계면활성제 시스템에서의 중간상 생성에 관한 연구

임 종 주

동국대학교 공과대학 화학공학과

Intermediate Phase Formation in Surfactant Systems

Jong-Choo Lim

Dep. of Chem. Eng., Dongguk University, Seoul, Korea

INTRODUCTION

Formation of an intermediate phase is of great interest since it brings about a substantial improvement in detergency and other applications, provided that the phase is capable of solubilizing significant quantities of the oil. The intermediate phase sometimes forms immediately upon contact and sometimes later, depending on the compositions and relative volumes of the initial fluids.1-4

Diffusion path analysis is one way in which the isothermal diffusional process between two semi-infinite nonequilibrium phases brought into contact can be described. It allows bulk phases and interfacial compositions to be plotted on the equilibrium phase diagram as an invariant path between the two initial compositions.

As is well known, phase diagrams in surfactant systems are rather complex. Thus, considerable effort is required to generate an entire diagram for use in the diffusion path analysis. Diffusion path analysis with only limited information on phase behavior can be extended to predict the minimum surfactant concentration in an aqueous solution needed to initiate formation of an intermediate phase following contact with an oil.

Although diffusion path analysis has been found to be useful in interpreting intermediate phase formation, variations of soil composition with time during the washing process is an important factor in surfactant systems. Therefore, a new oil contacting technique has been utilized in which observations are made of a single oil drop brought into contact with a much larger volume of surfactant solution.5-6

For the oil contacting experiments, no similarity solution such as discussed above exists. Accordingly, a theory has been developed to interpret experimental results based on the assumption of quasi-steady state. That is, compositions within the oil drop and the surrounding surfactant solution are assumed to change slowly with time. The analysis is also adapted to the case of a thin oil film on a solid surface immersed in an agitated surfactant solution, which is closer to the situation encountered in practice.

EXPERIMENTAL

The pure nonionic surfactant, n-dodecyl polyoxyethylene monoethers (C12En) were obtained from Nikko Chemical Co., Japan, and were used as received. Reagent grade oleyl alcohol, n-decanol, sodium octanoate, and potassium octanoate were obtained from Sigma Chemical Co.

Contacting experiments were conducted using the technique described previously.1,6

RESULTS AND DISCUSSION

Consider mass transport in a ternary system with a moving interface as illustrated in Figure 1. At time t=0, two semi-infinite phases of uniform compositions are contacted without mixing along the plane x=0.  It is assumed that the mass density of the system is constant throughout and that convective currents from any source are absent.

Ternary diffusion effects are neglected. In addition, diffusion coefficients are taken as independent of composition within each phase. Another important assumption is that the moving planar interfaces are at local equilibrium. This requires that diffusion through the bulk phases be slow in comparison to adsorption and desorption at the interfaces.

With the assumptions listed above, the transport equations with given boundary conditions yield similarity solutions. The concentration distribution of oil in an L2 phase which initially is pure oil and occupies the region x>0 is readily obtained.

For a surfactant below its cloud point the solubility of oil in the L1 phase is quite low and the flux of oil into the L1 phase is low as well. Then the surfactant mass balance at the interface can be used to solve for initial surfactant concentration, wsA, which is given by

wsA = wsB F1(woC) + wsC F2(woC)                                          (1)

with F1 and F2 are given by

F1(woC) = {1+[□oC□0.5(exp□oC2)(1+erf□oC)Do/Ds']}                          (2)

F2(woC) = {[(1+erf□oC)Ds/(1-erf□oC)Ds'] - □oC□0.5(exp□oC2)(1+erf□oC)Do/Ds']}  (3)

where □o=x/2(Dot)0.5 in the L2 phase and B and C denote points at the tie-line of the L1-L2 coexistence curve.

The above approach can be extended to the limiting tie-line where formation of an intermediate phase is expected. According to Eqn. (1), the higher the surfactant solubility in the L2 phase at the limiting tie-line, the higher the initial surfactant concentration required to produce intermediate phase formation. That is, higher surfactant concentrations are needed for more lipophilic surfactants as well as for shorter chain hydrocarbons, triglycerides, and more polar oils. Since surfactant concentration is frequently of the order of 0.1 wt% or even lower during washing process, this analysis suggests that surfactant below the cloud point are likely to be ineffective in removing pure oils in which surfactant solubility is appreciable.

It should be emphasized that this last conclusion and indeed the entire present analysis apply only for the case of a ternary system where both the surfactant and the oil are pure components. If the oil is a mixture and its volume is small compared to that of surfactant solution L1, preferential solubilization of some components into the L1 phase could cause oil composition to change with time.

The same approach can be used to the case of a surfactant above its cloud point to predict development of intermediate phases. If the surfactant is above its cloud point, at least one intermediate phase forms. In this case the criterion for improved detergency is that water, which solubilizes little oil, not be the only intermediate phase.

Consider another diffusional process which occurs when a small spherical drop of an immiscible liquid is injected into a surfactant solution of much larger volume (see Figure 2). If the characteristic time (R2/Di) for diffusion within the drop for all species (R=drop radius, Di=diffusivity of species i) is much less than the characteristic time of the experiment, the quasi-steady-approximation may be used. Then in the absence of convection and with diffusion of each species assumed to be proportional to its own concentration gradient, the diffusion equation is given by

d       dwi

□□□ ( r2 □□□□□) = 0                                                     (4)

dr       dr

where wi is the mass fraction of species i.

Equation (4) can be solved with appropriate boundary conditions at the interface r=R(t). The species mass balance equations are given by

d      4                dwi'                          dR

□□□ (□ □□□ □R3wi) =□' [Di' □□□ (4□r2)]   + 4□R2 wi'(R) □'  □□□             (5)

dt     3                 dr       r=R                 dt

where Di' is the diffusion coefficient of species i in the aqueous solution and wi' and wi denote the local mass fractions of species i in the aqueous solution and in the oil phase respectively.

We also require local equilibrium at the interface. Considerable simplification of the solution can be achieved by making the assumption that mass transfer of oil into the surfactant solution, L1 phase, is negligible. For rather lipophilic conditions, i.e., above the system PIT, there is indeed very little solubility of either nonpolar or polar oil in the L1 phase, provided that the polar oil is a long-chain alcohol or fatty acid and the assumption should be reasonable. If the oil is denoted as component 1, its mass balance equation simplifies to

d    4

□□□ (□□□ □R3w1) = 0                                                    (6)

dt   3

Using another assumption that the surfactant concentration w2' in the L2 phase is very small at the interface above the system PIT, we can obtain the surfactant concentration distribution in terms of bulk surfactant concentration w2∞'.

w2'= w2∞'(1-r/R)                                                        (7)

As a further simplification, we fit the L1-L2 coexistence curve by a polynomial

w2 = w20 + A1 x + A2 x2                                               (8)

After some mathematical manipulations, performing the integration yields the following result:

t = Ks (R02 / D2'w2∞' )                                                  (9)

where Ks = (3/4)A3 [w1F4/3w102/3-w102] + (1/2)A1 [(w10/w1F)2/3-1] and w1F denotes limiting tie-line composition.

Equation (9) predicts that the time required to initiate intermediate phase formation is proportional to the square of the initial drop size and inversely proportional to the initial surfactant concentration and the surfactant diffusion coefficient. Ks is a constant that includes the effects of the shape of the coexistence curve and the location of the limiting tie-line.

It is noteworthy that the preceding analysis does not require extensive information on phase behavior (e.g., on the single phase and multiphase regions involving the liquid crystalline phase). All that is needed is the coexistence curve between the aqueous surfactant solution L1 and the oil phase L2 for the temperature and oil composition of interest. This feature is especially significant for multicomponent mixed soil systems, where the effort required to determine a complete phase diagram is enormous.

REFERENCES

1. K.H.Raney and C.A.Miller,  J. Colloid Interface Sci., 119, 539(1987).

2. K.H.Raney, W.J.Benton, and C.A.Miller, ibid., 110, 363(1986).

3. K.H.Raney, W.J.Benton, and C.A.Miller,  ibid., 117, 282(1987).

4. F.Mori et al, Colloids and Surfaces, 40, 323(1989).

5. J.C.Lim, C.A.Miller, and C.H.Yang, Colloids and Surfaces, 66, 45(1992).

6. C.A.Miller et al., Prog. Col. Polym. Sci., 84, 243(1991).

Figure 1. Ternary system with one moving interface.

Figure 2. Schematic illustration of a spherical drop immersed in a large quantity of            aqueous surfactant solution.