Langmuir 1991, 7, 1822-1826
1822
Crystallization of Hydroxyapatite on Polymers Evangelos D a h , +Jannis K. Kallitsis,+and Petros G. Koutsoukos'J Department of Chemistry, University of Patras, GR-26110, Patras, Greece, and Department of Chemical Engineering and the Institute of Chemical Engineering and Processes at High Temperatures, P.O. Box 1239, GR-26110, Patras, Greece Received August 30,1990. In Final Form: February 25,1991 Four copolymers were prepared through the reaction of NN-bis[(diethoxyphosphinyl)methyl]-1,4benzenediaminewith 1,4- or 1,3-benzenediamineand terephthaloyl or isophthaloyl or sebacoyl dichloride at varying molar ratios. A fifth copolymer was prepared by copolymerization of bis(3-aminopheny1)phoephinicacid and 1,3-benzenediaminewith ieophthaloyldichloridein dimethylamine. All five copolymers contained phosphinyl groups and upon introduction in calcium phosphate aqueous solutions, supersaturated only with respect to 8-tricalcium phosphate and hydroxyapatite, three of them induced the precipitation of stoichiometric hydroxyapatite, (Caa(PO&OH, HAP). The investigation of the crystal growth process was done at constant supersaturation,which enabled us to measure even very low rates of crystallization. The apparentgrowthorderwas found to be 1.25f 0.18, avalue found for the crystallization of HAP on various substrates. The surface energy estimate of 92 mJ m-? from the kinetic data was of the same order of magnitude for the overgrowth of HAP on both inorganic and polymeric substrates. The rates of precipitation showed a linear dependence on the phosphate content of each copolymer,while their structureplayed b o a decisiverole. Thus, "open"structuredcopolymersyielded high rates of precipitation while copolymers in which the phosphorus-containinggroups were "buried", not being accessible to the Ca2+ ions in solution, failed to induce hydroxyapatite formation. It is suggested that the phosphoruscontaining groups act as the active centers for nucleation of the inorganic phase.
Introduction The deposition of sparingly soluble salts on polymers is of paramount importance not only for fundamental research concerning biomineralizationl-3 but also for practical applications,such as the design and development of new materials suitable for prosthetic applications in bone and teeth.' So far, structural aspects of the substrates employed and their relationship to the overgrowingphase have been considered for the explanation of observed cases of deposition of sparingly soluble salts on polymers. Hydroxyapatite (Caa(PO&OH, HAP) is considered as the model compound for the inorganicconstituent of bone and teeth. Blood serum may be considered as an aqueous solution, supersaturated with respect to a number of calcium phosphates (in order of decreasing solubility): calcium phosphate dihydrate (CaHPOc2H20,DCPD),octacalcium phosphate (CaH(PO&2,5H20, OCP), tricalcium phosphate (Ca3(PO&, @-TCP),and HAP. Due, however, to the presence of macromolecules such as proteins, enzymes, etc. in biological fluids, extensivecomplexation of the free calcium takes place, thus reducing the actual supersaturation, which is just sufficient for the formation of &TCP and HAP at physiologicalconditions. The formation of TCP, however, at such conditions has never been convincingly demonstrated." As a result, it t
Department of Chemistry.
* Department of Chemical Engineering and the Institute of Chemical Engineering and Processes at High Temperatures. (1)Mann, S.;Heywood, B. R.; Rajam, S.; Brichall, J. D. Nature 1988, 334,692. (2) Addadi,L.; Weiner,S.Proc. Natl. Acad. Sci. U.S.A. 1986,82,4110. (3)Addddi, L.; Moradian, J.; Shay, E.; Maroudas, N. G.;Weiner, S. Proc. Natl. Acad. Sci. U.S.A. 1987,84,2732. (4)Williams, D. F. Shell Polym. 1986,9,75. (5)Howell, D. S.;Pita,J. C.; Marquez, J. F.; Madruga, J. E.J. Clin. Invest. 1968,47,112. (6)Boekey, A. L.; Posner, A. S. J. Phys. Chem. 1976,80,40. (7)Moreno, E. C.; Zahradnik, R. T.; Glazman, A.; Hwu, R. Calcif. Tissue Res. 1977,24,47.
0743-7463f 91f 2407-1822$02.50f 0
has been recommended that in vitro experiments should be conducted at low supersaturations.8*g A number of studies have been done on the formation of HAP on synthetic HAP seed ~ r y s t a l s as ~ ~well J ~ as on other substrates.1s14 In these investigationsthe capability of both inorganic and organic substrates was examined with respect to their capability of inducing HAP nucleation and subsequent growth. However, psrticularly when polymeric substrates having certain desirable chemical and mechanical properties need to be used as substrates for HAP deposition, it is not always possible to use them due to lack of their ability to provide the active sites for nucleation and growth of calcium phosphates and HAP in particular. In the present work we have used phosphorus-containing copolymers1bJ6having the main structural characteristicsof the comerciallyavailable polymeric products under the trade name Nomex and Kevlar, as nucleators of HAP. The main reason for our choice of polymers was their outstanding mechanical and chemical resistance properties, which would make them serious candidates for implants." The introduction of dimethoxyphosphinyl groups was decisive for the selective deposition of HAP on the otherwise inert Nomex and Kevlar polymers. The introduction of such groups not only offers the possibility of having a more favorable polymeric conformation but also may provide the nucleation sites for HAP through Ca2+ion accumulation.1sJ8 The evaluation of the polymers employed for HAP nucleation and (8)Tomazic, B.;Nancollae, G.H. J . Colloid Interface Sci. 197450, 451. (9)Tomazic, B.; Tomson, M. B.; Nancollae, G.H. Calcif. Tissue Res. 1976,19, 263. (10)Nancollae, G.H.;Mohan, M. S . Arch. Oral Biol. 1970,15,731. (11)Koutsoukos, P. G.; Amjad, Z.; Tomeon, M. B.; Nancollae, G.H. J. Am. Chem. SOC.1980,102,1553. (12)Koutsoukoe,P. G.;Nancollas,G.H. J.Cryst. Growth 1981,59,10. (13)Koutaoukos, P.G.;Nancollas, G.H.colloids Surf. 1987,28,95. (14)Dalae, E.;Kallitsis, J.; Koutsoukos, P. G.J. Cryst. Growth 1988, 89,287. (15)Thiele, H.;Awed, A. J. Biomed. Mater. Res. 1969,3,431. (16)Kallitsie, J.; Tsolis, A. J. Appl. Polym. Sci. 1986,31,635. (17)American Cyanamid Co. Eur. Pat. 0 258692 A2, 1987. (18)Crenshaw, M.A.; Rietedt, H.Biomineralization 1976,8,1.
0 1991 American Chemical Society
Crystallization of Hydroxyapatite on Polymers
chart I
"R:p=0
L
-r-k
s
I
r Y
growth was done by the constant supersaturation approach,*lwhich is unique for the accuracy and reproducibility it offers in kinetic measurements of crystal growth from aqueous solutions.
Experimental Section A. Preparation of t h e Copolymers Used as Substrates. The copolymers employed as substrates are shown in Chart I. N,"-Bis[ (diethoxyphosphiny1)methyl)-1,Cbenzenediamine (compound I)
I
was prepared as described elsewhere." Copolymers A-D were synthesized through the reaction of various concentrations of I with 1,4-or 1,3-benzenediamineand terephthaloyl or isophthaloyl or sebacoyl dichloride according to procedures described elsewhere in detail.10 Copolymer E was obtained from the copolymerization of the bis(3-aminopheny1)phosphinicacid and 1,3benzenediamine with isophthaloyl dichloride in dimethylamine at 0 "C. The copolymers were obtained as powders and were characterized by infrared spectroscopy(Perkin-Elmer Model 437 grating IR spectrometer) and X-ray diffraction (Phillips 1300/00). Specific surface areas were measured by a multiple point BET nitrogen adsorption isotherm, using NTHe mixtures (PerkinElmer sorptometer, Model 212D). The phosphorus content was determined as vanadomolybdate.lB."0 The properties of the copolymersof Chart I, used in this work are summarized in Table (19) Kallitsie, J. Eur. Polym. J. 1986,22, 257. (20) Standard Methods for Examinution of Water and Wastewater;
A P H A Washington, DC, 1976; p 476.
Langmuir, Vol. 7, No. 8, 1991 1823 Table I. Characteristics of Copolymers Used as Substrates for HAP Overgrowth expt no. polymerO [ x / ( x + y)] X 100 % P (w/w) SSA/m2 g-1 7.1 1.7 10.3 1 c1 5.3 1.3 9.5 2 C2 3.2 0.8 8.6 3 C3 4 A 7.6 1.6 7.2 7.6 5 B 1.5 14.8 5.0 6 E 1.1 15.7 7.1 1.7 17.2 7 Di 12.0 2.2 11.4 8 Dz 2.4 0.6 13.1 9 D3 a Letters correspond to the copolymers of Chart I and subscripts to different ratios x / ( x + y).
I. The powders were suspended in 0.1 mol dm-3calcium nitrate solutions for 24 h under continuous stirring. Next they were washed with 1 L of distilled water. Analysis of the washings showed no calcium desorption. Preequilibration with calcium was necessary for avoiding any alteration of the solution supersaturation, caused possibly by the Ca2+uptake, which under our experimental conditions was negligible. Analyses for total phosphorus following the preequilibration did not show any phosphorus release in the solution, which reflected the stability of the C-P bonds of the polymers prepared. B. Crystallization Experimentr. All experiments were done at 25.0 f 0.1 OC in a 0.260 dm3 double-walled reactor thermostated with circulating water from a water bath. Stock Solutionsof calcium nitrate and potassium dihydrogen phosphate were prepared from solid reagents (Merck, purise) using triply distilled, COrfree water. Standardization was carried as described elsewhereeBPrior to standardization, all solutions were filtered through membrane fiiters (0.22 pm, Millipore, Bedford, MA). The supersaturated solutions were prepared in the g h reactor by mixing equal volumes (0.1 dm3 each) of calcium and phosphate solutions. The solution pH was adjusted by the slow addition of standard potassium hydroxide under nitrogen atmosphere which was ensured, by bubbling water-vapor-saturated prepurified nitrogen (Linde Hellas) through the supersaturated solution. All experiments were conducted at pH 7.40. Following pH adjustment, all solutions in this work were stable at least for 3 days, as indicated from the constancy of pH and of the solution composition. Past a waiting period of 4 h for each experiment, a quantity of 50 mg of powdered copolymer was introduced in the supersaturated solution. The powder was thoroughly dispersed in the magnetically stirred supersaturated solutions. It should be noted that the preequilibration of the polymers with the 0.1 mol dm-3 calcium nitrate solutions did not have any effect on their capability of inducing HAP overgrowth. In preliminary experiments it was verified that polymers introduced in the supersaturated solutions without any pretreatment induced HAP precipitation as well. Preequilibration was considered necessary considering the limited ion binding capacity of the phosphoruscontaining polymer, which however was not effectively demonstrated in our experimental conditions. The precipitation procBB8, accompanied with proton release, triggered the addition of calcium nitrate, potassium dihydrogen phosphate, and potassium hydroxide titrants from a pH-stat, modified in a way to allow the solution supersaturation to be kept constant.11.21-agThe precipitation process was monitored by a glass/saturated calomel pair of electrodes (Metrohm) standardized with NBS standard buffer solutions, while periodical analysis of samples withdrawn from the working solution confirmed the constancy of calcium and phosphate concentrations throughout the course of precipitation within 2 % .ll
Results and Discussion The overgrowth of HAP on the water dispersedpolymers A, B, and C (Chart I) started immediately without any (21) Tomon, M.B.;Nancollas, G. H. Science
1978,200,1069.
(22)Amjad,Z.; Koutsoukce, P. G.;Nancoh,G . H. J. Colloidlnterface Sci. 1984, 101, 260. (23)Heughebaert J. C.; Zawacki, S.; Nancollas, G. H. J. Colloid Interface Scr. 1990, 135, 20.
D a b et al.
1824 Langmuir, Vol. 7,No. 8, 1991
Table 11. Cryatallitation of HAP at Surtained Superraturation on Phorphorur-Containing Polymeric Subrtntes. rate/lP expt Cat/lo-' AGl kJ mol-' mol min-1 m-2 no. polymer moldm-s DCPD OCP TCP HAP +1.5 +0.1 -1.6 -4.7 22.6 1 c1 0.80 +1.6 +0.2 -1.5 -4.6 21.2 2 c1 0.75 18.7 +1.7 +0.3 -1.3 -4.5 3 c1 0.70 +1.9 +0.4 -1.2 -4.4 18.4 4 c1 0.65 +1.5 +0.1 -1.6 -4.7 19.6 5 C2 0.80 +1.5 +0.1 -1.6 -4.7 17.6 6 Cs 0.80 4.4 0.80 +1.5 +0.1 -1.6 -4.7 7 A +1.5 +0.1 -1.6 -4.7 0.8 8 B 0.80 c 0.80 +1.5 +0.1 -1.6 -4.7 9 E C 0.80 +1.5 +0.1 -1.6 -4.7 D1 10 +1.5 +0.1 -1.6 -4.7 c D2 0.80 11 c 0.80 +1.5 +0.1 -1.6 -4.7 Ds 12 I, Total phosphate was 1.67 X lo-'mol dm-8. pH = 7.40,25 "C. b Cat, total calcium. e No growth.
appreciable induction time. Polymers D and E failed to induce overgrowth at least to extents that would be detected through changes of the physicochemical parameters of the supersaturated solutions. The experimental conditions are summarized in Table 11. Ionic speciation in solution was calculated from the proton dissociation and ion pair formation constants for calcium and phosphate, the mass balance, and electroneutrality conditionsby successiveapproximationsfor the ionic strength." It should be noted that although the formation of HAP is thermodynamically possible, the formation of this salt may occur on the condition that the substrate contains active centers for the formation of the HAP nuclei. When the same substrates, without phosphinyl groupswere used to seed the supersaturated solutions, no growth occurred. The existence of the phosphinyl groups on the polymers provided the active centers required for the induction of the HAP overgrowth. The driving force of the calcium phosphate polymorphs is the change in Gibbs free energy, AG, for the transfer from the supersaturated solution to equilibrium
In eq 2 IP is the ionic product of the precipitating salt, its solubility product, u the number of ions, R, the gas constant, and T the absolute temperature. The following values were used for the thermodynamic solubility products of the various calcium phosphates: for HAP, K , O = 4.7 X 10-69;u for TCP, K , O = 1.2 X 10-29;25for OCP, K , O = 8.3 X 1W 28 (valueobtained from ref 26 after correction for ion pair formation); and for DCPD,KSo= 2.49 X 10-7.27 The relative solution supersaturation, u, is defined in eq 2 as K,O
[(Ca2+)s(P0,s)a(OH)]I/' U =
(K:)
- (Ka0)'/'=
'1'
(IP)"' - (K,'))'/' (2) (K:) where parentheses denote activities and KSois the thermodynamicsolubilityproduct of HAP" and was found to (24) Mc Dowel,H.; Gregory, T. M.; Brown, W. E. J. Res. Notl. Bur.
Stand., Sect. A 1977, M A , 273.
(28) Cr ow, T. M.; Moreno, E. C.; Patel, J. M.;Brown, W. E. J. Res. Notl. Bur.%ond., Sect. A 1974, 78A, 667. (28) Moreno, E. C.; Brown, W. E.; &born, G. Soil Su. R o c . 1960,W. (27) M a r c h 4 R. Ph. D.Thenin, State University of New York at Buffalo, Bullalo, NY 1970.
--
N
E c
-5.79
- 5.77 lop {IP:'
- 5.75 K':
- sa3
I
Figure 1. Kinetics of the overgrowth of HAP on phosphoruscontaining copolymers: pH 7.40,25"C.Growth on CIcopolymer. Insert: Kinetics of growth on ( 0 )HAP seed crystals (ref 11) and ( 0 )phospholipids (ref 28). strongly influence the rate of HAP precipitation as may be seen from Table 11. The dependence of the rate of precipitation, R, on the relative solution supersaturation may be described by eq 31e12
R = kS((IP)'/' - (K,O)'/')"
(3)
In eq 3 k is a proportionality constant and S a function of the active growth sites, which were'constant as the amount of polymer used to induce precipitation did not have any significant effect on the rate of precipitation normalized per unit surface area of the substrate. The exponent n in the above equation is a constant taken as the apparent growth order for the HAP overgrowth. Logarithmicplots of the rate of HAP formation on PPTA copolymer as function of the numerator of eq 2, which is linearly proportional to the relative supersaturation with respect to HAP, yielded the straight line shown in Figure 1. From the slope of this line, a value of n = 1.25 f 0.18 was found, the same as that for the seeded growth of HAP not only on synthetic HAP seed crystalsll but also on synthetic phospholipids.28 This coincidence may suggest that the mechanism of HAP formation is similar. Stoichiometric analysis of the inorganic phase showed a stoichiometry of Ca:P = 1.67 f 0.02. The analyeis was done by using samples of the phosphorylated polymers as blanks and the stoichiometry found was consistent with the solution concentrations of calcium and phosphate, which remained constant throughout the precipitation process. Small deviations from the stoichiometric coefficients of the growing crystalline phase would cause significant alterations in the solution composition. Moreover the exclusive formation of HAP was confirmed by powder X-ray diffraction analysis and by infrared spectroscopy. Comparative infrared spectra are shown in Figure 2. Examination of Tables I and I1 shows that the phosphorus content and the nature of the polymers are of key importance to the formation of HAP nuclei and their subsequent growth. In Figure 3 the effect of phosphorus content on the rates of mineralization is shown. Considering the polarity of the P-0 bond in which the negative charge is shifted toward the oxygen atom, it may be suggested that the formation of HAP may be initiated through the interaction of Ca2+ions with the negative end of the P-0 bond. Thus, entities such as Ca-0-P may (28) Mas, E.;Ioannou, P. V.; Koutaoukoe, P. C. Longmuir 1)89,6, 157.
Langmuir, Vol. 7, No. 8, 1991 1825
Crystallization of Hydroxyapatite on Polymers
ym -0
Mm *so0 L o w
-1
moo
Wavrnumbar /
Hoo Ixx)
r)o
100 600
400
cm-'
Figure 2. Infrared spectra of (a) synthetic hydroxyapatite, (b) PPTA copolymer, and (c) PPTA copolymer with hydroxyapa-
tite overgrowth.
2.1 -
22
'E
Figure 4. Relative arrangement of Ca atoms in the 010 plane of hydroxyapatite ( 0 )and of P atoms of monomer compound I in the same plane (0).Hydrogenbonds are indicated by a broken
.-c
-:
20-
7
1.9-
E
line.
\
0
As a result the chains "open", not being able to form
n
L
35
45 55 Phorpborur content(% mdr)
65
Figure 3. Dependenceof the rates of hydroxyapatitedeposition on the phosphorus content of PPTA copolymers.
be considered as the active sites for the nucleation process. Even stronger interaction between the P-containing groups and Ca2+ions is expected if partial hydrolysis of the >P(=O)-O-R bond to give >P(=O)-OH groups occurs during the equilibration with aqueous media, especially those containing Ca2+ ions. Ion binding of polymers containing >P(=O)-OH groups is well documented in the literature.29 Further work has shown that the presence of larger numbers of -P-OH groups on the polymers accelerated the process of HAP overgrowth.g0 Thus, in the same copolymer series, higher phosphorus content resulted in higher growth rates (Table 11). PPTA copolymers yielded higher HAP formation rates while the PMIA copolymersfailed to induce percipitation, despite the fact that the two categories of copolymers contain the same type of active groups. This difference may be due to their different conformation. Examinationof the conformation of PPTA31and PMIA32polymers shows that the former is linear and the chains are parallel with the maximum possible developmentof the hydrogen bonds. In the latter polymer the chain is ladderlike and the hydrogen bonds are formed every other amidic group. The introduction of the bulky phosphinylmethylgroup in polymer PPTA resulted in disruption of the linearity of the molecule,33 in which the chains are combined with hydrogen bonds. (29) Alexnndratoe, 5.D.; Strand, M. A.; Quillen, D. R.; Walder, A. J. Macromolecules 1986,18,829. (30) Dahs, E.; Kallitak, J.; Kouteoukoe, P. G.Colloids Surf., in press. (31) Nofiholt, M. 0. Eur. Polym. J . 1974,10,799. (32) Hakida, H.; Chatani, Y.;Tadokoro, H. J. Polym. Sci. 1976, 14, 427. (33) N~~topoulim, V.; Germain,G.;Kallitak, J.; Voliotis, S. Acta Crystallogr, Sect. C 1987, C43, 245.
hydrogen bonds, thus allowing for the formation of the HAP nuclei. In the case of PMIA on the other hand, in which the hydrogen bonds alternate, the introduction of the bulky phosphinylmethyl group group may favor the formation of a hydrogen bond between the -NH group of a chain and its - P 4 group. This, would result in preservation of the closed structure of the polymer, reducing consequently the number of active groups favoring the formation of HAP nuclei on the polymeric substrate. The presence of phosphorus-containing groups, which may be ionized in aqueous media, on synthetic polymers and on b i o p o l y m e r ~has ~ ~been ~ ~ shown to be responsible for the deposition of HAP. The PMIA copolymers showed however that it is not only the phosphorus groups or the phosphorus content of the copolymers but also the "openness" of the structure of the polymer, determined by hydrogen bonding between the polymeric chains. Since the monomeric units in the polymers retain theirgeometry,= lookinge.g. at the relative positions of Ca2+ ions in the 010 plane of HAP and P-containing groups in the same plane of the monomer (compound I), shown in Figure 4, it may be seen that nucleation of HAP is possible only when this favorable arrangement is allowed from the overall conformation of the copolymer used as substrate. PMIA copolymers that retain a closed conformation are unfavorable for the formation of the critical HAP nucleus. Similar considerations have been applied for the mineralization of biopolymers (collagen f i b r i l ~ ) . ~ * ~ ' j An important parameter for the description of both crystal growth and nucleation rates is the interfacial tension, y, between the solid substrate and the aqueous environment. Unfortunately, in this case y is not estab(34) Glimcher, M. J. In The Chemistry and Biology of Mineralized Cinnetuue Tissues; Vein, A,, Ed.;Ehvier: Amstardam, 1981; pp 617-
675.
(35) Glimcher, M. J. In Handbook of Physiology 7 : Endocrinology Vol. VIII; Greep, R. O., htwood, E.R., Eds.; American Phyeiological Society: Washington, DC, 1978; pp 26-116.
1826 Langmuir, Vol. 7, No.8, 1991
lishedunambiguously98but it may be used for comparisons between various substrates. The rate of nucleation, according to the “classical” nucleation theory is3’
-0476
c
Dalas et al. 0
(4)
In eq 4, D is the diffusion coefficient,d is the mean ionic diameter, /3 is a shape factor (32 for spheres), u is the molecular volume of the HAP overgrowth (=formulaweight/ k is Boltzmann’s constant, T is the (9 X 6.023 X absolute temperature, and 51 is the ratio IP/K,O for HAP. In a logarithmic form, eq 4 may be written as
-c K
(
According to eq 5 it is expected that the rates of HAP formation vary linearly with l/(ln 51)2. The data obtained from the kineticsof HAP overgrowthon PPTA copolymers yielded the straight line shown in Figure 5. From the slope of this line a value of 93 mJ m-2 was estimated for the HAP overgrowth. It is interesting to note that the correspondingvalues of surface energy for the overgrowth of HAP on various substrates have been reported as 152 mJ m-2on dicalcium phosphate dihydrate,= 70 mJ m-2 on collagen,13and 55 mJ m-2 on phospho1ipids.m Thus an average of 92 mJ m-2 may be obtained for the HAP based on heterogeneous nucleation processes. Considering the fact that the various surface energy values were obtained by using the constant composition approach, additional evidence for the consistency of the experimental system is provided in this work. (36)Bikerman, J. J. Phys. Status Solidi 1966,10,3. (37) Nielsen,A. E.Kinetic8 ojPrecipitation;Pergamon: Oxford, 19&4,
p 18. (38) Koutnoukoe,P.G.; Nancollas,G.H.J. Cryet. Growth 1981,53,10.
In0
x IO”
Figure 5. Dependenceof the rates of HAP overgrowth on PPTA copolymers on l/(ln Q)*.
Conclusions In the present work, it has been shown that it is possible to induce precipitation of hydroxyapatite selectively on polymers by introducing phosphorus-containing groups (by forming copolymers in this case) and by ensuring “open”structure, which make the phosphorus-containing groups accesible to the bulk solution calcium ions, a fact which appears to be necessary for the formation of the critical nucleus. The crystallization process is mechanistically similar to that of the growth of HAP on synthetic HAP crystals and other substrates.
Acknowledgment. We express our thanks to Dr.K. Gravalos of the University of Patras for the preparation of the copolymer poly(phenyleneisophthalamide)-co-(3,3diphenylphosphiny1)-p-hydroxyisophthalamide.
