Pore Vol. cc.,G. 0.50 with d = 50 A , 0.25 with d = 25 A. 0.25 with d = 75 A. 1 00 ~
Area, Sq. M./G. 200 200 67 167 ~
sintering with resultant area and activity decline. Also diffusion in and out of such pores is slower. Hon-ever, the presence of a fairly high T’o/Ao does not preclude the presence of appreciable numbers of small pores.
for 32-cycle bone char. The results given in Figure 9 indicate fairly good agreement, although the median value for pore wall separation is slightly greater than the pore radius. LITERATURE CITED
Median pore wall separation, d,
=
50 A.
By choosing an example with a n ider distribution, it can be shown that the wider the distribution the greater the disparity between 2Vo/Ao and the median pore wall separation. It is clear from the data that conventional measurements of pore volume, surface area, together \\ith calculation of their ratio to obtain a pore diameter figure, are not sufficient to describe many pore systems, since the pore distributions vary markedly in breadth, skeFmess, etc. I n many catalysts as !vel1 as adsorbents, very small pores are objectionable, because being closer together, they are more susceptible to
COMPARISON WITH BJH METHOD
(1) Barrett, E. P., private communica-
Because the B.J.H. method for determining pore size distribution ( 2 ) has found wide application and been confirmed by mercury porosimeter data (S), it is of interest to compare it with the parallel plate method. As the former method employs a cylindrical model and this method employs a plate model, an exact comparison cannot be carried out. However, as the Kelvin equation for cylindrical pore radius is the same as for plate separation, approximate agreement v, ould be expected between distribution curves on the basis of cylinder radius and plate separation. Therefore, a comparison was carried out ( 1 ) using the desorption isotherm
tion, Sept. 27, 1956 ( 2 ) Barrett, E. P., Joyner, L. G., Halenda, P. P., J . Ana. Chem. SOC.73, 373 (1951). (3) Joyner, L. G., Barrett, E. P., Skold, R., J . Am. Chem. SOC.73, 3155
(1951). (4) Pierce, C., J . Phys. Chem. 57, 149
(1953). (5) Ries, H. E., Jr , Van Kordstrand, R. A,, Johnson, XI. F. L., Bauermeister, H. O., J . .4m. Chem. SOC, 67, 1242 (1945). (6) Schull, C. G., Elkin, P. B., Roess, L. C., Zbid., 70, 1410 (1948). RECEIVED for review June 23, 1956. Accepted February 26, 1957.
Semiautomatic Subtraction of Titration Curves Versatile Curve-Plotting Device VINCENT L. STEVENS and EDWARD L. D U G G A N Department of Physiological Chemistry, School of Medicine, Universify of California, Berkeley, Calif.
b A simple plotting device has been designed for the routine subtraction of titration curves to yield the desired difference curve. All numerical records are eliminated; the corrected titration curve (experimental minus blank curve) is immediately plotted, point by point, on a chart recorder. The system is capable of addition, subtraction, division, and multiplication. Conversion of interpolated chart distances into logarithmic values is possible, though not developed in this work. A simple solenoid pen lifter has been designed; the recorder pen marks a point only when desired.
A
recording of titration curves eliminates tedious work, but much arithmetical analysis remains after the sample and blank curves are obtained. I n automatic titration, the shape of the blank (solvent) curve is a function of solvent volume. chart speed, and rate of alkali addition. With small volume increments or dilute alkali titrant, mere inspection of the two curves does not identify buffer regions nor locate pK values. The curve desired is that found UTOMATIC
after the careful subtraction of the quantity of alkali used in the blank titration from that required for the sample titration, for a given pH. Even using millimeters on the chart to represent the two titers, more than an hour is required for the production of a corrected titration curve, on a point by point basis. I n a n attempt to cope nith the work of correcting 30 sample titration curves (normal daily output), the follon ing apparatus waq designed and used on a routine bask. APPARATUS AND TECHNIQUE
A slide-wire is used as a preci...e measure of distances, converting any length to a corresponding direct current voltage. Because the measurement desired is the distance between the two curves minus that arbitrary distance known as offset, all measurements may be replaced by one setting which is constantly reduced by a voltage equal t o the offset distance involved. Two contactors on the same slidewire provide a potential which represents the distance between them. The arrangement of the chart table and Tsquares used in registration on the desired curl-es is shown in Figure l . One
T-square follom the blank curve, point by point, simultaneously setting its sliding contact on the slide-wire, DE. The other T-square follows the sample curve. The T-squares are referred to a s J-square, A, and L-square, B. to describe their appearance after the necessary trimming. The L-square holds a movable nooden block on which is mounted the slide-\T-ire contact. This allows the correction for the offset distance a t one pH value, the block remaining in this position for all measurements thereafter. Inaccuracy of measurement results if the block twists or slides after the one setting, so a wellmachined block should he inqtalled for dependable accuracy. The slide-xire is energized with 2 or 3 volts from a storage battery or from heavy-duty dry cells. The sliding Tsquares are equipped with a fixed silver contact a t A. or an adjustable siker contact a t B. Both T-squares are pulled into tight junction n ith the Elide-Lvire by spring loading a t C. The qpring is mounted on the overhang of each straight edge. in a position of desired tension against the far side of the hardwood block. The T-squares must slide easily along the table. Each spring base is mounted by a common screw clamp to the T-square. VOL. 29, NO. 7, JULY 1957
1073
The slide-wire is Advance wire, 1 min. in diameter, 140 cm. long, with a total resistance of 2 ohms. The greatest sensitivity of measurement is obtained without further resistance in series, although this approaches shorting of the batteries. Storage batteries should be used for the voltage source, with provision for frequent charging. Dry cells provide sufficient constancy if the slidewire is energized only during each short period of use. The potential obtained from the two contactors on the slidewire is divided suitably for insertion into the 10-mv. recorder. Each registration on the two curves provides one point on the recorder chart. Experimental curve charts and the related blank are taped to the wooden base with the chart lines and board edge parallel. The right edge of the Jsquare follows the blank curve, while the left edge of the L-square follows the experimental curve. Adjustment of the arbitrary offset is made by sliding the wooden bar on the L-square until zero potential is obtained, the L-square remaining set on the intersection of the curve and the starting pH. This adjustment is not changed for the remainder of the registrations on the two curves. Thus the offset distance is mechanically subtracted, leaving a remainder of distance which is the desired measure of difference between the two titrations. The registration of the two T-squares continues for a series of pH values. The curves may be surveyed a t increments of 0.1 to 1 pH unit, as desired. The increment taken is held for the entire series of measurements. Similar increments are taken along the timeaxis of the chart recorder by means of constant paper drive periods. The block diagrams of the electrical systems are shown in Figure 2. The upper diagram indicates the voltage source for the slide-wire table. The voltage reduction brings the potential into the range of the 10-mv. recorder. A helical slide-wire (Leeds & Northrup Co.) was used but a ten-turn Helipot could also be used. The setting on the voltage divider is constant for analysis of a curve pair. This unit may be used to provide expansion or reduction of the difference curve plot. Using a few calibrated distances along the slidewire, a full scale pen travel can be provided for 4-, 8-, 16, 32-, or 64-em. distance between the edges of the Tsquares. Since the original curve is on 11-inch paper (27 em.) the first three spans provide expansion of small difference curves. The last span gives more than 2 to 1 reduction of a difference curve. The third step shown introduces the necessary voltage subtraction for the center-zero recorder. The lower unit of Figure 2 provides a constant time measure for paper travel, moving the chart in equal increments along the abscissa (pH) of the final curve. Chart drive is on for a stated period--e.g., 10 seconds-then it is stopped with the timer. The remote switch, located beside the chart table, is normally closed. Opening the switch prints the desired point as the pen sole1074
ANALYTICAL CHEMISTRY
-
D A Figure 1.
B
I O cm.
Chart table and slide-wire arrangement A.
T-square T-square with mechanical offset Springs D, E Slide-wire
B. C.
F Remote Switch
0:
Recycling Timer I sec to 20 m i n (Misco 651) Chart Drive r u n s during t i m i n g
a
2-7 -
Recorder Chart Drive Reloy points are a switch i n parallel to usual toggle switch
Reloy c o i l Points
I
I
Figure 2. recorder
Block diagram of X
-Y
= -D -0
of Recorder Pen
I
plotting device for use with chart
Units provide distance measurement on Y-axis (ordinate) of flnal curve
noid opens. The timer starts again as the switch is released, while the solenoid is actuated to lift the pen. The recycling timer used an Eagle llicroflex unit which had been wired and cased by Microchemical Specialties Co., Berkeley, Calif. Repetitive precision of the timer is the chief requisite, so that the increments along the abscissa of the final graph are constant. Other precise timers with current-carrying relays will undoubtedly suffice. Power for the solenoid pen lifter (Figure 3 ) and the timer is obtained from a triple socket on the end of a special extension cord, to provide a microswitch (normally closed) a t the chart table, an ordinary electric plug a t the power outlet, and a socket located conveniently for the necessary hookup to timer and pen lifter. The cord is about 1 foot from plug t o socket and an additional 10 feet to the switch. This allows the operator to remain a t the chart table location, directing the time cycle and pen drop by pressing the microswitch momentarily. In practice the plotting time is a function of the necessary chart travel time, 3 seconds of the 10-second cycle being adequate for the placement of the two T-squares.
The plotted curve has its usual shape if increasing pH values, 4.0, 4.4, 4.8, etc., are used with an original zero balance a t the right border of the recorder chart. The accuracy of the Y value> obtained from this device is a function of battery stability and the precision of contact setting on the slide-wire. The present apparatus allows distance plots (nine replicates) with an average deviation of 0.5y0,for a distance range of 6 to 48 em.
*
EXTENSIONS AND APPLICATIONS
The chief use of the method is for analysis of titration data. Time required for curve-plotting will a l w y s be several seconds per point, so long as the T-square registrations are required. The curve subtraction process is not accurate unless the volume change during titration is held small by the use of a large sample (10.0 ml.), compared to the titrant volume (0.200 ml.) added. Thus the total volume change is 2% or less. For titrations over the
I l O V AC.
Figure 3. A. 6. C.
Solenoid pen lifter
Walls of casting Wire attachment Pen in writing position
complete pH range (2 to 12), titrant of 0.5M to 1.0M is required. The sample should require from 10 to 100 micromoles of titrant for complete titration. A titration of acetic acid (pK’ 4.57) ( 3 ) illustrates the use of the apparatus. ,- -4similar need for curve subtraction esists in spectrophotometry, where a complex absorbance curve may be simplified by the consecutive subtraction of the absorbance of each known component, allowing some prediction of the shsorbance of unknon-n components and of their identity. The series of spectral curves obtained by repetitive scanning of an enzymesubstrate mixture could be analyzed by the subtraction of a curve a t zero time from a curve for time t , yielding absorbance differences related to the transformation of substrate into one or more products. The plot of numerical values on the pen-drive itxis is possible using a meter stick slide-wire, the number becoming an equal number of millimeters, and an equivalent potential. The unit on the time axis could be the second. Chart motion :imi an accurate electric stop watch c m be controlled by the remote switch, the uperator acting to stop the watch anti chart a t the indicated interval for t81ieplot of the desired slidewire potential. Elegant systems of rapid cur\-e-plotting from nunierical data slioiiiti be possible, without’ use of relativel>-espensive chart recorders. The technique may be extended to include one or more coniputation steps. It should i )e possible, in one operation, to tr:iii4i rrni the spectral energy curves for solvent and sample into per cent transmittLtnce by division, using a dif‘ferent slide-wire arrangement, followed by conversion of this signal into a logarithmic signal which is plotted on the recorder. The final value could he absorbance. on a linear scale. il spectral energy recording attachment ( 1 ) provides scanning by driving the wave length cam of the Beckman DC spectrophotometer. The necessary logarithmic :iniplifiers exist (4, 6). If it is necessary to use tn-o slide-mire tables, with four T-square contactors, voltage subtraction or addition may be utilized. One application for this
0. E. F.
Hole in casting W i r e turn bolt Solenoid
assembly is the stepwise graphic analysis of titration curves of proteins or other polyfunctional acids. Amino acid analyses are possible for the particular protein specimen titrated. The titratration curve provides information regarding the balance between the nuniber of acidic residues (from analysis) itnd the number found in the titration. Such titration curves are complex in slope, without particular identification points. Perhaps analysis of such titration curves could be done easily on the basis of a graphic mat’ch of particular regions of the total curve with the buffer increment expected. The protein titration curve should exhibit buffering in the pH region of 4 to 8 which is determined in part by the number of histidyl residues present. Comparison is made by placing the protein titration curve on one slidewire table, and setting the T-squares on the histidyl buffer region. A particular voltage is taken from the slidewire for the distance the curve occupies on this chart, and a strip of unused chart paper for its printed pH markings is mounted on the other slide-wire table. On this chart paper is placed Lt typical sigmoid curve drawn on cellophane. This curve may be registered along the pH axis of the chart paper, so that any pK value may be assumed for the residues in the protein. One value is assumed, and the curve is so registered with the underlying chart paper by taping. The T-squares of t’his table are set on the asymptotic ends of the dissociation curve. The span adjustment for this curve is set so that the voltage output equals that obtained from the length on the titration curve which corresponds to the known number of residues of histidine ohtained from analysis. The assumed curve is subtracted for the residues from the segment of the protein titration curve by opposing the voltage outputs from the two slidewires, before the resultant signal is carried to the recorder. A true match for the segment of the titration curve would be shown by the absence of residual distance, after subtraction a t a number of pH values. The advantage of the method is the rapidity Ii-ith \rhic.li
the routine comparison could be made Adjustable span for the voltage outprit from the table holding the theoretic:il curve allow one drawn curve to replace a series of similar curves drann to different height scales. The trial assignment of another pK value for the protein residue requires release of the transparency and its translation along the pH scale of the chart paper before retaping. A set of theoretical curve$ could be used for comparison with segments of the protein titration curve. Such a set would include sigmoid ( urves drann with differing slopes to include the effects of statistical interaction, along the lines of the Bjerrum treatment of such equilibria (2, 5 ) . This simple apparatus provides the first analysis of titration curves of nucleic acids, with the understanding that further interpolations are necesw-p for segments of appreciable curvature. A second result of the method is the provision for the analysis of titration curves for dilute solutes. The
