Some introductory remarks are necessary concerning the thermodynamics of the formation of interfaces and the relation to heterophase polymerization techniques.
If two components are completely compatible they do
not form an interface, as is the case for dilute gases or two mutually soluble liquids. In this case, the free energy of mixing is negative. It is exactly the opposite if two incompatible components form an interface upon mixing. If a stable interface is formed, the free energy of formation must be positive. This behaviour finds its expression in a special form of the Gibbs-Helmholtz equation (equation (8.1)), where Us is the total surface energy for a given interface (S), o is the interfacial tension, and T is the absolute temperature1:
From the thermodynamic point of view only microemul-sions are stable, i.e. their formation follows other laws different to these for the formation of macro- and miniemulsions (for some exceptions, see below). In the thermodynamic sense, stability means that the structure of the emulsion does not change with time and that it is independent of the preparation technique. How-ever, emulsions can be prepared in such a way that their structure remains unchanged over longer periods of times, even up to years. In such cases, the emulsion is said to be kinetically stable. In the following text, the technical term "emulsion" is used in order to describe macroemulsions as well as miniemulsions. The prepara-tion of emulsions requires energy to disperse the organic phase (monomer or polymer solution in an organic sol-vent) in water. In order to obtain some ideas about the thermodynamics, the change in the Gibbs free energy of the system (AG), provided by the particular dispersing procedure at constant composition and pressure, can be expressed by the following:
AG - AH - TAS (8.2) The entropy (AS) is a measure of the extent of disorder in the system and hence measures the extent of size reduction of the organic phase (or increase in droplet number). The increasing disorder during the formation of an emulsion means a positive AS contributing to the stability. The term AH is the enthalpy of the system and can be considered as the binding energy of the organic bulk material or the energy input needed to achieve a certain average droplet size. If a volume change during the emulsification is neglected, the enthalpy corresponds to the internal energy which is the sum of the work required to expand the interfacial area (AW) and an amount of heat which results from wasting a
1 Note, for almost all systems (3(7/37) is negative.
part of the energy input2. The latter effect may lead to a temperature increase during emulsification. The term AW is given by equation (8.3) where AA is the increase in interfacial area and a is the interfacial tension between the organic phase and water. Note that, the increase in the energy of the emulsion compared to the non-emulsified components is equal to AW. This amount of energy can be considered as a measure of the thermodynamic instability of an emulsion.
AW = OrAA (8.3) In the above equation, AW is the free energy of the interface and corresponds to the reversible work brought permanently into the system during the emulsification process3. This makes an emulsion very prone to coa-lescence processes which lead to a decrease in AA and subsequently in AW. The conclusion is straightforward that ultimate stability against coalescence processes is only achieved if a approaches zero.
Equation (8.3) describes the influence of the interfa-cial tension on the emulsification process. For a given energy input, AA is lower the higher the value of a, and vice versa. Thus, a is a crucial parameter for any process that leads to a dispersion. If we define the inter-face as the area where the molecules of different phases meet a relationship must then exist between a and the surface tensions (y) of the neat phases4. The interfacial tension is in any case lower than the surface tension of the component with the higher value. The precise relationship between a and the surface tensions of the organic phase and water depends on the chemical com-position (more polar or more non-polar) and the orienta-tion of the molecules at the interface (more flat or more stretched) (1, 6). A simple relationship (equation (8.4) below) allows an estimation of a only from the interfa-cial tensions of the components (yo for the organic phase and yw for water) where O is a correction term which takes into account the different molar volumes5. Apply-ing this equation to predict a between polar organic liquids and water gives at least the same tendency as that obtained form experimental values (1).
a = yo + Kw - 2d>(yoyw)1/2 (8.4)
2 The amount of energy wasted as heat can be as high as 99% of the total input.
3 The total energy of the interface per surface area under isothermal conditions is given by equation (8.1).
4 Surface tension means the interfacial tension of the particular component to air, which is for a liquid saturated with its vapour and for a solid neat air.
5 cj> = 4(uot;w)1 / 2/(t;o/ 2 + V1J2)112, where V0 and uw are the molar volumes of the organic and water phases, respectively.
However, for a detailed description it is also necessary to take into account dispersion and polar forces. Thus, it is usual to express the interfacial tension in the form of the following equation (7):
a = yw + y0 - 2 ( y >o d) '/ 2 - 2 {yVy*)m (8.5) The superscripts, "d" and "p" in the above equation refer to the contributions of dispersion and polar forces to the interfacial tension, respectively. Using the values for water, i.e. yw = 72.8 mN n r1, y* = 22 A mN m"1 and yl = 50.7 mN m"1, and with some rearrangements, we obtain the following equation where Xl1 is the polarity of the organic phase (7):
a = 72.8 + y0 - [9.4 - 4.7ZS + 14.2 ( * P )1 / 21 K01/2
(8.6) Table 8.2 summarizes the yo and a values for water for different organic compounds and relates these values to the water solubility. The values given in Table 8.2 reveal that a is a measure of the compatibility of an organic compound with water, which means that it inversely relates to the water solubility of pure hydro-carbons. This relationship is broken if the molecule contains a hydrophilic group which can strongly inter-act with water (compare 1-octanol vs. benzene). This means that, on the other hand, a strong interaction with water leads to a stronger decrease in o despite the water solubility. Consequently, the values of the inter-facial tensions between pure water and pure organic liquids vary over a quite broad range, from some
Table 8.2. Values of yo, a and water solubility (Cw) for different organic compounds at 25° C
Organic compound y0 (mN m"1) a (mN m"1) Cw (M)c
Hexadecanea 27.3 53.3 2.4Xl(T11
Ethylbenzenea 29.2 38.4 1.6xl0"3
Benzene* 28.9 33.9 2.3 x 1(T2
1-Octanola 27.5 8.5 4.2xlCT3
Ethyl acetatea 23.9 6.8 1.0 1-ButanoF 24.6 1.8 1.08 Methylacrylate^ 24.2 13-14 0.64 Vinyl acetate*7 22.9 18-19 0.30 Ethyl acrylate^ 24.7 21-22 0.15 n-Propyl acrylate^ 24.8 26-27 5.OxIO-2
n-Butyl acrylate^ - 30-31 1.7xlO~2
Styrene*7 30.9 40-43 3.0xl0~3 ay0 and a values from ref. (1).
byo values form ref. (8) and a values from ref. (7).
rCw values from ref. (9).
1 Xl = yop/yo; Xod = yod/yo; Xpo + Xod = 1; (l - Xo p)1 / 2^1 - Xp0/2.
50 mN m 1 to about 1 mN m l depending on the par-ticular functional groups. In contrast to a, the y-values do not show any spectacular changes as they are in a quite close range between about 23 mN m"1 and 3 O m N m "1.
This chapter treats the subject of interfacial effects while a monomer is converted into its polymer. Hence, the question arises concerning the interfacial properties of polymers. For some polymers typically prepared by heterophase polymerizations, values of the surface tension (yp) and interfacial tension to water are listed in Table 8.3. Compared to the data shown in Table 8.2, the values for the polymers are higher and especially the a data can be understood in the same way as those of the low-molecular-weight compounds.
Equations (8.4)-(8.6) clarify that there is, for a given organic phase, a possibility to influence the interfacial tension by changing the dispersion medium, and hence changing yw. This is possible by adding organic water-soluble compounds as, for instance, alcohols. Methanol, ethanol, n-propanol and n-butanol are very efficient additives for reducing the surface tensions of aqueous solutions down into the range below 40 or 30 mN m"1. The higher the carbon number and the concentration of the alcohol, then the greater is the decrease in yw (10). This effect is utilized in so-called dispersion polymerizations for the preparation of large and fairly monodisperse particles (11, 12).
Another possibility for altering a is a complete change of the dispersion medium. Besides water other classes of suitable liquids are alkanes or perfluorocar-bon fluids. By using such materials a drastic decrease in Y can be achieved (cf. Table 8.4) when compared to water (yw = 72.8 mN m"1). Indeed, it is the state of the art (also in larger-scale technical processes) to use certain petroleum fractions as continuous phases for the polymerization of hydrophilic monomers (so-called inverse heterophase polymerizations) to prepare, for instance flocculants for waste-water treatment or as aids for paper production (14). The large-scale appli-cation of perfluorocarbon fluids, however, is restricted
Table 8.3. Values of the surface tension and interfacial tension to water for various polymersa
Polymer yv (mN m"1) a (mN m"1) Poly(butyl methacrylate) 31.2 36.7 Poly(vinyl acetate) 36.5 23.5 Polystyrene 40.7 32.7 Poly(methyl methacrylate) 41.1 26.0 Poly(vinyl chloride) 41.9 37.8
adata from ref. (7) at 20°C.
Table 8.4. Surface tension values of alka-nes and perfluorocarbon fluids (25°C) N Y (m N m~l) Y (mN m"1)
of CnHn + 2* of CnFn + 2* 6 17.9 12 7 19.8 13 8 21.1 14
adata from ref. (8).
fcdata from ref. (13).
due to the higher price and the special solubility characteristics. Nevertheless, the benefits of using per-fluorocarbon fluids as continuous phases is evident, as due to the low y values these fluids are capa-ble of dispersing organic monomers without addi-tives (13).
Regarding the topic of this chapter, possibly the most important way to influence the interfacial ten-sion of a disperten-sion is the addition of surfactants1. The special importance of surfactants in heterophase poly-merizations is treated below. If an interface is com-pletely covered by surfactants, o is governed by the hydrophilic head groups of the surfactant. This situation can be treated approximately in analogy to a micelle.
The free energy contribution of the head group (AGhg) can be expressed by the following equation, according to ref. (15):
AGhg = AGei + Ahgam[c (8.7) The first term on the right-hand side of equation (8.7) is the contribution of the head group repulsion, while the second is the interfacial energy contribution where Ahg is the total surface area of the head groups and amic is the interfacial tension. Within the framework of the GOUY-CHAPMANN theory, the dressed micelle model allows the estimation of <rmic values, which are for sodium dodecyl sulfate (SDS), sodium octyl sulfate, and teradecyltrimethylammonium bromide, 15-16, 11 and 11-14 mN m"1, respectively (15). Note that these val-ues are up to a factor of 3 lower than those of the pure monomers (cf. Table 8.2). A further decrease of a is possible in the case of emulsions of organic liq-uids where the interface is saturated with stabilizer. For example, a value of about 4 mN m"1 was determined for a toluene emulsion stabilized with potassium lau-rate (16).
1 The terms surfactant, stabilizer and emulsifier will be used inter-changeably in the remainder of this chapter.