gion, cf. Dixon (12) and Pearse and Gaydon (13). The rate constant for light emission, ks has been determined by Clyne and Thrush (14) as 1.2 X lo1 1. mole-1 sec-I. Hence at [O] = 1 x lop6mole l,-I, 18 = ks [O][CO] = 1.2 X [CO] sec-1. Comparison to our NO/O, results gives 6 ppb as the approximate limit of sensitivity. However, the phototube response curve shows that in the wavelength region of the COjO emission, the tube sensitivity is some 5 times higher than in the region of the N O / 0 3 emission. This then places the limit of sensitivity at about 1 ppb. Again, interference by other pollutants could in practice result in a higher useful limit. It must be noted that the rate constants for light emission of the NO/03 and CO/O reactions, quoted in this paper, were measured by comparison to the NOjO reaction in the same apparatus. The absolute values then were obtained (2, 14) by using the directly measured absolute value for the NOjO reaction (7). The fact that the intensity ratios used here depend on relative measurements made in one apparatus enhances their accuracy. SO*. This major air pollutant is also known to participate in chemiluminescent reactions, e.g., with 0 atoms (15). (12) R. N. Dixon, Proc. Roy. SOC.(London),A275,431 (1963). (13) R. W. B. Pearse and A. G. Gaydon, “The Identification of
Molecular Spectra,” 3rd ed., Chapman and Hall, London, 1963, p 123. (14) M. A. A. Clyne and B. A. Thrush, “Ninth Symposium (International) on Combustion,” Academic Press, New York, 1963, p 177. (15) M. F. R. Mulcahy, “Twelfth Symposium (International) on
Combustion,” The Combustion Institute, Pittsburgh, Pa., 1969, p 329.
However, no rate constants for light emission of SOz reactions are available; hence, the limit of sensitivity cannot presently be estimated. Application. The natural atmospheric background levels of 03,NO, and CO are, according to Tebbens (4), approximately 10, 20, and 100 ppb, respectively. Because the lightemitting reactions are of first order in the pollutant concentrations, linear responses can be predicted. It thus appears highly likely that the homogeneous chemiluminescent detector can be used for the monitoring of these pollutants over the full range of their concentrations in polluted air. Of course, experimental confirmation remains desirable. Many chemiluminescent gas reactions occur (16). Therefore, the method described probably can be extended to analysis of further gases and to other environments. ACKNOWLEDGMENT
We have benefited from discussion with J. Hodgeson, R . K. Stevens, and A. E. O’Keeffe of the National Air Pollution Control Administration. RECEIVED for review November 5,1969. Accepted February 12, 1970. This paper is based on a presentation given at the 158th National American Chemical Society Meeting, New York, September 1969. Work supported by the National Air Pollution Control Administration under Contract CPA-22-69-11. (16) T. Carrington and D. Garvin, “Comprehensive Chemical Kinetics,” Vol. 3, C. H. Bamford and C. F. H. Tipper, Ed., Elsevier, Amsterdam (in press).
Sensitive, Wide-Range, Temperature-Controlled Cell E. W. Owen’ Lawrence Radiation Laboratory, University of California, Livermore, Calif. 94550 A temperature-controlled cell has been developed in which the temperature can be changed rapidly over a wide range (-190 to 300 “C). This range can be extended downward by using a lower-temperature coolant, and upward to the temperature limitations imposed by the materials. The cell, thermally isolated from the environment, is cooled by liquid nitrogen and heated by an electric heater. The control system operates according to a minimum-time-control law while making large temperature changes and according to a proportional-control law while holding the temperature at a set point. The proportional controller is a pulse-frequency-modulated system and thus consists of discrete rather than analog elements. The circuits are built from integrated-circuit logic gates and comparators. The cell was developed for use as a chromatographic column in a gas-separation facility, and should be applicable to systems having similar temperature-control requirements.
THE CELL WAS designed with a number of thermal considerations in mind. While these were dictated by the needs of a gas-separation process (I), similar specifications are encountered in the design of chemical cells, reactors, and Present address, Department of Electrical Engineering, University of California, Davis, Calif. 95616. (1) F. F. Momyer, “The Radiochemistry of Rare Gases,” National Academy of Sciences, National Research Council, NAS-NS 3025, October 1960.
columns of other types. The thermal design of the cell is governed by several specifications. 1. A wide temperature range, extending both above and below ambient temperature, is required. Within this temperature range, the temperature must be controlled to within 1 or 2 “C. 2. Large changes of temperature must be made as quickly as possible. Since the dynamic response depends on the mass of material to be heated or cooled, this requirement implies that the weight of the cell must be small compared with the weight of its contents. In addition, the geometry of the cell must facilitate the rapid exchange of heat between the heat sources and the contents of the cell. 3. The active material of the cell must be maintained at uniform temperature throughout. In the gas-separation cell, the chromatographic process depends on the temperature of the adsorbant. In other cells, similar temperaturedependent reactions or processes are likely to take place. 4. The dynamic behavior of the cell should be simple so that a simple control system can be used; complex dynamic behavior requires a complex control system. Therefore, the thermal behavior of the cell should be capable of being described by a simple mathematical representation. 5. Economy of operation must be considered. In particular, the liquid coolant should be conserved. Consideration of these five factors led to rejection of most of the conventional designs in favor of a novel design conANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970 e
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LN out
Heat
Active material
os
1c
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oc 1H
Temperature -
1
Fr
OH,
ture
CB
5T
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1
of a c t i v e material
TU
Gcs - f l o w cel I and container
Bubble pump
.. .
in
Gas-flow scheme
Section A - A Center cross section, gas - flow cell
Figure 1. Temperature-controlled cell and its bubble pump. Large arrows, gas flow; large double-pointed arrows, LN flow A active material (200 g of charcoal adsorbent) BP bubble pump BPH bubble-pump heater (Nichrome wire, 20 0) CB ceramic bead E electrical connection Fi fin Fr frame for heating wire IC inner container (0.035-inch copper sheet) IH inner heater (75 inches of No. 22 Nichrome wire) LN liquid nitrogen OC outer container (0.035-inch copper sheet) OH outer heater (200 inches of No. 22 Nichrome wire) os outer shell (0.015-inch copper sheet) Tu tube w walls
cept. The conventional method of controlling the temperature of a cell is to place it in a liquid bath or surround it by a metallic mass. A bath or metallic moderator has two functions: it acts as a thermal buffer between the object and the outside environment, and it serves as a heat source or sink in the heating or cooling of the cell. The use of a bath is ideal in applications where the temperature is held stationary or is slowly varied over a small range. However, since the mass of the bath or metallic moderator increases the thermal inertia, a bath is undesirable if a fast response is required. Furthermore, there is no bath material that remains liquid over the wide temperature range of this cell. The concept adopted in this design is thermal isolation of the cell from the outside environment by careful insulation. This reduces to a minimum the mass that must be heated or cooled. It also results in simple dynamic behavior and hence requires only a simple control system. In addition, since 580
ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
there is little flow of heat through the insulation, the liquid coolant is conserved. However, the lack of a thermal reservoir such as that provided by a bath means that the heating and cooling systems must be capable of rapidly delivering small amounts of thermal energy to the cell; otherwise, the temperature cannot be held accurately at a set point. Some of the requirements for the design of the cell are in conflict with each other; hence, compromises must be made. For example, there is a tradeoff between a rapid response and a uniform temperature. A rapid response requires a cell with a small mass. However, if the temperature of the active material is to be uniform, high conductivity paths must be placed between the heat sources and sinks and the active material. This can only be done with metal fins or by the choice of a geometry that requires a large amount of metal. CONSTRUCTION OF CELL
A cell was designed and built with these compromises in mind (Figure 1). The gas-flow chamber is functionally a U-tube both surrounding and surrounded by coolant and heating elements. The basic U-shape is considerably modified to increase its surface area and thus to facilitate heat transfer. It consists of two concentric, vertical cylindrical, copper containers, the outer one (OCin Figure 1) 3 l / 2 inches in diameter and 4 inches high, the inner one (IC)1‘ 1 2 inches in diameter and 3’12 inches high. Thus the vertical walls of the two containers are separated by a distance of about 1 inch, and their bases are separated by a distance of about ‘ 1 2 inch. They are fixed at these distances by two vertical connecting walls on two opposing sides (W in Figure 1) extending from the top of the cell to the bottom of the inner container, leaving a ‘/2-inch space at the bottom. The two containers are connected also by a tube (Tu)that pierces both chambers and connects the inner chamber with the outside. The result is the modified U-shape, that is, a longitudinally split outer chamber whose two compartments are connected at the bottom, thus permitting gas flow (from “Gas in” in Figure 1) down one compartment, around the central tube at the bottom, and up through the other Compartment (to “Gas out”). The basic shape and the gas-flow pattern are seen most clearly in “Gasflow scheme” in Figure 1. The gas-flow cell is surrounded by a lightweight copper shell (OS in Figure 1) 4llz inches in diameter, only slightly
Set Point
(TS)
Pulse-frequency 7
e
Thermoon woll
modulator
.
Amplifier
Error
I
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Voltoge-tofrequency converter
I
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I
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I I
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I
I To heater
1-1
drive
Figure 3. Block diagram of control system larger than the outer diameter of the cell. Its function is to contain and direct the flow of coolant and its vapor, at atmospheric pressure, over the outer and inner walls of the gas-flow cell. Liquid nitrogen (LN) enters at the top and flows downward between the cell and the outer shell. The coolant or its vapor then moves over the bottom of the container and upward through Tu and the inner chamber to its outlet to the atmosphere (“LN out” in Figure 1). The entire assembly (gas-flow cell and its surrounding shell) is placed in a dewar flask and covered with packed glass fiber insulation. The bubble pump for the coolant (BP in Figure 1) is placed in another dewar flask. Heat is applied to the cell by an outer heater (OH in Figure 1) uniformly distributed over the outside of the outer container, The wire was strung through small ceramic beads (CB) (to prevent electrical contact between the wire and the cell), wound around the outer container, and shop-cemented in place. The inner wall of the cell is heated by an element (ZH) wound on an insulated frame (Fr) of alumina. Vertical fins (Fi in Figure 1) attached to the outside walls facilitate heat transfer to the active material in the gas-flow tube. An increase in the number of fins improves the temperature uniformity of the cell, but at the expense of increasing the thermal inertia. The cell has several advantages that can best be appreciated by comparison with a standard cylindrical column. The modified U-shape greatly increases the surface area, bringing the particles of absorbent closer on the average to a heating or a cooling wall, thereby promoting heat transfer and uniformity of temperature. In addition, the greater surface area provides more space for mounting the heater wires. MATHEMATICAL MODEL OF CELL
Before a control system can be designed, there must be a mathematical description of the object to be controlled. If a complex model is necessary, the control system has a corresponding complexity. The design of this cell allows its thermal behavior to be described by a simple model. The dynamic model of the cell is based on the assumption that the thermal behavior of the cell is similar to the behavior of the two-material system shown in Figure 2. In this model, the inner case and fins of the cell are represented by a sheet of material with infinite thermal conductivity and finite thermal capacity. The active material is assumed to have finite thermal conductivity and capacity. The model can be reduced to the schematic shown in Figure 3. For the simple model to be valid, the outer container must be of light-weight construction. Otherwise the outer case acts as an independent heat-storage element. Heat-flow from the cell to the outside is reduced to negligible proportions by the vacuum insulation of the dewar jar.
Since the model is second-order, the behavior of the system is described by two variables T , and T,, the temperatures of the cell contents and the cell wall, respectively, which are measured and which form the inputs to the control system. The measurements are made by thermocouples placed at representative positions on the case and within the active material. HEATING AND COOLING DEVICES The selection and design of the heating and cooling devices is governed by several requirements: rapid response, low thermal inertia, and delivery of finely controlled quantities of heat. Liquid nitrogen, because of its availability, suitable temperature, and cheapness, is used as the coolant. It is delivered to the cell by a bubble pump, a device that is a close relative of the coffee percolator. The bubble pump (BP in Figure 1) is made by mounting a 2042 heating coil of fine nichrome wire (BPH) in a standard glass funnel. When an electric current of sufficient intensity flows in the heating coil, a bubble is formed which rises up the stem of the funnel, forcing a quantity of liquid nitrogen into a tube leading to the cell. One reason for choosing the bubble pump is its speed. The device has little inertia; its response is characterized by a transportation lag of negligibly small value. The bubble pump is difficult to control by changing the level of the input voltage, because there is no flow from the pump until a threshold voltage is reached, and further increase in voltage causes the flow to rise quickly to a saturation level. Therefore, a pulsed mode of operation is used. Pulses of equal height and width are applied to the heater of the pump. Each pulse has enough energy to create a bubble and, hence, to pump a small quantity of coolant, and the average pumping rate is determined by varying the spacing between the pulses. Since the pulses can be spaced as far apart as desired, it is possible to meter out extremely small quantities of coolant. This mode of operation proved to be ideal for the fine control of temperature. The pumping rate of the bubble pump depends to some degree on the coolant level. However, since the bubble pump is within a closed-loop system, these variations have little effect on the operation of the system. Therefore, the coolant can be replenished by a crude level-control system. The electric heater of the cell also operates in the pulsefrequency mode. An ac pulse with the same width as the cooling pulse is delivered to the heater by an SCR (siliconcontrolled rectifier) circuit . CONTROL SYSTEM The control system has two modes of operation, a maximum-rate mode and a proportional mode (2). The maxi(2) J. E. Gibson, “Nonlinear Automatic Control,” McGraw-Hill Book Co., New York, N. Y., 1963. ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
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Once the error has been changed to a frequency, the signals are processed as discrete binary levels rather than as analog signals. Therefore, the system has the inherent advantage of a switching system over an analog system. The discrete controller is constructed of inexpensive integrated circuit elements. n e behavior of the system is best described by the phaseplane plot shown in Figure 4. As has already been pointed out, the thermal behavior of the cell is adequately represented by two variables, the temperature of the cell wall T, and the temperature of the contents of the cell T,. At equilibrium, these two temperatures are equal to the set-point temperature T,; therefore, the equilibrium states are along a 45" line through the origin. A large increase in temperature is accomplished by first heating the cell at the maximum rate and then cooling at the maximum rate. As equilibrium is approached, the system enters a rectangular region in which the proportional mode is employed. Although the minimum-time-control law requires a curved switching line, a straight-line approximation to the switching line is adequate. Precise switching is not necessary because a motion close to the equilibrium point is captured by the proportional controller.
Slope of switching line = m
%+ .
Proportional ,region , I
e% e.
/
0 Tc
Figure 4. Motions of system in phase plane
DISCRETE CONTROLLER
mum-rate mode allows large excursions of temperature in a minimum time; the proportional mode holds the temperature at the set point without hunting and using an excessive amount of energy. A block diagram of the control system is shown in Figure 3. Two temperatures, the temperature of the contents of the cell T, and the temperature of the cell wall T,,,, are measured and amplified. The error signal used in proportional-mode operation is formed by subtracting a linear combination of the amplified temperature signals from a set point. A voltage-to-frequency converter changes the error voltage to a frequency. The square wave output of the voltage-tofrequency converter is changed to a series of fixed-width pulses by a monostable. The distance between the pulses (pulse frequency) depends on the error voltage.
Figure 5 shows that the discrete controller can be divided into a number of functional parts. The proportional cs.maximum-rate logic determines whether the proportional mode or the maximum-rate mode should be used. If the system is in the proportional mode, the proportional-mode logic determines whether the system should be heated or cooled. The maximum-rate logic serves the same function when the system is in the maximum-rate mode. The heatand-cool logic is the final stage of the discrete controller. This circuit receives the output of the three other logic boxes and the output of the monostable and decides whether the bubble pump or the electric heater should be turned on. The discrete controller (Figure 6) is constructed of integrated-circuit comparators, which convert the analog inputs into logical levels, and integrated-circuit logic gates. The heat-and-cool logic circuits provide the output that
Pulse train from pulse-frequenc
i modulator
--
To bubble-pump drive
F
TS TC
Tw
ponents of discrete controller
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ANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
From monostable
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D
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r
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AC
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.
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-
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c - Cool
V
- Heat
I
Heat logic
1
Comparator
Summer
Nand gate
Maximum-rate logic
Figure 6. Circuit diagram of the discrete controller; m, and md are the slopes of the switching lines (see Figure 4); a and b define the extent of the proportional mode (see Figure 7)
20
+3 TS
---_
4I
- - ._
2b
Inside rectangle Proportional mode O u t s i d e Max im um r a t e mode
-
-
I I I I
Tc
Figure 7. Proportional-us.-maximum-ratelogic;
turns the heater and the bubble pump on or off. When the system is in the maximum-rate mode, the output of these logic circuits is either a logic-1 level to the pump transistor and a log-0 level to the heater drive or vice uersa. While the system is in the proportional mode, the heat-cool logic transmits the pulses generated by the pulse-frequency modulator either to the pump or to the heater.
Apply maximum rate if A = H J K L .
A , H, J , K , L have the meanings indicated by Figure 6 The function of the heat-and-cool circuits can be expressed by a simple logical statement. For the cool logic the statement is: the bubble pump should be on when the system is in the maximum-rate region and cooling is indicated by the maximum-rate logic, or when the system is in the proportional mode and cooling is indicated by the cooling-us.-heating comparator and a pulse is present. This logical function, exANALYTICAL CHEMISTRY, VOL. 42, NO. 6, MAY 1970
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-lm'T - T c
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+
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