This study analyzed mechanical relaxation data by the well-known Gaussian function from which the relaxation intensity was determined for various moisture contents over a range of temperatures (-81-0°C). These data were used to suggest a range of bonding mechanisms for sorbed water

Ma, Erni

Nakao, Tetsuya

Zhao, Guangjie

English

Wood and Fiber Science (E-Journal)

TECHNICAL NOTE: ANALYSIS OF MECHANICALRELAXATION INTENSITY OF WOOD ATVARIOUS MOISTURE CONTENTSErni Ma*PhD StudentTetsuya NakaoProfessorDepartment of Natural Resources Process EngineeringShimane UniversityMatsue, Shimane, 690-8504, JapanGuangjie ZhaoProfessorCollege of Material Science and TechnologyBeijing Forestry UniversityBeijing 100083, China(Received January 2010)Abstract. This study analyzed mechanical relaxation data by the well-known Gaussian function fromwhich the relaxation intensity was determined for various moisture contents over a range of temperatures(–81-0C). These data were used to suggest a range of bonding mechanisms for sorbed water.Research on mechanical relaxation of wood isvery helpful in providing insight into the condi-tion of adsorbed water in wood and interactionsbetween water and wood substance. This reportinvestigated mechanical relaxation data from aprevious study (Cheng et al 1999). Temperaturespectra of loss modulus at 1 kHz for spruce wereanalyzed by a Gaussian function, and mechan-ical relaxation intensity was determined for var-ious moisture contents over –81-0C.ANALYSIS AND DISCUSSIONThe Gaussian function can be written as:f ðxÞ ¼ 1ffiffiffiffiffi2ppseðxmÞ22s2 ð1Þwhere 1ffiffiffiffi2ppsis the height of the curve’s peak, m isthe position of the center of the peak, and s2 isvariance and represents the width of the curve. Itis convenient to consider that a Gaussian func-tion represents a relaxation process to which asimple form of Eq 1 was applied as follows:E00 ¼ A expðBðT  TpÞ2Þ ð2Þwhere E00 is loss modulus (GPa), A = 1ffiffiffiffi2pps, therelaxation intensity (GPa), B = 12s2, T is tem-perature (C), and Tp is the point that the relax-ation takes place (C).The values of Tp are –81, –67, –55, –40, –26,–10, and 0C, and B is taken as –0.01 for allcases.Considering the shape of experimental tempera-ture spectra of loss modulus, seven peaks wereexpected for every moisture content (MC) con-dition. The superposition of these seven relaxa-tion processes, given by Eq 3, was used todescribe the total dynamic loss modulus.E00 ¼X7i¼1Ai expðBðT  TpiÞ2Þ þ jðTÞ; ð3Þ* Corresponding author: maerniya@yahoo.com.cnWood and Fiber Science, 42(3), 2010, pp. 406-408# 2010 by the Society of Wood Science and TechnologyjðTÞ ¼ aðT  20Þ2 þ b ð4Þwhere a, b are two constants and j(T) is consid-ered as the dynamic loss caused by wood sub-stance rather than adsorbed water, eg the internalfriction of lignin, etc. By fitting the observedloss modulus data using Eq 3, the relaxationintensity A and values of constants a and b couldbe determined for each MC (Table 1).Figure 1 shows temperature dependence of ob-served and calculated loss modulus at 6.5% MCas an example. It is obvious that the theoreticalcurve agrees well with the experiment results.Good agreements were also obtained for theother moisture contents. Figure 2 presents therelation between MC and mechanical intensityat different temperatures. The figure suggeststhat the intensity curves can be divided intothree groups based on the mechanical intensitypeaks. The first group is 0-–40C (b1) havingthe highest intensity value at 4.8% MC. Thesecond group is –55 and –67C (b2) with a max-imum at 6.5% MC. The third group is at –81C(b3), rising monotonically with MC.To clarify the relationship quantitatively, anonlinear regression equation relating MC withthe relaxation intensities b1, b2, and b3 wasdeveloped in which the values of the constantswere determined by the least-squares technique:mc ¼ mcb1 þ mcb2 þ mcb3¼ 21:1Ab1 þ 6:3Ab2 þ 14344A3b3 ð5ÞCalculated moisture contents of b1, b2, and b3from Eq 5 were plotted against RH and the re-sults are given in Fig 3. As shown in this figure,Table 1. Mechanical relaxation intensity A and values ofconstants a and b at various moisture contents (MCs).T (C)Mechanical relaxation intensity (GPa)0% MC 4.8% MC 6.5% MC 8.6% MC 16% MC81 0.018 0.035 0.06 0.074 0.167 0.03 0.05 0.076 0.074 0.07155 0 0.063 0.076 0.064 0.05540 0.018 0.07 0.063 0.058 0.02726 0.006 0.056 0.038 0.035 0.00710 0 0.026 0.015 0.09 0.0010 0.002 0.004 0.003 0.002 0a (106) 2.8 2.8 3.8 3.8 3.3b 0.079 0.083 0.071 0.072 0.084Figure 1. Temperature dependence of observed and calcu-lated loss modulus E00 at 6.5% moisture content.Figure 2. Relation between moisture content and mechan-ical relaxation intensity A at different temperatures.Figure 3. Plots of calculated moisture contents for b1, b2,and b3 vs RH and an experimental isotherm.Ma et al—MECHANICAL RELAXATION INTENSITY OF WOOD WITH MOISTURE CONTENT 407b1 + b2 could be regarded as “monomolecularadsorbed water” and b3 is similar to “multilayeradsorbed water” in the sorption theory (Skaar1988). What should be noted is that the mono-molecular water still exists in two forms, b1 andb2. The behavior of b1 serves as good evidenceto the unexpected phenomenon that dynamicYoung’s modulus increases slightly in the lowMC region (Takahashi and Nakayama 1995).This indicates that b1 is probably related towater molecules bonding at more than one woodsorption sites, whereas b2 might correspond tothe condition in which only one bond formsbetween a water molecule and sorption site.The three existing forms of adsorbed water inwood proposed in this study from the analysisof mechanical relaxation results is needed to befurther proven by sorption isotherm data, dimen-sional change measurements, etc. However, it isfelt to be worthy of presenting the idea at thisstage.REFERENCESCheng P, Nakao T, Kobayashi S (1999) Vibrationalproperties of wood in frequency ranges including ultra-sonic waves, temperature dependences of dynamicYoung’s modulus and loss tangent. Mokuzai Gakkaishi45(1):51-56.Skaar C (1988) Wood–water relations. Springer-Verlag,Berlin, Germany. 283 pp.Takahashi A, Nakayama Y (1995) Wood science se-ries, Physics, 2nd ed. Kyoritsu Press, Tokyo, Japan.174 pp.408 WOOD AND FIBER SCIENCE, JULY 2010, V. 42(3)

Technical Note: Analysis of Mechanical Relaxation Intensity of Wood at Various Moisture Contents

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Technical Note: Analysis of Mechanical Relaxation Intensity of Wood at Various Moisture Contents

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