Nanomedicine, Volume I: Basic Capabilities
© 1999 Robert A. Freitas Jr. All Rights Reserved.
Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999
3.2.4 Diffusion Cascade Sortation
Nanodevices may also use diffusion to sort molecules. One of the remarkable features of diffusive sortation is that an input sample consisting of a complex mixture of many different molecular species can sometimes be completely resolved into pure fractions without having any direct knowledge of the precise shapes or electrochemical characteristics of the molecules being sorted. This can be a tremendous advantage for nanodevices operating in environments containing a large number of unknown substances. Another major advantage is the ability to readily distinguish isomeric (though not chiral) molecules. As one example of many possible, molecules suspended in water will diffuse into an adjacent region of pure water at different speeds, giving rise to dissimilar time-dependent concentration gradients which may be exploited for sortation by interrupting the process before complete diffusive equilibrium is reached.
For simplicity, assume we wish to separate two molecular species initially present in solution in equal concentrations (c1 = c2), but having unequal diffusion coefficients (D1 < D2). Consider a separation apparatus with two chambers. Chamber A contains input sample concentrate. Chamber B contains pure water. A dilating gate (Section 3.3.2) separates the two chambers. The gate is opened for a time Dt approximated by:
which relates the diffusion coefficient to the mean displacement DX, taken here as L, the length of Chamber B. Table 3.4 gives an estimate of the time required for diffusion to reach 90% completion for glycine, a typical small molecule, in aqueous solution.
After Dt has elapsed, the gate is closed. (A gate with 10-nm sliding segments moving at 10 cm/sec closes in 0.1 microsec.) The faster-diffusing component D2 approaches diffusive equilibrium in Chamber B, but the slower-diffusing component does not; it is present only in smaller amounts. This gives a separation factor c2/c1 ~ D2/D1 for each diffusion sortation unit. If n units are connected in series, with each unit receiving as input the output of the previous unit, the net concentration achieved by the entire cascade is ~(D2/D1)n. Such cascades are commonplace in gaseous diffusion isotope separation875 and other applications.
Figure 3.1 shows a 2-dimensional representation of an efficient design for a simple diffusion unit that might be used in a sortation cascade. Each unit consists of 5 chambers of equal volume, 7 dilating gates, 3 flap valves, 3 pistons, and 2 sieves which pass only water (or smaller) molecules. Each chamber is roughly cubical with L ~ 35 nm along the inside edge; including full piston throws and drives, controls, interunit piping and other support structures, each unit measures ~125 nm x 100 nm x 80 nm or ~0.001 micron3 with a mass of ~10-18 kg.
The following is a precise description of one complete cycle of operation for each unit:
1. The cycle begins with fluid to be sorted in Chamber A, Chambers B and W full of pure water with piston W all the way out, Chambers R and D empty with pistons R and D all the way in, and all valves and gates closed.
2. Gate AB is opened for a time Dt, then closed. For a small molecule such as urea (MW = 60 daltons), Dt = 1 microsec; for a large molecule such as the enzyme urease (MW = 482,700 daltons), Dt = 35 microsec.
3. Valves AI- and AI+, and gate AR, are opened. Piston R is drawn fully out, slowly to preserve laminar flow and to prevent mixing. Fluid in Chamber A is drawn into Chamber R. Fluid passing through the DO gate of the previous unit in the cascade enters Chamber A through valve AI-. Fluid passing through the RO valve of the subsequent unit in the cascade enters Chamber A through valve AI+. All valves and gates are closed. Chamber A is now ready for the next cycle.
4. Gates WB and BD are opened. Piston W is slowly pushed all the way in while piston D is slowly pulled all the way out. Concentrated solution in Chamber B is transferred into Chamber D as pure water in Chamber W is transferred into Chamber B, again preserving laminar flow. Both gates are closed; Chamber B is now ready for the next cycle.
5. Gates RW and DW are opened. Pistons R and D are slowly and simultaneously pushed halfway in while piston W is pulled all the way out. Forced at high pressure (~160 atm) through ~0.3 nm diameter sieve pores (Section 3.3.1), half of the solvent water present in Chambers R and D is pushed into Chamber W, filling Chamber W with water. (This design allows for easy backflushing if sieve pores become clogged.) Both gates are closed; Chamber W is now ready for the next cycle.
6. Valve RO and gate DO are opened. Pistons R and D are slowly and simultaneously pushed the rest of the way in. Concentrated return fluid passes through valve RO and back to the AI+ input port of the previous unit in the cascade for further extraction. Concentrated diffusant fluid passes through gate DO and on to the AI- input port of the subsequent unit in the cascade for further purification. The valve and gate are closed; Chambers R and D are now empty and ready for the next cycle.
7. Return to Step (1). Adjacent units operate in counterphase while previous and subsequent units operate in synchrony, in a twophase system.
Increasingly purified sample passes through a multi-unit sortation cascade as described above. For small molecules, a cascade of n ~1000 units (total device volume ~1 micron3) completely resolves two mixed molecular species with D2/D1 = 1.01. As a crude approximation, D ~ 1 / MW1/3 for small spherical particles,390 so this cascade separates small molecules differing by the mass of one hydrogen atom which should be sufficient for most purposes. Structural isomeric forms of the same molecule, such as a-alanine and b-alanine, often have slightly different diffusion coefficients, thus are also easily separable using a diffusion cascade. However, stereoisomeric (chiral) forms cannot be sorted by diffusion through an optically inactive solvent like water.
For large molecules, a 1 million-unit cascade (total device volume ~1000 micron3) provides D2/D1 ~ 1.00001, sufficient to completely separate large molecules differing by the mass of a single carbon atom. The fidelity of such fine resolutions depends strongly upon the ability to hold constant the temperature of the chamber, since D varies directly with temperature (Eqn. 3.5). Device temperature stability will be determined by at least three factors: (1) the accuracy of onboard thermal sensors in measuring T (DT/T < 10-6; Section 4.6.1), (2) the rapidity with which the temperature measurement can be taken (10-9 to 10-6 sec; Section 4.6.1), and (3) the time that elapses between the temperature measurement and the end of the diffusive sortation process (which may be of the same order as the gate closing time, ~10-6 sec).
Most of the waste heat is generated in this device by forced water sieving (Section 3.3.1). To remain within biocompatible thermogenic limits (~109 watts/m3), each unit may be cycled once every ~3 millisec, a 0.8% duty cycle of a ~23 microsec sieving stroke. Subject to this restriction, each unit would consume ~1 picowatt in continuous operation. A unit presented with a ~0.1 M concentration of small molecules processes ~106 molecules/sec (e.g., ~1 gm/hour of glucose using 1 cm3 of n = 1000-unit cascades), or ~104 molecules/sec for a unit presented with large molecules at ~0.001 M, circulating ~109 molecules/sec of water as working fluid while running at 340 cycles/sec. Additional chamber segments on each unit, combined with more complex diffusion circuits among the many units in a cascade, should permit the simultaneous complete fractionation of the input feedstock even if hundreds of distinct molecular species are present.
By 1998, diffusion-based separation had been demonstrated in microfluidic devices.2689
Last updated on 7 February 2003