research article diffusion-limited aggregation in potato...

Hindawi Publishing CorporationAdvances in Condensed Matter PhysicsVolume 2013 Article ID 781058 7 pageshttpdxdoiorg1011552013781058

Research ArticleDiffusion-Limited Aggregation in Potato Starch and HydrogenBorate Electrolyte System

Tuhina Tiwari1 Manindra Kumar1 Kamlesh Pandey2

Neelam Srivastava1 and P C Srivastava3

1 Department of Physics (MMV) BHU Varanasi 221005 India2 Centre for Experimental Mineralogy and Petrology University of Allahabad Allahabad 211002 India3 Department of Physics BHU Varanasi 221005 India

Correspondence should be addressed to Neelam Srivastava neelamsrivastava bhuyahoocoin

Received 27 May 2013 Accepted 11 September 2013

Academic Editor Dilip Kanhere

Copyright copy 2013 Tuhina Tiwari et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Natural growth of diffusion-limited aggregate (DLA) without any external stimuli in boric acid doped starch system is reportedhere Fractals grown were confirmed to be of diffusion-limited aggregate (DLA) pattern having fractal dimension sim149 Effect ofsubstrate and humidity on growth pattern has also been discussed The existence of a different vibration band of H

3BO3in FTIR

confirmed that growth structures are related to boric acid XRD pattern has shown broad peak along with some sharp peaks Broadpeak is related to starchrsquos amorphous nature as where intense sharp peaks are due to boric acid

1 Introduction

Nature prefers symmetry Mountains snowflakes branchesof trees shores of continent and so forth are some visibleexamples of symmetrical structures in nature More patternsof self-similar structures encountered with mankind arecancer piles and so forth Retinal circulation of the normalhuman retinal vasculature is also statistically self-similarand fractal Hence fractals are one of the most importanttopics in biology and medicinal field which generally coversthe study of (a) the understanding of spatial shape andbranching structure and (b) the analysis of time varyingsignal By knowing the branching structures of tissues andorgans biologists use this to discriminate between normaland pathological structures

This hasmade the growth phenomenon of complex struc-ture an interesting area of research for a long time [1ndash11] Several models have been presented to understand thephenomena out of which diffusion limited aggregationmodelhad receivedmuch attention as this is very common in nature[12ndash14] Fractals are self-similar objects with non integerdimension they are also important to determine the macro-scopic properties of the system by microscopic dynamics of

system which has been an area of scientific interest for along time Electrodeposition chemical dissolution electricalbreakdown and chemical redox reaction are all the examplesof experimentally observed fractals

Under external stimuli transport properties of dispersedand mixed ion conductors are studied using percolationtheory along with fractal concept It is supposed that clustersofmolecules are randomly formed in solution and attached toeach other At saturation clusters are large enough to nucleateand then grow on their own or other solid surfaces Forion transport polymer matrix is supposed to have flexibilitycomparable to liquid systems Considering this fact polymerelectrolytes were recognized as ideal frameworks for thedeveloping of fractal structure due to presence of randomwalks of free ions if the walking species has aggregatingtendency [15ndash17] literature shows the growth of boric acidcrystals and formation of clusters of various shapes and sizes[18ndash20] Hence it has been planned to study fractal growingphenomenon in starch doped boric acid systems

In present study large size (2-3 cm) fractal growthwithoutany external stimuli has been investigated The structure isdue to boric acid clusterswhich are confirmed by the presenceof intense hydrogen borate peaks in XRD analysis as well

2 Advances in Condensed Matter Physics

as FTIR spectroscopy Possible chemical structure has beenproposed for the system SEM has been used to reveal thesurface morphology

2 Experimental

21 Sample Preparation Potato starch (PS) (C6H10O5)119899

(Loba Chemie) H3BO3(Anchor Laboratories) Glutaralde-

hyde (GA) (C5H8O2) (Loba Chemie) and distilled water (as

a solvent) was used in the study Materials were used asreceived GA is added in the system Samples have beenprepared using solution cast technique at 30∘C For 1 gm ofstarch 03 gmH

3BO3and 2mLGAwaterwere taken together

in 10mL of solvent mixture was stirred at 30∘C on magneticstirrer for one hour and heated till it dries Samples were thenleft in atmosphere to dry at room temperature sim20ndash24∘CWithin one week fractals were visible

22 Devices and Technique Optical photographs of the sam-ples were taken by Sony Cybershot (DSC-S730) and foropticalmicrograph cameraCatalyst biotechCC130 is used IRspectral studies have been carried out by Jasco FTIR 5300to confirm the complexation SEM micrographs have beentaken using JEOL JXA 8100 Electron Probe Micro-analyserPhilips X-pert model with Cu119870

120572(120582 = 1542 A) is used for

XRD study Crystallite size (119863) andmicrostrain (120585) have beencalculated using Scherrerrsquos semiempirical formula

119863 = 09

120582

120573 cos 120579

120585 =

120573

4 tan 120579

(1)

where 120573 is the full width half maxima of the highest intensitypeak and 120582 is the Cu119870

120572wavelength = 154 A

3 Result and Discussion

31 Computation of Fractal Dimension Optical photographof the fractal is shown in Figure 1(a) while close view of theramified structure is given in Figures 1(b) and 1(c)

The microscopic views 1(b) and 1(c) of the growthstructure indicates growth is starting froma seed on growingit is divided into branches no two tips are touching eachother they are changing their pathways by bending whenthey reach to be very close to each other or the growth stopsthere

All these observations are indicating that the pattern ofgrowth is of the DLA type which is further confirmed byfractal dimension

Fractal dimension has been calculated by extracting thedata from the real picture 1(b) using software ldquoxyExtractrdquoTheextracted image of the pattern is given in Figure 2

There are differentmethods for calculating fractal dimen-sion ldquo119889

119891rdquo for example box counting method [21 22]

mass radius relation [23] scaling relation of two-pointdensity-density correlation function [24]We have calculated

the fractal dimension by calculating filled area [25] and theformula used in calculation is

119889

119891=

log [119872 (NL) 119872 (119871)]log119873

(2)

where 119871 represents the unit length 119873 is the number of unitlength 119872(NL) is the filled area of a square of length NLand119872(119871) is the filled area of a square of unit length Fractaldimension calculated by this is found to be 149

32 Effect of Substrate and Storage Condition on Fractal For-mation As suggested by earlier study [18] growth pattern ofboric acid depends strongly on the type of material and thesurface condition of substrate We have monitored growthat two different substrates in two different conditions Thesubstrates were borosilicate glass and poly propylene at twodifferent humidity levels The main observations were asfollows

(i) In glass Petri dish samples stuck to it while in poly-propylene they can be easily taken out as shown inoptical photograph given in Figure 3(a)

(ii) Besides branches become sharper in glass Petri dishinstead of polypropylene This sharpness was furthercontrolled by atmospheric humidity

(iii) In low humidity atmosphere (20RH) the growthis quite thick and multilayer hence branches are notvery clear whereas in high humid atmosphere (70RH) the branches are quite sharp and well definedwith reduced multilayer

(iv) The samples kept in 20RHwere becoming orange incolour while samples kept in 70 RHwere colourlessas depicted in Figures 3(b) and 3(c)

Further the effect of humidity and substrate on fractaldimension is summarized in Table 1

Effect of Humidity on Fractal Dimension In low humidityatmosphere (20 RH) the growth is quite thick and multi-layer resulting in greater fractal dimension whereas in highhumid atmosphere (70RH) the branches are quite sharpand well defined with reduced multilayer resulting in lowerfractal dimension

Effect of Substrate on Fractal Dimension Sharp branches aremore pronounced in glass Petri dish instead of polypropyleneeven at a low humidity level some thick multilayer branchescan be seen in polypropylene dish therefore fractal dimen-sion in polypropylene substrate is greater

Sha et al [18] while discussing the bifurcation growth ofboric acid from its water solution have discussed that boricacid molecules have an affinity towards borate glass Thisaffinity of boric acid towards borate glass substrate seems tobe the reason why samples strongly stuck on borate glass andcannot be taken out In the same paper they also discussedthat on PVCorVaseline coated glass no structural growth canbe seen In present system growth is seen in both the casesthat is in borosilicate glass and Polypropylene Petri dish

Advances in Condensed Matter Physics 3

(a) (b) (c)

Figure 1 (a) Optical photograph of the fractal (b) close view of the ramified structure and (c) fractal pattern where tips are not touchingeach other

200

400

600

800

1000

1200

(au

)

200 400 600 800 1000 1200(au)

Figure 2 Extracted image of the real pattern

Table 1 Fractal dimension of sample in different substrates a differ-ent humidity

S no Humidity Substrate Fractal dimension1 20 Glass 1822 20 Polypropylene 1893 70 Glass 1444 70 Polypropylene 149

Here it seems that starch matrix is playing an importantrole in fractal growth phenomenon Though a very clearexplanation of nucleation in the present study is not foundit is known that any kind of temperature or concentrationfluctuation [15 18] can cause nucleation In present casesample was prepared in methanol medium and left to dryin atmosphere The excessive methanol will evaporate with

time Probably evaporating molecule is disturbing the localconcentration and when suitable numbers of particle arearound then they result in nucleation site Besides it is alsoobserved that whenever the Petri dish surface is not smoothdensity of fractal growth was higher especially in case of glassPetri dish this was very prominent

The difference in colour found was attributed to thepresence of glutaraldehyde As it is a known fact in aqueoussolution of glutaraldehyde GA is present in the monomerform while nonaqueous form contains polymeric chain [2627] GA is known to be in colourless to pale straw colouredform It is supposed that the polymeric form containslarge number of monomer units so the colour darkens andbecomes orange in colour As the sample was kept in 70RH which means abundance of water so the GA was presentin monomer form while the sample kept in 20 RH wasdeprived of water so the GA was in the polymeric formHence the difference in colour occurs

33 Morphological Study (SEM) Figure 4 shows SEMmicro-graph at 200 magnificationsThe micrographs show granuleswith some sticky structure on that The granule can beperceptibly assigned to potato starch morphology as wehave discussed in our earlier studies [28 29] The granulesize varies from 62 120583m to 35 120583m As seen in the opticalmicrograph the fractal structures are embossed on the starchfilm For gold coating (required for SEM measurement)material is dried up to 10minus6 Torr hence it seems that layerof embossed structures was detached from the film Thusonly an impression is left on the starch structure indicatingpresence of boric acid which will further be confirmed usingother techniques in the paper The size of crystallites inembossed structure is estimated by magnifying the image1600 and is found to vary from sim8 120583m to 22120583m Theestimation has a chance of being underrestimated and notexact as it was quite difficult to separate out the embossedstructure size from the grains size of potato starch


In polypropylene In glass

(a)

RHsim70 () RHsim20 ()

8x 5001205838x 500120583

(b)


8x 5001205838x 500120583

(c)

Figure 3 (a) Sample in polypropylene and glass Petri dishes (b) Sample kept in different humidity levels in polypropylene Petri dish(c) Sample kept in different humidity levels in glass Petri dish

Figure 4 SEM micrograph of the complexed system

34 Possible Chemical Structure It is a known fact thathydrogen borate splits into tetrahydroxyborate and hydrogenion on addition of water as given by the following reaction

H3BO3+H2O 997888rarr B(OH)

4

minus+H+ (3)

Structure possibilities of boric acid with phenol groupsare discussed in literature which shows that while interactingwith materials having multiple hydroxyl groups boric aciduses two hydroxyl groups and then a water molecule isliberated Applying the same concept the possible structurefor starch and boric acid are presented In Figure 5(a)structure of cross-linked host polymer with GA is given [30]There is possibility for tetrahydroxyborate anion to makebond with its electronegative oxygen at any ndashOH site byremoving water One such structure is shown in Figure 5(b)The structure is supported by FTIR where the removal ofndashOH from the structure is clear

35 FTIR Analysis For structural changes vibrational spec-troscopy is one of the major tools and is widely used Bycomparing the prepared materials peak with that of originalonemay get a picture of the elements and their bond vibrationthrough FTIR analysis In present study system has beenanalyzed in transmission mode FTIR Figure 6(a) shows thetransmitted peaks of pure as well as complexed materialsInferences drawn are listed as follows

(i) Most of the H3BO3peaks are present in the com-

plexed system

(ii) The peaks at 641 cmminus1 and 811 cmminus1 are shifted to648 cmminus1 and 803 cmminus1 which indicate the interactionof matrix and boric acid


OHOH

OH OH OH

OHOHOHOHOH

HO

HO

O

O

O

O

O

OO

O

O

O

HH HH

H HH H H

H

HHHH

HHHHH

H

(a)

OH

OHHOHHOH

OH

OHOH

OHOHOHOHHO

HO

OH

O

OO

O

OO

O

O

O

B

O

OO

HHHH

HHHHH

H

HH H H

H HH H H

H

(b)

Figure 5 Structure of potato starch with GA (a) before and (b) after complexation

4000 3000 2000 1000Wavenumber (cmminus1)

Tran

smiss

ion

()

(A)

(B)

(C)

(D)

(a)

020406080

100

400900140019002400290034003900

S4 S3S2 S1

Wavenumber (cmminus1)

T(

)

(b)

Figure 6 (a) FTIR of (A) potato starch (B) GA (C) boric acid and (D) complex material (b) FTIR of S1 sample kept in 20RH that isrelative humidity (without growth region) S2 sample kept in 70RH (without growth region) S3 Sample kept in 70RH (growth regiononly) S4 Sample kept in 20RH (growth region only)

(iii) The 1026 cmminus1 peak in complexed system is due to theformation of structure forming B

4-O groups

(iv) 1194 1462 cmminus1 in the pure hydrogen borate is presentalmost at the samewave number showing vibration ofatoms in ndashO-Blt bond in orthoboric acid

(v) Thepeak at 1623 cmminus1 is solely due to presence of alde-hyde group

(vi) The intermolecular hydrogen bonding is present inhydrogen borate at 3214 cmminus1 and in the complex at3216 cmminus1

It must be noted that in the pure starch there are a lotof hydrogen bonding peaks indicating the presence of waterbut in the complexed system only one such peak at 3216 cmminus1could be found This is an obvious change since addition ofboth GA and borate is decreasing the concentration of ndashOHbonds Beside this both are occupying the space in matrix


0

20

40

60

80

100

120

140

160

10 20 30 40 50 60

Inte

nsity

(au

)

121100

2120579

Figure 7 XRD pattern of complexed system

hence will also reduce the amount of water absorbed in thesystem

It has been tried to analyse the spectroscopic changes inthe data of the following

(i) sample kept in 20RH that is relative humidity(without growth region) S1

(ii) sample kept in 70RH (without growth region) S2

(iii) sample kept in 70RH (growth region only) S3

(iv) sample kept in 20RH (growth region only) S4

Figure 6(b) shows the IR spectra of above four materialsThe data taken from the matrix shows where there is nofractals growth peaks of boric acid are missing and theportion taken from fractal growth area are dominated byboric acid peaks confirming that ramified patterns are madeup of boric acid

As stated earlier that the fractals are grown in twodifferent atmospheres one in the ambient (70RH) and otherin the low humidity (20RH) we found that surprisinglyfractals from 20RHor low humidity atmosphere have somepeaks related to starch also whereas the sample kept at ambi-ent atmosphere or 70RHhave very nominal representativesof starch peaks It is supposed to be due to the possibilityof easy movement of boric acid ion assisted by presence ofhigh water content but when the sample kept at 20RH themovement of boric acid ions is correlatedwith starch and saltions are comparatively more bound with starch matrix

36 XRD Analysis The XRD pattern of complexed materialis shown in Figure 7 The data is in agreement with JCPDSand clears the presence of hydrogen borate The peaks withtheir corresponding planes are given in Figure 7 The twomajor intense peaks present at the position (∘2120579) 148997 and275618 corresponds to the plane (100) and (121) of hydrogenborate From theXRDpattern it is evident that the presence ofbiopolymer as a host matrix is giving the amorphous natureto the complexed system

4 Conclusion

Phenomenon of large size (of cm dimension) fractal growthwithout external stimuli in the potato starch system hasbeen studied Growth pattern was found to be of DLA typewith fractal dimension of 149 Fractals dimension dependson humidity and substrate At high humidity and in glasssubstrate its value is low System is of amorphous nature butthe presence of H

3BO3is giving some crystalline peak in

XRD pattern Fractal structures were found to be embossedon granule structure of potato starch Further the crystallitesize of embossed structure estimated from SEM is found tobe of the order of crystallite size estimated from XRD

Acknowledgment

DST New Delhi is acknowledged for providing the financialsupport to the project on ldquoDevelopment of sodium ionconducting-electrochemical applicationrdquo (DSTReference no-SRS2CMP00652007 dated 08042008) Instruments pro-cured in the project are used in present work

References

[1] T A Witten and L M Sander ldquoDiffusion-limited aggregationa kinetic critical phenomenonrdquo Physical Review Letters vol 47no 19 pp 1400ndash1403 1981

[2] H E Stanley and N Ostrowski On Growth and Form Fractaland Non Fractal Patterns in Physics Martinus Nijhoff LeidenThe Netherlands 1986

[3] B Mandelbrot Fractals Form Chance and Dimension Free-man San Francisco Calif USA 1977

[4] R Jullien ldquoAggregation phenomena and fractal aggregatesrdquoContemporary Physics vol 28 pp 477ndash493 1987

[5] J Feder Fractals Plenum Press New York NY USA 1988[6] F Family and T Vicsek Dynamic of Fractal Surfaces World

Scientific Singapore 1991[7] T Vicsek Fractal Growth Phenomena World Scientific Singa-

pore 2nd edition 1992[8] P Meakin ldquoThe growth of rough surfaces and interfacesrdquo

Physics Report vol 235 no 4-5 pp 189ndash289 1993[9] A L Barabasi and H E Stanley Fractal Concepts in Surface

Growth CambridgeUniversity Press NewYork NYUSA 1995[10] T Halpin-Healy and Y-C Zhang ldquoKinetic roughening phe-

nomena stochastic growth directed polymers and all thataspects of multidisciplinary statistical mechanicsrdquo PhysicsReport vol 254 no 4ndash6 pp 215ndash414 1995

[11] M Marsili A Maritan F Toigo and J R Banavar ldquoStochasticgrowth equations and reparametrization invariancerdquo Reviews ofModern Physics vol 68 no 4 pp 963ndash983 1996

[12] J T Donnell II and L X Finegold ldquoTesting of aggregationmeasurement techniques for intramembranous particlesrdquo Bio-physical Journal vol 35 no 3 pp 783ndash798 1981

[13] P Meakin D P Landau K K Mon and H B Schuttler EdsComputer Simulation Studies in Condensed Matter SpringerBerlin Germany 1988

[14] M Nazzarro F Nieto and A J Ramirez-Pastor ldquoInfluence ofsurface heterogeneities on the formation of diffusion-limitedaggregatesrdquo Surface Science vol 497 no 1ndash3 pp 275ndash284 2002


[15] N Srivastava A Chandra and S Chandra ldquoDense branchedgrowth of (SCN)x and ion transport in the poly(ethyleneoxide)NH4SCN polymer electrolyterdquo Physical Review B vol 52 no 1

pp 225ndash230 1995[16] A Chandra and S Chandra ldquoExperimental observation of

large-size fractals in ion-conducting polymer electrolyte filmsrdquoPhysical Review B vol 49 no 1 pp 633ndash636 1994

[17] A Chandra and S Chandra ldquoLarge size fractals in ion con-ducting polymers a novel experimental observationrdquo CurrentScience vol 64 no 10 pp 755ndash757 1993

[18] Q Sha J Zhang and J Sun ldquoBifurcation growth of boric acidcrystals observed at the air-solution interfacerdquo Physica StatusSolidi A vol 147 no 1 pp 129ndash134 1995

[19] M Tachikawa ldquoA density functional study on hydrated clustersof orthoboric acid B(OH)

3(H2O)119899(119899 = 1ndash5)rdquo Journal of Molec-

ular Structure vol 710 no 1ndash3 pp 139ndash150 2004[20] W Wang Y Zhang and K Huang ldquoPrediction of a family of

cage-shaped boric acid clustersrdquo Journal of Physical ChemistryB vol 109 no 18 pp 8562ndash8564 2005

[21] B B Mandelbrot The Fractal Geometry of Nature WH Free-man amp Co San Francisco Calif USA 1982

[22] H R Bittner P Wlczek and M Sernetz ldquoCharacterization offractal biological objects by image analysisrdquo Acta Stereologicavol 8 no 1 pp 31ndash40 1989

[23] BMandelbrot ldquoHow long is the coast of Britain Statistical self-similarity and fractional dimensionrdquo Science vol 156 no 3775pp 636ndash638 1967

[24] A Bunde and S Havlin Fractals and Disordered SystemsSpringer New York NY USA 1991

[25] T Vicsek Fractal Growth Phenomena World Scientific Singa-pore 1987

[26] E Arthur Robertson and R L Schultz ldquoThe impurities incommercial glutaraldehyde and their effect on the fixation ofbrainrdquo Journal of Ultrasructure Research vol 30 no 3-4 pp275ndash287 1970

[27] I Migneault C Dartiguenave M J Bertrand and K CWaldron ldquoGlutaraldehyde behavior in aqueous solution reac-tion with proteins and application to enzyme crosslinkingrdquoBioTechniques vol 37 no 5 pp 790ndash802 2004

[28] T Tiwari K Pandey N Srivastava and P C Srivastava ldquoEffectof glutaraldehyde on electrical properties of arrowroot starch +NaI electrolyte systemrdquo Journal of Applied Polymer Science vol121 no 1 pp 1ndash7 2011

[29] T Tiwari N Srivastava and P C Srivastava ldquoElectrical trans-port study of potato starch-based electrolyte systemrdquo Ionics vol17 no 4 pp 353ndash360 2011

[30] K El-Tahlawy R A Venditti and J J Pawlak ldquoAspects of thepreparation of starch microcellular foam particles crosslinkedwith glutaraldehyde using a solvent exchange techniquerdquo Car-bohydrate Polymers vol 67 no 3 pp 319ndash331 2007

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


FluidsJournal of

Atomic and Molecular Physics

Journal of



Advances in Condensed Matter Physics

OpticsInternational Journal of



AstronomyAdvances in

International Journal of


Superconductivity


Statistical MechanicsInternational Journal of


GravityJournal of


AstrophysicsJournal of


Physics Research International


Solid State PhysicsJournal of

Computational Methods in Physics

Journal of



Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014


PhotonicsJournal of


Journal of

Biophysics


ThermodynamicsJournal of


as FTIR spectroscopy Possible chemical structure has beenproposed for the system SEM has been used to reveal thesurface morphology

2 Experimental

21 Sample Preparation Potato starch (PS) (C6H10O5)119899

(Loba Chemie) H3BO3(Anchor Laboratories) Glutaralde-

hyde (GA) (C5H8O2) (Loba Chemie) and distilled water (as

a solvent) was used in the study Materials were used asreceived GA is added in the system Samples have beenprepared using solution cast technique at 30∘C For 1 gm ofstarch 03 gmH

3BO3and 2mLGAwaterwere taken together

in 10mL of solvent mixture was stirred at 30∘C on magneticstirrer for one hour and heated till it dries Samples were thenleft in atmosphere to dry at room temperature sim20ndash24∘CWithin one week fractals were visible

22 Devices and Technique Optical photographs of the sam-ples were taken by Sony Cybershot (DSC-S730) and foropticalmicrograph cameraCatalyst biotechCC130 is used IRspectral studies have been carried out by Jasco FTIR 5300to confirm the complexation SEM micrographs have beentaken using JEOL JXA 8100 Electron Probe Micro-analyserPhilips X-pert model with Cu119870

120572(120582 = 1542 A) is used for

XRD study Crystallite size (119863) andmicrostrain (120585) have beencalculated using Scherrerrsquos semiempirical formula

119863 = 09

120582

120573 cos 120579

120585 =

120573

4 tan 120579

(1)

where 120573 is the full width half maxima of the highest intensitypeak and 120582 is the Cu119870

120572wavelength = 154 A

3 Result and Discussion

31 Computation of Fractal Dimension Optical photographof the fractal is shown in Figure 1(a) while close view of theramified structure is given in Figures 1(b) and 1(c)

The microscopic views 1(b) and 1(c) of the growthstructure indicates growth is starting froma seed on growingit is divided into branches no two tips are touching eachother they are changing their pathways by bending whenthey reach to be very close to each other or the growth stopsthere

All these observations are indicating that the pattern ofgrowth is of the DLA type which is further confirmed byfractal dimension

Fractal dimension has been calculated by extracting thedata from the real picture 1(b) using software ldquoxyExtractrdquoTheextracted image of the pattern is given in Figure 2

There are differentmethods for calculating fractal dimen-sion ldquo119889

119891rdquo for example box counting method [21 22]

mass radius relation [23] scaling relation of two-pointdensity-density correlation function [24]We have calculated

the fractal dimension by calculating filled area [25] and theformula used in calculation is

119889

119891=

log [119872 (NL) 119872 (119871)]log119873

(2)

where 119871 represents the unit length 119873 is the number of unitlength 119872(NL) is the filled area of a square of length NLand119872(119871) is the filled area of a square of unit length Fractaldimension calculated by this is found to be 149

32 Effect of Substrate and Storage Condition on Fractal For-mation As suggested by earlier study [18] growth pattern ofboric acid depends strongly on the type of material and thesurface condition of substrate We have monitored growthat two different substrates in two different conditions Thesubstrates were borosilicate glass and poly propylene at twodifferent humidity levels The main observations were asfollows

(i) In glass Petri dish samples stuck to it while in poly-propylene they can be easily taken out as shown inoptical photograph given in Figure 3(a)

(ii) Besides branches become sharper in glass Petri dishinstead of polypropylene This sharpness was furthercontrolled by atmospheric humidity

(iii) In low humidity atmosphere (20RH) the growthis quite thick and multilayer hence branches are notvery clear whereas in high humid atmosphere (70RH) the branches are quite sharp and well definedwith reduced multilayer

(iv) The samples kept in 20RHwere becoming orange incolour while samples kept in 70 RHwere colourlessas depicted in Figures 3(b) and 3(c)

Further the effect of humidity and substrate on fractaldimension is summarized in Table 1

Effect of Humidity on Fractal Dimension In low humidityatmosphere (20 RH) the growth is quite thick and multi-layer resulting in greater fractal dimension whereas in highhumid atmosphere (70RH) the branches are quite sharpand well defined with reduced multilayer resulting in lowerfractal dimension

Effect of Substrate on Fractal Dimension Sharp branches aremore pronounced in glass Petri dish instead of polypropyleneeven at a low humidity level some thick multilayer branchescan be seen in polypropylene dish therefore fractal dimen-sion in polypropylene substrate is greater

Sha et al [18] while discussing the bifurcation growth ofboric acid from its water solution have discussed that boricacid molecules have an affinity towards borate glass Thisaffinity of boric acid towards borate glass substrate seems tobe the reason why samples strongly stuck on borate glass andcannot be taken out In the same paper they also discussedthat on PVCorVaseline coated glass no structural growth canbe seen In present system growth is seen in both the casesthat is in borosilicate glass and Polypropylene Petri dish


(a) (b) (c)


200

400

600

800

1000

1200

(au

)

200 400 600 800 1000 1200(au)










(a)


8x 5001205838x 500120583

(b)


8x 5001205838x 500120583

(c)





4

minus+H+ (3)




plexed system



OHOH

OH OH OH

OHOHOHOHOH

HO

HO

O

O

O

O

O

OO

O

O

O

HH HH

H HH H H

H

HHHH

HHHHH

H

(a)

OH

OHHOHHOH

OH

OHOH

OHOHOHOHHO

HO

OH

O

OO

O

OO

O

O

O

B

O

OO

HHHH

HHHHH

H

HH H H

H HH H H

H

(b)



Tran

smiss

ion

()

(A)

(B)

(C)

(D)

(a)

020406080

100

400900140019002400290034003900

S4 S3S2 S1


T(

)

(b)



4-O groups






0

20

40

60

80

100

120

140

160

10 20 30 40 50 60

Inte

nsity

(au

)

121100

2120579











4 Conclusion




Acknowledgment


References








































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




(a) (b) (c)


200

400

600

800

1000

1200

(au

)

200 400 600 800 1000 1200(au)










(a)


8x 5001205838x 500120583

(b)


8x 5001205838x 500120583

(c)





4

minus+H+ (3)




plexed system



OHOH

OH OH OH

OHOHOHOHOH

HO

HO

O

O

O

O

O

OO

O

O

O

HH HH

H HH H H

H

HHHH

HHHHH

H

(a)

OH

OHHOHHOH

OH

OHOH

OHOHOHOHHO

HO

OH

O

OO

O

OO

O

O

O

B

O

OO

HHHH

HHHHH

H

HH H H

H HH H H

H

(b)



Tran

smiss

ion

()

(A)

(B)

(C)

(D)

(a)

020406080

100

400900140019002400290034003900

S4 S3S2 S1


T(

)

(b)



4-O groups






0

20

40

60

80

100

120

140

160

10 20 30 40 50 60

Inte

nsity

(au

)

121100

2120579











4 Conclusion




Acknowledgment


References








































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





(a)


8x 5001205838x 500120583

(b)


8x 5001205838x 500120583

(c)





4

minus+H+ (3)




plexed system



OHOH

OH OH OH

OHOHOHOHOH

HO

HO

O

O

O

O

O

OO

O

O

O

HH HH

H HH H H

H

HHHH

HHHHH

H

(a)

OH

OHHOHHOH

OH

OHOH

OHOHOHOHHO

HO

OH

O

OO

O

OO

O

O

O

B

O

OO

HHHH

HHHHH

H

HH H H

H HH H H

H

(b)



Tran

smiss

ion

()

(A)

(B)

(C)

(D)

(a)

020406080

100

400900140019002400290034003900

S4 S3S2 S1


T(

)

(b)



4-O groups






0

20

40

60

80

100

120

140

160

10 20 30 40 50 60

Inte

nsity

(au

)

121100

2120579











4 Conclusion




Acknowledgment


References








































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




OHOH

OH OH OH

OHOHOHOHOH

HO

HO

O

O

O

O

O

OO

O

O

O

HH HH

H HH H H

H

HHHH

HHHHH

H

(a)

OH

OHHOHHOH

OH

OHOH

OHOHOHOHHO

HO

OH

O

OO

O

OO

O

O

O

B

O

OO

HHHH

HHHHH

H

HH H H

H HH H H

H

(b)



Tran

smiss

ion

()

(A)

(B)

(C)

(D)

(a)

020406080

100

400900140019002400290034003900

S4 S3S2 S1


T(

)

(b)



4-O groups






0

20

40

60

80

100

120

140

160

10 20 30 40 50 60

Inte

nsity

(au

)

121100

2120579











4 Conclusion




Acknowledgment


References








































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




0

20

40

60

80

100

120

140

160

10 20 30 40 50 60

Inte

nsity

(au

)

121100

2120579











4 Conclusion




Acknowledgment


References








































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




























FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



research article diffusion-limited aggregation in potato...

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