Drying 2004– Proceedings of the 14th International Dr ying Symposium (IDS 2004) São Paulo, Brazil, 22-25 August 2004, vol. A, pp. 69-88 69 DRYING OF NANOPOROUS AND NANOSTRUCTURED MATERIALS Zdzislaw Pakowski Faculty of Process and Environmental Engineering, Lodz Technical University, Lodz, Poland [email protected]Keywords : drying stress , self-assembly, aerogels , gels ABSTRACT Drying is considered a macro scale process and understanding of drying on the molecular scale remains still far from satisfactory. The last decade marks a spectacular development of nanotechnology. Together with the advent of this new discipline a necessity of drying of nanomaterials emerged. This paper presents the new materials and the role that drying plays in their processing. It is shown that drying on a molecular level is a complex problem that not always can be explained by classical theories. The drying stress in nanomaterials and ways to reduce it are d iscussed. Self-assembly processes induced by drying in nanosuspensions are reported, which may be used for control of structure of nanomaterials. The diffusion in nanoporous solids is also presented. A role of a supercritical drying and other drying technologies in the production of nanoporous materials is explained. Finally some challenges facing drying in this area are identified and conclusions about the possibilities of future developments in this area are drawn. INTRODUCTION Drying has always been a unit operation and as such it fitted well into the, so called, first paradigm of chemical engineering, placing unit operations in focus (early 20-ties of 20 th century). Then the times of the second paradigm came (the 50-ties), where momentum, heat and mass transfer and reaction engineering became the core of chemical engineering – again drying was there as a process of simultaneous heat and mass transfer. However, the end of 20 th century marks a gradual tra nsition “beyond the molecular frontier” in chemical engineering (NAS, 2003). We are now in the years of the third paradigm (Ying 2001, Charpentier 2002). The role of the present and future chemical engineering is now foreseen not only in processing and separating the products in macroscopic scale but also in active creation of products of specified or designed molecular structure.
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Drying 2004 – Proceedings of the 14th International Drying Symposium (IDS 2004)São Paulo, Brazil, 22-25 August 2004, vol. A, pp. 69-88
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DRYING OF NANOPOROUS AND NANOSTRUCTURED MATERIALS
Zdzislaw Pakowski
Faculty of Process and Environmental Engineering,Lodz Technical University, Lodz, Poland
Drying is considered a macro scale process and understanding of drying on themolecular scale remains still far from satisfactory. The last decade marks a spectaculardevelopment of nanotechnology. Together with the advent of this new discipline anecessity of drying of nanomaterials emerged. This paper presents the new materialsand the role that drying plays in their processing. It is shown that drying on a molecularlevel is a complex problem that not always can be explained by classical theories. Thedrying stress in nanomaterials and ways to reduce it are discussed. Self-assembly
processes induced by drying in nanosuspensions are reported, which may be used forcontrol of structure of nanomaterials. The diffusion in nanoporous solids is alsopresented. A role of a supercritical drying and other drying technologies in theproduction of nanoporous materials is explained. Finally some challenges facing dryingin this area are identified and conclusions about the possibilities of future developmentsin this area are drawn.
INTRODUCTION
Drying has always been a unit operation and as such it fitted well into the, so called, first paradigmof chemical engineering, placing unit operations in focus (early 20-ties of 20 th century). Then the times of
the second paradigm came (the 50-ties), where momentum, heat and mass transfer and reactionengineering became the core of chemical engineering – again drying was there as a process ofsimultaneous heat and mass transfer. However, the end of 20 th century marks a gradual transition “beyondthe molecular frontier” in chemical engineering (NAS, 2003). We are now in the years of the thirdparadigm (Ying 2001, Charpentier 2002). The role of the present and future chemical engineering is nowforeseen not only in processing and separating the products in macroscopic scale but also in activecreation of products of specified or designed molecular structure.
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This paper attempts to identify the challenges that are facing the drying operation in this area. If thereader feels that the paper is not coherent enough please note that the subject is still emerging, 42 % ofliterature quoted here is not older than 1-3 years. For the same reason the paper has no ambition to besystematic – the selection of references can be biased and possibly not all important papers have beenpresented here.
WHY NANOMATERIALS ?
Nano is the prefix that equals 10 -9. One nanometer is equal to 10 ( ngströms). Water moleculesize is approximately 3.5 i.e. 0.35 nm. Talking about nanomaterials we have in mind structures that arecomparable in size to molecules. How small it means we can try to imagine quoting the old adage“there’s more water molecules in a glass of water than glasses of water in all Earth’s oceans” (a quickcalculation indicates that about 1000 times more!).What is a nanomaterial ? The word applies if in a system composed of two phases: continuous anddispersed, the pieces of dispersed phase are of order of 1 –100 nm. Nanoporous are the materials wherethe dispersed phase is gas or vacuum and the continuous phase is solid, otherwise we can havenanopowders, nanoalloys (Nazarov, Mulyukov, 2003), nano-filled plastics (Chen Chi et al., 2003),nanodispersions and possibly nanoemulsions.It has been observed that nanomaterials exhibit superior physical, mechanical, thermal and opticalproperties than their counterparts of micrometeric scale of dispersion. Since the dispersion scale is closeto atomic level nanomaterials are like continuous phase, e.g. nanoporous solids do not resemble typicalporous solids at all as the pores cannot be seen by a naked eye. For instance monolithic nanoporoussilicas (aerogels) look like glass with only light bluish tinge, however, since their surface is notcontinuous they do not reflect light.It is expected that nanomaterials can open up totally new possibilities for technology. Besidesan immediate application in nanotechnology (nanomachines) and electronics, superselective catalysis,controlled drug delivery etc. nanomaterials can generate construction materials of unusual strength thatcan make today’s fantasies future’s reality like, for instance, a lift going from the Earth to orbit,suspended on a rope made of carbon nanofibres.
The estimated total world market only for nanopowders (Rittner, 2002) was $ 492.5 million in the year2000 and it is estimated to reach $900.1 in the year 2005. This is a clear indication of the rapid growth ofthis sector.
NANOPOROUS AND NANOSTRUCTURED MATERIALS
It is worth noticing that the word nanopores is a neologism that exists in parallel to the poreclassification of IUPAC (IUPAC, 1972) shown in Table 1. Speaking of nanopores, we typically assumethat they are 1-100 nm in size, however even finer pores like in zeolites (0.3-1.3 nm), microporous silica(<1 nm) etc. are also included.
Table 1. Pore terminology according to IUPAC
Terminology Pore diameter dMicropores d < 20 or d < 2 nmMesopores 20 < d < 500 or 2 nm< d < 50 nmMacropores 500 <d or 50 nm <d
Nanoporous materials were always around us created by nature: gels, natural zeolites, cell tissues etc.Novel nanoporous materials have been obtained by man some 70 years ago by supercritical drying
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(Kistler, 1931). The term nanostructured materials applies rather to materials created by molecularengineering however it has been also used to all materials, which have at least one dimension in 1-100 nmrange. Strictly speaking we will use the word nanostructured materials to ordered nanostructuredmaterials (ONM) that were synthesized as recently as 1992 (Kresge et al. , 1992).The 7 th International Conference on Nanostructured Materials (Wiesbaden, June 2004) distinguished thefollowing groups (apparently omitting nanoporous materials as the ones having their own specializedsymposium ISA – International Symposium on Aerogels):
• Nanoparticles• Nanotubes and nanowires• Nanodispersions• Nanostructured surfaces and films• Nanocrystalline materials
Below we will briefly describe the materials belonging to each group.
Nanoporous solids
A typical nanoporous solid is a gel formed by a sol-gel process (Brinker, Scherer, 1990). We will describehere a chemical gel obtained by hydrolysis and condensation of silica precursors, usually TEOS(tetraethyl orthosiloxane). By performing a two-step chemical reaction:
hydrolysis Si(OEt) 4 + 4 H 2O → SiOH 4 + 4 EtOH
condensation n Si(OH) 4 → (SiO2)n + n H 2O
clusters of condensed silica are formed. They are amorphous aggregates several nanometers in size andare suspended in solvent (ethanol and water mixture) forming a sol. The sol undergoes gelation whenclusters that move around by Brownian movements react and join each other forming one solid porousstructure with pores filled with solvent. The structure is shown schematically in Fig. 1.
Figure. 1 Schematic of gel structure
It resembles a 3D network where clusters form strands and they in turn form pores typically 2-50 nm insize. The structure exhibits some degree of organization and it’s mass fractal dimension is dependent onthe mechanism of gelation. In silica gels produced by the chemistry explained above the diffusion limitedcluster-cluster aggregation (DLCCA) mechanism dominates (Brinker, Scherer, 1990, Abo Zebida, 2001).This gives mass fractal dimension of ca. 1.5. Resulting gels can be molded into a desired shape.Depending on the drying procedure they are converted either to xerogels (obtained by convective drying,)
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which shrink by action of capillary forces) or aerogels (obtained by supercritical drying), whose porestructure remains intact after drying.Using metal alcoxides as precursors allows one to synthesize aerogels containing metal oxides like Al 2O3,V2O5, F2O3 etc. By using mixtures of alcoxides composite gels, containing clusters of different metaloxides, can be obtained. It is even possible to place two or more different metals into one precursor(Mehrotra, 1992). This opens endless possibilities in catalysis, especially since aerogels have immensesurface area reaching 1400 m 2 /g. Besides aerogels are extralight with densities in the range 3 – 200 kg/m 3.
Entirely organic gels have been also produced and turned into aerogels (Pekala et al., 1992). Usuallypolycondensates of resorcinol or melamine with formaldehyde are used. Recently a team of LawrenceLivermore Natl. Lab. has been working on resorcinol based dendritic precursors (Fox et al., 2002) thatwould give aerogel a more organized, predetermined structure of much higher strength, that would, inturn, make supercritical drying unnecessary (see next paragraph).It is worth noting that nanoporous solids made of pure carbon can also be obtained. One possibility isreduction of organic aerogels with hydrogen at high temperature. The other is by using silica aerogel ormolecular sieve as template. In a recent paper (Ryoo et al., 1999) the sucrose and H 2SO4 solution in waterwas used to impregnate a silica molecular sieve. The material was dried and heated under vacuum toabout 1000 °C and the sucrose carbonized. Silica was then removed by washing in NaOH solution. Theunique electrical properties of carbon aerogels or ONMs open many possibilities of their application(catalysts like MCM-41, sensors, supercapacitors, fuel cells etc).
Nanoparticles
Nanoparticles are one of the earliest produced nanomaterials and numerous methods of their synthesisexist. From our point of view we can classify them as:
(a) methods that do not involve drying at any stage – these include inert gas condensation(vaporization of solid into inert gas at very low pressure and subsequent condensation) and flamesynthesis,
(b) methods that use drying in the synthesis – the aerosol method: water solutions of specifiedcomponents are first atomized into a carrier gas stream to form micrometric droplets, the dropletsare then evaporated leaving behind nanometric particles, particles can by further calcined oroxidized at higher temperature in the same gas carrier, finally the particles can be fractionated inelectrostatic fractionating columns – the method is used for production purposes but is alsoapplied for generation of calibrated nanoparticles used for testing of filtration materials (Pakowskiet al., 2001b).
(c) methods that use drying for post processing – the sol-gel method described earlier, the reversemicelle method, the solvated metal atom dispersion (SMAD) and others – drying is used there toseparate the product usually in the form of sediment from solvent in which they were synthesized.
Nanoparticles can be used to produce monolithic solids (by press sintering), as fillers in polymers, innanosuspensions etc. Care should be exercised when working with nanoparticles (Pakowski, AboZebida,1999). Airborne nanoparticles can easily enter the respiratory tract and are so small that they canpenetrate lung vacuoles causing adverse effects in humans even if their material is not toxic.
Nanotubes and nanowires
The first synthesized nanotubes were multiwall carbon nanotubes similar to fullerenes. They weresynthesized in 1991 by chemical vapor deposition in high temperatures under vacuum. Since then singlewall carbon nanotubes were obtained together with nanotubes of many other materials including metals,metal oxides and other inorganic materials. Their applications are endless however they are still too short(up to only 1 µm) to be used as construction materials, despite of their incredible strength. Drying haslittle to do with nanotubes, with an exception of post processing of nanotubes as coatings in the form of
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suspensions. Lately carbon nanotubes were synthesized hydrothermally (Gogotsi et al., 2001). It isinteresting to know that among carbon nanotubes synthesized by this process at pressures of 100 MPa andtemperatures 700-800 °C, there are some that are closed at both ends and retain liquid water inside atpressures up to 30 MPa even after heating in vacuum. Drying such a nanomaterial would be virtuallyimpossible.
Nanodispersions
They are systems in which the dispersed phase is composed of nanoparticles evenly distributed in acontinuous liquid phase. Nanoparticles are usually stabilized against self agglomeration by surfactants.They can form a base of many novel fluids including micellar solutions, ferrofluids, dispersednanocrystals (such as quantum dots or nanotubes). An example of nanodispersion is a dispersion ofliposomes which are colloidal nanocapsules with lipidic mono or bi-layer. Their direct application iscontrolled drug delivery. Other applications span from drug delivery to oil recovery. Some recentapplications of nanodispersions include cosmetics (paraffin nanoparticles in water) and materials forrestoration of frescoes (calcium hydroxide nanoparticles in water).
Nanostructured surfaces and films
Nanofilms can be easily produced be the Langmuir-Blodgett technique, where the material of interest isfirst dissolved in a volatile organic solvent, then spread on a surface of water forming a monomolecularlayer, which can be subsequently transferred onto a solid surface by immersion and after drying, form afilm. Repeated immersions can produce films of multimolecular thickness.Recently multilayer nanofilms have been produced by self-assembly technique (Borato et al., 1997). Thistechnique allows building in protein molecules into films of conducting polymers. The idea is based onspontaneous adsorption of polymeric materials by electrostatic interactions. The methodology allowedbuilding nanofilms on quartz substrate by repeated dipping in polycation and polyanion solutionsseparated by washing and drying. A multilayer film of lysozome and polystyrene sulfonate was made inthis way. It is interesting to know that drying stage directly affects the amount and quality of adsorbedmaterial. Dehydration of proteins results in significant, measurable conformational changes which areonly partly reversible (Prestrelsky et al., 1993). Rapid drying leaves lysozome layer “shrunk” anddiscontinuities in the film may develop leaving space for other molecules to absorb. This opens uppossibilities of controlling the film structure.
Figure. 2 a) Partly ordered structure of polystyrene nanoparticle film obtained by one-stage drying (Evers et al., 2002) b)perfect monolayer obtained by two-stage drying (Palberg and Schöpe, 2002)
Drying of water suspensions of spherical colloidal polymeric particles (diameter 67 to 104 nm) on silicasubstrates was reported to influence the structure of films (Evers et al., 2002) leaving partly ordered dry
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residue. The degree of order in such films was attributed to charge carried by colloidal particles. Thehigher the charge the more defective structure was observed. Similar behavior of films of suspensions ofspherical particles was earlier simulated by a simple two-dimensional computer model (Skjeltorp,Meakin, 1988) explaining fractal type of structures of defects formed by evaporation of solvent from thinfilms. However, by applying a two stage drying technique where first the particles self-assemble on alayer of perfluorinated oil and then after oil evaporation they are fixed on an oppositely charged substrate,it was possible to obtain perfect colloidal monolayers – see Fig.2b.
Nanocrystalline materials
Nanocrystalline materials are either produced as bulk materials or single nanocrystals. The bulk materialsare e.g. alloys with crystals in the nanometric range. Drying has no influence on their properties.A good example of single nanocrystals are quantum dots made of semiconducting materials and capableof storing one electron charge. Usually obtained by ion sputtering they are hydrophobic by nature andtheir surface must be derivatized (covered with functional groups that are hydrophilic) in order to bewetted with water. In this form they can be used as markers in biology although they are typically used inmicroelectronic devices. Their compatibility with biological and electronic environments makes themgood candidates for interfacing the two worlds (Winter et al., 2001). Quantum dots in aqueousenvironment are nanosuspensions and may cause similar dryings problems as the ones discussed earlier.
DRYING STRESS AND DEFORMATION
As we all know the surface tension of liquid is the principal culprit responsible for the drying stress.Surface tension is a manifestation of self-attraction of liquid molecules. Even in nanometric pores watermolecules are small enough to form continuous menisci like the one in a multiwall carbon nanotubeshown in Fig. 3, although the tube is approximately only 150 water molecules across.
Figure. 3 Aqueous liquid in a multiwall carbon nanotubes (Gogotsi et al., 2001- by permission)
If we consider that the tube walls are perfectly wetted at the surface tension of water equal to 0.073 N/mthe pressure of the liquid phase with respect to gas phase would be close to -60 bar by virtue of Kelvin’slaw of capillary pressure.
)cos(d
4pp lg θ
σ=− (1)
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where σ is surface tension, d pore diameter and θ the angle of wetting.For liquid saturated porous solid exposed to gas, when menisci begin to form, this underpressure isresponsible for the drying stress in the solid. The strain or deformation caused by this stress will in turndepend on the solid strength and size. The equilibrium size and moisture content relationship is known asthe shrinkage curve. The knowledge of the curve allows the evolution of drying stresses and strainsduring drying be computed from a suitable mathematical model (Kowalski, 2003).
An immediate result of the action of capillary pressure is that it causes compression of the solid at thesurface where the menisci form while the interior of the body remains uncompressed. This differentialstrain causes cracking. In nanoporous solid such pressure gradients cannot be quickly relaxed by liquidflow because of their small permeability.
In his excellent series of papers on drying of gels summed up in a book (Brinker, Scherer, 1990) G.W.Scherer analyzed the mechanics of deformation of gels during drying. Let us present some of hisconsiderations on drying of one side of a saturated infinite gel plate of thickness L. He calculated thedistribution of pressure along the plate thickness as:
−ααα
+>=< 1)sinh()L / zcosh(
LVH
PPEG
(2)
where P is pressure in the pores, <P> is average tension in liquid, H G is viscosity of the gel network, V E isvolumetric evaporation (drying) rate, z is local distance and L is total thickness of the gel
andG
L2
DHL η
=α (3)
where η L is viscosity of the liquid and D is Darcy permeability of the gel.
The difference P-<P> is the value of stress at the surface, where it is the greatest. If this stress is largerthen the strength of material cracking will occur. Very often for gels α 1 and the maximum stress will be
D3V
L ELx
η=σ
(4)
From the above equation it can be seen that larger stress will develop for thicker gels, higher evaporationrates and smaller permeability. The capillary pressure is not directly visible in Eq.4 but if α is small themaximum stress it is proportional to capillary pressure and this in turn depend on pore size by virtue ofEquation (1).Taking into account that stress is related to solid size the drying stress curve corresponding to a solid of
smaller size will be located higher than the actual one – c.f. Fig. 4. It is obvious that solids whose strengthis situated below the drying stress line will be destroyed during drying.There are practically four ways to bypass the drying stress line:
Enlarge the pores – it was found that certain chemicals called DCCA (drying control chemicaladditives) actually enlarge the pores of gels and result in smaller shrinkage in convective drying.An additional effect is that DCCA, by selective evaporation, form a film on the menisci thusreducing the contact angle and also block the smallest pores where capillary forces are the largest.Unfortunately DCCA are low volatility components (formamide, dimethylformamide) which are
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retained in the pore structure during selective evaporation (Pakowski, Bartczak, 1997) from whereit is difficult to remove them.
Figure. 4 Schematic of methods of elimination cracking in drying gels: A – by increasing strength, B – by increasing pore size,C – by reducing size or drying rate
Reduce the size of the solid – drying of monolithic blocks of solids is much more destructive thandrying of small granules or films. In numerous papers on nanopowder production by wet route theproblem of drying was not even mentioned owing to minuscule size of the product.
Strengthen the structure – this is a promised land of nanoporous solids drying. So far nanoporoussolids produced by sol-gel technology were extremely fragile so that convective drying lead tosubstantially shrunk solids named xerogels. Freeze drying, on the other hand, causeddisintegration of structure by ice crystals of much larger size than the pores and resulted in solidsin the form of powders.Please note that due to rapidly increasing value of the drying stress at small pore diameters thestrength must be increased by several times. How can we possibly do this ?Maturing of gels reinforces its structure. It was observed that gels stored after gelling in solventrich in precursor slowly repaired all possible skeleton defects by building in new molecules(Einarsrud, 1995). This increased their shear modulus and modulus of rupture thus resulting instronger gels. As reported, such gels could be dried by convective drying and their shrinkage ismuch less noticeable than in xerogels.Dendrimeric aerogels (Fox et al., 2002) are examples of aerogels that can be processed byconvective drying without significant shrinkage. No data on their mechanical properties in the wetform for comparison with traditional silica aerogels were reported yet.
Reducing or eliminating surface tension – this is a last resort in all cases when little or nodeformation is allowed. Adding surfactants to solvents or replacing the actual solvent with asolvent of much lower surface tension would reduce the drying stress, however, total eliminationof surface tension is only possible in supercritical drying (see the paragraphs below). Taking intoaccount that supercritical drying requires expensive high pressure autoclaves and additionalsolvents a possibility of convective drying of nanoporous solids by increasing their strength willbe probably the most frequently investigated way of nondestructive drying of nanoporous solids.
The dynamics of crack formation in drying nanosuspensions can provide valuable insight into theirmechanism of drying (Dufresne et al., 2003). Experiments performed on drying of up to 30% vol.suspension of 6, 11 and 26 nm nanoparticles in water from one end of glass or sapphire capillaries hasshown that water transport in such system is never diffusive i.e. there is no concentration gradient ofliquid in the solid phase and no menisci of water penetrate the solid phase but water moves by Darcy
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flow. At the constant drying-rate period the drying rate is limited, as usually, by evaporation rate from thesurface but in the falling rate period the drying rate decreases due to increasing resistance to Darcy flowcaused by compaction of the suspension close to the front of crack tips.
It is interesting to observe crack formation in drying of gels films, which depending on conditions mayform intricate patterns (Pauchard et al., 2003). A simple mechanism of crack formation in gel films wasproposed earlier (Allain, Limat, 1995) but in fact we are rather interested in drying of films without
cracks or other defects. In certain conditions it is possible when gel films after the initial compressions bycapillary forces “springback” to regain much of it’s original thickness as predicted by a model of dryingswith shrinkage (Cairncross et al., 1996). The predictions are qualitatively identical to experimentalobservations (Prakash et al., 1995). It is interesting to know why some gels crack and some gels springback. One can believe that thin gel films which have larger pores and are elastic in a wider range will notcrack. Thicker films with smaller pores and less strength will probably develop cracks.Additionally we have to take into account the time scale. Slow drying will usually allow the dryingstresses to relax and shrinkage but no cracks will be observed (Fig. 5a). When drying is fast an instantcracking is observed in non-elastic gels or skin hardening (Fig.5b) in more elastic ones.
Figure. 5 Shrinking depends on drying rate. a) gel cylinder dried slowly shrunk towards center b) a clinical case of casehardening – gel cylinder rapidly dried convectively first developed a skin which prevented further shrinkage then the gel
inside cracked and shrunk towards the walls leaving an empty shell (Kubacka 1996)
It is worth adding that no aerogel has been produced so far that would elastically deform like ananoporous sponge. Certainly that would be a breakthrough in applications but is most likely hardlypossible.
DIFFUSION IN NANOPORES
Drying is always necessary in synthesis of nanomaterials by the wet route. Liquid moistureprovides the environment in which the nanomaterial is formed and it can be removed from it only bydiffusion. Diffusion is a tendency of matter to move in such a way as to eliminate spatial differences incomposition (Kärger, Ruthven, 1992). In drying of nanomaterials the moisture will diffuse throughnanopores which, as we defined earlier, extend over a part of macropore range, full mesopore range andalso a part of micropore range.
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The classification of pores by IUPAC (Table 1), although somewhat arbitrary, results from considerationof differences in forces that control the adsorption and diffusion of molecules in pores. In microporessurface forces dominate and molecules of adsorbate never escape fully from the influence of walls, evenin the center of the pore. In mesopores capillary forces related to meniscus formation dominate, whilemacropores contribute very little to adsorption and diffusion characteristics beside, of course, extendingthe path of diffusion, which is reflected in the well-known formula of Krischer
τε= 0eff DD (5)
where D eff is the effective diffusivity through the porous solid, ε is porosity, τ is the tortuosity defined asa ratio of the path really traveled by the molecule to the end-to-end distance it traveled and D 0 is thediffusivity in continuous phase .In micropores we can hardly speak about liquid and gas phases, instead we have one adsorbed phase thatwill move by jumps of molecules from one to another adsorption site on the wall.At this level the diffusivity of molecules can be explained by the random-walk theory that reflects theBrownian nature of movements of molecules. The resulting formula for self-diffusivity in a 3D isotropicsystem is (Kärger, Ruthven, 1992 – eq. 2.20)
t6l
D2
= (6)
where l 2 is the mean square displacement (end-to-end) traveled by the molecule and t is time elapsedduring that travel. It is accepted that in dilute systems the binary Fickian diffusivity approaches self-diffusivity.
Figure 6 2D structure of a gel simulated by Monte Carlo method usingDLCCA mechanism on 128x128 grid seeded with 2000 monomer
grains.
Mesopores can be simultaneously filled by liquid and vapor. Only in solids with a very high yield stressliquid menisci can exist during evaporation. In these solids a moving evaporation front would beobserved. Otherwise in convective drying the solids will be compressed or crushed by the drying stresses.The flow of gases through mesopores would take either a form of Darcy flow at high pressures orKnudsen flow at low pressures. In aerogels the pore size is so small that the flow of gases may takea form of Knudsen diffusion even under normal pressure since mean free path of an ideal gas at 1 atm and300 K is 230 nm. The resulting diffusivity can be measured experimentally. It can also be simulated bya relatively simple Monte Carlo simulation (Hasmy et al., 1998). In our simulation (Pakowski et al.,
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2001a) we took a 3D lattice 64x64x64 pixels, each pixel equal in size to one monomer and performed aDLCCA gelling process on it until a single stable cluster was obtained. For illustration a 2D structure ofa gel obtained by this mechanism is shown in Fig. 6.We then took one molecule of given chemical species, which in the actual scale could be approximatedby a material point and placed it at random location within the lattice. The molecule was then allowed tomove in random direction until it hit the skeleton. It was then reflected in a direction defined by theKnudsen cosine law. After a specified number of moves the total traveled distance Λ and the mean square
displacement l2 were calculated. The Knudsen diffusivity can be then calculated from the formula
identical to the random walk formula (Eq. 6) if time t is calculated as v/ Λ – where v is molecule velocityand Λ is the total traveled distance:
Λ=
2
eff l
v61
D (7)
By calculating the molecule velocity from the kinetic theory of gases as
MRT8
vπ
= (8)
where R is the universal gas constant and M – molecular mass, a formula for calculation of gas effectivediffusivity can be obtained. For three gases used He, N 2 and CO 2 the diffusivities measuredexperimentally were indeed proportional to square root of molar mass as predicted by this method even atatmospheric pressure. We believe that the same calculation can be done for water or other moleculesdiffusing in the aerogel structure in vapor form. For liquid diffusion this kind of simulation is notapplicable since free path of molecules in condensed phase is much smaller than the pore size. The sameis true about the diffusion of supercritical fluid during aerogel drying because of much higher pressures.The pore network connectivity theory was used to predict the effective diffusivity instead (Jarzebski et al.,1995). Experimental measurements (Wawrzyniak, 1999) of binary diffusivity of ethanol-near critical CO 2 in silica aerogels of density 100 kg/m 3 show that the diffusivity range is ca. 2 to 4.5 .10-9 m2 /s, which isonly little less than the same diffusivity if the liquid phase, and confirms the predictions based of poreconnectivity.
But how water molecules diffuse through living cell walls? It was observed that protons smaller thanwater molecules cannot penetrate through these membranes while water molecules easily pass back orforth depending on osmotic pressure. The 2003 Nobel prize was awarded to these who discovered why -Peter Agre and Roderick MacKinnon. They discovered aquaporins – a class of proteins that formnanochannels in cell membranes. Plants have 35 different proteins of this type, mammals, includinghumans, have 10 (Barlow, 2002). They are so narrow that water molecules can pass through them only ina single file: one after another. Computer simulations revealed the mechanism of water moleculemovement through aquaporins (Tajkhorshid et al., 2002). Water molecules passing the channel are forced,by the protein's electrostatic forces, to rotate at the center of the channel, breaking the alternative donor-acceptor arrangement that is necessary for proton transmission – Fig. 7.
It seems still a far way to go for the drying science to explain all mechanisms of water transport in tissues.A recent paper (Chiralt, Fito, 2003) briefly summarizes what is known about water transport in planttissues during the osmotic dewatering. Besides the symplasmic transport where diffusion through cellmembranes dominates there is also the apoplastic transport external to cell membranes and possibly othermechanisms (e.g. fluid phase endocystosis – Hawes et al., 1995). This makes the simulation of the netwater flow through such systems too complex for the present day computers.
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Figure. 7 Water transport through aquaporin water channel Figure 8 Single cell of an apple tissue(by permission of Nobel Museum, Stockholm, Sweden) (courtesy of D. Chiralt)
It was suggested that water behavior in nanopores and in aquaporins can be studied in a model system ofcomposed of a hydrophobic carbon nanotube (Hummer et al., 2001) immersed in water. Carbonnanotubes are fullerene type structures like the one shown in Fig. 9.
Figure. 9 Single-wall carbon nanotubes: inner diameter 0.8 nm, length 1.35 nm usedfor simulation of water transport (Hummer et al., 2001- by permission)
It was found that two stable energetic states are available for the system the tube and water – full orempty. Therefore water molecules move in short bursts (picoseconds) forming files of molecules. Thismovement is initiated by even small perturbations of ambient conditions.
DRYING OF NANOSUSPENSIONS AS SELF-ASSEMBLY PROCESS
In systems far from equilibrium complex transitory structures may emerge (Whitesides, Grzybowski,2002). Drying of thin films provides an example. When a liquid film contains nanoparticles they undergoa self-assembly process, which leads to structures that may find applications in fabrication of nanoscaledevices. It was reported (Sear et al., 1999) that silver nanoparticles 4-6 nm in size passivated withoctanethiol and suspended in hexane or heptane formed self-assembled structures upon drying. The form
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of structures observed was dependent of the concentration of suspended nanoparticles. At lowerconcentrations (ca. 0.3 mg/ml) almost circular islands were observed while at three times higherconcentrations bands or ribbons were formed.The interparticle and particle/solvent interactions depend on the type of solvent (different behaviors wereobserved in hexane than in chloroform). The process was simulated by Monte Carlo simulations (Rabaniet al., 2003) using a thermodynamic model on a square 2D lattice of 1000x1000 grid points, each 1 nm insize. Grid cells are occupied initially by liquid or nanoparticles. As the film thins during drying grid cells
can also be occupied by gas. Liquid cells attracts themselves and so do nanoparticles and liquid cells andtwo nanoparticles together but these interaction differ in strength. These differences make that during theevaporation the aggregation of nanoparticles occurs. Finally a self-assembled structure of nanoparticlesremains on the surface as shown in Fig. 10.
Figure. 10 A pattern of 4 nm nanocrystals of CdSe covered with a monolayer of trioctyl phosphine oxide self-assembledduring drying of thin film of their suspension in chloroform on graphite surface (picture by atomic force microscopy) (From
http://research.radlab.columbia.edu/mrsec/nuggets.html - Materials Research Science and Engineering Center, ColumbiaUniversity)
Although the model is coarse-grained and does not include the solvent film fluctuations observed in pureliquids (Elbaum, Lipson, 1994), it correctly predicts many types of self-assembly behavior in films ofnanoparticle suspensions especially the spinodal nucleation and subsequent coarsening observedexperimentally. Moreover several new types of structures not yet confirmed by experiments werepredicted.Experimental results from Sandia National Laboratories (Doshi et al., 2000, Yunfeng Lu et al., 2002)indicate that it is possible to produce inorganic-organic nanoporous films by dip coating process in whichdrying actually induces self assembly thus improving the structure of films.
TECHNICAL IMPACT
Many of the nanomaterials discussed here will be produced without the drying process by the dry route.Others will be produced or used as suspensions and do not require drying. An exception are theseproduced by sol-gel technology (films, layers, monoliths) or other wet methods of fabrication(nanopowders). As one can expect in the case of the nanomaterials quality aspects far surpass theeconomic side of the process, but still the drying methods can be roughly classified into three groups withrespect to their increasing cost per kg of product. Their description is provided below.
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Convective drying
This cheap method can be applied only to those nanomaterials which can withstand the drying stresses:thin films, nanopowders, strengthened monoliths etc. Unfortunately, only data reporting laboratory scaledrying experiments are published. Details of industrial scale technologies are closely guarded secrets. Theonly information leak is that, in the case of drying some nanopowder suspensions, they are dried in spray
dryers. Even at this scale of dispersion agglomeration of nanoparticles occurs and preventive measuresare being sought.
Freeze drying
Freeze drying is unable to produce monolithic nanoporous solids for most inorganic materials since theice crystals that form during freezing are larger than the pore size. It was, however, reported that freeze-drying of resorcinol-formaldehyde gels was successful (Kocklenberg et al., 1998) owing to much higherelasticity of such gels. The resulting xerogels retained their micro and mesopores characteristic to gels buta number of large pores (3 µm or more) appeared.Nanopowders have been obtained by either freeze drying of the sols (Wenming Zhen et al., 2001) orspray freeze-drying where sols are cooled and sprayed into vacuum where they instantly freeze and thendry. As always, owing to low drying temperatures freeze drying finds application principally in drying ofthermosensitive nanosuspensions.
Supercritical drying
The most expensive but only way to completely eliminate the action of surface tension is supercriticaldrying. The following 3D phase diagram of equation of state explains the process.In convective drying the initial moisture state is in liquid form at point A, located at saturation line atgiven initial temperature. During drying the moisture is heated to the wet bulb temperature (point B) andthen gradually converted from liquid to vapor along the path BD. By heating further the remainingmoisture expands to point E where the drying ends. As clearly visible in Fig. 11 the trajectory BD passesthrough the two-phase region where surface tension responsible for drying shrinkage exists.On the other hand in supercritical drying the moisture is first heated in the autoclave at constant volume.It simultaneously raises the pressure until a point B’ is reached, which is located well in the supercriticalfluid region (above T c and P c). During the AB’ path moisture gradually changed its state from liquid togas without existence of surface tension at any time. From point B’ the supercritical fluid is expandedisothermally to point D’ and then cooled down to point E. This process produces no shrinkage.Supercritical drying requires that the temperature surpasses the critical temperature of moisture. Thistemperature for water is very high (374 °C) causing thermal degradation of most materials. At the sametime the critical pressure of water is also high (217.7 bar) and very strong autoclaves would be needed.However, numerous solvents exist with temperatures much lower than that. One of them, carbon dioxideis of particular interest mainly because of low critical parameters (T c=31 °C, P c=72.9 bar) but also due toneutral environmental impact and low cost. Unfortunately, liquid CO 2 is not miscible with water and an
intermediate solvent must be used, usually alcohol. This is why in sol-gel technology siloxanes are usedas precursors – their hydrolysis produces alcohols and can be performed in alcohol as solvent.
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Figure 11 - 3D trajectories of convective drying (ABDE) and supercritical drying (AB’D’E),C is the critical point. Distances not to scale.
When using CO 2 for supercritical drying the drying stage must be preceded by the solvent replacementstage. Practically the whole process is composed of the following four major stages:
Solvent replacement stage – the gel is placed in the autoclave fully covered by solvent in order toprevent the surface from convective drying, the autoclave is closed and liquid CO 2 is poured into
the autoclave through the entry valve when it slowly displaces the solvent that leaves through theexit valve. The stage lasts until last drops of the solvent are visible leaving the autoclave. Diffusional replacement – since the pores of gel are also filled with solvent it must slowly diffuse
out and be replaced by liquid CO 2. Depending on the gel size this stage may last from minutes tohours. During that period the flow of liquid CO 2 through the autoclave is either very slow or doneperiodically. If this stage is too short deep in pores not all solvent may be replaced by CO 2 and theresulting critical temperature of mixture may be higher than that of pure CO 2. Those regions willretain some solvent in liquid form and then will dry and crack in the fourth stage.
Supercritical transition – all valves are closed and the autoclave is heated to temperature insupercritical fluid region. This stage also has some dangers – if heating rate is to fast thermalexpansion of liquid in aerogel pores may cause cracking of the gel (Scherer, 1992).
Isothermal expansion – once the supercritical stage is reached the fluid may be released slowly
until atmospheric pressure. If decompression rate is to fast the gel may also crack due to pressuregradients inside the gel.
Once the autoclave is pressurized after closing it is possible to use a supercritical CO 2 from the beginninginstead of stages 1-3. It is however believed that this method may cause stresses due to largeconcentration gradients.
Most of inorganic aerogels obtained by supercritical drying are hydrophilic in nature. This is a directresult of hydroxyl groups remaining on the surface and immense surface areas available. Such aerogels
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soak water when immersed and crack instantly, however, usually they may withstand repeated cycles ofadsorption – desorption of water molecules from gas phase. For that reason methods of hydrophobizationof aerogels have been investigated and hydrophobic aerogels have been finally obtained.An idea is to replace the surface hydroxyl groups either during synthesis or in post-processing. Usuallysubstitution of one hydroxyl group in TEOS precursor with either –H, -CH 3 or similar group is enough asthese groups will be forced to the surface. It is enough to substitute ca. 20% of all TEOS used for theprocess. Unfortunately gelling time increases several times and more defects are observed in the final
network – the gels are not transparent anymore (Kowalska, 1996). Post-processing of dry aerogels byhigh temperature reaction with methanol (Lee et al., 1995) has been suggested but is difficult anddangerous to perform. Our group worked out a relatively simple and cheap method of hydrophobizationof silica aerogels that we used for treatment of aerogel covered nonwoven fiber-glass filters (Pakowski,Maciszewska, 2003). The aerogel was kept for several hours in vapors of trimethylchlorosilane (TMCS).A rapid reaction leads to replacement of the surface hydroxyl groups with trimethylsilane groups thatprovide hydrophobicity for the gel. A critical factor in this process is time – for longer exposure times thehighly reactive TMCS molecules will penetrate the pores and cracks in the gel will result. One has toremember that in this process only the surface of the gel is hydrophobic, when the gel is crushed theresulting powder will be hydrophilic again.
In turn, other nanomaterials can be hydrophobic and changing this property may be important in order toallow them to be used in medicine or biology in aqueous environment. Wetting of nanomaterials has alsobeen studied and useful information can be obtained e.g. from the latest Third International Symposiumon Contact Angle, Wettability and Cohesion, Providence, RI, USA, 20-23 May 2002 were six paperswere presented on the subject.
CHALLENGES FOR DRYING
No doubt the nanomaterial sector will grow rapidly in the nearest future. The drying technology has tofollow. This would require leaving the macroscale we are used to and going down to the level of singlemolecules. This road has been already paved by physicists and we have to learn the understanding of theunderlying phenomena from them. Some phenomena occurring at the level of molecule, like self-assembly processes in nanosuspensions can instantly be converted into production tools other can help inunderstanding basis mechanisms of water transfer in nanopores or capillaries. Understanding the role ofprocess parameters in these extremely sensitive phenomena is critical to be able to reach reproducibleresults.
A large scale production of nanopowders must be mastered since these materials are the most commonproducts of this sector. Methods of avoiding agglomeration in spray and freeze drying will be sought.Nanoporous materials (aerogels) will also be produced in large scale and perhaps soon become the mostpopular and effective transparent thermal insulation materials. Besides lowering the costs of supercriticaldrying, used in their technology, by optimizing the times of each process stage, new ways of reducingdrying stresses or strengthening the gel structure have to be sought: dendrimeric precursors, reinforcingby maturing etc.The ability of controlling the hydrophobic and hydrophilic properties of nanomaterials, especiallynanopowders is also studied and may bring in immediate applications.
It has been demonstrated that numerical simulations already help in understanding some of thephenomena related to drying in nanoscale: self-assembly of nanoparticles, water transport throughnanotubes and aquaporins, water vapor diffusion in nanopores etc. We are yet to see simulations at largerscale using molecular dynamics software, this, however may not be a too distant future.
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CONCLUSIONS
As demonstrated, drying plays an important role in the production of many nanomaterials. Theunderstanding of drying at nanometric scale is far from satisfactory but first steps have already beenmade. Many of us, in the nearest future, will be attracted to enter into the area either by their owncuriosity or by government or industrial grants. The subject is difficult and requires expensive laboratoryequipment and fast computers. But rewards are immediate in the form of new products and technologies
that spin off from this research. All this encourages a chemical engineer interested in drying to enter thisfascinating area.
ACKNOWLEDGMENTS
This paper was supported by research grant No. 7 T09C 026 20 of the State Committee for ScientificResearch (KBN).
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