The Physical Chemistry of Foam Formation

Chemistry for Everyone

From Foam Rubber to Volcanoes: The Physical Chemistry of Foam Formation Lee D. Hansen* and V. Wallace McCarlie Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602; *[email protected]

In this article the process of foam formation is used to illustrate how application of physicochemical principles and knowledge of the physical properties of materials contribute to understanding a wide range of phenomena. Foams are commonly encountered in nature and in foods and are one of the most common forms of matter produced by the chemical industry. About three million tons of synthetic cellular polymers are produced annually in the United States alone (1), but foams are rarely if ever discussed in chemistry textbooks. The physical chemistry underlying the production process is not well known outside the industry. Foamed or cellular plastics and rubbers are commonly encountered as shoe soles (closed-cell foam rubber), as padding in furniture (open-cell foam rubber), as insulating board and packing material (e.g., Styrofoam), as food (e.g., whipped cream, popcorn, and meringue), and as cosmetics, toiletries, and cleansing agents (e.g., shaving cream and window cleaner). Foams are a nonequilibrium (metastable) dispersion of gas bubbles in a liquid, solid, or elastomer and cannot easily be classified as a gas, liquid, or solid phase of matter. Many materials of biological origin such as wood, straw, and cork can also be classified as foams. Some types of volcanic rocks are also foams. A classroom discussion of foams can be used to illustrate a number of issues in materials science and physical chemistry. Foams are characterized as open-cell if the bubbles are interconnected so gas can flow between the spaces and closedcell if the wall around each bubble is continuous. Foam density, the ratio of the volume of the unexpanded solid or liquid phase to the volume of the foam, is a crucial determinant of foam properties. For example, compare the properties of the high-density foam rubber used for shoe soles to those of a low-density foam rubber used for soundproofing and as flexible insulation in winter clothing. Synthetic foams are produced by dispersing a gas in a liquid. Either cooling the foam to a temperature below the liquid-to-glass or liquid-to-solid phase transition temperature or chemically cross-linking the liquid molecules produces a metastable, but long-lived, elastomeric or rigid material. The process often involves heating a polymer to a temperature above the melting temperature (often by the mechanical work of extrusion or injection) in the presence of a high-pressure gaseous blowing agent or a chemical blowing agent that generates a gas during the foaming process (1–4). The number, size, and size distribution of the bubbles formed depends on both the thermodynamics and kinetics of bubble formation. Freons (chlorofluorocarbons) were commonly used blowing agents in the past, but because they cause destruction of the stratospheric ozone layer (5, 6), most freons have now been banned for many applications. Freon blowing agents have largely been replaced by low molecular weight hydrocarbons, such as pentane and butane. But because of the potential for fire and explosion, these are less desirable.

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The Process of Foam Formation Foaming a liquid involves five processes: (a) dissolution of the gas in the liquid, (b) decompression of the gas over the solution so that the solution becomes supersaturated, (c) nucleation of bubbles, (d) growth of bubbles, and (e) cooling or cross-linking the liquid to form a stable foam. These processes are described in more detail below.

Dissolution of Gas Henry’s law describes the solubility of a gas in a liquid as a function of the gas pressure over the liquid, (1)

Cg = K H p

where Cg is the equilibrium concentration of the gas in the liquid, p is the pressure of the gas over the liquid, and KH is an equilibrium constant dependent on temperature, the gas, and the liquid. The solubility of a gas in a liquid can either increase or decrease with increasing temperature, but the effects of temperature on solubility are usually quite small, except at temperatures where the liquid undergoes a phase transition. The phase transition need not be a transition between states of matter. Liquid polymers often exhibit molecular phase transitions such as unfolding, which changes the properties without changing the state. It must also be kept in mind that the temperatures of phase transitions are affected by pressure and the presence of the solute gas (7).

Decompression If the blowing agent is added as a gas, for example butane or CO2, changing the conditions by extruding or injecting the saturated solution into a space where the solute is at a low pressure creates a supersaturated solution of the gas in the liquid. If a solid chemical blowing agent, for example, azodicarbonamide [H2NC(⫽O)N⫽NC(⫽O)NH2], is dispersed in the liquid, the supersaturated solution of gas is formed when thermal decomposition of the blowing agent occurs, often coincident with melting of a polymer powder or granules during passage through an extruder screw and orifice. The concentration of gas in the supersaturated solution determines the total volume of bubbles that can be blown and, therefore, the relative foam density, as shown in eq 2 (assuming negligible gas solubility at atmospheric pressure), V liq V liq ρfoam = = ρliq V foam V liq + Vg −1

L = 1 + 22.4 mol

T foam K 273 K

mol Cg L

(2)

where Tfoam is the Kelvin temperature of the foam during

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1.0

10

0.8

8

log (p bub / Pa)

Relative Foam Density

ρfoam ρliq


100 °C 200 °C

0.6

0.4

6

4

2

0.2

0.0

surface tension = 0.020 N/m surface tension = 0.050 N/m

0 0.0

0.2

0.4

0.6

0.8

1.0

-6

-4

Cg / (mol Lⴚ1)

log (r

-2

0

/ cm)

Figure 1. Dependence of foam density, ρfoam, on the concentration of dissolved gas, Cg, and the temperature at which the foam is blown. A concentration of 1 mol L᎑1 is approximately equal to 5 weight percent of azidodicarbonamide or of butane.

Figure 2. Dependence of bubble size (radius, r ) on the pressure of the gas in the bubble, pbub, and on the surface tension of the liquid. Note this is a log–log plot covering seven orders of magnitude.

bubble formation. A plot of eq 2 is given in Figure 1, which shows approximate equivalent concentrations of azodicarbonamide or butane in weight percent. Note that gas concentrations greater than about 0.1 mol L᎑1 must be achieved to obtain low-density foams. The effects of decompression are easily demonstrated by observing what happens when a bottle of soda is opened or the trigger on a can of shaving cream is pressed.

the bubble will grow and at equilibrium:

Nucleation Bubbles will nucleate at locations in the liquid with a low surface tension, created either by the presence of an unwetted surface or by shear forces (8–10). Just as boiling beads are added to a liquid to provide surfaces for smooth formation of many small bubbles and prevent the “bumping” caused by formation of a few large bubbles, nucleating agents such as alumina, silica, talc, clay, or other polar materials are usually added to nonpolar polymers, and hydrophobic materials such as fatty acids are added to aqueous liquids. Under the highly supersaturated conditions used to make foams, the number concentration (number兾volume) of such particles determines the number concentration of bubbles and, hence, the size of the bubbles. The rate of nucleation is also proportional to the supersaturation, that is, Cg − Cequilibrium. The effects of bubble nucleation are easily demonstrated by adding a spoonful of finely divided, insoluble material to a glass of freshly opened soda water. Bubble Growth The energy required for bubble growth is given by the product of surface tension and the change in area, γdA. The surface tension, γ, is the energy required for formation of a unit of new surface between the gas in a bubble and the liquid. The energy for blowing the bubble comes from pressure–volume work, that is, pdV from the gas expansion. Thus, if (3)

pbub dV > γ dA

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pbub dV = γ d A

(4)

Assuming spherical bubbles, bubble volume is V =

4 πr3 3

(5)

and bubble surface area is A = 4 πr 2

(6)

where r is the bubble radius. Taking the derivatives dV兾dr and dA兾dr and substitution into eqs 3 and 4 gives the pressure required for bubble growth

p bub >

2γ r

(7)

and the pressure inside the bubble at equilibrium

p bub =

2γ r

(8)

The equilibrium relation between pbub and r for the range of surface tension values commonly encountered for molten polymers is shown in Figure 2. Temperature and the identity of the polymer have only small effects on the surface tension of the liquid, and thus the relation shown in Figure 2 is little affected by temperature or the polymer used. Pressures from hundreds of atmospheres down to a fraction of one atmosphere are required to produce the bubble sizes desired in cellular plastics and most other foams. Note that Figure 2 is a log–log plot covering seven orders of magnitude on both axes. Also note that because of the inverse relation between pbub and r (eq 7), higher pressures are required to blow small bubbles than to blow large bubbles. Because p (≈ pbub) decreases linearly with Cg (eq 1), once a bubble begins to grow, growth will continue until the gas


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concentration in the liquid around the bubble reaches the equilibrium pressure (eq 8). Thus, large concentrations of nucleating agents are required to obtain very fine cell foam, and low concentrations produce coarse foam. Also, decompression must be done smoothly and evenly throughout the liquid or a broad range of bubble sizes will form. A gel-type shaving cream, whipped cream, foam rubber, popcorn, and pumice may be used to illustrate bubble growth.

Table 1. Examples of Henry’s Law Constants for Gas Solubility in Polymeric Materials Polymer Polyethylene

Cooling or Cross-Linking To form a stable foam, the walls of the bubbles must be stabilized against collapse before the pressure inside the bubbles decreases either from diffusion of the gas or from a decrease in temperature. Stabilization can be done by a phase change to a solid, by a rapid and large increase in viscosity, or by cross-linking the liquid phase that forms the bubble walls. Polypropylene

Effects of Physical Properties: An Example To summarize and illustrate what has been said thus far, an example is useful. Approximate calculations can be used to determine the feasibility of making a particular foam from a given mix of materials. Let us assume a relative foam density of 0.1 and bubbles of radius 0.1 mm are desired. From eq 8 (Figure 2) and assuming an average surface tension for a liquid polymer, that is, about 0.035 N兾m, this size bubble will require pbub = 700 Pa and, from eq 2 (Figure 1), Cg = (9兾22.4)(273兾Tfoam): Tfoam depending, of course, on the nature of the polymer. Assuming Tfoam = 150 ⬚C = 423 K gives C g = 0.26 mol L ᎑1 . The Henry’s law constant for the gas兾polymer mix must thus be greater than Cg兾p = KH = (0.26兾700) = 0.37 mmol L᎑1 Pa᎑1. The values of KH for various representative gases and polymers are given in Table 1. Adjusting the processing temperature Tfoam or addition of surface active agents to decrease γ allows an exact match to be made between the properties of the blowing gas and polymer and the conditions required to produce the desired product. Kinetics of Foam Formation So far only the thermodynamics of bubble growth have been discussed, but the kinetics of bubble growth and of permeation of the gas in the other phase are also important (11). In synthetic products bubbles must grow to the proper size before cooling or cross-linking stabilizes the foam. Bubble growth rate, Rbub, is proportional to the ratio of the driving force and the restraining force (viscosity): k p bub − R bub =

2γ r

(9)

η

Viscosity, η, is the rate at which a fluid deforms under an applied force. If the rate of diffusion of the gas through the liquid (i.e., the permeability) is low, diffusion may instead become the rate-limiting step. Because permeability increases exponentially and viscosity decreases exponentially with temperature, in either case the rate of bubble growth increases exponentially with temperature. Thus, small adjustments of www.JCE.DivCHED.org

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Polyisobutylene Polystyrene

Poly(methyl methacrylate)

KH/ (mmole L᎑1 MPa᎑1)

Gas

T/⬚C

N2

(melt)

49

CO2

(melt)

120

000

200

020

141

030

133

040

127

050

125

060

120

CHCIF2

(melt)

190

C3H8

100

900

C4H10

100

2200

N2

(melt)

59

CO2

(melt)

440

CHCIF2

(melt)

220

N2

(melt)

25

CO2

(melt)

270

N2

(melt)

22

CO2

(melt)

97

CHCIF2

(melt)

170

N2 CO2

(melt) (melt)

20 110

NOTE: Data estimated from refs 19 and 23.

temperature produce large changes in the rate of bubble growth, but only small changes in the thermodynamics of bubble formation. A full theoretical treatment of the kinetics of bubble formation would have to take into account changes in viscosity, permeability, and phase of the nongaseous component with the temperature changes that inevitably accompany the actual foaming process. Such a model is beyond the scope of this article. Discussion The processes of foam formation are readily demonstrated with common materials. Compare the consequences of opening a cold bottle of soda with opening a warm, wellshaken bottle to show the effects of temperature and bubble nucleation. A can of shaving cream can also be used to illustrate the effects of decompression of a soluble gas in a liquid (Henry’s Law). Popping popcorn illustrates the use of a liquid (H2O) above the boiling point as a blowing agent. The common lecture demonstration of adding concentrated sulfuric acid to sucrose results in a rigid carbon foam where water acts as the blowing agent and the heat from the reaction drives the foaming process. Rodriguez (12) gives the following recipe for a foamed synthetic polymer. Addition of HCl or H2SO4 to an aqueous phenol–formaldehyde solution with a volatile liquid (e.g., isopropyl ether) dispersed in it reacts


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to form a rigid foam. The heat of the reaction volatilizes the liquid, which acts as the blowing agent. Foams are encountered much more commonly than we realize. Foams are encountered as cleaning agents, as foods, as building materials, as padding and insulation (13), and as rocks. In a volcano the gas content and properties of the molten rock determine whether the volcano will erupt with relatively quiet lava flows or erupt explosively (14–16). If conditions are right for foam formation (i.e., gas concentration, surface tension, and viscosity as discussed above), as the magma approaches the surface and external pressure decreases, an explosive eruption will occur (17, 18). Popping of popcorn is a similar phenomenon. Water released at the crystalline-to-gel transition of the starch in the corn foams the gel. An intact hull is not necessary for the explosive foam formation to occur. The properties that must be considered in development of a foamed polymer product are the solubility of the gas in the molten or liquid polymer (19), bubble nucleation of the gas in the polymer (9, 10, 20, 21), bubble growth as determined by the surface tension of the liquid polymer, the viscosity of the liquid, and the permeation rate of the gas through the liquid (22). The simplified model presented here is valid for the initial stages of foam formation and is sufficient to permit preliminary selection of a suitable blowing agent, concentration, temperature, and nucleating additive for a given application. Production of a finished product, however, is done more by art than by design. The Encyclopedia of Chemical Technology (1) contains a review of the foamed plastics industry and Kumar and Weiler (4) describes development of a new product that uses CO2 as the blowing agent. Control of the rate of bubble growth is important in producing a quality product. If permeation rates are too high, large bubbles will grow at the expense of small bubbles. Recall that less internal pressure is required for growth of large bubbles than for growth of small bubbles. Also, because all bubbles are not nucleated at precisely the same time, too rapid bubble growth depletes the gas from surrounding liquid too rapidly and prevents nucleation at nearby sites. As mentioned earlier, the kinetics of bubble formation and growth is usually too complex to model theoretically. Consequently, proper conditions are determined by trial and error. A problem related to gas permeability and unique to closed-cell foams is shrinkage and wrinkling or cracking that can occur on cooling the foamed material to room temperature. The pressure inside the bubbles diminishes as the foam is cooled. If the pressure in the bubbles at room temperature is less than atmospheric, and if air cannot diffuse into the bubbles fast enough to relieve the pressure difference, the foam will be squeezed and rubbers will wrinkle and rigid materials may crack. Data in Table 1 show that N2 and CO2 have smaller KH values than butane and freons with two or more carbon atoms. This is one reason why freon has been difficult to re-

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place as a blowing agent for foamed polymers. Butane has similar physical properties, but remains in the product and increases flammability. The release of large quantities of gaseous butane during manufacture is also obviously undesirable. Because of their different physical properties, including smaller KH values, N2 and CO2, although environmentally benign, cannot always provide the desired product. Chemical blowing agents usually produce CO2 or N2 but act differently because the gases are released during the blowing process. Further studies need to be done to develop a better understanding of the kinetics of decomposition of the commonly used chemical blowing agents and the relation between the decomposition reaction and the physical processes involved in foam formation. Literature Cited 1. Suh, K. W. Foamed Plastics. In Encyclopedia of Chemical Technology, 4th ed.; Howe-Grant, M., Ed.; John Wiley & Sons: New York, 1994; Vol. 11, pp 730–782. 2. Shi, C.; Huang, Z.; Kilic, S.; Xu, J.; Enick, R. M.; Beckman, E. J.; Carr, A. J.; Melendez, R. E.; Hamilton, A. D. Science 1999, 286, 1540–1543. 3. Park, H.; Youn, J. R. Poly. Eng. Sci. 1995, 35, 1899–1906. 4. Kumar, V.; Weiler, J. J. Eng. Ind. 1994, 116, 413–420. 5. Pool, R. Science 1988, 242, 666–668. 6. Jones, M. New Scientist 1988, 118, 56–60. 7. Handa, Y. P.; Capowski, S.; O’Neill, M. Thermochimica Acta 1993, 226, 177–185. 8. Lee, S.-T. Polym. Eng. Sci. 1993, 33, 418–422. 9. Colton, J. S.; Suh, N. P. Polym. Eng. Sci. 1987, 27, 485–492. 10. Blander, M.; Katz, J. L. AIChE Journal 1975, 21, 833–848. 11. Debrégeas, G.; de Gennes, P.-G.; Brochard-Wyart, F. Science 1998, 279, 1704–1707. 12. Rodriguez, F. Principles of Polymer Systems, 4th ed.; Taylor and Francis: Washington, DC, 1996; pp 487–501. 13. Durian, D. J.; Weitz, D. A. Foams. In Encyclopedia of Chemical Technology, 4th ed.; Howe-Grant, M., Ed.; John Wiley & Sons: New York, 1994; Vol. 11, pp 783-805. 14. Cooper, H. S. F., Jr. Natural History 2001, 110, 90–91. 15. Eichelberger, J. C. Science 1997, 278, 1084–1085. 16. Vergniolle, S. Science 1997, 275, 1278–1279. 17. Mader, H. M.; Zhang, Y.; Phillips, J. C.; Sparks, R. S. J.; Sturtevant, B.; Stolper, E. Nature 1994, 372, 85–88. 18. Morrissey, M. M.; Chouet, B. A. Science 1997, 275, 1290– 1293. 19. Sanchez, I. C.; Rodgers, P. A. Pure Appl. Chem. 1990, 62, 2107–2114. 20. Jackson, M. L. Ind. Eng. Chem. Res. 1994, 33, 929–933. 21. Han, J. H.; Han, C. D. J. Polym. Sci. 1990, 28, 711–741. 22. Stewart, C. W. J. Polym. Sci. 1970, 8, 937–955. 23. Encyclopedia of Polymer Science and Engineering; Kroschwitz, J. I., Ed.; John Wiley & Sons: New York, 1989; Vol. 15, p 782.


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The Physical Chemistry of Foam Formation

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