Langmuir 1996, 12, 3793-3801
3793
Film Formation of Acrylic Latices with Varying Concentrations of Non-Film-Forming Latex Particles Joseph L. Keddie,* Paul Meredith,† Richard A. L. Jones, and Athene M. Donald Polymer and Colloid Group, Cavendish Laboratory, Department of Physics, University of Cambridge, Madingley Road, Cambridge CB3 0HE, United Kingdom Received January 16, 1996. In Final Form: May 8, 1996X We have employed ellipsometry and environmental SEM (ESEM) to determine the kinetics of film formation in mixtures of film-forming (FF) and non-film-forming (NFF) acrylic latices. We find that an increasing concentration of NFF latex leads to progressively larger voids. We have also found that minimizing the number of NFF-NFF particle contacts within the mixture results in a denser material. The rate of void closure during the early stages of film formation is enhanced by the presence of NFF latex particles, because the particles lead to a higher surface area that provides a stronger driving force for void closure. Despite this effect, a latex with a higher concentration of NFF particles takes longer to reach full density. We have applied the Mackenzie-Shuttleworth theory to our densification data and found a value for the viscosity of the FF latex that is consistent with the literature. In some cases, we see evidence for polymer viscosity changing with time, indicative of hydroplasticization. We find that our calculated viscosity of the FF latex decreases with increasing temperature and increases with the addition of 40 wt % NFF particles. We comment on the implications that this work has for the measurement of the critical pigment volume concentration.
I. Introduction In a previous paper we monitored the development of acrylic latex films during their film formation.1 We identified the conventional stages of film formation (I through IV) plus an intermediate stage (II*) that is particularly evident in latices near their glass transition temperature (Tg). The two primary techniques that we employedsellipsometry and environmental scanning electron microscopy (ESEM)shave the advantage of being nondestructive and capable of analyzing both wet and dry latices. In this paper, we report how mixing a nonfilm-forming (NFF) latex with a film-forming (FF) latex affects microstructure and the kinetics of the filmformation process. We focus most of our attention on changes in density and microstructure during stages III and IV. We apply a theory of sintering to describe the kinetics during these final stages of film formation with and without added NFF particles. Most previous studies of the kinetics of film formation have been conducted on a single component latex. In general practice, when used as a coating or paint, a latex contains many other components, such as pigments and extenders. The properties of a latex might be tailored by mixing it with a “functional latex” that has desired optical, mechanical, or electronic properties. Most latex paints can therefore be considered to be a ceramic/polymer or polymer/polymer composite material. This line of reasoning has led us to study the film formation of mixtures of FF and NFF latices. Furthermore, it has recently been suggested by Winnik and Feng2 that blends of a latex with glass transition temperature (Tg) above room temperature with one having a Tg below room temperature is an effective approach to eliminating film-forming aids, * Author to whom correspondence should be addressed. Current address: Department of Physics, University of Surrey, Guildford GU2 5XH, United Kingdom. † Current address: Procter & Gamble (Health and Beauty Care) Ltd., Rusham Park, Whitehall Lane, Egham, Surrey TW20 9NW, United Kingdom. X Abstract published in Advance ACS Abstracts, July 15, 1996. (1) Keddie, J. L.; Meredith, P.; Jones, R. A. L.; Donald A. M. Macromolecules 1995, 28, 2673. (2) Winnik, M. A.; Feng, J. J. Coat. Technol. 1996, 68 (852), 39.
S0743-7463(96)00046-7 CCC: $12.00
thereby minimizing the emission of volatile organic compounds. Our work is partly motivated by a desire to understand the kinetics of film formation. The time required for a latex to form a continuous film (a stage IV latex) has a direct bearing on its applicability as an adhesive, coating, or paint. If it takes days or weeks for a latex to reach stage IV, its usefulness is limited, especially if it is intended to be glossy and nonpermeable to gases or solvents. A desire to understand the kinetics of latex film formation has prompted experimental studies of the time dependence of permeability,3,4 surface roughness,5,6 hiding,7 and optical reflectivity.8 A second motivation for this work is to understand the development of film microstructure. The control of void content in a latex is essential in many applications. For instance, in a barrier coating, the voids should be minimal. In decorative coatings, on the other hand, void formation might be purposely enhanced, to achieve a desired optical effect. A better understanding of the process of film formation should then lead to better control of void distribution and hence the mechanical, barrier, and optical properties. Recent microscopy and optical characterization by Feng et al.9 has addressed some of these issues. Their work revealed that the clustering of non-filmforming particles leads to turbidity in latex blends. A third motivation is the recent increased interest in waterborne core-shell latices as a possible replacement for the addition of organic solvents as a film-forming aid.10 In these core-shell systems, a polymer core with a high (3) Balik, C. M.; Said, M. A.; Hare, T. M. J. Appl. Polym. Sci. 1989, 38, 557. (4) Roulstone, B. J.; Wilkinson, M. C.; Hearn, J. Polym. Int. 1992, 27, 51. (5) Butt, H.-J.; Kuropka, R.; Christensen, B. Colloid Polym. Sci. 1994, 272, 1218. (6) Goh, M. C.; Juhue´, D.; Leung, O. M.; Wang, Y.; Winnik, M. A. Langmuir 1993, 9, 1319. (7) Anwari, F.; Carlozzo, B. J.; Chokshi, K.; Chosa, M.; DiLorenzo, M.; Heble, M.; Knauss, C. J.; McCarthy, J.; Rozick, P.; Slifko, P. M.; Stipkovich, W.; Weaver, J. C.; Wolfe, M. J. Coat. Technol. 1992, 64 (804), 79; 1991, 63 (802), 35. (8) Gate, L. F.; Preston, J. S. Surf. Coat. Int. 1995, 78, 321. (9) Feng, J.; Winnik, M. A.; Shivers, R. R.; Clubb, B. Macromolecules 1995, 28, 7671. (10) Juhue´, D.; Lang, J. Macromolecules 1995, 28, 1306.
© 1996 American Chemical Society
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Table 1. Latex Chemical Compositionsa and Physical Characteristics chemical composition latex no.
MMA (mol%)
2-EHA (mol%)
number av diameter (nm)
Tg (K)
1 1B 2 4
74.8 65.2 54.3 42.9
24.3 33.9 44.8 56.2
566.2 333.7 286.3 554.2
335 314 286 268
a
All latices contain 0.9% methacrylic acid.
glass transition temperature (Tg) is usually enveloped by a polymer shell with a lower Tg. The film-forming behavior is believed to be controlled by the properties of the shell. The results of our present study, in which we have examined the film formation of mixtures of latices, could be usefully compared to studies of core-shell systems. Along this vein, there has been work in which the mechanical properties of core-shell pressure-sensitive adhesives have been compared with the properties of a mechanical mixture of the two components.11 Moreoever, dynamic mechanical analysis by Winnik and Feng2 has demonstrated that the mechanical properties of latex blends are greatly improved by hard, non-film-forming particles. Many previous experiments have indicated that coalescence of latex particles in the absence of an aqueous solvent is driven by the minimization of surface energy1,12,13 in a process commonly referred to as viscous or “dry” sintering. Hence, it is logical for models for the viscous sintering of porous materials14,15 and composites16 to be used to describe the later stages of film formation in a FF latex or in a mixture of FF and NFF latices (or a latex with pigment). In this work, we therefore have fitted equations derived for the closure of voids in a viscous medium to our density measurements during the filmformation of latex mixtures. II. Experimental Procedure (i) Materials. We studied the same series of latex compositions, all based on copolymers of methyl methacrylate (MMA) and 2-ethylhexyl acrylate (2-EHA), which was used in our previously-reported work.1 The glass transition temperatures of the copolymers ranged from 335 to 268 K, depending on the ratio of MMA to 2-EHA. All of the latices are initially about 55 wt % polymer. Number-average particle sizes (determined with photocorrelation spectroscopy) and glass transition temperatures, Tg (determined with differential scanning calorimetry on dried latex), are listed in Table 1 for each of the latex compositions used. The polydispersity of the particle diameters (represented by the ratio of the weight-average and number-average diameters) is 1.1. Latices 2 and 4 are film-forming at room temperature and are used as the matrix in films. Latices 1 and 1B are nonfilm-forming at room temperature. We prepared thorough mixtures containing 0, 10, 20, and 40 wt % NFF latices by mixing the two latex dispersions and agitating for several hours. In most of the experiments, we added latex 1 to latex 2 and latex 1b to 4; this allowed us to test whether the effects we observed were found exclusively in one materials system or applied more generally. (ii) Ellipsometry. All of the ellipsometry experiments described here were performed on a Jobin-Yvon Uvisel phasemodulated17 spectroscopic ellipsometer in one of two modes: angular and kinetic. Angular scans near the Brewster angle yield highly accurate measurements of optical properties, but (11) Lovell, P. A. Personal communication. (12) Sperry, P. R.; Snyder, B. S.; O’Dowd, M. L.; Lesko, P. M. Langmuir 1994, 10, 2619. (13) Dillon, R. E.; Matheson, L. A.; Bradford, E. B. J. Colloid Sci. 1956, 6, 108. (14) Mackenzie, J. K.; Shuttleworth, R. Proc. Phys. Soc. 1949, 62 (12-B), 838. (15) Scherer, G. W. J. Am. Ceram. Soc. 1987, 70, 719. (16) Scherer, G. W.; Jagota, A. Ceramic Trans. 1991, 19, 99.
they typically take 2 to 3 min to perform. Kinetic scans are much faster (taking milliseconds), and they thereby facilitate the study of a latex that is changing rapidly with time. In a typical angular scan, we measured the ellipsometric angles (ψ, the amplitude attenuation and ∆, the phase difference between the s and p waves) at 0.05 degree increments in the angle of incidence, φι, using a fixed wavelength of polarized light (λ ) 413.3 nm). We conducted our measurements around the Brewster angle of the latex (varying from about 53° to 57° with the passage of time). We used the same equations as described previously1 for determining the effective real and imaginary refractive indices as a function of time. In a kinetic scan, ellipsometric angles were determined at a fixed angle and wavelength (typically 53° and 413.3 nm) at intervals of 2 or 3 s. We thereby continuously obtained effective refractive index as a function of time during the process of film formation. In some experiments we placed the sample on a hot stage at a fixed temperature during a scan. A thorough discussion of the theory of ellipsometry can be found elsewhere.18,19 (iii) ESEM. In an environmental scanning electron microscope (ESEM)20 samples are imaged in the presence of water vapor or some other auxiliary gas such as nitrogen or nitrous oxide.21 The observation chamber can be held at pressures up to 40 Torr, through the use of differential pumping, while the gun and column remain at 10-6-10-7 Torr. Dehydration can be inhibited by use of the correct sample temperature control and pumpdown procedure.22 Wet samples can therefore be imaged in their “natural state”. Additionally, if the sample is correctly biased with respect to the collection electrode, ionized gas in the chamber results in charge suppression at the specimen surface. As a result, the sample does not need to be electrically conducting and does not need to be coated with a conducting layer, as is required in conventional SEM. This flexibility in observation environment also means that microstructural changes, for example, those occurring during the film formation of a latex, can be studied in situ and in pseudo real time without recourse to complicated and potentially damaging specimen preparation. We followed the same experimental procedure as described earlier.1 We inserted a wet latex film into the specimen chamber with its temperature set at ca. 276 K. We then partially evacuated the chamber and progressively replaced the mixed atmosphere with water vapor. After this procedure we observed no significant loss of sample moisture. We set the correct equilibrium imaging pressure (3-6 Torr) and then observed the surface of the latex film in various stages of dehydration during the film formation process. We also observed the microstructure of samples that had been aged in air for varying amounts of time. These samples were placed in the chamber without any previous surface treatment, pumped down under dry conditions, and then imaged in water vapor.
III. Results and Discussion (i) Optical and Microstructural Effects of NFF Particles. It is useful to bear in mind when interpreting our data that according to the Lorentz-Lorenz equation, the real component of the refractive index, n, is particularly sensitive to microscopic voids in the latex, and it increases with material density.1,19 Additionally, concepts from Rayleigh scattering can be applied to a void-containing latex.19 The optical properties of the latex can be modeled (17) Jasperson, S. N.; Schnatterly S. E. Rev. Sci. Instrum. 1969, 40, 761. (18) Azzam, R. M. A.; Bashara, N. M. Ellipsometry and Polarized Light; North-Holland: Amsterdam, 1987; (a) p 40; (b) p 361. (19) Meeten, G. H. Optical Properties of Polymers; Elsevier Applied Science Publishers: London, 1986; p 361. (20) Danilatos, G. Adv. Elecron. Electron Phys. 1990, 78, 1. (21) Meredith, P.; Donald, A. M. J. Microsc. (Oxford) 1996, 181, 23. (22) Cameron, R. E.; Donald, A. M. J. Microsc. (Oxford) 1994, 173, 227. (23) In our earlier work, we normalized the time of film formation by dividing by the final film thickness. This normalization took into account differences in the total amount of aqueous solvent among the latices of varying thickness and thereby allowed comparison of the kinetics. In the present experiments, the addition of NFF latex does not substantially alter the film thickness, and so it is not necessary to normalize the thickness when comparing the data.
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Figure 1. Refractive index as a function of time for mixtures of 0 (O), 10 (4), and 20 (×) wt % latex no. 1B in latex no. 4. The straight solid lines demarcate the transitions between the various stages that are identified by Roman numerals.
Figure 3. Refractive index as a function of time for mixtures of 0 (O), 10 (4), and 20 (×) wt % latex no. 1 in latex no 2. The straight solid lines demarcate the transitions between the various stages that are identified by Roman numerals.
Figure 2. Extinction coefficient as a function of time for mixtures of 0 (O), 10 (4), and 20 (×) wt % latex no. 1B in latex no. 4. The straight solid lines demarcate the transitions between the various stages that are identified by Roman numerals.
Figure 4. Extinction coefficient as a function of time for mixtures of 0 (O), 10 (4), and 20 (×) wt % latex 1 in latex 2. The straight solid lines demarcate the transitions between the various stages that are identified by Roman numerals.
as a continuous polymer medium (refractive index of n ) 1.5, for instance) with voids (n ) 1.0) of a given size well below the wavelength of light. The imaginary component of the refractive indexsthe extinction coefficient, ksis a complicated function of both the optical absorption inherent in a material and optical scattering by voids and surface roughness. In the case of the latex studied here, in which the polymers are not strongly absorbing, k is primarily a function of scattering from voids, increasing with void size and number. The coefficient is also expected to increase with surface roughness. According to simulations,18 with an increase in surface roughness of 10 nm, k increases by about 0.03, whereas n is only slightly affected. It is not straightforward to decouple the effects leading to a particular extinction coefficient. Complex refractive indices obtained from a series of successive angular scans at room temperature are shown in Figures 1-4 for latex compositions 2 and 4 with varying amounts of NFF latex (1 and 1b). The data for the latices with “0 wt % NFF” (i.e., single-component latex) are the same as reported earlier1 and are included for comparison. The refractive index of latex 4, with a low Tg (268 K), increases sharply at the onset of optical clarity while its extinction coefficient drops. This result indicates that it forms a dense film with few voids quite soon after the
onset of optical clarity. This is not the case when NFF particles (as few as 10 wt %) are added to the latex. With an increasing amount of particles added, n after the onset of optical clarity decreases, while k increases substantially. The behavior of both the real and imaginary components of the index indicates a decrease in latex density and an increase in voiding with the addition of an increasing amount of NFF particles. In latex 2, by comparison, the drop in n and the rise in k near the onset of optical clarity indicate the development of air voids even when no NFF latex particles are present. When NFF particles are added to latex 2, the trends in the optical properties not only persist but are exaggerated. The changes in the complex refractive index have a greater magnitude as more NFF particles are added to the FF latex. An obvious interpretation of this result is that NFF particles create a greater number and/or volume fraction of air voids, in the same way that they do in latex 4. We expect that the refractive index varies with the composition of the copolymer in the latex. In a mixture of latices, then, an index difference could account for a slight increase in k with increasing concentration of particles. The decrease in k with time, however, can only be explained by void coalescence and surface smoothing.
3796 Langmuir, Vol. 12, No. 16, 1996
Figure 5. ESEM micrograph of a mixture of 20 wt % latex 1 and 80 wt % latex 2 after onset of stage II*. NFF particles are larger than FF particles and appear brighter because of a topological effect (being elevated slightly on the sample surface). Some regions show a densely-packed array (identified as “A”; other areas near inclusions show sub-micrometer voids (“B”). Magnification bar ) 2 µm.
After long times or elevated temperatures, we have found that the extinction coefficient of latex mixtures is only slightly higher than the FF latex alone. In our previous paper1 we showed an image of latex 2 about 1 h after the onset of optical clarity. We found a densely-packed (although somewhat random) array of particles, indicative of a stage III latex. When there are 20 wt % latex 1 particles present (Figure 5), voids are apparent, particularly around the NFF particles. The size of voids in this material is notably greater than that found in the FF latex of a similar age. Thus, in a stage II* latex, microstructural evidence indicates that the addition of NFF particles enhances void formation. This finding supports our above explanation for the decreased n and increased k that we have observed with the addition of NFF latex (Figures 1-4). On Figures 1-4 we have identified with Roman numbers the various stages of film formation, and we have drawn lines to “map” when the stages develop. With or without the addition of NFF particles, the onset of stage II* (signaled by the development of optical clarity and labeled on the figures) occurs at approximately the same time. This result indicates that the mechanism for the onset of optical clarity is not altered by the addition of NFF particles. On the basis of this and other recent work,24 we propose that evaporationsnot particle deformationsis rate-controlling for the stage II to II* transition (and the onset of optical clarity) in latices 2 and 4 at temperatures well above their Tgs. The duration of the later stages of film formation (II* through IV), on the other hand, is increased by the presence of NFF particles. This fact is readily apparent by the boundaries of the stages seen in Figures 1-4. With a greater amount of NFF particles, the rate of change in density (determined by our optical measurements) is initially greater, probably because the NFF particles create enhanced void formation in the latex. Considering the effect of surface energy, we expect larger voids to have a greater driving force to close. Despite an initially faster rate of change, the completion of coalescence and densification of the latex takes longer with 20% NFF particles in latex 4. More time is required to complete film formation primarily because there is a greater volume of voids in the first place. Figure 6 shows the effect of 40 wt % latex 1 particles on the kinetics of film formation of latex 4. Results from latex 4 without any NFF inclusions are shown for
Keddie et al.
Figure 6. Kinetic scan showing refractive index as a function of time for latex 4 (‚‚‚) and for a mixture of 40 wt % latex 1 and 60 wt % latex 4 (s) at about 293 K. Full density is approached in the mixture, albeit over a much longer time than found for latex 4 without NFF inclusions. A scan of latex 4 on a stage at 283 K (- -) is shown for comparison.
comparison. With 40 wt % NFF latex n drops at the point of optical clarity, and it then rises abruptly. We have observed similar behavior in latex 2 after the onset of optical clarity. We attribute the drop in index to air void formation brought on by the evaporation of aqueous solvent from the space between particles. Latex 4 without any NFF particles becomes optically clear at the same time. Voids are not formed in pure latex 4, however, because all of the particles can flow and deform concurrently with the evaporation of the solvent. Although the inclusions slow down the rate of film formation compared to single-component latex 4, the effect is not catastrophic. Within several hours the refractive index of the latex approaches its maximum (n ∼ 1.5, corresponding to a fullydense material). We interpret this to mean that void elimination is nearing its completion. The extinction coefficient is much higher (>0.3) in the mixture than in latex 4 (≈0.025). Light can pass through the latex film, although it is hazy. In contrast, when 40 wt % latex 1 particles are added to latex 2 (Figure 7), the material does not become optically transparent, and its refractive index n (and hence its density) increases over a period of weeks. The results of two trials are shown. The only difference between the trials is the length of time spent stirring. In trial 1, the mixture was stirred for about 3 h; in trial 2, it was stirred for several days. Shortly after these films are cast, the refractive index changes rapidly with time as a result of the evaporation of water. (This initial change is not shown in Figure 7.) In both trials, this initial change is followed by a much slower change that takes place over several weeks. The value of n at earlier times is higher in trial 2 than in trial 1, but the rate of change of n is similar in both trials. We attribute the differences in n to differences in density resulting from differing degrees of initial particle mixing and subsequent packing. Figure 8 shows the microstructure of a four-week-old sample (40 wt % latex 1 in latex 2) used in trial 1 of the ellipsometry experiments. In regions around clusters of NFF particles, there are particularly large voids (up to about 5000 nm in length). A latex from trial 2 (Figure 9) has smaller and far fewer voids, even though it is much younger (4 days) than the film in Figure 8. Note that the (24) Keddie, J. L.; Meredith, P.; Jones, R. A. L.; Donald, A. M. Film Formation; ACS Symposium Series; American Chemical Society: Washington, DC, in press.
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Figure 10. ESEM micrograph of a mixture of 40 wt % latex 1 and 60 wt % latex 2 in stage 2 of film formation. Latex 1 particles can be identified by their larger size. Magnification bar ) 2 µm. Figure 7. Refractive index as a function of time for a mixture of 40 wt % latex 1 and 60 wt % latex 2 for two trials, as indicated: O ) trial 1; 4 ) trial 2. Dashed line is a guide for the eye.
Figure 8. ESEM micrograph of a mixture of 40 wt % latex 1 and 60 wt % latex 2 (trial 1) after aging 4 weeks at room temperature (ca. 293 K). Large voids (up to about 2 µm) are seen, especially near clusters of hard particles (labeled with arrows). In other regions FF particles have formed a continuous matrix with no evidence for particle-particle boundaries. Magnification bar ) 5 µm.
Figure 9. ESEM micrograph of a mixture of 40 wt % latex 1 and 60 wt % latex 2 (trial 2) after aging 4 days at room temperature (ca. 293 K). Magnification bar ) 2 µm. Voids in this latex mixture are smaller and less prevalent than in the latex shown in Figure 8.
NFF particles in Figure 9 are better dispersed; there are very few clusters. (The morphology seen in the micrographs is representative of the entire sample.) These ESEM results indicate that clusters of NFF particles create voids that are eliminated very slowly. The degree of mixing appears to be better in trial 2, and this observation makes sense in the light of the higher refractive index found at earlier times in Figure 7. The observed clusters of NFF particles create air voids in the latex, and these
voids lower the density and hence the refractive index. We expect that voids associated with NFF-NFF contacts will be stable with time unless a FF polymer can flow around the NFF particles. Our ESEM observations reveal that indeed voids near NFF-NFF particle contacts are not eliminated even after extended times. In an area in which a NFF particle is isolated, however, it is apparent that the surrounding FF polymer is able to flow around it and eliminate the void space. In both Figures 8 and 9 there is no evidence for boundaries between FF particles. Diffusion has apparently occurred across the polymer/ polymer boundaries, creating a continuous matrix. If the boundary region had differed significantly from the rest of the film in either its chemistry or topography,21 then this would be evident in the ESEM analysis. Other workers have studied particle packing and ordering in latex in great detail. Monodisperse, chargestabilized latices having a low salt concentration and no ionic surfactant have been found to produce a well-defined rhombic dodecahedron structure.25,26 Salt and surfactant27,28 have been found to have a large influence on the ordering of the latex particles. Factors such as the evaporation rate of water,27 the means of film deposition,25 and polydispersity of particle size have been shown to affect the surface structure in a PBMA latex.27 In the FF latices studied here, we have previously1 only observed random packing with a few isolated regions displaying hexagonal close packing in the surface plane. The lack of more pronounced ordering probably results from either the particle polydispersity or the effects of surfactants. Figure 10 shows the packing of a mixture of latex 1 and 2 prior to film formation. In stages II and II*, we have observed that mixtures of FF and NFF latices with different sizes are not significantly more disordered than are the single latices studied previously. On the basis of a simple geometric argument, the densest packing of latex particles should be obtained when the film-forming particles are much smaller than the nonfilm-forming particles. Then the interstices between the non-film-forming latex in a packed array could be filled by the film-forming latex (just as sand can be added to a container filled with marbles). If the non-film-forming latex was smaller, however, then there would be significant clustering of the NFF particles at higher volume fractions, and the FF latex would have to flow into the void space (25) Wang, Y.; Juhue´, D.; Winnik, M. A.; Leung, O. M.; Goh, M. C. Langmuir 1992, 8, 760. (26) Joanicot, M.; Wong, K.; Richard, J.; Marquet, J.; Cabane, B. Macromolecules 1993, 26, 3168. (27) Juhue´, D.; Lang, J. Langmuir 1993, 9, 792. (28) Wang, Y.; Kats, A.; Juhue´, D.; Winnik, M. A.; Shivers, R. R.; Dinsdale, C. J. Langmuir 1992, 8, 1435.
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contained within the clusters. We expect that such a process would be exceedingly slow to produce a fully-dense material. (ii) Rate of Void Closure. We have observed changes in the optical properties of fully-dried latex mixtures taking place over several days. We interpret these changes as resulting from the closure of voids in the latex. In modeling these data, we shall treat the latex as a viscous material and assume that the driving force for void closure is the minimization of the surface energy associated with the polymer/air interface. A recent study of the time dependence of optical clarity in latices dried below their Tgs supports the notion that voids close by viscous flow under the action of surface energy.8 Void closure was modeled using the equation:
dr γ )dr 2η
(1)
resulting in fair agreement with experimental data. Equation 1 assumes that an isolated, spherical void of radius r shrinks as a function of time t. γ is the surface energy at the air/polymer interface, and η is the viscosity of the polymer (assumed to form a continuous medium around the void). We suggest that the equation derived by Mackenzie and Shuttleworth (MS)14 is more applicable in describing the rate of void closure in a latex, since it explicitly takes into account the effect that all of the other voids have on the rate of closure of each individual void. Having the same dimensions as eq 1, the equation used by MS is
( )
γ 1 dr )dr 2η F(r)
(2)
where the dimensionless function F(r) is defined as the relative density, i.e., the measured density divided by the density of the void-free material. The variable F(r) contains the microstructural information about the material; it is a function of not only the void radius but also the packing configuration and particle size. Equation 2 accurately predicts that the void closure rate in a highly porous (i.e., low relative density) material will be greater than in an isolated void. It also predicts that as a material approaches its maximum density, the influence of neighboring voids will diminish, and thus its rate of void closure will decrease to that predicted by eq 1. That is, when spherical voids are sufficiently small, their shrinkage rate is similar to that of an isolated bubble described by eq 1. When eq 1 or 2 are integrated, it is usually assumed that viscosity is independent of time. The resulting equation would then not apply to systems in which the viscosity varies strongly with time, such as in cross-linking materials. Following the approach of Mackenzie and Shuttleworth, the variables in eq 2 can be separated and the equation integrated to yield an expression relating time, t, to F 3
γxz (t - t0) ) fMS(F) - fMS(F0) η
(3)
where
fMS(F) )
()[ (
2 3 3 4π
1/3
)
1 + g(F)3 1 ln 2 (1 + g(F))3
(
x3 tan-1 and
)]
2g(F) - 1
x3
(4)
g(F) )
(1 -F F)
1/3
(5)
where z is the number of voids per unit volume and F0 is the density at a time of t0. Note that z and the void radius, r, are both used to calculate the relative density, F. Equations 3-5 can be used to construct a theoretical curve expressing F as a function of reduced time, k(t - t0). Here k is a sintering constant defined as γz1/3/η, and t0 is taken as the theoretical (and imaginary) initial time when F0 is close to zero. The theoretical dependence of F on reduced time is shown as the solid line in Figure 11. If a material (with a viscosity constant with time) densifies by a viscous sintering mechanism, the time dependence of the density should be adequately described by the MS model. Indeed, the model has been successfully applied to the sintering of monodisperse, spherical silica particles29 and to porous xerogels.30 We shall next describe our efforts in applying the sintering model to the densification of FF latices and FF-NFF mixtures. We have analyzed the data from Figure 7 (trial 1) by converting the refractive index of the latex, n, to the relative density, F, via the Lorentz-Lorenz equation31 in the form
(n2 - 1)(nd2 + 1) F)
(n2 + 1)(nd2 - 1)
(6)
using an experimental value of nd ) 1.499 for the fullydense latex. The data are replotted in Figure 11 using a value of the sintering constant, k, of 3 × 10-8 s-1. We found this value of k to provide the best fit of the data to the theoretical expression shown as the solid line in the figure. Using estimated values of γ (0.03 J/m2, which is the literature value for poly(2-EHA) and many other hydrocarbons32 ) and z (7 × 1018 voids/m3, assuming one void is associated with each FF particle), we find that the value of η is approximately 2 × 1012 Pa s. Note that because of the approximations used in calculating η, our analysis yields only an estimate of the order of magnitude. To enhance the usefulness of this calculation of viscosity, we compared it to values for the FF latex without NFF particles. We calculated density as a function of time using index measurements of latex 2 immediately after film formation at room temperature (≈293 K) and proceeding over the course of several days. We found that these measurements could not be adequately described by the MS model over the entire range of times. We suggest that the model does not apply because the polymer viscosity changes with time. Acrylic polymers are known to be plasticized by water,12,33 so as the latex ages and trace amounts of water evaporate from it, we expect that the viscosity increases. Accordingly, our studies show that the rate of densification in a “fresh” latex is significantly higher than in an aged latex with a similar porosity. To circumvent the effects of hydroplasticization, we placed a recently-cast latex film in an evacuated desiccator for 40 h and held it at a temperature of 275 K. We anticipated that this treatment liberated the water within the acrylic, thereby producing a latex with a viscosity that is constant with time. By holding the polymer at a temperature below its Tg in the (29) Sacks, M. D.; Tseng, T.-Y. J. Am. Ceram. Soc. 1984, 67, 532. (30) Brinker, C. J.; Scherer, G. W. Sol-Gel Science; Academic Press, Inc.: San Diego, CA, 1990; p 702. (31) Born, M.; Wolf, E. Principles of Optics; Pergamon: New York, 1975; p 87. (32) Wu, S. In Polymer Handbook, Third Edition, Brandrup, J., Immergut, E. H., Ed.; John Wiley & Sons: Chichester, 1989; p VI-416. (33) Bodnyan, J. G.; Konen, T. J. Appl. Polym. Sci. 1964, 8, 687.
Film Formation of Acrylic Latices
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a topic of experimental investigation. The low shearlimiting viscosity (η0) of a suspension of hard spheres in a solvent with viscosity µ was measured as a function of the volume fraction of spheres, φ0, for silica suspended in cyclohexane35 and for polystyrene in water.36 De Kruif et al.36 correlated the data for φ0 ranging from 0 to 0.6 via
η0/µ ) (1 - φ0/0.63)2
Figure 11. Relative density as a function of normalized time for latices at room temperature: (O) mixture of 40 wt % latex 1 with 60 wt % latex 2; (∆) single latex 2 . The sintering constant k equals γz1/3/η. The solid line is the theoretical prediction of the MS analysis obtained from eqs 3-5. Table 2. Sintering Constants (k) and Calculated Effective Viscosity (η) for Two Latex Compositions at Two Temperatures
latex composition
temperature (K)
sintering constant, k (s-1)
calculated ηa (Pa s)
latex 2 latex 2 40 wt % latex 1 in latex 2 40 wt % latex 1 in latex 2
293 318 293 318
8 × 10-7 2 × 10-5 3 × 10-8 2 × 10-6
7 × 1010 3 × 109 2 × 1012 3 × 1010
a Viscosity is calculated with γ ≈ 0.03 J/m2 (the literature value (for poly(2-EHA)32 and a typical value for many hydrocarbons) and z ≈ 7 × 1018 voids/m3.
dry state, we sought to minimize the amount of film formation. After this drying procedure, we studied the optical changes of the latex at room temperature with the same procedure used for the mixture. The results of this experiment are also shown in Figure 11. At shorter times, the data still deviate from the theory, but the deviation is less pronounced than in latices that have not been predried. In this latter case, the data fit the theory only over narrow regions of time. Fitting the data from predried latex to the theory, we calculate the viscosity for dried latex 2 to be ca. 7 × 1010 Pa s (see Table 2). The viscosity of other acrylic polymers (PMMA and PBMA) near their Tg is likewise in the range of 1010 Pa s,34 so our calculated value is certainly reasonable. We suggest that latex mixtures also undergo the influence of hydroplasticization of the latex. We find that over approximately the first 3 days after casting, the index (and film density) changes more quickly than over the several days following. We expect that because of water evaporation, the effects of hydroplasticization are minimized at longer times. The fact that NFF particles create voids in the latex, however, could enhance the rate of evaporation compared to the single latex. More pathways could be created for the escape of water. As seen in the results listed in Table 2, the addition of 40 wt % NFF particles leads to a calculated viscosity that is at least an order of magnitude higher than in a latex without added particles. We attribute this higher viscosity of the latex to the effects of NFF particles. The effect of hard spheres on suspension viscosity has previously been (34) van Krevelen, D. W.; Hoftyzer, P. J. Properties of Polymers: Their Estimation and Correlation with Chemical Structure; Elsevier: Amsterdam, 1976; p 343.
(7)
This expression predicts that a suspension containing about 43 vol % hard spheres should exhibit a viscosity that is an order of magnitude greater than that for the solvent alone. If we model the FF latex as a viscous solvent and treat the NFF particles as hard spheres in a suspension (and noting that volume percent and weight percent have a similar value), then this prediction is in the range of what we found experimentally in our estimates of viscosity from the MS analysis. Equation 7 describes the viscosity over long times and thereby predicts the overall viscous behavior. A similar equation37 has been developed for short times (i.e., at high frequency relative to the diffusion time scale), and it provides a more local description of the solvent in the vicinity of a hard sphere. This equation likewise predicts an increase in the suspension viscosity, albeit a lower one. The trends in suspension viscosity that we find in this study are thus consistent with other experimental work and theoretical predictions. Moreover, theoretical calculations16 based on a self-consistent model describing nonsintering particles in a sintering matrix have predicted a higher viscosity and a slower sintering rate as a result of the nonsintering inclusions. (iii) Sintering at Elevated Temperatures. We also explored the effect of polymer viscosity on the kinetics of film densification. Whereas in our previous work we compared the behavior of latices with different Tgs, in this study we varied the temperature of the experiment. Heating a mixture of 40 wt % latex 1 in latex 2 at 318 K causes the refractive index to increase by ≈0.15 over ca 80 000 s (nearly 1 day), as seen in Figure 12. At room temperature, a similar magnitude of change takes place over about 30 days (Figure 7). When we apply the MS analysis to these data, shown in Figure 13, we find a viscosity that is ca. 2 orders of magnitude lower than that which we find at room temperature, as seen in Table 2. Such a strong temperature dependence of viscosity is expected for a polymer above its Tg.34 Latex 2 without the addition of NFF particles likewise has a viscosity that is well below its value at room temperature. The lower viscosity of latex 2 at 318 K results in a higher densification rate. Despite this greater rate, though, the mixture does not obtain its maximum density (corresponding to a refractive index of ca. 1.5) even after 1 day at 318 K. The complex refractive index indicates that some voids remain in the latex. Even though the FF polymer can flow with greater ease than it can at room temperature, it does not fill all of the voids in the material. Our ESEM observations have revealed that even when heated to a temperature of 318 K for several hours, those voids associated with clusters often remain. (iv) Implications for CPVC Measurements. Our work has relevance to the formulation of a latex paint or coating with a high solids (e.g., pigments and extenders) content. Although this present work has not explored the effect of pigment addition, NFF particles are equivalent to pigment particles in being non-deformable under the (35) Krieger, I. M. Adv. Colloid Interface Sci. 1972, 3, 111. (36) de Kruif, C. G.; van Iersel, E. M. F.; Vrij, A.; Russel, W. B. J. Chem. Phys. 1986, 83, 4717. (37) Lionberger, R. A.; Russel, W. B. J. Rheol. 1994, 38, 1885.
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Keddie et al.
voids being dominant. Measurements of latex density39,40 and permeability3 have indicated that air voids are almost always present in a dried latex, and above the CPVC, void formation is enhanced. Our results confirm that air voids can exist in a film-forming latex, even without the presence of NFF inclusions. Additionally, we have observed the effects of increased clustering of particles at higher concentrations. The probability of clusters of NFF particles resulting is predicted to be inversely related to their concentration.39 We have observed this trend and its detrimental effects on latex density. It has been recognized for some time that gloss measurements can be used to determine CPVC.38 More recently measurements of changes in hiding as a function of time, similar in concept to our work, have been used to determine CPVC while also providing greater insight into film formation.7,8 Our work demonstrates that optical properties (and latex density) are strongly dependent on the age of a latex. We therefore suggest that when analyzing a series of samples with varying PVC in order to determine the critical point, it is important that the samples have the same age at the time of the measurement. We predict that the apparent CPVC, if determined from optical or density measurements, should increase with increasing age of the samples. IV. Summary
Figure 12. (a, top) Refractive index as a function of time for a mixture of 40 wt % latex 1 and 60 wt % latex 2 at a temperature of 318 K for two trials. Data points (O ) trial 1; 4 ) trial 2) were deterined from kinetic scan measurements. The solid line is a guide to the eye. (b, bottom) Extinction coefficient as a function of time for the same samples.
Figure 13. Relative density as a function of normalized time for latices at 318 K: (O) mixture of 40 wt % latex 1 with 60 wt % latex 2; (∆) single latex 2 . The solid line is the theoretical prediction of the MS analysis.
conditions of latex film formation. Our results support several commonly-held concepts regarding the critical pigment volume concentration (CPVC).38 Floyd and Holsworth39 suggested that the CPVC indicates a transition point from polymer being the dominant phase to air
Using the two noninvasive techniques of ellipsometry and ESEM, we have studied all of the stages in the film formation of mixtures of FF and NFF latices. We have determined the effect of NFF particle concentration on the kinetics of the process and on the material microstructure. We have performed our experiments at room temperature and at 318 K. The effects of NFF particles on the film formation of latex can be summarized as follows. During stages II and II*, the packing configuration might be disrupted by NFF particles, particularly if their size differs from the filmforming particles. In this study, however, the single component latex formed a disordered array, and so the addition of NFF particles does not noticeably disrupt the packing. NFF latex particlesseven at low concentrationssresult in an increase in the size of voids and a decrease in latex film density. According to eq 2, larger voids close at a faster rate, and this idea could explain the differences in the rate of change in the optical properties with varying concentrations of NFF particles. Even so, the length of time required to produce a fully-dense (stage IV) latex increases with the concentration of NFF particles. Our ESEM analysis indicates that voids associated with an isolated NFF particle close at a greater rate than an interstitial void within a cluster of NFF particles. In latex 2, which is expected to be more viscous than latex 4, the densification takes place over a period of weeks when there are 40 wt % latex 1 particles. Our results also indicate the importance of a uniform mixture in order to maximize the densification rate. If the NFF particles are poorlydispersed, then clusters of them can create voids that are nearly impossible to eliminate, even at elevated temperatures. We suggest that when the number of contacts between NFF particles is minimized (i.e., when particle clustering is eliminated) the void volume fraction in an aged material will also be at a minimum. We have applied concepts and equations of sintering to the analysis of our optical measurements of latex mixtures. (38) Asbeck, W. K.; Van Loo, M. Ind. Eng. Chem. 1949, 41, 1470. (39) Floyd, F. L.; Holsworth, R. M. J. Coat. Technol. 1992, 64 (806), 65. (40) Parker A. A.; Opalka, S. M.; Dando, N. R.; Weaver, D. G.; Price, P. L. J. Appl. Polym. Sci. 1993, 48, 1701.
Film Formation of Acrylic Latices
Using estimated values for surface energy and void density, we calculate that the calculated η of a dehydrated FF latex at 293 K is about 7 × 1010 Pa s. This value is reasonable for an acrylic polymer slightly above its glass transition temperature. We find that at 318 K, the calculated viscosity is nearly 2 orders of magnitude lower, which also is reasonable. The addition of 40 wt % NFF latex slows down the sintering ratesregardless of the temperaturesand yields a calculated viscosity that is at least an order of magnitude higher. This result can be understood in light of the effects of hard spheres on suspension viscosity. Our conclusions from this study support many of the notions regarding the CPVC in other latex/particle systems. We have found that voids are present in a latex mixture, even when the concentration of “hard” particles is low. As the particle concentration increases, so does
Langmuir, Vol. 12, No. 16, 1996 3801
the void size. Particle clustering creates voids that are filled at exceedingly slow rates. Time-dependent optical properties could affect the value determined experimentally for CPVC. Acknowledgment. This work was supported by the DTI, ICI plc, Schlumberger Cambridge Research, Unilever plc and Zeneca plc through the Colloid Technology Programme. J.L.K. acknowledges support as an Oppenheimer Research Associate at the University of Cambridge. We thank Drs. R. Cameron, L. Gate, D. Heyes, C. Meekings, G. Meeten, D. Taylor, and P. Sakellariou for useful discussions and advice. ICI Paints in Slough supplied the latices used in this work. We benefited from the technical support of A. Eddy. LA960046Z
