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Deposition of colloidal particles in monolayers and multilayers
Thin Solid Films. 99 (1983) 243 248
243
D E P O S I T I O N O F C O L L O I D A L PARTICLES IN M O N O L A Y E R S AND MULTILAYERS* GEORGE L. GAINES, JR. General Eh, ctric Corporate Research and Develapment, P.O. Box 8. Sehenectac!v. N Y 12301 ( U.S.A. )
(Received September 1~ 1982; accepted September 22, 1982)
Preliminary observations are reported on the deposition of alumina, silica, zinc sulfide and gold colloidal particles on solid surfaces. The alumina, which is positively charged, can induce subsequent deposition of the other colloids (which are negative) onto glass, as pointed out by Iler in 1966. However, more uniform, reproducible and rapid deposition occurs on two monolayers of docosylamine sulfate applied to the glass by the Langmuir-Blodgett technique. The zinc sulfide sol, which is not stable to flocculation, deposits as three-dimensional aggregates. The deposition of colloidal gold was followed by optical absorption measurements, and layers containing a substantial fraction of the close-packed limit were obtained.
1. INTRODUCTION
The deposition of colloidal particles on solid substrates has been the subject of much study, because of the importance of the process in such practical applications as filtration and the prevention of particulate fouling. Several analyses of the rate of deposition of particles on initially clean surfaces in various geometries have been carried out 1-4. If the colloidal sol is stable, with repulsive interactions between the particles which prevent their flocculation, and there is an attractive interaction with the solid substrate, deposition is not expected to progress beyond a single layer of particles 5. In many experimental studies, maximum coverages attained have been low. For example, Bowen and Epstein 6 and Rajagopalan and C h u 7 reported that area coverage of particles did not exceed 10%-40% in their systems. Under certain circumstances, however, quite dense monolayers may be formed. In 1966, Iler 8 reported that colloidal boehmite alumina and colloidal silica could be used to form multiple monolayers (by alternate immersion in the two oppositely charged sols) which, on the basis of their optical properties, appeared to have volume fractions of about 50% solid. Kenney e t al. 9 have studied the deposition of colloidal hydrous metal oxides and in certain cases have also observed packing densities of * Paper presented at the First International Conference on Langmui~Blodgett Films, Durham, Gt. Britain, September20-22, 1982. 0040-6090/83/0000-0000/$03.00
© ElsevierSequoia/Printedin The Netherlands
244
G.L. GAINES,JR.
greater than 50[~o,as estimated from electron micrographs and chemical analysis. (It may be noteworthy, however, that these high coverages were only observed after long times - many hours of immersion in the sol.) Feder and Giaever l° found that ferritin, a relatively rigid spherical protein, could attain nearly complete coverage under certain conditions, although very low coverages were more commonly observed. Since Iler's original publication, his method of sequential colloid deposition has been used to alter the charge on surfaces 11 and to deposit uniform polymer coatings on glass f i b e r s t2'13 and microspheres ~4'~5. Because of the possibility of forming layers of a wide variety of inorganic as well as organic substances using colloidal metals, oxides or other inorganic sols, polymer latexes etc. this technique seems to provide a valuable adjunct to the classical Langmuir Blodgett method for producing organic multilayers. The reports which have appeared, however, have contained little quantitative information on the completeness of the layers which arc formed, the conditions which lead to their formation, or the rate at which they form. Clearly such information is needed to decide on the applicability of the technique. In this report, I present preliminary observations on the deposition of several kinds of colloidal particles on solid surfaces. 2.
E X P E R I M E N T A L DETAILS
The surface charge (on treated Pyrex glass capillaries in 5 x 10 3 M KCI) was estimated with the alternating streaming current apparatus described by Groves and Sears 16. Absorption spectra were recorded on a Perkin-Elmer 575 spectrophotometer. Boehmite alumina (Sol-AI, from the Barnes Hind Pharmaceutical Co.) was dispersed in distilled water by stirring 1 g of the solid powder in 10 ml overnight; further dilution was made with distilled water to give the 0.251',, sol as used by ller. The pH of the diluted sol was 4.4. Silica sols (Ludox, from Du Pont) were diluted, typically with (2 5) x 10 3 M HC1, to give 2"; sols in the same pH range. Zinc sulfide sols were prepared by the method of Chiu 17. Gold sols were prepared by sodium citrate reduction of gold chloride solution, as described (as "standard") by Turkevich et al.l Glass substrates to be coated with docosylamine sulfate monolayers ~" were initially rendered hydrophobic by treatment with a 2'~i, solution of dimethyldichlorosilane in CCI 4 and were then dipped through the amine monolayer spread on 0.05 M ( N H 4 ) 2 S O 4 solution (pH 5.7). The surface pressure was maintained at about 30 m N m I with oleic acid as piston oil. A monolayer transferred both on insertion and withdrawal of the substrate. All procedures were carried out at room temperature, 23 + 1 C . 3.
RESULTS A N D DISCUSSION
3.1. Considerations on m a x i m u m packing Since most of the sols used consist of spherical (or nearly so) particles, it is first worthwhile to consider the maximum packings which may be achievable. For uniform rigid spheres in an infinite hexagonally close-packed three-dimensional
COLLOIDAL PARTICLES IN MONOLAYERS AND MULTILAYERS
245
array, of course, the volume fraction occupied is well known to be 74.05'Yo. In a single layer, the corresponding value is 60.46~o. Such densities can only be achieved if the particles can rearrange to a close-packed array after they arrive at the surface. Feder and Giaever 1° and Feder 2° have examined the limit of packing of disks which stick wherever they arrive on a clean surface; if Feder's "jamming limit" for disks is multiplied by the volume ratio of spheres to disks, a volume fraction limit of 36.5°,~ for uniform spheres in a single layer is implied.
3.2. Alumina/silica layers Visual observations of alternating layers of boehmite and silica deposited on black glass are in accord with Iler's observations. Alternating immersions of 1 min duration (with thorough rinsing, as noted by Iler) suffice to produce strong interference colors when observed in reflected light. Thus six, eight and ten immersions using a silica sol of 22 nm particles (Ludox TM) produce coatings which are respectively deep violet, blue and gold in color. Surface charge measurements and electron microscopy, however, suggest that the individual layers obtained in this simple way may not be completely uniform and distinct. The initial high negative charge (~ potential, about 80 mV) of glass is reduced substantially, and the charge may be reversed by treatment with a positive boehmite sol; subsequent treatment with a negative silica sol again makes the surface more negative. However, quantitative reproducibility has not yet been achieved. The deposition of gold particles on boehmite-treated glass (see below) has also not been reproducible. Electron micrographs (Fig. 1) suggest clumping of the fibrillar boehmite particles and considerable heterogeneity in the silica deposit.
(a)
(b)
Fig. 1. Transmission electron micrographs of (a) colloidal alumina and (b) alumina plus silica deposits. Carbon-coated grids were immersed in 0.25% alumina sol for 1 min and rinsed. For (b), the grid was subsequently immersed for 1 min in 2 ~ silica sol and rinsed.
246
G.L. GAINES,JR.
3.3. Zinc' sulfide deposition The procedure described by Chiu ~7 yields nearly monodisperse zinc sulfide particles which are readily dispersed by ultrasonication in water. Such sols, however, are rather unstable and flocculate in periods of 24 48 h. Correspondingly, when glass substrates coated with a docosylamine sulfate monolayer are exposed to these sols, deposition occurs but coverage is spotty and consists of three-dimensional agglomerates of the colloidal particles (Fig. 2).
3.4. Colloidal gold The extensively studied optical properties of gold SOIs 21 and discontinuous gold films 22 provide a convenient method for examining the deposition of gold particles. The citrate gold sol used in the present experiments consists of spherical particles with a mean diameter of 20 nm is. It shows strong absorption in the blue, with a m a x i m u m at 522 nm (Fig. 3).
!
04~
O2
J oO40o
I 600 WAV[ L[NGTH,
i
i 8o0
n m
Figi 2. Scanning electron micrograph of the deposit from zinc sulfide sol on two monolayers of docosylamine sulfate on glass. Fig. 3. Visibleabsorption of gold sol and of deposits on two monolayers ofdocosylamine sulfate on glass slides: curves A E, slides immersed for 0, 15, 60, 120 and 220 rain (relative 1o absorption in airJ: curve F, gold sol, 31 pg Au ml- l (1 cm cell, relative to absorption in H2O ). Neither clean glass nor silylated glass substrates exhibit any detectable coloration after immersion in this sol for 24 h, followed by rinsing. When glass which has been pretreated to produce a positive surface charge is used, however, substantial optical absorption develops. As noted above, with alumina sol pretreatment, the results have so far not been reproducible. While absorbances of 0.2 have occasionally been observed after 16 h immersion in the gold sol, in most cases the optical density is lower and the peak position varies, suggesting variations in the state of aggregation of the gold particles.
247
COLLOIDAL PARTICLES IN MONOLAYERS AND MULTILAYERS
With glass coated with two monolayers of docosylamine sulfate, however, the deposition of gold particles is much more rapid, reproducible and proceeds to much higher densities. Presumably this pretreatment provides a higher and more uniform surface charge. Figure 3 illustrates the spectra obtained as a function of time of immersion in the sol. Even after only a few minutes of immersion, the absorbance peak is substantially shifted from that of the sol, and there appears to be a slight further red shift as the density of deposition increases. Even at the highest absorbance attained so far (0.9), however, the peak is within the range 630-670 nm. It is interesting to note that at absorbances of 0.25 or greater the deposits have an appearance very similar to that of bulk metallic gold in reflection. The density of the deposit can be estimated from the decrease in absorbance of the sol when a large area of substrate is immersed in a small volume of sol. Such measurements have been performed, and the results are summarized in Table I. The density of a close-packed layer of gold spheres 20 nm in diameter (specific gravity, 19.3) would be 23.4 I.tgcm ~2; hence the deposits already observed have densities of a substantial fraction of this value. Further studies of the morphology of these deposits and analysis of their optical properties are now in progress. TABLE 1 ABSORBANCE AND GOLD CONTENT OF DEPOSITS OF COLLOIDAL PARTICLES ON DOCOSYLAMINESULFATE MONOLAYERS
Time immersed a (h)
Ab
Gold content (lag cm 2)
2.5 3.7 48.0
0.201 0.264 0.346
4.3 6.2 9.6
a Different sol concentrations (10-50 lag m1-1) and area-to-volume ratios were involved, so that quantitative rate comparisons are unwarranted. bThe absorbance of a single layer is equal to 0.5 times the absorbance of the immersed slide. ACKNOWLEDGMENTS
I am indebted to Mr. J. N. Groves for assistance with the streaming current measurements and to Dr. S. Y. Hobbs for the electron microscopy. REFERENCES 1 2 3 4 5 6 7 8 9 10 11
Z. Adamczyk and T. G. M. Van de Ven, J. Colloid Interface Sci., 80 (1981 ) 340. Z. Adamczyk and T. G. M. Van de Ven, J. Colloid Interface Sci., 84 ( 1981 ) 497. R. Rajagopalan and J. S. Kim, J. Colloid Interface Sci., 83 ( 1981) 428. J.S. K i m a n d R. Rajagopalan, Colloids S u r f , 4(1982) 17. E. Dickinson, J. ColloidlnterJaceSci.,81(1981) 132. B.D. Bowen and N. Epstein, J. Colloid Interface Sci., 72 (1979) 81. R. Rajagopalan and R. Q. Chu, J. Colloid Interface Sci., 86 (1982) 299. R.K. Iler, J. Colloidlnterface Sci., 21 (1966) 569; U.S. Patent 3,485,658, 1969. J.T. Kenney, W. P. Townsend and J. A. Emerson, J~ Colloid Interface Sci., 42 (1973) 589. J. Feder and I. Giaever, J. Colloid Interface Sci., 78 (1980) 144. R. Rajagopalan and C. Tien, Can. J. Chem. Eng., 55 (1977) 256.
248
12 13 14 15 16 17 18 19 20 21 22
G . L . GAINES, JR.
D . G . Peiffer and L. E. Nielsen, J. Appl. Polym. Sci., 23 (1979) 2253. D . G . Peiffer, J. Appl. Polym. Sci., 24 (1979) 1451. G . M . Halpern, J. Vac. Sei. Technol., 17 (1980) 1184.
D.G. Peiffer, T.J. Corley, G.M. HalpernandB. A. Brinker, Polymer, 22(1981)450. J . N . Groves and A. R. Sears, J. Colloid Interface Sci., 53 (1975) 83. G. Chiu, J. Colloidlnterface Sei., 83 (1981) 309. J. Turkevich, P. C. Stevenson and J. Hillier, Discuss. Faraday Soe., 1 / ( 1951 ) 55. G . L . Gaines, Jr., Nature (London). 298 (1982) 544. J. Feder, J. Theor. Biol.,87(1980) 237. J. Turkevich, G. Garton and P. C. Stevenson, J. ColloidSci., Suppl., 1 (1954) 26. S. Norrman, T. Anderssom C, G. Granqvist and O. Hunderi, Phys. Rev. B, 18 (1978) 674.
243
D E P O S I T I O N O F C O L L O I D A L PARTICLES IN M O N O L A Y E R S AND MULTILAYERS* GEORGE L. GAINES, JR. General Eh, ctric Corporate Research and Develapment, P.O. Box 8. Sehenectac!v. N Y 12301 ( U.S.A. )
(Received September 1~ 1982; accepted September 22, 1982)
Preliminary observations are reported on the deposition of alumina, silica, zinc sulfide and gold colloidal particles on solid surfaces. The alumina, which is positively charged, can induce subsequent deposition of the other colloids (which are negative) onto glass, as pointed out by Iler in 1966. However, more uniform, reproducible and rapid deposition occurs on two monolayers of docosylamine sulfate applied to the glass by the Langmuir-Blodgett technique. The zinc sulfide sol, which is not stable to flocculation, deposits as three-dimensional aggregates. The deposition of colloidal gold was followed by optical absorption measurements, and layers containing a substantial fraction of the close-packed limit were obtained.
1. INTRODUCTION
The deposition of colloidal particles on solid substrates has been the subject of much study, because of the importance of the process in such practical applications as filtration and the prevention of particulate fouling. Several analyses of the rate of deposition of particles on initially clean surfaces in various geometries have been carried out 1-4. If the colloidal sol is stable, with repulsive interactions between the particles which prevent their flocculation, and there is an attractive interaction with the solid substrate, deposition is not expected to progress beyond a single layer of particles 5. In many experimental studies, maximum coverages attained have been low. For example, Bowen and Epstein 6 and Rajagopalan and C h u 7 reported that area coverage of particles did not exceed 10%-40% in their systems. Under certain circumstances, however, quite dense monolayers may be formed. In 1966, Iler 8 reported that colloidal boehmite alumina and colloidal silica could be used to form multiple monolayers (by alternate immersion in the two oppositely charged sols) which, on the basis of their optical properties, appeared to have volume fractions of about 50% solid. Kenney e t al. 9 have studied the deposition of colloidal hydrous metal oxides and in certain cases have also observed packing densities of * Paper presented at the First International Conference on Langmui~Blodgett Films, Durham, Gt. Britain, September20-22, 1982. 0040-6090/83/0000-0000/$03.00
© ElsevierSequoia/Printedin The Netherlands
244
G.L. GAINES,JR.
greater than 50[~o,as estimated from electron micrographs and chemical analysis. (It may be noteworthy, however, that these high coverages were only observed after long times - many hours of immersion in the sol.) Feder and Giaever l° found that ferritin, a relatively rigid spherical protein, could attain nearly complete coverage under certain conditions, although very low coverages were more commonly observed. Since Iler's original publication, his method of sequential colloid deposition has been used to alter the charge on surfaces 11 and to deposit uniform polymer coatings on glass f i b e r s t2'13 and microspheres ~4'~5. Because of the possibility of forming layers of a wide variety of inorganic as well as organic substances using colloidal metals, oxides or other inorganic sols, polymer latexes etc. this technique seems to provide a valuable adjunct to the classical Langmuir Blodgett method for producing organic multilayers. The reports which have appeared, however, have contained little quantitative information on the completeness of the layers which arc formed, the conditions which lead to their formation, or the rate at which they form. Clearly such information is needed to decide on the applicability of the technique. In this report, I present preliminary observations on the deposition of several kinds of colloidal particles on solid surfaces. 2.
E X P E R I M E N T A L DETAILS
The surface charge (on treated Pyrex glass capillaries in 5 x 10 3 M KCI) was estimated with the alternating streaming current apparatus described by Groves and Sears 16. Absorption spectra were recorded on a Perkin-Elmer 575 spectrophotometer. Boehmite alumina (Sol-AI, from the Barnes Hind Pharmaceutical Co.) was dispersed in distilled water by stirring 1 g of the solid powder in 10 ml overnight; further dilution was made with distilled water to give the 0.251',, sol as used by ller. The pH of the diluted sol was 4.4. Silica sols (Ludox, from Du Pont) were diluted, typically with (2 5) x 10 3 M HC1, to give 2"; sols in the same pH range. Zinc sulfide sols were prepared by the method of Chiu 17. Gold sols were prepared by sodium citrate reduction of gold chloride solution, as described (as "standard") by Turkevich et al.l Glass substrates to be coated with docosylamine sulfate monolayers ~" were initially rendered hydrophobic by treatment with a 2'~i, solution of dimethyldichlorosilane in CCI 4 and were then dipped through the amine monolayer spread on 0.05 M ( N H 4 ) 2 S O 4 solution (pH 5.7). The surface pressure was maintained at about 30 m N m I with oleic acid as piston oil. A monolayer transferred both on insertion and withdrawal of the substrate. All procedures were carried out at room temperature, 23 + 1 C . 3.
RESULTS A N D DISCUSSION
3.1. Considerations on m a x i m u m packing Since most of the sols used consist of spherical (or nearly so) particles, it is first worthwhile to consider the maximum packings which may be achievable. For uniform rigid spheres in an infinite hexagonally close-packed three-dimensional
COLLOIDAL PARTICLES IN MONOLAYERS AND MULTILAYERS
245
array, of course, the volume fraction occupied is well known to be 74.05'Yo. In a single layer, the corresponding value is 60.46~o. Such densities can only be achieved if the particles can rearrange to a close-packed array after they arrive at the surface. Feder and Giaever 1° and Feder 2° have examined the limit of packing of disks which stick wherever they arrive on a clean surface; if Feder's "jamming limit" for disks is multiplied by the volume ratio of spheres to disks, a volume fraction limit of 36.5°,~ for uniform spheres in a single layer is implied.
3.2. Alumina/silica layers Visual observations of alternating layers of boehmite and silica deposited on black glass are in accord with Iler's observations. Alternating immersions of 1 min duration (with thorough rinsing, as noted by Iler) suffice to produce strong interference colors when observed in reflected light. Thus six, eight and ten immersions using a silica sol of 22 nm particles (Ludox TM) produce coatings which are respectively deep violet, blue and gold in color. Surface charge measurements and electron microscopy, however, suggest that the individual layers obtained in this simple way may not be completely uniform and distinct. The initial high negative charge (~ potential, about 80 mV) of glass is reduced substantially, and the charge may be reversed by treatment with a positive boehmite sol; subsequent treatment with a negative silica sol again makes the surface more negative. However, quantitative reproducibility has not yet been achieved. The deposition of gold particles on boehmite-treated glass (see below) has also not been reproducible. Electron micrographs (Fig. 1) suggest clumping of the fibrillar boehmite particles and considerable heterogeneity in the silica deposit.
(a)
(b)
Fig. 1. Transmission electron micrographs of (a) colloidal alumina and (b) alumina plus silica deposits. Carbon-coated grids were immersed in 0.25% alumina sol for 1 min and rinsed. For (b), the grid was subsequently immersed for 1 min in 2 ~ silica sol and rinsed.
246
G.L. GAINES,JR.
3.3. Zinc' sulfide deposition The procedure described by Chiu ~7 yields nearly monodisperse zinc sulfide particles which are readily dispersed by ultrasonication in water. Such sols, however, are rather unstable and flocculate in periods of 24 48 h. Correspondingly, when glass substrates coated with a docosylamine sulfate monolayer are exposed to these sols, deposition occurs but coverage is spotty and consists of three-dimensional agglomerates of the colloidal particles (Fig. 2).
3.4. Colloidal gold The extensively studied optical properties of gold SOIs 21 and discontinuous gold films 22 provide a convenient method for examining the deposition of gold particles. The citrate gold sol used in the present experiments consists of spherical particles with a mean diameter of 20 nm is. It shows strong absorption in the blue, with a m a x i m u m at 522 nm (Fig. 3).
!
04~
O2
J oO40o
I 600 WAV[ L[NGTH,
i
i 8o0
n m
Figi 2. Scanning electron micrograph of the deposit from zinc sulfide sol on two monolayers of docosylamine sulfate on glass. Fig. 3. Visibleabsorption of gold sol and of deposits on two monolayers ofdocosylamine sulfate on glass slides: curves A E, slides immersed for 0, 15, 60, 120 and 220 rain (relative 1o absorption in airJ: curve F, gold sol, 31 pg Au ml- l (1 cm cell, relative to absorption in H2O ). Neither clean glass nor silylated glass substrates exhibit any detectable coloration after immersion in this sol for 24 h, followed by rinsing. When glass which has been pretreated to produce a positive surface charge is used, however, substantial optical absorption develops. As noted above, with alumina sol pretreatment, the results have so far not been reproducible. While absorbances of 0.2 have occasionally been observed after 16 h immersion in the gold sol, in most cases the optical density is lower and the peak position varies, suggesting variations in the state of aggregation of the gold particles.
247
COLLOIDAL PARTICLES IN MONOLAYERS AND MULTILAYERS
With glass coated with two monolayers of docosylamine sulfate, however, the deposition of gold particles is much more rapid, reproducible and proceeds to much higher densities. Presumably this pretreatment provides a higher and more uniform surface charge. Figure 3 illustrates the spectra obtained as a function of time of immersion in the sol. Even after only a few minutes of immersion, the absorbance peak is substantially shifted from that of the sol, and there appears to be a slight further red shift as the density of deposition increases. Even at the highest absorbance attained so far (0.9), however, the peak is within the range 630-670 nm. It is interesting to note that at absorbances of 0.25 or greater the deposits have an appearance very similar to that of bulk metallic gold in reflection. The density of the deposit can be estimated from the decrease in absorbance of the sol when a large area of substrate is immersed in a small volume of sol. Such measurements have been performed, and the results are summarized in Table I. The density of a close-packed layer of gold spheres 20 nm in diameter (specific gravity, 19.3) would be 23.4 I.tgcm ~2; hence the deposits already observed have densities of a substantial fraction of this value. Further studies of the morphology of these deposits and analysis of their optical properties are now in progress. TABLE 1 ABSORBANCE AND GOLD CONTENT OF DEPOSITS OF COLLOIDAL PARTICLES ON DOCOSYLAMINESULFATE MONOLAYERS
Time immersed a (h)
Ab
Gold content (lag cm 2)
2.5 3.7 48.0
0.201 0.264 0.346
4.3 6.2 9.6
a Different sol concentrations (10-50 lag m1-1) and area-to-volume ratios were involved, so that quantitative rate comparisons are unwarranted. bThe absorbance of a single layer is equal to 0.5 times the absorbance of the immersed slide. ACKNOWLEDGMENTS
I am indebted to Mr. J. N. Groves for assistance with the streaming current measurements and to Dr. S. Y. Hobbs for the electron microscopy. REFERENCES 1 2 3 4 5 6 7 8 9 10 11
Z. Adamczyk and T. G. M. Van de Ven, J. Colloid Interface Sci., 80 (1981 ) 340. Z. Adamczyk and T. G. M. Van de Ven, J. Colloid Interface Sci., 84 ( 1981 ) 497. R. Rajagopalan and J. S. Kim, J. Colloid Interface Sci., 83 ( 1981) 428. J.S. K i m a n d R. Rajagopalan, Colloids S u r f , 4(1982) 17. E. Dickinson, J. ColloidlnterJaceSci.,81(1981) 132. B.D. Bowen and N. Epstein, J. Colloid Interface Sci., 72 (1979) 81. R. Rajagopalan and R. Q. Chu, J. Colloid Interface Sci., 86 (1982) 299. R.K. Iler, J. Colloidlnterface Sci., 21 (1966) 569; U.S. Patent 3,485,658, 1969. J.T. Kenney, W. P. Townsend and J. A. Emerson, J~ Colloid Interface Sci., 42 (1973) 589. J. Feder and I. Giaever, J. Colloid Interface Sci., 78 (1980) 144. R. Rajagopalan and C. Tien, Can. J. Chem. Eng., 55 (1977) 256.
248
12 13 14 15 16 17 18 19 20 21 22
G . L . GAINES, JR.
D . G . Peiffer and L. E. Nielsen, J. Appl. Polym. Sci., 23 (1979) 2253. D . G . Peiffer, J. Appl. Polym. Sci., 24 (1979) 1451. G . M . Halpern, J. Vac. Sei. Technol., 17 (1980) 1184.
D.G. Peiffer, T.J. Corley, G.M. HalpernandB. A. Brinker, Polymer, 22(1981)450. J . N . Groves and A. R. Sears, J. Colloid Interface Sci., 53 (1975) 83. G. Chiu, J. Colloidlnterface Sei., 83 (1981) 309. J. Turkevich, P. C. Stevenson and J. Hillier, Discuss. Faraday Soe., 1 / ( 1951 ) 55. G . L . Gaines, Jr., Nature (London). 298 (1982) 544. J. Feder, J. Theor. Biol.,87(1980) 237. J. Turkevich, G. Garton and P. C. Stevenson, J. ColloidSci., Suppl., 1 (1954) 26. S. Norrman, T. Anderssom C, G. Granqvist and O. Hunderi, Phys. Rev. B, 18 (1978) 674.