Orgaz_A Semi-empirical Model for Coating Flat Glass by Dipping Into Metal-Organic Solutions

8/3/2019 Orgaz_A Semi-empirical Model for Coating Flat Glass by Dipping Into Metal-Organic Solutions

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JOU RNA L OF MATE RIAL S SCIENCE 22 (1987) 1291-1294

A sem i-em pir ica l m odel for co at ing f la t g lass b yd ipp ing in to meta l -o rgan ic so lu t ions

F. O R G A Z , F. C A P E L/nstituto de Cer#mica y Vidrio, Argand a del Rey, Madrid, Spain

A so l -ge l p rocess was used to p rod uce co loure d coa t ings o f com pos i t ion S i02 RmOn, whereR = chromium, manganese, i ron, cobal t and copper. Microscope s l ide glasses were dippedinto the solut ions and extracted ver t ical ly a t d i fferent speeds . Viscosi ty, densi ty and surfacetension were measured for each solut ion. Capi l lary numbers and dimensionless th icknesseswere then ca lcu la ted . The resu l ts showe d tha t cap i ll a ry numbers d id no t depe nd on thedimensionless th icknesses . A f low rate constant for each solut ion was observed. A s impleformula was used to calcula te the heat t reated coat ing thicknesses from the l iquid coa t ingthicknesses . Final ly, a method based on a semi-empir ical approach was successful ly appl ied topred ic t adequa te ly the th ickness ob ta ined as a func t ion o f the p roper t ie s o f the so lu t ions andthe wi thdrawal speed .

1 . I n t r o d u c t i o n

Coat ing glasses, ceramics and metals with glassy filmsis one of the most useful applications of the sol-gelprocess [1-3]. The product ion of satisfactory coatingsfrom a metal-organic solution requires deposition ofa sufficiently adherent and thick layer in a predictableand reproducible manner. The dip-coating thicknessapplied from a solution depends on factors related tothe solution and to the withdrawal speed. The proper-ties of the solutions that may affect the thickness of thelayer (such as viscosity, density and surface tension) inmetal-organic solutions have been experimentallyexpressed as one para mete r [4]. However, some theor-etical hydrodynami c models have been proposed inpolymer processing for viscous, capillary and high-Reynolds number withdrawal [5-7]. Starting from theclassical La nda u-L evi ch theory of dip-coating [8],most o f the theoretical and experimental research oncapillary withdrawal (C a ~ 1 and R e < 1) shows adependence of the coating phenomena on the capil-lary number, Ca = ~ lV/a ,where t/is the viscosity ofthe solution, V is the withdrawal speed and a is thesurface tension. Fo r low capillary numbers (C a < 1),theory fits the experimental linear relationship betweendimensionless film thickness and capillary number.Several mathematical functions have been proposedfor these withdrawal conditions [9, 10]. The L an da u-Levich equation is expressed by

T = 0.944 C a 1/6 (1 )

where T is the dimensionless thickness given by T =H (~g /~? V) 1/2, ~is the density of the solution, g isthe acceleration due to gravity and H is the thick-ness of the liquid coating. For high capillary numbers(C a > 1), where shear effects are large (large t/and V)and surface tension effects are small (small o-), a limit-ing value of T between 0.53 and 0.67 is obtained [11];this depends largely on a balance between inertial andviscous forces [12].

0022 2461/87 $03.00 + .12 1987 Chapman and Hall Ltd.

The dimensionless flow, J = j(o g/t l V 3)1/2is relatedto the dimensionless thickness, T, by the expressionJ = (T - T2/3), j being the flux of liquid per unitplate width and per unit time [13].

Yang et al . [14] derived a model based on an empiri-cal approach to predict the thickness of a copolymerof styrene -hexyl methac rylate film. The approachthey adopted was t o determine T from the experimen-tal flow rate J using the solution of the Navie r-Sto kesequation for the const ant thickness region. Assumingthat T = J, they derived the equation

t p = J ( e s / e o ) [ ( ~ - ~ o ) / ~ o ] 8 4 ( ~ v / e s g ) 1/2( 2 )

The objective of this paper was to derive a semi-empirical model for the sol-g el dip-coating process inorder to predict the thickness of the heat-treated coat-ing as a function of the properties of the solutions(a, ~, ~/) and the withdrawal speed. It was then necess-ary to establish the empirical relationships between (a)dimensionless thickness and capil lary number, and (b)between the thicknesses of the heat-treated coatingand liquid coating for this type of solution.

2 . E x p e r i m e n t a l m e t h o d s2.1. Preparat ion and proper t ies of the

so lu t ionsColoured coatings obtained by a sol -gel process using80SiO2-20R,~O,(wt %) composit ions, where R = Co,Cr, Mn, Fe or Cu, were used. The.starting solutionswere prepared by mixing tetraethyl orthosilicate(TEOS), water, e thano l and nit rates o f the respectivetransition metals. This corresponds to a 3 : 1 volume

ratio of TEOS to ethanol, and approximately 5:1mole ratio of water to TEOS, and concentrations oftransi tion metal oxides of 20 wt %. Acetic acid wasadded to adjust the rheology of the solutions and todelay the gelling time. The mixture was left to standfor a period of time (usually 10 h), being subsequentlydiluted with methanol in order to obtain a final 8 to

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TA B L E I P r o p e r t ie s o f t h e s o lu t i on s

S o l u t i o n D e n s i t y Vi s c o s i t y S u r f a c e t e n s i o n( w t % ) ( g c m - 3 ( c P ) * ( d y n c m - l ) .

8 0 S i O 2 - 2 0 M n z O 3 0 . 9 1 8 7 2 . 1 5 2 4 . 3 48 0 S i O 2 - 2 0 C o 2 0 3 0 . 9 1 94 2 . t l 2 7 . 9 28 0 S i O 2 - 2 0 C r 2 0 3 0 . 9 26 7 2 . 9 6 2 2 . 2 080S iO2 -20C uO 1 .0400 5 .73 34 .5460SiO ~-40F e203 0 .9890 3 .93 45 .50

* I c P = l M P a s e c ; l d y n c m -~ = 1 0 - S N c m - l .

1 0 w t % o x i d e c o n c e n t r a t i o n . T h e e x p e r i m e n t a l p r e p -a ra t ion p roce dure i s r epo r t ed e l sewhere [3 ]. Th e p rop e r-t ie s o f t he so lu t ions a t 27 C a re g iven in T ab le I . Vi s-c o s it y m e a s u r e m e n t s w e r e m a d e w i th a n U b b e l o h d ev i s c o m e t e r. P y k n o m e t r i c d e t e r m i n a t i o n s w e r e u s e d t oob ta in the dens i t i e s o f the so lu t ions . T he su r face t en -s io n w a s d e t e rm i n e d b y t h e m a x i m u m b u b b l e p r e s su r em e t h o d [1 5] .

2 . 2 . C o a t i n g t e c h n i q u e a n d h e a t t r e a t m e n t s

Mic roscope s l ide g l a s ses p rev ious ly c l eaned wi thw a t e r a n d m e t h a n o l w e r e d i p p e d i n t o t h e s o l u t i o n sand ex t r ac t ed ve r t i ca l ly a t d i f f e ren t speeds (va r i edf r o m 5 t o 4 0 c m r a i n - ' ) . A l l t h e s l id e s w e r e p e r m i t t e dt o r e m a i n i n t h e s o l u t i o n f o r 3 0 s ec b e f o r e p u l l in g u p .Af te r coa t ing , t he s l ides were immedia t e ly hea ted to5 0 0 C a t 7 C m i n -1 i n a n a i r fl o w a n d h e l d f o r o n eh o u r.

2.3 . F i lm th ickness and f i lmdensitym e a s u r e m e n t s

T h e f i l m t h i c k n e s s w a s d e t e r m i n e d w i t h a t w o - b e a min te r f e rence t echn iqu e us ing the M i rau sys t em a t t achedt o a L e i t z m i c r o s c o p e . T h i s w a s d o n e b y s c r a t c h i n gt h r o u g h t h e u n t r e a t e d f il m d o w n t o t h e s u b s t r a t e u s in ga sha rp b l ade . Th ickness was ca l cu la t ed us ing the

0 . 3 0

0 . 2 5

~' 0.20

oa~

0 .15

_.m._ ~

0 . 1 0E

0 . 0 5

0 0

0o ~-~-b--Ooo o

0

x n x w ): w

A A A

&

i I I I

2 4 6 8Cepi l l e ry num ber, ( r~vl~) x l o 4

I0

Figure 1 D e p e n d e n c e o f d i m e n s i o n l e s s t h i c k n e s s ,H / H o, o n t h ec a p i ll a r y n u m b e rCa = ~IV/a: ( O ) i r o n , ( O ) c o p p e r, ( * ) c o b a l t , ( m )m a n g a n e s e , ( A ) c h r o m i u m .

1 2 9 2

A

E=L 4

0

o /

I I I 1 t

I 0 2 0 3 0 4 0 5 0H 0 (p.m)

Figure 2 Va r i a t i o n o f th e l i q u i d c o a t i n g t h i c k n e s s , H =P / A o s , a sa f u n c t i o n o f t h e c h a r a c t e r i s t i c t h i c k n e s s H e =01V/Q~g)m: (0)i r o n , ( e ) c o p p e r , ( * ) c o b a l t, ( m l ) m a n g a n e s e ( A ) c h r o m i u m .

e q u a t i o n t = ( 2 / 2 )m w h e r e 2 i s t h e w a v e l e n g t h o f t h el ig h t a n d m i s th e f r a c t i o n a l d i s p l a c e m e n t o f t h e f r in g es y s te m . T h e d e n s i t y o f t h e h e a t - t r e a t e d c o a t i n g w a sd e t e r m i n e d b y t h e r e l a t io n Q =P/At where P i s t hecoa t ing we igh t , t i s t he th i ckness and A i s t he cove reda r e a .

3 . E x p e r i m e n t a l r e s u l ts a n d d i s c u s s i o n3 .1 . Re la t ions h ip be twe en d im ens ion le s s f ilm

thickness and capillary number.Fig . 1 shows the d imens ion les s fi lm th i ckness , T =H/Ho, f o r e a c h s o l u t i o n , a s a f u n c t i o n o f t h e c a p i l la r y

0 . 1 8

0 . 1 6

0 . 1 4

0 .12

%~ 0 A 0

~0 . 0 8

0 . 0 6

0 . 0 4

0 . 0 2

0 .020

//

I 0 2 0 3 0 4 0 5 0

0 " ( d y n c m 1 )

Figure 3 E x p e r i m e n t a l l y d e t e r m i n e d f lo w r a t e s J a g a i n s t s u r f a c et e n s i o n o f t h e s o l u t i o n s .

//

II

II


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~ - i 0

~ - 2 0

- 3 0

i I I I I I I

0 I 0 0 2 0 0 3 0 0 4 0 0Tem pera ture (C)

O O O . . - -

5 0 0 6 0 0

n u m b e r , Ca = r lV /a . T h e H 0 v a l u e s a r e g i v e n b yH o = (~ V/ G g) ~/2w h e r e r / a n d G a r e t h e v is c o s it y a n ddens i ty o f t he so lu t ion , r e spec t ive ly. Th e th i ckness o fthe l i qu id coa t ing , H , was ca l cu la t ed us ing the expres -s ion H - - P / A G , whe re P i s t he l i qu id coa t ing we igh t ,A is t he coa ted a re a an d G is the dens i ty o f t he so lu -

t ion . The r e su l t s i n F ig . 1 show tha t t he d im ens ion les sf il m th i c k n e s s d o e s n o t d e p e n d o n t h e c a p i l l a r y n u m -b e r. A s s u m i n g t h a t T = J , a fl o w r a t e c o n s t a n t J f o re a c h s o l u t i o n e x is ts o v e r t h e r a n g e o f c a p i ll a r y n u m -b e r s u s e d i n t h es e e x p e r i m e n t s . T h e v a l u e s o f J w e r eob ta ine d f ro m the s lopes o f t he s t r a igh t l i nes in F ig . 2 .

F i g. 3 s h o w s t h e d e p e n d e n c e o f t h e e x p e r i m e n t a l l yd e t e r m i n e d f l o w r a te s J o n t h e s u r f a c e t e n s i o n o f t h eso lu t ions . F ro m the s lope o f the J = K~r s t r a igh t l i ne ,a v a l u e o f K = 4 x 10 3 c m d y n ~ ( 4 0 0 c m N - ~) w a so b t a i n e d . H a v i n g d e t e r m i n e d t h e v a l u e o f K , t h e li q u i dc o a t i n g t h i c k n e s s H c o u l d b e c a lc u l a t e d f r o m t h e

p r o p e r t i e s o f t h e s o l u t io n s t /, G , a a n d f r o m t h e w i t h -d r a w a l s p e e d , u s i n g t h e e q u a t i o n

H = 4 x 10 3aO1 V/Qsg ) 1/2 (3 )

3 .2 . Ge l -g lass t r ans i t ion and re la t ionsh ipbe tween l iqu id coa t ing and f ina lhea t - t r ea ted coa t ing th icknesses

T h e s o l u t i o n s a r e g e ll e d o n t h e g l a ss s u b s t r a t e i m m e d i -a t e l y a f t e r w i t h d r a w a l a n d c o n v e r t e d t o g l a s s y f i l m s

Figure 4 Percentage weight loss for SiO2-Cr20 3 gels .

b y h e a t in g . C h e m i c a l l y a n d p h y s i c a l l y b o u n d w a t e ra s w e ll as o rg a n i c m a t e r i a ls a r e t h e n r e m o v e d . F i g s 4and 5 show we igh t l o sses and d i ff e ren ti a l t he rm a l ana ly -sis ( D TA ) c u r v e s f o r s i l i c a - c h r o m i u m o x i d e ge ls .We i g h t l o ss es o f a p p r o x i m a t e l y 3 0 w t % w e r e o b s e r v e dw h e n g e ls d r i e d a t 5 0 C w e r e h e a t - t r e a t e d a t 6 0 0 C .

F r o m 5 0 t o l l 0 C a w ei g h t l os s o f a p p r o x i m a t e l y1 0 w t % w a s o b s e r v e d , d u e p r i m a r i l y t o r e m o v a l o fu n b o u n d e t h a n o l - m e t h a n o l a n d p h y s ic a ll y a d s o r b e dw a t e r. T h i s c o r r e s p o n d s t o t h e e n d o t h e r m i c p e a ko b s e r v e d in t h e D T A c u r ve . A t t e m p e r a t u r e s a b o v e110 C c a r b o n i z a t i o n a n d o x i d a t i o n o f o rg a n i c c o m -p o u n d s o c c u r s . T h i s g i ve s r is e t o a n e n d o t h e r m i c p e a kn e a r t o 2 0 0 C a n d a b r o a d e x o t h e r m i c b a n d b e t w e e n2 5 0 a n d 4 5 0 C d e p e n d i n g o n g e l c o m p o s i t i o n . W e i g h tl o ss c a u se s s h r i n k a g e a n d a n i n c r e a s e o f a d h e s i o na n d m e c h a n i c a l a n d c h e m i c a l s t a b il it y. A l l th e s i l i c a -t r a n s i t io n m e t a l o x i d e g el s s h o w e d s i m i la r b e h a v i o u r.

I f the w e igh t o f a pa ra l le l - s ided f i lm o f a rea A anddens i ty Q i s P, t hen the f i lm th i ckness t is g iven s implyby t = P / A ~ . T h e r a t i o b e t w e e n h e a t - t r e a t e d t o a n dl i q u id c o a t i n g H t h i c k n es s e s c a n t h e n b e g i v e n b y t h ee x p r e s s i o n

t / H - P / A Q P / A G ( Q ~ ) ( 9 ) = ( P ~ ) W (4)

w h e r e W is th e r a t i o b e t w e e n h e a t - t r e a t e d c o a t i n g

I x o / L

I] I I / I I [

0 2 0 0 4 0 0 6 0 0 8 0 0oTe mpera tu r e (C)

Figure 5 D T A curves for S iO2-Cr=O3 gels hea ted in s tagnant a i r a t7o Cm in I .

.-; : : :L

.E

g( J

0.7

0.5

O~

0.1

O/

I I I J I I l

2 4 6Liquid coating thickness (p.m)

Figure 6 Theoret ical and exper imental re la t ionship between heat-treated an d liquid coating thicknesses fo r 60SiO2-40Fe203 solution.

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TA B L E I I D e n s i ty , w e i g h t l o ss e s a n d(Os /oo)Wv a l u e s o f h e a t -t r e a t e d g l a s s y f il m s

S o l u t i o n D e n s i t y W =P o l P ( O s / o o ) W( w t % ) ( g c m - 3 )

8 0 S i O 2 -2 0 M n 203 3 .1 0 .45 0 .1380SiO 2 20Co2 O 3 3 .6 0 .49 0 .128 0 S I O 2 2 0 C r 2 0 3 4 . 7 0 . 3 6 0 . 0 78 0 S i O 2 - 2 0 C u O - 0 . 3 96 0 S I O 2 4 0 F e 2 0 3 2 . 8 0 . 3 2 0 . 11

weight and liquid coating weight, 0s is the density ofthe solution and Q0 is the density of the heat-treatedglassy film. Table II gives the ~0, W and W(Os/OO)values for the different solutions studied. As anexample, Fig. 6 shows that the experimental relation-ship between heat-treated and liquid coating thick-nesses can be fitted to Equation 4 within the experi-mental error. This experimental relationship wasobserved for all metal-organic solutions.

3.3. Comparison of the theoretical with theexperimental results

Using Equations 3 and 4 the analytical expressionrelating the glassy film thickness, the properties of thesolutions and the withdrawal speed is

to = ~o \ ~sg J (5)

if an empirically determined value of K = 4 10 3cm dyn i is used. Equat ion 5 is similar to theanalytical equation derived by Yang et aI. [14] (Equa-

tion 2), provided th at J be equal to K a and the expres-sion [(t/ - qs)/r/0] 84 be replaced by W. In Fig. 7 theheat-t reated glassy film thicknesses of coatings con-taining iron or manganese are plotted as a function ofthe square root of the substrate withdrawal speed andcompared with the values obtained from Equation 5.Good agreement between the derived semi-empiricalmodel and the experimental results was observed.Consequently, Equation 5 can be applied to predictadequately the thickness of the heat-treated sol-gelcoating from the properties of the metal -org anic sol-utions used. Only slight deviations of the experimental

0.7 f0. 6

;o.o S f

I I I I I I

I 2 3 4 5 6 7

v l /Z (crn /Zr a i n - l /Z )

Figure 7 ( )T h e o r e t i c a l a n d ( - ) e x p e r i m e n t a l c o a t i n g t h i c k -n e s s e s a s a f u n c t i o n o f w i t h d r a w a l r a t e d u r i n g d i p p i n g , f o r ( O ) i r o na n d ( e ) m a n g a n e s e s o lu t i on s .

results from the theoretical square-root straight linewere noticed.

R e f e r e n c e s1 . H . D I S L I C H , J . N o n - C r y s t . S o l i d s57 (1983) 371 .2 . S . S A K K A , ibid. 73 (1985) 651 .3 . F . O R G A Z a n d H . R AW S O N ,ibid. 82 (1986) 378 .4 . H . S C H R O E D E R , T h i n S o l i d s F i l m s5 (1969) 87 .5 . P. G R O E N V E L D , C h e m . E n g . S c i .25 (1970) 1579 .6. ldem , ib id .25 (1970) 33 ,7. Idem , ib id .25 (1970) 1259 .8 . L . L A N D A U a n d V. L E V I C H ,A c t a P hy s . U R S S17

(1942) 42 .

9 . R . S P I E R S , C . S U B B A R A M A N a n d W. W I L K I N S O N ,C h e m . E n g . S c i .29 (1974) 389 .

10 . D . W H I T E an d A . TA L L M A D G E ,ibid. 20 (1965) 33 .1 I. B . D E R YA G I N a n d A . T I T I E V S K A AYA ,D o k l . A k a d .

N a u k . S S S R50 (1945) 30 .1 2. B . D E RY A G I N a n d S . L E V I , " F i l m C o a t i n g T h e o r y "

( F o c a l P r e s s , L o n d o n , 1 9 6 4 ) .1 3. J . V O N R O S S U M .A p p l . S c i . R e s .A7 (1958) 121 .1 4. C. YA N G , J . J O S E F O W I C Z a n dL . A L E X A N D R U ,

T h i n S o l i d s F i l m s74 (1980) 117 .1 5. S . S U D G E N , J . C h e m . S o c .125 (1924) 27 .

Rece ived 3 Februa ryand accep ted 5 Augus t 1986

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Orgaz_A Semi-empirical Model for Coating Flat Glass by Dipping Into Metal-Organic Solutions