A Rapid Mixing


217-220 (1979)


for Quasielastic Light Scattering of Reacting Systems



of Biochemistry,


of Minnesota,

S. Paul,



Received May 2, 1979 A simple mixing device for studying fast reactions by quasielastic light scattering is described. The convection due to mixing is minimized and rapidly damped, so that light scattering measurements can be made immediately after mixing.

The possibility of using quasielastic light scattering (QLS)’ to study kinetics in chemically reacting systems has been of interest for some time (1). The technique should be particularly useful for macromolecular reactions that involve changes in hydrodynamic properties, but that are not accompanied by other readily observable signals such as spectral, turbidity, or pH changes. Two basically different approaches have been suggested. The first involves determining the effect of reaction on the spectrum or autocorrelation function of light scattered from a solution at dynamic equilibrium (( 1- 3), and references cited therein) or in an electrophoretic field (4). While this approach is ingenious and conceptually elegant, it has proved difficult in practice. The second approach is to combine QLS with rapid mixing. If the autocorrelation function can be measured in a time (as fast as lo-30 s with current instrumentation) short compared with the reaction half-life, then the time variation of the autocorrelation decay rate can be analyzed to obtain the kinetic parameters of the system. We have used this method to study the kinetics of assembly of T4 bacteriophage (5). One limitation of rapid mixing QLS for studying fast reactions is the convective r Abbreviations tering.

used: QLS, quasielastic light scat-

disturbance arising from mixing. A device in which convection is minimized and very rapidly damped would be desirable. This paper describes a simple design for such a device, which allows QLS measurements to be made immediately after mixing. METHOD AND RESULTS Design

A general theme of design of a rapid mixing apparatus is: (i) The reaction components, each driven by an individual syringe, flow quickly to a mixing chamber; (ii) the fresh mixture, entering the observation cell, replaces the old mixture; and (iii) the old mixture, leaving the observation cell, forces a piston to a preset stop. Spectral or fluorescence change is recorded shortly after mixing. However, such a design, in addition to being complicated in its construction, does not work well for experiments with relatively long observation times (on the order of minutes), because of the diffusional mixing between the fresh and the old mixtures. In our design the old mixture is removed completely before each new run. The flow of the mixture is stopped by a Teflon float, which has a fine vent to let the air flow out. The apparatus (Fig. 1) consists of three parts: the syringe drive, the mixing block, 217

0003-2697/79/l 502 17-04$02.00/O Copyright All rights

0 1979 by Academic Press, Inc. of reproduction in any form reserved.



and the scattering celi. The first two parts are constructed according to a design used in many stopped-flow apparatuses (6). The details are given in the figure legend. The scattering cell is made of a segment of hollow glass cylinder (t), which is attached to the funnel-shaped outlet (s) of the mixing chamber(h). A Teflon float (k) with a small vent hole (n) at its center, fits the cell cylinder snugly, and can be moved up or down freely. The upward movement is stopped when the hook (p) on the float hits the Teflon stopping block (r) fastened to the cylinder by two O-rings (0). The stopping block also has a vent hole at its center. Operation

To get the mixing apparatus ready, the contents of the mixing chamber and the scattering cell are first removed by a Pasteur pipet and a Hamilton syringe. The float is then inserted into the cell and pushed all the way down to the bottom. Finally the stopping block is loaded inside the cell near the opening. When the syringes are pressurized by the driving block, the two components are mixed in the mixing chamber and flow upward through the funnel outlet and into the scattering cell. The mixture then forces the float to move upward until it is stopped by the stopping block. The air originally trapped in the mixing chamber is vented through the center holes in the float and in the stopping block, so that the space under the float is completely filled with the liquid mixture, and the convective turbulence is damped out rapidly. The mixing is followed by QLS measurements. The optical arrangement and detailed procedures of the QLS experiment have been described in Ref. (7). Performance Tests

The completeness of mixing by this type of setup has long been established for raoid reactions. It will certainlv not be a I


B. syrirge



b 0

scale II 1




FIG. 1. Mixing apparatus for QLS experiments. (A) Syringe drive: a, aluminum driving block; b, aluminum syringe block; c, stainless-steel rods; d, glass syringes; e, threaded copper rod; f, polyethylene tube, connected to needles on mixing block. (B) Mixing block and scattering cell; g, %-in. diameter-channels; h, ‘%-in. diameter x %6-in. high-mixing chamber; i, Plexiglas mixing block; j, scattering cell; k, Teflon float; m, air chamber: n. &-in. vent hole; o, O-rings; p, steel wire hook; r, stopping block; s, funnel-shaped outlet; t, glass cylinder, made of a scattering cell with bottom cut off; u, sections of number 18 stainless-steel needles.

problem in our applications to slower reactions. Therefore, the major concern is the time required for the turbulence to settle down. A sensitive test may be carried out by observing the Auctuations in intensity of light scattered from large particles moving in and out of the light beam. An aqueous suspension of sawdust is used as our test sample, because the particles have approximately the same specific gravity as water and are large enough (-0.1 mm) to scatter strongly in a suspension sufficiently dilute that occupation number fluctuations are significant. The intensity is measured by a photodiode (United Detector Technology, PIN5DP), and the signals are recorded on an oscilloscope (Tektronix, Model 546) after



amplification (PAR, Model 184 preamplifier and Model 114 amplifier). Figure 2 shows the turbulence due to mixing and its decay with time. For a control, one part of sawdust suspension is added to one part of water in a test tube and mixing is achieved by inverting the tube several times. It is seen in Fig. 2A that fast local oscillations of the solution are present after mixing (top trace). The frequency of fluctua-



tions decreases significantly in the first 20 s (lower trace), but it takes 20 to 30 min for the oscillations to settle down completely. Figure 2B shows the results of mixing with our apparatus. Only very small turbulence is observed even right after mixing. It should be mentioned, however, that the degree of turbulence depends very much on the rate at which the reaction mixture is pushed upward into the cell. Mixing for the

FIG. 2. Performance test by observing scattering fluctuations of an aqueous suspension of sawdust. The time scale is 50 &division. (A) Mixing by inverting the test tube. Top trace: immediately after mixing; bottom trace: 20 s later. (B) Mixing done with the apparatus. Top trace: immediately after mixing; bottom trace: 60 s later.



experiment in Fig. 2B was carried out very slowly (-4 s). When the syringe drive is pushed rapidly (-1/3 s), the turbulence may be substantially larger (though still less than for mixing by inverting the test tube), and the oscillations may last for several minutes. We also carried out a QLS test, in which a sample of polystyrene latex spheres was diluted in the mixing apparatus, and the diffusion coefficient and the hydrodynamic size of the particles were determined immediately after mixing. With the channel time set at 20 +s on our 64-channel correlator, the total sweep time is roughly threefold the decay time of the correlation function. The data acquisition time per correlation function is 20 s, and the process is repeated continuously. In this manner, we obtained a diffusion coefficient of (0.396 2 0.012) x 10’ cm% at 20°C corresponding to a hydrodynamic diameter of 108.4 + 3.3 nm. This compares favorably with that provided by the manufacturer, 109 nm. Also, there was no detectable time dependence of the measured diameter during the settling period of about 4 min. Both facts indicate that the performance of the mixing apparatus is satisfactory.

larger frictional surface per unit volume. However, with a small cell, the light beam may be distorted by the glass because of its large curvature; and the light scattered from the glass wall may provide a large noise background as the wall is close to the center of the cell. Therefore, an optimized diameter for the cell should be chosen. The good agreement between the size obtained from our QLS measurements and the nominal value is not really a very sensitive test, because it is known that the homodyne QLS autocorrelation function is not affected by uniform motion of the dissolved particles (8), though velocity gradients across the scattering volume will be detected. The mixing device described in this paper may be even more useful in heterodyne QLS experiments, such as laser velocimetry or electrophoretic light scattering, where uniform motions introduced by turbulence will be detected and affect the interpretation of results. REFERENCES 1. Yeh, Y., and Keeler, R. N. (1%9) Quart. Rev. Biophys. 2, 315. 2. Bloomfield, V. A., and Benbasat, J. A. (1971) Macromolecules



The mixing apparatus described here works better than mixing by inverting the test tube or stirring for two reasons: (i) The mixing can be carried out gently, reducing the initial turbulence to a minimal level; and (ii) the presence of the special float eliminates the air space in the cell and provides additional frictional surfaces to speed up the damping of turbulence. It would seem better to have a cell with a very small diameter, which would yield a

4, 609.

3. Benbasat, J. A., and Bloomfield,

V. A. (1973)

6, 593.

4. Beme, B. J., and Giniger, R. (1973) Biopolymers 12, 1161. 5. Benbasat, J. A., and Bloomfield, V. A. (1975) J. Mol.


95, 335.

6. Strittmatter, P. (1964) Rapid Mixing and Sampling Techniques in Biochemistry, p. 71, Academic Press, New York. 7. Lim, T. K., Baran, G. J., and Bloomfield, V. A. (1977) Biopolymers 16, 1473. 8. Beme, B. J., and Pecora, R. (1976) Dynamic Light Scattering, with Applications to Chemistry, Biology, and Physics, Chap. 5, Wiley-Interscience, New York.

A rapid mixing device for quasielastic light scattering studies of reacting systems.

ANALYTICAL BIOCHEMISTRY A Rapid Mixing 99, 217-220 (1979) Device for Quasielastic Light Scattering of Reacting Systems Studies G.J. WEI AND VI...
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