Langmuir 1995,11, 2755-2760
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Surface Pressure Feedback Control for Langmuir-Blodgett Film Transfer. 2. Effect of Floating Monolayer Film Properties on 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 January 31, 1995@ The relationship between the optimum process control parameters for surface pressure feedback control during Langmuir-Blodgett (LB) film transfer and the properties of floating monolayers is investigated using a computerized Langmuir trough equipped with proportional-integra1 (PI) feedback control. The monolayer materials used in this study were arachidic acid, a crystalline solid at room temperature, carboxylic acid-terminated poly(dimethylsi1oxane)(Mn = 2 loo), a liquid, and carboxylic acid-terminated 1,2-hydrogenated poly(butadiene) (Mn= 2822), a viscous liquid. The proportional (Kp)and integral (KI) control constants as well as the barrier velocity (v)are optimized by introducing a step change to the surface pressure set point while the surface pressure vs time is recorded. A process control performance index, which calculates a positive number by integrating the initial portion of the surface pressure vs time curve, is then used to optimize the control constants. Our results show that the optimum Kp for arachidic acid is smaller than that for the other two materials by a factor of 40. This result appears to correlate strongly with the two-dimensional compressibility of the floating monolayer films. The optimum barrier velocities were also found to vary with certain monolayer material properties, while optimum KIvalues did not show a strong dependence on monolayer material properties. 1. Introduction
It has been shown recently by Morelis et a1.l that the process control dynamics of the surface pressure feedback loop for Langmuir-Blodgett (LB) film preparation have a direct impact on the quality of the transferred LB layers. Therefore, precise control of the surface pressure during film transfer may be essential for producing defect-free ultrathin films using the LB technique. Adjustment or optimization of the process control constants, however, is necessary for achieving precise control of the surface pressure especially at the high transfer rates which will be needed for large-scale production of LB films. In a previous paper,2we have shown that optimization of the process control parameters for surface pressure feedback control during LB film transfer can be carried out simply by introducing a step change to the surface pressure set point (near the surface pressure where film transfer will take place) while recording the surface pressure response vs time. The area under the initial portion of the response curve is then used to calculate one of several available process control performance in dice^.^ When the value of the performance index is minimized, by systematically adjusting the process control constants, the surface pressure feedback control system is considered “optimized. Petty et al.4have pointed out that the floating monolayer film is a n integral part of the surface pressure feedback control loop. Therefore, the values input for the process control parameters (i.e., used to maintain a constant
* To whom correspondence should be addressed. FAX(203)4864745; telephone (203)486-4716;e-mail,
[email protected]. t Current address: Industrial Technology Research Institute, Hsinchu, Taiwan. * Abstract published in Advance ACS Abstracts, June 15,1995. (1) Morelis, R. M.; Girard-Egrot, A. P.; Coulet, P. R. Langmuir 1993, 9, 3101. (2) Mirley, C. L.; Lewis, M. G.; Lee, D. H. T.; Koberstein; J. T. Langmuir 1994,10,2370. (3)Dorf, R. C. Modern Control Systems, 3rd ed.; Addison-Wesley Publishing Co.: Menlo Park, CA, 1980. (4) Petty, M. C.; Barlow, W. A. InLangmuir-Blodgett Films;Roberts, G. G., Ed.; Plenum Press: New York, 1990; p 110. 0743-7463/95/2411-2755$09.00/0
surface pressure during film transfer) should depend critically on the properties of the floating monolayer. In this paper, we investigate the effects that the floating monolayer film properties have on the values for the control optimum proportional (Kp) and integral (KI) constants as well as the barrier velocity ( v )for a computercontrolled Langmuir trough. For this study, three different monolayer materials were chosen for comparison: arachidic acid, a crystalline solid at room temperature; carboxylic acid-terminated poly(dimethylsi1oxane)(diacid PDMS), a liquid at room temperature; carboxylic acidterminated 1,2-hydrogenatedpoly(butadiene)(diacid 1,2hPB), a viscous liquid at room temperature. 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%. The carboxylic acid-terminated PDMS was synthesized by Dr. I. Yilgor of GoldschmidtChemical C ~ r p .The ~ synthesis procedure produces PDMS chains that have a carboxylicacid group on each end so that the functionality of acid end groups is exactly two. Gel permeation chromatography (GPC) and vapor pressure osmometry ( W O ) gave an M, = 2100 and a polydispersity of 1.93. The carboxylic acidterminated 1,2-hPB was obtained from Nisso Chemical Corp. Prior to use of this material,it was purified by precipitatingfrom HPLC grade toluene solution with HPLC grade methanol. The precipitatewas then dried in a vacuum oven at room temperature until a constant weight was reached. W O gave an Mn = 2822, while GPC gave a polydispersity of 1.3. End-grouptitration gave a functionality of acid groups of 1.5. Water used for the trough subphase was obtained from a Super-Qwater purification system (Millipore). A final 0.22 ,um filter helped remove bacteria from the delivered water which typically gave a resistivity of 18 MQ. Cadmium chloride, used M, was obtained in the subphase at a concentrationof 2 x from Janssen-Chimica with a purity of 99.999%. Potassium M was used to buffer bicarbonate at a concentrationof 2.4 x the subphase to pH = 7.65. This was also obtained from JanssenChimica with a purity of 99.7%. Chloroform, 99%,from Aldrich Chemical Co. stabilizedwith ethanol was used as the spreading solvent for the monolayer films. ( 5 ) Yilgor, I.; McGrath, J. E. Adv. Polym. Sci. 1988, 86, 86.
0 1995 American Chemical Society
2756 Langmuir, Vol. 11, No. 7, 1995
Mirley et al.
2.2. Equipment. The Langmuir trough used in this study was designed and built in-house. It is a constant perimeter-type trough that uses a barrier made of Teflon-coated,0.75 in. wide, Kapton tape (DuPont) which had been heat sealed into a continuous loop. The trough itself is made of FEP-coatedstainless steel and has a total volume of approximately 12 L. A PFAcoated thermocouple with digital readout recorded the subphase temperature to f l "C, and a pH meter monitored the pH to *0.05. The trough was housed inside a laminar flow cabinet in a certified class 100 clean room which is 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. This was interfaced to an IBM compatible personal computer using an A/D converter DT2805 from Data Translation Co. The balance was calibrated using a series of hanging weights to convert the millivolt output of the balance to surface tension units of millinewtons per meter. 2.3. Control Algorithm. The hardware components for the surface pressure negative feedback control system have been described in detail in a previous publication2 and so will not be repeated here. The computer control algorithm calculates the distance the trough barrier has to move in order to maintain a constant surface pressure (input by the user) for LB film transfer of floating monolayers. The following equation shows this calculation using only the integral-proportional control constants.
where D1 is the distance to move in millimeters, Kp is the proportional control constant, or gain, in units of millimeters per millivolt, KI is the integral control constant in inverse seconds, E(t) is the absolute value of the average error in the surface pressure at time t in millivolts (equal to the difference between the set point surface pressure and its value at time t),and D is the summation ofthe surface pressure error 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 initiate barrier movement before repeating the cycle. Derivative control was not used in this study but was included as an option for the surface pressure feedback control system. We have found that values input for the derivative control constant, KD,either had no effect on the quality of control or caused the feedback system to become unstable. As part of the control algorithm, a second distance for barrier is also calculated and then compared to D1. The movement, Dz, second distance is simply calculated by multiplying the present barrier velocity by 0.6 s. The two distances are then compared, and the smaller ofthe two is chosen as the distance for the barrier to move. DZessentially acts as a saturation limit for the control system to ensure that the surface pressure does not become unstable for reasonable values of the control constants. 2.4. Performance Index for Optimization of Process Control Constants. The criterion used for optimization of our surface pressure feedback control constants was that if a disturbance to the surface pressure occurred during feedback control, it would be desirable to have the surface pressure return as quickly as possible to its set point value with little or no oscillations. The performance index chosen to best represent these control system specificationswas the integral time-squared error (ITSE)3and is given by the following equation.
ITSE = JtE2(t) dt
(2)
where E ( t )is the error in the surface pressure signal (millivolts). Since the error in the surface pressure signal is multiplied by the time, the ITSE weights events occurring at shorter times (such as overshoot) more heavily. Additionally, because the surface pressure vs time data were in a digitized format, the integral in the above equation was replaced by a summation over a time interval of 50 s for the actual ITSE calculation. This time interval was found to be sufficientlylong for the surface pressure to return to its set point value after an applied step change.
3. Results and Discussion 3.1. Estimation of Kp and KI. The isotherms for arachidic acid, diacid PDMS, and diacid 1,2-hPBare shown
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Figure 1. fl-A isotherms for (a)arachidic acid, (b) diacid 1,2hydrogenated poly(butadiene) (1,2-hPB), and ( c ) diacid poly(dimethylsiloxane) (PDMS). Subphase conditions are [CdClzl =2 x M, [ F C O 3 I = 2.4 x M, T = 20 "C, and pH = 7.65. Compression speed was 4 mrdmin.
together in Figure 1. Solutionsof the monolayer materials were prepared in chloroform to a concentration of 4 mg/ mL. A 100 p L quantity of solution was spread onto the water subphase which contained cadmium chloride and was buffered to a pH of 7.65. After 10min each monolayer was compressed to collapse at a barrier velocity of 4 mm/ min. As can be seen from Figure 1, the overall shapes of the isotherms are very different from one another. Arachidic acid, a crystalline solid a t FO "C, has a sharp rise in the isotherm at an area of 20 A2/molecule. The slope of the n-A isotherm is linear up to collapse a t 62 mN/m. This type of isotherm is typical of fatty acid materials that are crystalline solids a t room temperature. The floating monolayers have compressibilities equal to that of bulk matter, and the area per molecule for close-packedchains is on the order of that for single crystah6 The isotherm for diacid PDMS, a liquid at 20 "C, shows several transitions in its isotherm which are believed to be due to changes in polymer chain conformation of the diacid PDMS molecules rather than phase changes, as typically seen with the fatty acid monolayer materials.' The surface pressure for diacid PDMS begins to increase at an area of about 410 A2/molecule,reaches a plateau, and then increases linearly from 22 to 29 mN/m again until collapse at 30 mN/m. The transition in the isotherm before collapse has been associated with the orientation of the diacid PDMS chains perpendicular to the water surface. The resulting monolayer film consists of cloqepacked helices with a cross-sectional area of 100 A2/ molecule. Diacid 1,2-hPB, a viscous liquid at 20 "C, has an isotherm that does not show a plateau region in the isotherm as found with the diacid PDMS. The surface pressure begins increasing a t an area of 145A2/molecule, then increases linearly from 5 to 14 mN/m until its reaches collapse at 15 or 16 mN/m. Unlike arachidic acid and diacid PDMS, the diacid 1,2-hPB shows a fairly gradual transition at the collapse point. This type of isotherm resembles that for expanded-type polymeric monolayer films as defined by Crisp.8 As shown previously,2 the slope of the n - A isotherm in the linear region below the collapse point was used to (6) Gaines, G. L. Insoluble Monolayers at Liquid-Gas Interfaces; Interscience Publisher: New York, 1966. (7) Lenk, T. J.; Lee, D. H. T.; Koberstein, J. T. Langmuir 1994, I O ,
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(8) Crisp,
D.J . Colloid Sci.
1949, I , 161.
Effect of Floating Monolayer Film Properties
Langmuir, Vol. 11, No. 7, 1995 2757
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Figure 2. Surface pressure vs time for arachidic acid step change experiment: FRR = 10 mV/mm, KI= 0 s-l, u = 480 mdmin. The surface pressure set point is 30 mN/m.
estimate a value for the proportional control constant. This linear region was chosen such that the surface pressure where film deposition would take place was included. The slope was calculated using a linear regression fit of the raw isotherm data which consisted of two data columns: the surface pressure signal in units of millivolts and the relative barrier position in units of millimeters. The absolute value of this slope was renamed the film response ratio (FRR) and is related to the proportional control constant as follows.
film response ratio (FRR)= l/Kp
(3)
The surface pressure range of the linear regression fits for the monolayer materials was determined by taking the derivative of the isotherms and locating the points near collapse where the derivative was a constant. For arachidic acid this range was 10-60 mN/m, for diacid PDMS, 22-29 mN/m, and for diacid 1,2-hPB, 5-12 mN/ m. The corresponding surface pressures for LB film deposition were 30,25,10 mNlm for arachidic acid, diacid PDMS, and diacid 1,2-hPB, respectively. The absolute values of the isotherm slopes or FRRs determined by regression analysis were 4.20 f0.08,O. 110 f 0.012, and 0.117 f 0.032 mV/mm for arachidic acid, diacid PDMS, and diacid 1,2-hPB, respectively. The coefficients of determination, R2, for the linear regression fits were all found to be greater than 0.99. Values reported for the slopes represent the averages of at least two measurements and include the standard error. Since Kp = l/FRR, the corresponding estimates of the proportional control constant are 0.24 f 0.01, 9.1 f 1.0, and 8.6 f 2 m d m V , respectively. It is clear from the FRR values that the arachidic acid monolayer material has the steepest slope and therefore is most sensitive to changes in surface pressure with barrier position. These results also show that estimated proportional control constant for arachidic acid is much smaller than those predicted for the diacid PDMS and 1,2-hPB materials. An estimate of&, for each of the monolayer materials, was obtained by measuring the frequency of the surface pressure oscillations when the feedback control system was unstable or displaying underdamped behavior during a step change experiment. A plot of surface pressure vs time for arachidic acid with FRR = 10 mV/mm, KI = 0 s-l, and u = 480 m d m i n is shown in Figure 2. With these values for the control constants, the surface pressure response became unstable and oscillated around the set point (30 mN/m) at a constant frequency. This frequency
was then measured and used to estimate KI for the feedback control ~ y s t e m .The ~ value obtained for KIwith arachidic acid was 0.10 s-l. By use of the same procedure but different control constants, KIvalues for diacid PDMS and diacid 1,2-hPB were estimated to be 0.09 and 0.08 s-l,respectively. These results indicated that the integral control constants among the three monolayer materials were approximately the same and did not appear to vary significantly with the floating monolayer film properties. 3.2. Evaluation of Optimum Control Parameters by Step Change in Surface Pressure Set Point. A disturbance to the surface pressure was introduced during feedback control by applying a step change to the set point from a lower to a higher value while still remaining in the linear slope region of the isotherm. For our studies the step changes for the surface pressure set points were 2530, 23.5-25, and 8-10 mN/m for arachidic acid, diacid PDMS, and diacid 1,2-hPB,respectively. During a typical experiment, the monolayer would be spread using the conditions described previously and brought to the lower surface pressure set point. The values for Kp and KIwould be input along with the new surface pressure set point. Once feedback control was initiated, the surface pressure vs time was recorded for approximately 2 min. The ITSE was then calculated from the surface pressure response curve according to eq 2. To optimize the two control constants and the barrier velocity, KIwas initially set to a value of zero while Kp and u were varied together. After Kp and u were optimized by the above procedure, KI and u were varied while keeping the proportional control constant at its optimum value. Finally, u was kept at its optimum value while varying Kp and KI together. In this way, the control constants were varied together systematically in order to determine their optimum values. When the Kp,est,mated values obtained from the slopes of the individual n-A isotherms were input into the control algorithm,in each case the feedback control system became unstable, after initiation of the corresponding step change in the surface pressure, and oscillated with a constant frequency about the set point surface pressure. This indicated that the estimated proportional constants were too high and so had to be decreased. Figure 3 shows the surface pressure vs time curves for each of the monolayer materials as the FRR is varied (KI= 0 s-l, u = 480 mm/ min). For arachidic acid, the range of FRR values where the surface pressure response exhibited stable behavior extended from 20 to 70 mV/mm, while for diacid PDMS and diacid 1,2-hPB the range of FRR values for stable surface pressure responses extended from 0.4 to 2 mV1 mm. These results from the step change experiments confirmed what was found from the KP,estlmabd data: the optimum Kp values for more liquid-like diacid PDMS and diacid 1,2-hPB monolayer materials were much larger than Kp for arachidic acid. It was also noted that the surface pressure response curves for the diacid PDMS and diacid 1,2-hPB materials gave intrinsically noisier traces, which may indicate that it is more difficult to control the surface pressure of highly compressed floating monolayers which are liquids compared to those which are solids. Figure 4 shows the ITSE, calculated from the surface pressure vs time curves shown in Figure 3, plotted against FRR or 1/Kp as a function of the barrier velocity (KI= 0 s-l) for each of the monolayer materials. It is clear that in each plot a minimum in the ITSE occurs at a specific value of FRR corresponding to its optimum value: for arachidic acid, FRRoptimum = 40 mV/mm for u 2 10 mm/ min; for diacid PDMS, FRROptlmum = 1mV/mm for u 2 75 = 1mVlmm for m d m i n ; for diacid 1,2-hPB, FRRoptimum
2758 Langmuir, Vol. 11, No. 7, 1995
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