Abstract:
Methods of analyzing analytes from a liquid medium are disclosed. A system and apparatus for the analysis of analytes from a liquid medium are further disclosed. In particular, methods and apparatus of analyzing analytes by freezing liquid medium and partitioning the analyte into a sorptive stirrer are disclosed. Further, the methods and apparatus of the present invention can be useful in concentrating and isolating target chemicals of high value.

Description:
FIELD OF THE INVENTION 
       [0001]    The invention relates to selective trace and ultratrace analysis of analytes. In particular, this analysis is achieved by simultaneously freeze concentrating and extracting the analyte into a sorptive or by a sorptive material. Further, the methods and apparatus of the present invention can be useful in conducting ultratrace analysis for toxic chemicals that may be present in drinking water. Further, the methods and apparatus of the present invention can be useful in concentrating and isolating target chemicals of high value. 
       BACKGROUND OF THE INVENTION 
       [0002]    Analytical chemistry is concerned with both identification and quantification of chemicals. Trace and ultratrace analysis is focused on miniscule quantities. Trace and ultratrace analysis can be important in many areas of analytical chemistry. For example, it can be useful in forensic analysis, quality control, and the analysis of toxins. Sample preparation, including preconcentration, is a key step for almost all analyses. Sample preparation and preconcentration, along with highly sophisticated instrumentation becomes increasingly important when trace and ultratrace detection of analytes is necessary. In addition to more historic sample preparation techniques such as liquid-liquid extraction and simple solvent evaporation, multiple techniques have been introduced over the past several decades to aid analysts in determined low concentrations of analytes such as solid-phase extraction (SPE), solid-phase microextraction (SPME), and stir bar sorptive extraction (SBSE). While the compatibility of each analyte with these techniques must be individually evaluated, these sample preparation techniques have generally produced decreased limits of detection, decreased analysis times, and decreased organic solvent use. Although current sample preparation techniques are excellent for analysis in the parts-per-billion (ppb; μg/L) and high parts-per-trillion (ppt; ng/L) range, ultratrace analysis is still very difficult for analytical chemists to achieve without arduous sample preparation and/or extremely sophisticated and expensive instrumentation. In some cases, even with the most sensitive instruments, analysis of a compound of interest at a desired concentration may still not be possible without concentrating large sample volumes (e.g., greater than 500 mL). Therefore a technique with the ability to more easily determine ultratrace concentrations of interest could be a foundational technique in the field of analytical sample preparation. Furthermore, such a technique would allow more applicable standards to be set of toxic compounds of interest and help ensure human health, to include safe drinking water standards. 
         [0003]    The ability to analyze contaminants at ultratrace concentrations is a critically important, but currently challenging, aspect of ensuring safe drinking water. The EPA Maximum Contaminant Level Goal (MCLG) is zero for several compounds, but the enforceable contaminant level, called the Maximum Contaminant Level (MCL), is set, in part, according to the ability of laboratories to measure accurately and consistently the level of the contaminant with available analytical methods. This typically limits MCLs to the parts-per-billion or microgram per liter range. The ability to more easily analyze compounds at extremely low concentrations would be a tremendous achievement in the analytical chemistry field and would have a broad impact, including, for example, in assisting with the provision of safe drinking water. The present invention allows analysis of select compounds in liquid solution at much lower limits-of-detection (LODs) than currently available. In the absence of the present invention, performing trace and ultratrace analysis of certain classes of solutes in drinking water samples, and ultimately ensuring safe drinking water, will remain difficult and force undesirable analytical alternatives (e.g., expensive instrumentation and/or concentrating large sample volumes). 
         [0004]    In the past several decades, multiple sample preparation techniques have been introduced to extend the reach of analytical methods into the low parts-per-billion, parts-per-trillion, and even parts-per-quadrillion range by purifying and pre-concentrating target analytes and using sophisticated instrumentation. Sample preparation techniques such as SPE, SPME, and SBSE can extend the concentration range for analysis to ultratrace levels. Although these sample preparation techniques may work well for certain analytes, each has disadvantages, such as limited preconcentration factors among others. For example, SBSE has limitations on the type of analytes for which the procedure can be used due to the limited number of sorbent phases available. Further, SPE typically has a need for a drying step prior to analysis. 
         [0005]    Further, although freeze concentration (FC) has received little attention the field of analytical chemistry, it has been used for decades to concentrate solutes from solutions and has found common application in the food industry for creating frozen concentrates of fruit juices and ice beer. As the name implies, FC is a technique for concentrating solutes by freezing a solution. Solutes are concentrated based on the direct relationship between freezing point depression and solute molality. If a solution is slowly frozen, local regions of solvent with a low solute concentration are frozen first and the solution left behind is more concentrated. Although higher solute concentrations decrease the freezing point of a solution, the rate of freezing is generally too fast to freeze out pure solvent when high solute concentrations are present. Therefore, the solution is typically stirred vigorously during FC to counteract incorporation of the solute into the frozen solvent. However, FC is indiscriminant as to the solutes that are concentrated. 
         [0006]    Accordingly, it is an objective of the claimed invention to develop a method and apparatus of selective preconcentration and isolation which can discriminate particular compounds. The method and apparatus may be used to facilitate trace and ultratrace analysis or isolation of high value compounds. 
         [0007]    A further object of the invention is to allow the trace and ultratrace analysis of toxic chemicals which currently cannot be easily analyzed at the desired concentrations (e.g., maximum contaminant levels; MCLs). 
       BRIEF SUMMARY OF THE INVENTION 
       [0008]    The invention provides apparatuses and methods for performing trace and ultratrace analysis by simultaneously freeze concentrating and extracting the analyte into or by a sorptive material. The analyte can be extracted from the sorptive material, identified by qualitative analysis, and/or quantified by quantitative analysis. In a preferred embodiment, the apparatuses and methods of the invention can be applied to the monitoring of drinking water. 
         [0009]    An advantage of the invention is that it provides apparatuses and methods that can be applied to very low concentrations of analyte in a liquid medium. 
         [0010]    While multiple embodiments are disclosed, still other embodiments of the present invention will become apparent to those skilled in the art from the following detailed description, which shows and describes illustrative embodiments of the invention. Accordingly, the drawings and detailed description are to be regarded as illustrative in nature and not restrictive. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]      FIG. 1  illustrates an apparatus of the present invention including a u-shaped bracket. 
           [0012]      FIG. 2  illustrates an apparatus of the present invention including a magnetic stir plate. 
           [0013]      FIG. 3  illustrates the method and the different stages of concentration as they occur during the course of the method. 
           [0014]      FIG. 4A  shows that there are three material phases with which the analyte while associated in the present invention: liquid, solid, and stir bar.  FIG. 4B  shows the concentration profile of the analyte near the ice-liquid interface. 
           [0015]      FIG. 5A  illustrates the behavior of an analyte (i.e., the fraction of analyte extracted into the stir bar) as the analyte undergoes the methods of the present invention.  FIG. 5B  indicates the fraction extracted into the stir bar as the K SB  of the analyte increases.  FIG. 5C  shows that the present invention is advantageous for analysis over SBSE. 
           [0016]      FIGS. 6A-C  are photographs showing the concentration of the methyl violet at various points during Example 1. 
           [0017]      FIG. 7  indicates the results of the analysis based on peak area that the signs of both chemicals where enhanced by using the methods of the present invention. 
           [0018]      FIG. 8  shows the comparative peaks for SBSE and the present invention. 
           [0019]      FIG. 9  indicates the concentration factors as a function of temperature for benzaldehyde. 
           [0020]      FIG. 10  indicates that concentration factors decreased with the increase of stir speed. 
           [0021]      FIG. 11  illustrates the relationship between concentration and concentration factor. 
           [0022]      FIG. 12  indicates there is little to no correlation between the concentration factor and the solution concentration. 
           [0023]      FIG. 13A  indicates the level of detection for benzaldehyde using the present invention while  FIG. 13B  indicates the level of detection for benzaldehyde using SBSE. 
           [0024]      FIG. 14  illustrates the lower limit of qualification for SBSE. 
           [0025]      FIG. 15A  indicates the concentration factor at the lower limit of qualification for the present invention and SBSE.  FIG. 15B  shows that the lower limit of qualification of benzaldehyde for the present invention as compared to that of SBSE. 
           [0026]      FIG. 16  illustrates the analysis of benzyl alcohol using the present invention as compared to SBSE. 
           [0027]      FIG. 17A  shows the limit of detection of benzyl alcohol using the present invention while  FIG. 17B  shows the limit of detection of benzyl alcohol using SBSE. 
       
    
    
       [0028]    Various embodiments of the present invention will be described in detail with reference to the drawings, wherein like reference numerals represent like parts throughout the several views. Reference to various embodiments does not limit the scope of the invention. Figures represented herein are not limitations to the various embodiments according to the invention and are presented for exemplary illustration of the invention. 
       DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0029]    The present invention relates selective concentration of solutes for trace and ultratrace analysis. The methods and apparatus of the present invention have many advantages over existing trace and ultratrace analyses. For example, the present invention increases the concentration factor (i.e., the ratio of the concentration of analyte in the prepared sample to that in the original solution) of selected solutes over existing sample preparation methods. 
         [0030]    The embodiments of this invention are not limited to particular apparatuses for performing the methods of invention, which can vary and are understood by skilled artisans. It is further to be understood that all terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting in any manner or scope. For example, as used in this specification and the appended claims, the singular forms “a,” “an” and “the” can include plural referents unless the content clearly indicates otherwise. Further, all units, prefixes, and symbols may be denoted in its SI accepted form. Numeric ranges recited within the specification are inclusive of the numbers defining the range and include each integer within the defined range (e.g., 1 to 5 includes 1, 1.5, 2, 2.75, 3, 3.80, 4, and 5). 
         [0031]    So that the present invention may be more readily understood, certain terms are first defined. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which embodiments of the invention pertain. Many methods and materials similar, modified, or equivalent to those described herein can be used in the practice of the embodiments of the present invention without undue experimentation, the preferred materials and methods are described herein. In describing and claiming the embodiments of the present invention, the following terminology will be used in accordance with the definitions set out below. 
         [0032]    The term “analyte,” as used herein, is a substance whose chemical constitutes are being identified and measured. “Solute,” as used herein, is the minor component in a solution, dissolved in the solvent. Further, analyte may be used interchangeably with solute. 
         [0033]    The term “ICELES” as used herein, is an abbreviation for “ice concentration extraction linked with extractive stirring,” which can be used to describe an exemplary method of the invention. 
         [0034]    The term “K solid ,” as used herein, refers to the effective partitioning constant between the solid and the liquid phase. Additionally, log K solid  is defined as the log value of K solid . 
         [0035]    The term “K ow ,” as used herein, refers to the octanol-water partition coefficient, or the ratio of the solubility of a compound in octanol to its solubility in water. The higher the K ow , the more non-polar the compound. Additionally, log K ow  is defined as the log value of K ow . 
         [0036]    The term “K SB ,” as used herein, refers to the effective partitioning coefficient between the stir bar and the liquid phase. Additionally, log K sb  is defined as the log value of K sb . 
         [0037]    The term “limit of blank” or “LOB,” as used herein is highest apparent analyte concentration expected to be found when replicates of a blank sample containing no analyte are tested. 
         [0038]    The term “limit of detection” of “LOD,” as used herein is the lowest analyte concentration likely to be reliably distinguished from the LOB and at which detection is feasible. 
         [0039]    The term “lower limit of quantification” or “LLOQ,” as used herein, is the lowest concentration at which the analyte can not only be reliably detected but at which some predefined goals for bias and imprecision are met. 
         [0040]    The term “parts-per-billion” or “ppb,” as used herein is one part per 1,000,000,000 parts and corresponds to 1 μg/L with a density of water of 1.0 g/mL. Similarly, “parts-per-trillion”or “ppt,” as used herein in one part per 1,000,000,000,000 and corresponds to 1 ng/L with a density of water of 1.0 g/mL. 
         [0041]    The term “weight percent,” “wt-%,” “percent by weight,” “% by weight,” and variations thereof, as used herein, refer to the concentration of a substance as the weight of that substance divided by the total weight of the composition and multiplied by 100. It is understood that, as used here, “percent,” “%,” and the like are intended to be synonymous with “weight percent,” “wt-%,” etc. 
         [0042]    The methods, systems, apparatuses, and compositions of the present invention may comprise, consist essentially of, or consist of the components and ingredients of the present invention as well as other ingredients described herein. As used herein, “consisting essentially of” means that the methods, systems, apparatuses and compositions may include additional steps, components or ingredients, but only if the additional steps, components or ingredients do not materially alter the basic and novel characteristics of the claimed methods, systems, apparatuses, and compositions. 
         [0043]    It should also be noted that, as used in this specification and the appended claims, the term “configured” describes a system, apparatus, or other structure that is constructed or configured to perform a particular task or adopt a particular configuration. The term “configured” can be used interchangeably with other similar phrases such as arranged and configured, constructed and arranged, adapted and configured, adapted, constructed, manufactured and arranged, and the like. 
         [0044]    Apparatuses 
         [0045]    Embodiments of the invention include methods and apparatuses for selective trace and ultratrace analysis. The methods and apparatuses according to the invention are capable of concentrating analytes from a sample for analysis at trace and ultratrace levels. The invention overcomes the shortfalls of conventional trace and ultratrace analysis techniques by reducing the sample volume while permitting trace and ultratrace analysis. Additionally, the invention is capable of targeting desired analytes. 
         [0046]    The apparatuses for performing trace and ultratrace analysis can include a vial or other suitable container, sorptive stirrer, and cooling source. In some aspects the apparatus further includes a magnet. In some aspects the apparatus further consists of a stir plate. In some aspects the apparatus may include an overhead stirrer. In some aspects, the apparatus may optionally include at least one measurement device. In some aspects the apparatus may optionally include a control system. 
         [0047]    The apparatus includes a container in which the sample to be analyzed is placed. Any suitable container for holding the sample that will permit the rotation of a sorptive stirrer can be used including, for example, but not limited to, a beaker, flask, test tube, or vial. The container can be supported on its own or by any suitable support, including, for example a test tube or vial holder, a clamp, a bracket, or an arm. 
         [0048]    The apparatuses and methods of the invention employ a sorptive stirrer comprising a sorptive material. The analyte can be absorbed into or adsorbed by the sorptive material. The sorptive material can be a coating, a jacket, or a layer on a stirrer. In some embodiments the sorptive stirrer can have a layer, jacket, or coating that is chemically-inert, or sufficiently inert so as not to impact the analyte&#39;s adsorption by or absorption into the sorptive material. A preferred chemically-inert coating, layer, or jacket is glass. Other suitable chemically-inert coating, layers, or jackets can be used. 
         [0049]    In some embodiments of the invention, the sorptive stirrer is a magnetic stir bar with a sorptive jacket or sorptive layer is contained within the vial. In some embodiments the sorptive stirrer is an overhead stirrer with sorptive jacket or sorptive layer can be used. Preferably, the magnetic stir bar with sorptive jacket/layer is a magnetic bar contained within a sealed glass container which is fitted or coated with a sorptive layer. Preferably, an overhead stirrer with sorptive jacket/layer is an overhead stirrer with a stir rod that can be inserted into the sample container which is coated or fitted with sorptive material such that the sorptive material is immersed in the sample within the container. 
         [0050]    The sorptive material can be selected to target specific analytes. In an embodiment of the invention, the sorptive material can include, but is not limited to, polydimethylsiloxane, polydimethylsiloxane/ethylene glycol copolymer, molecularly imprinted polymers, ion exchange material, or other common sorbent phases. In a preferred embodiment, the sorptive layer is polydimethylsiloxane. 
         [0051]    The apparatus also includes one or more magnets for stirring the stir bar. A magnet can be part of a stir plate, U-shaped bracket having magnets in each arm, or donut-shaped ring having magnets housed in the ring on opposite sides. Further, a magnetic field may be generated by electric current through an appropriate electric circuit. In embodiments using a U-shaped bracket, the vial and optionally the cooling source can be between the bracket arms and as the bracket rotates it causes the stir bar to spin. In embodiments using a donut-shaped ring, the vial is housed in the hole in the ring and as the ring is rotated, it causes the stir bar to spin. In embodiments with electric current generated magnetic fields, the vial is housed such that the magnetic fields rotate the stir bar within the container. 
         [0052]    The apparatus can include a cooling source in order to freeze the sample. A cold bath is preferred cooling source. However, any suitable cooling source can be used to freeze the sample, including for example use of a jacketed beaker (i.e. a double-walled beaker with inlet and outlet to allow coolant flow), coolant, cooled air system, thermoelectric device, helium, or nitrogen system. 
         [0053]    In some embodiments of the invention, the container is held by a holder that is connected to a stepper motor that lowers the container within the holder into the cooling source, such as a cold bath. The stepper motor is directed by a control system to maintain a given rate of descent of the container into the cooling source. 
         [0054]    In some embodiments of the invention, the apparatus may include at least one measurement device or a plurality of measurement devices. Such measurement devices are those suitable to measure one or more variables of the system such as temperature, speed, pH, and combinations thereof. Such a measurement device can measure the cooling source, the container, magnetic field (e.g., strength and/or position), spectroscopic behavior of the analyte, the sorptive stirrer, etc. For example, in an embodiment of the invention, temperature is monitored at various points in the apparatus to ensure consistent freezing of the sample. In further aspects of the invention, the apparatus comprises an optional controller or software platform. The software platform provides a user or system to select speed and temperature of freezing as well as speed of stirring. As a result, use of the apparatus provides significant use flexibility to concentrate a variety of analytes for particular user-identified purposes. For example, the controller or control software for operation of the apparatus may permit a user or system to select both the temperature of the system and the speed of stirring. In a further aspect, the control software may determine the timing of the lowering of the vial and the overall concentration process. In a still further aspect of the invention, the control system includes the above described measurement devices. 
         [0055]    In some embodiments of the invention, the entire apparatus or select components of the apparatus may be contained in a cooled container to control the temperature of the apparatus and sample. 
         [0056]    According to an embodiment of the invention shown in the exemplary and non-limiting  FIG. 1 , the sample container  1  containing the sample and the sorptive stirrer  3 , is lowered into a cooling source  5  which is surrounded by a magnet  7 . Further the sample container is held by a sample holder  9  which can be lowered incrementally by a motor  11 . 
         [0057]    According to an embodiment of the invention shown in the exemplary and non-limiting  FIG. 2 , the sample container  1  containing the sample and the sorptive stirrer  3 , is lowered into a cooling source  5 ,  5 ′, which is located on top of a magnetic stir plate  7 . 
         [0058]    Methods 
         [0059]    The methods according to the present invention for conducting trace and ultratrace analysis of an analyte or concentrating a solute in a solvent can include providing an analyte for analysis, stirring the analyte and simultaneously cooling the analyte. The simultaneous cooling and stirring of the composition allows the solvent to freeze and solutes to become concentrated. According to the present invention, the analyte contained in a liquid medium is placed in the container along with the sorptive stirrer compatible with the analyte(s) of interest. Sorptive stirrer comprises a sorptive material. The analyte can be absorbed into or adsorbed by the sorptive material. In some embodiments, a step can be added to coat the stirrer with the sorptive material. 
         [0060]    As the container is lowered into the cooling source, or alternatively as the solvent reaches its freezing point, the solvent begins to crystalize on the bottom of the container in an upward direction (relative to the bottom of the container) and the sorptive stirrer continues to stir on top of the frozen solvent. Once the solvent is completely frozen, the sorptive stirrer is removed from the top of the frozen solvent and can be analyzed by an analytical technique, such as gas-chromatography mass-spectroscopy (GCMS), thermal desorption GCMS, liquid chromatography, fluorometry, spectroscopy, or any other analytical technique. The analysis can include extraction of the analyte from the sorptive material. Preferably the extraction of the analyte is into a liquid solvent or into the gas phase such that it is amenable for follow-on analysis. Subsequent analytical techniques can be selected and applied to the analyte in a liquid, solid, and/or gas phase. 
         [0061]    According to an embodiment of the invention shown in the exemplary and non-limiting  FIG. 3 , the method and the different stages of concentration as they occur during the course of the method are shown. The sample container  1  containing the liquid phase sample  13  and the sorptive stirrer  3  is cooled so that the crystalline phase  15  forms during the method. 
         [0062]    While an understanding of the mechanism is not necessary to practice the present invention and while the present invention is not limited to any particular mechanism of action, it is contemplated that, in some embodiments, there are three material phases to consider: liquid, solid, and sorptive stirrer as shown in  FIG. 4A . Some among of analyte (A) will be associated with each of these phases as shown in  FIG. 4A .  FIG. 4B  shows the concentration profile of the analyte near the ice-liquid interface. Even though the analyte contained within the solid phase is not truly in equilibrium with other material phases in the system, the distribution of the analyte between the solid and liquid solution is described by an effective partition coefficient, K solid . According the present invention, the effectiveness of the method for purposes of analytical sample preparation is indicated by the fraction of analyte extracted (f extr,SB ). For the present invention, the extracted analyte is analyzed from the sorptive stirrer. Equation 1 defines the fraction of the analyte extracted: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     
                       extr 
                       , 
                       SB 
                     
                   
                   = 
                   
                     
                       mol 
                       
                         A 
                         , 
                         SB 
                       
                     
                     
                       
                         mol 
                         
                           A 
                           , 
                           SB 
                         
                       
                       + 
                       
                         mol 
                         
                           A 
                           , 
                           solid 
                         
                       
                       + 
                       
                         mol 
                         
                           A 
                           , 
                           l 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where mol A,SB , mol A,solid , mol A,l  are the amounts of analyte in the sorptive stirrer, solid, and liquid solution, respectively. Since the concentration of an analyte in any phase can be expressed as the amount of the substance (mol) per unit volume (L), Equation 1 can be written as Equation 2: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     
                       extr 
                       , 
                       SB 
                     
                   
                   = 
                   
                     
                       
                         C 
                         
                           A 
                           , 
                           SB 
                         
                       
                        
                       
                         V 
                         SB 
                       
                     
                     
                       
                         
                           C 
                           
                             A 
                             , 
                             SB 
                           
                         
                          
                         
                           V 
                           SB 
                         
                       
                       + 
                       
                         
                           C 
                           
                             A 
                             , 
                             solid 
                           
                         
                          
                         
                           V 
                           solid 
                         
                       
                       + 
                       
                         
                           C 
                           
                             A 
                             , 
                             l 
                           
                         
                          
                         
                           V 
                           l 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Where C A,SB , C A,solid , and C A,l  represents the concentration of the analyte in the sorptive stirrer, solid, and liquid solution, respectively. V SB , V solid , and V l  are the volume of the sorptive stirrer, solid, and liquid solution, respectively. If the distribution of the analyte is presumed to be in equilibrium, Equation 2 can be simplified to Equation 3: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     
                       extr 
                       , 
                       SB 
                     
                   
                   = 
                   
                     
                       
                         K 
                         SB 
                       
                        
                       
                         V 
                         SB 
                       
                     
                     
                       
                         
                           K 
                           SB 
                         
                          
                         
                           V 
                           SB 
                         
                       
                       + 
                       
                         
                           K 
                           solid 
                         
                          
                         
                           V 
                           solid 
                         
                       
                       + 
                       
                         V 
                         l 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    During the methods of the present invention, the volume of solid (V solid ) increases and the liquid volume (V l ) decreases until V l  becomes negligible. Therefore, the equation describing the fraction of the analyte extracted into the stir bar becomes Equation 4: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     
                       extr 
                       , 
                       SB 
                     
                   
                   = 
                   
                     
                       
                         K 
                         SB 
                       
                        
                       
                         V 
                         SB 
                       
                     
                     
                       
                         
                           K 
                           SB 
                         
                          
                         
                           V 
                           SB 
                         
                       
                       + 
                       
                         
                           K 
                           solid 
                         
                          
                         
                           V 
                           solid 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Since K SB V SB  must be much greater than K solid V solid  for an effective extraction to occur, wherein the fraction of analyte extracted approaches 1, and since the volume of the sorptive stirrer (V SB ) is small compared to the solid volume (V solid ), the K SB  must be much greater than K solid  for efficient extraction to occur according to the present invention. 
         [0063]    According to some embodiments of the invention, the log K SB  is between −0.7 and 4.0; more preferably between −0.6 and 3.0; most preferably between −0.5 and 2.5. According to a further embodiment of the invention, for water as a solvent, K solid  is generally on the order of 0.1 to 0.0001 (pK solid  of 1 to 4) depending on the solvent, stir rate, solute concentration, and freeze rate. Without seeking to be limited to a particular theory, it is believed that because K solid  decreases as the solute concentrations decreases, a K solid  of approximately 0.01 is considered conservative for the analysis according to the present invention. Thus, preferably the invention extracts at least 80% of the analyte, more preferably at least 85% of the analyte, more preferably at least 90% of the analyte for those analytes with a K SB  greater than 15. By comparison, this presents a significant advantage over the conventional methods of stir bar sorptive extraction.  FIG. 5A  illustrates the behavior of an analyte (i.e., the fraction of analyte extracted into the sorptive stirrer) as the analyte undergoes the methods of the present invention. As shown in  FIG. 5A , for analytes with smaller K SB , concentration into the stir bar is more pronounced over the last few mL of freezing and analytes with K SB s that are typically too low for stir bar sorptive extraction are able to be extracted into the sorptive stirrer at over 80%.  FIG. 5B  indicates the fraction extracted into the sorptive stirrer as the K SB  of the analyte increases. Using a K solid  of 0.01, the fraction extracted rises to above 90% as the log K SB  of the analyte increases to just over 1, whereas a log K SB &gt;3 is necessary to extract over 90% of the analyte under the same conditions.  FIG. 5C  shows that the present invention is advantageous for analysis over SBSE. 
       EXAMPLES 
       [0064]    Embodiments of the present invention are further defined in the following non-limiting Examples. It should be understood that these Examples, while indicating certain embodiments of the invention, are given by way of illustration only. From the above discussion and these Examples, one skilled in the art can ascertain the essential characteristics of this invention, and without departing from the spirit and scope thereof, can make various changes and modifications of the embodiments of the invention to adapt it to various usages and conditions. Thus, various modifications of the embodiments of the invention, in addition to those shown and described herein, will be apparent to those skilled in the art from the foregoing description. Such modifications are also intended to fall within the scope of the appended claims. 
       Example 1 
       [0065]    A dye solution was tested according to the methods and apparatus of the invention. The aqueous dye solution in the amount of 10 mL was placed in a vial with a sorptive stir bar. The vial was then placed into a jacketed beaker (i.e. a double-walled beaker with inlet and outlet to allow coolant flow). The concentration of methyl violet into the stir bar was visually confirmed.  FIG. 6  is a series of photographs showing the concentration of the methyl violet at various points during the test. In  FIG. 6A , the dye solution is visible prior to application of the methods of the invention.  FIG. 6B  shows the dye visibly separated on top of the crystalline phase during of the method, where approximately 50% of the dye solution has been frozen.  FIG. 6C  shows the dye solution visibly separated on top of the crystalline phase during the methods, where the dye has been concentrated and the majority of the water has been separated and frozen. 
       Example 2 
       [0066]    Two molecules: dimethyltrisulfide (DMTS; log K ow =1.87) and benzaldehyde (BA; log K ow , =1.48) were concentrated according to the methods and apparatus of the present invention. Aqueous samples (100 nM; 12.6 ppb for DMTS and 10.6 ppb for BA) were prepared by the methods of the present invention and also by SBSE. The results of both the present invention and SBSE were analyzed by GCMS.  FIG. 7  indicates the results of the analysis based on peak area. The signals of both DMTS and BA were enhanced using the methods of the present invention. The present invention produced a concentration factor of three times and eight times for DMTS and BA, respectively, compared to SBSE. For example,  FIG. 8  shows the comparative peaks for SBSE and the present invention.  FIG. 9  indicates the concentration factors as a function of temperature for BA.  FIG. 10  indicates that concentration factors decreased with the increase of stir speed.  FIG. 11  illustrates the relationship between concentration and concentration factor.  FIG. 12  indicates there is little to no correlation between the concentration factor and the solution concentration. The level of detection (LOD) for BA was also determined and is comparatively shown in  FIGS. 13A and 13B . The LOD of BA was decreased five times using the methods of the present invention. Further  FIG. 14  illustrates the lower limit of qualification for SBSE, while  FIGS. 15A and 15B  indicate the concentration factor at the lower limit of qualification for the present invention and SBSE. As shown, the lower limit of qualification for the present invention is much lower than that of SBSE. This is further shown in  FIG. 15B . Thus, the methods of the invention are capable of detection of solutes and much lower concentrations than existing methods. 
       Example 3 
       [0067]    Benzyl alcohol was analyzed according to the methods and apparatus of the present invention. Results of the present invention are compared to results of SBSE as shown  FIG. 16 . The limit of detection was also determined for both the present invention and SBSE for benzyl alcohol as shown in  FIG. 17A  and  FIG. 17B , respectively. The LOD of benzyl alcohol extracted according to the methods of the present invention was approximately 40 nM as compared to 1 μM. Therefore, the LOD was decreased twenty-five times using the methods of the present invention. This Example further confirms that the methods of the invention are capable of detection of solutes and much lower concentrations than existing methods. 
         [0068]    For the invention being thus described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the inventions and all such modifications are intended to be included within the scope of the following claims. 
         [0069]    The above specification provides a description of the methods and apparatus of the present invention. Since many embodiments can be made without departing from the spirit and scope of the invention, the invention resides in the claims.