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Fractal Dimension as a Tool to Guide Zeolite Synthesis
\
Chaos\ Solitons + Fractals Vol[ 8\ No[ 00\ pp[ 0792Ð0701\ 0887 9859Ð9668:87:, ! see front matter Þ 0887 Elsevier Science Ltd[ All rights reserved
Pergamon
PII] S9859!9668"87#99993!5
Fractal Dimension as a Tool to Guide Zeolite Synthesis MELKON TATLIER and AYS žE ERDEM!S žENATALAR$ Department of Chemical Engineering\ Istanbul Technical University\ Maslak\ 79515 Istanbul\ Turkey "Accepted 5 January 0887#
Abstract*The borderlines on the composition diagrams between the regions of reaction mixture com! positions from which zeolites A\ X and HS\ as well as amorphous material\ may be formed are drawn by using appropriate data from the literature[ The fractal dimension is introduced as a helpful tool to depict and quantify the irregular nature of zeolite A synthesis[ The random type of behavior\ frequently occurring during the synthesis of zeolite A\ seems to point to the existence of a factor not yet taken into consideration[ Þ 0887 Elsevier Science Ltd[ All rights reserved
0[ INTRODUCTION
Zeolites are microporous crystalline materials with unique properties which enable them to be used in diverse processes such as catalysis\ ion exchange and adsorption ð0Ł[ These hydrated aluminosilicates may occur naturally or be synthesized in laboratory conditions[ Although they have been discovered more than 199 years ago and their _rst synthesis was accomplished in the late 0839|s\ the exact mechanism of their synthesis is still not known[ Because of the complexity of their synthesis mechanism\ it has been di.cult to design a speci_c type of zeolite beforehand[ Zeolites are synthesized hydrothermally and their synthesis follows a route which includes the periods of induction\ nucleation and crystal growth ð1Ł[ Besides the unpredictable nature of the synthesis mechanism of the zeolites\ an additional problem may lead to confusion in some cases[ The metastable nature of the zeolites is another cause of the unpredictability involved with their synthesis[ Zeolites like any crystalline material for which the crystallization occurs from solution and more than one possible crystalline structure exists\ tend to transform into more stable phases as time proceeds ð2Ł[ This undesirable aspect of zeolite synthesis causes confusion about the type of zeolite expected to be obtained especially when the duration of the transformation is relatively short[ Furthermore\ the lack of reproducibility of the results obtained in zeolite synthesis creates additional problems[ This type of inconsistency may be due to the pretreatments the reactants undergo\ such as preheating\ aging or it may be due to the nature of the reactants used or the order of mixing applied[ Zeolite A is one of the most commonly used zeolites[ Its hydrophilic nature allows it to be distinguished as a strong adsorbent\ whereas its largest use is as a detergent builder[ Zeolite A most readily transforms into zeolites X and HS in the _rst place and afterwards zeolite Y may appear ð2\ 3Ł[ It is very di.cult to designate the synthesis conditions of zeolites A\ X and HS both for the possibility of transformation and the proximity plus complexity of the regions in which these zeolites may be synthesized[ The most signi_cant parameters determining
$Author for correspondence 0792
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MELKON TATLIER and AYSžE ERDEM!SžENATALAR
which one of these zeolites will be formed are time\ temperature and the molar ratios of SiO1:Al1O2\ Na1O:SiO1 and H1O:Na1O[ Selecting appropriate values for these parameters is a di.cult task to perform and the conditions suitable to form zeolite A can only be discovered experimentally for the moment[ Although developed quite recently\ the signi_cance of fractal geometry has been rapidly understood[ It has found widespread use in diverse areas of science to simulate irregular shapes and chaotic movements ð4Ł[ The fractal dimension is one of the most useful tools of fractal geometry[ In the case of very complex structures where ordinary measurements become mean! ingless\ fractal dimension is of great help[ It takes into account how fast a curve\ surface or volume changes by measuring with smaller and smaller scales[ There exists several types of fractal dimension\ of which self!similarity\ compass and box counting should be especially mentioned ð5Ł[ The box counting fractal dimension is employed to a great extent in various areas of science both for practical reasons and because self!similarity is not a prerequisite[ The fractal dimension has also been the subject of interest concerning zeolites[ Surface irregularity is a crucial factor in processes such as catalysis\ adsorption\ di}usion and crystal growth ð6Ł[ In order to be able to cope with the e}ects caused by such irregularity\ fractal dimension has been of some help ð7Ð09Ł[ However\ the utility of the fractal dimension shouldn|t be con_ned within these boundaries[ It might also help to learn more about the nature of synthesis of zeolites[ In this study\ the boundaries on the composition diagrams between the regions of reaction mixture compositions from which zeolites A\ X\ HS and their mixtures may be formed are investigated by making use of the concept of the fractal dimension[ For this aim\ appropriate data from the literature are used ð3Ł[ As a result of the limitations of data available\ only certain ranges of values for the parameters time\ temperature and molar ratios are taken into account[ Thus the fractal dimension of the borderlines on the composition diagrams between the regions of zeolites A and X and HS are determined by using the box counting method ð5Ł and comments are made about the irregular movements of these borderlines in relation to the synthesis of zeolites[ Moreover\ the relationships between the fractal dimension and the concerned variables are displayed and the possibility of employing these relations as a guide for tailoring zeolite synthesis is discussed[
1[ THEORETICAL BACKGROUND
Zeolites may be synthesized using suitable reagents in hydrothermal conditions[ The set of reagents commonly employed to produce zeolite A are sodium aluminate\ sodium silicate\ sodium hydroxide and water[ The zeolite thus produced is in the sodium form and is called NaA[ The composition of the reaction mixture is generally represented by the molar ratios of water to sodium oxide "H1O:Na1O#\ sodium oxide to silica "Na1O:SiO1# and silica to alumina "SiO1:Al1O2#[ In order to obtain zeolite NaA\ these three variables should be chosen suitably and their relationship with time and temperature should also be taken into account[ According to the patents found in the literature\ zeolite NaA may be synthesized from a wide region of com! positions where the values of the oxide ratios H1O:Na1O\ SiO1:Al1O2 and Na1O:SiO1 can vary in the ranges 14Ð199\ 9[4Ð0[2 and 0Ð2\ respectively[ Another set of ranges for the same ratios are given as 24Ð199 for H1O:Na1O\ 0[1Ð1[4 for SiO1:Al1O2 and 9[7Ð0[2 for Na1O:SiO1 whereas the temperature of the solution is said to di}er between 19Ð064>C ð00\ 01Ł[ Values up to 3[4 ð00Ł and 09 ð02Ł can also be found in the literature for the SiO1:Al1O2 ratio and those up to 09 ð02Ł for the Na1O:SiO1 ratio[ Zeolite NaX is reported to be synthesized under the conditions where H1O:Na1O 24Ð59\ SiO1:Al1O2 2Ð4 and Na1O:SiO1 0[1Ð0[4 ð01Ł[ It seems highly possible to synthesize zeolites A and X with the same initial molar ratios of the related oxides[ When the formation of totally amorphous products and zeolites HS and Y are also taken into account\ the
Fractal dimension as a tool to guide zeolite synthesis
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di.culty to design the synthesis of a speci_c type of zeolite within the corresponding region might be easily understood[ In our study\ suitable data from literature are obtained to determine the regions on the composition diagrams from which zeolite A and di}erent types of zeolites\ as well as their mixtures are reported to be synthesized ð3Ł[ The employment of a single source allows the data obtained to be comparable[ Zeolite Y is not included because of the lack of data as well as its relationship to zeolite X in the _rst place[ In order to determine the borderlines between the regions producing zeolite A and others\ the relationships between the variables similar to those plotted in the original reference ð3Ł are employed[ The data are also replotted holding di}erent variables constant[ The borderlines are constructed by taking into consideration only those points pertaining to zeolite A which are located at the closest distance in the x and y directions\ to those pertaining to another type of zeolite or amorphous material[ They are drawn by employing the midpoints between zeolite A and the other substances and are produced in the same manner for all cases[ No particular attempt is made to de_ne any closed region[ Temperature and the H1O:Na1O molar ratio are held constant at 099>C and 19\ respectively\ because of the limitations of the data available from the literature[ The molar ratio of SiO1:Al1O2 varies in the range of 1Ð 6[2 whereas that of Na1O:SiO1 varies between the values of 0Ð1[ The investigated period of time is limited to 0Ð2 hours[ Accordingly\ the e}ects of time and the molar ratios of Na1O:SiO1 and SiO1:Al1O2 on the synthesis of zeolite A are investigated by the help of the fractal dimensions of the borderlines[ The fractal dimensions of the borderlines representing the conversion of zeolite A into zeolites X\ HS or amorphous products are calculated using the box counting method[ Five di}erent mesh sizes\ namely 0:05\ 0:13\ 0:21\ 0:37 and 0:53 have been employed[
2[ RESULTS AND DISCUSSION
The borderlines concerning the conversion of zeolite A into zeolites X\ HS and amorphous material or vice versa were determined according to the data available[ Time and molar ratios of Na1O:SiO1 and SiO1:Al1O2 were each kept constant in turn while the changes in the other two variables were investigated[ Fig[ 0"aÐc# depict respectively the borderlines of zeolite A region after 0\ 1 and 2 hours of reaction[ In Fig[ 0"a#\ zeolite A is seen to have the tendency to occur more commonly in regions with relatively higher Na1O:SiO1 and lower SiO1:Al1O2 molar ratios[ The other types of substances occurring at this step of synthesis are zeolite X and:or amorphous material[ In Fig[ 0"b#\ the borderline formed after 1 hours is observed to separate zeolite A both from zeolite X or amorphous material and zeolite A¦HS mixture[ The irregular shape of the borderline signi_es the di.culty of prediction concerning the relationship between the variables within this region[ As an example\ we may see that when the SiO1:Al1O2 molar ratio is kept constant at the value of 2[2 and the Na1O:SiO1 molar ratio is increased step by step\ _rst zeolite X is formed which is followed by the production of zeolite A[ As we proceed further\ we may obtain zeolite A¦HS mixture followed again by zeolite A[ Afterwards zeolite A¦HS mixture is formed and _nally we end up with zeolite A[ The other signi_cant points to notify are the tendency of zeolite X and:or amorphous material to disappear with time as zeolite A replaces them and the movement of zeolite A towards regions with higher SiO1:Al1O2 molar ratios[ Fig[ 0"c# depicts the situation after the third hour of synthesis[ There is no zeolite X region left whereas zeolite A is con_ned more to the higher SiO1:Al1O2 molar ratio region accompanied by some decrease in its stability area[ Figure 1"aÐf# are drawn by keeping the SiO1:Al1O2 molar ratio constant[ From Fig[ 1"a# which corresponds to a low SiO1:Al1O2 molar ratio of 1\ it may be seen that only a limited region of pure zeolite A con_ned to the earlier times of the synthesis is present[ At longer times\ conversion to HS starts taking place[ In Fig[ 1"b#\ we may notice the struggle of zeolite A to extend its
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Fig[ 0[ The diagrams showing the stability areas of "ž# zeolite A\ "# zeolite A¦HS mixture\ "# zeolite X and:or amorphous material\ and "¦# amorphous material at H1O:Na1O 19 and T 099>C^ "a# t 0 hr^ "b# t 1 hr^ "c# t 2 hr[
existence towards longer synthesis times[ The result of this struggle is an unexpected irregular behavior[ Zeolite X is also seen to be synthesized at low Na1O:SiO1 ratios[ As the SiO1:Al1O2 molar ratio increases further in Fig[ 1"c#\ we may easily notice the presence of zeolite A at longer synthesis times[ The stability area of zeolite A gradually tends to move towards higher Na1O:SiO1 molar ratios and longer times parallel to the increase in SiO1:Al1O2 ratio\ as may be seen from
Fractal dimension as a tool to guide zeolite synthesis
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Fig[ 1[ The diagrams showing the stability areas of "ž# zeolite A\ "# zeolite A¦HS mixture\ "# zeolite X and:or amorphous material\ "×# zeolite X\ and "¦# amorphous material at H1O:Na1O 19 and T 099>C^ "a# SiO1:Al1O2 1^ "b# SiO1:Al1O2 2[2^ "c# SiO1:Al1O2 3[2^ "d# SiO1:Al1O2 4[2^ "e# SiO1:Al1O2 5[2^ "f# SiO1:Al1O2 6[2[
Fig[ 1"dÐf#[ In the meanwhile\ zeolite A¦HS mixture region loses ground\ zeolite X stops forming and the region yielding amorphous material spreads over the ground previously occupied by zeolite A[
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Fig[ 2[ The diagrams showing the stability areas of "ž# zeolite A\ "# zeolite A¦HS mixture\ "# zeolite X and:or amorphous material and "¦# amorphous material at H1O:Na1O 19\ T 099>C^ "a# Na1O:SiO1 0^ "b# Na1O:SiO1 0[1^ "c# Na1O:SiO1 0[3^ "d# Na1O:SiO1 0[5^ "e# Na1O:SiO1 0[7^ "f# Na1O:SiO1 1[
Figure 2"aÐf# represent the cases where the Na1O:SiO1 molar ratios are kept constant[ Fig[ 2"a# represents the situation where the Na1O:SiO1 ratio is equal to 0[ In this case a very limited amount of zeolite A is present which is con_ned to a region denoting lower SiO1:Al1O2 molar ratios and longer synthesis times[ In Fig[ 2"b#\ zeolite A is seen to form in a region surrounded
Fractal dimension as a tool to guide zeolite synthesis
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Fig[ 3[ The stability areas of "ž# zeolite A and "¦# zeolite X and:or zeolite HS at H1O:Na1O 19\ SiO1:Al1O2 4 and Na1O:SiO1 09[
by zeolite A¦HS mixture from one side and zeolite X and:or amorphous material from the other side[ According to the Fig[ 2"c\d#\ zeolite X does not form and zeolite A tends to occur preferentially at higher SiO1:Al1O2 molar ratios as the Na1O:SiO1 ratio and time are increased[ The same tendency may be observed for the zeolite A¦HS mixture such that the two separate regions become almost distinguishable by a speci_c value of time[ In Fig[ 2"e\f#\ the regions from which zeolite A¦HS mixture and zeolite A are obtained proceed further into each other and struggle not to lose ground[ As a result\ borderlines with irregular shapes are obtained[ Figure 3 shows the relationship between the variables time and temperature[ This relationship is obtained from experiments employing a di}erent synthesis composition ð02Ł[ In this case the synthesis mixture forms a clear solution\ as opposed to the commonly used gel mixtures[ All the same\ the almost linear relationship between time and temperature obtained may be expected to hold true for both methods and for most of the compositions[ The fractal dimensions of the borderlines of zeolite A regions were determined by using the box counting method as mentioned above[ In Fig[ 4\ the relationship between the fractal dimen! sion and time is shown[ The fractal dimension of the borderline of zeolite A region increases signi_cantly within the second hour of synthesis denoting an irregular behavior[ Fig[ 5 represents the relationship between the fractal dimension and the SiO1:Al1O2 molar ratio[ The most irregular shape is obtained at SiO1:Al1O2 2[2 and the fractal dimension has a tendency to decline after this point[ Figure 6 depicts the relationship between the fractal dimension and the molar ratio of Na1O:SiO1[ As the Na1O:SiO1 molar ratio increases\ _rst a slight increase in the fractal dimension is observed resulting in a moderate peak at the Na1O:SiO1 ratio of 0[1[ The tendency of the fractal dimension to decrease comes to an end when the Na1O:SiO1 ratio attains the value of 0[3[
Fig[ 4[ The relationship between the fractal dimension and time when T 099>C\ H1O:Na1O 19\ SiO1:Al1O2 1Ð6[2 and Na1O:SiO1 0Ð1[
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MELKON TATLIER and AYSžE ERDEM!SžENATALAR
Fig[ 5[ The relationship between the fractal dimension and the SiO1:Al1O2 molar ratio when T 099>C\ H1O:Na1O 19\ Na1O:SiO1 0Ð1 and t 0Ð2 hr[
After this point\ a signi_cant rise of the fractal dimension is observed[ The relatively moderate appearance of the _rst peak probably signi_es a smoother mode of conversion and the cor! responding region represents generally the transformation of zeolite X and:or amorphous material into zeolite A[ Another possibility is that the conversion takes place very rapidly and a more irregular behavior than the one observed is left unnoticed[ The second peak denotes a highly irregular type of conversion and involves zeolite A and zeolite A¦HS mixture[ From the results obtained\ it is possible to claim that the fractal dimensions of the borderlines of zeolite A may give signi_cant information about the degree of unpredictability involved with the synthesis procedure[ In Figs 4Ð6\ a common aspect observed is that the most irregular behavior of zeolite A occurs just after it begins to spread widely into the zeolite A¦HS region or at the time it tends to disappear and be converted into the zeolite A¦HS mixture[ In other words\ irregularity is most probable to occur when zeolite A and zeolite A¦HS mixture both hold important ground[ Another important fact is that the most irregular type of behavior is closely related to the variable time[ In the cases where the most unpredictable type of behavior takes place\ as the Na1O:SiO1 or SiO1:Al1O2 molar ratios are varied keeping the synthesis time constant\ the formation of zeolite A seems to occur in a random manner as may be seen from Figs 1"b# and 2"e\f#[ Such random behavior causes unpredictability concerning the reaction times that provide zeolite A[ On the other hand\ the conversion of zeolite A into zeolite X and:or amorphous material or vice versa seems to happen more smoothly and no highly irregular shapes are obtained[ Additionally\ it may be possible to predict about the proximate regions for which no data is available since we learn about the tendency of further conversion of a speci_c type of a zeolite[ For example\ in the case that the Na1O:SiO1 molar ratio exceeds the value of 1 in Fig[ 6\ it is highly probable that zeolite A will _rst be con_ned to a narrower region denoting very
Fig[ 6[ The relationship between the fractal dimension and the Na1O:SiO1 molar ratio when T 099>C\ H1O:Na1O 19\ SiO1:Al1O2 1Ð6[2 and t 0Ð2 hr[
Fractal dimension as a tool to guide zeolite synthesis
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short reaction times and then will tend to disappear[ This will cause a decrease in the fractal dimension since the amount of zeolite A present in the related limited region will not be su.cient to exhibit a highly irregular behavior[
3[ CONCLUSIONS
The fractal dimension may be an e.cient tool to display and quantify the irregular behavior seen during zeolite A synthesis[ We may easily claim that when we obtain the fractal dimensions of the borderlines of the zeolite A regions over a wide range of the variables employed\ it will be possible to deduce the manner of synthesis at points in between\ thus creating the opportunity of making a logical guess about the type of zeolite expected to be formed[ This task may be realized by taking into account the meaning and amount of the irregularity[ However\ the results achieved in this study only involve zeolite A obtained under speci_c conditions and other type of zeolites as well as zeolite A under much di}erent conditions should be separately investigated[ The irregular type of behavior may hold true for the cases where more than one type of zeolite may be synthesized under almost similar initial conditions[ If it may be shown that the conversion of one type of a zeolite to another type occurs each time in a speci_c manner and order then some prediction related to the irregularity will be possible[ There exists some kind of a random behavior during zeolite A synthesis[ The reason for this randomness is probably due to an e}ect not taken into consideration within the course of synthesis[ Zeolites A\ HS and X may be synthesized with quite similar initial conditions so that a factor acting randomly might easily determine the type of the zeolite to be formed[ Since even making small changes in the amounts of the reactants may result in unexpected behavior\ it seems likely that varying the relative amounts of the reactants a}ects the local concentrations and:or the motion in solution and thus the formation of subunits in a random manner[ This fact\ in turn a}ects the type of zeolite to be formed[ The manner of the motion of the reactants for example\ may cause transient changes in the relative amounts and types of subunits thus a}ecting the duration of the formation or transformation of a speci_c zeolite type[ The observation that even small changes in the amounts of the Na1O:SiO1 and SiO1:Al1O2 molar ratios may vary the time necessary for zeolite A to form and that this situation may occur repeatedly over and over in an unexpected manner\ supports this view[
REFERENCES 0[ Davis\ M[ E[\ Zeolites and molecular sieves] Not just ordinary catalysts[ Ind[ En`[ Chem[ Res[\ 0880\ 29\ 0564Ð0572[ 1[ Budd\ P[ M[\ Myatt\ G[ J[\ Price\ C[\ Carr\ S[ W[\ An empirical model for the nucleation and growth of zeolites[ Zeolites\ 0883\ 03\ 087Ð191[ 2[ Tassopoulos\ M[\ Thompson\ R[ W[\ Transformation behavior of zeolite A to hydroxysodalite in batch and semi! batch crystallizers[ Zeolites\ 0876\ 6\ 132Ð137[ 3[ Kostinko\ J[ A[\ Factors in~uencing the synthesis of zeolites A\ X and Y[ In Intrazeolite Chemistry\ ed[ G[ D[ Stucky and F[ G[ Dwyer[ ACS\ Washington D[C[\ 0872[ 4[ Sze\ S[ J[\ Lee\ T[ Y[\ Fractal structure of porous solids characterized by adsorption[ Phys[ Rev[\ 0884\ B40\ 7698Ð 7603[ 5[ Peitgen\ H[ D[\ Jurgens\ H[ and Saupe\ D[\ Chaos and Fractals] New Frontiers of Science[ Springer\ New York\ 0881[ 6[ Avnir\ D[\ Farin\ D[\ Pfeifer\ P[\ Chemistry in noninteger dimensions between two and three[ II[ Fractal surfaces of adsorbents[ J[ Chem[ Phys[\ 0872\ 68\ 2455Ð2460[ 7[ Sulikowski\ B[\ The fractal dimension in molecular sieves] Synthetic faujasite and related solids[ J[ Phys[ Chem[\ 0882\ 86\ 0319Ð0314[ 8[ Sheintuch\ M[\ Brandon\ S[\ Deterministic approaches to problems of di}usion\ reaction and adsorption in a fractal porous catalyst[ Chem[ En`[ Sci[\ 0878\ 33\ 58Ð68[
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09[ Giona\ M[\ Schwalm\ W[ A[\ Adrover\ A[\ Schwalm\ M[ K[\ First order kinetics in fractal catalysts] renormalization analysis of the e}ectiveness factor[ Chem[ En`[ Sci[\ 0885\ 40\ 1162Ð1171[ 00[ Weber\ H[\ U[S[ Patent 2\947\794[ 01[ Milton\ R[ M[\ U[S[ Patent 1\771\132[ 02[ Wengin\ P[\ Ueda\ S[ and Koizumi\ M[\ The synthesis of zeolite NaA from homogeneous solutions and studies of its properties[ In New Developments in Zeolite Science and Technolo`y\ Proc[ of the 6th Int[ Zeolite Conf[\ ed[ Y[ Murakami\ A[ Iijima and J[ W[ Ward[ Elsevier\ Tokyo\ 0875[
Chaos\ Solitons + Fractals Vol[ 8\ No[ 00\ pp[ 0792Ð0701\ 0887 9859Ð9668:87:, ! see front matter Þ 0887 Elsevier Science Ltd[ All rights reserved
Pergamon
PII] S9859!9668"87#99993!5
Fractal Dimension as a Tool to Guide Zeolite Synthesis MELKON TATLIER and AYS žE ERDEM!S žENATALAR$ Department of Chemical Engineering\ Istanbul Technical University\ Maslak\ 79515 Istanbul\ Turkey "Accepted 5 January 0887#
Abstract*The borderlines on the composition diagrams between the regions of reaction mixture com! positions from which zeolites A\ X and HS\ as well as amorphous material\ may be formed are drawn by using appropriate data from the literature[ The fractal dimension is introduced as a helpful tool to depict and quantify the irregular nature of zeolite A synthesis[ The random type of behavior\ frequently occurring during the synthesis of zeolite A\ seems to point to the existence of a factor not yet taken into consideration[ Þ 0887 Elsevier Science Ltd[ All rights reserved
0[ INTRODUCTION
Zeolites are microporous crystalline materials with unique properties which enable them to be used in diverse processes such as catalysis\ ion exchange and adsorption ð0Ł[ These hydrated aluminosilicates may occur naturally or be synthesized in laboratory conditions[ Although they have been discovered more than 199 years ago and their _rst synthesis was accomplished in the late 0839|s\ the exact mechanism of their synthesis is still not known[ Because of the complexity of their synthesis mechanism\ it has been di.cult to design a speci_c type of zeolite beforehand[ Zeolites are synthesized hydrothermally and their synthesis follows a route which includes the periods of induction\ nucleation and crystal growth ð1Ł[ Besides the unpredictable nature of the synthesis mechanism of the zeolites\ an additional problem may lead to confusion in some cases[ The metastable nature of the zeolites is another cause of the unpredictability involved with their synthesis[ Zeolites like any crystalline material for which the crystallization occurs from solution and more than one possible crystalline structure exists\ tend to transform into more stable phases as time proceeds ð2Ł[ This undesirable aspect of zeolite synthesis causes confusion about the type of zeolite expected to be obtained especially when the duration of the transformation is relatively short[ Furthermore\ the lack of reproducibility of the results obtained in zeolite synthesis creates additional problems[ This type of inconsistency may be due to the pretreatments the reactants undergo\ such as preheating\ aging or it may be due to the nature of the reactants used or the order of mixing applied[ Zeolite A is one of the most commonly used zeolites[ Its hydrophilic nature allows it to be distinguished as a strong adsorbent\ whereas its largest use is as a detergent builder[ Zeolite A most readily transforms into zeolites X and HS in the _rst place and afterwards zeolite Y may appear ð2\ 3Ł[ It is very di.cult to designate the synthesis conditions of zeolites A\ X and HS both for the possibility of transformation and the proximity plus complexity of the regions in which these zeolites may be synthesized[ The most signi_cant parameters determining
$Author for correspondence 0792
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MELKON TATLIER and AYSžE ERDEM!SžENATALAR
which one of these zeolites will be formed are time\ temperature and the molar ratios of SiO1:Al1O2\ Na1O:SiO1 and H1O:Na1O[ Selecting appropriate values for these parameters is a di.cult task to perform and the conditions suitable to form zeolite A can only be discovered experimentally for the moment[ Although developed quite recently\ the signi_cance of fractal geometry has been rapidly understood[ It has found widespread use in diverse areas of science to simulate irregular shapes and chaotic movements ð4Ł[ The fractal dimension is one of the most useful tools of fractal geometry[ In the case of very complex structures where ordinary measurements become mean! ingless\ fractal dimension is of great help[ It takes into account how fast a curve\ surface or volume changes by measuring with smaller and smaller scales[ There exists several types of fractal dimension\ of which self!similarity\ compass and box counting should be especially mentioned ð5Ł[ The box counting fractal dimension is employed to a great extent in various areas of science both for practical reasons and because self!similarity is not a prerequisite[ The fractal dimension has also been the subject of interest concerning zeolites[ Surface irregularity is a crucial factor in processes such as catalysis\ adsorption\ di}usion and crystal growth ð6Ł[ In order to be able to cope with the e}ects caused by such irregularity\ fractal dimension has been of some help ð7Ð09Ł[ However\ the utility of the fractal dimension shouldn|t be con_ned within these boundaries[ It might also help to learn more about the nature of synthesis of zeolites[ In this study\ the boundaries on the composition diagrams between the regions of reaction mixture compositions from which zeolites A\ X\ HS and their mixtures may be formed are investigated by making use of the concept of the fractal dimension[ For this aim\ appropriate data from the literature are used ð3Ł[ As a result of the limitations of data available\ only certain ranges of values for the parameters time\ temperature and molar ratios are taken into account[ Thus the fractal dimension of the borderlines on the composition diagrams between the regions of zeolites A and X and HS are determined by using the box counting method ð5Ł and comments are made about the irregular movements of these borderlines in relation to the synthesis of zeolites[ Moreover\ the relationships between the fractal dimension and the concerned variables are displayed and the possibility of employing these relations as a guide for tailoring zeolite synthesis is discussed[
1[ THEORETICAL BACKGROUND
Zeolites may be synthesized using suitable reagents in hydrothermal conditions[ The set of reagents commonly employed to produce zeolite A are sodium aluminate\ sodium silicate\ sodium hydroxide and water[ The zeolite thus produced is in the sodium form and is called NaA[ The composition of the reaction mixture is generally represented by the molar ratios of water to sodium oxide "H1O:Na1O#\ sodium oxide to silica "Na1O:SiO1# and silica to alumina "SiO1:Al1O2#[ In order to obtain zeolite NaA\ these three variables should be chosen suitably and their relationship with time and temperature should also be taken into account[ According to the patents found in the literature\ zeolite NaA may be synthesized from a wide region of com! positions where the values of the oxide ratios H1O:Na1O\ SiO1:Al1O2 and Na1O:SiO1 can vary in the ranges 14Ð199\ 9[4Ð0[2 and 0Ð2\ respectively[ Another set of ranges for the same ratios are given as 24Ð199 for H1O:Na1O\ 0[1Ð1[4 for SiO1:Al1O2 and 9[7Ð0[2 for Na1O:SiO1 whereas the temperature of the solution is said to di}er between 19Ð064>C ð00\ 01Ł[ Values up to 3[4 ð00Ł and 09 ð02Ł can also be found in the literature for the SiO1:Al1O2 ratio and those up to 09 ð02Ł for the Na1O:SiO1 ratio[ Zeolite NaX is reported to be synthesized under the conditions where H1O:Na1O 24Ð59\ SiO1:Al1O2 2Ð4 and Na1O:SiO1 0[1Ð0[4 ð01Ł[ It seems highly possible to synthesize zeolites A and X with the same initial molar ratios of the related oxides[ When the formation of totally amorphous products and zeolites HS and Y are also taken into account\ the
Fractal dimension as a tool to guide zeolite synthesis
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di.culty to design the synthesis of a speci_c type of zeolite within the corresponding region might be easily understood[ In our study\ suitable data from literature are obtained to determine the regions on the composition diagrams from which zeolite A and di}erent types of zeolites\ as well as their mixtures are reported to be synthesized ð3Ł[ The employment of a single source allows the data obtained to be comparable[ Zeolite Y is not included because of the lack of data as well as its relationship to zeolite X in the _rst place[ In order to determine the borderlines between the regions producing zeolite A and others\ the relationships between the variables similar to those plotted in the original reference ð3Ł are employed[ The data are also replotted holding di}erent variables constant[ The borderlines are constructed by taking into consideration only those points pertaining to zeolite A which are located at the closest distance in the x and y directions\ to those pertaining to another type of zeolite or amorphous material[ They are drawn by employing the midpoints between zeolite A and the other substances and are produced in the same manner for all cases[ No particular attempt is made to de_ne any closed region[ Temperature and the H1O:Na1O molar ratio are held constant at 099>C and 19\ respectively\ because of the limitations of the data available from the literature[ The molar ratio of SiO1:Al1O2 varies in the range of 1Ð 6[2 whereas that of Na1O:SiO1 varies between the values of 0Ð1[ The investigated period of time is limited to 0Ð2 hours[ Accordingly\ the e}ects of time and the molar ratios of Na1O:SiO1 and SiO1:Al1O2 on the synthesis of zeolite A are investigated by the help of the fractal dimensions of the borderlines[ The fractal dimensions of the borderlines representing the conversion of zeolite A into zeolites X\ HS or amorphous products are calculated using the box counting method[ Five di}erent mesh sizes\ namely 0:05\ 0:13\ 0:21\ 0:37 and 0:53 have been employed[
2[ RESULTS AND DISCUSSION
The borderlines concerning the conversion of zeolite A into zeolites X\ HS and amorphous material or vice versa were determined according to the data available[ Time and molar ratios of Na1O:SiO1 and SiO1:Al1O2 were each kept constant in turn while the changes in the other two variables were investigated[ Fig[ 0"aÐc# depict respectively the borderlines of zeolite A region after 0\ 1 and 2 hours of reaction[ In Fig[ 0"a#\ zeolite A is seen to have the tendency to occur more commonly in regions with relatively higher Na1O:SiO1 and lower SiO1:Al1O2 molar ratios[ The other types of substances occurring at this step of synthesis are zeolite X and:or amorphous material[ In Fig[ 0"b#\ the borderline formed after 1 hours is observed to separate zeolite A both from zeolite X or amorphous material and zeolite A¦HS mixture[ The irregular shape of the borderline signi_es the di.culty of prediction concerning the relationship between the variables within this region[ As an example\ we may see that when the SiO1:Al1O2 molar ratio is kept constant at the value of 2[2 and the Na1O:SiO1 molar ratio is increased step by step\ _rst zeolite X is formed which is followed by the production of zeolite A[ As we proceed further\ we may obtain zeolite A¦HS mixture followed again by zeolite A[ Afterwards zeolite A¦HS mixture is formed and _nally we end up with zeolite A[ The other signi_cant points to notify are the tendency of zeolite X and:or amorphous material to disappear with time as zeolite A replaces them and the movement of zeolite A towards regions with higher SiO1:Al1O2 molar ratios[ Fig[ 0"c# depicts the situation after the third hour of synthesis[ There is no zeolite X region left whereas zeolite A is con_ned more to the higher SiO1:Al1O2 molar ratio region accompanied by some decrease in its stability area[ Figure 1"aÐf# are drawn by keeping the SiO1:Al1O2 molar ratio constant[ From Fig[ 1"a# which corresponds to a low SiO1:Al1O2 molar ratio of 1\ it may be seen that only a limited region of pure zeolite A con_ned to the earlier times of the synthesis is present[ At longer times\ conversion to HS starts taking place[ In Fig[ 1"b#\ we may notice the struggle of zeolite A to extend its
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MELKON TATLIER and AYSžE ERDEM!SžENATALAR
Fig[ 0[ The diagrams showing the stability areas of "ž# zeolite A\ "# zeolite A¦HS mixture\ "# zeolite X and:or amorphous material\ and "¦# amorphous material at H1O:Na1O 19 and T 099>C^ "a# t 0 hr^ "b# t 1 hr^ "c# t 2 hr[
existence towards longer synthesis times[ The result of this struggle is an unexpected irregular behavior[ Zeolite X is also seen to be synthesized at low Na1O:SiO1 ratios[ As the SiO1:Al1O2 molar ratio increases further in Fig[ 1"c#\ we may easily notice the presence of zeolite A at longer synthesis times[ The stability area of zeolite A gradually tends to move towards higher Na1O:SiO1 molar ratios and longer times parallel to the increase in SiO1:Al1O2 ratio\ as may be seen from
Fractal dimension as a tool to guide zeolite synthesis
0796
Fig[ 1[ The diagrams showing the stability areas of "ž# zeolite A\ "# zeolite A¦HS mixture\ "# zeolite X and:or amorphous material\ "×# zeolite X\ and "¦# amorphous material at H1O:Na1O 19 and T 099>C^ "a# SiO1:Al1O2 1^ "b# SiO1:Al1O2 2[2^ "c# SiO1:Al1O2 3[2^ "d# SiO1:Al1O2 4[2^ "e# SiO1:Al1O2 5[2^ "f# SiO1:Al1O2 6[2[
Fig[ 1"dÐf#[ In the meanwhile\ zeolite A¦HS mixture region loses ground\ zeolite X stops forming and the region yielding amorphous material spreads over the ground previously occupied by zeolite A[
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Fig[ 2[ The diagrams showing the stability areas of "ž# zeolite A\ "# zeolite A¦HS mixture\ "# zeolite X and:or amorphous material and "¦# amorphous material at H1O:Na1O 19\ T 099>C^ "a# Na1O:SiO1 0^ "b# Na1O:SiO1 0[1^ "c# Na1O:SiO1 0[3^ "d# Na1O:SiO1 0[5^ "e# Na1O:SiO1 0[7^ "f# Na1O:SiO1 1[
Figure 2"aÐf# represent the cases where the Na1O:SiO1 molar ratios are kept constant[ Fig[ 2"a# represents the situation where the Na1O:SiO1 ratio is equal to 0[ In this case a very limited amount of zeolite A is present which is con_ned to a region denoting lower SiO1:Al1O2 molar ratios and longer synthesis times[ In Fig[ 2"b#\ zeolite A is seen to form in a region surrounded
Fractal dimension as a tool to guide zeolite synthesis
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Fig[ 3[ The stability areas of "ž# zeolite A and "¦# zeolite X and:or zeolite HS at H1O:Na1O 19\ SiO1:Al1O2 4 and Na1O:SiO1 09[
by zeolite A¦HS mixture from one side and zeolite X and:or amorphous material from the other side[ According to the Fig[ 2"c\d#\ zeolite X does not form and zeolite A tends to occur preferentially at higher SiO1:Al1O2 molar ratios as the Na1O:SiO1 ratio and time are increased[ The same tendency may be observed for the zeolite A¦HS mixture such that the two separate regions become almost distinguishable by a speci_c value of time[ In Fig[ 2"e\f#\ the regions from which zeolite A¦HS mixture and zeolite A are obtained proceed further into each other and struggle not to lose ground[ As a result\ borderlines with irregular shapes are obtained[ Figure 3 shows the relationship between the variables time and temperature[ This relationship is obtained from experiments employing a di}erent synthesis composition ð02Ł[ In this case the synthesis mixture forms a clear solution\ as opposed to the commonly used gel mixtures[ All the same\ the almost linear relationship between time and temperature obtained may be expected to hold true for both methods and for most of the compositions[ The fractal dimensions of the borderlines of zeolite A regions were determined by using the box counting method as mentioned above[ In Fig[ 4\ the relationship between the fractal dimen! sion and time is shown[ The fractal dimension of the borderline of zeolite A region increases signi_cantly within the second hour of synthesis denoting an irregular behavior[ Fig[ 5 represents the relationship between the fractal dimension and the SiO1:Al1O2 molar ratio[ The most irregular shape is obtained at SiO1:Al1O2 2[2 and the fractal dimension has a tendency to decline after this point[ Figure 6 depicts the relationship between the fractal dimension and the molar ratio of Na1O:SiO1[ As the Na1O:SiO1 molar ratio increases\ _rst a slight increase in the fractal dimension is observed resulting in a moderate peak at the Na1O:SiO1 ratio of 0[1[ The tendency of the fractal dimension to decrease comes to an end when the Na1O:SiO1 ratio attains the value of 0[3[
Fig[ 4[ The relationship between the fractal dimension and time when T 099>C\ H1O:Na1O 19\ SiO1:Al1O2 1Ð6[2 and Na1O:SiO1 0Ð1[
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Fig[ 5[ The relationship between the fractal dimension and the SiO1:Al1O2 molar ratio when T 099>C\ H1O:Na1O 19\ Na1O:SiO1 0Ð1 and t 0Ð2 hr[
After this point\ a signi_cant rise of the fractal dimension is observed[ The relatively moderate appearance of the _rst peak probably signi_es a smoother mode of conversion and the cor! responding region represents generally the transformation of zeolite X and:or amorphous material into zeolite A[ Another possibility is that the conversion takes place very rapidly and a more irregular behavior than the one observed is left unnoticed[ The second peak denotes a highly irregular type of conversion and involves zeolite A and zeolite A¦HS mixture[ From the results obtained\ it is possible to claim that the fractal dimensions of the borderlines of zeolite A may give signi_cant information about the degree of unpredictability involved with the synthesis procedure[ In Figs 4Ð6\ a common aspect observed is that the most irregular behavior of zeolite A occurs just after it begins to spread widely into the zeolite A¦HS region or at the time it tends to disappear and be converted into the zeolite A¦HS mixture[ In other words\ irregularity is most probable to occur when zeolite A and zeolite A¦HS mixture both hold important ground[ Another important fact is that the most irregular type of behavior is closely related to the variable time[ In the cases where the most unpredictable type of behavior takes place\ as the Na1O:SiO1 or SiO1:Al1O2 molar ratios are varied keeping the synthesis time constant\ the formation of zeolite A seems to occur in a random manner as may be seen from Figs 1"b# and 2"e\f#[ Such random behavior causes unpredictability concerning the reaction times that provide zeolite A[ On the other hand\ the conversion of zeolite A into zeolite X and:or amorphous material or vice versa seems to happen more smoothly and no highly irregular shapes are obtained[ Additionally\ it may be possible to predict about the proximate regions for which no data is available since we learn about the tendency of further conversion of a speci_c type of a zeolite[ For example\ in the case that the Na1O:SiO1 molar ratio exceeds the value of 1 in Fig[ 6\ it is highly probable that zeolite A will _rst be con_ned to a narrower region denoting very
Fig[ 6[ The relationship between the fractal dimension and the Na1O:SiO1 molar ratio when T 099>C\ H1O:Na1O 19\ SiO1:Al1O2 1Ð6[2 and t 0Ð2 hr[
Fractal dimension as a tool to guide zeolite synthesis
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short reaction times and then will tend to disappear[ This will cause a decrease in the fractal dimension since the amount of zeolite A present in the related limited region will not be su.cient to exhibit a highly irregular behavior[
3[ CONCLUSIONS
The fractal dimension may be an e.cient tool to display and quantify the irregular behavior seen during zeolite A synthesis[ We may easily claim that when we obtain the fractal dimensions of the borderlines of the zeolite A regions over a wide range of the variables employed\ it will be possible to deduce the manner of synthesis at points in between\ thus creating the opportunity of making a logical guess about the type of zeolite expected to be formed[ This task may be realized by taking into account the meaning and amount of the irregularity[ However\ the results achieved in this study only involve zeolite A obtained under speci_c conditions and other type of zeolites as well as zeolite A under much di}erent conditions should be separately investigated[ The irregular type of behavior may hold true for the cases where more than one type of zeolite may be synthesized under almost similar initial conditions[ If it may be shown that the conversion of one type of a zeolite to another type occurs each time in a speci_c manner and order then some prediction related to the irregularity will be possible[ There exists some kind of a random behavior during zeolite A synthesis[ The reason for this randomness is probably due to an e}ect not taken into consideration within the course of synthesis[ Zeolites A\ HS and X may be synthesized with quite similar initial conditions so that a factor acting randomly might easily determine the type of the zeolite to be formed[ Since even making small changes in the amounts of the reactants may result in unexpected behavior\ it seems likely that varying the relative amounts of the reactants a}ects the local concentrations and:or the motion in solution and thus the formation of subunits in a random manner[ This fact\ in turn a}ects the type of zeolite to be formed[ The manner of the motion of the reactants for example\ may cause transient changes in the relative amounts and types of subunits thus a}ecting the duration of the formation or transformation of a speci_c zeolite type[ The observation that even small changes in the amounts of the Na1O:SiO1 and SiO1:Al1O2 molar ratios may vary the time necessary for zeolite A to form and that this situation may occur repeatedly over and over in an unexpected manner\ supports this view[
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09[ Giona\ M[\ Schwalm\ W[ A[\ Adrover\ A[\ Schwalm\ M[ K[\ First order kinetics in fractal catalysts] renormalization analysis of the e}ectiveness factor[ Chem[ En`[ Sci[\ 0885\ 40\ 1162Ð1171[ 00[ Weber\ H[\ U[S[ Patent 2\947\794[ 01[ Milton\ R[ M[\ U[S[ Patent 1\771\132[ 02[ Wengin\ P[\ Ueda\ S[ and Koizumi\ M[\ The synthesis of zeolite NaA from homogeneous solutions and studies of its properties[ In New Developments in Zeolite Science and Technolo`y\ Proc[ of the 6th Int[ Zeolite Conf[\ ed[ Y[ Murakami\ A[ Iijima and J[ W[ Ward[ Elsevier\ Tokyo\ 0875[