Method and apparatus for measuring and controlling electrolytically-active species concentration in aqueous solutions
10254246 ยท 2019-04-09
Assignee
Inventors
- Thomas E. McNeel (Memphis, TN, US)
- Richard A. Clark (Memphis, TN, US)
- Richard D. Lusk, Jr. (Memphis, TN, US)
- Chamindu Liyanapatirana (Memphis, TN, US)
Cpc classification
International classification
Abstract
A method is provided for measuring an electrolytically-active species concentration in an aqueous or non-aqueous solution for use in providing control of the concentration of the species in a source solution thereof based on the measurements. In the method, a sample containing an electrolytically-active species is added into a measurement cell that has a working electrode and an auxiliary electrode, and a constant current is applied to the measurement cell while the working and auxiliary electrodes are in contact with the sample with monitoring of voltage difference across the electrodes until a change in the voltage difference is detected. A feedback signal is generated based on a parameter of the change in the voltage difference that is directly proportional to the amount of the electrolytically-active species in the sample, which can be used for process control. An apparatus is also described.
Claims
1. A method for measuring and controlling the concentration of an electrolytically-active species in an aqueous or non-aqueous solution, comprising: a) reacting at least one reactant that comprises a first reactant and a second reactant to produce a reaction mixture, wherein the reaction mixture comprises an electrolytically-active species in aqueous solution; b) introducing a sample of the reaction mixture comprising the electrolytically-active species into a measurement cell, wherein the measurement cell comprises a working electrode and an auxiliary electrode; c) applying a constant current to the measurement cell while the working electrode and auxiliary electrode are in contact with the sample with monitoring of voltage difference across the working electrode and auxiliary electrode until a change in the voltage difference is detected; d) generating a feedback signal based on a measured parameter of the change in the voltage difference, wherein the measured parameter of the change in the voltage difference is a measured duration of time of applying the constant current in step c) until the voltage difference is detected, and wherein the measured duration of time is directly proportional to the amount of the electrolytically-active species in the sample; and e) using the feedback signal of step d) to control the amount of the electrolytically-active species, or a precursor thereof, or a component thereof, or a reactant for producing the electrolytically-active species in the aqueous solution or non-aqueous solution, wherein the first reactant is an alkali metal hypochlorite, the second reactant is ammonia, and the electrolytically-active species is monochloramine, and wherein the measured parameter of the change in the voltage difference is a measured time interval beginning when the constant current is applied to the measurement cell and ending when the applied voltage has reached a level at which all of the monochloramine has been depleted and the voltage difference is detected.
2. The method of claim 1, wherein said using the feedback signal in e) comprises using the feedback signal to control a rate of feeding of the at least one reactant to a process unit wherein the reacting occurs.
3. The method claim 1, wherein the measurement cell has only the working electrode and the auxiliary electrode as electrodes of the measurement cell.
4. The method of claim 1, wherein the constant current is in the range of from about 10 milliampere (mA) to about 1 ampere (A).
5. The method of claim 1, wherein the working electrode and the auxiliary electrode independently comprise graphite, glassy carbon, or any combinations thereof.
6. The method of claim 1, wherein the selected amount of the sample is from about 1 mL to about 10 mL, wherein the measurement cell has a fixed cell volume which defines the selected amount of sample.
7. The method of claim 1, wherein the reacting of the at least one reactant comprises combining the first reactant and the second reactant to form the electrolytically-active species in situ in the aqueous solution; wherein the feedback signal is used to control a rate of feeding of at least one of the first reactant and the second reactant.
8. A method for measuring and/or controlling the concentration of an electrolytically-active species in an aqueous or non-aqueous solution treated with the electrolytically-active species, comprising: a) adding at least one electrolytically-active product comprising monochloramine to an aqueous solution to provide a treated aqueous or non-aqueous solution; b) introducing a sample of the treated aqueous solution or treated non-aqueous solution into a measurement cell, wherein the measurement cell comprises a working electrode and an auxiliary electrode; c) applying a constant current to the measurement cell while the working electrode and auxiliary electrode are in contact with the sample for electrolytic reduction of the monochloramine to chloride ion and ammonia with monitoring of voltage difference across the working electrode and auxiliary electrode until detecting of a change in the voltage difference at a measured duration of time of applying the constant current; d) generating a feedback signal using the measured duration of time of step c), wherein the measured duration of time is directly proportional to amount of the electrolytically-active product in the sample; and e) using the feedback signal of step d) to control the amount of the electrolytically-active product, or a precursor thereof, or a component thereof in the aqueous solution or non-aqueous solution.
9. The method of claim 8, wherein the aqueous solution that is treated is industrial process water, waste water, cooling water, boiler water, municipal water, food processing water, or pulp.
Description
BRIEF DESCRIPTION OF DRAWING
(1)
(2)
(3)
(4)
DETAILED DESCRIPTION OF THE PRESENT INVENTION
(5) The present invention relates in part to a method for rapid and accurate measurement of electrolytically-active species concentration in an aqueous solution for use in providing improved control of the concentration of the species in a source solution thereof. In the method, a sample containing an electrolytically-active species can be added in a selected amount into a measurement cell that has a working electrode and an auxiliary electrode, and a constant current is applied to the measurement cell while the working and auxiliary electrodes are in contact with the sample with monitoring of voltage difference across the electrodes until a detectable change in the voltage difference occurs. A feedback signal is generated based on a parameter of the change in the voltage difference that is directly proportional to the amount of the electrolytically-active species in the selected amount of the sample. The feedback signal can be used for process control. The measured parameter of the change in the voltage difference can be, for example, a measured duration of time of applying the constant current through the sample in the cell until the voltage difference is detected.
(6) An apparatus also is provided which can be used to perform the indicated method. The apparatus has the measurement cell and a measurement circuit that is interoperable therewith. The measurement cell can be configured as a two-electrode cell. For example, the two-electrode cell can have a working electrode, such as a cathode, and an auxiliary or counter electrode, such as an anode, without need of any additional electrodes for providing the cell functions described herein. When a constant current is applied to the measurement cell, the voltage drop across the working and auxiliary electrodes can be relatively small as long as readily-reducible species (or readily-oxidizable as applicable) species is present in the cell. When all of the electrolytically-active species in a sample has been reduced (or oxidized as applicable), the applied voltage must increase to maintain the constant current. The length of time that elapses between the initial application of the constant current until the increase in applied voltage occurs is directly proportional to the amount of oxidant (or reducing agent as applicable) in the cell. Specifically, the measurement circuit can detect the voltage difference change corresponding to a coulometric titration end-point for the sample in the cell, and can generate a feedback signal proportional to a parameter associated with the voltage difference change, such as the duration of time that elapses between initial application of the constant current until the increase in the applied voltage occurs. The measurement circuit is robust and configured to provide an adequate constant level of current to the cell. A differential voltage measurement made across a measurement cell of the indicated apparatus having only the working and auxiliary electrodes as electrodes can be sufficient to detect the point at which an electrolytically-active species, such as an oxidant, has been depleted and the water itself is broken down (forming hydrogen and oxygen) to maintain the constant current. A reference electrode is not required to make these measurements, and thus a three-electrode configuration of the cell is not required in an apparatus of the present invention.
(7) Many oxidant products, the reactants used to make them, or both, can have a very short life span (and/or are not stable) with regard to potency/efficacy. For instance, in water treatment (or other treatments of aqueous solutions) with biocides, for example, it can be important to be able to constantly monitor the oxidant concentration in treated solutions to maintain proper potency thereof. The systems of the present invention can be used, for example, to constantly monitor the total concentration of oxidant in a solution that is being treated or has been treated with an oxidant. The oxidant can be generated in-situ in the treated solution or prepared in advance before addition to the solution. Using the systems of the present invention, analysis results can be obtained in a relatively short period of time based on samples drawn from a source solution of interest, such as a treated water, and used to rapidly generate feedback signals for process control based on the analysis results.
(8) The coulometric measurement system of the present invention can have many advantages, including the capability to rapidly and accurately measure the concentration of an electrolytically-active species in an aqueous solution based on relatively small samples drawn or diverted from a source fluid. The feedback signal generation capabilities of the method of the present invention can be used to improve process control, such as in reaction chemistries related to oxidants in the reaction products, in the reactants, or both. The coulometric measurement method of the present invention further offers several advantages over the indicated alternative techniques for quantitative analysis of electrolytically-active species. For example, the measurement procedure of the present method does not require any additions of analysis chemicals, such as the titrants or color-development reagents required by some existing analytical methods. Routine maintenance and chemical costs associated with the analyses can be significantly reduced or avoided. Also, the multiple levels of serial dilution typically required by colorimetric methods are not necessary in the present invention. In this manner, dilution errors can be eliminated. In addition, an apparatus of the present invention can be assembled with components at lower cost than the unit costs of existing commercially-available on-line titration or colorimetric analytical devices. Further, with fewer moving parts than normally encountered with on-line titration or colorimetric equipment, the coulometric cell used in the present invention can have fewer failure modes, and consequently can be more reliable.
(9) The systems of the present invention can have wide applications. They can be used anywhere that detection and process control are needed or desired with respect to reactants or treatment compounds used in aqueous solutions or non-aqueous solutions. The systems can be used, for example, in industrial water treatment (e.g., cooling water, boiler water, influent/effluent treatment, process water treatment (e.g., pulp, paper), disinfection of potable water, disinfection for food-processing applications (e.g., food sterilizing baths, food washing/rinsing baths, food chiller baths, food heating baths, or other aqueous systems which can be used in food processing), waste water treatment, municipal water treatment, and any other system or process in which bleach, chlorine, bromine, or other oxidizing agents are used or wherein reducing agents are used. The electrolytically-active species that are oxidants, for example, may be used as biocides and/or for other purposes in these various aqueous systems. It will be appreciated that some electrolytically-active compounds can be an oxidizing agent in some reaction chemistries and a reducing agent in other reaction chemistries.
(10) Referring to
(11) Referring to
(12) Referring to
(13) The measurement circuit, such as illustrated in
(14) An electrolytically-reducible species that can be analyzed by the system of the present invention is not necessarily limited. The electrolytically-reducible species can be, for example, halo-containing oxidant, a peroxide, or a peroxide source. The halo-containing oxidants can be, for example, a haloamine such as monochloramine (NH.sub.2Cl), dichloramine (NHCl.sub.2), trichloramine (NCl.sub.3), monobromamine (NH.sub.2Br), dibromamine (NHBr.sub.2), tribromamine (NBr.sub.3), monoiodamine (NH.sub.2I), diiodamine (NHI.sub.2), triiodamine (NI.sub.3), monofluoramine (NH.sub.2F), difluoramine (NHF.sub.2), trifluoramine (NF.sub.3), or any combinations thereof; an N-halamine sulfonamide such as chloramine T (sodium-N-chloro-p-toluenesulfonamide), dichloramine-T (N,N-dichloro-p-toluenesulfonamide), or any combinations thereof; an alkali hypohalite such as sodium hypochlorite (NaOCl), potassium hypochlorite (KOCl), lithium hypochlorite (LiOCl), sodium hypobromite (NaOBr), potassium hypobromite (KOBr), lithium hypobromite (LiOBr), sodium hypoiodite (NaOI), potassium hypoiodite (KOI), lithium hypoiodite (LiOI), sodium hypofluorite (NaOF), potassium hypofluorite (KOF), lithium hypofluorite (LiOF), or any combinations thereof; an alkaline earth hypohalite such as calcium hypochlorite (Ca(ClO).sub.2), calcium hypobromite (Ca(BrO).sub.2), calcium hypoiodite (Ca(IO).sub.2), calcium hypofluorite (Ca(FO).sub.2), magnesium hypochlorite (Mg(ClO).sub.2), magnesium hypobromite (Mg(BrO).sub.2), magnesium hypoiodite (Mg(IO).sub.2), magnesium hypofluorite (Mg(FO).sub.2), or any combinations thereof; a hypohalous acid such as hypochlorous acid (HOCl), hypobromous acid (HOBr), hypoiodous acid (HOI), hypofluorous acid (HOF), or any combinations thereof; chlorine dioxide (ClO.sub.2); a diatomic halogen such as chlorine (Cl.sub.2), bromine (Br.sub.2), iodine (I.sub.2), fluorine (F.sub.2), or any combinations thereof. The peroxide and peroxide sources, which jointly can be referred to herein as a peroxy compound, can be, for example, hydrogen peroxide, peroxide salt, perborate, percarbonate, persulfate, peroxyurea compound, persilic acid, percarboxylic acid, peracetic acid, or hydrogen peroxide adduct of urea, pyrophosphate, phosphate, citrate, sodium sulfate, or sodium silicate, or any combinations thereof. Specific examples of peroxy compounds include, but are not limited to, alkali peroxide, alkaline earth peroxide, alkali perborate salt, alkaline earth perborate salt, alkali percarbonate salt, alkaline earth percarbonate salt, alkali persulfate salt, alkaline earth persulfate, peroxyurea compound, persilic acid, percarboxylic acid salt, peracetic acid salt, hydrogen peroxide adduct of urea, pyrophosphate, phosphate, citrate, sulfate, or sodium silicate, or any combinations thereof. Additional examples include without limitation percarbonates like sodium percarbonate, perborates like sodium perborate, peroxides like sodium, magnesium or calcium peroxide, hydrogen peroxide adducts of urea such as urea hydrogen peroxide (carbamide peroxide), and hydrogen peroxide adducts of pyrophosphates and phosphates like sodium phosphate perhydrate.
(15) As non-limiting illustrations, the systems of the present invention can be used to generate a signal that is directly proportional to an assay of bleach (sodium hypochlorite) that can be used (a) as a source of chlorine in industrial processes, or (b) for the on-site generation of other oxidizing biocides, such as sodium hypobromite or monochloramine. The system can also be used to assay these oxidizing biocides as they are generated. In a specific non-limiting example of an application, the system can be used to provide an assay of the monochloramine solution produced by a system that combines bleach with an ammonia solution. This reaction can proceed by the following general equation:
NaOCl+NH.sub.3.fwdarw.NH.sub.2Cl+NaOH.
(16) The feedback signal for this reaction can monitored by an intelligent digital process controller, which can adjust the bleach feed rate so that the level of monochloramine in the output of the system can be maximized. A coulometric measurement procedure can be used, for example, in which the reaction product (NH.sub.2Cl), which is an oxidant, is reduced electrolytically in the measurement system of the present invention, and the cathodic current is integrated to generate a value that is directly proportional to the amount of monochloramine in the solution. If the electrolysis is carried out using a constant current of C amperes, then:
NH.sub.2Cl+H.sup.++2e.sup..fwdarw.NH.sub.3+Cl.sup.
and the amount of chloramine in an analyzed sample can be calculated by the following equation:
(17)
wherein C=constant cathodic current in amperes. As indicated, as the analysis is performed on a fixed and known volume of sample, then a determination of the mass amount of monochloramine in the sample also permits the concentration of the monochloramine in the sample to be calculated.
(18) The total oxidant concentration of monochloramine product in the reaction mixtures can be very dependent upon the molar ratio of bleach and ammonia used to prepare the mixture. Referring to
(19) Likewise, a solution of sodium hypochlorite (bleach) can be directly analyzed in a similar manner, wherein:
NaOCl+2H.sup.++2e.sup..fwdarw.NaCl+H.sub.2O
and the amount of bleach in an analyzed sample can be calculated by the following equation:
(20)
wherein C=constant cathodic current in amperes.
(21) The cell currents and analysis times can be determined by the volume of solution in the cell as well as the concentration of oxidant in the solution. There can be several practical considerations in the design of the equipment. The applied current used in methods of the present invention can be, for example, in the range of from about 10 mA to about 1 ampere range, or from about 25 mA to about 750 mA, or from about 50 mA to about 500 mA, or from about 100 mA to about 250 mA, or other ranges. High current levels can generate heat in the cell contents, even to levels high enough to damage the cell. The smaller the volume of solution analyzed, the lower the current required for the analysis. However, some solutions for analysis may contain suspended solids, which could clog very small diameter tubing or very thin flow cells if used in the measurement cell or related flow lines. Hence, there are tradeoffs that can be taken into account in the design of a practical device. An example of a sample analysis system design for the indicated reaction system for producing monochloramine with bleach and ammonia reactants is a design which has a test duration of about 100 seconds for a 1% solution of monochloramine. If the cell volume is 6 mL (which can be, for example, approximately 15 cm of ID tubing with a coaxial graphite electrode), a cell current of 100 mA can require about 37 minutes to electrolyze all of the monochloramine in the cell, while a cell current of one ampere can only take about 3.7 minutes. A smaller cell volume thus can reduce analysis times and be more convenient.
(22) The present invention thus relates in part to a robust, low-maintenance, low-cost apparatus for the determination of total electrolytically-active species levels in aqueous solutions and to use an output signal from this apparatus to control the feed of water treatment chemicals to industrial, municipal, and commercial water systems, or other systems.
(23) The present invention includes the following aspects/embodiments/features in any order and/or in any combination:
(24) 1. The present invention relates to a method for measuring and controlling the concentration of an electrolytically-active species in an aqueous or non-aqueous solution, comprising:
(25) a) introducing a sample comprising an electrolytically-active species (e.g., in a selected amount) into a measurement cell, wherein the measurement cell comprises a working electrode and an auxiliary electrode;
(26) b) applying a constant current to the measurement cell while the working electrode and auxiliary electrode are in contact with the sample with monitoring of voltage difference across the working electrode and auxiliary electrode until a change in the voltage difference is detected; and
c) generating a feedback signal based on a measured parameter of the change in the voltage difference, wherein the measured parameter of the change in the voltage difference is directly proportional to the amount of the electrolytically-active species in the sample.
2. The method of any preceding or following embodiment/feature/aspect, further comprising reacting at least one reactant before step a) to produce a reaction mixture from which the sample is derived.
3. The method of any preceding or following embodiment/feature/aspect, wherein the reaction mixture comprising an electrolytically-active reaction product in aqueous or non-aqueous solution.
4. The method of any preceding or following embodiment/feature/aspect, wherein the measured parameter of the change in the voltage difference is a measured duration of time of applying the constant current in step b) until the voltage difference is detected.
5. The method of any preceding or following embodiment/feature/aspect, wherein the generating of the feedback signal comprises generating a feedback signal using the measured duration of time, wherein the measured duration of time is directly proportional to an amount of the electrolytically-active reaction product in the sample.
6. The method of any preceding or following embodiment/feature/aspect, further comprising using the feedback signal to control a rate of feeding of at least one reactant to a process unit wherein the reacting occurs.
7. The method of any preceding or following embodiment/feature/aspect, wherein the generation of the feedback signal comprises generating a feedback signal using the measured duration of time, wherein the measured duration of time is directly proportional to an amount of a reactant in the sample.
8. The method of any preceding or following embodiment/feature/aspect, wherein the electrolytically-active species is an oxidizing agent, and the method further comprises combining the oxidizing agent and a second reactant to produce a reaction mixture comprising at least one reaction product in aqueous solution or non-aqueous solution.
9. The present invention relates to a method for measuring and controlling the concentration of an electrolytically-active species in an aqueous solution or non-aqueous solution, comprising:
a) combining at least a first reactant and a second reactant to produce a reaction mixture comprising an electrolytically-active reaction product in solution;
b) introducing a sample of the reaction mixture (e.g., in a selected amount) into a measurement cell, wherein the measurement cell comprises a working electrode and an auxiliary electrode;
c) applying a constant current to the measurement cell while the working electrode and auxiliary electrode are in contact with the sample with monitoring of voltage difference across the working electrode and auxiliary electrode until detecting of a change in the voltage difference at a measured duration of time of applying the constant current;
d) generating a feedback signal using the measured duration of time of step c), wherein the measured duration of time is directly proportional to an amount of the electrolytically-active reaction product in the sample; and
e) optionally, using the feedback signal of step d) to control a rate of feeding of the first reactant and/or the second reactant in step a).
10. The method of any preceding or following embodiment/feature/aspect, wherein the electrolytically-active reaction product is an oxidant.
11. The method of any preceding or following embodiment/feature/aspect, wherein the electrolytically-active reaction product is a halo-containing oxidant, a peroxide, or a peroxide source.
12. The method of any preceding or following embodiment/feature/aspect, wherein the first reactant is an oxidizing agent in solution.
13. The method of any preceding or following embodiment/feature/aspect, wherein the first reactant is an alkali metal hypochlorite, the second reactant is ammonia, and the electrolytically-active reaction product is chloramine.
14. The method of any preceding or following embodiment/feature/aspect, wherein the constant current has a value in the range of from about 10 milliampere (mA) to about 1 ampere (A).
15. The method of any preceding or following embodiment/feature/aspect, wherein the working electrode and the auxiliary electrode independently comprise graphite, glassy carbon, or any combinations thereof.
16. The method of any preceding or following embodiment/feature/aspect, wherein the selected amount of the sample is from about 1 mL to about 10 mL, wherein the measurement cell has a fixed cell volume which defines the selected amount of sample.
17. The method of any preceding or following embodiment/feature/aspect, further comprising:
i) introducing a second sample composed of the first reactant into the measurement cell;
ii) applying a second constant current to the measurement cell while the working and auxiliary electrodes are in contact with the second sample with monitoring of voltage difference across the working and auxiliary electrodes until detecting of a change in the voltage difference at a measured duration of time of applying the second constant current;
iii) generating a feedback signal using the measured duration of time of step ii), wherein the measured duration of time is directly proportional to amount of the oxidizing agent in the second sample; and
iv) using the feedback signal of step iii) to control a rate of feeding of the first reactant in step a).
18. The present invention relates to a method for measuring and/or controlling the concentration of an electrolytically-active species in an aqueous or non-aqueous solution treated (e.g., to be treated, and/or currently being treated, and/or after being treated) with the electrolytically-active species, comprising:
a) treating the aqueous or non-aqueous solution with at least one electrolytically-active product (for instance, but not limited to, combining at least a first reactant and a second reactant to produce an electrolytically-active reaction product which is formed in situ or before introduction in an aqueous or non-aqueous solution to provide a treated aqueous or non-aqueous solution);
b) introducing a sample of the treated aqueous solution in a selected amount into a measurement cell, wherein the measurement cell comprises a working electrode and an auxiliary electrode;
c) applying a constant current to the measurement cell while the working electrode and auxiliary electrode are in contact with the sample with monitoring of voltage difference across the working electrode and auxiliary electrode until detecting of a change in the voltage difference at a measured duration of time of applying the constant current;
d) generating a feedback signal using the measured duration of time of step c), wherein the measured duration of time is directly proportional to amount of the electrolytically-active product in the sample; and
e) optionally, using the feedback signal of step d) to control a rate of feeding of the electrolytically-active product or a component thereof, or a precursor thereof (such as, but not limited to, the first reactant and/or the second reactant) in step a).
19. The method of any preceding or following embodiment/feature/aspect, wherein the aqueous solution that is treated is industrial process water, waste water, cooling water, boiler water, municipal water, food processing water, or pulp.
20. The present invention also relates to an apparatus for measuring and controlling the concentration of an electrolytically-active species in an aqueous solution, comprising:
a) a measurement cell comprising a working electrode, an auxiliary electrode, and structure defining a cell volume for receiving a sample comprising an electrolytically-active species in an aqueous or non-aqueous solution;
b) a measurement circuit connected to the working electrode and the auxiliary electrode, wherein the measuring circuit is operable to i) provide a constant current to the measurement cell, ii) monitor and detect a change in voltage difference across the working electrode and auxiliary electrode, and iii) generate a feedback signal based on a measured parameter of the change in the voltage difference, wherein the measured parameter of the change in the voltage difference is directly proportional to the amount of the electrolytically-active species in the sample.
21. The apparatus of any preceding or following embodiment/feature/aspect, wherein the digital processing unit comprises a clock operable for measuring the parameter as a duration of time of applying the constant current until a change in the voltage difference is detected.
22. The apparatus of any preceding or following embodiment/feature/aspect, wherein the working electrode and the auxiliary electrode independently comprise graphite, glassy carbon, or any combinations thereof.
23. The apparatus and/or method of any preceding or following embodiment/feature/aspect, wherein instead of an aqueous solution, a non-aqueous solution is present and/or used.
(27) The present invention can include any combination of these various features or embodiments above and/or below as set forth in sentences and/or paragraphs. Any combination of disclosed features herein is considered part of the present invention and no limitation is intended with respect to combinable features.
(28) For purposes of the present invention, it is to be understood that every aspect of the present invention can apply to non-aqueous solutions that have conductivity for purposes of being detected in the methods and apparatus of the present invention.
(29) Applicants specifically incorporate the entire contents of all cited references in this disclosure. Further, when an amount, concentration, or other value or parameter is given as either a range, preferred range, or a list of upper preferable values and lower preferable values, this is to be understood as specifically disclosing all ranges formed from any pair of any upper range limit or preferred value and any lower range limit or preferred value, regardless of whether ranges are separately disclosed. Where a range of numerical values is recited herein, unless otherwise stated, the range is intended to include the endpoints thereof, and all integers and fractions within the range. It is not intended that the scope of the invention be limited to the specific values recited when defining a range.
(30) Other embodiments of the present invention will be apparent to those skilled in the art from consideration of the present specification and practice of the present invention disclosed herein. It is intended that the present specification and examples be considered as exemplary only with a true scope and spirit of the invention being indicated by the following claims and equivalents thereof.