Gas Adsorption Characterization of Ordered Organic-Inorgani

8/9/2019 Gas Adsorption Characterization of Ordered Organic-Inorgani

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Gas Adsorption Characterization of OrderedOrganic-Inorganic Nanocomposite Materials

Micha l Kr uk a nd Mietek J aroniec*

Dep a r tm en t of Ch emi str y, K e n t S ta te Un i ver si ty, K en t, O h i o 4 4 24 0

Received J anu ary 31, 2001

A critica l review of a dsorption methods tha t a re currently used in the chara cterization ofordered orga nic-in org an ic n an o com p osite m at e rials is p rese n ted , an d th e ad so rptionmethodology that is potentially useful for this characterization, but has not yet been applied,is discussed. The ordered orga nic-inorga nic na nocomposites in clude surfa ce-functiona lizedordered m esoporous ma teria ls (OMMs) w ith siliceous fra meworks (synthesized either viapostsyn th esis surfa ce modificat ion or via direct co-condensa tion met hod), periodic mesoporousorg an o sil icas, an d su rfactan t-con ta in in g OM M s. Th is re vie w covers th e m e th od s ford e te rm in atio n o f th e sp e cif ic su rface are a an d p o re vo lu m e . T h e avai lab le m e th o d s fo rmesopore size ana lysis ar e critically compar ed and eva luat ed, with special emphasis on there ce n t d e ve lo p m e n ts re late d to th e ap p licat io n o f ad van ce d co m p u tatio n al m e th o d s fo rstudy ing a dsorption in porous media a nd t o the direct modeling of a dsorption using highlyordered surface-functionalized OMMs as model adsorbents. The review also covers adsorption

methods for studying the surface properties of organic-inorga nic na nocomposites, includingthose based on adsorption of molecules of different polarities. An emphasis is placed on theemerging opportunity for studying the surface properties of nanocomposites using low-pressure a dsorption of nonpolar molecules, such a s nitrogen a nd a rgon. The opportunitiesa nd cha llenges in a dsorption char acteriza tion of specific surface sites, uniformity of coatedor bonded la yers, bonding density of groups on the surfa ce, t ype of surface species, an d soforth , a re presented. Thus, t his review provides a n overview of a dsorption studies dea lingwith organic-inorga nic nan ocomposites, a critical discussion of ads orption methods a va ilablefor such studies, a nd some recommendat ions for thorough char a cterizat ion of these ma teria lsusing gas adsorption.

Introduction

The discovery of sur facta nt-templa ted ordered meso-porous materials (OMMs) in the early 1990s 1,2 createdremarka ble new opportunit ies in the field of synthesisand applicat ion of organic-inorganic nanocomposites(OINs) because it pa ved the wa y to na nocomposites wit hwell-defined ordered porous str uctures, ta ilored sur faceproperties, and framework compositions. 3,4 The fam ilyof ordered organic-inorgan ic na nocomposites (OOINs)currently includes OMMs wit h silica-based fram eworksand surfaces functionalized with chemically bondedorganic groups,3 OMMs with organosilica frameworks(these ma teria ls w ill be referred t o as periodic mesopo-rous orga nosilica s (P MOs)),3,4 and surfactant-containingOMMs.5

Surfa ce-functionalized silica-based OMMs can besynth esized via chemical m odificat ion of surfa ctant -freeOMMs with organosilanes,2 co-conden sa tion of siloxanea n d or g a n os i lox a n e p r ecu r s or s i n t h e p r es en ce ofs u rf a c t a n t s ,6-10 or chemical reaction of as-synthesized(surfactant-containing) OMMs with organosilanes.11-15

The first of these methods was originally demonstratedin 1992 for MCM-41 silica (which exhibits uniformcylindrical pores arranged in a two-dimensional (2-D)

hexagonal (honeycomb) structure), whose surface wasmodified wit h t rimethylsilyl groups.2 The current wide-spread use of this functionalization method can largelybe at tributed to the va st knowledge on t he react ions oft h e s i l ica s u rfa c e wit h modify in g o rg a n ic a g e n t s t h a thas accumulated during the last 50 years, giving riset o ma n y u s ef u l ma t e ria ls , in clu din g a wide v a rie t y o fchroma tographic packings.16-18 OMMs with silica-basedframew orks and organic groups on the surface can alsobe synt hesized via co-condensa tion of silica precursors(such a s tetra ethyl orthosilicat e, TEOS ) a nd orga nosilicaprecursors (such as organotriethoxysilane) in the pres-ence of a proper structure-directing agent. The latterca n be ch os en a mo n g ion ic a lky la mmo n iu m s u rf a c-t a n t s ,6 n e u t ra l a lk y la min es ,7 oligomeric sur facta nts, 8

a nd triblock copolymers. 9,10 The resulting ordered sur-f a c t a n t-organosilicate composite needs to be freed ofsurfactan t to open its porosity, w hich can be a chievedvia solvent extra ct ion 6-10 or , i n ce rt a i n ca s e s, v iacalcinat ion a t tempera tures sufficiently high t o ensurequa ntita t ive surfacta nt removal, and yet low enough top res erv e t h e org a n ic g ro u ps a t t a c h ed t o t h e s i licaframework.19 The co-condensation approach is a com-bination of the surfactan t t emplat ing, originally devel-oped for purely inorganic ma terials, a nd t he w ell-knownco-condensa tion a pproach for the sy nth esis of disorderedorganosilicas with pendent organic groups,20 a n d t h u s

* To whom corresponden ce should be addr essed. E-mail: J a [email protected] .edu. P hone: (330) 672 3790. F ax: (330) 672 3816.

3169Chem. M ater. 2001, 13 , 3169-3183

10.1021/cm0101069 CC C: $20.00 © 2001 American C hemical SocietyP ubl ish ed on Web 05/03/2001


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shares the benefits of these two methodologies, includ-ing t he pore structure uniformity, pore size a djust ingcapability, and tailorability of the surface propert ies.Another approach to the synthesis of OOINs is basedon the direct react ion of as-synthesized OMMs withorganosilanes. Despite the fa ct tha t t he feasibility of thisapproach wa s demonstrat ed in 1990,11 this methodologyha s not received much a tt ention (except for the w ork ofthe Mobil scientists)12 until recently. The la st 2 years

brought the rea lizat ion tha t t he modificat ion of surfac-t a n t -con t a in in g O M Ms n ot on ly lea ds t o O OI N s ofstructures similar to those at ta ined via m odificat ion ofsurfactant-free materials but also allows one to achievehigh loadings of organic groups.13-15

The a forementioned three a pproa ches for th e synth e-s is of O OI N s s h a r e m a n y a t t r a c t iv e f e a t u r es . Th eordered silica-based support imparts good mechanical,thermal, and chemical stability, addit ionally allowingfor t he pore size an d pore structure ta iloring, w hereassurfa ce orga nic groups allow for int roduction of desiredsurface characterist ics, such as sorption, or catalyt icproperties. 3 Because of that , the synthesis, character-izat ion, an d a pplicat ion of these materia ls have recently

attracted much attention, resulting in the developmentof ma n y p ot e n t ia l ly u s ef u l c a t a ly s t s , a ds o rbe n t s , a n dseparat ion media.3

Reported for the first time in 1999, PMOs are novelmaterials synthesized via surfactant templat ing usingorganosilane precursors with two trialkoxysilyl groupsb r id g ed b y a n or g a n ic g r ou p.21-23 Af t er s u rfa c t a n tre mov a l by e xt ra c t ion 21-23 or ca lc in a t io n (u n der a noxygen-free at mosphere a nd a t su fficiently low t emper-at ure to prevent the degrada tion of framew ork orga nicgroups),24 P MOs exhibit ordered mesoporous voidsreadily accessible to various adsorbate molecules. 21-24

U nlike the previously d iscussed surfa ce-functionalized

silica-based ma terials w ith fra meworks tha t exhibit onlyS i-O-Si linkages, PMO frameworks feature Si-R-S ilinkages, where R is an organic group (such as -C H 2-C H 2-,21,22,24,25 -C H 2-,26 -C HdC H-,22,23 or -C 6H 4-24,27), i n a d d it ion t o S i-O-Si l in k a g e s. D is orde redma terials (referred to a s bridged silsesquioxanes) withsuch h ybrid organosilica fra meworks were r eported in198928 an d ha ve been a ct ively st udied because of theirinterest ing propert ies, such as large specific surfacear eas a nd pore volumes, ta ilored fra mework properties,and surface functionality.29,30 The bridged silsesquiox-anes are often highly porous, but their porous structuresa re dis orde red a n d p ore s ize dis t r ibu t ion s a re broa d.Therefore, the sha ping of their porous st ructures usin g

proper structure-directing agents, which is an essenceof P M O s y nt h es is ,21-23 i s a h ig h ly p r om i si n g n ew approach. P MOs are envisioned to have ma ny rema rk-able properties related to the possibility of tailoring oftheir framework properties between those of ceramicsand organic materials.3,4 This ta iloring ca n be a chievedby select ing a suitable organic bridging group. Alter-n a t iv e ly , a ra n g e of ma t e ria ls in t erme dia t e bet we e npure organosilicas (with each silicon atom bonded to onecarbon atom of the bridging organic group) and puresilicas can be obtained via co-condensation of organo-silica precursors w ith silica precursors.23,24 The resultingma terials w ere indeed found to exhibit propert ies tha tsystema tically chan ged a s t he proportion of organosilica

to silica components varied.24 Surfa ce propert ies ofPMOs can also be tailored using the above two strate-gies (tha t is, t he selection of the bridging orga nic groupand the content of the organosilicate component), pro-vided that the organic groups are actually exposed onthe surface rat her tha n buried in the framew ork. To thise n d, P M O s wit h -C HdC H- bridges w ere reported tou n derg o re a c t ion s in v olvin g t h e o rga n ic g rou p ,22,23

clearly demonstrat ing that these groups were actually

accessible. In addit ion, wett ing behavior3,22

a n d l o w -pressure gas adsorption properties 31 indicat ed the ex-posure of -C HdC H- a nd -C H 2-C H 2- groups on thepore surface. Because of the presence of silanols in thestructure of PMOs, it is additionally possible to modifyt h e P M O s u rf a ce v ia ch em i ca l b on d in g of or g a n icgroups.24 T h e re ma rk a ble p ro p e rt ie s o f P M O s ma k et h e m a t t ra ct iv e f rom t h e p o in t of v ie w of a dv a n c ednanostructured materials design.3,4

As-synthesized OMMs constitute another excit inggroup of OOINs.5 T h e y a re k n o wn t o be c a p a ble o fundergoing phase transit ions from one ordered phaseto a nother,32 an d chemical rea ctions, such as those withorganosilanes t hat were a lready discussed. Their com-

p os i t ion (s i lica : s u rfa c t a n t mola r ra t io ) u n de r g ive nsynt hesis conditions is often independent of the surfa c-tant chain length or even surfactant structure.33-35 I nthese composites, surfacta nt ions a re locat ed in the voids(pores) in the silicate framework.5 The external surfacesof part icles of these composites are also likely to becovered by a relat ively dense layer of surfactant ions,a s re ce n t ly f ou n d f or M CM -41 a n d M CM -48.34,36,37

Because of the presence of surfacta nt , internal porousstructures (that is surfactant-filled voids in the silicatefram ework)of a s-synthesized OMMs were usua lly foundla rg e ly or f u lly in a c ce ss ible t o a ds o rba t e s , s u ch a snitrogen.34,36-38 Nonetheless, t he ordered surfa ctant-silicate composites a re capable of a dsorbing nonpolarmolecules from solutions 33,39 a n d ca t a ly zin g ch e mica lre a c t io n s in t h e l iq u id p h a s e .40 T h is s h o ws t h a t t h esurfactan t micelles confined in a periodic inorgan icframework can effectively solubilize organics, which wasalso confirmed by the feasibility of expanding t he sizeof v oids in t h e s i l ica t e f ra me work by s we ll in g a p re-formed surfacta nt-silicate nanocomposite using neutralamines.41

G a s a ds o rpt ion is c ommo nly u s e d in O O I N c h a r-acterizat ion,2,6-10,12-15,19,21-25,27,31,34-38,40,42-63 allowingone to determine t he specific surface ar ea, pore volume,an d pore size distribution as w ell a s to study the surfa cepropert ies. Many well-known adsorption methods for

characterizat ion of porous materials are applicable toOOINs,51,64-68 but the custom-ta ilored structures ofthese materials create new challenges with respect toaccuracy, reliability, a nd chara cterizat ion capability an dopen new opportunities in the development of adsorp-tion characterization methods. This review is intendedto present the currently available gas adsorption meth-ods suita ble for cha ra cterizat ion of OOINs. The discus-s ion wil l cov er t h e me t h odolog y of a ds o rpt ion da t aanalysis rather than adsorption data acquisit ion meth-odology, whose description ca n be found elsewhere.64,65,68

First, it is discussed wha t t ypes of adsorption isothermsand hysteresis loops are typically observed for OOINsa n d wh a t s t ru ct u ra l in forma t io n t h e y p rov ide a s we ll

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as w hat kind of informa tion can not be readily obtainedf rom t h e m on t h e ba s is o f o u r cu rre n t k n o wledg e.

Se con d, t h e me t h ods f or e va lu a t io n of t h e s pe cif ics u rf a c e a re a a n d p o re v o lu me a re p re s e n t e d wit h a nemphasis on the issues specific for OOINs. Third, thea p p ro a c h e s t o e v a lu a t e t h e p o re s ize a n d p o re s izedistribut ion (P SD ) a re critica lly discussed, highlightingthe recent developments related to the advances in thecomputational modeling of adsorption in porous mediaand to the application of OMMs as model adsorbents totest the exist ing methods for calculat ion of PSDs andt o de ve lop a n ov el , a ccu ra t e , a n d re lia ble p ore s izeanalysis methodology. Finally, the opportunities in thech a ra ct e riza t io n of t h e s u rfa c e p rop ert ies of O O I Nsusing specific and nonspecific adsorba tes a re discussedwit h a n e mph a s is on t h e de t ect ion of s u rf a ce g ro u ps

and the est imation of the surface coverage of organicligands.

The Shape of a Gas Adsorption Isotherm as aSource of Qualitative Structural Information

Classification of Gas Adsorption Isotherms. E x-perimental gas adsorption isotherms usually fall intosix cat egories,65,68 out of which five (Types I-V accord-in g t o t h e I U P AC cla s s if ica t io n ,65 s e e F ig u re 1) a rerelevant to the present discussion. Type I isothermsexhibit prominent adsorption at low relative pressures(t h e re la t iv e p res s u re is de fin ed a s t h e e q u il ibr iumvapor pressure divided by the saturat ion vapor pres-

s u re ) a n d t h e n le v e l o f f . T y p e I is o t h e rm is u s u a l lyconsidered t o be indicat ive of ad sorption in m icroporesor mon ola y e r a ds o rpt ion du e t o s t ron g a ds o rbe n t-a d s or b a t e i nt e r a ct i on s (w h i ch m a y b e t h e ca s e f orchemisorption, which involves chemical bonding be-tw een the a dsorbat e and t he adsorbent surfa ce; we willnot discuss chemisorption here).68 I t should be notedt h a t p o re s a re c la s s i f ie d h e re in o n t h e ba s is o f t h e irdia meter (or w idth) a s m icropores (below 2 nm ), meso-pores (betw een 2 a nd 50 nm), a nd ma cropores (above50 nm).65 In the case of nonpolar gases commonly usedfor characterization of porous solids (nitrogen, argon),64-68

ch e mis orp t ion is u n l ik ely a n d t h e ref ore a cla s s ica linterpretation would associate Type I with microporos-

ity. However, Type I isotherms may also be observedfor mesoporous materials with pore sizes close to themicropore ra nge. In pa rticular, in the case of a dsorptionof N2 at 77 K or Ar at both 77 and 87 K in cylindricalpores, a Type I isotherm would have to level off below the relative pressure of about 0.1 for the material to beexclusively microporous, a s inferred from th e results ofrecent studies of siliceous OMMs.35,69 Consequently,when a Type I isotherm does not level off below the

relative pressure of 0.1, the sample is likely to exhibitan appreciable amount of mesopores or even be exclu-sively mesoporous. However, such Type I behavior maybe in dica t iv e of s ome de gre e o f broa de n in g o f t h emesopore size distribution. This is because ma terialswit h h ig h ly u n iform cy l in drica l p ore s ma y e xh ibitdiscernible st eps on a dsorption isotherms (and there-f ore t h e s e is ot h e rms a re cla s s i fied a s Ty p e I V , a sdiscussed later) at relat ive pressures down to 0.1 orperhaps even lower (for N 2 at 77 K a nd Ar a t 77 an d 87K ).35,69 Type I isotherms are quite common for OMMswith organic groups bonded to a silica framework, bothp rep a re d v ia ch e mica l bon din g47 an d co-condensa-tion.19,54

Adsorption on many macroporous solids proceeds viamultilayer formation in such a manner that the amountadsorbed increases gradually as the relat ive pressureincreases, although the multilayer buildup close to thes a t u ra t ion v a p or p res s u re ma y be q u it e a bru pt . Th isunrestricted multilayer formation process gives rise toType II a nd II I isotherms. In t his case, the a dsorptionand desorption branches of the isotherm coincide; thatis, there is no adsorption-desorption hysteresis. De-pending on the surfa ce properties of a given solid, theremay be a pronounced stage of the monolayer formation(Type II) or the adsorption isotherm may be convex inthe whole pressure range (Type III). The latter behaviorca n be o bs erv ed wh e n la t e ra l in t era c t ion s bet we e nadsorbed molecules are strong in comparison to interac-t ions betw een the a dsorbent surface and a dsorbat e. N2adsorption isotherms similar to Type II were reportedfor several as-synthesized (surfactant-containing) OM-Ms .37,38 Type III adsorption isotherms were reported forwater adsorption on certain OOINs with hydrophobicsurfaces. 44,46,48,53

Adsorption on mesoporous solids proceeds via multi-layer adsorption followed by capillary condensation(Type IV and V isotherms). Therefore, the adsorptionprocess is initially similar to that on macroporous solids,but at higher pressures the amount adsorbed rises verysteeply due to the capillar y condensa tion in mesopores.

After these pores are f illed, the adsorption isothermlevels off. Ca pillary condensation a nd capillary evapora -tion often do not t ake place at the sa me pressure, wh ichleads t o the appeara nce of h ysteresis loops. However,it wa s suggested long ago64 and unequivocally confirmeda f t e r t h e discov ery of O M Ms70,71 t h a t t h e ca p il la r ycondensation-evaporat ion in mesopores may also bereversible (this behavior w ill be denoted herein a s TypeIVc).68 T y p e I V in g e n e ra l , a n d I V c in p a rt ic u la r , ist y p ica l f or ma n y O O I Ns wit h a c ce ss ible me sop ore s ,a l t h o u g h wh e n t h e s ize o f t h e p o re s is c lo s e t o t h emicropore range or PSD is broad, Type I isotherms canbe observed. The distinction between Types IV and Vis ana logous to tha t betw een Types II and III . Fina lly,

Figure 1. Classification of gas adsorption isotherms (afterrefs 65 and 68).

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i t s h ou ld b e n o t ed t h a t s om e O OI N s m a y e xh i bi tadsorption isotherms tha t can be regarded as a combi-nation of the aforementioned five types of isotherms asa result of th e presence of severa l different t ypes of poresin the structure.

Classification of Adsorption-Desorption Hys-teresis Loops. As w as already mentioned, the a dsorp-tion process on mesoporous solids is often accompaniedby a dsorption-desorption hys teresis. This phenomenonwas a subject of numerous studies,64,68,72-75 but its originis st ill not fully understood. The h ysteresis is usua llyat tributed to t he thermodynam ic or netw ork effects orthe combinat ion of these t wo effects.68,72 The therm o-d y n a m ic e ff ect s a r e r el a t ed t o t h e m et a s t a b i li t y ofa ds o rpt ion or de sorp t ion (or bot h ) bra n c h es of t h eadsorption isotherm. Namely, the capillary condensationor evaporat ion may be delayed a nd ta ke place at higheror lower pressures, respectively, in comparison to thepressure of coexistence betw een the ga slike and liquid-like phases in the pore. In addition, the hysteresis mayalso be caused by pore connectivity (network) effects,

wh ich a re expected to play an importa nt r ole in desorp-tion processes. Na mely, if la rger pores ha ve a ccess tot h e s u rrou n ding on ly t h ro ug h n a rro we r p ore s, t h ef orme r c a n n o t be e mp t ie d a t t h e re la t iv e p re s su recorresponding to t heir capillary evapora t ion since thelat ter are st ill f i l led with the condensed adsorbate. Sothe larger pores may actually be emptied at the relativepressure corresponding to the capillary evaporation inthe sma ller connecting pores (or a t t he relat ive pressurecorresponding to t he lower limit of adsorption-desorp-tion hysteresis). Hyst eresis loops observed experi-mentally most likely arise from some combination oft h er m od y n a m ic a n d n et w o r k e ff ect s , a l t h ou g h t h ela t t e r a re of t e n p a rt icu la r ly p romin en t . Ads orp t ion

isotherms for certain porous solids may also exhibitlow-pressure hysteresis loops (loops that do not close,even at low relative pressures). Low-pressure hysteresisma y a r is e f ro m s we ll in g o f t h e a ds o rbe n t du rin g t h ea ds o rpt ion p roce ss or wh e n p h y sica l a ds o rpt ion isaccompanied to some extent by chemisorption pro-cesses.65

According to the IUPAC recommendations,65 hyster-esis loops are classified into four types. The Type H1loop exhibits parallel and nearly vertical branches (seeF ig ure 2). Th is k in d of h y s t e res is loop wa s of t enreported for materials that consisted of agglomerates(assemblages of rigidly joint particles) or compacts ofapproximately spherical part icles arranged in a fairly

uniform wa y.65 More recently , it ha s become clear 68 t h a tH1 hyst eresis loops ar e a lso cha racterist ic of ma terialswith cylindrical pore geometry and a high degree of poresize un iformity. 32,76 H e n ce , t h e a p p ea ra n ce o f t h e H 1hyst eresis loop on t he a dsorption isotherm for a poroussolid generally indicates its relat ively high pore sizeuniformity and facile pore connectivity. The Type H2h y st e re si s l oop h a s a t r i a n gu la r s h a pe a n d a s t ee pde sorp t ion bra n c h . S u ch beh a v ior wa s obs erv ed f or

many porous inorganic oxides and was attributed to thepore connectivity effects,74 wh ich w ere often consideredt o be a re su lt o f t h e p re s en ce o f p ore s w it h n a rro w mouths (ink-bottle pores), but the latter identificationmay be grossly oversimplified. Indeed, H2 hysteresisloops w ere observed for m at erials w ith relat ively uni-form channel-like pores, w hen the desorption bran chh a p p e n e d t o be lo c a t e d a t re la t iv e p re s s u re s in t h ep rox imit y of a lowe r p res s u re l imit of a ds o rpt ion-desorption hysteresis.76 This lower limit is characteristicof a given a dsorbat e at a given temperature (a relat ivepressure of about 0.4 for N 2 at 77 K; 0.34 and 0.26 forAr at 87 and 77 K, respectively). It should be noted that,in certain relatively rare cases, hysteresis extends below

this limit; that is, low-pressure hysteresis is observed.Th u s , t h e a p p ea ra n ce of a H 2 h y s t ere s is loop in t h eproximity of the lower pressure limit of adsorption-desorption hyst eresis should not be rega rded a s evidenceof poor pore connectivity or ink-bottle pore shape. Infact, novel materials having uniform cagelike pores (andt h u s s u it a ble a s mode l s o lids wit h in k -bot t le p ore s )exhibited adsorption isotherms with broad hysteresisloops but w ithout a ny dra ma tic differences in steepnessof adsorption and desorption branches. 77-79 These hys-teresis loops seemed to be interm ediat e betw een TypesH 2 a n d H 1, ra t h e r t h a n be in g T y p e H 2, a s c o u ld beexpected from the aforementioned simplistic interpreta-tion.

Isotherms w ith Type H3 loops tha t do not level off atrelative pressures close to the sa tura tion vapor pressurewere reported for materials comprised of aggregates(loose assembla ges) of plat elike par ticles formin g slitlikep or es . Ty pe H 4 l oop s f ea t u r e p a r a l le l a n d a l m os th orizon t a l bra n c h es a n d t h e ir occu rren ce h a s bee nattributed to adsorption-desorption in narrow slitlikep ore s. H o we ve r , re ce n t e xp erimen t a l da t a f or we ll-defined systems q uestion t his interpretat ion. Nam ely,t h e Ty pe H 4 l oop w a s r ep or t ed f or M C M-41 t h a texhibited particles w ith interna l voids of irregular sha peand broad size distribution (between 5 and 30 nm).80

Hollow spheres with walls composed of ordered meso-

porous silica also exhibited hysteresis behavior of theH4 t ype.81 This would suggest that H4 hysteresis loopsma y merely a rise from the presence of lar ge mesoporesembedded in a matrix with pores of much smaller size.Because Type H3 loops are quite similar to Type H4loop s, on e c a n a ls o e x pe ct t h a t t h e f orme r a re n otat tributable solely to platelike materials with slit likep or es . I t s h ou ld b e n ot e d t h a t a n a p pe a r a n ce of ahysteresis loop similar to Type H4 but of triangularshape with an almost horizontal desorption branch thatfalls st eeply close to the lower limit of a dsorption-desorption hy steresis ma y be indicat ive of the presenceof disordered doma ins r esulting from colla pse of la mel-lar structures.82

Figure2. Classification of adsorption-desorption hysteresisloops (aft er r ef 65).



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Determination of Specific Surface Area andPore Volume

Specific Surface Area. C u r re nt l y, t h er e a r e t w omajor methods used to evaluate specific surface areaf r om g a s a d s or pt i on d a t a : t h e B r u n a u e r-E mme t t-Teller (BE T) method64-68,83 a n d t h e com pa r a t i vemethod.64,68 The evalua tion of the specific surfa ce areausing the BE Tm ethod is based on the evalua tion of themonolayer capacity (that is , the number of adsorbedmolecules in the monolayer on the surfa ce of a ma terial)by fit t ing experimental ga s adsorption da ta to the BE Tequation. Thus, obtained monolayer capacity is mult i-plied by the cross-sectional ar ea of the adsorbed mol-ecule in the monolayer formed on a given surface. Thecomparative method is based on the comparison of theadsorption isotherm for a given porous material withthe adsorption isotherm for a suitable reference adsor-bent of known specific surface area.

Th e de riv a t ion of t h e B E T e q u a t ion in volv es t h ef ol lowin g ma j or a s s u mp t ion s : t h e s u rf a c e is f la t ; a l ladsorption sites exhibit the same adsorption energy;t h e re a re n o la t e ra l in t era c t ion s bet we e n a ds o rbe d

molecules; the adsorption energy for all molecules exceptfor the f irst layer is equal to the liquefact ion energy;and an infinite number of layers can form. In the caseof adsorption on actual porous solids, these assumptionsu s u a l ly do n o t h o ld. I n p a rt ic u la r , s u rf a c e s a re g e o -metrically and energetically heterogeneous, there arelateral interact ions between adsorbed molecules, andinteract ions of adsorbed molecules vary with the dis-tance from the surface.64,66,68 Therefore, one sh ould notexpect the monolayer capacity derived using the BETme t h o d t o be p a rt ic u la r ly a c c u ra t e . I n a ddit io n , t h evalues of cross-sectional areas (denoted as ω) o f a d -sorbed molecules, even those most commonly u sed, a rec u rre n t ly s o me wh a t u n c e rt a in a n d ma y a c t u a l ly v a ry

from one type of surface to another. 64,68,84,85

Moreover,the very concept of determination of the specific surfacea re a on t h e ba s is o f mo le cu la r s ize a n d mon ola y e rcapacity should be treated with some caution becausethe ability of molecules to effectively cover the surfaceis dependent on the molecular size and surface corruga -tion.68,86 Clearly, adsorbed molecules cannot satisfacto-rily probe surface roughness on t he scale sma ller t hantheir size. Therefore, the surfa ce a rea s determin ed usinglarger molecules may be smaller than those obtainedusing smaller molecules. Because one usually employssmall N2 molecules or Ar a toms t o eva lua te th e specifics u rf a c e a re a , t h e a f o re me n t io n e d p ro ble ms wit h t h ein a de q u a t e p robing of t h e s u rfa c e ro u g h n es s a re n ot

expected to be severe for many OOINs. However, forOOINs with fa irly large organic surface groups that don o t f o rm c o mp a c t la y e rs , t h e s u rf a c e ma y be h ig h lyrough and diff icult t o probe adequately by a ny kind ofad sorbate, a nd even the very concept of the surfa ce ma ybe somewha t ill-defined. In a ddition, one needs to keepi n m i nd t h a t t h e v a l u e o f t h e m o n ol a y er ca p a ci t ymu lt ip lied by t h e cros s -s e ct ion a l a re a of a ds o rbe dmolecules essentia lly provides the ar ea of the surfa cedrawn through the centers of adsorbed molecules, whichmay be different from the geometrical surface area ofthe solid. For instance, in the case of approximatelycylindrical pores, the underestimation of the geometricspecific surface area would be by the factor of about

w /(w - σ ), w here w i s t h e p ore dia me t e r a n d σ i s t h ed ia m e t er of t h e a d s or b ed m ol ecu le . I n t h e ca s e ofnitrogen adsorption, t his fa ctor is more t han 10% fortypical OOINs w ith cylindrical pores of dia meter below 4 n m.

Despite a ll these problems an d limitat ions, the B ETmethod is currently a standard in the specific surfacearea evaluation,68 perhaps largely because other meth-o ds , e x c e p t f o r t h e c o mp a ra t iv e a n a ly s is t h a t is de -

scribed below, do not offer any appreciable advantages,a n d a t t h e s a me t ime t h e ir l imit a t io n s a re le s s we ll-understood, an d t hese methods th emselves may be moredifficult t o apply. Moreover, even the a ssessment of thes pe cific s u rf a c e a re a u s in g t h e comp a ra t ive me t h odoften employs data for reference samples for which thes pe ci fi c s u r fa c e a r ea w a s e va l u a t e d u s in g t h e B E Tmethod. Because the BETmethod is so commonly usedand it is often unclear wh at alterna tive approaches canbe used to substitute it , it is worthwhile to discuss how to use th is met hod effectively for OOI Ns. The discussionwill be focused on t he a pplicat ion of N2 and Ar a dsorp-tion because t hese gases a re most commonly used in th eB E T a n a ly s is.68

In general, it is recommended to use adsorption dataat relative pressures below 0.3 in N 2 B ET calculat ions.67

However, even in this case the results will depend tosome extent, sometimes considerably, on the choice ofthe relat ive pressure interval used.87 This needs to beta ken into a ccount when the specific surface ar eas fordifferent sa mples a re compared. I t is a dvised t o reportthe relat ive pressure ra nge used along with the resultsof the B ET calculations.65,68 Moreover, it is often a dvisedt o e s t a bl is h a re la t iv e p res s u re ra n g e w h e re t h e B E Tequation provides the best description of the experi-me n t a l da t a a n d t h e n t o u s e t h is ra n g e t o de t e rmin ethe B ET monolayer capacity for a given sa mple. Because

a selection of such a range is often largely arbitrary andthe use of different ranges for different samples mayma k e t h e c o mp a ris o n o f t h e ir s p e c i f ic s u rf a c e a re a sdifficult , w e do not recommend this pract ice. Instea d,we suggest using t he sam e ra nge of relat ive pressuresfor a given adsorbat e and t ype of adsorbents, if only thisprocedure is practical and applicable (some criteria ofapplicability of a given relat ive pressure ra nge tha t a rerelevant to OOINs cha ra cterization are discussed lat er).This would not only help in comparat ive studies, butwo u ld a ls o p e rmit t h e e va lu a t io n o f t h e a ccu ra c y ofcalculat ions using model adsorbents, whose specifics u rfa c e a re a s ca n be e v a lu a t e d in de pe n den t ly wit hreasona ble accuracy. These model adsorbents current ly

include uniform spherical nonporous part icles84

a n dOMMs (including OOINs), wh ose specific surfa ce area scan be determined, respectively, using electron micros-copy data and using the combination of data from twoor three different experimental techniques, includingpowder X-ray diffraction (XRD).52,69,76 The studies ofuniform spheres by J elinek and Kovats provided con-v in cin g e viden ce t h a t N2 B E T s p e c if ic s u rf a c e a re aevaluated from data in the relative pressure range from0.05 to 0.23 is in a greement w ith t he geometrica l surfa cear ea w hen the cross-sectional a rea (ω) for N 2 on silicawas 0.135 nm 2, and wa s 0.168 nm2 for nitrogen on thesilica surfa ce fully covered w ith a dense layer of ligandswith long alkyl chains.84 The latter ω value is close to



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the commonly accepted one (0.162 nm 2),65,67 bu t ωs u g ge st e d f or s i lica is q u i t e lo w. A lt h o ug h i t is n otimprobable that the N 2 molecule can orient on the silicas ur fa ce i n s uch a w a y t h a t ω ) 0.135 nm 2 c a n b eat ta ined, there is another possible interpreta t ion of thedat a of J elinek and Kovat s. Namely, the validity of thederived cross-sectional areas rested upon an assumptionthat the values of the BET monolayer capacity deter-mined in the pressure range used were correct . How-

ever, there is evidence tha t suggests th a t th e monolayercapacity evaluated for silica is overly large when theconsidered relat ive pressure range is used in the B ETa n a ly s is , a n d con s eq u e n t ly ω ) 0.135 nm 2 w a s a nunderest ima tion of the a ctual va lue. The evidence wa sobta ined from studies of a dsorption in uniform MCM-41 pores, w hose size wa s evalua ted using independentmethods.88,89 The well-defined pore geometry of MCM-41 allowed for a reliable calculat ion of the stat ist icalfilm thickness of ad sorbat e in the pores,76 to f ind out a twhich relative pressure the thickness corresponding tothe sta t ist ical monolayer is a t ta ined, and consequentlyt o de t e rmin e t h e mo n o la y e r c a p a c i t y a s t h e a mo u n tadsorbed corresponding to this relat ive pressure. 52 I t

was found that the statistical film thickness of nitrogenin silica pores is much larger t han tha t usua lly assumed,and as a result the monolayer capacity is much smallert h a n t h a t r es ul ti ng f rom t h e B E T a n a l ys is i n t h erelat ive pressure intervals t ypically used. The ma gni-tude of the monolayer capacity overest imation for N 2adsorption on silicas is quite similar t o the ra t io of thes t a n d a r d N2 cross-sectiona l a rea to t he cross-sectiona lar ea determined by J elinek and K ovat s.84 Therefore, thedeviat ions of their r esults from t he commonly a cceptedvalue of ω for N2 on the silica surface might h ave merelyresulted from th e inability of the B ET method to providethe correct monolayer capa city. This a rgument is basedon the a ssumption t hat the commonly used monolayerstatistical film thickness for N 2 (0.354 nm)68 is valid fort h e s il ica s u rf a ce . I f N2 molecules actua lly exhibito rie n t a t io n e f f e c t s , t h is a s s u mp t io n ma y be in v a l id .An y wa y , i t is c lea r t h a t , wi t h o u t a ddit ion a l da t a f romother experimenta l techniqu es, the conclusion of J elineka n d K ov a t s a b ou t ω of n i t rog e n on s i lica s a p p ea rspremature and this is probably not ω, but th e calcula-tion of the monolayer capa city tha t should be corrected.The latter correction can actually be achieved by chang-in g t h e p res s u re ra n g e u s ed in t h e B E T ca lc u la t io n sbeca use this ra nge has a prominent effect on the resultsin th e ca se of silicas.87 However, from the practical pointof view, the relative pressure range for the BE T calcula-

t ions a nd the corresponding ω

determined by J elineka n d K ov a t s ca n be u s ed t o o bt a in a n a ccu ra t e a s s es s -ment of the specific surface area for silicas, if only otherc o n dit io n s re q u ire d f o r t h e a p p lic a bi l i t y o f t h e B E Tequation are fulfilled in this relat ive pressure range.These conditions will be discussed below. Although t heuse of MCM-41 as a model adsorbent suggested t ha t t here su lt s of J e lin ek a n d K ov a t s f or s i lica s s h ou ld bereinterpreted, the use of OOINs as model adsorbentsprovided a confirmat ion of their results for stronglyhydrophobic surfaces. In this case, the B ET ana lysis inthe r elat ive pressure range from 0.05 to 0.23 appearsto provide a generally correct estim at e of the monolayercapacity.52

These findings are direct ly relevant to the specificsurface area determination for OOINs. In the case ofsuch materials with surfaces that interact with nitrogenor argon similarly to the silica surface (for instance,siliceous OMM w ith chemically bonded polymeric am i-nopropyl ligan ds),45 the m onolayer capacity calculat edu s in g t h e B E T met h o d in t h e re la t iv e p res s u re ra n g esimilar to tha t used by J elinek and Kovats w ill be mostlikely overestimated. To compensate for the resulting

error, one can use a lower value of ω, such a s 0.135 nm2

,keeping in mind that this value does not have an actualphysical significance. Alternatively, the pressure rangeu s e d f o r t h e B E T a n a ly s is f o r s i l ic a s wil l n e e d t o bemodified 52 or a n empirical correction to compensa te fort h e e rror f rom t h e de t ermin a t ion of t h e mon ola y e rcapacity using the BETmethod for silicas in the typicalrelat ive pressure ra nge can be introduced. In the caseof OOINs with strongly hydrophobic surfaces, such asthose covered by dense layers of long alkyl chains, theBE T monolayer capacity calculated in a typical relat ivepressure ra nge (such a s 0.05-0.23) is likely t o be corr ecta n d a n a c cu ra t e e st ima t e of t h e s p e cific s u rfa c e a re acan be derived from it using the cross-sectional area

commonly used for N2 (tha t is, 0.162 nm2). The s tu diesof Ar a dsorption at 87 K on siliceous OMMs an d OOINsindicate that the BET monolayer capacity obtained inthe relative pressure ra nge similar to the a bove is ratheraccura te, a nd reasonable values of th e specific surfacear ea can be obta ined when ω ) 0.138 nm 2 is used.69 I nall cases, one needs to keep in mind that the derivedspecific surfa ce a rea ma y a ctually reflect th e area of thesurface dra wn through centers of a dsorbed molecules,a n d t h e ref ore i t ma y be a p prop ria t e t o in t ro duce asuitable correction for the pore sha pe, a s discussedabove. In many routine studies, the introduction of theaforementioned corrections may not be necessary, al-though the a pproximat e nat ure of thus obtained specific

surface area est imates should be kept in mind.

In a ddition, one needs to restrict the B ET calculat ionsto a range of gas adsorption data wherein the assump-tions of the m ethod a re most closely fulfilled, if only sucha ra nge can be found. This is an importa nt problem inthe case of OOINs, whose adsorption isotherms are ofteneither of Type IVc wit h t he capillar y condensa tion stepbelow the relative pressure of 0.3, or Type I. In thesec a s e s , t h e a ds o rp t io n in t h e re la t iv e p re s s u re ra n g epotentia lly usable for the B ET an alysis does not proceede xcl us iv el y a s a m u lt i la y e r f or m a t i on , a s t h e B E Tequation a ssumes, but ha s contribution from capillarycondensation or micropore filling phenomena or both of

t h e a bo v e . I t is c le a r t h a t t h e da t a f ro m t h e c a p il la rycondensa tion or micropore filling regions a s w ell as fromthe plateau observed after the pores have been filledshould not be used, if possible, in the B ET an alysis. Soin t he case of the Type IVc isotherm, one is forced t oselect t he dat a at relat ive pressures below the onset ofcapillary condensation. For the Type I isotherm, theremig h t be n o ra n g e o f da t a p oin t s , wh e re a ds orp t ionwould proceed in a w a y close to unrestricted multila yerformation, and perhaps the best choice is to use datas o me wh e re be lo w t h e re la t iv e p re s s u re a t wh ic h t h eisotherm levels off. Obviously, the r esulting B ET mono-layer capacity w ill need to be treated with caution.68 I tca n b e con cl ud ed t h a t , d es pi t e i t s l im i t a t ion s a n d



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shortcomings, the days of the BE Ta na lysis are not over.The method can still provide useful information about

the specific surfa ce a rea , alt hough some ca ution shouldb e t a k en t o s e lect a pr oper r a n ge of d a t a f or t h ecalculat ions a nd use a ppropriat e values of the m olecularcross-sectional areas. When an accurate determinationof the geometrica l specific surfa ce area is required, onecan introduce suita ble corrections for the pore shape.F in a l ly , i t n e e ds t o be k e p t in min d t h a t e v e n wh e nt h es e p re ca u t i on a r y m ea s u r es a r e t a k en , t h e B E Ts pe cific s u rf a ce a re a s de riv ed f rom Ty p es I I a n d I Visotherms ma y st ill be somewha t ina ccura te, althoughperha ps closer t han within 20% (which wa s provideda s a n e st i m a t e o f a c cu r a cy of t h e B E T m o nol a y ercapacity in t he w ell-known monograph; r ef 64, p 61) oft h e a c t ua l v a l ue. H ow e ver , l ow e r a c cu r a cy ca n b e

e xp ect e d f or is ot h e rms of Ty p es I , I I I , a n d V, bu tfortuna tely these last tw o types a re not common in thecase of the specific surface ar ea evaluation for OOINsusing N2 or Ar.

A f t e r t h e ma n y p ro ble ms a s s o c ia t e d wit h t h e B E Ta na lysis w ere considered, the concept of the compara tiveana lysis of adsorption da ta can be readily appreciated.Th e com pa r a t i v e a n a l y s is i s b a s ed on t h e i d ea ofcomparing the a dsorption isotherm for ma terial und ers t u dy w i t h t h e a d s or pt i on i sot h er m of a r ef er en cemacroporous solid of the same surface properties withrespect to the adsorbate used. The adsorption on thema croporous reference solid proceeds as mult ilayeradsorption essentially in the entire relat ive pressure

range, except perhaps the relative pressures very closeto the sa tura t ion vapor pressure, where capillar y con-densation ma y also be observed. I f t he compared solidis a lso macroporous, the adsorption on its surface a lsoproceeds via mult ilayer formation. When the amountad sorbed on th e compared solid is plotted a s a functionof the amount adsorbed on the reference adsorbent att h e s a me re la t iv e p re s s u re v a lu e s , a s t ra ig h t l in e isobserved because the amount adsorbed on one of thesesolids is proportional to the other, whereas the propor-t ion a l i t y con s t a n t is s imply t h e ra t io of t h e s pe cifics u rfa c e a re a s of t h e s e t w o s o lids. Th is s i t u a t ion isdepicted in Figure 3 for two macroporous silicas modi-fied with octyldimethylsilyl (ODMS) ligands. One of

t h e s e a ds o rbe n t s w a s ch os e n a s a re fe ren ce ( for t h ela t t e r , t h e a mou n t a ds o rbe d is e x pre ss e d a s s t a n da rdreduced adsorption, Rs, w hich will be defined below). Soi f t h e s pe cif ic s u rfa c e a re a of t h e re fe ren ce s ol id isknown, the specific surface area of the compared solidcan readily be determined from the comparat ive plot .This is advantageous because once an accurate surfacearea evaluation is achieved for the reference solid, thespecific surface area of the compared material can be

accurately evaluat ed from a dsorption data in essentia llyan y relat ive pressure range. The an alysis a long t he linesdescribed above can be carried out for both Types II andIII isotherms. Initia l part s of Types IV a nd V isotherm s(tha t is , the pa rts a t r elat ive pressures below the onsetof capillary condensation) also provide straight lineswhen an appropriate reference adsorbent is used (seeFigure 3). This a llow s one to a ssess th e specific surfacearea. Moreover, the slope of a l inear segment of thecomparat ive plot at relat ive pressures where the me-s o p o re s a re a lre a dy f i l le d wit h c o n de n s e d a ds o rba t eprovides a n est ima te of the externa l surface area of thema t e ria l , w h e rea s t h e in t erce pt of t h e l in e p a s s in gthr ough this segment w ith t he “Amount Adsorbed” axis

of the plot reflects the adsorption capacity of mesopores.This quantity can be recalculated to the correspondingvolume of mesopores (see below). In the case of Type Iisotherms, the external surface area an d th e microporea nd/or mesopore volume ca n be determ ined in th e sam ema nner. H owever, because a dsorption in pores of sizewithin or close to micropore ra nge is enha nced a t low relat ive pressures, the slope of the init ial part of thecompa ra tive plot for th e Type I isotherm w ill in generalbe higher th an tha t corresponding t o the specific surfacea re a . Th e ref ore , t h e re su lt in g s pe cif ic s u rf a ce a re aest imates for Type I isotherms should be tr eated withca u t ion , e sp ecia l ly wh e n t h e comp a re d ma t e ria l islar gely or exclusively microporous.

This discussion was based on an assumption that thereference solid exhibits the surface propert ies verysimilar to those of the compared solid in the ca se of theadsorbat e used. I f this is not th e case, the compara t iveplot a na lysis becomes more complicated. The differencesin surface propert ies may cause various deviat ions ofthe compara t ive plot from linear ity. These deviat ionsthemselves can be an alyzed t o gain some useful infer-e nce s a b ou t t h e n a t u r e of t h e s u rf a ce of t h e com -pared.51,90,91 To obtain good est imates of the specificsurfa ce area , especia lly from Types IV an d V isotherms,is necessary to have a reference adsorbent whose surfacep rop ert ies a re a s clos e a s p os s ible t o t h os e o f t h e

compared solid so a s to eliminate the aforementioneddeviat ions. This is i l lustrated in Figure 3, where thecomparative plots for OOIN with a highly hydrophobicsurface were obtained using the reference adsorbentsof a similar surface natur e and largely different surfa cenat ure. When th e a ppropriat e reference a dsorbent w asemployed, the initial pa rt of the plot w a s approximatelyl in e a r a n d cou ld be u s ed t o de t ermin e t h e s p ecificsurface area, w hereas in the other case, such determi-na tion wa s impossible because t he compar at ive plot w asstrongly bent downward. In both cases, the mesoporevolume and the external surface area could be deter-mined and were acceptably close, which reflects thewell-known observation tha t surface propert ies a ffect

Figure 3. Compara tive plots calculated for a microporous (as-synth esized etha nol-wa shed C12 MC M-41),36 mesoporous(ODMS-modified MCM-41),52 a nd m acroporous (ODMS-modi-fied silica )52 hydrophobic adsorbents using reference da ta formacroporous ODMS-modified si l ica. The solid l ine withoutsy m b ol s show s t he com par a t i ve pl ot for t he hy d r ophob i cmesoporous adsorbent calculated using the reference data forsil ica. Data partial ly taken from ref 52.



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the low-pressure part of the adsorption isotherm morestrongly than the mult ilayer adsorption part at higherrelative pressures.

The comparative analysis is very useful in character-izat ion of a dsorbents. H owever, th e number of referenceadsorption isotherms currently a vailable in th e litera-ture is l imited a nd, as fa r a s we know, only one of themwa s re port e d in a t a bu la r f o rm f or a ma t e ria l wi t h a norganic-modified surface (that is , for strongly hydro-

phobic ODMS-modified silica).52 Therefore, there seemt o be cu rren t ly on ly t wo ch oice s of re fe ren ce da t arelevan t for OOINs, one being the da ta for silica 64,87 a ndt h e o t h e r o n e be in g t h e da t a f o r t h e a f o re me n t io n e dmodified material.52 U n f o rt u n a t e ly , in n o n e o f t h e s ecases wa s an est imate of the specific surface area m adeindependent from the BET analysis, although in bothcases the accuracy of the BE T specific surface area wa sgenerally assessed 52 an d thus fairly accura te est ima tesof the actual specific surface area can be established. Itwould be desirable to acquire the reference adsorptionisotherms for various types of surfaces encountered incases of OOINs. Finally, i t should be mentioned thatthere a re several different versions of the compara t ive

ana lysis, which a re essentia lly equivalent , but differ inwa ys of expressing am ounts adsorbed on the referencesolid, or on both the reference solid and the comparedsolid. In the t-plot method,64 the amount adsorbed forthe reference is expressed as the st at ist ical f i lm thick-ness curve (t-curve). H owever, the d etermina tion of th et -c urv e u s u a l ly re q u ire s k n owle dg e of t h e s p ec if icsurface area, which is often not known with satisfactoryaccuracy.92 Th e ref ore , i t wa s s u g ge st e d t o be m orecon v en ien t t o e xp res s t h e a mo u n t a ds o rbe d f or t h ereference ad sorbent a s the sta nda rd reduced a dsorption,that is, the amount adsorbed (as a function of pressure)divided by the amount a dsorbed at an a rbitra rily chosenrelat ive pressure (usually 0.4).64,68 This modification ofthe compar at ive plot met hod is referred to a s the Rs plotmethod and is perhaps the most popular today. Otherlegit imat e choices can also be ma de in the expressionof the amount a dsorbed for th e reference adsorbent.90,91

Pore Volume Determination. The total pore vol-ume of a given adsorbent can be calculated from thea mo u n t a ds o rbe d a t a re la t iv e p re s s u re c lo s e t o t h es a t u ra t ion v a p or p res s u re (f or in s t a n ce , a t a re la t iv epressure of 0.99) simply by convert ing this am ountadsorbed to the corresponding volume of liquid adsor-bat e at t he tempera ture of the a dsorption measurement.In t he case of N2 at 77 K a nd Ar at 87 K, th e conversionfactors from t he a mount a dsorbed (expressed in cm3 S TP

g-1

; STP stands for standard temperature and pressure)to the volume of liquid adsorbate are 0.0015468 and0.001279,69 respectively, under the assumption that thedensity of condensed adsorbate in the pores is equal tothe density of bulk liquid adsorbat e. This a ssumptionappear s to be sa tisfa ctory for mesopores. The tota l porev olu me de t ermin ed a s de scribed a bo ve re flect s t h evolume of all pores in which th e ca pillary condensat ionan d micropore filling ha ve ta ken place plus th e volumeof adsorbed film on the surface of the pores in whicht h e ca p illa ry con de n sa t io n did n ot t a k e p la c e. Th edetermination of the mesopore volume and microporevolume using the comparat ive method was discusseda bo v e . I n t h e c a s e o f t h e t wo O O I N s a mp le s wh o s e

comp a ra t iv e p lot s a re p res e nt e d in F ig u re 3, t h e s ecalculations provide the volume of ordered pores. Thelat t er ar e often referred to as prima ry pores, to dist in-guish them from disordered, for instance, interparticle,mesopores a nd m a cropores of the size below a bout 200-400 nm tha t a re often referred to as seconda ry (textura l)p ore s. I t s h ou ld be n o t ed t h a t t h e ra n g e f or p ore s inwh ich ca p illa ry con de n sa t io n t a k e s p la c e a t re la t iv ep re s s u re s dis t in g u is h a ble f ro m t h e s a t u ra t io n v a p o r

pressure varies from one a dsorbat e to another a nd it isaddit ionally dependent on temperature. For instance,the upper limit of this range is similar for N 2 a t 77 Kand Ar at 87 K and appears to be about 200-400 nm ,whereas it is only about 20 nm for Ar at 77 K.

For some ads orbents, the pore volume simply cann otbe correctly determined using a given adsorbate becausethe pores are not fully f illed w ith the a dsorbat e at anyrelative pressure discernible from the saturation vaporp re ss u re . F o r i ns t a n ce , t h i s i s t h e ca s e f or w a t e radsorption on hydr ophobic surfa ces of certa in OOINsbeca u s e t h e h y drop h obic s u rf a c e g ro u ps h in der t h eformation of mult ilayer (or clusters) of water. 44,46,48,53

Another exa mple is provided by benzene a dsorption on

OOINs with phenyl groups on the surface. The presenceof the latter apparently prevents the adsorbed moleculesf r om a c ce ss in g a p a r t of ot h er w i s e a v a i la b l e p or ev olu me, p roba bly beca u s e of t h e s t e r ic h in dra n ce .55

Therefore, it is often beneficial to use sma ll molecules,s u c h a s N 2 or Ar , t h a t ca n m or e r e a d i ly p rob e t h ea ccessible pore volume of OOINs.

Determination of Pore Size and Pore SizeDistribution

Pore Diameter. The st ructura l propert ies of OOINswith accessible ordered porosity are expected to fulfillcerta in geometrical relat ions arising from the uniform

orde red n a t u re of t h e p o res . I n t h e c a s e of ma t e ria lswith uniform cylindrical pores, the diameter of orderedpores, w , is related t o their volume, V p, and geometricalsurface area, S , through the following simple equation:w ) 4V p/S ,70 which was employed in some studies ofOOINs.24,42 Although both V p a n d S ar e ava ilable fromgas adsorption da ta , this relat ion for th e pore diameteri s n ot a s u sef ul a s i t s eem s t o b e b eca u s e of t h eu n c e rt a in t y in t h e de t e rmin a t io n o f t h e g e o me t ric a lsurface area using the available methods. Therefore, oneshould search for relat ions tha t involve par am eters tha tcan be determined with sa tisfactory a ccura cy, providinga reliable method for the pore diameter evalua tion forOOINs. A very useful relation involves the pore diam-

eter, pore volume, and (100) interplanar spacing, d 100,for 2-D hexagonal structures similar to that of MCM-41: 88,89

wh e re F is the density of pore wa lls of the ma terial a ndc is a consta nt chara cterist ic of the pore geometry an dequal to 1.213 for cylindrical pores. The (100) interpla-nar spacing can be evaluat ed using XRD or tra nsmissionelectron microscopy. Equation 1 was employed in porediameter calculations for a variety of OMMs, includingMCM -41 silica,69,76,89,93-95 non-silica porous oxides,94 a nd

w ) cd 100( V pF

1 + V pF)

1/2

(1)



9/15

P M O s .31 The results for different samples of the samecomposition69,76 a s we ll a s f o r s a mp le s wit h di f f e re n tcompositions31 are remarkably consistent despite thefact that , in most cases, the pore wall density used inc a lc u la t io n s wa s e s t ima t e d f ro m t h e l i t e ra t u re da t ara t h e r t h a n me a s u re d. U n f o rt u n a t e ly , P M O s a re t h eo n ly g ro u p o f O O I N s f o r wh ic h e q 1 is dire c t ly a p -plicable. In the case of OOINs with silica frameworksand organic ligands on the surfa ce, one can a t tempt t o

introduce th e density of organic groups to th e calcula-t ions, as w as proposed in ref 63 without providing theactua l calculat ion procedure. F or OOINs obta ined viapostsyn thesis surfa ce modification of MC M-41 or sim i-larly structured materials, an equation was derived todetermine the pore size from the ratio of pore volumesbefore and after modification, the pore size of unmodi-fied ma terial, an d the w eight percenta ge of the organicmoieties introduced.45 This simple equation was em-ployed in th e pore dia meter calculat ion for OOINs us edas model adsorbents to determine t he reference t-curveof N2 on t he orga nic-modified silica .

Pore Size Distribution. There are many methodsfor calculation of pore size distributions (PSDs), 64,66,68

and most of them are potentially applicable for OOINs.However, the ordered na ture of OOINs a nd t he tendencyto custom-tailor their structures impose stringent re-q u ir em e nt s on t h e a c cu r a cy a n d r el ia b i li t y of t h emethods for the PSD calculat ion. Unfortunately, manyof t h e a v a i la ble me t h ods do n o t f u lf il l t h e se cr i t er iabecause either they do not allow one to assess the poresize with acceptable accuracy or they produce artifacts,which w ould be potentia lly mislea ding. PS Ds for OOINsare usually evaluated using methods based on eithert h e K e lv in e q u a t ion 96-102 or t h e H or v a t h-K a w a z o emethod 103 a n d i t s modifica t io n s.104 The first groupincludes the methods of Barrett , J oyner, and Halenda(B J H),96 Cra n s t o n a n d I n k le y ( CI ) ,97 Dollimore andHeal (DH),98 a n d B ro e k h o f f a n d de B o e r ( B dB ) . 99-102

Th e B J H m et h od w a s com m on ly u s ed i n O OI N scharacterizat ion.21,22,25,38,44,49,53,57Although the B J H, CI ,and DH methods are often considered as appreciablydifferent , all of th em a re ba sed on the general conceptof an a lgorithm outlined in the B J H work,96 althoughthe latter originally suggested a simplification that wasl a t er e li m in a t e d i n t h e C I a n d D H a p pr oa c he s. Toimpleme n t t h e a lg ori t h ms p rop os ed in t h e s e t h re emethods, the knowledge of a relation between the poresize and capillar y condensa tion or evaporat ion pressureand the t-curve is required, and a choice needs to bema de as to which bran ch of the isotherm is a ppropriatef or P S D ca lcu la t ion s . Th e o rigin a l B J H , CI , a n d D Hworks a re not fully consistent a s fa r a s th e select ion oft h e s e re la t io n s a n d t h e c h o ic e o f t h e bra n c h o f t h eisotherm are concerned. These inconsistencies are ca-pable of affecting the result s of ca lculations much morethan the minor differences in the algorithms, 105 beingmos t l ik ely re sp on s ible f o r cla ims t h a t t h e s e t h re emethods appreciably differ.

Th e B J H , C I , a n d D H m et h od s a s s u me t h e s a m egeneral picture of the adsorption-desorption process.Adsorption in mesopores of a given size is pictured asmultilayer adsorption followed by capillary condensation(f il li n g of t h e p or e cor e, t h a t i s, t h e s pa c e t h a t i sunoccupied by the multilayer film on the pore walls) at

a relat ive pressure determined by the pore diameter.The desorption is pictured a s capillary evapora t ion(emptying of the pore core with retention of the multi-la y e r f i lm) a t a re la t iv e p re s s u re re la t e d t o t h e p o rediameter, followed by thinning of the mult ilayer. I t ha srecently been confirmed using MCM-41 with approxi-mately cylindrical pore geometry (that is assumed int h e B J H , C I , a n d D H a l g or i t hm s ) t h a t t h i s g en er a lp ict u r e r ef le ct s t h e a c t ua l n a t u r e of a d s or pt i on i n

mesopores.69,76

These methods also adopted the conceptof a common t-curve for mesopores of different sizes.This ha s a lso been tested using MCM-41 and found t obe acceptably accurate,35,36,69,76 although some increasein the sta tistical film thickness wa s observed as t he poresize approached the micropore ra nge. The B dB method,which is from the computation point of view an exten-s ion of t h e B J H , C I , a n d D H me t h ods , a t t e mpt e d t oaccount for the differences in the statistical film thick-ness in pores of different size. The aforementionedmodel studies indicate that this type of correction isgenerally beneficial, although certainly not crucial.

B eca use the concept underlying the B J H, CI , and D Halgorithms a ppears to be correct , i t is importa nt to (i)

establish a n a ccura te relation between the pore size a ndcapillary condensation or evapora t ion pressure, ( ii)determine the correct t-curve (or a set of t-curves), and(iii) verify whether adsorption or desorption, or bothbranches of the isotherms, are suitable for the accuratepore size a ssessment. This w ould allow one to performa c cu ra t e P S D ca lc ula t ion s u s in g t h e s e s imple a lg o-rithms. To t his end, t heoretical considerat ions,64 non-loc a l de n s it y f u n ct ion a l t h e ory (N L D F T) c a lc ula -tions,75,106 computer simulations,107 and studies of modeladsorbents69,76 strongly suggested that the Kelvin equa-t ion commonly used to provide a relat ion between t hecapillary condensation or evaporation pressure and thepore size underest imates the pore size. The D FT cal-culations,75,108 computer simulations,107 and novel meth-ods based on the use of OMMs as model adsorbents 69,76

provided consistent results for N 2 at 77 K in cylindricalpores having diameters from about 2.5 to 4.0 nm. Thisra nge is part icularly important from t he point of view of OMM and OOIN chara cterizat ion because it coversthe typical pore sizes of these materials. The relations(determined using OMMs69,76 a n d O O I N s52 a s mo de ladsorbents) between the pore diameter a nd the capillar ycondensa tion pressure for N 2 at 77 K a nd Ar a t 87 K insilica and hydrophobic (ODMS-modified) pores ar eprovided in Table 1.

U n f or t u n a t el y , f or l a r g er p or e s iz es , t h e r es u lt s

derived on the basis of DFT dat a75,108

and those obta inedusing model OMM materials diverged (the data fromcomputer simulations107 did not extend beyond w ) 5nm, so comparison could not be made). This divergenceis likely to be related to the fact that it is diff icult tounequivocally a ssign t he bra nches of hysteresis loopsand the equilibrium tra nsit ion point from D FT calcula-t ions to the experimentally measured adsorption anddesorption bra nches of isotherms. Ind eed, two versionsof the DF T-ba sed procedures to calculat e P SD s provideconsistent results a t r elative pressures wh ere hysteresisis not observed experimentally a nd t hus t he equilibriumtransit ion point can be unequivocally assigned to theposit ion of both these branches. However, in the hys-



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teresis region, this assignment needs to be modifiedbeca u s e a ds o rpt ion a n d de sorp t ion bra n c h es do n otcoincide. In principle, the experimenta l desorptionbranch should correspond to a certain point between theDFT desorption bra nch an d t he equilibrium tr an sit ionp oin t , wh e re a s t h e e xp erimen t a l a ds o rpt ion bra n c hshould correspond to a certain point between the equi-librium tr an sit ion point and the meta sta ble desorptionbranch determined from DFT. Clearly, different legiti-m a t e a s s ig n m en t s ca n b e m a d e con s is t en t w i t h t h eabove identification. Similar problems are encounteredin the case of computer simulations of adsorption. It ist h u s n o t s u rp ris in g t h a t t h e t wo c u rre n t D F T - ba s e d

procedures to calculate P SD s for cylindrica l pores fromN2 dat a a t 77 K provide significa ntly different pore sizeestimates in the hysteresis region. For instance, for thesame MCM-41 sample whose pore size w as est imateda s 5. 5 n m u s in g e q 1, 76 one of the DFT-based proce-dures 75,109 p rov id ed a p or e d ia m e t er of 5. 1 n m , 110

whereas the other one108 suggested 6.0 nm. This indi-c a t e s t h a t t h e a s s ig n me n t o f t h e D F T p re dic t io n s t oe xp erimen t a l h y s t e res is loop s n e eds t o be cla r i f ie dbefore procedures to calculate PSDs using the DFT-based dat a can be regar ded as fully reliable for ma teri-als whose isotherms exhibit pronounced hysteresis.

B e c a u s e t h e re l ia bi l i t y o f a dv a n c e d c o mp u t a t io n a lmethods to calculate PSDs is yet to be improved, it is

suggested to perform P SD calculat ions for OOINs usingthe B J H, C I, or DH algorithms. In doing so, adsorptionra ther t ha n desorption dat a should be employed to avoida r t i fa c t s a n d t o i m pr ov e a c cu r a cy of t h e p or e s iz ede t e rmin a t io n . I t wa s a lre a dy dis c u s s e d h e re in t h a td es or pt i on i s of t en d el a y ed b eca u s e of n et w o r keffects.64,68,72-74 Surprisingly, the delayed desorption caneven be observed for MCM-41, which is one of the mosthighly ordered mesoporous materials currently known.This effect probably arises from nonuniformity in di-am eter a long t he MCM-41 pores, w hich causes a situ-at ion where wider pore parts cannot be emptied untiln a r r o w e r p o r e p a r t s s e p a r a t i n g t h e m f r o m t h e s u r -

rou n din g a re a a re e mpt ied or t h e re la t iv e p res s u reapproaches the lower limit of adsorption-desorptionhysteresis. 111 Spectacular effects of delayed capillaryevaporat ion ar e observed for Type H4 hy steresis loops,where desorption can be observed at much lower pres-sures than those attributa ble to the actual pore sizes.80,81

Therefore, we suggest avoiding use of desorption datain t h e p o re s ize a n a ly s is . I t s h o u ld be n o t e d t h a t t h ecombined a na lysis of both bran ches of adsorption iso-t h e rms ma y p ro v ide v a lu a ble in s ig h t s in t o t h e c o n -nectivity 74 a n d s ize of con s t r ict ion s in t h e p oro usstructure.58,112 How ever, recent st udies of highly orderedMCM-4136,111 suggest tha t our current knowledge of thedesorption behavior in uniform pores is far from being

Table 1. Values of the Capillary Condensation Pressure (p /p 0) and the Corresponding Pore Diameters (w ) in Nanometersfor Nitrogen on the Silica and ODMS-Modified Surfaces at 77 K and Argon on the Silica Surface at 87 K 52,69,76

p /p 0 w silica(N2) w ODMS(N2) w silica (Ar) p /p 0 w silica(N2) w ODMS (N2) w silica(Ar)

0.05 2.08 1.70 1.92 0.43 4.36 4.16 4.080.06 2.15 1.79 1.99 0.44 4.44 4.24 4.160.07 2.22 1.86 2.06 0.45 4.52 4.32 4.230.08 2.28 1.94 2.12 0.46 4.60 4.41 4.310.09 2.34 2.01 2.18 0.47 4.69 4.50 4.390.10 2.40 2.07 2.24 0.48 4.78 4.59 4.470.11 2.46 2.14 2.30 0.49 4.87 4.68 4.55

0.12 2.51 2.20 2.35 0.50 4.96 4.78 4.640.13 2.57 2.26 2.41 0.51 5.06 4.88 4.730.14 2.62 2.32 2.46 0.52 5.16 4.98 4.820.15 2.68 2.38 2.51 0.53 5.27 5.09 4.920.16 2.73 2.43 2.56 0.54 5.38 5.20 5.020.17 2.78 2.49 2.61 0.55 5.49 5.32 5.120.18 2.83 2.55 2.66 0.56 5.61 5.44 5.230.19 2.89 2.61 2.71 0.57 5.73 5.56 5.340.20 2.94 2.66 2.76 0.58 5.86 5.69 5.460.21 2.99 2.72 2.81 0.59 5.99 5.83 5.580.22 3.04 2.78 2.86 0.60 6.13 5.97 5.700.23 3.10 2.83 2.91 0.61 6.28 6.12 5.840.24 3.15 2.89 2.96 0.62 6.43 6.27 5.970.25 3.21 2.95 3.02 0.63 6.59 6.43 6.120.26 3.26 3.01 3.07 0.64 6.75 6.60 6.270.27 3.32 3.07 3.12 0.65 6.93 6.78 6.43

0.28 3.37 3.13 3.17 0.66 7.12 6.97 6.600.29 3.43 3.19 3.23 0.67 7.31 7.17 6.780.30 3.49 3.25 3.28 0.68 7.52 7.38 6.970.31 3.55 3.31 3.33 0.69 7.74 7.60 7.170.32 3.61 3.37 3.39 0.70 7.97 7.83 7.380.33 3.67 3.44 3.45 0.71 8.22 8.08 7.600.34 3.73 3.50 3.51 0.72 8.48 8.35 7.840.35 3.79 3.57 3.56 0.73 8.77 8.64 8.100.36 3.86 3.64 3.62 0.74 9.07 8.94 8.380.37 3.93 3.71 3.69 0.75 9.39 9.27 8.670.38 3.99 3.78 3.75 0.76 9.74 9.62 8.990.39 4.06 3.85 3.81 0.77 10.12 10.01 9.340.40 4.13 3.93 3.88 0.78 10.54 10.42 9.710.41 4.21 4.00 3.94 0.79 10.99 10.88 10.120.42 4.28 4.08 4.01 0.80 11.48 11.37 10.57



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sat isfactory, and t hus it ma y be very difficult to developa r el ia b l e m et h od ol og y f or t h i s k in d of s t r uct u r a lcharacterizat ion.

R e la t io n s be t we e n t h e p o re s ize a n d t h e c a p il la rycondensa tion pressure suita ble for th e BJ H, CI, a nd D Hcalculations ha ve recently been esta blished for N 2 at 77K a nd Ar at 87 K using MCM-41 silica s w ith pore sizesf rom a b ou t 2 t o 6.5 n m .69,76 These relat ions werereported in the form of empirical equations extrapolatedover the entire m esopore ra nge, and the a greement ofon e o f t h e m wit h t h e e x pe rime n t a l da t a (de t ermin edusing eq 1) for more than 60 MCM-41 samples is shownin Figure 4a. I t would be desirable to test the validity

of the extra polat ion beyond t he pore size range a t ta in-able for good-qua lity MCM-41, but this is currentlydifficult because of the problems in finding model extra-lar ge-pore ma teria ls (SB A-15 silica 113 tha t wa s the mostp rom i si n g o f t h e m h a s b ee n s h ow n t o h a v e s m a l lcon n e ct in g p ore s in t h e p ore wa l ls of la rg e u n iformpores).61 F in a l ly, t h e a p plica t io n o f t h e B J H , CI , a n dD H a p p roa c h es re q u ire s t h e a v a i la bi l it y of p rop ert-curves. The t-curves for N 2 a t 77 K a n d Ar a t 87 Ka dsorption on silica 69,87 a nd t he t-curve for N 2 adsorptionat 77 K on the surface of ODMS-modified silica werereported.52 All of these t-curves ar e highly useful in thecharacterizat ion of OOINs.13,31,45,50-52,59-62 A s c a n beseen in Figure 4b, PS D calculat ions provided remark-

ably consistent results for N2 a t 77 K a n d A r a t 87 Kwhen the B J H-based a lgorithm with proper r elat ionsbetween the pore size and capillary condensation pres-sure a nd suitable t-curves were used, a nd calculat ionswere based on adsorption rather than desorption data.62

However, there is a need to derive t-curves for someother types of OOIN surfaces. To this end, a suitableprocedure was outlined in ref 52 and should be helpfulin th is endeavor.

Some comments need to be ma de about the BdB an dHK methods that have recently become increasinglyp op u la r . Th e B dB me t h od 99-102 con s t i t u t es a ma j orimprov eme n t o v er t h e B J H , CI , a n d D H me t h ods intheir original form.96-98 However, one can read ily verifytha t t he predict ions of the BdB method 100,102 a re incon-sistent with the data on OMMs (Table 1). Because ofits rather complicated nature, i t is not clear how theB dB me t h od ca n ben e fi t f ro m t h e ca l ibra t ion u s ingO M Ms . I n con t ra s t , t h e B J H , C I , a n d D H a p p roa c h esallow for easy introduction of appropriate corrections.Consequently, the applicat ion of proper t-curves andrelations between the pore size and capillary condensa-t io n p re s s u re in t h e s e t h re e me t h o ds is e x p e c t e d t o

provide much more reliable results tha n t he a pplica tionof the BdB method.

Although common for OOINs, 2,12,46-48 the use of theHK m ethod 103 or its va rious modifications104 is stronglydiscouraged. In some cases, these approaches are ca-pable of correctly reproducing t he m esopore size, 93 bu tthis is a result of the choice of para meters ra ther tha ntheir sound theoretical basis. The HK method does notcapture the actual nature of adsorption in mesopores(multilayer adsorption followed by capillary condensa-tion), but tacitly assumes that the initially empty poresbecome completely filled at relative pressures that arerelated t o their size.114 This a ssumpt ion is also incorrecti n t h e m i cr op or e r a n g e f o r w h i ch t h e m et h od w a soriginally developed.115 Th u s , t h e H K me t h od a n d i t smodificat ions a re notorious in producing a rtifa cts,114-116

such as prominent peaks in the micropore range foressentially mesoporous materials.114,115 The ar t if icialna ture of these peaks w as r ecognized by some materia lsscientists,12 but their a ppear a nce ma y be misleading foro t h e rs . T h u s , t h e u s e o f t h e H K me t h o d is s t ro n g lydiscouraged, unless one is able to separate the actualinformation from the many art ifacts.

I n t h is s e c t io n , t h e me t h o do lo g y f o r a c c u ra t e P SDcalculations for OOINs with cylindrical pore geometry,wh ic h is mo s t c o mmo n f o r t h e s e ma t e ria ls , wa s dis -cussed. For other OOIN pore geometries, one can use

the methods for cylindrical pores, although the pore sizeassessment would be less accurate and some art ifactsma y a ppear on P SDs. Alterna tively, methods to calcu-l a t e P S D s f or ot h e r p or e g eom e t ri es , s u ch a s s li t -like,117-119 or spherical,120 can be employed, but someo f t h e s e me t h o ds we re de v e lo p e d f o r ma t e ria ls wit hsurfaces of propert ies largely different from those ofOOINs (for instance, carbon surfaces),117,119 a n d n o n eof t h e m w a s t e s t ed u s in g mode l a ds o rbe n t s . So t h e irreliability for OOIN s is un certa in. The discussion a boutP SD c a lc u la t io n s wa s re s t r ic t e d t o N2 a n d A r a ds o r-bat es. Some other a dsorbates ma y also be useful in PS Dcalculat ions, but their a dsorption behavior is less w ellunderstood. However, in the case of adsorbates such as

Figure 4. (a) The experimental relations between the MCM-41 pore diameter and capil lary condensation (experimentaladsorption) relative pressure as well as capillary evaporation(experimental desorption) relative pressure. The dashed lineshows predictions of the Kelvin equation with the statisticalfi lm thickness correction, whereas the solid l ine shows therelation between the pore size and t he capil lar y condensa tionpressure (the Kelvin equat ion with t-curve correction a ndadditional correction) proposed in ref 76. Data partially takenfrom refs 36 a nd 76. (b) Pore size distributions for MCM-41and ODMS-modified MCM-41 calculated from N 2 d a t a a t 7 7K an d Ar dat a a t 87 K using the BJ H method calibra ted usingMCM-41 and OOINs.52,62,69,76 Dat a t ake n fr om r e f 62.



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wa t e r o r be n ze n e t h a t a re c a p a ble o f in t e ra c t in g in amore specific way with the OOINs surface, the feasibil-ity of PSD determination is questionable because sur-face propert ies rather than PSD may have a predomi-nant effect on adsorption behavior, as seen from recentstudies. 44,46,48,53

Characterization of Surface Properties

T h e a bi l i t y o f a ds o rba t e s t o dis c r imin a t e be t we e nin o rg a n ic a n d o rg a n ic s u rf a c e s h a s lo n g be e n re c o g -nized.18,121-128 E a rly wo rk wa s do n e la rg e ly o n s i l ic asurfaces modified by esterification 18,122,128 or chemicalbonding of orga nosilanes.18,121,123-127 These surface modi-ficat ions often led to dram at ic cha nges in the a dsorptionbehavior, which manifested itself in a significant de-cre a s e in t h e a mo u n t a ds o rbe d ( s ome t imes by mo ret h a n 1 or d er of m a g n it u d e)18,121,123 a n d a ds o rpt ionenergy,121-123 and in the transition from Type II to TypeIII adsorption behavior.124,126 Adsorption of polar mol-ecu les , s u ch a s w a t e r ,123-127 me t h a n o l ,123 t r ie t h y -lamine,127 and some rather large nonpolar molecules,such as benzene,121,123 hexane, 123 an d carbon tetra chlo-

ride,123

wa s p a rt icu la r ly a f f e ct e d by in t rodu ct ion ofhydrophobic organic groups on the silica surface. Thesefindings constitute a good basis for a qua litat ive assess-ment of the surface properties of organic-modified silicasurfaces. Moreover, in some cases, a more quantitativecharacterizat ion could be made, including the assess-ment of the sur fa ce concentra tion of sila nol groups usingtriethylamine adsorption.127 Water adsorption has al-ready been employed in OOIN studies.38,44,46,48,49,53,55

U nmodified silica OMMs exhibited Types IV38,44,49,53 orV46,48 adsorption isotherms that changed to Type V38,49

(from Type IV) or III 44,46,48,53 after chemical bonding oforganosilanes or esterification. This was accompaniedby a decrease in th e wa ter upta ke. These cha nges were

clearly correlated with the size46,48

a n d s t ru c t u re48

ofthe orga nic groups intr oduced. Surfa ces of OOINs ha vea ls o bee n s t u die d u s in g a ds o rpt ion of ben zen e ,44,53

n -hexane, acetone, and methanol.53 Adsorpt ion of n -hexane was enhanced after surface modificat ion withorganic groups, whereas adsorption of benzene, acetone,a n d me t h a n o l wa s re duce d. P h e n y l-modified s i licaexhibited markedly different adsorption of n -butanola n d tert -butyl alcohol, as adsorption of more bulkyalcohol took place at lower relat ive pressures a nd w ithhigher f inal uptake.55

Nitrogen a dsorption wa s reported t o be influenced bythe presence of surface orga nic groups to a m uch sma llere xt e nt t h a n a d s or pt i on of p ol a r or l a r g e n on pol a r

molecules (see ref 18, p 699 for an account of Kiselev’swork). However, nitrogen a dsorption w a s found to ha vesome importa nt a dva nta ges, including the possibility ofq u a l i t a t iv e e s t ima t io n o f t h e s t re n g t h o f a ds o rbe n t-adsorbate interact ions 84,85,122,126,128 or even calculationof the ent ha lpy of ad sorption122 on the basis of the BE TC -constant.64,66,68 This approach was employed in theOOIN st udies. 42,56,57 Moreover, a method to evaluatet h e o rg a n ic ma t t e r c ov era g e on min era l s u rf a ce s w a sp ro p o s e d o n t h e ba s is o f t h e e n t h a lp y o f a ds o rp t io ne v a lu a t e d f ro m t h e B E T C -constant.129 Although thevalue of C i s u s e f ul in a comp a ris on of t h e s u rfa c epropert ies, the calculat ion of the adsorption enthalpyfrom it is not r ecommended beca use of the approximat e

nature of the BET model (ref 68, p 102). Moreover,surfaces of appreciably different adsorption propertieswith respect to N 2 (such a s those of MCM-41 modifiedwith trimethylsilyl, butyldimethylsilyl, and polymericoctylsilyl)45 ma y provide very similar B ET C -constants,thus suggesting similarity for significant ly different

surfaces.Despite t hese ambiguit ies, the informa tion from the

BE T an alysis, such as the specific surface area 90,121,126

or the monolayer capacity,130 is useful in the analysisof surface properties of mat erials. Na mely, it a llows onet o re c a lc u la t e t h e a ds o rp t io n is o t h e rms s o t h a t t h e yexpress the adsorption per unit ar ea or t he number ofsta t ist ical layers on the surfa ce (which w ill be referredt o a s r el a t i ve a d s or pt i on ), w h i ch op en s m a n y n ew op port u n it ies in a ds o rpt ion da t a in t erp ret a t ion . I npart icular, relative a dsorption curves for sa mples modi-fied with the same type of chemically bonded organicligand, but wit h different surfa ce coverage, a re expectedto grad ually decrease in the low-pressure ra nge as the

surface coverage increases.59

This behavior is illustratedin Figure 5a for ODMS-modified silicas. This findingsuggests the possibility of development of a simplemethodology to calculate the surface coverage of bondedgroups from low-pressure nitrogen ad sorption da ta .59 Asimilar decrease in low-pressure adsorption was ob-s er v ed w i t h t h e i n cr ea s e i n t h e l oa d i n g of or g a n icmolecules coat ed or chemically bonded on t he silicas u rf a ce , a l t hou g h i n t h e ca s e of a s im i la r s u rf a cecoverage, the chemical bonding had a larger effect onlow-pressure a dsorption, presuma bly because of a moreuniform coverage and removal of strongly interact ingsites during the chemical modification. 130 On the basisof the low-pressure a dsorption da ta , i t wa s possible to

Figure 5. (a) Relative adsorption curves for silicas modifiedwith different coverages of ODMS ligands. (b) Adsorptionenergy distributions for ethane silica PMO (HMM-1), 31 ODMS-modified MCM-41,45 and siliceous MCM-41.31 Data taken fromrefs 31, 59, and 45.



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evaluat e the fra ction of the surfa ce coated by t he organicmodifier by employing bare silica surface as well as achemically bonded a nd subsequently coat ed surface a sreferences. This, in combination with elemental analysisda t a , a l lowe d u s t o demon s t ra t e t h a t t h e c oa t e d la y e ro n t h e M CM - 41 s u rf a c e wa s h ig h ly n o n u n if o rm, 50,51

w h e r ea s a s a t i sf a ct or y u n if or m it y of cov er a g e w a sobs erv ed f or con v en t ion a l s i lica s wit h s ign ifica n t lylarger pores.130 Nitrogen a nd a rgon relat ive adsorption

curves for different bonded groups of the same surfacecoverage w ere found to be appreciably different , w henthe groups were dissimilar 45,62 a nd close to one a notherwhen the groups were similar.131 The use of a compara-t ive method to analyze low-pressure adsorption dataa ls o a l lows on e t o s t u dy s u rfa c e p rop ert ies90,91 a n dorganic groups on the silica surface in particular.51,52,62

The theoretical foundations of this analysis were re-cently outlined t o fa cilitate the prospective applica-tions.91 When silica is used as a reference adsorbent ,the presence of organic groups on the surface of meso-p orou s s i lica re su lt s in down w a rd de via t ion s f romlinear ity on the compara t ive plot . The extent of thesedeviat ions is dependent on the type of organic surface

groups 51 and on their surface coverage. On the otherha nd, w hen a reference adsorption isotherm for st ronglyhydrophobic surfaces is used to an alyze a dsorption da tafor somewhat more polar surfaces, upward deviat ionsof the comparative plot are observed.52

A very useful methodology to ana lyze low-pressureN2 and Ar dat a is ba sed on the calculation of ad sorptionenergy d istribut ions (AED s).66,132,133 AED s w ere foundto provide information about the presence of differents u rfa c e g rou p s, s u ch a s s i la n o ls, a l iph a t ic g rou p s,aromatic rings, and so forth, on the surface of modifiedsilica.45,51 Obviously, t he informat ion is obta ined onlyabout groups that are accessible to the adsorbate, andfor instan ce silan ol groups covered by a dense chemi-cally bonded 45 or coated layer 130 will not be detected.In combinat ion with elementa l ana lysis dat a, AED s mayconstitute t he basis for eva luation of uniformity of thedis t r ibu t io n o f bo n de d o rg a n ic l ig a n ds o n t h e O O I Nsurface.60 This was demonstrated in the case of trim-ethylsilyl liga nds bonded on the MC M-41 surfa ce usingtwo different modification procedures, one on the cal-cined sa mple and the other one on the as-synthesizedsam ple. The AED s for the m odified ma teria ls suggestedt h a t t h e d is t r ib ut i on of b on d ed l ig a n d s w a s m or euniform in the second case, as expected from the facttha t organosilane is l ikely to displace electrostat icallybonded surfactant ions that are likely to be uniformly

distributed on the silicate surfa ce. Illustra tive AED s a reshown in Figure 5b. It can be seen that siliceous MCM-41 has very similar adsorption propert ies to ethane-s i lica P M O 31 a n d v ery di ff ere n t on e s f rom O D M S-modified MCM-41.45 This can be at tributed to the factt h a t e t h a n e-silica differs from silica only by substitu-t ion of some of t he siloxane bridges by ethan e groups,bo t h o f wh ic h a re e x p e c t e d t o in t e ra c t we a k ly wit hnitrogen, result ing in similar nitrogen adsorption pro-perties.31 In contra st, the surfa ce of a n ODMS -modifiedsa mple ha s its sur face effectively covered by octy l chainst h a t in t e ra c t wi t h n i t ro g e n v e ry we a k ly . 45 Consistentinformation can be extracted from AEDs calculated onthe basis of both N 2 and Ar dat a, showing th e sensitivity

of the lat ter gas to the surface propert ies of OOINs. 62

I t s h ou ld b e n ot e d t h a t t h e e xa c t s h a pe o f AE D i ssomewhat model-dependent because of the many as-sumptions involved in the AED calculations.89,132 There-fore, in the case of comparative studies, it is importantto calculate AEDs consistently using the same set ofpara meters, the sa me model of adsorption behavior, andthe same computat ion

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