2726
Langmuir 1995,11, 2726-2733
A Study of Latex Film Formation by Atomic Force Microscopy. 1. A Comparison of Wet and Dry Conditions F. Lin and D.J. Meier” Michigan Molecular Institute, 1910 West St. Andrews Road, Midland, Michigan 48640 Received September 9, 1994. I n Final Form: April 10, 1995@ We discuss mechanisms that have been proposed for film formation from latex systems and point out that major problems exist, in that the relative role played by the water/air, the polymedair, and the polymedwater interfacial tensions in promotingfilm formation has not been established. Even the relative role played by “plasticization”of latex polymers by water has remained as an unanswered question. In order to clarify this problem, we have investigated the rate of film formation of “wet”and “dry”latex systemsby atomic force microscopy. The role of the water surface tension (in creatinga “capillary pressure”) was clearly revealed by forming a “wet”latex system through condensation of water into the interstitial space of initially dry latex particles. Poly(iso-butyl methacrylate) (PiBMA)was used as the model latex because of its appropriate glass transition temperature, Tg 65 “C, and its hydrophobic character. The rate of film formation (at 70 “C)was found to be approximately 10-timesfaster under “wet”conditions than when “dry”. Separate experiments showed that Tg of PiBMA was unaffected by water, and hence plasticization was not a factor in the enhanced rate. These results clearly show in this system that the dominant factor in promoting film formation was the water surface tension and resulting negative capillary pressure. Furthermore, it is shown that the capillary pressure in wet systems can be of sufficient magnitude to explain the observed deformation of the latex particles at 50 “C, i.e., 15 “C below TP Capillary pressures and forces increase with decreasingamounts of water in the interstitial regions of spherical particles, and capillary pressures can reach very high values with seemingly insignificant amounts of water. The equilibrium between the amount of interstitial water and the relative humidity of the atmospheric water is shown, and it indicates that even with low relative humidities the capillary pressures can still be quite large. We maintain that capillary pressure typically is the dominant driving “force”for film formation. These results are in contrast to the conclusions of others.
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Introduction Discussions about the mechanism of latex film formation have continued for almost half a century and the issues are still being debated. Many mechanisms and theoretical models have been proposed, but the models presented are typically incomplete or wrong and experimental proof has been lacking. In the early 1950s, Bradford et al. recognized part of the basic mechanism by stating “... sintering of synthetic latex particles takes place by the viscous flow of the polymer, the surface tension of plastic furnishing the necessary shearing stress.” In a later paper,2 they recognized that film formation occurs in two steps as water evaporates: (1)loss of water to a point of irreversible contact of the particles and (2) development of the film and fusion of the particles. Later, Brown3 in a seminal paper pointed out that capillary pressures arising from the surface tension of water in the interstitial regions as well as from the polymerlair or polymerlwater interfacial tensions are the driving forces for the film formation. In addition, he correctly pointed out that the rheological properties of the latex control the resistance part of film formation and that elastic deformation rather than viscous flow could also lead to film formation. Brown developed a theoretical model for film formation driven by capillary pressure, but the details of his model have been justly criticized by others (e.g., Mason41, and we shall point out additional problems in a later section. Vanderhoff et aL5 and Voyutskii6 pro-
* Author to whom correspondence should be addressed. Abstract published in Advance A C S Abstracts, J u n e 1, 1995. (1)Dillon, R. E.; Matheson, L. A.; Bradford, E. B. J. Colloid Sci. 1951, 6, 108. (2) Henson, W. A,; Taber, D. A,; Bradford, E. B. Ind. Eng. Chem. 1963, 45, 735. (3) Brown, G. L. J. Polym. Sci. 1956,22, 423. (4)Mason, G. Br. Polymer J. 1973, 5, 101. (5) Vanderhoff. J . W.: Tarkowski, H. L.: Jenkins. M. C.: Bradford, E. B. J. Macromol. Chem.’1966,1, 361.
posed models in which coalescence follows either rupture or elimination of the stabilizing entities on the particle surfaces to allow polymer contact and interdiffusion between neighboring particles. Mason4 pointed out that Brown and Vanderhoff had made mistakes in their theoretical models by confusing forces and pressures, and he in turn proposed an “improved‘‘ model for latex film formation. However, his model is also flawed as a result of using an incorrect expression for the capillary pressure (actually the same incorrect expression used by Brown). Sheetz7proposed an entirely different mechanism for the process of film formation, in which heat of the surroundings provides the energy source. The heat is converted to useful (film forming) work by its role in the evaporation of water. In his theory, he correctly pointed out that the water-polymer wetting angle was neglected in Brown’s models3 Sheetz7 and Vanderhoff et ale8also pointed out the importance of the kinetics of water diffusion through the film as film formation proceeds. This is an issue that is typically overlooked in discussions of film formation. In a very important paper, Eckersley and Ruding critiqued the various models and theories that had been proposed for the film formation from polymer latices. They then developed a new model and presented experimental data in support of the model. Although several mistakes present in earlier theories were corrected, their model is still flawed since it depends on the incorrect FrenkellO model for the film formation process itself, as will be discussed in a following section.
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(6)Voyutskii, S. S. J. Polym. Sci. 1958, 32, 528. (7) Sheetz, D. P. J. Appl. Polym. Sci. 1965, 9, 3759. (8)Vanderhoff, J. W.; Bradford, E. B.; Carrington, W. K. J . Polym. Sci. Symp. 1973, 41, 155. (9) Eckersley, S. T.; Rudin, A. J . Coatings Tech. 1990, 780, 89. (10)Dobler. F.: Pith. T.; Lambla, M.; Holl, Y. J. ColloidInterfaceSci. 1992, 152, 1.
0743-7463/95/2411-2726$09.00/0 0 1995 American Chemical Society
A Study of Latex Film Formation Frenkel model
Multiple-particlemodel
Figure 1. Frenkel and multiple-particle models of particle deformation. The dotted lines show that the center-to-center particle spacing is retained in the multiple-particle model in contrast to the Frenkel model. More recently, Dobler et a1.”J2 published a series of papers on the coalescence mechanism in which they concluded that the polymerlwater interfacial tension alone could drive the system to coalesce, but that the major driving force during water evaporation from a latex was from the capillary pressure from the waterlair interface. Although we agree with this conclusion (our results to be discussed show the same), we believe their experiments were too limited in scope and lack details of the coalescence process which would allow a proper analysis of the problem. The previous models and theories have made a significant contribution to latex-coating science and have given a qualitative or perhaps a semiquantitative picture of the mechanism of the latex film formation. However, we believe that the past models are incomplete and often based upon incorrect assumptions. For example, most of the theories have used Frenkel’s modello of coalescence, in which two spheres coalesce or deform with a reduction in their center-to-center spacing. Although Frenkel’s analysis of the coalescence of two spheres is valid, it is an inappropriate model for latex film formation, since the interaction between contacting spherical particles is not just between pairs of particles but is between close-packed neighboring particles, in which a given sphere has (ideally) 12 nearest neighbors. Two objections can be raisea to the simple Frenkel model: (1)a sphere deforming with its twelve neighbors will undergo only a very slight deformation before overlap and interaction of the deformed zones occurs and (2)deformation of the particles in the plane of the film of a real latex system does not change the centerto-center spacing. This was demonstrated by Goh et a1.I3 and also by our experiments where the interparticle spacing could be accurately measured using atomic force microscopy (AFM). Our results clearly showed that the lateral interparticle spacing remained constant during the film formation process. The change in particle (and film) dimensions which is required to fill the interstitial space takes place normal to the plane of the film. Figure 1contrasts the Frenkel model with what we believe is a more realistic model for the film formation process, i.e., one in which the lateral dimensions remain constant. As film formation proceeds with a reduction in the interstitial volume, the interstitial “channels” by which water is transferred to the surface for evaporation will become narrower. It is quite possible that local fluctuations in the film formation process will eventually close off some interstitial regions such that the water therein (11)Dobler, F.; Pith,T.; Lambla, M.; Holl, Y. J.ColloidInterfaceSci. 1992,152,12. (12)Frenkel, J. J.Phys. W.S.S.R.) 1943,9 , 385. (13)Goh, M. C.;Judue, D.; Leng, 0-M.; Wang, Y., Winnik, M. A. Langmuir 1993,9 , 1319.
Langmuir, Vol. 11, No. 7, 1995 2727
is no longer a part of the continuous water phase with direct contact to the film surface. Elimination of water from these regions will then be by permeation through the polymer. Sheetz7 and Vanderhoffs recognized the importance of the diffusion (permeation) of water in the film-forming process, but not in this context. A model allowing a quantitative prediction of the filmforming process in terms of known interfacial and rheological properties has been lacking, as has been definitive experimental proof of the correctness of any model. In this and in following papers, we plan to present a model for a latex system that does allow quantitative predictions and then to present definitive experimental data about the kinetics of film formation as a function of known molecular, rheological, particle, and other system variables. It is perhaps appropriate here to point out that a semantic confusion exists in the literature on latex film formation, in that the terms “coalescence“ and “film formation” are often used as synonyms. The two terms are not synonymous, “coalescence”implies the fusion of the latex particles together by polymer interdiffusion across the particle interfaces, while “film formation’’only implies that a film is formed by the distortion of the particles to eliminate the interstitial voids. Film formation does not imply that interdiffusion of polymer chains between particles must occur. Brown3clearly recognized this distinction when he pointed out that cross-linked particles were capable of film formation, but that interdiffusion and coalescence were precluded. Studies of the interdiffusion of polymer molecules between partic1esl4-l7 may not be relevant to the process of film formation itself, since coalescence (interdiffusion) may occur at a much later time after a film has formed. Of course, interdiffusion is of great importance for the development of physical properties of the film. The results to be presented in this paper concern “film formation”. Experimental Approach A critical study of latex film formation requires welldefined model latices as well as experimental techniques that allow a detailed examination of the film-forming process. We have used an atomic force microscope (AFM) to obtain quantitative kinetic data as film formation takes place in a latex system. The AFM is uniquely suited for this purpose since it allowsquantitative data of the particle peak-to-valley dimensions (“corrugation height”) to be obtained without the necessity of any surface treatment, e.g., staining, replicating, and depositing a conductive film. For convenience in drying and handling of the model latices, it was desirable to choose a polymer for which the glass transition temperature, Tg,was above room temperature, but not inconveniently high for the later film formation studies. Also, it was desirable that polymerization techniques be available such that latices could be prepared in a variety of sizes and in monodisperse form, preferably “surfactant free” to avoid complications from a surfactant. Poly(n-butyl methacrylate), used by a number of other investigators, was chosen first, but its Tg 32 “C proved to be too close to room temperature to ensure that particle distortion did not occur during drying and handling. Poly(isobutylmethacry1ate) (PiBMA) was then chosen as the model lattice. It’s Tg(-65 “C) is
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(14)Winnik, M. A.;Wang, Y.; Haley, F. J.Coatings Tech. 1992,81I , 51. (15)Boczar, E.M.;Dionne, B. C.; Fu, 2.;Kirk, A. B.; Lesko, P. M.; Koller, A. D. Macromolecules 1993,26, 5772. (16)Pekcan, 0.Trends Polym Sci. 1994,2,236. (17) Kim, K. D.; Sperling, L. H.; Klein, A,; Wignall, G. D. Macromolecules 1993,26,4624.
Lin and Meier
2728 Langmuir, Vol. 11, No. 7,1995
sufficientlyabove room temperature that latices could be recovered in an undeformed state during handling at room temperature. The film formation process could then be followed from the initial undeformed state to the final film by heating to modest temperatures above Tg, e.g., 70-90 "C. The driving force for latex film formation results from the particle and the water interfacial energies (neglecting hydrostatic pressure effects from water permeation from closed cells, as mentioned above). The relative contribution of each interfacial energy depends on the state of the latex, i.e., the extent of particle deformation, the presence and amount of air and water in the interstitial regions, and transport rates. In this first paper, we report on the relative role played by the various interfacial energies in promoting film formation, in which we compare the rates of film formation of a latex system under both dry and wet conditions. In the dry state, film formation is driven by the polymer surface tension alone, while in the wet case there are additional factors for film formation arising from the water/air interface (capillary pressure) and from the watedpolymer interface. In the present experiments, we ensured that the initial wet and dry states of the latex were identical by forming the "wet" state by condensing water from a water-saturated atmosphere onto a dry latex film. For a polymedwater wetting angle 0 -= go", water will condense into the interstices of the latex since the chemical potential of water condensed in the interstices will be lower (from the negative capillary pressure) than that of the saturated atmosphere. We also followed the amount of water condensed by the weight gain of samples placed in a saturated atmosphere, with results to be discussed in a later section.
Figure 2. Corrugation height and center-to-center spacing measurements using AFM. Initial
Standard tip
Experimental Methods Latex Preparation. The PiBMA latices of the present investigationwere prepared by a one-step surfactant-free emulsion polymerization. In a typical preparation, 24 mL of isobutyl methacrylate monomer and 0.09 g of potassium persulfate were added to 150mL ofwater in a three-necked 250 mL flask equipped with a mechanical stirrer. Polymerizationwas carried out at 80 "C in a temperature-controlled water bath and was complete in 6 h. The molecular weight of the various samples was controlled by the addition of dodecylmercaptan as a chain-stoppingagent. The latex used in the present investigationhad a molecular weight of approximately 100 000 (from GPC results in THF solution, based on polystyrene standards). Swple Preparation for Film Formation. Films were prepared by spreading and drying a monolayer of the latices on freshly cleaved mica at room temperature. One set of samples was kept dry, while another set was sealed in vials in the presence of a pool of water which provided a water-saturated atmosphere. Supports kept the samples from directly contacting the water pool below. Each set of samples was placed in a 70 "C oven for selected periods of time and then removed and dried at the room temperature for AFM scanning. Each sample used for scanning was a fresh one; i.e., they were not scanned and then returned to the oven for additional heating times. Atomic Force Microscopy. ATopoMetrix TMX 2000 atomic force microscope was used, and scanningwas done under ambient conditions and in the "contact mode". The profile of each AFM image was analyzed to obtain the corrugation height, and the recorded values are averages of data taken in different regions of the film. A typical AFM image used to obtain corrugation height data is shown in Figure 2, which also shows the high degree of particle uniformity. The AFM data were obtained using pyramidal silicon nitride tips, with a tip angl? of approximately 110" and a tip radius of approximately 400 A. As is shown in Figure 3, such tips will not correctlyimage the corrugationheight of close-packed latex spheres until the progress of the film formation has reduced the corrugation height to approximately one-half of the original sphere radius, or in the present case to corrugation heights of less than about 80 nm. The corrugation
After partial deformation height
Figure 3. ShowingAFM inability to monitor exact corrugation heights until partial film formation has occurred. height data to be presented are all below 80 nm. It should be pointed out that even though corrugation heights cannot be accuratelydetermineduntil film formationhas proceeded to some extent, this problem does not affect measurement of the centerto-center spacing of the close-packed spheres. The center-tocenter spacing can be accurately measured during the whole progress of film formation, and, as mentioned, it remained invariant as film formation proceeded. 4. Differential Scanning Calorimeter (DSC). Samples of PiBMA were placed in sealed aluminum DSC pans, one of which was dry and the other having a small pool of water. The glass transition temperatures were determined using a duPont 2000 DSC, at a temperature ramp of 10 "C/min from room temperature to 80 "C. The data (fromthe third scan) are shown in Figure 4 and reveal that the glass transition temperature of PiBMAis not affected by water. This observationis of importance in interpreting data from the present investigation, as will be discussed in a following section;
Film Formation and Models As water evaporates from a latex suspension, the spherical latex particles will eventually be brought together (ideally) into a close-packed array, with each particle surrounded by 12 nearest neighbors. As the water continues to evaporate and no longer fills all of the interstitial space, a negative capillary pressure will
Langmuir, Vol. 11,No. 7,1995 2729
A Study of Latex Film Formation
latex particles
water meniscus
Figure 6. Water condensed in interstitial region of latex particles showing the radii of curvature r1 and a capillary pressure
r-2,
and giving
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develop throughout the system from the curvature of the water meniscus in the interstitial space at the uppermost surface of the array. The net effect is to produce a normal (compressive) stress which acts on the particles to eliminate the interstitial volume and produce a coherent film. This normal stress will increase as water evaporates from the upper surface and as the radius of curvature of the water layer decreases. If the spherical particles are rigid and not deformed by the capillary or other interfacial stresses, the continued reduction of the water volume will cause the upper water surface to move downward into the particle array or will create air cavities in the interior. The negative capillary pressure acting on the particles is difficult to estimate during this stage because of the complex topology of the water surfaces in the cavities, but it must continuouslyincrease to the value where the water no longer forms a continuous phase and is isolated at the contact points between pairs of spheres, as shown in Figure 5. At this point, the radii of curvature, rl and 73, of the water meniscus indicated in Figure 5 are well-defined and lead to a capillary pressure, AP = yw(l/rl 1/73), where yw is the surface tension of water. r1 and r 2 are of opposite sign, with rl being negative (if the polymedwater wetting angle 0 < 90")and r 2 being positive. As the water continues to evaporate, both r1 and r 2 will become smaller, with changes that are interrelated to the watedpolymer wetting angle 0by the following equation, the derivation of which is shown in Appendix 1:
10'
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Fractional amount of water
Figure 6. Negative capillary pressure A€' as a function of r2/R and fractional amount of water (Vw/Vs)and of the polymer/ water wetting angle for spheres with R = 155 nm. 8
wetting angle
+
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This reduces to 7-2 = (r1 2 r 1 ) ~ - ~r1 for zero wetting angle (note that rl in this equation has been defined with respect to a circle outside of the meniscus and hence is the negative of r1 that appears in the equation for AP). The maximum value r2/R can have without the water forming a continuous phase will vary from 0.423 for 0" wetting angle (and with r1lR = 0.155) to 0.50 with rl/R = 00 for a 60" wetting angle. Figure 6 shows the (negative) capillary pressure as a function of r2/R and of the fractional amounts of water (VwNspheres) for several wetting angles and shows that the capillary pressures can reach very high values with very
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small amounts of interstitial water. The capillary forces (F = AP x area of the meniscus "ring") also increase with decreasing radii of curvature or decreasing amounts of water, but the increase is much more modest, as shown in Figure 7. These results are of importance since it is often claimed18that capillary pressures are not important because of the rapid evaporation of water from latex systems. These claims overlook the fact that at any finite humidity there will be water a t equilibrium in the interstitial regions with a concomitant capillary pressure (18) Speny, P.R.;Snyder, B. S.;O'Dowd,M. L.; Lesko, P.M.Langmuir 1994,10,2619.
2730 Langmuir, Vol. 11, No. 7, 1995
that can be very large even at low relative humidities (see Appendix 2). The calculated values assume perfect nondeformed spheres, and values will be less in a real latex system where the particles can deform in response to high stress levels. However, even allowing for particle deformation, capillary pressure will typically be the predominate stress responsible for film formation as long as the wetting angle is < 90” and the humidity is finite. It typically will outweigh the stresses from the polymer/ air and polymedwater interfacial tensions that also promote film-formation, since the radii of curvature of the water meniscus will be much smaller than the curvature of the particles. Vanderhoff et al. came to similar conclusionsconcerning the effect of radii of curvature on capillary pressures, but the conclusions of 0thers~9~ about capillary forces have been in error in stating that the capillary forces decrease and become negligible as the amount of water (i.e., rdR) in the interstices decreases. Brown3 stated that the “maximum” capillary pressure during water evaporation was AP = 2y/r at r/R = 0.155, Le., at the point where the water phase becomes discontinuous and “rings” of water form at the contact points (with 0” wetting angle). The factor “2”in the equation for AP indicates that Brown took the radii of curvature rl and r2 ofthe water surface to be equal (to “r”),Le., implying that the meniscus surface is spherical, which it is not. The pressure at r/R = 0.155 is not a “maximum”,for it can reach much larger (negative) values with decreasing values of r1 and r2, as Figure 6 shows. Unfortunately, most authors following Brown have used this incorrect value for the capillary pressure in their own models. Although we believe that the theoretical portions of Brown’s paper are in error, he must be given credit for being the first to present a reasonable qualitative description of most of the factors involved in latex film formation.
Lin and Meier 6.0 0
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Results and Discussion As discussed above, the present experiments were designed to vary the driving force for film formation. Under dry conditions, the only driving force for film formation is that from the polymer surface tension (neglecting the trivial contribution from gravity). However, in a watersaturated atmosphere, close-packed spheres will condense water a t their contact points, provided the water wets the polymer with a contact angle of less than 90”. The condensed water will produce a negative capillary pressure from the water/air interface and will also create a polymer/ water interface, replacing in part the polymedair interface of the original particles. The fact that water did condense from a saturated atmosphere into the present latex system was demonstrated in separate weight-gain experiments. In an attempt to avoid complications from distortion of the spheres that would occur a t temperatures above Tg(65 “0,these experiments were conducted a t room temperature and at 50 “C. The room temperature weight-gain data are shown in Figure 8 and the 50 “C data in Figure 9a. These data were obtained on samples which were approximately 1 mm thick, and because they are much thicker than the monolayer samples used to obtain the film formation (corrugationheight) data, water adsorption occurred over a much longer time period. Although both sets of weight-gain data were taken at temperatures below Tg,the results are surprisingly different. The amount of water condensed at room temperature appeared to reach a plateau of about 5.5%
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over a 6 week period. Only a small fraction of water actually condensed compared to the total free space for water condensation in close-packed spheres (-35% based on the sphere volume). The reason for reaching an apparent equilibrium amount much below the total interstitial volume is that the negative capillary pressure and hence the negative chemical potential becomes zero when r1 = -r2 (rl and r2 are of opposite curvature, see Figure 5 ) . The fractional amount of water absorbed (-5.5%) in the present experiment corresponds to rdR = 0.39. Assuming that the amount of water adsorbed is an
A Study of Latex Film Formation 0.5 0.4
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Langmuir, Vol. 11, No. 7, 1995 2731
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Wetting angle 0 Figure 10. Relative radius of curvature r/R where the radii of curvature -rl and r2 are equal (zero capillary pressure) vs wetting angle. equilibrium value (AP = 0, or rl = q),the radius of curvature rdR = 0.39 corresponds to a wetting angle of approximately 54”. This follows from Figure 10, which shows the values for rl = -rz as a function of the wetting angle. I t is interesting to note that with wetting angles smaller than about 44O, the water will condense to form a continuous phase (rdR 2 0.48) at equilibrium instead of being isolated in meniscus “rings” as in the present experiments. These calculations, of course, assume that the particles remain as uniform spheres. In contrast to the samples held at room temperature, where the amount of water condensed eventually approached a plateau value, samples held at 50 “C absorbed about 3% water in 50 h, as shown in Figure 9a, but thereafter the amount of water continuously decreased with time until virtually no condensed water remained. An AFM investigation of the 50 “C samples showed that the corrugation height was reduced from the original 155 nm to almost a plateau value of about 40 nm in 200 h, as shown in Figure 9b. These results clearly indicate that although the samples were approximately 15 “C below Tg, the capillary pressures were still sufficient to deform the spheres to eliminate the interstitial volume. Comparable AFM measurements of the samples held at room temperature were not successful. At this temperature, the particles did not deform or coalesce sufficiently to hold them in place during AFM scanning; i.e., they behaved as loose “soccerballs” which were moved about by the probe during scanning. It is, of course, possible that samples held at 25 “C for very extended periods would also deform to eliminate the interstitial volume, but there was no indication of this happening in the more than 1000 h of these experiments. An indication of the time required can be obtained using the WLF equation.lg The necessary C1 and CZparameters were determinedz0by time-temperature superposition of stress relaxation data and are CI=15.95and CZ= 195 at a reference temperature of 100 “C. With these values, the shift in the time scale is approximately 2 x lo4for a shift in temperature from 50 to 25 “C;i.e., the peak in absorption which occurred at 50 h at 50 “C would require approximately lo6 h at 25 “C. AFM corrugation height data showing the rates of film formation for the wet and dry samples are shown in Figure 11. These data clearly show that film formation occurs very much faster in the water-saturated atmosphere than (19)Williams, M. L.; Landel, R. F.; Ferry, J. D. J.Am. Chem. SOC. 1955, 77,3701. (20) Lin, F.; Meier, D. J. Unpublished data.
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log time (hrs) Figure 11. Corrugation heights by AF’M of “wet”and “dry” p i ~ latex u systems as a function of time at 70 “c. in ‘‘drf‘ air. To reach the same film roughness (corrugation height) requires approximately 10 times longer for the “dry” than for “wet” system. The much faster film formation in the “wet”system could result from either the changed surface energetics in the wet system (watedair and watedpolymer vs polymer/air) or from modification of the rheological properties of the latex polymer by water (plasticization). However, the latter can be dismissed on the basis of the DSC results which clearly showed that PiBMA had the same Tgunder both wet and dry conditions. This result is not too surprising since it merely shows, as expected, that PiBMA is a hydrophobic polymer. Hence, for our system the faster deformation of the wet latex must have resulted from the changes in the surface or interfacial energetics. For condensation to occur (chemical potential or AP negative), the watedpolymer wetting angle must be less than 90” (cos 0 > 0). Young’s equation, cos 0 = (yp - ypw)/yw,requires that yp > ypwif cos 0 is to be greater than zero. Thus, the driving force for film formation from the interfacial energies of the polymedair or polymedwater surfaces is actually less in the wet system than in the dry. Consequently, we must conclude that the observed enhancement of the rate of film formation in the wet system is simply due to the capillary pressure arising from the surface tension of the condensed water in the interstitial space. In contrast, other investigators18 have concluded that the dominant factor for faster film formation under “wet” conditions was from the plasticization of the polymer by water, since the rapid evaporation of interstitital water eliminated it as the driving force for film formation. As discussed above, these claims overlook the fact that, at any finite humidity, there can be very appreciable capillary pressures arising from the interstitital water. Also, those conclusions concerning plasticization were reached using hydrophilic copolymers (with acrylic acid as a comonomer), which obviously could be plasticized by water. We believe our results with PiBMA clearly show that our PiBMA polymer is not plasticized by water and that the faster rate under wet conditions must have resulted from capillary pressures. With polymers that are plasticized by water, faster rates could be the result ofboth plasticization and capillary pressures. In any event, we believe that capillary pressures from the intersitial water is the predominant driving stress for film formation under most conditions. In a separate experiment, latex was spread on a mica film and the water was evaporated rapidly (10 min) at 70 “C. The measured corrugation height was essentially the same as that of the undeformed latex particles; i.e., even though capillary forces were present during drying, the
Lin and Meier
2732 Langmuir, Vol. 11, No. 7, 1995 X
\
Figure 12. Model to obtain relationships between radii of curvature rl and r2 and wetting angles (see Appendix 1).
10 min drying time was too short to allow significant particle deformation. The interplay of time and temperature on the kinetics of film formation will be discussed in a following paper.
Conclusions The present experiments were designed primarily to allow quantitative measurements of the effect of capillary pressures on the kinetics of latex film formation, in which a comparison was made using AFM to establish the rate of film formation of dry and wet latex systems. The wet system was formed by allowing water to condense from a water-saturated atmosphere into the interstitial space of an initially dry latex system spread on mica. The progress of film formation of both types of systems was followed using an atomic force microscope to measure the particle deformation (corrugation height) as a function of time. Film formation proceeded much more rapidly when the latex was wet than when dry. To reach the same degree of film formation (corrugation height) required only about l/lO the time under wet than under dry conditions. Plasticization of the PiBMA latex by water was shown not to be important, thus proving that the dominant role .infilm formationfrom this latex system is from the surface tension of the interstitial water (capillary pressure). An analysis of the capillary pressures and forces of rigid spherical particles with meniscus "rings" of water in the contact region shows that the capillary pressure increases and becomes very large with a decreasingamount of water. The capillary force (capillary pressure x area of the water "ring") also increases with decreasing amounts of water, in spite of the smaller water area and comments to the contrary in the l i t e r a t ~ r e . ~However >~ the increase in capillary forces are much more modest compared to the capillary pressures. The amount of water adsorbed from a saturated atmosphere at 25 "C by a multilayer latex film reached a plateau value of about 5.5% at 25 "C, but required more than 6 weeks to do so. However, at 50 "C, the amount of water adsorbed reached a maximum value at about 3%in about 50 h, but then the amount steadily declined with time until virtually no water remained. AFM measurements of the surface corrugation proved that the decreasing amount was due to the deformation of the latex particles to eliminate the interstitial space and showed that capillary pressures from the water meniscus were large enough to deform the latex particles a t 50 "C, i.e., at a temperature 15 "C below the glass transition temperature.
Appendix 1 Relationship between the Radii of Curvature and Wetting Angle. Figure 12 shows two latex spheres of radiusR in contact, with a water meniscus a t their contact point. The outer surface of the meniscus has a negative radius of curvature of rl and a positive radius of curvature of r2 as shown (r2 is measured from the contact point to the midpoint of the curved meniscus surface, which is assumed to be spherical). The origin of the radius of curvature r1 is displaced from the center of a latex particle by z. We wish to obtain the relation between rl and r2 as a function of the wetting angle 0,which is given by the difference in the tangent angles 61 of the latex particle and 9 2 of the meniscus a t their intersection, 38. Taking the center of the coordinate system a t the center of the left-hand latex particle as shown, the equations for the latex particle R and the meniscus surface r1 are, respectively, x 2 + y 2 = R 2 and ( x - z ) 2 + y 2 = r l2
+
with z2 = R2 (r1+ ~ - 2 (note )~ that because of the origins taken for r1 and R, r1 is the negative of the rl which appears in the Laplace equation for the capillarypressure). Solving these equations for the intersection 3,p of the meniscus with the latex sphere, we obtain
The tangent to the latex sphere a t the intersection 33 is then
and for the meniscus
2r,2
+ 2rlr2 + r:
(4R2r,2- r:(r2
+ 2r1)2)1/2
The desired relationship between the wetting angle 0 and r1 and 7-2 is then
o = o2 - 6,= tan-'
I
2r,2
+ 2r1r2+ r:
+
1.-
( m 2 r , 2 - r;(r2 2r1)2)1/2 2~~ 2r1r2 r: tan-' (4R2r,2- r:(r2 2r1)2)1'2
I
+
+
+ +
1.
which reduces to r2 = -r1+ (r12 2Rr1)1/2 when the wetting angle is 0".
Appendix 2 Equilibrium Amount of Interstitial Water vs Relative Humidity. Water will condense in the interstitial regions of close-packed spheres until the chemical potential equals that of the water in the atmosphere, p(interstitia1) = p-
Langmuir, Vol. 11, No. 7, 1995 2733
A Study of Latex Film Formation (atmosphere). Relative to bulk water, the chemical potential of the interstitial water is p -p, =
J
wetting angle
(ri
vy, - + -
'
'0 '40
i
,/
,/
OM)
i
where is the molar volume of water, yw is the surface tension of water, and rl and 7-2 are the radii of curvature of the water meniscus. The chemical potential of the atmospheric water is p
- p, = RT In E = RT ln(rh) Po
where r h is the relative humidity. Equating the two expressions, we obtain
,
I
I
1
I
0.3
0.4
0.5
0.6
0.7
-r'Z
0.8
0.9
Relative humidity
Figure 13. Relative radius of curvature rdR vs relative humidity and wetting angle. which is a form of the Kelvin equation. rl and r2 are also related through the polymerlwater wetting angle (see Appendix 1)
+
+ +
2 ~ ' 2r1r2 r t (4R2r12- r;(r2
1
Note that in this equation rl is the negative of r1 in the equation above involving the relative humidity. The difference arises from the fact that the origin of r1 in the wetting angle expression is taken as being outside of the meniscus, as discussed in Appendix 1. These equations
together then give the desired relationships among rdR, the relative humidity, and the wetting angle. Results are shown for several wetting angles in Figure 13, in which we have used yw = 75 dydcm, R = 1.55 x loT5cm, and T = 298 K. These results, together with the relationship between r2 and capillary pressure shown in Figure 6, indicate that even at very low humidity levels capillary pressures can be very large. However, we again point out that these results are for undeformed spheres and that pressures will be less in a system of deformable particles.
Acknowledgment. The authors express their sincere thanks to the National Science Foundation Industry1 University Cooperative Research Center in Coatings for support of this work. LA940725E
