Eikelboom, Pleun Pieter
|1.||A flow injection back titration method for determining the concentration of a component of interest in a sample, comprising the steps of: (a) forming a stream of titrant; (b) reacting a preselected amount of sample with a preselected amount of backtitrant, the amount of sampie being stoichiometrically less than the amount of backtitrant, so that there is an excess of backtitrant; (C) introducing at least the excess backtitrant into the flowing stream of titrant, so that the backtitrant reacts with the titrant; (d) measuring a physical property of the stream of titrant effective to detect the reaction between the backtitrant and titrant; and (e) determining the concentration of the component of interest in the sample based on the time which elapses rom a reference point until the excess backtitrant has been consumed in the reaction with the titrant.|
|2.||The method of Claim 1 wherein the sample is introduced into the flowing stream of titrant before reacting the sample with the backtitrant, said method being characterized by the simultaneous reactions of sample with backtitrant and backtitrant with titrant.|
|3.||The method of Claim 1 wherein the measured physical property is pH.|
|4.||The method of Claim 1 wherein the measured physical property is absorbance of light at a particular wavelength.|
|5.||The method of Claim 1 wherein the measured physical property is an electrochemical response.|
|6.||The method of Claim 1 wherein the measured physical property is recorded in graphic form.|
|7.||The method of Claim 6 wherein the graphic representation of the measured physical property produces a peak indicating the presence of the backtitrant, and wherein the concentration of the component of interest is determined by measuring the width of the peak.|
|8.||The method of Claim 7 wherein the first derivative of the graphic representation'is used to identify the beginning and end of the peak.|
|9.||The method of Claim 1 wherein the backtitrant and the sample are introduced to a titration vessel by injecting them into a means for delivering the titrant to the vessel, and are thus transported to the vessel by the flowing titrant.|
|10.||The method of Claim 1 wherein the physical property is measured in a titration vessel.|
|11.||The method of Claim 1 wherein the stream of titrant flows at a constant rate.|
FIELD OF THE INVENTION
This invention relates to a new method for the automated chemical analysis of samples. More specifically, this invention relates to flow injection analysis.
BACKGROUND OF THE INVENTION
The need for repeatable accurate chemical analysis methods continues to grow as the number of samples to be analyzed increases. A variety of analyzers have been built in an attempt to keep up with this need. For liquid-phase analysis, the major emphasis has been on continuous flow systems. Recently, most of the new developments in this area concern flow injection analysis (FIA). FIA is based on a system capable of forming a reproducible concentration gradient of sample in a flowing stream. The sample is continually diluted by the incoming fluid, so that a plot of the sample concentration over time forms a gradient curve. Adding reagents to the flowing stream changes the resulting sample gradient curve and creates a new gradient curve describing the concentration of a reaction product. Flow injection analyzers monitorthe stream and record the concentration of either an analyte in the sample or a reaction product. By keeping the fluid stream constant, any changes in the gradient curves can be attributed to changes in the concentration of the sample. Accordingly, the gradient curves are carefully measured and the results are used to determine the characteristics and components of the sample.
More recently, a type of FIA known as flow injection titrimetry (FIT) has been developed (see e.g. U.S. Pat. No. 4,798,803 to Wolcott et al.). This process combines the best features of flow injection analysis with conventional titrimetry techniques. Conventional titration is the volumetric determination
of a sample in a known volume of a solution by the slow addition of a reagent of a known strength until the sample has completely reacted. Completion of the reaction is typically indicated by a color change (indicator) or an electrochemical change in the solution. When the end of the reaction has been indicated, the amount of analyte can be calculated from the amount of reagent needed to complete the reaction.
FIT is derived from this same principle, but is performed in continuously flowing streams, producing rapid, simple, reliable, versatile and accurate analysis systems. In FIT, a reagent (termed the titrant) continuously flows through a titration cell where some property (typically pH) is continuously monitored. A sample having a different value for the physical property being measured is admitted into the cell and is continually mixed with the incoming titrant. Thus, the concentration of sample in the titration cell forms a gradient curve which is monitored just as in other flow injection techniques. In FIT, however, the solution is monitored until the sample has completely reacted with the titrant as evidenced by the value of the physical property returning sharply to near the pre-sample level. As the titrant is flowing at a constant rate, any changes in the time it takes the sample to be completely titrated are attributable to changes in the concentration of the sample. Thus, in FIT the analyst measures the width of the peak representing the changing value of the property, rather than measuring peak height as in other flow injection techniques.
The concept of flow injection titration has been proven successful for the analysis of many compounds. However, the procedure has been heretofore limited to samples which can be directly titrated. Many samples can not be titrated directly in a convenient manner for a variety of reasons. For example, the rate of reaction may be prohibitively slow, or other components in the sample may interfere with the reaction between the component of interest and the titrant. Presently, if the sample can not be directly titrated, then flow injection analysis is considered unavailable. Thus, there is a need for a flow injection technique to analyze components which are not directly titratable.
In conventional titration applications, components which are not directly titratable are often analyzed using a process known as back titration. In back titration a component of interest in the sample is exposed to an excess of a carefully measured reagent (termed the back-titrant), and allowed to completely react (see e.g. Skoog, Holler and West, Analytical Chemistry. 5th Ed., 1990). After the reaction has been completed, the analyst titrates the
remaining back-titrant with titrant to determine the exact amount of back- titrant that was not used in the reaction with the component of interest in the sample. Once the amount of excess back-titrant is known, the amount of back- titrant that reacted with the component of interest in the sample can be calculated by simply subtracting the amount of back-titrant that was in excess from the total amount of back-titrant used. Given the amount of back-titrant required to completely react with the component of interest in the sample, the concentration of the component of interest in the sample can then be determined, provided that the reaction between the component of interest in the sample and the back-titrant is understood.
Thus, back titration is a known method for conventionally titrating analytes which are not directly titratable. There is a need to provide a flow injection method which corresponds to conventional back titration.
SUMMARY OF THE INVENTION
The present invention unites flow injection titrimetry with some of the principles behind back titration, making it possible to analyze species which are not directly titratable in continuous flow systems. The invention comprises forming a stream of titrant; introducing a preselected amount of a back-titrant and a preselected amount of sample into the stream of titrant; allowing the component of interest in the sample to react with the back-titrant and the back-titrant to react with the titrant; and measuring a physical property of the stream of titrant effective to detect the addition of the back-titrant and the reaction between the back-titrant and titrant so that the concentration of the component of interest in the sample can be determined.
In a preferred embodiment of the invention, a stream of titrant is formed and the pH (or some other property) of the stream is then monitored to establish a baseline. Next, a preselected amount of the sample and the back- titrant are added to the stream of titrant. The amount of back-titrant and sample are preselected such that there will be an excess of the back-titrant. When the back-titrant is first added to the stream of titrant, the pH (or other property) changes rapidly, indicating the beginning of the titration. The back- titrant begins reacting with the component of interest in the sampie immediately on contact, and continues until all of the component of interest in the sampie has been consumed. The remaining back-titrant then reacts with the titrant until it too has completely reacted. At that point the pH (or whatever property is being monitored) returns sharply to the baseline value, and the system is ready for another injection of sample and back-titrant.
As both the rate of reaction of the back-titrant with the titrant, and the rate of un reacted back-titrant washing out of the vessel are kept constant from run to run, the variances in the time it takes for the pH (or whatever property is being monitored) to return to the baseline value is completely attributable to the concentration of component of interest in the sample that is analyzed. Thus, the concentration of the component of interest in the sample injected can be determined by measuring the width of a peak representing the change in the measured property.
Additional advantages and features of the present invention will become apparent from a reading of the detailed description of a preferred embodiment which makes reference to the following set of drawings in which:
BRIEF DESCRIPTION OFTHE DRAWINGS
FIG. 1 is a block diagram and schematically shows a preferred embodiment of the interconnection of various components suitable for carrying out the present invention;
FIG. 2 is a schematic drawing of a titration vessel suitable for use in the present invention; and
FIG. 3 is a graphic representation of raw data obtained from the analysis of a sample using the method and apparatus of the present invention.
DETAILED DESCRIPTION OFTHE INVENTION
The invention can be accomplished using an apparatus which comprises a pump capable of delivering a uniform rate of titrant, two sample injection valves, an exponential dilution titration vessel, and a sensor. One of the valves is for introducing a sample, and the other is for introducing a back- titrant. The sensor can be a potentiometπc probe (such as a pH electrode, or a metallic electrode), a conductimetric probe (such as a pair of wires, spaced apart and exposed to the fluids in the titration vessel), an amperometπc detection technique, or a photometric probe (such as a fiber optic probe or even a photometric sensing system comprising simply a beam of light directed through the reaction chamber).
One example of an apparatus suitable for carrying out the invention is shown in FIG. 1. The aoparatus includes a reservoir 10 for holding titrant and a pump 11 for delivering the titrantto a titration vessel 14. The pump 1 1 must preferably be capable of delivering a stable flow rate and should be resistant to the titrant being pumped. Typically the flow rate is in the range between 1 and 2 ml/mm, but higher or lower rates can be used. One pump suitable for such an
application is an FMI lab pump, model number RPG-150 RH1 CKC. The pump 11 is connected to the reservoir 10 and the titration vessel 14 by tubing 16. This tubing can be constructed from any material inert towards the titrant, sample, and back-titrant. Preferably, this tubing has an inner diameter in the range of approximately 0.5 to 1 mm. In the preferred embodiment of this invention the tubing isTEFLON™ tubing having an inner diameter of 0.8mm.
The apparatus also includes a sample injection valve 12 and a back- titrant injection valve 13 positioned in series between the pump and the titration vessel. These valves allow known volumes of material to be simultaneously added to the tubing 16 which carries the titrant to the titration vessel. The valves therefore should be capable of precise delivery. One example of a valve suitable for such an application is a manual sample inject valve produced by Omnifit (part number 1106). Automatic valves, such as those typically used in automatic liquid chromatography, can also be used. The titration vessel can be any apparatus which allows the sample, back-titrant and titrantto be mixed together. Accordingly, the titration vessel can take many forms and sizes such as a long section of tubing or an apparatus such as the one shown in FIG. 2. The vessel shown in FIG. 2 includes a lower inlet port 22, and an upper outlet port 23. The tubing 16 from the pump 1 1 is connected to the inlet port 22, whereas the outlet port is typically connected to waste.
The titration vessel should be able to provide a reproducible sample and back-titrant concentration gradient for the analysis to succeed. Thus, the concentration of the sample and back-titrant should preferably be uniform throughout the vessel so that at any moment the makeup of the fluid leaving the chamber via the outlet is nearly identical to the makeup of the fluid remaining in the vessel. Towards this end, the vessel 14 shown in Fig. 2 also includes a mixing chamber 20 where the sample, back-titrant and titrant can all be mixed together. The mixing is preferably facilitated by a stirrer 21. The stirrer 21 serves at least three functions within the vessel 14: it helps to establish a uniform concentration gradient; it promotes the reactions by bringing the sample, back-titrant and titrant together; and it helps to eliminate bubbles in the vessel 14 by forcing the flow in a helical manner upwards through the chamber with a maximum of rotational mixing but with a minimum of up and down mixing. The stirrer 21 can be magnetic or mechanical (e.g., stirrers mounted on rotating shafts) so long as it provides for a helical flow, and does not trap bubbles.
The titration vessel 14 also includes a sensing means 15, shown in Fig. 2 as being located within the mixing chamber 20. Alternatively, the sensing means 15 could be located after the mixing chamber, so long as it is certain that the back-titrant will not be substantially completely reacted by the time it first reaches the sensing means. The sensing means in a preferred embodiment is a pH electrode, inserted through a hole in the top of the titration vessel 14, but any sensing means capable of monitoring any physical parameter which changes in response to the presence of the back-titrant can be used. For example, any of the sensing means known for conventional back titration can be used in the present invention.
In order to carry out the method of the invention, a titrant solution is chosen that is preferably substantially miscible with the sample, the back- titrant and the reaction product. Most preferably, the titrant is also inert towards the component of interest in the sample, although some reaction between the titrant and the component of interest in the sample is acceptable so long as the rate of the reaction is consistent from run to run.
The rate of the reaction between the titrant and the back-titrant is another important factor in selecting a titrant. The reaction should be relatively fast in order to ensure that the endpoint of the titration occurs before the back-titrant gets too diluted by the incoming titrant. If the endpoint for the titration occurs very late in the analysis the back-titrant is often so diluted that no clear endpoint can be seen. Therefore, it is important to select a titrant which readily reacts with the back-titrant so that the excess back-titrant can be titrated before becoming too diluted. Furthermore, the concentration of the titrant should be carefully adjusted so as not to interfere with the reaction between the back-titrant and the component of interest in the sample. As will be discussed more fully below, for the analysis to succeed the component of interest in the sample which is not flushed from the vessel should be completely consumed in the reaction with the back-titrant. Thus, it is important that the titrant is not so concentrated that it eliminates the back-titrant from the system before the back-titrant has consumed the component of interest in the sample. As previously discussed, however, the back-titrant remaining in the titration vessel 14 should be completely reacted by the titrant before the concentration gradient of the back titrant is too low, so that the FIT endpoint is clearly discernible. Thus, the concentration of the titrant should be carefully optimized to balance these considerations.
Once an appropriate concentration for an appropriate titrant is chosen, the titrant is placed in the reservoir 10 and pumped through the system at a preferably constant rate by the pump 11. The rate of pumping is set to maximize the number of analysis that can be run in a given time period without destroying the resolution of the analysis. Typically, the flow rate is set in the range of from 1 to 2 mi/min. Alternatively, the pump can produce varying flow rates, but the variances should be reproducible to ensure adequate precision.
After the preferably constant rate of flow has been established, the titration vessel is monitored and a chosen physical property is recorded in order to establish a baseline. The chosen physical property can be any measurable parameter, including such things as electrochemical responses, colorimetric responses, and pH readings. Other physical properties which are known in conventional back titration applications can also be used in the present invention. At a certain moment, a preselected amount of the sample and the back-titrant are introduced into the stream of titrant and begin to react. The sample and the back-titrant may be introduced into the stream of titrant by admitting them directly to the titration vessel, or they may be introduced into the stream of titrant by injecting them into a conduit means so that they are carried to the titration vessel by an inert solvent or gas (see e.g. Halldorson et al., U.S. Patent application serial No.07/732,345). Most preferably, the sample and back-titrant are introduced into the stream of titrant by injecting them into the same conduit means that delivers the titrant to the titration vessel so that the flowing titrant carries the sample and back titrant to the titration vessel.
The sample and the back*-titrant can be any number of materials so long as the back-titrant reacts with both the component of interest in the sample and the titrant. Furthermore, the chosen physical characteristic should be different for the back-titrant and the titrant so that the presence of back- titrant in the titration vessel can be detected. Accordingly, when the back- titrant is introduced to the titration vessel 14, the physical property rapidly changes, indicating the beginning of the analysis. Likewise, afterthe back- titrant has been substantially completely reacted, the physical property should rapidly return to near the value observed for the system before the back-titrant was added. A physical property which generally exhibitsthese characteristics is effective to detect the reaction between the back-titrant and titrant.
In the preferred method of addition, the back-titrant immediately begins to react with both the component of interest in the sample and the
titrant. The back-titrant is consumed at a rate which is equal to the sum of the rate at which the back-titrant reacts with the component of interest and the rate at which the back-titrant reacts with the titrant. After the portion of the component of interest which remains in the titration vessel 14 has been completely consumed in the reaction with the back-titrant, the back-titrant remaining in the titration vessel is consumed at a slower rate, reflecting the fact that only one reaction is proceeding. When the back-titrant has been neutralized, the measured physical parameter responds by sharply moving towards the baseline. This signals the endpoint for the FIT analysis. It should be noted thatthe more concentrated the component of interest in the sample is, the longer it will take to be consumed by the back titrant, and therefore the longer it will be present in the titration vessel 14. Consequently, the more concentrated the component of interest in the sample is, the faster the back-titrant will be neutralized, since the back-titrant is consumed at a faster rate when two reactions are proceeding (i.e. the reaction with the component of interest in the sample and the reaction with the titrant). Therefore, as long as the concentration of the titrant and the amount of added back-titrant are kept constant from run to run, then any variance in the time it takes to completely react the back-titrant is attributable to variances in the concentration of the component of interest in the sample. Thus, the time it takes to neutralize the back-titrant corresponds to the concentration of the component of interest in the sample.
Additionally, it should be noted that the effectiveness of this method depends on there being an amount of sample which is stoichiometrically less than the amount of back-titrant. Forthis invention, an amount of sample stoichiometrically less than the back-titrant simpiy means that there will be back titrant remaining after the component of interest in the sample has been substantially completely reacted. Accordingly this term takes into account the reactions between the titrant and back-titrant, the component of interest in the sample and the titrant (if any), and the component of interest in the sampie and back-titrant.
Having an amount of component of interest in the sample which is stoichiometrically less than the amount of back-titrant is important as if there is too much component of interest in the sample so that some component of interest in the sample remains after the back-titrant has been completely consumed, then only a minimum value for the concentration of the component of interest in the sample can be determined. Likewise, the amount of back- titrant should be optimized so that there is enough to react with substantially
all of the component of interest in the sample which remains in the vessel, yet not so much that the time for the analysis becomes unreasonable. Thus, the preselected amount of sample and back-titrant should be balanced so that while an excess of back-titrant for all samples which might be analyzed is assured, this excess is as small as possible.
In one embodiment of the invention, the sample and back-titrant are introduced to the titration vessel by using the injection valves 12 and 13 to admit the material into the tubing 16 carrying the titrant to the titration vessel 14. In the preferred embodiment, the back-titrant is injected into the valve closest to the titration vessel (valve 13 in Fig. 1), but the order of injection of sample and back-titrant is not important so long as it is consistent from run to run.
After being injected into the tubing 16, the sample and the back- titrant are carried by the stream of titrant to the reaction vessel 14. As the back-titrant enters the vessel 14, the measured physical characteristic of the vessel 14 changes sharply in response to the back-titrant. In the preferred embodiment the measured characteristic is pH, and the titrant is acidic while the back-titrant is basic, so that when the back-titrant enters the vessel 14, the pH jumps from acidic to basic values. A moment later, the component of interest in the sample enters the vessel 14, and begins to react with the back- titrant. When all of the component of interest in the sample has reacted with the back-titrant, the remaining back-titrant reacts with the titrant until substantially all of the back-titrant remaining in the vessel has reacted. At that time, the pH of the vessel returns sharply towards its baseline value. The sharp return of the pH signals the endpomt of the analysis, even though there may still exist a small amount of unreacted back-titrant within the vessel 14.
The time lag between the pH change from acidic to basic and back to acidic is one measure of the unreacted back-titrant and accordingly, a measure of the concentration of the component of interest in the sample. The first derivative of the curve formed by recording the pH as it changes over time can be used to more clearly identify the start and especially the end of the analysis. In practice, the starting point for calculating the time lag is unimportant so iong as it is before the earliest possible endpoint (i.e. before an endpoint would be seen in an analysis where there was not an excess of back- titrant). Consequently, as long as the time it takes to reach the endDoint is measured from the same reference point for every analysis, it is generally irrelevant what that reference point is.
More specifically, the concentration of the component of interest in the sample can be calculated using the formula known for use in normal flow injection titrimetry
(pw) = ki * log(c) + k 2 where pw is the the above discussed time lag, i.e. the peak width for the peak representing the change in the physical property being measured, c is the concentration of the component of interest in the sample and ki and k 2 are constants. However, in back titration, c is not the concentration of the component of interest in the sample but the concentration of the back-titrant which is left after reaction with the component of interest in the sample. In back titration, the concentration of the component of interest in the sample is equal to the difference between the original back-titrant concentration and the back-titrant concentration after reaction with the component of interest in the sample. Furthermore, the original back-titrant concentration is a constant for each series of analysis, so the original concentration can be def meα as equaling k3. Substitution yields the following equation : pw = i * log(k3 - concentration of the component of interest in the sample) + k 2 Solving this equation for the concentration of the component of interest in the sample yields concentration of the sample = k.
For each system, the constants kι-3 can be determined using a conventional nonlinear least squares fit procedure Thus, the concentration of the component of interest in the sample can be obtained from the measuring the peak width representing the change in the physical property being measured as it responds to the presence of the back-titrant.
EXAMPLE - Determination of % NCO in "ISONATE™ " M143
ISONATE™ is a brand of modified methylene di-p-phenylene isocyanate (MDI). Pure MDI is unstable and has a melting point of approximately 40°C. Therefore, MDI is typically modified prior to shipping in order to increase stability and to reduce its melting point so that it is in liquid form without requiring external heating. In ISONATE ™ , the modification consists of forming a tπmer. When the tnmer is formed the number of free isocyanate (NCO) groups is cut in half, as 3 MDI molecules each having 2 NCO
groups form 1 molecule having only 3 free NCO groups. This can be clearly seen when looking at the reactions involved in forming the trimer:
p,p'-Methylene Diphenyl dilsocyanate (MDI)
R N =C — O
2 R N = C = O
R N C = O
R N =C — O
R N = C =N R + CO 2
R N C =0
MDI-Dimer D i -MDI -car bod i imide
R N = C =N R + R N = C = O
R N C = O
R N =C N R
Tri MDI uretone imine
The characteristics of ISONATE™ depend on the level of oligomeπzation achieved. The level of oligomeπzation can oe determined by measuring the percentage of free NCO in the reaction mixture. "Equivalent weight" is an indirect measure of the percentage of NCO. For this product, the "equivalent weight" is defined as 4200/%NCO. For ISONATE ™ M143 the equivalent weight must be between 143-146. Thus, the trimeπzation reactions must continue until the percentage of NCO in the sample falls in the acceptable range. Therefore, a method for analyzing the reaction products is needed in order to stop the reaction at the appropriate time. The method and apparatus of the present invention were tested to determine if they could provide acceptable results in a flowing system. Accordingly, for this example the sample is the reaction mixture and the component of interest is the NCO.
The current American Society for Testing and Materials (ASTM) method for determining the percentage of NCO in MDI and its derivatives involves reacting the sample with 2N di-n-butylamine. Each of the free isocyanate groups in ISONATE™ readily reacts with di-n-butylamine to form the corresponding urea as seen in the following reaction :
R N = C = O C 4 H 9 - — N c .
R N C N C4H9
Therefore, since Di-n-butylamine readily reacts with ISONATE™ and is basic (so it can be easily titrated with an acidic titrant) it was chosen as the back-titrant.
Next, acidified solvents were evaluated for use as a titrant. It was observed that the ISONATE™ sample readily dissolved in toluene. Furthermore, the reaction of ISONATE™ with di-π-butylamme was observed to be very rapid in toluene. Unfortunately, however, the reaction left a film on the reaction vessel walls. It was observed that this reaction product could be easily dissolved in acetone. Therefore, acetone was studied as a possible titrant, and it was discovered that ISONATE™ , di-n-butylamine and the reaction product readily dissolved in the acetone. It was also observed that the reaction between ISONATE ™ anq di-n-butylamine in acetone was as fast as when the reaction was
carried out in toluene. Furthermore/acetone can be easily acidified by adding hydrochloric acid. Unfortunately, acidified acetone inevitably contains some water and water is known to react with isocyanate groups such as those contained in ISONATE™ . Therefore, the reaction of ISONATE™ and water was studied. These studies revealed that the reaction between ISONATE™ and water was much slower than the reaction between ISONATE™ and di-n- butylamine. Therefore, it was determined that any water in the acetone would not critically affect the analysis. Consequently, acetone acidified with hydrochloric acid was chosen as the titrant in this example. Once the titrant and the back-titrant were chosen, an apparatus substantially similar to the one shown in FIGS. 1 and 2 was constructed. The titration vessel 14 was constructed from a 10 ml Chrompack glass vial. The vial was fitted with a cap and a pH electrode was inserted through a hole in the cap. The vessel 1 was stirred with a small Teflon ™ stir bar and the inlet and outlet ports were connected by a glass blower. When in use, the titration vessel had an effective volume of approximately 5.5 mis. The pump selected was an FMI lab pump, model number RPG-150 RH1 CKC. The sample and back-titrant valves were obtained from Omnifit (part number 1 106) and the tubing was ail either Teflon ■"* or Tefzel ™ with an inner diameter of 0.8mm. In order to analyze the sample, the first step was to make a 0.015 N solution of hydrochloric acid in acetone. Next, the acidified acetone was placed in the reservoir 10, and the pump 1 1 was set to circulate the solution throughout the apparatus at approximately 2 ml/min. Meanwhile, the pH of the titration vessel 14 was continuously recorded. After a steady flow of titrant was achieved and an adequate baseline was established, about 80μl of sample was injected via valve 12 into the tubing 16 carrying the titrant to the titration vessel 14. Simultaneously, approximately 150μl of di-n-butylamine was added to the line via valve 13. As valve 13 is situated in closer proximity to the titration vessel than valve 12, the basic di-n-butylamine reached the titration vessel first. When the di-n- butylamine reached the titration vessel 14, the pH responded accordingly, moving sharply from acidicto basic values. A moment later the sample reached the titration vessel and began to react with the di-n-butyiamine. This reaction was evidenced by a decrease in the pH of the material in the titration vessel. The gradual decrease in pH continued as the di-n-butylamine reacted with the ISONATE™ and the titrant until all of the di-n-butylamine had either reacted or been washed out of the titration vessel. At that point a rapid change in the pH occurred, as the pH returned to acidic values.
Thus, the graphic representation of the pH formed a peak as the pH rose sharply when the di-n-butylamine first entered the cell, slightly decreased as the reactions proceeded, and then sharply decreased when the di-n- butylamine disappeared. The width of the peak representing the changing pH was then measured. A representative peak obtained from a sample is formed from the curve 30 in the graph presented in FIG. 3. In order to help identify where the peak begins and ends, a first derivative of the graph can be taken. FIG. 3 also presents the first derivative 31 of the peak formed by the curve 30. Accordingly, the peak width of the curve representing the changing pH 30 was indirectly obtained by measuring the time it took for the first derivative 31 to go from its maximum value to its minimum value. The first derivative 31 also shows that while it may be possible to directly titrate this particular species (given the minimum labelled 32), the endpoint for the back titration (the minimum labelled 33) is much sharper, and hence much more precise. This process was repeated for several samples, and then the measured peak widths were plotted against the equivalent weights obtained for each sample via the traditional ASTM method. The resulting plot yielded a curved line, due to the logarithmic relationship between peak width and concentration. Consequently, the peak widths were used to calculate the concentration of the component of interest in the sample according to the equation above.
Forthis system, concentration of the component of interest in the sample is equal to % NCO, and equivalent weight is equal to 4200/% NCO Substituting these changes into the general equation, yields:
Equivalentweight = 4200
The constants kι_3 were obtained using a conventional nonlinear least squares fit procedure. A second graph was created, plotting equivalent weight obtained using the above equation versus the equivalent weight obtained via the traditional ASTM method. This plot resulted in a straight line, with an extrapolated intercept at the origin. Thus, the method of the present invention is shown to be as effective as the current ASTM method for
determining equivalent weight of MDI derivatives, but the method of the invention is faster, safer and less expensive than the ASTM method.
It should be understood that in order to simplify the discussion of the present invention, acid-base systems were primarily described. Other systems such as those based on oxidation-reduction reactions are capable of being analyzed by the methods of the invention and are therefore intended to be within the scope of the invention.
It should be realized by one of ordinary skill in the art that the invention is not limited to the exact construction or method illustrated above, but that various changes and modifications may be made without departing from the spirit and scope of the invention as described within the following claims.
Next Patent: FERROELECTRIC THIN FILM TRAVELLING WAVE ROTATION SENSOR