Fundamental Study on Moisture Sorption Behavior of Texiles : Moisture Sorption Isotherm of Cellulosic Fibers

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(1)Fundamental Studies on Moisture Sorption Behavior of Textiles 一 Moistyre Absorption and Desorption Isotherms of CbMulosic Fibers 一. A Dissertation Presented by l〈AZUNORI KOHATA. to. Department of Practical Life Studies Faculty of Teacher Education. Hyogo University ot’ Teacher Education Hyogo 673−14， Japan. 1984.

(2) ．Fundamental Studies on Moisture Sorption B．ehavior of Textiles 一 Moisture Absorption arid Desorption lsotherms of Cellulos．ic ’Fibers 一一. by Kazungri KOHATA. ContentS. 1. Abstruc’ 煤D Chapte’ 秩@1．. Chapter 2．. Introduction．. 2. Brief SurVey on the Theories of Sorption lsotherms of Textile Fibers．. 14. 2−1． Brunaue．r， Emmett and Teller i s，Theory of Adsorption 工sotherm．. 15. 2−2． Thermodynainic Approach to Adsorption lsotherm by Hill．. Chapter 3．. 21. Apparatus Constructed for Measuri．ng the Sorption. Ch．apter 4．. prbparation and characterization of Test specimens．. Chapter 5．. Experimental Results and Discussion． f5−1’． Thermodynamics of Moisture Absorption． ’5−2． Ab＄orption and Pesorption Hysteresis． 5・一3．． Analyses of APsorption lsotherms． of Cellulosic. Fibers in Terms of Theories of BET Multilayer. Qノ﹂戸［◎ ﹂． ◎6 ノ7 31 り﹂つ 4﹂ β︻◎. Isotherm．. Adsorption and of Hill’s Thermodynamic Approach．. 5−4． Structural Characterization of Adsorbed Water by. 80. Means Qf Differential Scanning Calorimetry．. Chapter 6．. Conclusion．. 128.

(3) 一1一. Abstract Twel ve kind’s of cell．ulosic ．fiber ， including’natural，．negenerated， and ，．. 1四割老，鼎賑賑．ll謙。ぎe鼎㍊：dll締。稀題n乳甜r1巴ol邑t16rllb13「p・． means of two ，types 一〇f gravimetric methods 1−a weighing bottle method and 一a−. sorption balance method wi，th quartz spring in vacuum． From the temperature depen’dence of the’ sorption isotherms， the exess. energy of moisture absorption on to the cellulose fibers was found to be largest in dry state， rahgin．g up to a．values at least，．mo’r．e th．an． 100 cal／gr’. of l iquid water， and to decrease down to almost zero’with increasing relative humidity up to saturation． These results suggest that the adsorbed waters were very firmly bound in the dry state to the adsorbent in an extent to form the crystal lattice of ice， whereas the waters were loosely absorbed in the saturated state to form bulk water． The sorption isotherms at a given temperature of 30 OC were analyzed in terms of the Brunauer， Emmett and TeHer’s （BET） multilayer adsorption. l舗翻舗鵬，lh麗lll、ll，ll丁直s constants・v・・。・and nmax・The. 1濃ldnmax・。li9魏u理dl臨。lf，温lelhlaざ隻1翻。譜d。寵「Σ1継ら1− mediate range of relative hutnidities， was found to be 6 for almost every cellulosic fibers with exceptions of 7 for Na−carboxymethylated rayon and of 4 for tri−acetate raYon．. 記。掬1留二ef翻’ll臨t；。認，聖maXまん＞a謙1もt，991。鴇1詰t’Ve volumd ”oi m6n61ayer’adgo“bth‘ofi−6F’watbF per gr “of 6ry mateVial， for. most of cellulosic fibers with−except．i．ons of di一・and．tri−acetate rayonsi. 諮一v哩1階lltlyt織1鍛麟二認ll牒。m艦lll臨1 cell’ 浮撃盾唐пffibers’. C一’. Und acdtatbJfib’ brs in’the brdeif’pf・des’Cendin−g wqteyi’. accessibility， possibly reflecting the differences’ 奄氏@chemical and physical structures of noncrystalline region of the materials． 4） When plotting the moisture regains with n ＝ 1 （Langmuir’s monolayer. 皐1羅’鋸1論1諜i器囎1瀦諮nll，tll。ll囎牌．vm’、離 in the water accessfibility； i．e．， the slope in the vicinity for acetate. rayons being about one−third to that in the vicinity for regenerated rayons． 5） When poltting the value’s of C， bonding energy characteristics between adsorbent and water molecules， against the nqmber of hydroxyl groups per cellobi， ose u，nil ， there found roughly a l inear relation． But plotting the vm， there hardly found any quantitative values of C against the normalized. corr6tation， 5ut 5ust a tendencSf thaT“the larger tVhe value oUf c’， the normal ized vm becomes larger．. Finally， the nature of adsorbed water was examined by comparing the moisture regains．of different n with those by a current micrQ−calorimetric investigations， deduciRg a conclusion that the adsorbed waters with n as large as 7 to 8 are still calssified as ’freezable bound−water’ and those with n less than 6 are as ’nonfreezable bound−water’．.

(4) 一一 2−. Chapter 1． lntroduction The interactions of moisture and fibers．haye many t．echnigal consegur．． ences： t Dhe weight changes are of direct financjal importance， and they may. also influence the composition of a blend or the aPparent count of a yarn． Because of the aSsociated heat effe’cts， conditiohing is a slow process， and. textiles buffer changes of temperature which the body woyld otherwise experience． Swellfing’ results in dimensional changes of yearns and fabrics 一. sometimes this is advantageous， as in the closing of pores of Ventile fabrics， but more often it is a nuisance，’causing garments to become ill− fitting． The changes in mechan’ical properties， such as the increased stren− gth of wet cotton and the l ower strength of wet rayon， influence the behavior. of textiles under different atmospheric conditions． The amount of water ・b…b・dby fibers va，i，、 c。n、id，，、bly．1， generaいh。、e ’. Bhう、h、b，。．b. …t・・ter a・e ea・i・・t・d・yr・・re p・・ne t・micr・br・1・grcal・ttacいess. prone to static electrification， and better conductors of electricity． Af「b・・us m・t・・「・1・xp。・ed t・uゆangi・g external…d「t「・・s att・『・・. ultimately a moisture content that remains constant so long as these condi− t’. 奄盾獅刀@remain unaltered． This constancy of moisture content is not a static. state but is the result of a dynamic equilibrium， in which the amount of. water evaporating from the fibers，in unit time is extactly counterba］enced’ by that condensing on them． The rate of evaporation depends on the amount of water a3ready taken up and on temperature， wh“e the rate of condensation depends on’ @the number of potential absorbing points in the fibers that. are sti11 unoccupied and on the concentration of water vapour in the sur−. rounding atmosphere． Hence， the fundamental v．ariables controlling the amount of water in the material are the constitution and structure of the fiber. itself， the temperature and concentration of water in the fiber surroundings； mpte sorption i sotherm． i s the curve that expresses the relation， at any.

(5) 一 3 一一. constant temperature， between the amount of water in the fiber and i・ts. concentration outsiqe， and is one of the most fundamentals to investigate the interactions of moisture and fibers． The amount of water in the fiber is generally expressed as a fraction or percentage of the weight of dry fiber， when it is called ’moisture regain’， though occasi．ona，］ly it is referred to ’しhe combined weight of fiber and water， when it js ca］led ’moisture content’；一th’. ?@concentration of water in the surrounding atmosphere. is expressed as the relative vapour pressure （．the partial pressure of. water vapour divided by the saturation vapour pressure at the temperature concemed）・oゆy 109 times th・t value・c・mm・・1y k・・wn as塵％・e1・tive h、mrd甫tゾ：. There have been two groups of direct methods of determining the sorption isotherm． ln the first， the sample is maintafined at given water vapour pre一一 ssure in an encl．osed space and the changes in its mass are measured． A simple. method of doing this with samples in weighing bottles has ’ b??氏@described 1）. by Bu11， water vapour at known pressures being provided by mixtures of. sulphuric acid and water in varying proportions． Other modifications of thi、 m，th。d have been、sed by個1。n et、1．2）and by U，q、h、，t and Wmi、m、．3） If the，appratug i’s evacuated， the approach to equilibriurn is speeded up．4） Contfinuou，s observation of the changes fin weight of the sample may be made by hanging fit on a quartz or tungsten spi’ral spring， as described by McBain5’6）. and by others．7’8） Ashpole has described a way of making these experiments ・F high h・mid帽…9）・h・・e th…i・・・i・k・f・uper・aturatう・・if th・t・m−. perature is not very closely controlled， and the approach to equilibrium is’slow．. The basic apparatus for the second group of methodg consists of a bulb. containing ．the fiber which is connected to a mercury manometer， or some other device fo．r measur’ing vapour pressure， and through a tap to reservoir of.

(6) 一4−. water． After the fibers and the space around them are dried under a high vacuurn， a known mass of water is admfitted， and the vapour pressure−is. measured after equVibrium has been reached． Thus， the total mass of water present within and around the fibers is kept constant durfing a test． This is repeated for successivd additions of water． This method yfie’ 撃р刀@more accurate results than the first met−hod， especially fin the difficult condi−. tions at very low and very high humidities， though it has been criticized on the ground that the vapour pressure is changing during the approach to 10）. Details of the method have been described by Urquhart and equilibrium．湘1r、m、，ll）and．ece，tly T，yl。，1 2・13）h、、 d，、crib，d、m。re ，1、b。，at。. arrangement specially for use below 4％ relative humidity． Sorption iso’しherms have be6n determine（l for many different systems. including text“e fibers， and five types of the isotherm have been noted； these are shown schematicaHy in Figure 1−1． The uptake of moisture by. textile fibers usually occurs in accordance to the isotherm shown as Type II， with an occasional tendency towards Ty’ 垂?@III． lt is not necessary to. dうscuss i・d・t・il h・・e th・th・・retical・i．9酬cance・f th・φff・ren．t tyPes・. but−some indication of their origin may be desirable， if only to provide a theoretical framework in which to fit the facts to be presented． It is generally agreed that the Type 1 isotherm is characteristic of. sorption where the substance forms only a unimole．cular layer on the substrate， but there is more difference of opinion with regard to the remaining types． According to an all−embracing theory，14） the Type II isotherm is characte−. ristfic of multimolecular sorption where the attracti．ve forces between the sorbing and the sorbed substances are greater than those between the mole− cules of the sorbed substance in the l iquid state， whereas the 丁ype III is. obtained when the forces between sorbing and sorbed substances are relatively small．． Type IV and Type V isotherms are obtained when the simpler relation一.

(7) 一5m. ships are coinplicated by t．he occurance of ’capillary condensation’． Accor− ding to other more circumscribed views，i5’i6） an isotherm of Type u， in， which we are prin．cipaMy interested， is the resul’t o’f twosimultaneously. occuring processes， direct chemical combination of water molecules to fiber mo］ecules producing on’e curve， while a ］ooser binding by van der Waals forces or fin solution proyides the other； the sum of the two effects provides the composite sigmoid curve， as shown in Ffigure 1−2． During a few decades sjnce as early as 1920， the moisture sorption. behavior of texbile fibers was studied in terms of the absorption and desorption isotherms by a number of au’しhors for some natural and regenerated cellulose fibers； such as by Urquhart， Williams and Eckersall for raw and soda−boiied cottons，3’11’17−24） by oguri， Nara and Terui for cotton and viscose rayon，25−27）’ ≠獅п@by Neal， Brownsett anci Farrow also for soda−boi］ed cotton，28−30） and speakman and cooper for wool．31 “一33） An of these fibers. are composed of hydrophilic polymers and−have relatively high degrees of hygroscopicity， so that the isotherms were significant not only in an academjc sense to study the interaction between the water molecules and fiber mole− cules， but also from a technical view point of determining the official regains for trading the fibers by weight． After．．．the pioneering stud」es of the absorption and desorption isotherms，. as rnentioned above， numerous investigations have been devoted mostly for. natural and regenerated fibers and for synthetic fibers of hydrophVic po，lymers， such as nylons and polyvinyl alcohol； i．e．， in a decade of 1940， 1） by Rowen by Bull for several kinds oi protain fincluding s’ilk fibroin，. and Balaine for moisture and nitrogen absorption on cellulose fibers， wool，・ilkr・岬・・6−6，34）by H・・hi・…d Y・m・t・f・r ・yl・n．6，35）and by H・tt・・ and Gartside for raw silk and s“k sericin． 36） ln a decade of lgso， Taylor. has investigated the sorption isotherm of viscose rayon and mercerized cotton.

(8) 一6一. （，。da−b。“，d、。tt。，）。ith、peci，1，ef・，ence at 1・w h・。iditi，・、1り2・37）Yan。. has finvestigated tAe sorption isotherrn of poiyvinyl alcohok38） and Thompson， Highes and Fordyce have studied the moisture sorption equilibrium as well as kinetics for’ 翌≠狽?秩@soluble po］yme“s of ceMulose ethers．39） same sort. of studies on the sorption isotherrn has been continued by Kataoka for cellulose acetate fibers，40） by Beever and’. ualentine also for cellulose and cellulose. acetate fibers with special reference at interval and integral sorptions of 。、ter vap。鵬4ト43）and by St、p1， f。剛，c。、e，、y。n at sat、，at」。，，eg、r， d，d、ced f，。m d，，sうty・、，d，w，m，g d、t，．44）エ， a decad，。〔96・， J，fferう，、. has ipvestigated v’ ?窒凵@comprehensively the sorption isotherm for cellulose 45−48）. and Daruwalla and Shet have extended and eight other texti］e polymers，. the interval and integral sorptions of water vapour on cellulose and ce］lulose acetates．49） Newns has carried out moisture sorption studies of regenerated. ce？lulose extensively in terms of sorption kinetics for almost two decades sO−54・）. frovn mi d−1950．. Theo’retical approach fo，r explaining the mois’ture sorption fisotherm of. textile fibers in terms of different sorption mechanisms， was originated． byP，ir、ef。，c。tt。，う，1929．15）H，。，deam。、tう。p。，t、nt、。，励、tう。，t。 the theory by postu］ating two possible forms of adsorbed water， one （alpha form） chemically bound to cel lulose molecules and the remender （beta fo．rm） adsorbed in 1’iquid form， as demonstrated in Figure 1−2，，i．e．， two−phase. adsorption theory． The theory was modified by Speakman adding the third form of water in capiHary condensation for the sorption isotherm of wool fib，r，．. A55）1．e．，three．ph，、e、d、。rpti。n th，。，y．丁h， t。。．。． th，ee．ph，se. theory was replaced with rnultilayer adsorption theories， which are essentially the same Sn cohcept as the multi−phase adsorption theories， but are more． realistic in adsorption me’ モ?≠氏Djsms as represented．’by．，Bruneuer，．Emmettee 56）. and Teller （BET） theory．.

(9) ［1. @7 e一. The BET theory 一is sirnply to extend the Langmuir’s unimolecular. adsorption theory，57） dynamicaMy balancing the evaporatton and condensation of water molecules from and onto the surfaces．of substrate， to mul，ti］ayers of adsorbed molecules， and has been generally accep’しed to give a reasonably. accurate acco，unt of the adsorpbion process． It does fit textile isotherms，. except at high hunidities at which several modifications have been suggested to account for ．this discrdpancy． The BET theory has been dfiscussed by cassie，58，59） Gilbert，60） and Hil161） largely with respect to the structure. of the outer layers of adsorbed water， on the basis of thermodynamic approach． The discrepancy of the textile fisotherm at high humidities frorn the BET theory. has been discussed not only by taking into account the capUlary condensation mechanism， but also by restrains on polymer swelling to yield a hydrostatic pressure acting so as to reduce the observed vapour pressure to that for. unconstrained absorption．58） A similar theory of，restrain has been recently employed by Newns in a study of absorption−desorption kinetics of regenerated cellulose．50） Despite of a great development of synthetic fibers following the first. invention of nylon 66 fiber by Du Pont in 1938， relatively few investigations. of the sorption isotherm have been performed for the synthetic fibers． This is becaUse most of the synthetic fibers being composed of hydrophobic polymers， such as poly−alpha−olefins， polyacrylonitrils， and polyesters， and having relatively low degree of hygroscopicity． Recently， however， a. special group of synthetic fibers principally composed of hydrophobic polymers， has appeared with a relatively high degree of hygroscopicity， possibly owing to chemical and／or physical modifications of the fiber structure as a water adsorbent． Therefore， it is a time to activate the studies of sorption. isotherm Of textile fibers， again， with a particular emphasis of investigating the interaction between water and textile po］ymers， especially the charac’1 er.

(10) 一8一. ヰ. and， comsequently， the structure of the adsorbed wa te r・『 by means of some. novel techniques， such as mic｝【o−ca］orimetry and／or mo］ecular spectroscopy being able to character「ze the nature of the adsorbed water experjmen’しally，. rather than theoretically． In this disertation， therefore， ’じhe absorption and desoγ’ption isothers. of twelve kninds of cellulosic fiber will be first observed under various condit「ons， and then the isotherms will be analyzed in terms of the BE丁. equat「on， not only to quantify the isotherms in terms of the parameters of the equation， as closely as possうble， but also to examine the physうcal. meani・g of th・p・・am・t…r・・e1・㌻i。・t・wid・ly va・壌ed伽e・truct・re of the spec「mens。 Finally， the natuγ・e and the structuγ・e bf adsorbed water. will be investigated expe酉mentally be means of the novel techniques， a differential sc．anning calorlmetry and a h「gh−resolution nuclear magnetic resonance spectroscopy， in order to solve the most fundamental problem ln the BET equation； i．e．， the structural characterization of the outer layers o’f the adsorbed water， γ・eally in contrast e窪ther to the so−called. free water， to the capillary−condensed water， or to the restrained water. accompanied with swelling pressure of specimen at high relative humid「一 tうes．. ＋Th， w・・d・d・。・pti・・i， used t・d…t・the attach…t・f・・t・・t・specifう・ sites as distinct from the random m「xing of molecules which occurs 「n SOlution．.

(11) ．9 一一. ℃①§250εく. （耳）. （1）. （皿）. （IV）. （V）. iv一 Pressure一一一一一一一一一一L. Fi uu r， e 1 一1’ ． F fi ve ty pes of ・ so rpti on i sotherm ．. v.

(12) ．．． ID，￠. ［ U. 甲⊂Φり. 20. 嘱. ﹂Φα. Cotton at. Q5。c l l1. 巴. @ 1. こ. 巴. @ Total water @ sorbed. ヨ. Φ10 ．至. 。. Σ. Dissotved @ater ，︳一4一一一一. ノ’. I 0. 20. 一＿一哨一一一一. va堂er in@hydrate. 40 60 80 100. Retative humidity per cent. Fi’gur・ e 1−2． Composite sigmoid absorption. curves.

(13) ヨリ一ロ一. Ref＝erences 1） M． Bu11，」． Amer． Chern． Soc．， 66，］499 （1944）．. 2） A．F’． Mellon， A．H． Korn， and S．R． Hoover，」． Ameγ・． Chem． Soc．， 69， 827 （1947）； 70， 114 （1948）．. 3） A．R． Urquhaγ・t and A．M． Williams， J． Text． Inst．， 15， T138 （］924）．. 4） S．W． Benson， D．A． Ellis， and R．W． Zwanzi9， J． Amer． Chem． Soc。， 72， 2102 （1950）． 5）」．W． M、B，i， and A．図． B、，k， J． A。，，． Ch，。． S。c．，48，．. U90（1926）．. 6） J．M． McBain， S．J． Good， A．M． Bark， D．P． Davis， H．J． Wi］1avoys， and R． Buck「ngham， Tγ・ans。 Faraday Soc．， 29， 1086 （1933）． 7） S．L．図adorsky， Rev． Sci． Instrum．， 21， 393 （1950）． 8） P．M． Hauser and A．D． McLaren．， Ind． Eng． Chem．，月旦， 112 （1948）． 9） D．K． Ashpole， Pγ・oc． Roy． Soc．， A212， 112 （1952）．. 10）」．B． Speakman，」． Soc． Chem． Ind．， 49， T209 （1930）．］1） A．R． Urquhart and A．M． Wう11うams，」．丁ext．工nst．， 15， T433 （1924）． 12） J．B． Taylor，」． Text． Inst．， 43， T489 （1952）． 13） J．B． Taylor，」． Text． Inst．， 45， T642 （1954）．. 14） S． Brunauer， 1匪Physical Adsorpt「on of Gases and Vapoursu， Oxford Univ． Press， 1943， PP． 149 et seq． 15） F．T． Peiγ℃e，」． Text． Ins’し．， 20， T133 （1929）．. 16） A．J． Hailwood and S．卜｛orrobin， Trans． Faraday Soc．， 42B， 84 （1946）． 17） A．R． Urquhart and A．M． Williams，」． Text． Inst．， 15， T559 （1924・）． 18） A．R． Urquhart and A．M． Wi11．iams，」． Text． Inst．， 16， T155 （1925）．. 19）A・R・U・q・h・・tand A・M・Wmr・m・・」・Text・lh・t・・1ブ・T38（1926）・ 20）A・R・U「quha「t・」・Text・lnst・ D・18・丁55（1927）・ 2］） A．R． Urquhart， J． Text． Inst．， 20， T119 （1929）．. 22） A．R． Uγ、quhart and N． Eckersa11， J． Text． Inst．， 21，丁499 （1930）．. 23） A．R． Urquhart and N． Eckersa11， J． Text． Inst．， 23， T163 （1932）． 24） A．R． Urquhart and N． Eckeγ・sa11， J． Text． Inst．， 23， T135 （1932）．. 25） S． Ogur「 and M， Nara， Kogyo Kagaku Zashi， 33， 777 （1930）．.

(14) ＿ 1つ＿凸L. ︶︶︶︶︶︶︶︶︶︶︶︶︶︶︶︶ヘノ︶︶︶︶︶︶︶︶㍉ノ︶︶. S． Oguri and S． Terui， Kogyo Kagaku Zashi， 3．4．， 515 （193］）．. S． Oguri and S． Terui， Kogyo Kagaku Zashi？．ILt， 630 （1931）． S．M． Neal， J． Text． lnst．， 22， T320 （1931）． S．M． Neal， J． Text．’ hnst．， 22， T349 （1931）．. J．B． Speakrnan and C．A． Cooper， J． Text． lnst．， 27， T183 （1936） J．B． Speakman and C．A． Cooper， J． Text． lnst．，．ZL7， T186 （1936）. J．B． Speakman and C．A． Cooper， J． Text． lnst．， 2Z， T191 （1936）. つ﹂ ● ・・ T ︶︶︶. T． Brownsett， F．D． Farrow and S．M． Neal， J． Text． lnst．， 22，. 57. （1931）．. H．B． Rowen and R．L． Blaine， Ind． Eng． Chem．， 39， 1659 （1947）．. K． Hoshino and K． Yumoto， Nippon Kagaku Zashi，．Z90．， 104 （1949）． E．A． Hutton and J． Gartside， J． Text．｛［nst．， 40，丁16］（1949）．. J．B． Taylor， J． Text． lnst．， 47， T147 （1956）．. Y． Yano， Nippon Kagaku Zashi， 76， 668 （1955）． L．J． Thompson Highes and D．B． Fordyce， J． Polym． Sci．，. 22， 509 （1956）．. Kogyo Shikenjo Iho，＃46， 7 （1958） Iho，＃46， 7 （1958）． T． Kataoka， Sen−i. D．K． Beever and L． Valentine， J．. Appl． Chem．， 8， 103 （1958）．. D．K． Beever and L． Valentine， J．. Text． lnst．， 49， T95 （1958）．. D．K． Beever and L． Valentine， J．. Polym． Sci．， 32， 521 （1958）．. M．LL Staples， Tex’t． Res． J．， 28，. 900 （1958）．. R． Jeffries， J． Text． lnst．， 51，. T339 （1960）．. R． Jeffries， J． Text． Inst．， 51，. T399 （1960）．. R． Jeft’ries， J． Text． lnst．， 51， T441 （1960）．. 只・」e飾師J・Appl・P・］ym：S・『・. ， 8， 1213 （1964）．. Res． J．， 32， 165 （1962）． E．H． Daruwalla and R．T． Shet， Text．. A．C． Newns， Trans． Farday Soc．， 52 ， 1534 （1956）．（1959）． A．C． Newns， J． Polym． Sci．， 41， 425. A．C． Newns， Trans． Faraday Soc．，. 64， 3147 （1968）．. A．C． Newns， J． Chem． Soc．， Faraday Trans．， 1， 69， 444 （1973）．.

(15) 一 13 一一. ︶︶︶ 7 00Qノ 4 0J ︶［つ［﹂［﹂［霞つ﹂［だ JR. ︶︶︶. A．C． Newns， J． Chem． Soc．， Faraday Trans．，’. P， 71， 278 （1975）．. q．B． Speakman， Trans． Faraday Soc．， 40， 6一（1944）． S． Brunauer， P．H． Emmett， and F． Teller， J． Amer． Chem． Soc．， 60， 309. （1938）．，一. 1 Langmuir， J． Amer． Chem． Soc．， 40， 1361 （1918）．. A．B．D． Cassie， Trans． Faraday Soc．， 41， 458’. i1945）．. A．B．D． Cassie， J． Soc． Dyers ＆ Col．， ”Symposium Fibrous Proteins”， 86 （1 946）．. 60. G．A； Gilbert， J． Soc． Dyers ＆ Col．， ”Symposium Fibrous Proteins”， 96 （1946）．. ヨ. ︶. 6. T． HiH， J． Chern． Phys．， 14， 263 （1946）．.

(16) 一 14 一. Chapter 2． Brief Survey on the Basic Theories of Sorp．tion． Isoth．e−r． rn．一〇．一f．. Textile Fibers There have been several theories that attempt to explain the adsorption of moisture by textile materials． This fis due partly to our lack of knowledge concerning the sorpti’ 盾氏@process， but also to the absence of any ’ モ窒撃狽奄モ≠ test th №煤@may be appl icable to each the．ory． lt is re］atively easy ，to deveiop. a sorption isotherm to fit the experimental relation with the aid 6f two or three adjustable parameters， but this is not necessarily a sufficiently exacting criterion on which we can judge the theory． We can only ensure that the theory does not violate any physical prin．ciples which have been accepted． The theories fall roughly into two groups． peirce，1） and Brunauer，. Emmett and Teller，2） for example， consider the water molecules to be adsorbed on il！t［！！glznterna］ s u rfaces or E一！t l！esLtes i n the a d s orbenP， a n d a pa rt from s upplying. these siles the textile fis considered to play l ittle part in the process． On the other han，d， Katz，3） and Hailwool and Horrobin，4） consider the process to be one of solution． lt is probable that both these l ines of approach. are correct， the former at low water concentratiop， and the iatter as we. approach saturation． It is about fifty years since Peirce developed the first adsorption. isotherm for textiles in order to explafin the effect of adsorped water on the elastic properties of cotton． As mentioned in the previous chapter， he. made a most important contribution to the theory when he postulated two possible forms of adsorbed water， one chemicaHy bound to the cotton， and the remainder adsorbed in l iquid forrn． This concept has been employed by all succeeding investigators・『n the fie］d．丁his theory has been， however，. criticized by Gilbert5） on the grounds that there is no microscopic balan−. cing of the evaporation and condensation processes， in accordance with the.

(17) 。． 1員＿ 1㍉ノ. theories of Langmuir6） and Brunauer， Emmett and Teller （BET）．2） ln fact，. Peirce derivation is not clear at several points， but it has suppl ied many basic ideas for later workers， and such as its value can not be. overesimated． Hailwood and Horrobin4） have developed a sorption isotherm by analogy．. with simple solution theory basing on standard thermodynamics． They consider that the adsorbed water exists partly in chemical combination with the polymers， as water of hydration， and partly in sol id solution． Furthermore，. the three spcies， namely polymer， dissolved water and polymer hydrate， are considered to form an ideal solution， ln their derivation the authors con− sider the general case with ！llgtnLgi2gtggEL−g！一bxEing！一ignny degrees of hydration， but for si．mpl fi c i ty. it is proposed to take the case where the monohydrate only is formed； the. principles involved are not affected by this modification． In spite of the good descripbion of experimental data， such as th’e. heat ok wetting observed by Hedges for wool （keratin 一 water system），7）. with the above model by Hailwood and Horrobin， it has been criticized by Gee and Barrer．8） The main criticism is that the splid solution can not be considered as fi deal， especially when spec「es o’f to’しally different molecu］ar. size are included． Solutions pf long−chain polymers are known to differ. considerably from ideal solution． Cassie9） has questioned the doubt cast on Hedgesis experimental data for heat of wetting， whfich he considers to be the most reproducible data available for the keratin 一 water system． Ei℃」109」髭≡と＝三＿E田胆∈III1｝＿9E⊇璽＿1皇ll∈iと⊃⊥§＿lbggrこ∠＿gf＿6望§9tp1190＿工§9主bg12胆. As long as 1918， Langumir6） developed a sirnple theory o’F sorption. limited to the formation of unimolecular layers on sol id surfaces． He did. this simply by equating the rate of evaporation of gas molecules from the surface with the rate of condensation from the surrounding gas or vapour． Very simply then， the rate of evaporation wi11 be proportional to the.

(18) ．一 16 一一. surface covered by，adsorbed molecules （Aa）． The rate of condensation will Pe proportional to the uncovered surface （Ao） ’and the vapour pressure （p）．. Therefore，. k’aAa＝koP Ao ’ （1．） If the total surface 6re is A（＝ A一＋ AA）， then a o. kA A e. p一一一一一g−L’ ＝k＝＝kdv （2） koAo （A 一 Aa）（1 一 e） where e（＝ Aa／A） is the fractional adsorption for a pressure p， and k is the ratio of ’. 汲＝^ko． This relation gives the well−known isotherm which. describes only some adsorption processes， the more general shape befing more like the hormal textile regain curves wfith a point of inflection， as shown in Fig． 2・一1， can not be predic’ted．. one is， therefore， led to c6nsider adsprption in amounts greater than the monolayer． Langmuir did extend his th’ ?盾窒凵@in thfis way， but did not. derive an isotherm． Many years later， however， Brunauer， Emmett and Teller （BET）2）devel。P，d，m、1tう1、y，，6d、。，pti。，。echani、。、翻、， t。 th、t。f. Langmuir and extended fit to derive a multimolecular adsorption isotherm． The method is simply to extend the evaporation 一 condensation mechanism to. many layers of adsorbed molecules．． Consider a surface covered by groups of molecules； there will be free surface together with groups contafining 1， 2， 3 etc． Iayers of molecules． Let Ao be the area of uncovered surface， Al be the area covered by one l ayer molecules， and Ai be the area covered by i layers ef molecules； i．e．， the molecules can be arranged as shown in Fig． 2一一2， schematically．. For equilibrium one may equate the rates of evaporation and condensation. from successive layer， and for the first layer it follows.

(19) 一 17 一一. alp Ao＝klAl ，（3） and the general expression is. aip Ai−1＝kiAi 一一（4） The coeffic’ 奄?獅狽刀@ki inc］ude a term which governs the rate of evaporation. of the adsorbed molecu］es． These can leave the surface only if they acquire an energy equal to the energy of bindfing to the surface．. The fraction of molecules acquiring the necessary energy at any instant wiH be given by Boltzmann’s expression as exp（一一UVRT）， where U’ 堰@is the binding energy for the i−th layer， R fis the gas constant， and T is the. absolute temperature． Therefore， one can write. kl ＝bl exp（一UVRT），（s） and in general. ki＝biexp（一Ui／RT）（6） where b］， b2， b3， etc． are constants．. The total surface area Ao’ can be given by co. Ao’＝Z Ai （7） o. and total volume adsorbed v co. v＝ vo Z i Ai （8） o. where the area Afi is covered with i l ayers， and vo is the volume of gas. adsorbed per unit area of monolayer． Therefore，.

(20) 一18一. co v z fi A．一〇 1. ‘vA）＝v／v−a ＝一（9） v／（A. o o m oo. v z A． O l o. BET now make two assumptions；（1） that U2 ＝ U3 一一一：一丁一一 UL （heat Of liquefaction of gas），（2） that b2／a2 i b3／a3 ＝一一一一一一 d， i．e．， they’ assume. that the adsorbed gas is in a l iquid state from the second layer outwards，. so that the evaporation 一 condensation−mechanism is similar for all layers except the first layer． Thus， one can write A2 ＝ x Al， or in general Ai ＝ x Ai．1， where. ×＝（p／d） exp（UL／RT）（10） and for the first layer Al. ＝ A．．C x，. C ＝（aVbP ．d exp［（Ul. 一 UL）／RT］. where. o （ll）. Therefore， the following relations may be deduced for unresticted. adsorption of infinite layers：ココ A. ｰ0. （v／Vm）＝. 曾−. ○○. Al ＋ 2A2 ＋ 3A3 ＋. oo. Ao ’ Al ’ A2 “ A3 “ ”“一一一’. 1へ Al（1 ＋ 2x ． 3，2 ．一一一一一一一一一）. Ao “ A］（1 ＋x ＋ x2 ＋．一一．．．）. A。C・臼／（、一x）2］. Ao［1 ＋ Cx／（1 一 x）］.

(21) 一19一一. cx. ．一．（12）（1 ・一 x）（1 一 x ＋ Cx）. At saturation （p ＝ ps） v ＋ oo． But v ＋ oo when．x ＝ 1−in the above. expression for the isotherm given by Eq．（12）， so that from Eq．（10） it. foU ows. X＝（p／d） exp（ULIRT）（13） For v f oo， x ＝ p／ps， and. ，．L．CP （14）（p， ’ p）［i ＋（C T ，i）p／ps］. If the adsorption js restricted to a finite number of molecular layers，. the following relation may be obtained： v−c x i 一（n．＋ i）xn’＋ nxn’i v＝一1−i’i1iinyib一一」IV iN 一ii−ti−iiLt一一zil’i−rL6”Vli；ri（c．i），．ckn＋（i5）. where n represents the maximum number of adsorbed molecular layers which can be built up and is compa ti ble with space l imitations．工t 「s noted that. the Eq．（15） reduces to Langmuir’s eauation， Eq．（2） for monomolecular adsorption when n ＋ 1． The above relation of Eq．（14） may be put in a l inear form. p／v（p，一 p）＝ o／v．c）＋一一12−v：’E ！ci （p／p，） 06） m. and by ploting p／v（ps 一 p） against （p／ps）， vm and C may be determined from the s］op and fintercept． But vm ＝ Ao’vo， where Ao’ is the total area avai−. lable for adsorption． Therefore， if vo can be estimated， it is possible to determin A ’． o.

(22) 一 20 ．．. NoWs. C・（・1／bl）（b2／・2）exp［（UドUL）／RT］『．（17） and BET assume that alb2／a2bl ＝ 1． Therefore，. C・exp［IUドUL）／RT］．（18） from which one mqy determine the heat of absorption of the first layer． H。weve，， C、ssi，IO）h、、。bt、i，，d、， exp，essう。， f。， C，mp1。yi，g，th，，。。dyna而・. treatrnent and given reasons to suggest that alb2／a2bl 〉 1， and as a result the values for the heat of adsorption by BET equation of Eq．（18） may be too low．. The BET theory of sorption is generally accepted as giving a reasonably accurate account of the adsorption process’． It does fit textile ibotherm， except at high vapdur pressures nea’r saturation， and many mod’ifications have’ @been suggested， a’. 刀@will be discussed in a later chapter， to account. for this discrepancy． The BET theory has been discussed by cassiell） and Gilbert，5） largely. with respect to the structure of the outer adsorbed layers． BET allow only short−range forces sufficient to bind the first adso’窒b?п@layer； further layers are adsorbed at vapour pressures below saturatio，n by virtue of a と・hd・・s・ti・n−evap・・atr・n eq・111b蘭・At th・・am・t加・・h・wever・BET consi，der that the adsorbed water over and above the monolayer has the. properties of liquid water． These two considerations are incompatible， because， as Ca’ 唐唐奄?@has pointe’ п@out， no adsorption could take place on the. external layers if they’@were identical with l iquid water． Thesb could be no result’ 奄獅〟@decrease in free energy bn transferring water molecelues from. liquid wate’ 秩@to the outer adsorbed layers． It is also apparent frbm inspection. of the BET model that the outer layers of water molecules are distributed.

(23) 21. in a manner completely different from t，hat in l i’quid water， i．e．， in a rnore. ordered state than ．in a random state of l iquid． The terminology of internal. surface upon which the mono一 and multi−laye・rs of adsorbed molecules are built−up， seems to be visua］ized as a model， but fis difficult to．understand. unless the existence of any internal rnicrocleavage or microvoid is examined．工b§〔田g鯉躯1⊆．aE2塑gb．19一合鯉ご匹ユ9し王§匹b卿 In the absence of long−range forces binding these outer layers to the. surface， the adsorption of vapours on sol ids has received justification only. on the thermodynamic grounds； Brunauer， Emmett and Teller argue that there are no such long−range forces present． According to the law of thermodynamics，. adsorptfion must take place only if the absorbate suffers a reduction in free energy on befing transferred from an external l iquid to the absorbed state．丁he change うn free energy at constant pressure is. AG−A’H 一TAS ．（1 9） where △卜｛ is the heat exchange per mole， △S is the entγ・opy exchange per mole，. and T is the absolute tempe’. 窒≠狽浮窒?D. For a reduction in free energy， AG must be negative， and even if AS is. zero or negative； i．e．， the absorbed molecules are in a more ordered state than in the l iquid， then， provided that AH is negative （i．e．， heat is evolved in the adsorPtion process）’， adsorpbion can st“1 take place． However， ii’ the. heat evolved is from water adsorbed in the first layer only， then for subsequent layers where AH ＝ O， in order that AG be negative， AS must be. positive． ln other words， adsorption must then take place because the adsorbed molecules are in a more random state than in l iquid water； G．e．，. by some mixing or distributive process analogous to the BET evaporation 一一. condensation mechanism．.

(24) 一22一. Cassie first developed a theory of multimolecular adsorption on these. line and showed that the resulting isotherm relation was equivalent to that of BET．11） He did not postulate adsorption on internal surfac−e． s一， but con−. sidered adsorpt『oA sites d「strうbu’しed throughout the polymer． On these sites，. water molecules can combine chemically with the polymer with， evolution of heat， one coTT｝bined mo］ecule to a site， whilst the remainfing water exists in. a ljquid state adjacent to these occupied sites to form a sort of water cluster． Cassie．’s original derivation of the resul．ting free energy increase. in the polymer phase was critieized by Hill12） to be incorrect， although. the final isotherm relation was correct． What is essentially Hillis derivation is therefore discussed below． SupPose there are B mo］es of．adsorption sites per a given しmit mas’s of textile polym’ ?窒刀D Then we first consider the distribubion of A moles. of water over’ @these sites in such that X moles are combined． The remaining. （A 一 X） moles exist in a l iquid state with their entropy increased by. distributing them over thd × occupied sites， allowing any ’number to each group． We can then write. z）1GA＝AGx＋AG（A．一×）（20） where AGx is the free−energy change due to the distribution of × moles on B l oW−energy sites， and AG（A−x） is the free−energy change due to the. distribution bf （A 一 X） moles on the X occupied sites． AGx is made up of a heat term，！xHx（＝ wX） where w i s the heat of reaction. between l iquid water and the low energy sites （heat is evolved， so that w is negative）， and al so an entropy term given by. T！tsSx＝RT（ln Cx ＋× l n j，）（21） where js is the partition function for the bound water molecules， and is.