Langmuir 1994,10, 2370-2375
2370
Surface Pressure Feedback Control for Langmuir-Blodgett Film Transfer. 1. Optimization of Process Control Parameters C. L. Mirley, M. G. Lewis, J. T. Koberstein,* and D. H. T. Lee? Institute of Materials Science, U-136, University of Connecticut, Storrs, Connecticut 06269 Received February 3,1994. In Final Form: April 19, 1994@ A recent investigation has shown that the process control dynamics of the surface pressure feedback system used during Langmuir-Blodgett (LB)film transfer have a significant impact on the quality of deposited films. Precise control of the surface pressure during LB film transfer may therefore be essential for producing defect-free ultrathin films, especially at the high deposition rates that will be required for large-scaleproduction. To achieve precise control with a surface pressure feedback control system, careful adjustment or optimizationof the process control constants is required. In this paper, two procedures are described for optimizing the surface pressure feedback control constants for a computer-controlled LB trough. The criterion used for optimization is that when a disturbance to the surface pressure occurs during feedback control, the surfacepressure should return as quickly as possible to ita setpoint value with little or no overshoot. Optimum proportional (Kp) and integral (KI) control constants, as well as barrier velocity (v),are determined for arachidic acid deposition by introducingtwo types of disturbances during surface pressure feedback control: (1)a step change to the surface pressure setpoint and (2) rapid transfer of the floating monolayer film to a glass substrate using the vertical dipping method (pulsed input). The results show that both procedures give the same values (or range of values) for the optimum KP,KI,and v . In our control system, we also find that, at low transfer rates, the control of the surface pressure during film transfer does not critically depend on the values set for feedback control constants, as long as the control system is stable.
1. Introduction In order to take advantage of the unique electrical, optical, or biological properties of Langmuir-Blodgett (LB) films, these floating monolayers must first be transferred to some type of solid substrate or support. The overall objectiveduring transfer is to produce mono- or multilayer ultrathin films on solid substrates that are free from defects and that retain the same degree of molecular orientation and packing of the floating monolayer. Some of the factors which have been identified as having a significant effect on the quality of transferred LB films are the viscosity or flow properties of floating monol a y e r ~ , subphase ~-~ ~0nditions,4~~ dipping speed! and even trough size and methods of compre~sion.~ Recently, Morelis et al. have investigated the film quality of behenic acid multilayers deposited on calcium fluoride substrates as a function of the gain of the surface pressure feedback servoloop used during compression.* They found that the number of crystalline defects in the transferred LB films was largest when the gain for surface pressure feedback control was set to its highest value. Their results indicate that process control dynamics of the surface pressure feedback loop also have an important
* To whom correspondence should be addressed. t Current address: Industrial Technology Research, Hsinchu,
Taiwan. * Abstract published in Advance ACS Abstracts, June 1,1994. (1)Buhaenko, M. R.;Goodwin, J. W.; Richardson, R.M.; Daniel, M. F.Thin Solid Films lM, 134,217. (2) Malcolm, B. R. Thin Solid Films 1986,134,201. (3)Albrecht, 0.; Ginnai, T.; Harrington, A;Marr-Leisy, D. Thin Solid Films 1989,178,171. (4) Biddle, M. B.; Rickert, S. E.; Lando, J. B. Thin Solid Films 1985, 134,121. (5)Veale, G.; Peterson, I. R.J. Colloid Interface Sci. 1986,103,178. ( 6 )Grundy, M. J.; Musgrove, R. J.;Richardson, R. M.; Roser, 5.J.; Penfold, J. Lungmuir 1990,6, 519.
impact on the quality of transferred LB films and that precise control of the surface pressure during transfer may be essential for producing defect-free LB layers. Precise control of the surface pressure during film transfer requires careful adjustment of the process control constants of the feedback loop. When the constants are adjusted properly and a disturbance is introduced to the system, such as during film transfer, the surface pressure response should be stable and respond as quickly as possible to bring the surface pressure back to its setpoint value. The control constants are expected to change depending on the properties of the floating monolayer filmg and the position on the n-A isotherm where film transfer takes place, as well as on the film transfer rate. Manufacturers of commercially available computer-controlled Langmuir troughs unfortunately provide no procedures for optimization of the surface pressure feedback control constants. Additionally, in some commercial troughs access to the control parameters themselves is difficult at best. To date, surface pressure feedback control during film transfer has not been problematic for laboratoryscale production of LB films due to the extremely low transfer rates usually employed. However, film transfer rates will be very important for large-scale production of ultrathin films using the LB technique where these rates are anticipated to be much higher than those currently used. In this paper, we outline two procedures using classical control theory techniques for optimization of the surface pressure feedback control constants of a computerized Langmuir trough with proportional-integral-derivative (PID) control. Optimization and estimation of the proportional (Kp) and integral (KI) constants, as well as optimization of the barrier velocity for arachidic acid, will be presented for both procedures.
(7) Nakayama,T.;Equsa,S.;Gemma,N.;Muira,A.;Azuma,M.Thin Solid Films 1989,178,137. (8)Morelis, R.M.; Girard-Egrot, A.P.; Coulet, P. R. Lungmuir 1993, (9)Petty,M. C.; Barlow, W. A.InLungmuir-BlodgettFilms; Roberta, 9,3101. G. G., Ed.; Plenum Press: New York, 1990;p 110.
Q743-7463/94/2410-237Q$Q4.5Q/Q 0 1994 American Chemical Society
Surface Pressure Feedback Control for LB Film Transfer 2. Experimental Details 2.1. Materials. Arachidic acid used in this study was purchased from Sigma Chemical Co. The listed purity for this CZOcarboxylic acid was 99%, and it was used without further purification. Water used for the trough subphase was obtained from a Super-Q water purification system (Millipore). A h a l 0.22-pmfilter helped remove bacteria from the delivered water which typically gave a resistivity of 18 MQ. Cadmium chloride used in the subphase at a concentration of 2 x 10-4 M was obtained from Janssen-Chimica with a purity of 99.999%. Potassium bicarbonate at a concentration of 2.4 x 10-4 M was used to buffer the subphase to pH 7.65. This was also obtained from Janssen-Chimica witha purity of99.7%. Chloroform,99%, from Aldrich Chemical Co. stabilized with ethanol was used as the spreading solvent for the monolayer films. 2.2. Equipment. The Langmuir trough used in this study was designed and built in-house. It was a constant perimetertype trough that uses a barrier made of Teflon-coated,0.75-in.wide, Kapton tape (DuF'ont) which had been heat sealed into a continuous loop. The width of the moving barrier was 34 cm with a travel distance of 56 cm. The trough itself was made of FEP-coated stainless steel and had a total volume of approximately 12 L. The trough was housed inside a laminar flow cabinet in a certified class 100clean room which was maintained at 20 "C and 51% relative humidity. The pressure sensor used was a Wilhelmy plate type composed of a 0.5-cm-wide filter paper suspended from a Perkin-Elmer AD-2 autobalance. The Wilhelmy plate, which was located about 3 in. from the substrate dipping mechanism, was interfaced to an IBM compatible personal computer using an A/D convertor DT2805 from Data Translation Inc. The balance was calibrated using a series of hanging weights to convert the millivolt output of the balance t o surface tension units ofmillinewtonsper meter. To move the barrier, a three-componentsystem was designed and assembled in-house. This consisted of a computer which sends the movement commands to the barrier and an SMC-25 VLSI integrated chip (Anaheim Automation) which receives commands from the computer for barrier movement and sends clock pulses to drive the barrier motor. Since VLSI chips are oRen intolerant to electrical interference, it is connected via optoisolators to reduce noise levels. An HPMC-100 (Portescap) motion control unit receives clock pulses from the SMC-25 chip and drives the barrier movement. The motion control unit consists of a two-phase disk magnetic motor, a dual-channel current source, and a translator and damping circuitry board. It features an open-loop positioning system with closed-loop velocity control. The velocity feedback coils help prevent unwanted vibrations in the barrier that can be caused by use of a discontinuous current for the stepping motor. The two-phase disk magnetic motor is connectedto a lead screw which is in tun? connected to the barrier's moveable arm. With this system, the barrier can move at speeds of 2.5-480 mdmin. 2.3. Dipping Mechanism. The deposition device is a standalone unit that is not part of the surfacepressure feedback control system. It uses a brushless-type dc servomotor connected to a twin screw to raise and lower a substrate vertically through a floatingmonolayer film. Tachometerfeedback is used to position the substrate and control the number of dip iterations. Dipping speeds available range from 0.1 to 130 mdmin. Details regarding the design and construction of the trough are included in ref 10, and are available upon request from the authors.1° 3. Results and Discussion 3.1. Control Algorithm. The components of the surface pressure negative feedback control loop consist of the Wilhelmy plate pressure sensor, A/D convertor, computer, SMC-25 step motor controller, HMPC-100 motion control unit, and the barrier itself. When the system is in the feedback control mode, for every movement of the barrier, the surface pressure signal from the pressure sensor is measured six times and averaged. This measurement is made in millivolts with a resolution of f0.05mV. An error in the signal, E(t),is calculated which (10)Lee, D. H.T. Ph.D. Thesis,University of Connecticut, 1989.
Lungmuir, Vol. 10, No. 7, 1994 2371 is equal to the surface pressure setpoint (input by the user) minus the average output value. Since electrical noise in the balance can give rise to errors, a deadband is created where the barrier will not move unless the error is larger than some minimum value. The deadband is adjustable and is U S U ~ Y set to f 0 . 1 mV for our system. To prevent the barrier from stalling in the deadband region, the absolute values of the errors are summed up over time and when this sum exceeds 2 mV, the control system moves the barrier as if the error were 0.1 mV. When the surface pressure error is greater than f 0 . 1 mV, the control program initiates a series of calculations in order to determine how far and in what direction the barrier should move. The required distance for barrier movement may be calculated by one of two different methods. In the first method, the distance to move is calculated using the control parameters that are input by the user. Using only proportional-integral control, the distance for the barrier to move is calculated as follows:
where D1 is the distance to move in millimeters, Kp is the proportional control constant in millimeters per millivolt, E(t)is the absolute value of the average surface pressure error at timet, KIis the integral control constant in inverse seconds, and CE is the summation of the absolute value ofthe error signal over all past time. The 0.6 s is the time required for the control program to sample the surface pressure, calculate the distance to move, and move the barrier before the cycle is repeated. The role of each of the individual control parameters becomes clearer upon examination of eq 1. Kp represents the sensitivity of the surface pressure, for a monolayer film a t the control surface pressure, to changes in barrier position. For example, floating monolayer films that have a steep slope in their isotherm will exhibit large shifts in the surface pressure for relatively small changes in barrier position. The proportional constant for such stiff films needs to be small in order to control the surface pressure effectively. For our control system, the proportional constant is also related to the two-dimensional compressibility of the floating monolayer film.ll In control systems that rely strictly upon proportional control, a sustained disturbance usually leads to a condition known as offset where the steady-state value of the controlled variable becomes permanently displaced from its setpoint value. To minimize offset, integral control is usually included as part of the feedback loop. Equation 1shows that the integral control constant, KI, is multiplied by the summation of the absolute value of error over all past time and by 0.6 s. This product, which is a fraction of the overdl error, is then added to E(t)and multiplied by Kp to give the distance for barrier movement. Although derivative control was not used extensively in this study, it was included as an option in the surface pressure feedback control algorithm. In general, where the integral control response lags behind the input error and serves to reduce offset, derivative control response leads the input error and helps reduce overshoot of the controlled variable. Values for the derivative control constant (KD)could not be estimated for arachidic acid surface pressure control but had to be determined empirically. When the surface pressure response was exhibiting overshoot, values input forKDI0.01 s did not significantly reduce the amplitude and frequency of the surface pressure ~
(11)Mirley, C. L.; Lewis, M. G.; Koberstein, J. T.; Lee,D. H.T. Manuscript in preparation.
2372 Langmuir, Vol. 10, No. 7, 1994
Mirky et al.
oscillations around the setpoint. However, for KDvalues greater than 0.01 E, the feedback control system became unstable. The second method for calculating the required barrier movement is simply based upon the maximum distance the barrier can move in one sampling time period:
-
c
35
30 B
ITSE = JtatE2(t)dt
(3)
Because the surface pressure versus time data were digitized and therefore not continuous, the integral was replaced by a summation for our calculations. The time interval chosen for this study was 50 s, which was found to be a sufficient amount of time for the surface pressure to return to its setpoint value after an applied change. Two types of disturbances to the surface pressure were applied to facilitate optimization of the feedback control system: the iirst was a step change in the surface pressure setpoint, and the second was a rapid removal of monolayer material by withdrawing a substrate at high speed for a very short time (pulsed input). The results for arachidic acid will be described below. (A)Step Change in Surface Pressure Setpoint. During feedback control, a step change to the surface pressure setpoint was introduced to the system. For our studies, a step change from 25 to 30 mN/m for arachidic acid was chosen due to the fact that 30 mN/m was the surface pressure where film transfer was normally carried (12)Dorf,R. C. Modem Control Systems, 3rd ed.; Addison-Wesley
Publishing Co.: Menlo Park,CA, 1980.
40
Y
P
where D2 is the distance for the barrier to move and u is the barrier velocity in millimeters per second. The distances D1 and D2 are compared, and the lower of the two is chosen as the distance the barrier will move. The number of clock pulses necessary to effect a movement of this distance are then sent through the SMC-26chip on to the motor. This overall cycle is repeated continuously every 0.6 s. The second distance calculated, D2,effectively acts as a saturation limit for the control system to ensure that the surface pressure does not become unstable during surface pressure feedback control for reasonable values of the process control constants. Thisis a common feature oRen added to process control routines. 3.2. Determination of Optimum Control Parameters. One way to optimize process control systems is by introducing a disturbance to the system during feedback control while recording the control variable’s response versus time. To qualitatively measure a control system’s response, it is common practice to use performance indices. A performance index is a positive number that is calculated from the initial portion of the control system’s response versus time curve and which is based on certain system specifications. When control parameters for the system are adjusted properly, the performance index shouldreach an extreme value, usually a minimum. The system is then considered “optimized” for the control parameters which correspond to this minimum. In our control system, the control variable is the surface pressure. If during feedback control a disturbance is introduced into the system, it is desirable to have the surface pressure return as quickly as possible to the setpoint value with little overshoot or oscillation. The performance index chosen to best evaluate these system specifications was the integral time squared error (ITSEY2:
45
58
25 20
tn 15 0
10 20 30 40 50 60 70 80
Time (s)
(4 34
E
i
32 Y
f
30
P
28
c B
u 26 tn 24 0
10
20
30
40
50
60
T h e (s)
(b)
Figure 1. Surfacepressure versus time for arachidic acid step change experiment (a) FRR = 10 mV/mm, (b)FRR = 20-70 mV/mm. The surface pressure setpoint is 30 mN/m, KI = 0 s-l, and u = 480 mm/min.
out. To optimize the two control constants and the barrier velocity, KIwas initially set to zero while K p and u were varied together. After Kp and u were optimized, KIand u were varied while keeping the Kp at its optimum value, and then u was kept at its optimum value and Kp and KI varied together. In this way, the control constants were varied together systematically in order to determine their optimum values. In order to estimate a starting value for the optimum proportional control constant, we used the slope of the arachidic acid n-A isotherm in the linear region below the collapse point where deposition would take place. The slope was calculated using a linear regression fit of the raw data for the JC-Aisotherm. The raw data consisted of two data columns: one correspondingto the pressure signal from the electrobalance in units of millivolts and the other the barrier position relative to its starting point in units of millimeters. We renamed the absolute value of the slope of the isotherm the film response ratio (FRR). In terms of the proportional control constant, FRR = UKp. The slope or estimated FR%,hm for arachidic acid was determined to be 4.2 f 0.08 mV/mm (where the f value is the standard error). When the estimated FRRoptimum was input into the surface pressure feedback control algorithm, the system immediately became unstable and oscillated with a constant frequency about the surface pressure setpoint of 30 mN/m. This indicated that the estimated proportional constant was too high, and so FFtR had to be increased to eliminate oscillations in the surface pressure response. As shown in Figure 1,even a t a value of FRR = 20 mV1 mm, the surface pressure showed oscillating behavior. This type of control system response is referred to as underdamped behavior. At FRFt = 70mV/mm, the surface
Surface Pressure Feedback Control for LB Film Transfer
Langmuir, Vol. 10,No. 7, 1994 2373
barrier velocity. A minimum in the ITSE at FRR = 40 mV/mm (Kp = 0.025 m d m V ) was found for all values of u L 10 mm/min. Since the minimum for the ITSE was rather shallow, this indicated that there may actually be a range of optimum FRR or Kp values which satisfy the criteria set for optimization of the control constants. This was seen very clearly a t u = 10 mm/min where the ITSE did not change from FRR = 30-50 mV/mm. The reason for the discrepancy between the estimated I and experimentally determined FRRoptimum could be due to the rate at which the surface pressure signal from the electrobalance is sampled. For discrete-time control systems, as the data sampling time decreases, the critical value ofthe proportional gain used for control increases.13 In our control system, the data sampling time is most likely too slow to permit direct substitution ofthe isotherm slope for the proportional control constant. Parts b and c of Figure 2 show the ITSE versus barrier velocity and integral control constant, respectively, with FRR set to 40 mV/mm (Kp = 0.025 mm/mV). In contrast 600 to the ITSE plot for&, there was no true minimum found as the barrier velocity was changed from its maximum value to very low values. However, there appears to be a break point in the plot when u < 10 "/min, where the ITSE becomes very large. This was similar to the behavior found in the plot of ITSE versus FRR when the curve T begins to flatten out a t u = 10 m d m i n . 100 ~ ~ " " ~ " " ~ " " ~ I" " ~ " ' ~ ~ The explanation for this behavior is as follows: when 0 100 200 300 400 500 u < 10 m d m i n , the barrier movement is controlled not Barrier Velocity (mmlmin) by the magnitude ofEW but by the barrier velocity itself. According to the control algorithm, there are two distances calculated for movement of the barrier. One is proportional to the error in the surface pressure signal, while the other is proportional to the barrier velocity. Whichever one is smaller, that is the distance the barrier moves. If the barrier velocity is below a certain value, then the 3000t distance calculated from it will always be the smaller one. w When this happens, the surface pressure is effectively in E 2000 odoff control mode not PI control mode. 1500 The response of the surface pressure in odoff control tends to be very slow which is why the ITSE has such a 1000 large value in this control regime. Also the response curves for the surface pressure in this regime tend to have a ~ ~ . ? ~ ' ~ ~ ? ~ ' ' , ~ ~ ~ ~ ~ ~ saw-tooth , " ~ ~ , shape ' ' appearance. From Figure 2b it was 0 0.05 0.1 0.15 0.2 0.25 0.3 concluded that, for arachidic acid, the barrier velocity must be greater than 10 mm/min in order to be in PI control. K, (s.') However, it was also noted that if the barrier velocity was (4 too large, the movement of the barrier created waves in Figure 2. For step change experiments (a) integrated time the subphase which was also undesirable. Therefore, squared error (ITSE)versus FRR (barriervelocities are 10"/ during actual film deposition the optimum barrier velocity min (solid circles), 75 mdmin (open squares), and 480 mm/ should be between 10 and 75 m d m i n . min (solidtriangles);KI= 0 s-l),(b)ITSE versus barrier velocity Figure 2c shows the ITSE plotted against the integral (FRR = 40 mV/mm, KI= 0 s-l), and (c) ITSE versus integral control constant with FRR = 40 mV/mm and u = 75 mm/ control constant (FRR = 40 mV/mm, u = 75 "/min). Each min. As observed with the barrier velocity plot, there data point is the average of at least two measurements f the standard error. Where there is no error bar, the standard error was a breakpoint in the plot at a KI value of approximately is approximately equal to the size of the symbol. 0.1 s-l. Values of the integral constant below 0.1 s-l produced little change in the ITSE, but above this value pressure shows no oscillations but the response time, the ITSE increased rapidly. When KI =. 0.25 s-l, the which is the time it takes the system to reach the setpoint, system became unstable and began to show oscillating was long and the steady-state surface pressure had an behavior. Using only proportional control, the offset found offset of about 0.4 d i m . This type of control response for the surface pressure after a disturbance was 0.4 mN/ is referred to as overdamped behavior. As FRR was m. A value of KI = 0.05 s-l was sufficient to reduce this decreased from 70 mV/mm, the response time decreased offset to zero. Therefore, the optimum integral control but the surface pressure began to overshoot the setpoint. constant was found to be in the range of 0.05 5 KI 5 0.1 Therefore, there exists a trade-off: decreasing FRR (or S-1. increasing Kp) decreases the response time, but this also When a control system displays underdamped behavior, leads to overshoot or possible instability in the surface the frequency of the oscillations is often used to give an pressure feedback response. Figure 2a shows the ITSE, calculated from the data in (13) Ogata, K. Discrete Time-Control Systems; F'rentice Hall:EngleFigure 1, plotted against FRR or 1/Kp as a function of wood Cliffs, NJ,1987;p 375.
l-
700$1
* f
-
2374 Langmuir, Vol. 10, No. 7, 1994
__
s2
Mirley et al. Table 1. Comparison of Optimum Proportional (Kp) and Integral Control (g~) Constants and Barrier Velocity (v) for Arachidic Acid Step Change and Pulsed Input Control ExperimentsO KP ( d m W KI (8-l) u(dmin) step change 0.025 (0.238) 0.05-0.10 (0.095) 10-75 pulsed input 0.025 (0.238) 0.05-0.15 (0.097) 10-75
A
34 32
g!
i 0
tf
5cn
30
28 26 24
- - FRR=50
22
-FRR=7O
0
$
10 20 30 40 50 60 70 80 Time (s)
Figure 3. Surface pressure versus time for the arachidic acid
pulsed input experiment. FRR = 20-70 mm/mV. The surface pressure setpoint is 30 mN/m, KI= 0 s-l, and u = 75 mm/min. 2500
‘ I I I I ~ I I I I ~ I I I I ~ I I I I ~ I I I I f I I I I ~
2000t L
J
500f
10 20 30 40 50 60 70
80
FRR=l/K, (mV/mm)
Figure 4. ITSEversus FRR for the arachidic acid pulsed input experiment: first layer deposited onto a glass slide (solid circles), second layer (open squares),third layer (solid triangles).KI= 0 s-l, u = 75 mm/min.
estimate of the integral control constant for the system.12 An estimate of KI was made for arachidic acid using the surface pressure versus time curve shown in Figure l a , where FRR = 10 mV/mm. The estimated value of KIwas found to be 0.095 s-l which was in very good agreement with that determined from the control experiments. (B)Pulsed Disturbance to Surface Pressure Setpoint. To optimize the control parameters using actual deposition conditions, a method of rapidly depositing arachidic acid onto 1in. x 3 in. glass slides was developed. Initially, the substrate was immersed in the subphase before spreading the film. Once the film was compressed to its surface pressure setpoint of 30 mN/m and the control parameters set, the substrate would be pulled out a t a speed of 130 “/min for 2 s. In this way, a small amount of the floating monolayer removed very quickly from the water surface acted as a pulsed disturbance to the feedback control system. The transfer ratio calculated for each experiment was found to be 1.0 in all cases. The same analyses used to determine the optimum control constants and barrier velocity for a step change in surface pressure setpoint were applied to the surface pressure response curve data for a pulsed disturbance. Figure 3 shows typical surface pressure versus time curves as FRR was varied ( u = 75 mm/min, KI = 0 s-l). Figure 4 shows the plot of ITSE versus FRR for the first, second, and third layers of deposited arachidic acid. All of the curves showed identical behavior as found in the step change experiments: namely, that the ITSE has a rather shallow minimum at FRR = 40 mV/mm (Kp = 0.025 mm/ mV). As pointed out earlier, this shallow minimum for the ITSE could indicate that there exists a range of optimum Kp constants. It was also interesting to note that the curves for the
In parentheses are the estimatedvalues for the optimum control constants. Kp was estimated from the slope of the n-A isotherm at 30 mN/m. KI was estimated from the frequency of the surface pressure oscillations when Kp was set to 0.1 mm/mV.
first three layers overlapped each other even though the interactions between substrate and floating monolayer were completely different. For the first layer, the interactions consisted mainly of the headgroup-substrate type; for the second layer hydrocarbon tail-to-tail interactions predominated, while for the third layer headgroupheadgroup interactions predominated. Figure 4 seems to indicate that the type of interaction occurring between the substrate and the transferred floating monolayer during deposition does not significantly influence the optimum value for the proportional control parameter. The optimum barrier velocities and integral control constants determined for arachidic acid were 10 5 u 5 75 m d m i n and 0.05 I KI I 1.5 s-l, which were similar to the results found for the step change experiments. Table 1 summarizes the results found for both optimization methods as well as the estimated values calculated for Kp and K I . The results for both process control experiments show that the optimum control constants for LB film deposition can be determined by carrying out a few simple experiments whereby a change in the surface pressure setpoint is used to introduce a disturbance to the feedback control system. Analysis ofthe surface pressure response curves then allows the user to identify optimum control parameters. For our surface pressure control system, we can simplify this procedure even further by equating Kp,optimum to the absolute value of the inverse slope of the n-A isotherm multiplied by a factor of 0.11. 3.3. Control of Surface Pressure during LB Film Transfer. To see how well the optimized control parameters performed under actual film transfer conditions, a monolayer of arachidic acid was deposited onto a 1-in.wide glass slide a t 30 mN/m with Kp = 0.025 m d m V , Ki = 0.1 s-l, and u = 75 d m i n . As a comparison, deposition was also carried out using ordoff control mode with Kp = 0.05 m d m V , KI = 0, and u = 5 m d m i n . To deposit a single monolayer, dipping started with the substrate immersed in the subphase. After a period of 20 s after feedback control was initiated, the glass slide was pulled out at speeds of2.5,10,25, and 50 m d m i n for 20 s. Figure 5 shows the surface pressure versus time c w e s for deposition of arachidic acid under PI and ordoff control conditions at the various dipping speeds. The curves in Figure 5 show that, for deposition speeds less than about 10 m d m i n , both PI and odoff control modes were effective in maintaining a constant surface pressure of 30 mN/m during film transfer. However, at dipping speeds greater than 25 m d m i n , PI control with the optimized control constants was better for surface pressure control. This can be seen at the highest transfer speed where, at the end of the dip, the surface pressure has already returned to its setpoint value. For o d o f f control mode, the surface pressure does not reach 30 mN/m for a full 1min &r the start of deposition at the highest dipping speed. During this time, the surface pressure dropped to 16 mN/m, while during PI control the surface pressure change was f 6 mN/m.
Surface Pressure Feedback Control for LB Film Transfer
Time
(8)
(a)
E
CI
al
28 01 Q,
t
24
0 al
g
20
3
v)
16 0
20
40 60 80 100 120 140 Time (s)
(b) Figure 5. Surface pressure versus time for arachidic acid during film transfer with (a) optimum PI control (Kp = 0.025 d m V , KI= 0.1s-l, u = 75 mdmin) and (b)odoff control (Kp = 0.05 m d m i n , KI= 0 s-l, u = 5 mdmin). The substrate was a l-in.-wide glass slide that was pulled out of the subphase starting at t = 20 s and ending at t = 40 s. Substrate dipping
speeds are 2.5 d m i n (solid line), 10 mdmin (dotted line), 25 d m i n (dashedline),and 50 mm/min(dashed-dottedline).
Deposition of successive arachidic acid layers onto 1 in. 1 in. glass substrates a t a dipping speed of 50 m d m i n and under odoff control mode showed that the surface pressure could drop as low as 0-5 mN/m. While film transfer still took place under these conditions, polarized microscopy of these arachidic acid films decorated with 52 A of silver revealed that microcracks, 100-300 pm long and oriented perpendicular to the dip direction, appeared on the surface of transferred films three to five layers thick. No such defects were found for films deposited onto glass substrates at 50 d m i n using PI control. These results show that when the dipping speed is low, as is usually the case for most laboratory-scale preparation of LB films, as long as the surface pressure feedback control system is not unstable, the values input for the control constants are not critical. However, when the dipping x
Langmuir, Vol. 10, No. 7,1994 2375 speed is increased to give relatively fast transfer rates, proportional-integral control using optimized control constants is necessary for maintaining precise control of the surface pressure. Of course, the transfer rate of the floating LB film depends not only on the dipping speed but also on the size of the substrate. Consideration for the shape of a substrate should also be taken into account when adjusting the surface pressure feedback control constants. This is due to the fact that the substrate shape determines the type of sustained disturbance imposed on the surface pressure feedback control system; i.e., a flat rectangular or square substrate would produce a constant disturbance, whereas a flat circular substrate would produce a sinusoidally-varying disturbance. 4. Conclusions It has been shown recently that the process control dynamics of the surface pressure feedback loop for LB film preparation have a direct impact on the quality of transferred LB layers.* Precise control of the surface pressure during film transfer may therefore be essential for producing defect-free ultrathin films by the LB technique. Careful adjustment or optimization of the feedback control constants is required for achieving precise control. The criterion we have used to optimize the control constants is that the surface pressure should be stable and return as quickly as possible to its setpoint value when disturbances are introduced during feedback control. We have shown that optimizing the proportional and integral constants and the barrier velocity by introducing a step change to the surface pressure setpoint or by rapid transfer of the floating monolayer to a substrate gives equivalent results, also that, at low transfer rates, the control of the surface pressure during film transfer does not critically depend on the values set for the control constants as long as the feedback control system is stable. However, at high transfer rates, it is recommended to use optimized proportional and integral constants for maintaining control of the surface pressure during film transfer. While this study has focused primarily on obtaining precise surface pressure control during film transfer, the overall objective is to optimize the quality of deposited LB films. Future work in this area will be carried out to determine if using optimum proportional-integral control constants does indeed produce LB films with fewer defects.
Acknowledgment. C.L.M. wishes to thank the Eastman Kodak Company-Kodak Fellows Program, for their support and Dave Salminen of Pratt and Whitney for the informative discussions concerning process control theory. This material is based upon work supported in part by the US. Army Research Office and the Connecticut Department ofHigher Educationunder Grant No. 631606. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the Connecticut Department of Higher Education.
