulted in a greater reduction in M, σ _max, and ε _max. The E of wood was slightly enhanced by steaming at 100°C for 1–4 days and 120°C for 1–2 days, and thereafter it decreased. The slight increase in the E of sapwood was attributable to the reduction in hygroscopicity, while sufficient explanation was not given for a greater increase in the heartwood stiffness. Irrespective of the steaming temperature, the correlations between M and the mechanical properties of steamed wood were expressed in terms of simple curves. M values above 8% indicated a slight reduction in E and s max, whereas M values below 8% indicated a marked decrease in the mechanical performances. In addition, the e max decreased almost linearly with a decrease in the value of M. These results suggest that hygroscopicity measurement enables the evaluation of degradation in the mechanical performances of wood caused by steaming at high temperatures.     

Cellular UV-microspectrophotometric investigations on pine wood ( Pinus taeda and Pinus elliottii) delignification during biopulping with Ceriporiopsis subvermispora (Pilát) Gilbn. & Ryv. and alkaline sulfite/anthraquinone tr

Scanning UV-microspectrophotometry was used to investigate the topochemistry of lignin removal from pine wood (Pinus taeda and P. elliottii) chips during biopulping involving wood treatment with Ceriporiopsis subvermispora (Pilát) Gilbn. & Ryv. followed by alkaline sulfite/anthraquinone delignification. A delignification front starting from the lumen towards the compound middle lamella was clearly observed in micrographs recorded from individual cell wall layers of wood samples biotreated for 30 days. Lignin was removed without cell wall erosion. UV-micrographs of wood samples cooked for a short time (90 min pulping) showed that the S2 of biotreated samples are more homogeneously delignified compared to the S2 of the undecayed controls. Similarly, the compound middle lamella and cell corners are also more delignified in biotreated samples. On the other hand, UV-micrographs of samples cooked for a long time (150 min pulping at 170°C) showed that there are no significant differences in the contents of residual lignin retained in the S2 of undecayed and biotreated wood samples.     

Effect of extractions on dynamic mechanical properties of white mulberry (Morus alba)

Vibrational properties of wood are affected by several parameters, of which extractives can be one of the most important ones. Wood for European musical instruments has been often studied, but traditional Middle Eastern ones had been left unnoticed. In this study white mulberry (Morus alba L.), the main material for long-necked lutes in Iran, was extracted by five solvents of various polarities (water included). Free-free bar forced vibrations were used to measure longitudinal (L) loss tangent (tanδ), storage (elastic) modulus (E′) and specific modulus (E′/γ) in the acoustic range. Their anisotropy between the 3 axes of orthotropy was determined by dynamic mechanical analysis. Native wood had a quite low E _L′/γ but its tanδ was smaller than expected, and the anisotropy of tanδ and E′/γ was very low. Removal of extractives caused tanδ to increase and moduli to decrease. Acetone, the most effective solvent on damping despite a moderate extraction yield, increased tanδ _L by at least 20% but did not modify E′/γ as much. When used successively, its effects masked those of solvents used afterwards. Anisotropy of E′/γ was nearly unchanged after extraction in methanol or hot water, while tanδ was much more increased in R than in T direction. Results suggest that in white mulberry, damping is governed more by nature and localization of extractives rather than by their crud abundance.