Polymer Coatings Concepts of Solvent Evaporation Phenomena Charles M. Hansen Springdale Research & Development Center, P P G Industries, Inc., Springdale, P a . 15144
Advances in phenomenological understanding have generally been a result of improvements in the state of the art based on practical experience. In recent years more theoretical interest has been directed toward understanding solvent evaporation during polymer film formation and a clearer picture of this complex process has evolved. This i s presented in detail here, in the hope that the more theoretically minded reader will find satisfaction in the reduction of theory t o practice, and the coatings formulator will discover useful simple tools and concepts t o help solve daily problems.
T H E R E are two barriers to solvent evaporation from a polymer solution drying on an impermeable substrate: the resistance to solvent loss a t the air-liquid interface, R,, and the resistance to transport (diffusion) of solvent from within the film to the air interface, Rd. R, is affected by such factors as the vapor pressure of the solvent and its latent heat of vaporization, as well as solvent transport through a thin air layer. R, is reasonably constant during drying for a given system. Rd is most easily expressed in terms of a diffusion coefficient. This diffusion coefficient is not constant and decreases exponentially as the solvent concentration decreases. This resistance to solvent diffusion can commonly be as much as 10’ times greater in the later stages of drying than in the initial stages. Typical data for the diffusion of an organic solvent in a common polymer are shown in Figure 1, where the variation of the diffusion coefficient of chlorobenzene in poly(viny1 acetate) a t 25°C is shown. The drying of polymer films takes place in two distinct phases, depending on whether R, or Rd is dominant in retarding solvent loss. In the first phase, R, is much greater than Rd and the major resistance to solvent loss is at the air surface. Rd increases as solvent evaporates,
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however, and a t the dry-to-touch stage, Rd has become somewhat greater than the reasonably constant R,. At this point, the solvent concentration at the surface falls rapidly to zero, leaving as much as 10 to 20% of the solvent distributed within the film. This solvent is very important, since it functions as a very strong plasticizer. Some must escape via an Rd-controlled process before sufficient rigidity (sufficiently high glass transition temperature) is achieved. Five to 10% solvent can remain in a polymer film for years because of the exceptionally slow diffusion rates at zero solvent concentration which are encountered just within the film near the air surface. The solvent that reaches the surface evaporates almost immediately during the Rd-controlled stage, but considerable ratios never get to the surface within the lifetime of the film. The existence of two-phase film drying has been confirmed experimentally and by computer calculations (Hansen, 1965, 1967a). The log-log sketch for the evaporation of chlorobenzene from poly(viny1 acetate) shown in Figure 2 demonstrates the division of the drying process into two stages. The corresponding concentration ranges are also indicated in Figure 1. SIP is the volume ratio
of solvent to polymer. This basis is chosen because the plasticizing effect of the solvent is best expressed in terms of volumes and because diffusion of solvent molecules through the rather dense polymer matrix is almost entirely controlled by the volume requirement that a space large enough to allow motion of the solvent molecule must be available or created if the solvent molecule is to move. A dimensionless time variable, T = D,t/L2, based on diffusion theory, is chosen rather than time, t, since it incorporates the effect of variations in the dry film thickness, L. At long times the data for various film thicknesses (22 and 165 microns in Figure 2) coincide. If the diffusion coefficient at zero solvent concentration, Do, is not available, a plot using t/L’ conveys essentially the same information, and also accounts for the effect of film thickness in the analysis. Using t / L 2 emphasizes that doubling the film thickness will quadruple the time to a given state in the second phase. The transition between the two phases occurs when R , and Rd are of the same order of magnitude. The solvent concentration corresponding to the transition point, C,, is very close to the solvent concentration at which the linear relation between log D and solvent volume fraction ceases to be valid, or about 0.2 volume fraction for the data in Figures 1 and 2. During the transition, the solvent concentration a t the surface rapidly falls to zero.
rates in the first phase were shown to be directly related to instantaneous solvent activities. Sletmoe found no pronounced second phase in any of his systems, although about 1% of o-xylene has been found in 150-micron-thick short oil alkyd films after one day a t room temperature (Hansen, 1967a). His later work shows how to calculate initial evaporation rate and solvent balance for mixed solvent compositions. Tysal and Snowden (1968) attempted to follow the evaporation of mixed solvents from plasticizer, after determining that such results would be comparable to evaporation from polymer solutions as far as the first phase is concerned. By adjusting evaporation rate parameters, and with an analog computer to aid in curve fitting, reasonable agreement was found between experiment and theory, although much remains to be done before practical use of this approach can be anticipated. Because of the rapid loss of volatile solvent during the first phase, it has been implied that, for practical
First Phase
For the solvent loss in the first phase, the intuitive feelings regarding simple evaporation processes are valid, and generally lead to a correct analysis for rate of solvent loss under varying conditions. There is solvent a t the air surface and its loss can be hastened by application of heat and air circulation. Some subcooling of the film below ambient temperature will be encountered because of latent heat requirements. I t will take twice as long to get through the first phase if the film thickness is doubled, since twice the amount of solvent must pass through the air-liquid interface where the controlling resistance to solvent loss is found (Hansen, 1964b). For room temperature drying it is common to speak of fast and slow solvents, the most suitable measure of speed being the relative (n-butvl acetate = 100) evaporation ratio. Such data are readily available (Doolittle, 1954; Hoy et al., 1967) and correlate drying in the first phase very well on a relative basis. Solvent boiling points are sometimes used as a rule of thumb in this respect, but are inferior to the evaporation ratios. For a multicomponent solvent, the relative amounts of volatile solvent may vary during the first phase, the slower solvent being enriched in the remaining volatile material. Azeotropic solvent compositions may also be encountered, in which case this would be the composition at the end of the first phase. The most recent comprehensive work on measuring and predicting evaporation of solvent in the first phase has been reported by Sletmoe (1966, 1970), Tysal and Snowden (1968), and the New York Society for Paint Technology (1969). Sletmoe studied the instantaneous evaporation rates of single solvents from polymer solutions and compared these to the evaporation rates of the neat solvents. For the alkyd systems studied the time required for loss of solvent from 50 to 3 volume % was 2 to 3 times longer than that required to evaporate a comparable amount of solvent from an inert surface. Evaporation
9 ~ BASED -
0.I
0 2
03 VOLUME
ON
TOTAL
VOLUME
04 05 Ob 07 08 FRACTION CHLOROBENZENE
09
1 .o
Figure 1 . Diffusion coefficients of chlorobenzene in poly(viny1 acetate)
FIRST PHASE
SECOND PHASE
w
2 10 0 >
w
I 3
O Y E DAY
-
L - 30 M I C R O N S
0
IO
166 T,
I 65 ( Dot/L2
1 6 ~
)
I 0-j DIMENSIONLESS
I 0-2
Figure 2. Experimental drying curves for evaporation of chlorobenzene from poly(viny1 acetate) Ind. Eng. Chem. Prod. Res. Develop., Vol. 9, No. 3, 1970 283
purposes, evaporation ratios can be applied to predicting which solvents will be found in the film after long time lapse (Weigel and Sabino, 1969). How this enrichment can be used to accelerate attainment of full film rigidity with slower solvents is demonstrated in Table I. Solvents having linear or compact molecular structure (higher diffusion coefficients), for example, can be used to accelerate the second phase in spite of much lower evaporation ratios and enrichment in the first phase. A more detailed explanation of these data is included below. Internal diffusion in the first phase is primarily a function of the pure solvent viscosity (Chalykh and Vasenin, 1966), but is so rapid that the solvent concentration is essentially uniform throughout the film. Solvent loss in the first phase is controlled by phenomena a t the airliquid. surface. Transition Period
During the transition period Rd increases a t a rapid rate compared to the reasonably constant R,. The surface concentration eventually falls to zero, after the internal diffusion resistance slows transport of the solvent to the surface. This stage in the drying process is not simple, although some of the apparent anomalies of solvent evaporation can be traced to events occurring in this period. Perhaps the most significant factor is the concentration of the volatile solvent in the film at this point in the drying process, C,. This solvent must leave the film by an Rd-controlled process. In a single solvent-single polymer system, C, is related to the amount of solvent required to reduce T,,, the glass transition temperature (damping maximum at 1 cis) of the mixture to the film temperature. Where the polymer Tgis well below the film temperature, no clear, prolonged second phase can be expected. This is the case with very mobile, long oil alkyds. I t is likewise the case if the film is heated well above the polymer T,, or for rubbery materials a t room temperature. Diffusion in the polymer is relatively rapid in these cases. Any solvent remaining in a polymer with high TR after a high temperature bake can be considered a permanent part of the film, since times longer than the life of the film would be required to allow diffusion of the last few per cent out of the film. Polymers with higher T, would also be expected to enter the second phase with correspondingly higher C, because of the relation between C, and polymer Tg. Since the prevailing film temperature is not necessarily the same as ambient temperature, anomalies of slower drying can occur if excessive supercooling of the film is allowed. Such excess supercooling can be induced by high air velocities past the surface (Julke, 1962) and the resultant effect of a slower “through-dry” is often called case hardening. A similar effect has been reported for the evaporation of acetone from poly(viny1 acetate), resulting in a slower loss of solvent than with methyl ethyl ketone (Hansen, 1964a). The acetone cools the film excessively compared to the methyl ethyl ketone. (A drop of acetone evaporating from the tip of a sensitive resistance thermometer cools to about 1”C a t room temperature conditions.) The lower film temperature leads to higher C,. Other plasticizing materials in the film will reduce C,, since they reduce the Tg of the nonvolatile film components. The plasticizing effectiveness of the materials present in the transition region affect C,, smaller molecular species generally being the more effective plasticizers 284
Ind. Eng. Chem. Prod. Res. Develop., Vol. 9, No. 3, 1970
(Dimarzio and Gibbs, 1963; Hansen, 1967a; Jenckel and Huesch, 1953). Water is the most efficient plasticizer, on a volume basis, followed by methanol, other organic solvents, monomeric plasticizers, and polymeric plasticizers, in that order. C, in poly(viny1 acetate) increases in the order methanol (=0.11), ethylene glycol monomethyl ether (=0.145), chlorobenzene (=0.20), and cyclohexanone (= 0.25). C, is dependent on a number of factors and is important, since this is the start of the slow second phase controlled by internal diffusion. Reducing C, where possible, will help speed subsequent solvent loss. Second Phase
The second phase of solvent loss in polymer film formation is controlled by the slow diffusion of the solvent through the dense polymer matrix. This retarded diffusion is generally several orders of magnitude slower near the air surface than close to the substrate. Concentration profiles have been calculated to show that the solvent has distributed itself essentially uniformly throughout the inner three fourths of the film with a rapid drop of concentration near the air interface (Hansen, 1967a, 1968). Such films are softer near the substrate than close to the air surface because of the plasticizing action of the solvent. This same plasticizing action is responsible for the enormous variation of the solvent in polymer diffusion coefficient shown in Figure 1. Greater polymer segment mobility accompanies the added plasticizing action of higher solvent concentrations and solvent diffusion rates are increased. The activation energy required to move the polymer chain segments and create space for a solvent molecule to move can be 40 kcal per mole or more (Kokes and Long, 1953). This value is considerably higher than normal hydrogen bonding energies, which are generally closer to 5 kcal per mole. The only significant influence of hydrogen bonding on the second-phase diffusion process is that the polymer and solvent must have some physical similarity for solubility. Were this not the case, the solvent would not pentrate into the polymer. The suggestion that solvent is held for long times in the polymer film as a result of hydrogen bonding is completely unfounded. The rate of diffusion in poly(viny1 acetate) decreases in the order water > methanol > ethylene glycol monomethyl ether > chlorobenzene > cyclohexanone, showing no correlation with hydrogen bonding (Hansen, 1967a,b, 1968). Extensive studies on solvent content in poly(viny1 acetate), acrylic, and VYHH films after prolonged drying established the following approximate order for greatest solvent retention at very long times (Hansen, 1967a): cyclohexyl chloride > cyclohexanone > diacetone alcohol > methyl isoamyl ketone > methyl isobutyl ketone > mesityl oxide > 2-nitropropane > chlorobenzene > toluene > dioxane > gamma-butyrolactone > benzene > n-butyl acetate > ethylene glycol monobutyl ether > 1-nitropropane > ethylene glycol monoethyl ether > ethyl acetate > methyl ethyl ketone > nitroethane > ethylene glycol monomethyl ether > methanol. A similar series has been developed by Chalykh and Vasenin (1966). For a given polymer, the primary factor increasing solvent retention is a greater minimum cross section of the diffusing solvent. The nonplanar cyclohexyl group requires more space than a planar cyclic group and branched molecules have a greater cross section than linear ones.
A potential use for this type of information was cited earlier (Hansen, 1964a); poly(viny1 acetate) films formed from mixtures of ethanol and methyl ethyl ketone lost solvent more quickly than those formed exclusively using methyl ethyl ketone. The more slowly evaporating ethanol reduced C, through a greater plasticizing effectiveness and diffused more rapidly from the film because of its linear structure. Poor solvents do not necessarily diffuse more rapidly, as evidenced by the relatively slow diffusion of toluene in VYHH, approximately as predicted from the order of solvents listed above. The data in Table I show how additions of linear ethylene glycol monoethyl ether (EGMEE) (evaporation ratio 32) to the bulky methyl isobutyl ketone (MIBK) (evaporation ratio 165) in solutions of VYHH actually speeds up solvent loss in the second phase. Use of volume ratios rather than weight ratios also emphasizes the differences in the situations reported in Table I because of density differences in the solvents. The retained solvent was assumed to be entirely composed of the slowest solvent in the mixture. I n these experiments, 0.3- to 1.0-mil films were weighed periodically after application, with subsequent baking a t 95'C (with periodic weighings) to remove the last solvent Any factor helping to increase polymer chain segment mobility will help increase solvent diffusion coefficients. Increases in temperature or plasticizer content are obvious means t o do this, but added plasticizer softens the film more than the solvent it helps to remove. Conversely, any obstruction to free solvent diffusion, such as pigment particles, tends to retard solvent diffusion. Situations involving the diffusion of water must be regarded with caution because of the effects accompanying adsorption of water on the pigment surface (Funke et al., 1969). I t is conceivable that related phenomena are possible with organic solvents. Placing a polymer film with retained solvent under vacuum will not help remove the last traces of solvent: the solvent concentration a t the air surface is already zero. If heat connot be applied, a more suitable means of removing the final traces would be to let the film stand in moist air. Absorbed water will plasticize the polymer. Immersion of the film in water or methanol might also be considered, if side effects are not serious. Several techniques for the analysis of mixed solvents retained in polymer films have been used, including gas chromatography and radioisotopes (Hays, 1964; Julke, 1962; Murdock and Carney, 1961; Murdock and Wirkus, 1963: Weigel and Sabino, 1969). Solvent Diffusion
When polymer films are formed by solvent evaporation, solvent diffusion is most often the controlling factor in rapidly attaining films with high rigidity. In many instances. such diffusion appears to correlate on a relative basis with solvent evaporation ratios, but significant variations have been cited above. Actual measurements of diffusion coefficients can be tedious and time-consuming, although simplified methods for interpretation of the resulting data have been developed (Crank and Park, 1968; Hansen, 1967a,b). For diffusion coefficients above about cm' per second with films in the 20- to 100-micron thickness range, R , was found t o be a significant factor, as shown in Figure 1. In the concentration range higher than that corre-
Table I. Retention of Various Solvents in Vinylite VYHH
(87% vinyl chloride, 13% vinyl acetate copolymer, Union Carbide) Volatile Solvent Retained at Specificied f/L', Sec/Cm' Polymer Density/ Solvent Dissolving 25 G of Polymer
125 g methyl isobutyl ketone 100 g methyl isobutyl ketone 25 g. ethylene glycol monoethyl ether
Wt.
s/wt. P
Vol. S/Vol. P
3 x
3 x
Slowest Solvent Density
(10)"'
(10)"
(10)'"
1.10
0.116
0.088
0.197 0.150
1.46
0.102
0.062
0.149
(10)"
0.090
t L' = (10)'" secicm', 1 day for L = 1 mil. t L' = 3 x (10)" seclcm', 30 days for L = 1 mil.
sponding to the linear relation between log D and solvent concentration absorption and desorption techniques had to be abandoned for organic solvents such as methanol and chlorobenzene. R, leads to a variation of the calculated diffusion coefficient with variations in film thickness as well as decreasing calculated diffusion coefficients for increasing solvent concentrations. Averaged absorption and desorption data are not the answer for correcting diffusion coefficients for R,, since this factor slows down solvent transport in each case. Even when this resistance is negligible, averaging absorption and desorption data is incorrect (Hansen, 1967b), since some solvent is diffusing through a region where its concentration is less than that ascribed to the experiment. I n these regions, diffusion is relatively slower and the net result is that the true diffusion coefficient is higher than that found from the interpretation of the slowed down absorption or desorption process. The true diffusion coefficient is commonly 2 to 4 times higher than that indicated by absorption data, and up to 50 to 200 times higher than that found directly from desorption data (Hansen, 1967a). Phenomena encountered in solvent-polymer diffusion have been described in great detail in a recent collection (Crank and Park, 1968). Particularly intriguing is the solution process studied by Ueberreiter et a2. (1968). I t would appear that many of the factors described for film drying would apply to the solution process as well (in reverse order). Small molecules penetrate more rapidly into the solid polymer, and are generally associated with liquids having relatively low viscosity, such that the polymer can ultimately be removed from the interface more easily. Conclusions
The solvent diffusion coefficient is important for the two-stage drying phenomena encountered in polymer film formation by solvent evaporation. Indicators and guidelines used by formulators of polymer coatings are discussed and various apparent anomalies explained. The combination of solubility parameter concepts (Burrell, 1968; Hansen, 1969) and diffusion technology gives the practical formulator the best tools currently available to aid in solvent selection, and should provide guidelines in the selection of systems for more detailed theoretical study. Ind. Eng. Chern. Prod. Res. Develop., Vol. 9, No. 3, 1970
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literature Cited
Burrell, H., J . Paint Technol. 40, No. 520, 197 (1968). Chalykh, A. Ye., Vasenin, R . M., Vysokomol. Soedin 8, No. 11, 1908 (1966). Crank, J., Park, G. S., “Diffusion in Polymers,” Academic Press, London and New York, 1968. Dimarzio, E. A., Gibbs, tJ. H., J . Polym. Sci. A I , 1417 (1963). Doolittle, A. K., “Technology of Solvents and Plasticizers,” Wiley, New York, 1954. Funke, W., Zorll, U., Murthy, B. G. K., J . Paint Technol. 41, No. 530, 210 (1969). Hansen, C. M., Far2 och Lack 10. No. 7. 169 (1964a). Hansen, C. M., Ind.-Eng. Chem F u n d a m . 6 , No. 4, 609 (196713). Hansen, C. M., IND.ENG.CHEM.PKOD.RES. DEVELOP. 8, 2 (1969). Hansen, C. M., J . Oil Colour Chem. A s s . , 51, No. 1. 27 (1968). Hansen, C. M., Off. D i g . Fed. Soc. P a i n t Technol. 37, No. 480, 57 (1965). Hansen, C. M., Teknisk Licentiat thesis, Technical University of Denmark, 196413. Hansen, C. M., doctoral dissertation, Technical University of Denmark, 1967a; Danish Technical Press, Copenhagen, 1967.
Hays, D. R., Off. Dig. Fed. Soc. P a i n t Technol. 36, No. 473, 605 (1964). Hoy, K. L., Price, B. A., Martin, R. A., “Tables of Solubility Parameters,” Union Carbide Corp., Chemicals and Plastics, 1967. Jenckel, E., Huesch, R., Kolloid-2. 130, 89 (1953). Julke, E. K., Promotionsarbeit, Eidgenossiche Technische Hochschule in Zurich, pp. 87, 136, 1962. Kokes, R. J., Long, F. A.. J . A m e r . Chem. Sac. 75, 6142 (1953). Murdock, R. E., Carney, J. A., Off. Dig. Fed. Sac. P a i n t Technol. 33, No. 433, 181 (1961). Murdock, R. E., Wirkus, W. J., Off. Dig. Fed. Soc. P a i n t Technol 35, No. 466, 1084 (1963). New York Society for Paint Technology, J . Paint Technol. 41, No. 539, 692 (1969). Sletmoe, G. M., J . Paint Technol. 38, 641 (1966). Sletmoe, G. M., J . P a i n t Technol. 42, 246 (1970). Tysal, L. A., Snowden, A. J., IX F.A.T.I.P.E.C. Congress Book, p. 35, 1968. Ueberreiter, K.. in “Diffusion in Polymers,” J. Crank and G. S. Park, eds., Chap. 7, Academic Press, London and New York, 1968. Weigel, J. E., Sabino, E. G., Jr., J . Paint Technol. 41, No. 529, 81 (1969). RECEIVED for review March 26. 1970 ACCEPTED May 16, 1970
Flow Properties of PVC Plastisols Arie Ram and Zvi Schneider Department of Chemical Engineering, Technion -Israel Institute of Technology, H a i f a , Israel
Two PVC samples were studied in plastisol form by determining viscosities on a coneand-plate viscometer, over a wide range of concentrations, temperatures, a n d shear stresses. The particles were analyzed for shape and size distribution by electron microscopy, and found to represent bimodal spherical systems. The interaction between polymer and dispersant was studied by using t w o plasticizers-one
reactive, one inert. The
apparent viscosities of stable plastisols a t any shear stress may be described b y known two-parameter equations, such as those of Mooney and Eilers. From the physical viewpoint, the empirical parameters, suitably corrected, represent intrinsic viscosity and packing volume. The corrections allow for increase of the viscosity of the dispersing phase (measured by ultracentrifuge) due to partial polymer dissolution, and of the volume concentration due to swelling. The two parameters tend t o their theoretical values a t high shear stress. Simplified relationships between viscosity and weight concentration are included for practical use.
T H E PVC plastisols represent useful polymeric systems applied as dispersions of solid particles in a partially reactive solvent. The latter, in this case a plasticizer, induces swelling of the polymer particles as well as partial dissolution. Both effects are time-dependent a t any storage temperature and are usually reflected in a progressive rise of the system viscosity. As the temperature is increased,
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these changes are intensified up to a so-called “gelation point,” at which a close-packed dispersion of extremely high viscosity is obtained. At a higher temperature, the system fuses and flows as a polymer melt. Flow properties of colloidal suspensions and macromolecular solutions have been widely discussed (Frisch and Simha, 1956). While the viscosity buildup is closely
