Quasispherical three-dimensional Ag electrodeposits grown at constant potential and damped free convection exhibit a quasi-isotropic radial growth up to a critical radius rc≃0.3 cm and a mass fractal dimension DM=2.5. For r≫rc, DM→3. The product vrη’ is nearly constant, vr being the radial growth velocity, and η’ the apparent medium viscosity. It appears that vr is determined by the Laplacian field operating between cathode and anode.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

Arvia, Alejandro Jorge

Carro, P.

González, S.

Hernández Creus, A.

Marchiano, Susana Lucy

Salvarezza, Roberto Carlos

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PHYSICAL REVIEW E VOLUME 48, NUMBER 4 OCTOBER 1993Growth of three-dimensional silver fractal electrodeposits under damped free convectionP. Carro, S. L. Marchiano, A. Hernandez Creus, S. Gonzalez, R. C. Salvarezza, and A. J. ArviaDepartamento de Quimica Fisica, Facultad de Quimica, Universidad de La Laguna, Tenerife, Spainand Instituto de Investigaciones Fisicoquimicas Teoricas y Aplicadas (I1VIFTA), Universidad Ãacional de La Plata,La Plata, Argentina(Received 20 January 1993)Quasispherical three-dimensional Ag electrodeposits grown at constant potential and damped freeconvection exhibit a quasi-isotropic radial growth up to a critica1 radius r, -=0.3 cm and a mass fractaldimension DM=2. 5. For r))r„DM~3. The product v„g' is nearly constant, v, being the radialgrowth velocity, and g the apparent medium viscosity. It appears that v, is determined by the Lapla-cian field operating between cathode and anode.PACS number(s): 68.70.+w, 68.55.Jk, 82.20.WtThe formation of a new solid phase through electro-deposition of material on conducting substrates leads todense radial, needlelike, and branched aggregate struc-tures, depending on the experimental conditions [1].Since the pioneering works on the matter appeared [2,3],there has been increasing interest in exploring the fractalnature of rough metal electrodepo sits. Commonly,branched metal aggregates are grown using quasi-two-dimensional (2D) electrochemical cells leading to quasi-2D patterns [1,3] which evolve from diffusion-limited ag-gregation (DLA) patterns with a fractal dimensionDM = 1.7 [4] to den—se radial patterns with DM-=2 [5].Despite the relevance of 3D metal electrodeposits, thefractal characterization of these objects is seldom foundin the literature. It was shown [2] that 3D Cu electro-deposits in the micrometer size range behave as self-similar fractals with D~ =2.43, as predicted by DLA 3Dmodels [4—7]. In contrast, very little is known about 3Dobjects with larger sizes than the corresponding di6'usionlayer thickness, and conclusions derived from 2D objects[8—10] were taken for granted for 3D systems [11,12].The main problem in dealing with 3D electrodepositgrowth in aqueous solutions is the interference of freeconvection, which tends to produce anisotropic growthpatterns [13—16].This Rapid Communication describes aspects relatedto constant-potential damped-free-convection grown 3DAg electrodeposits with a Qnal size on the order of 1 cm.Results demonstrate the role played by the decrease offree convection in favoring the growth of isotropic elec-trodeposits with DM values compatible with the predic-tions of models in Laplacian fields [4]. A change of thedeposit structure from DLA-like to a dense radial patterncan also be observed at advanced growth stages.Runs were made using a Pt spherical cathode (0.076cm average diameter, sphericity deviation less than 10%)placed at the symmetry axis of a 3D cylindrical cell. Thecounterelectrode was a Ag spiral around the workingelectrode to approach a homogeneous primary currentdistribution. A saturated calomel electrode (SCE) wasused as a reference.The base solution was O.SOM Na2S04+ 0.010MHzSO4+0. 005M AgzSO4, and agarose (0.033—0.5 g/100ml range) was added to cover both sol and gel ranges.Sols behave as pseudoplastic Auids, with q' the apparentviscosity coefficient reading at 450-s shear rate, in the1.61—2.18-P range.Ag electrodeposits were made at constant potentialEd= —0.200 V (vs SCE), i.e., —0.580 V apart from the~ Q6- ((j)0.402—~ 00~ ~~t0'0 500 t000 ] 500 2000]0E0.80.60.4r0.2I1000I2000 3000t (s)EL0.4(c)00I4000I8000t(s)FIG. 1. Plots of r vs time for silver electrodeposits.Ed = —0.200 V, 0.50M Na2SO4+0. 010M HpSO4+ 0.005MAg2SO4+x g agarose/100 m1, 25'C. (a) x =0; (b) x=0.07; (c)x =0.5.1063-651X/93/48(4)/2374(4)/$06. 00 48 R2374 1993 The American Physical SocietyI'» ~ li' III ' ~. I( ) lll il I I I( ' ll ~,48 GRO%TH OF THREE-DIMENSIONAL SILVER FRACTAL. . . R2375equilibrium potential of the Ag/Ag+(aq) reversible elec-trode [17]. Current (I vs t) and the charge (g vs t) tran-sients were run with a Princeton Applied Research equip-ment. Runs were performed at 25'C under argon. A de-tailed description of the experimental procedure is givenelsewhere [16—18].In all solutions, the radius of gyration (r) vs time (t)plots display two difFerent regions with a crossoverdefined at (r„t,), where r, is a critical radius involving achange in either the object shape and/or density, and t, isthe time required to reach r, .In agarose-free solution the r vs t plot shows a linearportion (constant U„)followed by another r vs t relation-ship [Fig. 1(a)] involving an increase in U„[16].For r (r,a quasi-isotropic object grows, whereas for r ) r, apinecone-shaped object develops [Fig. 2(a)], although theobject density remains constant with growth.The r vs t plots of objects grown in sols [Fig. 1(b)] ex-hibit a first linear portion for r &r, with a v„valuegreater than that resulting for r ) r, . The value of r,determines the size of the object related to the quasi-(a)E 3—oCAO 2-0, o—1.L(b)E 3cr)O2—I-06I » rI—0.2( pg Cl'(Cm)]» » I» I » I ) I » » 1 I0 - 13 - 1.1 —0,9 - 07 -05tog, .[r(cm)]FIG. 3. log»oQ vs log, or plots for silver electrodeposits,Ed = —0.200 V, 0.50M Na2SO4+0. 010M H2SO4+0. 005MAgzSO4+ x g agarose/100 ml, 25 C. (a) x =0.07; (b) x =0.5.0.35cm(cI )Q5Q cmisotropic to anisotropic growth transition.As the agarose concentration is increased, 3D Agbranched aggregates grown up to Q = 1 C [Figs.2(a) —2(d)] change! their contour from an anisotropic(conelike) to a quasi-isotropic (spherical) one. Simultane-ously, the isotropic growth range extends to greatervalues of Q due to free convection damping. Besides, forr & r„v„decreaseswith agarose concentration.The r vs t plots for objects grown in the gel [Fig. 1(c)]are similar to those already described for sols, althoughin gel U, is smaller than in sols, and its change at r, takesplace without an appreciable change in the object shape.Ag electrodeposits grown in agarose-free solution showD~ =3.0+0.03 (Euclidean volume), and a surface fractaldimension, D, =2.5+0.05 [16]. The value of DM ofquasi-spherical Ag electrodeposits (r (r, ) grown inagarose-containing media was determined fromu —2.LI I I » » I » »—2.5O ++~+ +++++r0.70 cm0.70 cmFIG. 2. Photographs of silver dendritic deposits.Ed = —0.200 V, 0.50M Na2SO4+ 0.010M H2SO4+ 0.005MAgzSO~+x g agarose/100 ml, Q =1C, 25 C. (a) x =0; (b)x=0.033; (c) x=0.070; (d) x =0.5.» » I I » » » » » I-U -C9 -0.7 -0.5t og, .[r( cm)jFIG. 4. log, ~ vs log, or plot for silver electrodeposits,Ed = —0.200 V, 0.50M Na2SO4+ 0.010M H2SO4+ 0.005MAg2SO4+0. 5 g agarose/100 ml, 25 C.R2376 P. CARRO et al. 48TABLE I. Parameters related to the growth of the macroscopic object, 0.50M Na&SO4+0. 010MH2SO4+0. 005M Ag2SO4+ x g agarose/100 ml solutions.(g/100 ml)0 (blank)0.033 (sol)0.040 (sol)0.060 (sol)0.070 (sol)0.500 (gel){10 P)1.1301.6151.8202.1302.180Vr(10 cm s ')2.802.592.512.151.931.23g Vr{10 P cms ')3.164.184.574.584.215(D, /v„)(cm)0.0380.0420.0440.0500.0560.112(cm)0.100.370.350.380.400.30(r (r, )3002.782.702.662.542.50'This value of D~ was obtained from the charge vs volume plots as indicated in Ref. [16].where Q and M are the Ag electrodeposition charge andmass, respectively. For r &r„log, oQ vs log, or linearplots result [Figs. 3(a) and 3(b)], their slopes decreasingfrom DM =3 to DM —=2.5 as agarose concentration is in-creased (Table I). For r ) r, those plots show a slightpositive deviation from linearity which is enhanced in thegel [Fig. 3(b)], indicating a change in the object density.The density change in the gel can be better seenthrough the proportionalityM (2)where p, the object apparent density (Ag and voiddomains), results from the w ~ Q /EV ratio, wher w A isthe Ag atomic weight, F is Faraday's constant, and V isthe object apparent volume, V=(4/3)m. r . Then, DM3can be obtained from the log&op vs log&or plot (Fig. 4).This plot shows a linear decrease of log&~, with log&or—3 —3reaching r„the minimum value p =- 1.58 X 10 g cmi.e., the density of Ag+ ions in solution is approached.For r &r„Eq.(2) leads to DM=2. 5+0.02. Otherwise,for r )0.4 cm (Fig. 4) the limiting value p=2. 8X10—3gcrn is attained, i.e., DM —+3. Hence, a constant-density, more compact object is formed. This isconfirmed by inspecting the front view of an Ag electro-deposit grown in the gel (Fig. 5). The thickness of theouter low-density shell remains nearly constant as r in-creases from r, upwards. For those objects grown in 0.07g agarose/100 ml and 0.5 g agarose/100 ml and r &r„(D~ ) =2.52+0.03, a figure that is close to D~ values re-ported for 3D Cu electrodeposits [2] and computer simu-lations of 3D DLA models [4].The macroscopic behavior of Ag electrodepositsformed for r & r, in sols fits a Stokes-like relation-ship, as the product U„q' remains practically constant(4.4+0.3 X 10 P cm s ') within the range of g' coveredin this work (Table I). The value of 5, the thickness ofthe diffusion layer, can be estimated from the quotientD;/U„=5, where D; is the diffusion coefBcient of Ag+ions in solution. The value of D; becomes practically g'independent; it results in D;=1.1X10 cm s ' for allmedia. The value of 5 is always smaller than r, and it in-creases with agarose concentration. In addition, for con-stant Q, as g' is increased, p, v„,and DM decrease, andthe object size increases (Table I). Mass transport rateequations [19],for a constant density gradient at a planesurface, yield values of 5 considerably smaller than in thegel. This difference reflects the inhuence of free convec-tion on the Ag growth pattern. The significance of thecomparative scale of 5 and the aggregate has been exam-ined for 2D growth [8—10]. The DLA morphology is as-sociated with r & 5. This effect is clearly shown in Table Ias the increase of q' leads to an increase of 5, and to a DMvalue consistent with DLA morphology. The transitionfrom a DLA to a dense aggregate resembles that de-scribed from 2D electrodeposits grown far from equilibri-(c)0.5 ergFICx. 5. Photographs of an Ag electrodeposit at differentstages of growth. Ed= —0.200 V, 0.50M Na~SO4=0. 010MH~SO4+0. 005M Ag2SO4+0. 5 g agarose/100 ml, 25 C. {a)Q=0.040C; (b) Q=0.073C; (c) Q=0.400C; (d) Q=0.700C. Thevalue of r, for this electrodeposit is 0.30 cm.GROWTH OF THREE-DIMENSIONAL SILVER FRACTAL. . . R237750E 40-1.6Els2(b)30—2010—00I10I15I20I25 30r '(cm ')0, 8—0. 4+y+~+0W~0 500++++f I1000 1500I2000I2500I3000 3500t (s)FIG. 6. (a) I ' vs r ' plot and (b) I vs time plot for silver electrodeposits, E&= —0.200 V, 0.50M Na&SO4+0. 010MH&SO4+ 0.005M Ag&SO4+ 0.07 g agarose/100 ml, 25 'C.um [20,21].Ag electrodeposition in agarose-free solution producesdensity gradients at the solution adjacent to the electrodesurface that induce a visible free convection effect at t, .Then, for r & r„5is no longer uniform, and the growthof an anisotropic and compact object (D~ =3) is favored.In this case, individual branches may penetrate thediffusion layers, leaving pockets of undepleted solutionbetween them.On the other hand, isotropic Ag branched aggregatesare grown in the gel irrespective of r, and in this case, anincrease in compactness is observed. This effect may bedue to penetration of branch tips into the diffusion field.Then, as 5 increases, the diffusion layer forms a smoothenvelope around the aggregate. Then, under damped freeconvection the growth of the object appears to be deter-mined by the advance of the growing object front in thesolution under a Laplacian field. Accordingly, a particu-lar deposit morphology is related to a certain diffusionlayer profile.The cell can be modeled as two concentric spheres withr and ro the inner and outer spheres radii, respectively.Then, the primary current distribution is given byI=4rrtc V„/[(1/r)—(1/ro)], (3)where ~ is the solution-specific conductance and V„isthe anode-cathode potential difference corrected for theovervoltage terms. Data given in Fig. 6(a) show that Eq.(3) is fulfilled when Q &0.4 C. It should be noted thatI oc- r results for ro »r. Then, the linear portion in the rvs t plot (Fig. 2) should correspond to a linear I-vs-t rela-tionship. This prediction of the Ohmic model is, in prin-ciple, fulfilled by experimental data [Fig. 6(b)].This work was supported by the Gobierno de Canarias,Spain, under Contract No. 46/01. 06.88 and the ConsejoNacional de Investigaciones Cientificas y Tecnicas(CON ICET), Argentina.[1]M. Matsushita, in The Fractal Approach to the Heterogeneaus Chemistry, edited by D. Avnir (%'iley, New York,1989), p. 161 and references therein.[2] R. M. Brady and R. C. Ball, Nature 309, 225 (1984).[3] M. Matsushita, M. Sano, Y. Hayakawa, H. Honjo, and Y.Sawada, Phys. Rev. Lett. 53, 286 (1984).[4] P. Meakin, in The Fractal Approach to the HeterogeneousChemistry (Ref. [1]),p. 131.[5] B. Grier, E. Ben-Jacob, R. Clarke, and L. M. Sander,Phys. Rev. Lett. 56, 1264 (1986).[6] T. A. Witten and L. M. Sander, Phys. Rev. Lett. 47, 1400(1981).[7] B. B. Mandelbrot, in The Fractal Geometry of Nature,(Freeman, New York, 1982).[8] D. P. Barkey and P. D. LaPorte, J. Electrochem. Soc. 137,1655 (1990).[9] D. Barkey, J. Electrochem. Soc. 138, 2912 (1991).[10]D. Barkey, P. Garik, E. Ben-Jacob, B. Miller, and B. Orr,J. Electrochem. Soc. 139, 1044 (1992).[11]G. Daccord and R. Lenormand, Nature 325, 41 (1987).[12] E. Chassaing, B.Sapoval, G. Daccord, and R. Lenormand,J. Electroanal. Chem. 279, 67 (1990).[13]J. P. ICallungal and A. J. Barduhn, AIChE J. 23, 294(1977).[14]J. S. Huang and A. J. Barduhn, AIChE J.31, 747 (1985).[15] S. H. Tirmizi and W. N. Gill, J. Cryst. Growth 85, 488(1987).[16]A. Hernandez-Creus, A. E. Bolzan, P. Carro, S. Gonzalez,R. C. Salvarezza, S. L. Marchiano, and A. J. Arvia, J.Electroanal. Chem. 336, 85 (1992).[17]A. Hernandez-Creus, P. Carro, S. Gonzalez, R. C. Sal-varezza, and A. J. Arvia, J. Electrochem. Soc. 139, 1064(1992).[18]G. O. Aspinall, Polysaccharides (Pergamon, Oxford, 1970),p. 149.[19]B. Levich, Physiochemical Hydrodynamics (Prentice-Hall,Englewood ClifT's, NJ, 1967).[20] E. Ben-Jacob, P. Garik, T. Muller, and D. Grier, Phys.Rev. A 38, 1370 (1988); E. Ben-Jacob and P. Garik, Na-ture 343, 523 (1990).[21] P. Garik, D. Barkey, E. Ben-Jacob, E. Botchner, N. Brox-holm, B. Miller, B. Orr, and R. Zamir, Phys. Rev. Lett.62, 2703 (1989).View publication stats

Growth of three-dimensional silver fractal electrodeposits under damped free convection

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Growth of three-dimensional silver fractal electrodeposits under damped free convection

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