Langmuir 1991, 7, 1235-1240
1235
Comparative Study of the Surface Hydroxyl Groups of Fumed and Precipitated Silicas. 4. Infrared Study of Dehydroxylation by Thermal Treatments J. P. Gallas and J. C. Lavalley' Catalyse et Spectrochimie URA 04.414, ISMRa, Universitb, F 14050 Caen Cedex, France
A. Burneau and 0. Barres Laboratoire de Spectromgtrie de Vibrations, Universitb de Nancy I, B.P. 239, F 54506 Vandoeuvre Lhs Nancy Cedex, France Received March 22,1990. In Final Form: November 21,1990 Four types of silica, fumed, precipitated, gel and ex-ethoxy,activated at different temperatures, have been studied by IR spectroscopy in the v(OH) range in order to characterize the various types of SiOH groups, to compare their amount and their evolution with temperature, according to the nature of the sample. Fumed, precipitated, and gel samples activated at 973 K present the same amount of free hydroxyls. Taking into account gravimetric measurements, this allows the determination of the number of OH/nm2 at room temperature, 4,14,and 12,respectively. The large values obtained for precipitated and gel silicas are explained by the presence of a great number of inner and internal hydroxyls, the decrease of which has been followed versus temperature using DzO exchange and tert-butyl alcohol retroexchange. Inner OH groups are preponderant in the precipitated sample while internal groups are more important in the gel silica. The ex-ethoxy sample presents only inner groups. Their amount cannot be related to its surface area, since the later is underestimated due to the cross section of nitrogen used for BET determinations. The study also allows determination of the dehydroxylation process; several steps occur, the first one always being the departure of the more strongly bonded vicinal hydroxyl groups. The length of the silanol chains has been differentiated according to the preparation mode of the samples.
Introduction In part 2 of this series,' we presented an infrared study of hydroxyl groups of four types of silica (fumed, precipitated, gel, ex-ethoxy), all the samples being nondehydroxylated. In particular, the concept of inner and outer silanols was invoked in order to explain the results relative to water adsorption. Large differences were found in the total number and in the distribution of various types of hydroxyl groups according to the mode of preparation. In this paper we examine how these differences influence the dehydroxylation processes. Of the many works devoted to the study of the dehydroxylation of silica?+ only a few have been concerned with a comparative examination of different samples, under the same experimental condition^.^*^ Moreover the mechanism of dehydroxylation is generally oversimplified, being often limited to the following reaction: 23Si-OH
-
LSi-O-Sif0
+ H20
In the present study both transmission and diffuse reflectance IR spectra have been obtained in the v(0H) range using in particular isotopic exchanges. The results have been completed by gravimetric measurements which allow quantitative determinations of the hydroxyls. (1) Bumeau, A.; Barres, 0.; Gallas, J. P.; Lavalley, J. C. Langmuir 1990,6, 1364.
( 2 ) Kiselev, A. V.; Lygin, V. I. Infrared Spectra of Surface Compounds; John Wiley & Sons: New York, 1975. ( 3 ) Morrow, B. A.; Cody, I. A.; Lee, L. S. M. J. Phys. Chem. 1976,80, 761.
, R. S . J. Am. Chem. SOC.1958,62, il68. {a, L. S.;Titova, T. I. Langmuir 1987,3,
Experimental Section The materials used have already been described in ref 1. Samples A, P, G, and S are respectively a fumed silica (Aerosil 2001, precipitated (RhGne-Poulenc),gel (Rh8ne-Poulenc),and an ex-ethoxy sample. Their BET areas slightly depend on the gas used (for Nz or Ar they are 215 or 164,201or 160,392or 300, and 3.8 or 2.9 m2 gl for samples A, P, G, and S, respectively).s Those furnished by the suppliers are 200,175,and 320 m*gl for samples A, P, and G, respectively, and are those used in this paper. They have been heated at different temperatures under vacuum either as self-supportingdisks (transmissiontechnique) or as a powder mixed with KBr (diffuse reflectance). Each type of silica disk (16mm diameter, 10-20 mg mass) was pressed under 50 MPa. All spectra have been recorded at room temperature with a Fourier-transform infrared (FT-IR) spectrometer, either a Nicolet 60 SX or a Brucker IFS-88 equipped with a Harrick DRA 2CI attachement and a HVC-DRP cell.' Isotopic exchanges with DzO and retroexchanges with tertbutyl alcohol have been carried out 3 times at indicated temperatures, under a pressure of 1500 Pa during 15 min, followed Pa. by evacuation at a pressure less than Transmission IR spectraof the samples, silica S expected, are presented in normalized absorbance scales.' DRIFT spectraare shown in Kubelka-Munk units, F(R) = (1- R)*/2R. Results The mass of the different samples, A, P, and G, has been measured as a function of the evacuation temperature (Figure 1). Its decrease varies from A to G following A < P < G, which is in agreement with the total intensity of the v(0H) bands after water elimination, e.g. after evacuation at 373 K (Figure 7, ref 1). In the previous paper,l different silanol groups have been distinguished according to their perturbation and to ~
(8) Grillet, Y. To be submitted for publication in Adu. Colloid Znterface Sci.
0743-7463/91/2407-1235$02.50/0 0 1991 American Chemical Society
Gallas et al.
1236 Langmuir, Vol. 7, No. 6, 1991
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'
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Figure 1. Loss of mass of different silica samples as a function of the temperature of evacuation. their affinity or accessibility toward water: free silanols, us, divided into three groups according to their sensitivity to water (i) OHb, which are not inclined to adsorb water, considered as isolated on the outer surface (v(0H) 37403750 cm-l), (ii) OHII,on which water adsorbs according to .-HOH or --OH2 structures and situated on outer surfaces (u(0H) 3730-3740 cm-l), (iii) OHI, with the lowest wavenumber, on which water adsorbs with the -HOH.structure, and localized on inner surfaces (u(OH) 36903730 cm-l); terminal vicinal silanols, ut, 3715 cm-l; bound vicinal silanols, Ub, 3460-3530 cm-l; internal silanol, pint, 3650-3670 cm-', defined following their insensitivity to D2O exchange. However, due to the heterogeneity of the hydroxyls, there is an overlapping of the corresponding bands and the classification proposed above is only speculative. Figure 2 shows changes that occur when degassing temperatures were 523,723, and 873 K (only difference spectra are presented for reasons of clarity). Evacuation at 523 K (a) first eliminates the bound vicinal silanols of lower frequency (4= 3500,3450,3420, and 3380 cm-l for samples A, P, G, and S, respectively). There is a concomitant disappearance of a small number of terminal vicinal silanols in the case of sample A. At 723 K, all the vicinal silanols have practically disappeared. Subtracted spectra (Figure 2b) allow us to determine the corresponding 4 at 3545,3525,3515, and 3480 cm-l for samples A, P, G, and S, respectively. In the case of samples P, G, and S, elimination of a large amount of internal or inner silanols maskes that of terminal vicinal silanols, which is clearer for sample A. In all cases there is a concomitant creation of free silanols. The latter is smaller for sample S and the corresponding vf frequency is situated at a lower wavenumber (3733 cm- instead of 3742-3747 cm-l). When the degassing temperature is higher than 723 K, the decrease of intensity is mainly near 3735 and 3670 cm-l (Figure 212). The silanols that disappear are therefore different from those eliminated below 723 K and are considered respectively as a part of free silanols (geminal for instance) and inner or internal ones. Spectra of samples degassed a t 973 K only show one u(OH) band (Figure 3). It is almost the same (sharp and situated at 3747 cm-l) in the case of samples A, P, and G
3600 3300 WAVENUMBER
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3800 3300 WAVENUMBER
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Figure 2. Spectral variations induced by heating samples A, G, P, and S at different temperatures: (a) 523-373 K; (b) 723-523 K; (c) 873-723 K.
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Figure 3. Infrared transmission spectra of the different silicas after evacuation at 973 K. but broader and at lower frequency (3743 cm-l) for sample S. It is assigned to single isolated silanols. Geminal Silanols. Their existence is shown by =Si magic angle spinning (MAS) NMR which well differentiates geminal Si(OH)2 and single Si(0H) s i l a n ~ l s .As~ suminggthat the -9Oppm peak is characteristicof Si(OH)2, it has been foundlo that the ratio Si(OH)z/(SiOH + Si(0H)z) of silicon atoms holding hydroxyls keeps a rather constant value (-0.17), whatever the sample. Its evolution with temperature is difficult to measure precisely due to the line broadening.9-1' For low degassing temperatures, it can be assumed that most geminal silanols are hydrogen bonded and are therefore not easily discernible by infrared spectroscopy from the other hydrogen bonded silanol groups. For activation between about 673 and 973 K, infrared spectroscopy has shown that the isolated SiOH peak for silicas (9) Sindorf, D. W.; Maciel, G. E. J. Am. Chem.SOC.1983,105,1487.
(10) Legrand, A. P.; Hommel, H.; Tdbi, H.; Miquel, J. L.; Tougne, P. Colloids Surf., in press. (11) Morrow, B. A.; Gay, I. D. J. Phys. Chem. 1988,92, 5669.
Langmuir, Vol. 7, No. 6,1991 1237
Study of the Surface Hydroxyl Groups of Silicas
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Figure 5. Transmission spectra of a Suprasil sample (a) and of silica A exchanged by D20 at 673 K (v(0H) absorbances have been adjusted for comparison). 3600
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Figure 4. v(0H) bands of the different silicas after exchange by D20 at room temperature (a), 473 K (b), 673 K (c), and 873 K (d). Table I. Spectral Characteristics of the Band Due to Internal Silanols (Band Remaining after DIO Exchange) sample 298 K 473 K 673 K 873 K A
abs/(mS/s)
0.036 3655 0.036 3665 0.075 3655
0.023 3660 0.035 3660 0.052 3660
0.015 3670 0.020
0.004
Figure 6. Transmission spectra of silica A (a) activated at 673 K (- - -), then (b) exchanged by DzO at 673 K (-), and finally (c) retroexchanged by tert-butyl alcohol at room temperature Y (- -). Spectrum d .) corresponds to spectra a-c. P abs/(mS/s) 0.008 0.004 Y 673 K. Note that the spectrum of internal silanols is similar to those presented by vitreous silicas: Figure 5 allows A, G, and P is asymmetric to low wavenumber (see Figure comparison of the IR spectrum of internal OH groups after 3 for 973 K) and part of this might be due to geminal DzO exchange of sample A followed by evacuation a t 673 silanol species,12but no proof of this has been forthcoming. K and that of a Suprasil sample. Inner Silanols. As shown in ref 1, part of inner silInternal Silanols. Accordingto the literature,13J4they anols can be exchanged by DzO to give a broad band near are largely inaccessible to isotope exchange with DzO. We 2710 cm-' and a retroexchange with tert-butyl alcohol have exchanged a t 298,473,673,and 873 K the four samples showed that only part of the inner SiOD band was (Figure 4) previously and finally evacuated a t the same subsequently exchanged back to SiOH. Figure 6 shows temperature. The wavenumber and the normalized abthe relevant spectra for silica A, which had been activated sorbance of the band due to nonexchangeable OH groups at 673 K. The retroexchange with the alcohol a t room are reported in Table I (the band appearing at 3365 cm-l temperature shows that more that 97% of the isolated corresponds to the combination band (Y + S)OD of free SiOH band intensity of the free silanols can be regenerated. OD groups)! It appears that the amount of internal siIt can be seen that the band due to the inner OD groups, lanols decreases with increasing temperature. The apcharacterized by the residual band at 2710 cm-l after retparent shift toward higher wavenumbers of the residual band confirmsthe heterogeneity of the internal s i l a n ~ l s , ~ ~ J ~roexchange (Figure 6 4 , does not totally correspond to the shoulder a t such a wavenumber after DzO exchange (Figure those absorbing a t the lower wavenumber disappearing 6b), which means that part of the inner silanols are first. Such a low wavenumber (3500 cm-l) could be due exchangeable with the alcohol. This is confirmed by the to hydrogen bonding. difference of the absorbance near 3670 cm-l between the Table I shows a rather regular decrease with temperspectrum of the initially activated silica and that of the ature of the quantity of internal silanols for sample A, same sample exchangedwithD20 and retroexchanged with while a sharp decrease appears for samples G and P around tert-butyl alcohol (Figure 6d). From the intensity ratios, 80% of the absorbance at 3670 cm-l is due to inner sil(12) Van Rooamalen, A. J.; Mol, J. C. J. Phys. Chem. 1978,82,2748. anols, but only 66 % of such silanols are accessible to tert(13) Davydov, V. Ya.; Zhuravlev, L. T.; Kiselev, A. V. R k s . J. Phys. butyl alcohol. Profiles of bands due to internal silanol Chem. 1964,38,1108. (14) Tyler, A. J.; Hambleton, F. H.;Hockey,J.A. J. of Catal. 1969,13, groups (Figure 6b) and inner ones nonaccessible to tert35. butyl alcohol (Figure 6d) are quite similar showing that (15) Walrafen, S. E.; Samanta, S. R. J. Chem. Phys. 1978,69,493. both hydroxyls are in the same environment. (16) Hartwig, C. M. J . Chem. Phys. 1977,66,227. Y
G
abs/(mS/s) , . ,
0.003
-
(e.
1238 Langmuir, Vol. 7,No. 6, 1991
Gallas et al. NOH/ nmp
P
T/ K
3
Figure 7. Transmission spectra of silica G (a) activated at 673 K (- - -1, then (b) exchanged by D20 at 673 K (-1, and finally (c) retroexchanged by tert-butyl alcohol at room temperature (- * -1. Spectrum d (- -1 corresponds to spectra a-c.
-
AI \ Figure 8. Transmission spectra of silica S (a) activated at 673 K (- - -1, then (b) exchanged by DzO at 673 K (-1, and finally (c) retroexchanged by tert-butyl alcohol at room temperature (-
*
-).
The same experiment carried out on sample G shows that the characteristic wavenumber of inner OD groups (2730cm-l) is higher than for sample A while their amount is larger. Quantitative results will be specified in the discussion. Retroexchange experiments show that only about 50% of the total number of the inner silanols is exchangeable in the case of sample G (Figure 7). The spectrum of silica S activated at 673 K shows only one u(OH) band, broad, which does not allow observation, as was the case with sample A, the band due to isolated silanols. About 96% of silanols are exchangeable with DzO; however retroexchange experiments with tert-butyl alcohol shows that only a very small part of them is accessible to such a molecule (Figure 8). One can therefore deduce that silanols of sample S are almost exclusively inner ones (i.e. sample S is ultramicroporous).
473
'
673
ar73
Figure 9. Variation of the hydroxyl population versus temperature for silicas A, P, and G.
Discussion (1) Evolution of the Number of Hydroxyl Groups with Temperature. Gravimetric measurements (Figure 1) do not allow us to determine the absolute number of the hydroxyl groups at different temperatures since our study is limited to activation at 973 K, a temperature not sufficient to eliminate all hydroxyl groups.3 Infrared spectra of samples A, P, and G activated a t 973 K show a similar band (Figure 3) both in wavenumber and in intensity. Several authors have measured the integrated absorption coefficient of isolated OH groups; different values have been obtained: 2820,173040,18-3500,19 and 425520L mol-' cm-2. We used a value of 3000 L mol-' cm-2 since it led to a number of hydroxyl groups remaining after evacuation at 973 K of about 1.2 OH nm-2, a value well in agreement with that found by Curthoysm et al. for a similar silica sample activated in the same conditions. From this value and the curves in Figure 1, one can determine the variation of the number of OH groups with the evacuation temperature (Figure 9)and the number of OH groups a t room temperature: 4,12,and 14 OH nm-2 for samples A, G, and P, respectively. The choice of another value for the integrated absorption coefficient, for instance 4255 L mol-l cm-2, would lead to similar curves but shifted to lower values of NOH,of about 0.35 OH nm-2, which does not significantly change the number of OH groups at room temperature. Moreover curves of Figure 9 are quite similar to those independently obtained by Grillet8 on the same samples. Results obtained by this author relative to the very low apparent surface area of sample S using dinitrogen or argon as adsorbent, and ours showingthe occurrenceof a v(OH) band due to the residual OH groups after evacuation a t 973 K different from that observed on the other samples, do not permit us to determine the number of OH groups on sample S as a function of temperature. (17) Van Cauwelaert, F.H.; Jacobs, P. A.; Uytterhoeven,J. B. J. Phys. Chem. 1972, 76,1434. (18) Galkin, G. A.; Kiselev, A. V.;Lygin, V. I. Russ. J. Phye. Chem. 1969,43, 1117. (19) Baumgarten,E.;Wagner,R.;Lentea-Wagner, C.Fresenius'Z.Am1. Chem. 1989,335,375. (20) Curthoys, G.;Davydov, V. Ya.; Kiselev, A. V.; Kiselev, S. A.; Kuznetaov, B. V. J. Colloid Interface Sci. 1974, 48,68.
Study of the Surface Hydroxyl Groups of Silicas
Langmuir, Vol. 7, No. 6, 1991 1239 Table 11. Population of Outer and Inner Silanols (OH nm-2) at Different Temperatures, T sample tin kout T,K NOH Nout Ni. P Ninbm NiA 58.3 3184 673 2.28 1.66 0.61 4 0.155 0.46 P
/
P
G
773 873 39.3 3207 673 773 873 22.2 2755 673 873
1.91 1.54 6.67 4.35 2.36 6.69 2.53
1.55 1.34 3.70 2.87 2.05 3.19 1.98
0.34 0.21 2.97 1.46 0.31 3.5 0.55
3.6 5 20 20 6.7 6.7 7.7
0.095 0.042 0.148 0.073 0.046 0.522 0.071
0.25 0.17 2.82 1.39 0.26 2.98 0.48
dm3 cm-2), tb is the molar absorption coefficient of inner OH (m~l-~dm~cm-~),andfisaconstant, (1.66 X 10-3)Sm/s (mol L-' cm3 m-2 nm2) (see ref l),where S is the specific area of the sample (m2g-l), m is the mass of the disk (g), and s is the area of the disk (cm2). From relations 1-3 we deduce
Nod- 1 lout
+--1 A i n
kout
(4)
eIout
Figure 10 allowsus to determine kout and ei,, and, therefore, Their values are reported in Table 11. The values obtained for koutare in agreement with those reported in literature.17J8 Those of tin are in Ain/lout general lower than those already in particular 0 0.01 for sample G whose spectra show a greater difference between inner and internal silanols. Figure 10. Plots allowing determination of kout and ein from relation 4. Results show that the amount of both internal and inner groups (Nb)is larger for precipitated and gel silicas. From (2) Quantities of Outer and Inner OH Groups Ni, and p, it is possible to evaluate N i n b d (Table 11). According to the Sample. After activation at 673 K or The same amount of internal OH groups is observed for higher, free outer, inner, and internal silanols are present samples A and P, while the number of inner groups is and contribute therefore to the u(OH)band. It is possible much greater in the case of precipitated and gel samples. to distinguish the OH band due to free and outer silanols The repartition between internal and inner groups may vf (3745 cm-l) from that due to inner and internal groups be related to the microscopic texture of the samples. vin (3670 cm-9. Moreover, since the profiles of the bands (3) Dehydroxylation Process. The following mechdue to internal and inner silanols are quite similar, it is anism is generally considered a t temperatures up to 723 possible to determine the OH integrated intensity (lout), K in cm-I, due to free outer silanols and the absorbance (Ab) due to inner or internal groups: Ai, is obtained by multiplying the band due to internal groups (OHnonexchangeable by D20) by a factor p chosen in such a way that the substraction of Ain from the overall v(0H) band cancels the absorbance at 3670 cm-I. The proportion of (the reaction may be considered with or without the gemNinternall (Nintemal + Ninner) is givey by l/p. inal silanol in parentheses). Such a process would lead to When two species give rise to two different bands, with the simultaneous disappearance of terminal and bound a relation between their quantities, it is possible to vicinal silanols and to the concomitant appearance of determine the absorption coefficients and the amount of isolated silanols when considering geminal groups as each species by varying the experimental conditions.21The starting ones. Results obtained in the case of sample A, method is applied to quantify the amount of both inner for which ut is well differentiated from uht, do not show and internal groups (Nin) and outer free OH groups (Nout) however such a tendency; the intensity ratio of bands at of each sample at different temperatures. 3715 and 3520 cm-l, studied from difference spectra of The total amount of silanol groups NOH is given by Figure samples activated at different temperature (Figure 2), is 9 found to increase with temperature, suggesting that the relative number of terminal silanols to that of bound ones (1) NOH = N i n + Nout increases with temperature. This is even clearer in the Due to the variation with temperature of the half width case of precipitated and gel silicas since their absorption of the band corresponding to the outer OH, we use the between 3700 and 3730 cm-l stays almost constant up to whereas we use the absorbance integrated intensity lout, 523 K while those at 3520 cm-' largely decrease. The Ai, of the band due to inner OH. The following relations results are rather in favor of chains of bound hydroxyls have been used: on the hydroxylated compounds, the cooperative effects due to the hydrogen bonds increasing the interactions and lout = Noutkoutf (2) making easier the removal of the bound silanols with the Ain = Nbef (3) lower frequency where kout is the integrated coefficient of outer OH (mol-' (22)Stephenson,C.W.;Jack,K.H.Trans. Br. Ceram. SOC.1960,59, Nout and N i n for a given sample.
(21)Fujii, Y.;Yamada, H.; Mizuta, M. J. Phys. Chem. 1988,92,6768.
397.
Gallas et al.
1240 Langmuir, Vol. 7, No. 6, 1991 (HO)\
OH
O ,H
si
si’
OH
si /
-
(HO)
0
si/\si
+ Hz0 (6)
Reaction 7 is predominant a t low temperature for the precipited and gel silicas (constancyof the number of terminal silanols), while reaction 6 is more probable in the case of the fumed sample, as shown by the appearance of isolated groups. The condensation of silanols is expected to be a more facile process the greater the number of participating H-bonded SiOH groups. Therefore reaction 7 is expected to occur at a temperature lower than that in reaction 6, which in turn will occur at temperature lower than that in reaction 5. Reactions 5-7 are complete at 723 K although gravimetric measurements show that half of the total number of the initial silanols persist on silicas P and G. This number (6-7 OH nm-2) is too high to correspond only to free hydroxyl groups. Many reasons can be invoked to explain it, in particular the simultaneous presence of internal and inner hydroxyl groups and the undervaluation of the surface areas due to the cross section u of the molecules of the gas used (Nz) for BET measurements. We may for instance suppose the presence of buckles or chains of polysilicic acid not completely polymerized on the surface of precipitated silicas.23 In such a disordered structure, an important proportion of silanols would not be taken into account in the surface determination. Moreover,the existence of such buckles with several silicon atoms holding two OH groups (geminal silanols) would also explain the presence of a great number of internal and inner silanols. A partial elimination of the internal hydroxyls already occurs by heating silicas P and G from 523 to 723 K. This is only clearly evident in the case of fumed silica above 723 K. In all cases, it is complete when (23) Yates, D. E.; Healy, T. W., J. Colloid Interface Sci. 1976,559.
the temperature reaches 873 K. Above 873 K, only free hydroxyls stay on the surface. Due to the absence of vicinal groups at these temperatures, it is necessary to involve proton migration, although reported more difficult on silica than on a l ~ m i n a A . ~NMR and Raman studyz4has shown that dehydroxylation leads a t 873 K to the formation of cycles with three oxygen and three silicon atoms, their number being maximum at 873 K. Above this temperature, surface reconstructions occur to eliminate strains. Such reconstructions at high temperature must certainly be involved to explain the known hydrophibicity of silicas treated at high temperature. The behavior of the ex-ethoxy sample, S, is different due to the presence of a small number of free hydroxyls; however the total number of OH groups is important from gravimetric measurementss and can be only explained considering the presence of internal hydroxyls. Most of these groups are accessible to water ( u = 0.106 nm2) as shown by the results from D2O exchangebut not to nitrogen (a = 0.162 nm2), used for the determination of surface areas. The dehydroxylation process of the ex-ethoxy sample is certainly similar to that of other samples since the wavenumber of the eliminated OH increases with temperature, their lower value relative to that observed in the other cases resulting from stronger perturbations. I t leads to the appearance of bands due to free OH whose wavenumber increases with the temperature (3715-3743 cm-l) to reach a value close to that observed for the other samples after evacuation at 973 K (Figure 3). This band is always wider than that observed on the spectra of other samples, due certainly to the structure of the sample S. The ultramicroporosity leads to pertubed hydroxyls and makes the dehydroxylation more difficult, owing to diffusion phenomena.
Acknowledgment. We gratefully acknowledge financial help from CNRS (Action de Recherche Concede: “HydroxylesSuperficiels des Silices,Alumineset Aluminosilicates”). Registry No. SiOz, 7631-86-9. (24) Brinker, C. J.; Kirpatrick, R. J.; Tallant, D. R.; Bunker, B. C.; Montez,B. J. Non-Cryst. Solids 1988, 99,418.
