Amine oxide 계면활성제 용액에서의 알코올 drop의 동적 거동

임 종 주*, M.J. Rang**, and C.A. Miller**

* 동국대학교 공과대학 화학공학과

** Dep. of Chem. Eng., Rice University, Houston, Texas

Dynamic Behavior of Alcohol Drops in Dilute Solutions

of an Amine Oxide Surfactant

Jong-Choo Lim*, M.J. Rang**, and C.A. Miller**

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

** Dep. of Chem. Eng., Rice University, Houston, Texas

INTRODUCTION

The intermediate phase(s), which may be important in detergency and other applications, sometimes forms immediately upon contact and sometimes later, depending on the compositions and relative volumes of the initial fluids.1-4  Because variations of soil composition with time during the washing process is an important factor in these systems, a new 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.5-8  With this technique, it was found that the lamellar liquid crystalline phase began to form at various times after contact when drops of pure oleyl alcohol5 or of mixtures of oleyl alcohol with n-hexadecane7 were injected dilute solutions of pure linear ethoxylated alcohol.  A quasi-steady-state analysis was developed which yielded predictions in agreement with experimental results on how the time until initiation of liquid crystal formation varied with initial drop diameter and bulk surfactant concentration in the aqueous phase.

In this paper, results of similar contacting experiments for systems containing amine oxide surfactants and shorter chain alcohols which have appreciable solubility in water are presented.  Alcohol diffusion into the aqueous phase can cause the drop to shrink until intermediate phase formation begins instead of to grow as in the oleyl alcohol systems.4,7  Dynamic behavior observed using videomicroscopy could be explained in terms of the equilibrium phase diagrams constructed for this system and a quasi-steady-state diffusion model which is generalized version of the one developed previously.

EXPERIMENTAL

Tetradecyldimethylamine oxide (C14DMAO) was obtained from Hoechst and recrystallized twice from acetone.  Reagent grade n-hexanol, n-heptanol, and n-octanol were obtained from Sigma Chemical Co.  Water used for solution preparation was ultrapure having been double distilled and passed through a Nanopure (Sybron-Brinkman Inc.) ion exchange system.

Oil drop contacting experiments were conducted using the technique described previously5-8.

THEORY

Consider diffusional processes which occur when a small spherical drop of an immiscible liquid is injected into a surfactant solution of much larger volume.  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                                                   (1)

dr       dr

where wi is the mass fraction of species i.

Equation (1) 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) □'  □□□          (2)

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.  This condition assumes that diffusion through the bulk phases is slow in comparison to adsorption and desorption at the interfaces.

For the particular case where a drop rich in alcohol (i=1) is injected into a solution of surfactant (i=2) and water (i=3) and where surfactant concentration w2' at the interface is small in comparison with bulk surfactant concentration w2'∞, the following eqns. (3) and (4) can be obtained in terms of dimensionless drop diameter R*=(R/R0) and dimensionless time t*=(tD2'/R02).

(d/dt*) [R*3(1-x)] = - 3R* [D1'w1'R / D2'(w10 - w1'R □'/□)] (□'/□)           (3)      (d/dt*) [R*3w2] = 3R* w2'∞ (□'/□)                                        (4) where x = [1 - (w1 - w1'R □'/□) / (w1'0 - w1'R □'/□)].

After integration with R*=1, x=0, w2=w20 at t=0,

R*3 = [(1 + a0 w20) / (1 - x + a0 w20)]                                  (5)

with a0 = [D1'w1'R / D2'w2'∞ (w1'0 - w1'R □'/□)]

As a further simplification, we fit the coexistence curve between P asnd Q by a polynomial

w2 = w20 + A1 x + A2 x2                                           (6)       Consider the case of a short-chain alcohol whose solubility in the aqueous phase is high enough that its outward flux from the drop greatly exceeds surfactant influx to the drop.  For the large value of a0, taking w20=0 gives the following equation       [A1 / (A1 a0 -1)] (dR*3/dt*) = -3R* w2'∞ (□'/□)                            (7)

Integration of the above eqn. (7) gives

t* = [A1 / (A1 a0 -1)] (□ / 2w2'∞ □') (1-R*2)                              (8)

For the large value of a0,

tQ = [R02□ / 2D1'w1'R □'] (w10 - w1'R □'/□) (1-RQ*2)                        (9)

where tQ is the time required for the initiation of intermediate phase formation and RQ* is the value of R* when x is xQ at the limiting tie-line.

RESULTS AND DISCUSSION

Contacting experiments were performed in which drops of pure n-hexanol, n-heptanol, and n-octanol were injected into dilute aqueous solutions of C14DMAO at 30℃.  Extensive information on the phase behavior of these systems for the two shorter chain alcohols can be found elsewhere.9,10

Initially the alcohol drop shrank, the expected result when alcohol dissolution into the surfactant solution is more rapid than incorporation of water and surfactant by the drops.  The opposite behavior, i.e., swelling drops, was seen for a more lipophilic alcohol with a much lower solubility in water.5,7  Later an intermediate L3 phase, which had a higher water content than the L2 drop, began to form.  The observed dynamic behavior could be explained in terms of the equilibrium phase diagrams and a quasi-steady-state diffusion model.

As shown in Fig.1, variation of drop composition with time should be initially be along the L2 phase coexistence curve PQ as the drop loses alcohol and takes up surfactant and water.  When its composition reaches limiting tie-line Q, an intermediate L3 phase should begin to form at the interface.  After that, the L3 phase grows and the L2 phase shrinks.  Once the L2 phase disappears, composition of the L3 phase should follow the L3-L1 equilibrium coexistence curve until high water contents are reached.

The quasi-steady-state theory predicts that the ration of (RI/RQ) should be constant, where RI is the radius when the volume of the L2 phase has shrunk to zero and the drop consists entirely of the L3 phase at composition I.  Experimentally this ratio was found to be close to 1.12 (see Fig.2).  That is, overall volume increased during transformation from L2 with composition near Q to L3 with composition near I owing to the higher water content of the L3 phase.  The quantity (tI-tQ) was also found to be nearly proportional to RQ2, as predicted by the eqn. (9) (see  Fig.3).

REFERENCES

1. K.H.Raney, W.J.Benton, and C.A.Miller,  J. Colloid Interface Sci., 110, 363(1986).

2. K.H.Raney, W.J.Benton, and C.A.Miller,  J. Colloid Interface Sci., 117, 282(1987).

3. F.Mori, J.C.Lim, O.G.Raney, C.M.Elsik, and C.A.Miller,  Colloids and Surfaces,

40, 323(1989).

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

5. J.C.Lim and C.A.Miller, "Surfactant in Solution"  eds. K.L.MIttal and D.O.Shah,

Plenum Press 11, 491(1991).

6. F. Mori, J.C.Lim, and C.A.Miller,  Prog. Colloid Polym. Sci., 82, 114(1990).

7. J.C.Lim and C.A.Miller, Langmuir 7, 2021(1991).

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

9. C.A.Miller, M.Gradzielski, H.Hoffmann, U.Kramer and C.Thunig,  Prog. Colloid

Polym. Sci., 84, 243(1991).

10. H.Hoffmann, C.Thunig, and U,Munkert,  Langmuir, 8, 2629(1992).