tion. However, it was noted t h a t a n internally pigmented emulsion paint provided better freeze-thaw stability than did a corresponding normally pigmented paint. Maximum freeze-thaw stability would be expected if pigment were present on the periphery of the internal phase droplet since lower tack would result. Also, pigment contained in the periphery would be expected to increase the density of the internal phase resulting in internal phase settling. The fact that normal pigmented emulsions exhibit good suspension and show no remarkable improvement in freeze-thaw stabi1it.ysuggests t h a t the pigment is freely suspended in the aqueous medium. It is realized that the pigment location might vary with each type and grade; therefore, no general conclusions should be drawn on the basis of these data. DISCUSSION
External plasticization of nonfilm-forming dispersion resins offers unique formulating possibilities that do not exist in systems wherein all the binder is supplied as a dispersion or emulsion. It might be opportune t o discuss specific formulating possibilities, apart from those normally associated with interior latex paints, which appear promising in work with polystyrene. When formulating sealers, fire retardant paints (intumescent or noncombustible), calking or mastic compounds, and clear vehicle systems, it is evident that a fixed vehicle latex cannot possess all the performance characteristics necessary to satisfy the requirements of each application. Sealers require a hard, tough vehicle and sufficient inert loading to minimize topcoat penetration. The requirements c i n be satisfied with the postplasticized system by predetermining the optimum resin ratio in the internal phase, followed by pigmenting the vehicle to the desired pigment volume concentration. Fire-retardant paint vehicles must be formulated with noncombustible or intumescent
A plasticizer dispersed in a synthetic latex first forms an emulsion. As the system ages, the plasticizer probably diffuses from the emulsion droplets through the water phase and is then absorbed by the polymer particles. Plasticizers differ greatly in t h e speed of this process. Some plasticize the polymer so that films may be cast almost immediately after addition, while others require as long as 48 days to plasticize the latex. The action of several plasticizers on molded pieces of polymer is compared
materials. Such a formulation may be visualized as consisting of a resin-chlorinated plasticizer dispersion, pigmented with antimony oxide. A further possibility in fire retardancy suggests that intumescent latex paints might be made by inclusion of the intumescent agent in the plasticizer. Pigment loading of plasticizer may also be employed to prevent reaction between watersoluble salts and emulsifier, provided wetting aids are not included with the pigment, since they provide a bridge on which the ions can travel from internal to external phase, thus breaking the emulsion. Calking and mastic cdmpounds require higher than normal pigment loading to achieve application consistency. Workability, emulsion stability, and uniform drying without cracking in thick films are prerequisite performance characteristics. These can be achieved by employing, in part, a fugitive plasticizer in conjunction with a long fiber filler. The point of importance is that in the externally postplasticized system a part of the internal phase is initially available in its normal physical state making possible the introduction of various materials into what will eventually be the internal phase. In addition, the free choice of a part of the binder (plasticizer) makes possible tailoring of the internal phase. ACKNOWLEDGMENT
The author wishes to thank F. J. Hahn for his many helpful suggestions in the preparation of this paper. LITERATURE CITED
(1) Hahn, F. J., Ofic.Dig. Federation Paint R. Varnish Production CEubs, 317, 332 (June 1951). ( 2 ) Parker, C . H., Ibid., 333, 700 (October 1952). RECEIVED for review September 24, 1952.
ACCEPTEDJanuary 27, 1953.
with their action in the latex. The addition of small amounts of good swelling agents or solvents increases the rate of diffusion of plasticizer into the polymer. Data obtained by centrifuging plasticized latices show that “diffusion activators” shorten absorption time, thus permitting formation of cast films without a longagingperiod. A theory of the plasticizing process is developed in terms of the diffusion properties of a three-phase system of plasticizer droplets, water phase, and polymer particles.
R . E. DILLON, E. B. BRADFORD, A N D R . D. ANDREWS, J R . The Dow Chemical Co., Midland, Mich. RESENT synthetic latices cover a wide range of polymer P t y p e s . Some of these polymers are soft and tacky and form films freely at room temperature, whereas others are hard and must be modified to produce films. Some polymers of the latter type have physical properties that make them desirable in the coating field. A copolymer of 75% vinyl chloride and 25% vinylidene chloride belongs to this classification. When this Saran latex is dried a t room temperature, small white chips of chalklike material result rather than a continuous film. Satisfactory films can be obtained from this latex only after plasticizing. Dillon, Matheson, andBradford ( 7 )have presented data indicating that the factors affecting the formation of a film from a latex are the same as those appearing in Frenkel’s equation (9) for the coalescence of spheres by purely viscous flow
728
02 =
rt
3 2rnr
where r is the radius of the spheres; 7, the viscosity coefficient of the polymer; y, the surface tension; t, the time; and e, a factor related to the area of contact between the spheres. As e increases, the voids between the spheres become smaller, producing a more continuous film; thus e may be considered an index of the progress of film formation in the system. Once a latex is polymerized the only variable in Equation 1 that can be altered appreciably is 7. If the application process permits, the viscosity of the polymer may be lowered by heating t o promote the formation of a film, as in paper coating. The effect of heat on individual latex particles is shown in Figure 1. This is an electron micrograph of a sample vihich was prepared by
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25% added t o the latex, only small chalklike chips were obtained on drying after 24 hours' aging. It was necessary to allow several days to elapse before this system formed a continuous film. The effect of time on a plasticized latex is apparent from observations of electron micrographs of the surface of cast films. I n order to make these observations it was necessary to prepare replicas (4) of the surfaces. This was done by placing the specimen in an evaporating unit and coating the surface with a thin film of silicon monoxide. The coated film was then put into a solvent which dissolved the polymer film leaving the insoluble
Figure 1.
Heated and Unheated Polystyrene Latex Particles
depositing uniform polystyrene latex particles on the specimen film and then heating a t 115' C. for 4 hours. After this, more of the original latex particles were deposited on the film so that heated and unheated particles could be viewed in the same field. The sample was then shadowed ($4) with chromium. At the lower right of Figure 1 are two heated particles which show a large amount of coalescence; these may be compared with the particles a t the lower left which were not heated. The lengths of the shadows of the two particles a t the upper left corner illustrate the effect of heat on the sintering of particles to the specimen film. The lower particle was heated, whereas the upper was not. When the latex is to be used in a household paint, other methods must be found to control the viscosity, such &s plasticizing the polymer. The experimental sections of this paper discuss principally the mechanism of plasticizing the high solids content Saran latex (75 % vinyl chloride/25 % vinylidene chloride copolymer) mentioned previously. LOCATION OF PLASTICIZER
The plasticizer was added to the latex by one of two methods: 1. The plasticizer waR added directly to the latex with an equal volume of water and dispersed with a hand homogenizer or a colloid mill. The water was added to maintain the system a t 50y0 nonvolatile material. 2. A 50% plasticizer-in-water emulsion was made which was then added to the latex with sufficient agitation to make a stable system.
The second method was more successful with those plasticizers which had a tendency to separate from the latex. Considerable difference was found in the action of various plasticizers. A latex sample plasticized with 15% Flexol 3GH (triethylene glycol di-2-ethylbutyrate) by direct addition formed a continuous, transparent film within 24 hours of the time the plasticizer was added. (Plasticizer percentages in all cases are based on the nonvolatile content of the plasticized latex.) When Dow P5 (2biphenylyl diphenyl phosphate) was emulsified and
April 1953
Figure 2.
Surface of a n Unplasticized Saran Latex Film
replica which was rinsed in clean solvent and caught on a standard electron microscope specimen screen. Figure 2 is a replica of the surface of a film cast from unplasticized latex. Individual particles are clearly present in this surface with little indication of a tendency to coalesce and form a film. Figure 3 is a replica of the surface of a film cast from this latex plasticized with 15% Dow P5. The film was cast immediately after dispersing the plasticizer in the latex. When the film was dry, it was rinsed in methanol t o remove any excess plasticizer from the surface. The appearance is not a great deal different from that of the unplasticized material shown in Figure 2. After the plasticized latex had aged 14 days, another specimen was prepared in the same manner. Figure 4 shows the surface of this sample. Now the individual particles are much less distinct and are more coalesced than in either of the previous films. I n choosing a plasticizer for a latex which is to be used in a particular application, a number of factors must be taken into account. Several properties may be required of the formulated latex in addition to that of forming a satisfactory film. Many of these plasticizers require a long aging period. In order t o find a method of reducing aging time, some experiments on the mechanism of the plasticizing process were carred out. Two possible mechanism would permit the polymer to become
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Figure 3.
Surface of Film Cast from Plasticized Saran Latex with No Aging
plasticized: (1) The latex particles and plasticizer are brought together during the drying process, or (2) the latex particles absorb the plasticizer while still in the latex state and thus are plasticized before the film is cast. In order t o determine which takes place, the Saran latex was plasticized with 15% Adipol 2EH (2-ethyl hexyl adipate) which was added directly t o the latex and dispersed with a hand homogenizer. Immediately after mixing, a sample was centrifuged until the latex particles were thrown down. Examination of the sample showed a region of concentrated plasticizer-water emulsion a t the top, a clear water region below this, and the latex particles deposited in the bottom of the tube. At various time intervals, samples of the plasticized latex were centrifuged and observed. After 4 days, no plasticizer could be separated. Only the clear water phase a t the top and the latex deposited a t the bottom were observed. This can only be explained by a mechanism which permits the plasticizer to combine with the polymer in the latex svstem. As long as the polymer and plasticizer existed separately, they were separated by centrifuging; however, when the plasticizer entered the polymer particles, they could no longer be separated by this method. The authors were not able to obtain quantitative data on the rate of this process because under the experimental conditions the plasticizer-water emulsion was not completely broken; thus, the amount of free plasticizer could not be accurately measured. However, the total time necessary for all the plasticizer t o be absorbed by the polymer was measured. This method was found applicable only when the plasticizer had a density less than water. When the plasticizer had a density greater than water, the free plasticizer was also thrown down with the polymer. Instead of forming a separate phase on top of the polymer, it filled the voids between the spheres and could not be observed. Electron micrographs, however, indicate that the same mechanism-Le., plasticizer absorption in the latex state-takes place. Figure 5 is an electron micrograph of the unplasticiaed Saran latex. Figure 6 shows the latex after it has
730
Figure 4.
Surface of Film Cast from Plasticized Saran Latex Aged 14 Days
been freshly plasticized with Dow P-5; dark areas of plasticizer with embedded polymer particles can easily be distinguished. Figure 7 shows the plasticized latex of Figure 6 after aging. Now practically all the free plasticizer has been absorbed by the polymer. A comparison of the plasticized particles in Figure 7 with the heated polystyrene particles of Figure 1 shows a great similarity. In both cases the amount of coalescence is greater than is observed for the untreated particles. This is predicted by Equation 1 since the viscosities of both were lowered, and as a result the film-forming ability of the systems was increased. FACTORS AFFECTING AGING RATE
Centrifuge measurements of the type mentioned indicate t h a t a freshly plasticized latex consists of emulsion droplets of plasticizer and polymer particles suspended in the water phase. T o plasticize the polymer, the plasticizer must reach the polymer particles either by diffusion through the water phase or by plasticizer droplets and polymer particles coming into direct contact. Although direct contact probably takes place to some extent, the fact t h a t the emulsion remains stable throughout the plasticizing process, showing no tendency to agglomerate, suggests that the migration of plasticizer probably takes place primarily by diffusion through the water phase. The solubilities of most plasticizers in water are of the same order of magnitude-all very low. Very few data are available concerning diffusion rates of these materials in water, and the same may be said for their diffusion rates in the polymer; however, experience has shown that there is a vast difference in the ease of plasticizing polymers with different materials. This is also evident in plasticizing a latex. Plasticizers t h a t are readily absorbed by the solid polymer also plasticize a latex readily. Table I shows the length of time required for 15% of various plasticizers to be entirely absorbed by the latex. These values were obtained by observing the time when free plasticizer could
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no longer be separated by centrifuging. The first three matelisted in Table I were absorbed so fast t h a t they could not be separated immediately after being dispersed in the latex.
. rials
. Table I.
Time Required fm Saran Latex to Absorb 15qo Plasticizer Plasticizer Toluene Flexol3GH Plasticizer S.C. Adipol2EH Diootyl phthalate Butyl stearate
Time, Days 0 0 0 4 23 >48
These values correlate very well with the ability of molded pieces t o absorb these same plasticizers. Observations were made on pieces of molded polymer placed directly in the plasticizer for 2 hours, with the following results. Butyl stearate showed no effect on the surface of molded pieces. Dioctyl phthalate showed a slight surface effect of solvation. Adipol2EH was also a slow solvent, whereas plasticizer S.C. (triethylene glycol dipelargonate) was an active solvent. Flexol 3GH and toluene were both good swelling agents, toluene being absorbed faster than Flexol 3GH. I n molding and extrusion powders, obtaining a homogeneous polymer-plasticizer system offers some difficulty; however, heating and mechanical mixing can be employed in fabricating these materials to obtain a homogeneous dispersion. I n a latex, heating could be used as a means of promoting the diffusion of plasticizer into the polymer particles, but commercially i t would be desirable to have a more convenient method of facilitating this diffusion process.
Figure 5.
April 1953
Saran Latex Particles without Plasticizer
Consideration of the factors affecting the rate of diffusion reveals that concentration is very important. The initial plasticizer finds it very difficult t o penetrate the polymer and thus its rate of diffusion is slow. As soon as some plasticizer has diffused into the polymer, the effective internal viscosity for diffusion is lowered and the diffusion rate is increased ( 2 ) . T o accelerate the whole diffusion process, an inherently good solvent or swelling agent for the polymer was added t o the plasticizer to serve as a “diffusion activator.” A small amount of this material added t o the plasticizer made i t possible to incorporate a slow-diffusing plasticizer in a reasonable length of time. Figure 8 shows the effect of adding toluene t o Dow P5. Molded pieces of the Saran copolymer (thickness 0.32 em., surface area 14.2 square cm.) were placed in a series of plasticizer-toluene mixtures, left for 2 hours, and then weighed t o determine the total absorption of plasticiaer plus toluene per unit area. The amount of each component absorbed wm then determined by analyzing the change in concentration of the remainder of the mixture. Below 8% toluene content, the amount of plasticizer absorbed was too small to be measured by our techniques. Above this concentration of toluene, the amount of plasticizer absorbed is very dependent on the toluene concentration; in fact, the plasticizer curve crosses the toluene curve, indicating t h a t the diffusion rate of plasticizer molecules depends more strongly on swelling than the diffusion rate of the smaller toluene molecules. This principle was applied t o latex samples by plasticizing with 15y0 dioctyl phthalate and butyl stearate in combination with 5% of various swelling agents. The samples were then centrifuged to determine the time necessary for all the plasticizer to be absorbed by the polymer. Table I1 shows the results obtained. A comparison of these results with those of Table I shows considerable reduction in the total time required for absorption, Table I1 shows t h a t toluene was not effective in increasing the rate of absorption of butyl stearate; molded pieces of polymer placed in a mixture of toluene and butyl stearate similarly did not absorb a measurable amount. Carbitol acetate, however, did appreciably reduce the absorption time for butyl stearate, Also, this system was absorbed readily by molded pieces, Samples plasticized with 25% Dow P5 plus 5y0toluene cast continuous films after aging 24 hours. These films could be stripped from the glass plate on which they were cast. Samples
Figure 6.
Saran Latex Freshly Plasticized with Dow P5
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particle, T , being t h e only coordinate necessary t o consider. The diffusion in the water phase has certain simplifying features which make a relatively exact treatment possible. First, the diffusion constant of plasticizer in water will be relatively insensitive t o plasticizer concentration, so that the diffusion constant can be regarded as a constant, independent of concentration, Dw. I n addition, diffusion through the water phase may be treated as a steady-state process. For simplicity, it may be assumed that the polymer particles are sufficiently far apart so that each particle may be treated &s an isolated particle immersed in an infinite water phase; this is actually not a serious restriction.
Table 11.
Effect of Swelling Agents on Time Required for Saran Latex t o Absorb 15% Plasticizer
Plasticizer Dioctyl phthalate Butyl stearate
2
5
7 12 >48
Saran Latex Plasticized with Dow P5 and Aged
plasticized ~ 5 i t h25% Dow P5 alone did not produce continuous films after aging 24 hours; the films Tyere full of fine cracks and broke into many pieces if removed from the glass plate on which they were cast. These observations indicate t h a t the addition of a diffusion activator not only increases absorption rate but also decreases the aging time required of latices as measured by film-forming ability. Thus, diffusion is apparently the controlling factor in the aging process. THEORETICAL DISCUSSION
If it is assumed that plasticizer droplets and polymer particles are suspended in emulsion in the latex without direct contact and that the migration of plasticizer molecules into the polymer particles takes place through the water phase, the latex after addition of plasticizer can be regarded as a three-phase system in which one of the three phases (the plasticizer) is the diffusing material. The water and plasticizer phases can be assumed to be in equilibrium a t all times, the saturation concentrations of plasticizer in the mater phase and of water in the plasticizer phase both being very small. Since the rate of diffusion of plasticizer from plasticizer phase to water phase is much more rapid than the diffusion of plasticizer from the water into the polymer phase, the role of the plasticizer droplets in the diffusion process will be essentially t o act as a reservior to maintain a saturation concentration of plasticizer in the water phase, in the neighborhood of the plasticizer droplets. A detailed examination of the diffusion process will thus be required only for the water and polymer phases. The Water Phase. Because of the spherical symmetry of the diffusion into a polymer particle, it is necessary t o consider only the behavior in a representative solid angle; this is illustrated in Figure 9. Also, for the same reason, the process can be treated as a one-dimensional rather than a three-dimensional diffusion problem, the radial distance from the center of the polymer
732
Absorption Time, Days
IO-^
50
Figure 7.
Swelling Agent ( 5 % ) Methylathyl ketone Carbitol acetate Toluene Carbitol acetate Toluene
A B SORPTION G r n / C r n c AFTER 2 Hrs
IO
% TOLUENE IN M I X T U R E
0
20
10
30
Figure 8. Effect of Toluene on Absorption of Dow P5 by Molded Saran Polymer
The condition of steady-state diffusion requires that the rate of mass transport of plasticizer through any spherical area element enclosed by a given solid angle is a constant independent of r throughout the water phase; otherwise, the concentration of plasticizer as a function of r would not remain constant. This has been illustrated in Figure 9 by showing such shaded area elements a t r = R, T I , and rz. As T decreases, the shaded area decreases, and the velocity of transport and the associated concentration gradient in the radial direction both increase. Diffusion in the water phase can be assumed t o follow Fick’s law dC(T)
m=Dw-
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where m is the rate of mass transfer of plasticizer in the radial
. direction per unit area, and Dw, C(T),and T are the diffusion con. ~
stant, plasticizer concentration, and radial distance as defined previously. Solving this differential equation for m = constant, for the boundary conditionsC = CR,W a t T = R, a n d C = C, at r = a,and integrating the solid angle to include all of spherical space, one obtains the solution
M
.
.
. ‘
.
4i~RDm(Cm- CR,W;
C ( r ) = c,
.
(3 1
where M represents the total rate of transport of plasticizer through any spherical shell in the water phase, and consequently the total rate of diffusion of olasticizer into the polymer particle. The other quantities are as defined previously. Diffusion I I . I rate in the steady state is therefore proportional to the difference in concentration at the surface of the polymer particle and at effectively infinite distance, as well as t o the diffusion constant of the plasticizer. Steady-state diffusion rates may therefore vary between zero and a maximum value as the concentration a t the surface, CR,W, varies between the saturation value, C,, and zero. This can also be regarded 8s a variation between the cases where diffusion in the polymer phase and diffusion in Figure 9. Reprethe water phase are ratesentative S o 1 i d determining, respectively. Angle for Diffusion into a Polymer ParEquation 2 may also be solved ticle t o give the concentration as a function of radial distance, C ( r ) , by integration between the boundary conditions, C = CR.Wat r = R and C = C at r = T . The final result obtained, after substitution of Equation 3, is
- (Ca-C R , W ) R 7
(4)
A set of curves of C ( r ) corresponding to this equation are shown in Figure 10, for CR,Wvalues of C,, 0.8 C,, 0.5 C,, 0.2 C,, andzero. These curves are plotted in generalized form as C/C, US. r / R . If diffusion into the polymer particle is very slow, the value of CR,Wmay not be significantly different from C,. In this case, the steady-state treatment of Equations 3 and 4 will not be necessary, and it can simply be assumed t h a t the plasticizer concentration has the saturation value C , throughout the water phase, including the immediate neighborhood of the polymer particle, and that absorption kinetics are determined entirely by conditions inside the polymer particle. The Polymer Phase. Diffusion in the polymer phase is a more complicated process than diffusion in the water phase, since the simplifying features of the latter are no longer present. The diffusion constant, for example, cannot be assumed t o be a constant independent of plasticizer concentration, and Equation 2 therefore cannot be used. Also, diffusion in the polymer phase cannot be treated as a steady-state process since this would result in an accumulation of plasticizer a t the center of the polymer particle (where r = 0 ) ; however, a pseudo-steady-state treatment may be possible in certain cases. Both of these points are considered in more detail. A few studies (13, 18, 31) have been made of the diffusion of plasticizers in polymers, particularly from the standpoint of plasticizer loss from already plasticized materials. An average value of the diffusion constant was calculated in some cases (12, 31), but the data did not allow a detailed calculation of the April 1953
diffusion constant as a function of concentration. It was observed, however, that the diffusion constant depended strongly on plasticizer concentration (12). The most detailed studies of diffusion in polymers have been made with lower molecular weight substances, and various investigations (5, 6) have shown that the diffusion coefficient for solvents or swelling agents in polymers also depends strongly on the concentration of diffusing material already present, in the low concentration range. Boyer (2, 3) has derived the following expression for the form of this relationship: log D = A - B(Vz)’/z (5) where Wz is the weight fraction of polymer, and A and B are constants. Crank and Park (3, 16), however, prefer t o use a slightly different form t o represent their experimental data on a number of different systems log D = 01 @VI (6)
+
where VI is the volume fraction of solvent and 01 and @ are constants. Both of these expressions are approximately equivalent in the range of low concentrations (9), and in general the diffusion constant seems to depend approximately exponentially on concentration in this range. Barrer (1) has pointed out t h a t over the whole concentration range, the curve of D(C) versus C is probably S-shaped, the exponential dependence holding only a t low concentrations. Figure 8 shows that the diffusion coefficient for plasticizer in polymer is increased not only by the presence of absorbed plasticizer but also by the presence of an absorbed third component (toluene in this case). Some similar observations have been made by o,ther authors. Hartley (11)and Mandelkern and Long (16)found t h a t the rate of absorption of organic liquids by cellulose acetate films is greatly accelerated by the presence of very slight amounts of absorbed water in the polymer. Conversely, the presence of plasticizer has been observed by Doty (8) to increase the diffusion constant for water vapor in polymers. The polymer particles in a latex can undoubtedly be considered t o contain an equilibrium amount of absorbed water and the water phase an equilibrium concentration of dissolved polymer (essentially zero). Thus two of the three phase-pairs (plasticizerwater and polymer-water) will be in equilibrium very soon after adding the plasticizer t o the latex; the aging period is required t o allow the third pair of phases (polymer-plasticizer), which are not in direct contact, t o come t o equilibrium.
1.0
-
0.9 -
O
i
Y
2
4
6
8
/o
r/R
Figure 10. Concentration of Plasticizer OS. Distance from Center of Polymer Particle for Steady-State Diffusion in Water Phase
Since diffusion rate in a polymer is increased b y the presence of the diffusing material or of other absorbed substances in a very general way, i t would appear that the effect results primarily from the swelling of the polymer, which produces a more open structure, rather than from any specific interaction effects. Diffusion in polymers is believed to proceed by a “place change” mechanism (1) in which the diffusing molecule exchanges places with a polymer chain segment; the molecular mobility of the polymer which favors such a process will be enhanced by a more open structure, whether produced by the presence of low molec-
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ular weight components or by other means. Some interesting indirect evidence on this point is provided by recent experiments of McLoughlin and Tobolsky ( I S , 14) on the relaxation of stress in samples of polymethyl methacrylate subjected to mechanical strain. The relaxation of stress process is favored by increased molecular mobility in the same manner as diffusion, and it was found that relaxation rate was increased by the presence of absorbed water in the polymer (15) and, in addition, that relaxation rate was strongly affected b y the thermal history of the
U Figure 11.
Stages of
the Diffusion Process
sample (24). By heating samples above the transition tempcrature and then cooling them through the transition region a t different rates, samples with different amounts of “free volume” could be produced which differed in relaxation rate by as much as 1000-fold. This illustrates a method of producing a more open structure and increased molecular mobility with no absorbcd material present. The effect of free volume on diffusion in polymers has been discussed brieflv by Robinson and Crank ( 2 0 ) . In connection with measurements of diffusion of methylene chloride in polystyrene, Park ( 1 7 ) states that his results cannot be completely explained by the dependence of the diffusion constant on concentration, but that “polymer history” is also irivolved ; this may represent free volume effects such as those mentioned above. H e also postulates the presence of microscopic cracks in the polymer samples to explain certain results. It is evident, therefore, that diffusion in the polymer phase can be a complicated process. with a number of factors affecting the diffusion rate. There are some features which contribute t o a simplification of the picture, however. It has often been observed (10, 11, 22, 23) that >Then a polymer s~vellsin a liquid, a definite boundary between swollen and unswollen polymer can be seen, and birefringence measurements ( 1 9 ) indicate that the “shape” of the boundary remains about constant as it moves forward. If the diffusion constant is a function of concentration alone, the distance of advance should be proportional to the square root of time, according to classical theory. Actually, appreciable molecular orientation occurs adjacent to the boundary, and this tends to have a retarding effect on diffusion, particularly in the early stages, with the result that in some cases the distance of advance is more nearly proportional to time than t o the square root of time ( 1 1 ) .
134
A diffusion constant which increases strongly with concentration would lead to such a boundary where concentration varies rapidly over a short distance. If, in addition, the polymer is cross-linked or partly crystalline, so that crystallites act effectively as cross links, the swelling will have a maximum equilibrium value. One can then envisage cases in ahich the concentrationof plasticizerinalatexparticle as afunction ofradial distance from the particle center increases from zero to the equilibrium swelling value over a fairly short distance, for intermediate stages of the diffusion process, with essentially zero concentration inside this boundary and essentially the equilibrium swelling concentration outside. The total rate of absorption of plasticizer by the polymer particle will then be equal to the equilibrium swelling concentration multiplied by the rate a t which polymer volume is swept out by the moving boundary. This is illustrated schematically in Figure, 1I,B, where hypothetical curves of C ( r ) versus T are shown in the polymer phase for two successive values of time, t l and tz. The concentration of plasticizer in the polymer phase a t the polymer-water interface, C R , ~is, essentially the equilibrium swelling value here, and this value is different from the plasticizer concentration in the TrTater phase a t the same interface, CR W. I n general, the plasticizer will be much more soluble in the polymer phase than in the water phase, and the ciifference between CR,Pand CR w mill be even greater than is shoir n here. The curve for plasticizer concentration in the water phase in Figure, 11B, is one of the family of steady-state curves illustrated in Figure 10. The plasticizer phase is represented only in a generalized way in this diagram: the concentration 4 1 1 1 have some high value, which lies off the graph as drawn here, and the abscissa scale of radial distance no longer applies in this section. The state of the system a t zero time is represented in Figure 11A. Here plasticizer concentration is zero in the polymer phase and has its equilibrium saturation values in the watpr and plasticizer phases. ( I t will be remembered that the plasticizer phase contains a certain amount of absorbed water.) The final state attained when the diffusion process is complete drpends on a number of factors, such as the amount of plasticizer present and the relative solubilities of plasticizer in the polymer and water phases. If the swelling boundary in the polymer particle is moving a t a constant rate, and the change of area of the boundary is neglected as i t moves, the rate of absorption of plasticizer will be approximately constant with time during the intermediate stages of the diffusion process. In view of the various complicating factors which can affect diffusion rate, the changing area of the swelling boundary might actually be compensated by other effects so as to result in a constant absorption rate. I n any case, such a constant rate of absorption could be regarded as a type of “steady state,” even though this does not correspond to the conventional hydrodynamic definition of a steady state. The latter type of steady state, as mentioned previously, would lead to the accumulation of plasticizer a t the central point of the polymer particle with the concentration remaining constant a t all other points in the particle. However, the pseudo-steady state which is possible here has, like the true steady state, the property t h a t the rate of diffusion through the outer boundary remains constant; as a consequence, a steady state will also establish itself for diffusion in the water phase. Actually, a steady state of diffusion will probably be found in the water phase in any ca6e where the rate of diffusion into the polymer particle is not undergoing rapid change, and this will probably be true in most practical cases. The picture of the plasticizing process presented here suggests the possibility of there being two stages in the aging of a plasticized latex. It seems possible that the supply of plasticizer in free plasticizer droplets and in the water phase might become exhausted before the plasticizer had completely penetrated the polymer particle. This would give polymer particles with a swollen, soft exterior and a hard, unsivollen core as a product of the first stage of the aging. There would then be a period of time
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Vol. 45, No. 4
*
.
in which the plasticizer redistributed itself in the polymer particle to give a uniform concentration throughout, as the second stage of the process. The first stage only of the aging process would be measured by sedimentation measurements in the centrifuge, such as those described in a previous section, since no free plasticizer would remain a t the end of this period. The existence of such a second period in the aging would be more difficult to demonstrate but might be important in imparting satisfactory film-forming properties to the latex. Particles with a soft shell and hard core might form films with a fused yet lumpy surface such as that shown in Figure 4. Because of the complexity of diffusion in the polymer phase no attempt has been made t o treat this problem in detail. The problem is more complex, mathematically, than diffusion in the water phase, and additional experimental data on some of the phenomena involved would be desirable in order t o know what assumptions can reasonably be made in the mathematical development and what reference cases would be most useful to treat. A pseudo-steady state for diffusion in the polymer phase represents a very special case. In general, an explicit solution of the differential equation for diffusion giving the time-dependent, transient state will be required. SUMMARY
'
.
ties of good swelling agents or solvents t o the plasticizers, which swell the polymer structure and accelerate diffusion rate. I n analyzing the plasticizing process in terms of basic theory, diffusion through the water phase can be treated as a steady-state process. Diffusion in the polymer phase, however, must in general be treated as a transient phenomenon. LITERATURE CITED (1) Barrer, R. M., Kolloid-Z., 120, 177 (1951). (2) Boyer, R. F., J . A p p l . Phys., 2 0 , 5 4 0 (1949). (3) Boyer, R. F., J . PoEymer Sci., 5 , 139 (1950); Crank, J., and Park, G. S., Ibid., 5 , 1 4 0 (1950). (4) Bradford, E. B., J . A p p l . Phys., 23, 609 (1952). (5) Crank, J., and Park, G. S., Trans. Faraday Soc., 4 5 , 2 4 0 (1949). (6) Crank, J., and Robinson, C . , Proc. Roy. Soc., 204A, 549 (1951). (7) Dillon, R. E., Matheson, L. A., and Bradford, E. B., J . Colloid Sci., 6, 108 (1951).. (8) Doty, P., J . Chern. Phys., 1 4 , 2 4 4 (1946). (9) Frenkel, J., J . Phys. (U.S.S.R.), 9, 385 (1943). (10) Hartley, G. S., Trans. Faraday Soc., 42B, 6 (1946). (11) Hartley, G. S., Ibid., 4 5 , 8 2 0 (1949). (12) Liebhafsky, H. A., Marshall, A. L., and Verhoek, F. H., IND. ENO.. CHEM.,3 4 , 7 0 4 (1942). (13) McLoughlin, J. R., Ph.D. thesis, Princeton University, 1951. (14) McLoughlin, J. R., and Tobolsky, A. V., J . Polymer Sci., 7, 658 (1951). (15) Mandelkern, L., and Long, F. A., Ibid., 6 , 4 5 7 (1951). (16) Park, G . S., Trans. Faraday Soc., 4 6 , 6 8 4 (1950). (17) Ibid., 4 8 , l l (1952). (18) Reed, M. C., IND. ENG.CHEM.,35, 896 (1943); Reed, M. C., and Connor, L., Ibid., 4 0 , 1 4 1 4 (1948). (19) Robinson, C., Trans. Faraday Soc., 42B, 12 (1946). (20) Robinson, C., Proc. Roy. SOC.,204A, 339 (1950); Crank, J., and Robinson, C., Ibid., 204A, 549 (1951). (21) Small, P. A., J . SOC.Chem. Ind., 66, 17 (1947). (22) Smekal, A., Kolloid-Z., 120, 189 (1951). (23) Wheaton, R. M., and Harrington, D. F., IND. ENG.CHEM.,44, 1796 (1952). (24) Williams, R. C., and Wyckoff, R. W. G., J . A p p l . Phus., 17, 23 (1946).
Plasticizers dispersed in a synthetic latex form emulsion droplets in the latex. The plasticizer then apparently diffuses through the water phase and is absorbed by the polymer. The rate of the process is largely determined by the rate at which the plasticizer is absorbed by the polymer. Plasticizers which are readily absorbed plasticize the latex quickly and permit the formation of continuous films soon after formulation. Plasticizers which are slowly absorbed by the polymer require an aging period after formulation before comparable films can be cast. The aging period is considerably shortened by the addition of small quanti-
RECEIVPID for review October 13, 1952.
T h e detailed mechanism of the film formation of latex paint is not yet understood, but this paper presents a skeleton outline to assist in obtaining better understanding of the subject. A two-stage mechanism is proposed:
first, irreversible contact brought about by evaporation of water and, second, fusion of dispersed resin particles to form a strong continuous film. Photographs and tabulated data illustrate basis of this concept of film formation.
W . A . HENSON, D . A . TABER,
AND
ACCEPTED February 9, 1953:
E. B . BRADFORD
The Dow Chemical Co., Midland, Mich.
T
HERE is every indication that latex paints are permanently
.
established commercially. The basic phenomenon of film formation and pigment binding by latex, either natural or synthetic, is not new. However, recent developments make it clear t h a t a very wide variety of synthetic latexes will ultimately be used as binders for paint and related coating materials. It is timely, therefore, t o consider what is known about the mechanism involved in the formation of a relatively impermeable film from the discrete colloidal particles as they exist in a latex. It is the purpose of this paper to present one concept of this mechanism. A great deal more work must be done before there will be a clear understanding of this mechanism, but a systematic study of the principles involved will make possible the use of April 1953
latexes now unsuited as binders for paints and the deFign of new latexes superior t o those in use at this time. PAINT INGREDIENTS
Basically, any paint consists of one or more pigments dispersed in a fluid medium suitable for spreading on a surface and of such a viscosity as t o prevent sagging if the surface happens t o be vertical. I n the case of an oil-based paint (the word oil is here used loosely t o include drying oils, alkyd resins, varnishes, etc.) the oil performs two functions, I n t h e wet state it provides part of the fluidity of the system and hence acts as part of the vehicle. However, after the paint is applied, the oil, undergoing
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