HK40076216B - Chromatographic column having stationary phase thickness gradient - Google Patents

Description

Columns with stationary phase thickness gradient

Cross-references to related applications

This application claims the benefit of U.S. Provisional Application No. 62/940,038, filed November 25, 2019. The entire disclosure of the aforementioned provisional application is incorporated herein by reference.

Government support

This invention was developed with government support, as granted by the Centers for Disease Control and Prevention (CDC) under license number OH011082 and by the U.S. Air Force and Air Force Materiel Committee under license number FA8650-17-C-9106. The government owns certain rights to this invention.

Technical Field

This disclosure relates to a gas chromatography apparatus comprising a column having a stationary phase with a positive thickness gradient to enhance peak focusing.

Background Technology

This section provides background information relating to this disclosure, which is not necessarily prior art.

Gas chromatography (GC) is an analytical method that separates gaseous compounds via a separation column, allowing for the analysis and identification of compounds in a target sample. GC is widely used in many industries for the separation and identification of target analytes, such as volatile or semi-volatile organic compounds. GC is particularly suitable for analyzing complex samples with multiple target analytes that require individual detection. GC works by observing the “peaks” of chemicals passing through the separation column. Therefore, samples with different chemicals or target analytes are introduced into the column via an injector. The column comprises internal materials that are considered the stationary phase. Different fractions of the sample pass through the column at different rates (due to the physical and chemical interactions of each chemical with the materials contained in the column). As the target analytes elute and exit the column, a detector can distinguish substances eluted over time based on the rate at which the analytes pass through the column. These analytes can be identified and/or quantified electronically during or after detection. Improving the separation within the chromatographic column to enhance performance and GC detection capabilities is desirable.

Summary of the Invention

This section provides a general overview of the disclosure and is not a complete disclosure of the full scope or all features of the disclosure.

In some aspects, this disclosure relates to a gas chromatography apparatus for peak focusing of one or more target analytes. The chromatographic column has an inlet and an outlet, wherein the inlet receives a sample containing one or more target analytes exiting the column at the outlet. A stationary phase is deposited inside the column and has a positive thickness gradient. The stationary phase extends from the inlet to the outlet and has a first thickness at the inlet of the column and a second thickness at the outlet of the column. The second thickness is at least about 10% greater than the first thickness.

On the one hand, the first thickness is greater than or equal to about 10 nm to less than or equal to about 10 micrometers, and the second thickness is greater than or equal to about 30 nm to less than or equal to about 30 micrometers.

On the one hand, the second thickness is greater than or equal to the first thickness by at least approximately 100%.

On the one hand, the second thickness is greater than or equal to the first thickness by at least approximately 300%.

On the one hand, the chromatographic column is a microgas chromatographic column.

On the one hand, the stationary phase contains siloxane polymers.

On the other hand, the siloxane polymer includes at least one alkyl or aryl group, which includes 1 to 30 carbon atoms.

On the one hand, the cross-sectional shape of the chromatographic column is selected from the following group: circular, elliptical, rectangular, and triangular.

This disclosure also relates to a method for peak focusing in a gas chromatography apparatus. The method includes introducing two or more target analytes into the inlet of a chromatographic column, the column comprising a stationary phase deposited inside the column and having a positive thickness gradient. The stationary phase extends from the inlet to the outlet and has a first thickness at the inlet of the column and a second thickness at the outlet of the column. The second thickness is at least about 10% greater than the first thickness. The method also includes separating the two or more target analytes in the column. The method further includes eluting the two or more target analytes from the outlet of the column.

On the one hand, two or more target analytes are volatile organic compounds (VOCs).

On the one hand, at least one of the two or more target analytes contains an aromatic compound, and the overall peak focusing rate for the aromatic compound is greater than or equal to about 25%.

On the one hand, at least one of the two or more target analytes contains an alkane compound, and the total peak focusing rate for the alkane compound is greater than or equal to about 10%.

On the one hand, the first thickness is greater than or equal to about 10 nm to less than or equal to about 10 micrometers, and the second thickness is greater than or equal to about 30 nm to less than or equal to about 30 micrometers.

On the one hand, the second thickness is greater than or equal to the first thickness by at least approximately 300%.

On the one hand, the chromatographic column is a micro gas chromatography column.

On the other hand, the stationary phase includes a siloxane polymer comprising at least one alkyl or aryl group comprising 1 to 30 carbon atoms.

On the one hand, the cross-sectional shape of the chromatographic column is selected from the following group: circular, elliptical, rectangular, and triangular.

This disclosure also relates to a method for validating peak focusing in a gas chromatographic apparatus. The method includes performing a forward operation by introducing two or more target analytes into the inlet of a column comprising a stationary phase deposited inside the column and having a positive thickness gradient. The stationary phase extends from the inlet to the outlet and has a first thickness at the inlet and a second thickness at the outlet. The second thickness is at least about 10% greater than the first thickness. The forward operation includes separating two or more target analytes in the column and eluting two or more target analytes from the outlet of the column. The method also includes performing a reverse operation by introducing two or more target analytes into the outlet of a column comprising a stationary phase. The reverse operation includes separating two or more target analytes in the column and eluting two or more target analytes from the inlet of the column. The method further includes comparing the chromatographic resolution from the forward and reverse operations, wherein the peak focusing rate for at least one pair of corresponding peaks from the two target analytes is greater than 5%.

This disclosure further relates to a method of manufacturing a gas chromatographic apparatus having a column with a positive thickness gradient. The method includes introducing a precursor liquid into the column. The precursor liquid includes a stationary phase precursor and a low-boiling-point solvent, the low-boiling-point solvent evaporating along the length of the column to increase the concentration of the stationary phase precursor as it moves along the column, thereby creating a stationary phase thickness gradient. The method also includes reacting or crosslinking the stationary phase precursor to form a positive thickness gradient stationary phase extending from an inlet to an outlet and having a first thickness at the column inlet and a second thickness at the column outlet. The second thickness is at least about 10% greater than the first thickness.

On the one hand, the inner surface of the chromatographic column is silanized before the precursor liquid is introduced.

On the one hand, silanization involves passing reactive silanes in the gas phase through a column.

On the one hand, the chromatographic column includes an inlet and an outlet, and the introduction, reaction or cross-linking includes: dynamically coating the inner surface of the chromatographic column by partially filling the chromatographic column with a precursor liquid, applying pressure at the inlet to force the precursor liquid down the length of the chromatographic column, and applying a vacuum at the outlet to evaporate a low-boiling-point solvent.

On the one hand, the first thickness is greater than or equal to about 10 nm to less than or equal to about 10 micrometers, and the second thickness is greater than or equal to about 30 nm to less than or equal to about 30 micrometers.

On the one hand, the second thickness is greater than or equal to the first thickness by at least approximately 100%.

On the one hand, the second thickness is greater than or equal to the first thickness by at least approximately 300%.

On the one hand, the chromatographic column is a micro gas chromatography column.

On the one hand, the stationary phase contains siloxane polymers.

On the other hand, the siloxane polymer includes at least one alkyl or aryl group, which includes 1 to 30 carbon atoms.

Other applicable fields will become apparent from the description provided herein. The descriptions and specific embodiments in this overview are intended for illustrative purposes only and are not intended to limit the scope of this disclosure.

Attached Figure Description

The accompanying drawings described herein are for illustrative purposes only, representing selected embodiments rather than all possible implementations, and are not intended to limit the scope of this disclosure.

Figure 1 shows an example implementation of a gas chromatography apparatus system.

Figure 2 shows a cross-sectional view of a chromatographic column according to certain aspects of this disclosure, the column having a stationary phase with a positive thickness gradient to enhance peak focusing.

Figures 3A-3C depict peak focusing using a film thickness gradient column (FTGC) according to certain aspects of this disclosure. As shown in Figure 3A, the thinner to thicker film focuses the analyte peaks as the analyte travels along the column. Figure 3B is a diagram of the setup used for column performance evaluation. Figure 3C is a diagram of forward operation mode and backward operation mode/reverse operation mode.

Figures 4A-4C. Figure 4A illustrates the FTGC coating setup. The column was dynamically coated by partially filling it with a coating solution plug and then pushing the mixture out at a pressure of 5 psi. While pushing the solution out, a vacuum pressure of -2 psi was applied to the outlet to evaporate the solvent. Figure 4B is a SEM image near the column inlet with a film thickness of 34 nm. Figure 4C is a SEM image near the column outlet with a film thickness of 241 nm.

Figures 5A-5D. Figure 5A shows the separation of a mixture of _C7 to _C16 alkanes in forward operation mode. Figure 5B shows the separation of a mixture of _C7 to _C16 alkanes in reverse or inverted operation modes with the same parameters. Figure 5C shows the separation of a mixture of _C7 to _C16 alkanes in equal-time backward mode. Figure 5D shows the separation of a mixture of _C7 to _C16 alkanes using a column of uniform thickness.

Figure 6 illustrates the resolution differences between the forward mode, the same parameter mode, the isochronous reverse/reverse mode, and the uniform thickness column for _C7 to _C16 alkanes.

Figures 7A-7D. Figure 7A is a diagram showing the separation of a mixture of aromatic compounds in forward mode. Figure 7B is a diagram showing the separation of a mixture of aromatic compounds under the same parameters. Figure 7C is a diagram showing the separation of a mixture of aromatic compounds in isochronous reverse/inverse models. Figure 7D is a diagram showing the separation of a mixture of aromatic compounds in a control column with a column of uniform thickness. Peaks 1, 2, 3, 4, and 5 correspond to benzene, toluene, ethylbenzene, o-xylene, and 1,3-dichlorobenzene, respectively.

Figure 8 illustrates the resolution differences between the forward mode, the same parameter mode, the isochronous inverse mode, and the uniform thickness column for the separation of aromatic compounds.

Figures 9A-9C. Figure 9A shows the room temperature isothermal separation of _C5 and _C6 in forward mode. Figure 9B shows the room temperature isothermal separation of _C5 and _C6 in reverse/reverse mode with the same parameters. Figure 9C shows the room temperature isothermal separation of _C5 and _C6 in a column with uniform thickness.

Throughout the various views of the accompanying drawings, corresponding reference numerals denote the corresponding parts.

Detailed Implementation

The provision of exemplary embodiments makes this disclosure thorough and will fully communicate the scope to those skilled in the art. Numerous specific details, such as examples of specific compositions, components, apparatuses, and methods, are set forth to provide a thorough understanding of embodiments of this disclosure. It will be apparent to those skilled in the art that specific details are not required, exemplary embodiments may be embodied in many different forms, and none of these should be construed as limiting the scope of this disclosure. In some exemplary embodiments, well-known processes, well-known apparatus structures, and well-known techniques are not described in detail.

The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting. As used herein, the singular forms “a,” “an,” and “described” may also be intended to include the plural forms unless the context clearly indicates otherwise. The terms “comprises,” “comprising,” and “including” are open-ended and therefore specifically refer to the presence of the stated features, elements, compositions, steps, integers, operations, and/or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. While the open-ended term “comprising” should be understood as a non-limiting term used to describe and claim the various embodiments set forth herein, in some respects it may be understood alternatively as a more restrictive and binding term, such as “consisting of” or “substantially consisting of.” Therefore, for any given embodiment listing compositions, materials, components, elements, features, integers, operations, and/or process steps, this disclosure also specifically includes embodiments consisting of or substantially consisting of these listed compositions, materials, components, elements, features, integers, operations, and/or process steps. In the case of “consisting of…”, the alternative embodiment excludes any additional composition, material, component, element, feature, integer, operation and/or process step, while in the case of “consisting substantially of…”, any additional component, material, component, element, feature, integer, operation and/or process step that substantially affects the essential and novel characteristics is excluded from the embodiment, but any composition, material, component, element, feature, integer, operation and/or process step that does not substantially affect the essential and novel characteristics may be included in the embodiment.

Unless specifically indicated as to the order of execution, the methods, procedures, and operations described herein should not be construed as necessarily requiring them to be performed in the particular order discussed or illustrated. It should also be understood that, unless otherwise instructed, additional or alternative steps may be employed.

When a component, element, or layer is described as “above another element or layer,” “engaged to another element or layer,” “connected to another element or layer,” or “coupled to another element or layer,” the component, element, or layer may be directly above, engaged to, connected to, or coupled to another component, element, or layer, or there may be intermediate elements or layers present. Conversely, when an element is described as “directly above another element or layer,” “directly engaged to another element or layer,” “directly connected to another element or layer,” or “directly coupled to another element or layer,” there may be no intermediate elements or layers present. Other words used to describe relationships between elements should be interpreted in a similar manner (e.g., “between” vs. “directly between,” “adjacent” vs. “directly adjacent,” etc.). As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items.

Although the terms first, second, third, etc., may be used herein to describe various steps, elements, components, regions, layers, and/or portions, these steps, elements, components, regions, layers, and/or portions should not be limited by these terms unless otherwise indicated. These terms may be used only to distinguish one step, element, component, region, layer, or portion from another. Unless the context clearly indicates otherwise, terms such as “first,” “second,” and other numerical terms used herein do not imply order or sequence. Therefore, without departing from the teachings of the example embodiments, the first step, element, component, region, layer, or portion discussed below may be referred to as the second step, element, component, region, layer, or portion.

Spatial relative terms or provisional relative terms, such as “before,” “after,” “inside,” “outside,” “below,” “below,” “above,” “over,” etc., may be used herein for the convenience of describing the relationship between one element or feature and another element or feature as illustrated in the figures. In addition to the orientations depicted in the figures, spatial relative terms or provisional relative terms may be intended to cover different orientations of the apparatus or system in use or operation.

Throughout this disclosure, numerical values represent approximate measurements or limitations of a range to cover minor deviations from a given value, embodiments approximately having the mentioned value, and embodiments precisely having the mentioned value. Except for the working embodiments provided at the end of the detailed description, numerical values (e.g., numerical values of quantities or conditions) of all parameters in this specification (including the appended claims) should be understood to be modified in all cases by the term “about,” regardless of whether “about” actually appears before the numerical value. “About” indicates that the numerical value allows for some slight imprecision (accuracy of approximating the value by some method; approximating or reasonably approximating the value; almost). If the imprecision provided by “about” is not understood in this common sense in the art, then “about” as used herein at least indicates the variation that may arise from common methods of measuring and using these parameters. For example, “about” can include less than or equal to 5%, optionally less than or equal to 4%, optionally less than or equal to 3%, optionally less than or equal to 2%, optionally less than or equal to 1%, optionally less than or equal to 0.5%, and in some respects, optionally less than or equal to 0.1%.

Furthermore, the disclosure of a range includes the disclosure of all values as well as further subdivisions of the range throughout the entire range, including endpoints and subranges given for the range.

The example implementation will now be described more fully with reference to the accompanying drawings.

In all respects, this teaching pertains to gas chromatography. As shown in Figure 1, a simplified illustration of a gas chromatography system 20 typically has at least five components: (1) a carrier gas source 22; (2) a sample injection system 24; (3) one or more gas chromatography columns 30; (4) a detector 32; and (5) a data processing system 34. The carrier gas introduced as the carrier gas source 22 (also called the mobile phase) is a high-purity and relatively inert gas, such as helium, hydrogen, nitrogen, argon, or air. In conventional systems, the carrier gas flows simultaneously with the sample fluid to be tested through the column 30 (during the separation process). The sample injection system 24 introduces a predetermined volume of sample mixture comprising one or more target analytes to be tested (e.g., in gaseous form) into the column 30 in combination with the flowing carrier gas from the carrier gas source 22. Thus, the carrier gas and the sample (possibly containing one or more target analytes) are introduced into one or more columns 30. The sample moves through the column together with the co-injected carrier gas from the carrier gas source 22.

The target analytes from the sample are separated and delivered through column 30, thus eluting from the column. It should be noted that, depending on the delay in the respective target analyte species' passage through and separation by column 30, the eluted sample having one or more target analytes can be eluted from column 30 in fractions. Furthermore, the sample fractions eluted from column 30 can optionally be captured and re-injected downstream.

Typically, separation is achieved within a column 30 because the inner surface of the column is coated (or the interior of the column is filled) with a material used as a stationary phase. The term "column" is used broadly to include various flow paths through which fluids can flow, such as patterned flow fields from micro-features defined in one or more substrates, or other fluid flow paths recognized by those skilled in the art. The stationary phase adsorbs different target analytes in the sample mixture to varying degrees. Differences in adsorption result in different retardations in the travel of different chemical species down the column and, in this way, different mobilities, thus affecting the physical separation of the target analytes in the sample mixture. In some variations, the column is a micro gas chromatography column. As used herein, "micro-size" refers to a structure having at least one size less than about 500 μm, optionally less than about 400 μm, optionally less than about 300 μm, optionally less than about 200 μm, optionally less than about 150 μm, and in some variations, a structure having a size optionally less than about 100 μm, which can also encompass nanoscale features. As used herein, the terms microsize, microchannel, microfluidic channel, or microstructure refer to smaller structures, such as equivalent nanoscale structures. It should also be noted that while one dimension (such as diameter) may fall within the microsize range, other dimensions (such as length) may exceed the microsize range.

Various separated components elute from column 30 to one or more detectors 32 for analysis. Thus, one or more detectors 32 are located at the ends of one or more columns 30. Therefore, detectors 32 are used to detect various chemical substances or target analytes in a sample that emerges or elutes from column 30 at different times. Such detectors 32 typically operate in gas chromatography systems by destructive analysis of the elution fractions. Typical, non-limiting examples of detectors 32 include mass spectrometers (MS) (e.g., time-of-flight mass spectrometers (TOFMS)), flame ionization detectors (FID), photoionization detectors (PID), electron capture detectors (ECD), thermal conductivity detectors (TCD), etc. A data processing system 34 typically also communicates with detectors 32 to typically store, process, and record separation test results.

In wall-coated capillary columns, vapor interactions between the gas phase and the stationary phase coated on the capillary wall enable analyte retention. As analytes travel along the column, they encounter longitudinal and lateral mass transfer, which can lead to peak broadening, reduced GC resolution, and increased likelihood of co-elution. Typically, proper selection of the stationary phase within the column (to enable sufficient analyte interactions and retention), the application of temperature programming, and split/splitless sample injection enable improved chromatographic separation and resolution. However, in some cases, these methods are insufficient to achieve the desired separation. For example, in portable GCs, limited carrier gas supply prevents the use of split injection, and fine control of the temperature program is both difficult and limited by system power capacity. Furthermore, even for specialized separations (e.g., separation of highly volatile compounds via porous layer open tubular columns), it may be difficult to completely separate all relevant compounds. Therefore, additional methods for improving column separation are desirable.

Negative temperature gradient separation (NTGS) is a method used to improve column performance by sharpening elution peaks. In NTGS, the column inlet is heated, generating a temperature gradient through heat exchange with the surrounding environment. Because the temperature is lower towards the column outlet, the peak tip travels more slowly than its tail, resulting in overall peak focusing. This effect can be optimized by adjusting different temperature distributions along the column, enabling high versatility under various conditions. However, due to NTGS's dependence on heat exchange, focusing varies with ambient temperature, humidity, air convection rate, and the thermal conductivity of the packing material, reducing reproducibility and predictability (especially when using complex temperature distributions). Complex thermal control modules can be used to stabilize the temperature gradient, but this adds extra size, weight, complexity, and cost to the GC unit. Furthermore, the energy loss due to the aforementioned heat exchange is a relevant drawback for resource-constrained systems (e.g., microGC units). Additionally, the separation of highly volatile compounds often requires temperatures close to ambient, thus the generation of temperature gradients can be avoided or minimized, thereby suppressing the NTGS effect. Therefore, despite being general-purpose and adjustable, the use of NTGS in certain applications (e.g., portable GC) may be limited and challenging.

This disclosure provides a novel method for peak focusing during gas chromatography. In some aspects, the gas chromatographic apparatus for peak focusing of one or more target analytes includes a chromatographic column having an inlet and an outlet. The inlet receives a sample comprising one or more target analytes exiting the column at the outlet. A stationary phase is disposed and deposited within the column and has a positive thickness gradient. The stationary phase extends from the inlet to the outlet and has a first thickness at the inlet of the column and a second thickness at the outlet. As will be further described below, the second thickness is at least about 10% greater than the first thickness. In this way, the positive stationary phase thickness gradient is a gradient in which the stationary phase film thickness increases from the inlet toward the outlet. As the stationary phase thickness increases toward the outlet, the peak tip travels more slowly than its tail, thereby enabling overall peak focusing.

Figure 2 shows an example of a chromatographic column 50 prepared according to certain aspects of this disclosure, which is capable of focusing the peaks of one or more target analytes. In some aspects, the one or more target analytes may be volatile organic compounds (VOCs) having relatively high vapor pressures and therefore low boiling points at the temperatures and pressures used within the chromatographic column 50. VOC target analytes may include alkanes or aromatic compounds.

The chromatographic column 50 is defined by a wall 60. Therefore, the wall 60 of the chromatographic column 50 can define a structure having a hollow internal region 52, which can be at least partially occupied by the stationary phase 64. The cross-sectional shape of the chromatographic column 50 can be selected from the group consisting of: circular, elliptical, rectangular, and triangular. In some respects, the chromatographic column 50 is formed of metal, silica, glass, or a polymer. The chromatographic column 50 defines an inlet 70 and an outlet 72. As shown in Figure 2, the wall 60 has a constant thickness. Therefore, the first thickness of the wall 60 at the inlet 70, indicated by " _T1 ", is the same as the second thickness at the outlet 72, indicated by " _T2 ".

As described above, when a mixture of one or more target compounds in the sample/carrier mobile phase and stationary phase 64 pass through the column, the mixture interacts with the stationary phase. The target analytes interact with the stationary phase 64 to varying degrees or at different rates. The analyte that interacts least with the stationary phase 64 will be the first to exit or elute from the column 50. Typically, the target analyte that interacts most with the stationary phase 64 travels through the column 50 at the slowest rate and is therefore the last to exit. Different mixtures of target analytes can be separated by changing the characteristics of the mobile phase (carrier and sample) and the stationary phase 64. As will be described below, the stationary phase 64 in this technical context has a positive thickness gradient that enables the peaks of one or more target analytes to focus, which typically means that the analyte peaks focus as they travel from the inlet 70 to the outlet 72 of the column 50.

In some variations, stationary phase 64 may comprise silicon, such as silica or a siloxane polymer. A variety of siloxane polymers can form stationary phase 64. Typically, siloxane polymers are cross-linked polymers having a basic silicon and oxygen backbone, and side constituent groups that can be the same or different, usually described by a repeating structural unit (-O-SiRR'-) _n , where R and R' can be the same or different side constituents, and "n" can be any value greater than 2. Surface functionalization of silica or siloxanes can be performed in monomer or polymerization reactions with different short-chain organosilanes, thereby reacting with silanol groups. While the retention mechanism of the target analyte remains unchanged, differences in the surface chemistry of different stationary phases can lead to variations in selectivity for different target analytes. Siloxane polymers may include polyheterosiloxanes, where the side constituents or repeating units can be different. Examples of suitable side groups may be at least one unsubstituted or substituted alkyl or aryl group containing 1 to 30 carbon atoms, for example, including but not limited to: methyl, ethyl, propyl, butyl, pentyl, hexyl, heptyl, octyl, nonyl, decyl, phenyl, alkylphenyl, etc.

In all respects, the stationary phase 64 is deposited on the inner surface 66 of the wall 60 and defines a positive thickness gradient. In some variations, as will be further described below, the inner surface 66 may first be silanized, for example, by exposing the inner surface 66 to hexamethyldisilazane (HMDS) vapor to form a silane- or silanol-containing surface coating. Then, a precursor of a siloxane polymer (such as silicone OV-1, a vinyl-modified 100% dimethylsiloxane commercially available from Ohio Valley Specialty Company as OV-1 6001 or silicone OV-17, or a vinyl-modified 50% phenylsiloxane-50% methylsiloxane commercially available from Ohio Valley Specialty Company as OV-1 6017) may be injected and reacted to form the stationary phase. Crosslinking agents (such as Dow Sylgard ^™ 184 Reagent B (15% w/w, crosslinking agent)) may also be added together with the precursor to promote crosslinking. Clearly, stationary phase 64 is not limited to such materials, and these are provided merely as suitable examples for use in gas chromatography columns.

As shown in the figure, the stationary phase 64 extends from the inlet 70 to the outlet 72 along the inner surface 66 of the wall 60. The stationary phase 64 thus forms a continuous coating or film on the inner surface 66. The stationary phase 64 has a first thickness at the inlet 70, denoted by " _t1 ". The stationary phase 64 also defines a second thickness at the outlet 72, denoted by " _t2 ". The second thickness ( _t2 ) is at least about 10% greater than the first thickness ( _t1 ). Therefore, the stationary phase 64 defines a positive thickness gradient along the length of the column 50. In this way, the internal region 52 has a first diameter ( _d1 ) at the inlet 70 defined by the first thickness " _t1 " of the stationary phase 64. The internal region 52 has a second diameter (d2) at the outlet 72 defined by the second thickness " _t2 " of the stationary phase 64. The first diameter _{( d1} ) is greater than the second diameter ( _d2 ). In this way, the stationary phase 64 defines a positive thickness gradient within the column 50.

In some respects, the thickness gradient gradually increases along the length of column 50 between the first thickness ( _t1 ) and the second thickness ( _t2 ). The thickness variation of stationary phase 64 can be constant or vary along the length of column 50, but the thickness increases from inlet 70 to outlet 72.

In some variations, the second thickness ( _t2 ) is at least about 50% greater than the first thickness ( _{t1 )} , optionally at least about 100%, optionally at least about 150%, optionally at least about 200%, optionally at least about 250% greater than the first thickness ( _t1 ), and in some variations, optionally the second thickness ( _t2 ) is at least about 300% greater than the first thickness ( _{t1 )} . The first thickness ( _t1 ) may optionally be greater than or equal to about 10 nm to less than or equal to about 10 micrometers, and the second thickness ( _t2 ) may be greater than or equal to about 30 _nm to less than or equal to about 30 micrometers. In one variation, the first thickness ( _t1 ) is about 30 nm and the second thickness ( _t2 ) is about 30 micrometers.

Figures 3A-3C illustrate peak focusing according to certain aspects of this disclosure using a positive film thickness gradient (also referred to herein as a film thickness gradient column (FTGC)). As shown in Figure 3A, for a given analyte 80, as the analyte 80 travels down a column 84, the analyte peak 82 becomes increasingly focused, the column having a stationary phase 86 with a positive thickness gradient extending from the inlet 88 to the outlet 90 of the column 84. As shown in Figure 3A, as the analyte travels along the column in the direction of the box arrow, the film thickness of the stationary phase 86 increases from thinner to thicker (in the direction from the inlet 88 to the outlet 90), thus focusing the analyte peak 82. Figure 3B is an illustration of the setup used for column performance evaluation. The column 84 is mounted in fluid communication with an injector 94 of an Agilent 6890 benchtop GC 96 equipped with a flame ionization detector (FID) 98. Figure 3C is an illustration of the forward (top) operating mode and the reverse/inverted (bottom) operating mode. In other words, a sample containing at least two target analytes is introduced from inlet 88 in forward mode (top) and travels toward outlet 90 of column 84 in the direction indicated by the box arrow. In reverse or inverted mode (bottom), the sample containing at least two target analytes is introduced to outlet 90 of column 84 and then travels toward inlet 88 in the direction indicated by the box arrow.

In some aspects, this disclosure contemplates a method for peak focusing in a gas chromatographic apparatus. The method may include introducing two or more target analytes into the inlet of a chromatographic column comprising a stationary phase deposited within the column and having a positive thickness gradient. The stationary phase extends from the inlet to the outlet and has a first thickness at the inlet and a second thickness at the outlet. The second thickness is at least about 10% greater than the first thickness. The stationary phase may be any of those described above. The method includes separating two or more target analytes in the column. Furthermore, the two or more target analytes are then eluted from the outlet of the column.

In some aspects, two or more target analytes are volatile organic compounds (VOCs). In another aspect, at least one of the two or more target analytes contains an aromatic compound, and the total peak focusing rate for the aromatic compound is greater than or equal to about 25%, for example, it may be greater than or equal to about 26%, optionally greater than or equal to about 27%, and in some variants, optionally greater than or equal to about 28%.

On the other hand, at least one of the two or more target analytes contains an alkane compound, and the total peak focusing rate for the alkane compound is greater than or equal to about 10%, and in some variants, optionally greater than or equal to about 11%.

In another aspect, this disclosure contemplates a method for validating peak focusing in a gas chromatographic apparatus. The method includes performing a forward operation by introducing two or more target analytes into the inlet of a column comprising a stationary phase deposited within the column and having a positive thickness gradient. The stationary phase extends from the inlet to the outlet and has a first thickness at the inlet and a second thickness at the outlet, wherein the second thickness is at least about 10% greater than the first thickness. The stationary phase may have any of the designs and compositions described above. The forward operation includes separating two or more target analytes in the column and subsequently eluting the two or more target analytes from the outlet of the column. A reverse operation is then performed by introducing two or more target analytes into the outlet of the column, the column comprising the stationary phase. The reverse operation also includes separating two or more target analytes in the column and eluting the two or more target analytes from the inlet of the column. The method also includes comparing the chromatographic resolution from the forward and reverse operations, wherein the peak focusing rates of at least one pair of corresponding peaks from the two target analytes are greater than 5%, and optionally greater than or equal to about 10%.

This disclosure also contemplates a method for manufacturing a gas chromatographic apparatus having a column with a positive thickness gradient. The method includes introducing a precursor liquid into the column. The precursor liquid comprises a stationary phase precursor and a low-boiling-point solvent, the low-boiling-point solvent evaporating along the length of the column, thereby increasing the concentration of the stationary phase precursor as it moves along the column, and thus creating a stationary phase thickness gradient. The method further includes reacting or crosslinking the stationary phase precursor to form a positive thickness gradient stationary phase extending from the inlet to the outlet, and having a first thickness at the column inlet and a second thickness at the column outlet. The second thickness is at least about 10% greater than the first thickness.

In some aspects, the inner surface of the column is silanized before the introduction of the precursor liquid. Silanization may include passing a reactive silane in the gas phase through the column. In one embodiment, the reactive silane may be hexamethyldisilazane (HMDS) vapor, which forms a silane-containing surface coating on the inner surface. In some variations, the reactive silane may pass through the column multiple times.

Then, a precursor of the siloxane polymer (such as silicone OV-1, 100% dimethylsiloxane modified with vinyls, available from Ohio Valley Specialty, as OV-16001 or OV-17, or 50% phenylsiloxane-50% methylsiloxane modified with vinyls, available from Ohio Valley Specialty, as OV-16017) can be injected and reacted to form the stationary phase. A crosslinking agent (such as Dow SYLGARD ^™ 184 reagent B (15% w/w, crosslinking agent)) can also be added with the precursor to promote crosslinking. Clearly, the stationary phase is not limited to such materials, and these are provided merely as suitable examples of gas chromatography columns.

A chromatographic column includes an inlet and an outlet, and introduction and reaction (or crosslinking) can include dynamically coating the inner surface of the column. This can be achieved by partially filling the column with a precursor liquid, applying pressure at the inlet to force the precursor liquid down the length of the column, and applying a vacuum at the outlet to evaporate a low-boiling-point solvent. For example, a precursor liquid plug can be pushed through the column by applying a pressure of 5 psi at the inlet. A vacuum pressure of –2 psi can be applied to the outlet to evaporate the low-boiling-point solvent.

Example

Stationary phase thickness gradient gas chromatography (GC) columns enable analyte peak focusing and improve separation resolution. Theoretical analysis and simulations show that focusing increases along the column via a positive thickness gradient (i.e., stationary phase thickness). Peak focusing was experimentally validated using a 5-m long capillary column with a film thickness varying from 34 nm at the column inlet to 241 nm at the column outlet. This column was used to analyze _C5 to _C16 alkanes and aromatic compounds in both forward (thin-to-thick) and reverse (thick-to-thin) modes, and compared with a uniform thickness column of 131 nm.

A comparison of resolution between the forward mode and the uniform thickness column shows that the total focusing efficiency (i.e., the improvement in peak capacity) for alkanes is 11.7%, and the total focusing efficiency for aromatic compounds is 28.2%.

The focusing effect was also demonstrated for isothermal separation of highly volatile compounds and temperature-programmed separation with different heating rates. In all cases, the peak capacity from the positive mode separation was higher than that from other modes, indicating that a positive thickness gradient can focus analyte peaks. Therefore, as a general method for improving GC separation performance, this thickness gradient technique can be widely applied to various stationary phases and column types.

Test settings

FTGC was performed in an Agilent 6890 benchtop GC equipped with a flame ionization detector (FID, see Figure 3B). Ultra-high purity helium was used as the carrier gas. As shown in Figure 3C, peak focusing effects were evaluated using analytes injected from either the thinner coating end (forward mode, i.e., from thinner film to thinner film) or the thicker coating end (reverse mode, i.e., from thicker film to thinner film). The same setup was also used to evaluate uniform thickness columns (film thickness equal to average thickness) for comparison. All experiments were performed using a constant pressure temperature program. The temperature program methods and pressure heads are provided in Table 1.

Material

Analytical standards _C5 to _C16 , benzene, toluene, ethylbenzene, o-xylene, 1,3-dichlorobenzene, nitrobenzene, and dichloromethane were purchased from Sigma-Aldrich (St. Louis, Missouri). Vinyl-modified OV-1 (P/N 6001) and OV-17 (P/N 6017) were purchased from Ohio Valley Specialty (Mariette, Ohio). Dow SYLGARD ^™ 184 reagent B was purchased from Ellsworth Adhesive (Germantown, Wisconsin). Deactivated fused silica tubes (P/N 10010, 250 μm inner diameter) and RTX-5 columns (P/N 10205, 5 m length, 250 μm inner diameter, 0.1 μm film thickness) were purchased from Restek (Berfonte, Pennsylvania). DB-1MS column (P/N 122-0162, 5 m in length, 250 μm in inner diameter, 0.25 μm in thickness) was purchased from Agilent Technologies (Santa Clara, California). All materials were used as purchased without further purification or modification.

Column coating

OV-1 (75% w/w), OV-17 (10% w/w), and Dow SYLGARD ^™ 184 reagent B (15% w/w, crosslinking agent) were dissolved in dichloromethane to generate a 2% (w/w) coating solution (effective 5% phenyl stationary phase). A 5-m long capillary column (250 μm id) was silanized prior to coating by eight repeated injections of hexamethyldisilazane (HMDS) vapor. Subsequently, 80 μL of the coating solution was loaded into capillary 100 from the column inlet via a syringe pump (Figure 4A). A positive pressure of 5-psi was applied from the inlet to drive the coating solution toward the outlet. A negative 2-psi vacuum pressure of 110 was applied to the outlet through a 1-m dummy column (250 μm mi.d.), which ensured a constant coating plug velocity. During coating, a small amount of low-boiling-point dichloromethane evaporates rapidly under vacuum. As the coating solution plug moves from the column inlet to the outlet, the concentration of the coating solution gradually increases, thus increasing the film thickness. After coating, dry air flows continuously through the column for 2 hours, followed by crosslinking at 80°C for an additional 2 hours, and then deactivation with HMDS. The column is then aged at 230°C for 3 hours at a helium flow rate of 0.5 mL/min. Using the same method, a 1% (w/w) coating solution (same composition as above, but diluted) is used to coat a column with a film of uniform thickness, and a 5-psi positive pressure is applied from the inlet to drive the coating solution to the outlet (without applying a vacuum).

Simulation settings

Simulations of _C8 to _C15 separation were performed in forward and reverse modes, as well as with a uniform thickness equivalent to the average gradient film thickness (separation conditions in Table 1). For a 5 m column, the film thickness varied from 34 nm to 241 nm (inlet to outlet in forward mode, outlet to inlet in reverse mode). Notably, the calculation of the retention factor k(x,t) requires the value of the allocation coefficient K(t) (Eq.(2)), which is estimated based on the value in reference [22] (see the results in the S3 section on simulation parameters and results in Supporting Information). Table 2 provides the simulation retention time and FWHM, and Table 3 provides the resolution.

Uniform thickness control

The Restek RTX-5 column was used as a control for the separation of C7 to C16 alkanes in both forward and reverse modes, and no difference in separation was expected. Separation conditions are provided in Table 1. p-values for retention time and FWHM (more than 5 runs) were calculated using a paired “Student” t-test, and the resulting T-scores were converted to p-values. Significance was observed at p = 0.05; no significant difference was observed between forward and reverse modes for any analyte peak (see section S4 – Control experiment using a Restek RTX-5 column in Supporting Information). Similarly, for _C7 – _C15 , no significant difference was observed between forward and reverse modes when using a 5m Agilent DB-1MS column (data not shown).

stationary phase characterization

To characterize the thickness of the stationary phase, FTGC was first frozen in liquid nitrogen and then several sections were cut off. Scanning electron microscopy (SEM) images were taken near the column inlet (thinner film) and outlet (thicker film). Figures 2(B) and (C) show the film thickness increasing from 34 nm to 241 nm from the inlet to the outlet, with a gradient of approximately 41 nm/m. Uniform thickness columns were also characterized at the inlet and outlet, with a film thickness of 131 nm at both ends of the column.

The theoretical explanation for peak focusing is as follows:

The effective rate of the _analyte at position x (distance from the column inlet) and at a given time t are determined by the following formula:

Where _uM (x,t) is the velocity of the mobile phase, and k(x,t) is the retention factor:

The distribution coefficient K(t) is defined as follows:

Where R is the universal gas constant, and T(x,t) is the time-dependent column temperature at position x. ΔG is the change in Gibbs free energy associated with the analyte's movement from the stationary phase to the mobile phase, and can be calculated from the change in analyte enthalpy (ΔH) and the change in analyte entropy (ΔS).

ΔG＝ΔH－TΔS. (4)

The phase ratio β is defined as follows

Where d _{_i} and d _{_f} (x) are the inner diameter of the column and the film thickness, respectively. Therefore, equation (2) can be expressed as

Where A is a constant for a given column. The retention factor δk(x,t) varying along the column can be written as (see the derivation in the supplementary materials).

Equation (7) shows that the slight increase in the retention factor δk/k along the column at a distance δx has two contributions: the negative temperature gradient given by the first term and the positive film thickness gradient given by the second term. This retention factor gradient (δk/k) is related to the velocity gradient in Equation (1); therefore, both the negative temperature gradient and the positive film thickness gradient result in a velocity difference between the front and rear of the band, thus allowing band focusing (e.g., the spatial distribution of the analyte undergoes a spatially varying velocity gradient). At the outlet, this band is observed as a time-varying peak during elution, which may be narrower than the corresponding peak from the unfocused band. In other words, peak focusing (an observable quantity) exists as a result of in-column band focusing. The equivalence of these two gradients can be expressed as:

Compared to traditional temperature gradient-based peak focusing, membrane thickness gradients offer several advantages. First, the membrane thickness gradient is independent of column temperature, allowing the focusing of any volatile analyte at any operating temperature. Highly volatile compounds, particularly difficult to focus with NTGS, can be focused using the techniques of the present invention (e.g., with FTGC chromatographic apparatus and processes). Second, while the temperature gradient may vary with heater and environmental conditions (e.g., heater arrangement, heat dissipation, column size/weight, column channel arrangement, and ambient temperature and gas flow), the membrane thickness gradient remains constant, allowing for more reliable and reproducible GC operations (less susceptible to environmental influences). Finally, FTGC according to certain aspects of this disclosure can be used without additional accessories (e.g., heaters or coolers required for NTGS), significantly reducing apparatus complexity for future integration. However, despite these advantages, membrane thickness gradient-based separation may be less versatile than NTGS in some respects because the gradient is fixed, while the temperature gradient can be adjusted by changing the heat source and/or drain. Furthermore, the increased membrane thickness towards the column outlet can result in slow mass transfer, potentially negating the peak focusing effect. The mass transfer effect was examined in the following simulation.

For this simulation, the temperature gradient (i.e., NTGS) was not considered; only the film thickness gradient was analyzed. The time-dependent concentration c of the analyte peak traveling along the column was determined by solving the transient convection-diffusion equations.

Wherein, u _{_eff} (x,t) is given in equation (1). The effective diffusion coefficient u _{_eff} (x,t) can be calculated from the local diffusion D and the retention factor k(x,t).

d _{_f} represents the film thickness, and _DM represents the diffusion constant of the mobile phase. It is worth noting that D includes both longitudinal and transverse mass transfer/diffusion. _DM (x,t) can be expressed as...

The diffusion constants _DC (which depend on the molar weights of the analyte and mobile phase molecules, and the atomic and structural diffusion volumes) and _DS are used as the stationary phase diffusion constants. The local pressure p(x) is determined by the inlet and outlet pressures _pin and _pout.

L is the length of the column. _uM is the velocity in the flowing phase, given by the following formula:

Viscosity η is provided as a function of reference viscosity _η0 at temperature _T0 and gas type-related index _αn :

In equation (12), it is worth noting that, assuming the temperature along the column remains constant over a given time t, the temperature T(x,t) is provided as T(t). Equation (9) can be solved by applying a finite difference model to the discrete time (t) and position (i) vectors.

Δx and Δt are the simulated distance and time step. Combining these, we obtain...

The solution to equation (19) produces the time-dependent motion of the analyte peak along the column.

To simulate equation (19), several boundary conditions must be set. First, at t=0, the injection peak has a Gaussian peak shape, i.e.

Where σ represents the initial diffusion. It is noteworthy that the initial peak at time t = 0 is located at x = 3σ. At the column inlet, no additional analyte is injected into the column after the initial injection.

C(0,t)＝0. (21)

At the column outlet, the final mesh concentration is approximately the same as the mesh concentration on the left (because it cannot be calculated by equation (16), i.e.

C(L,t)＝C(L-Δx,t). (22)

By observation, using equation (19), peak retention time and full width at half maximum (FWHM) can be measured at the column outlet (i.e., x = L). Spatial variation concentrations are used to construct a two-dimensional concentration matrix that varies with location and time. For example, _C8 to C8... The separation of ₁₅ compounds was achieved using positive (i.e., thin-to-thick, or "forward" mode) and negative (i.e., thick-to-thin, or "reverse" mode) membrane thickness gradients. Simulations of membranes with uniform thickness (thickness equal to the average membrane thickness in both forward and reverse modes) were also performed as a control. Temperature was increased from 40°C to 240°C at a rate of 30°C/min. The pressure head was set to 3.45 psi (outlet set to ambient pressure, i.e., 1 atmosphere). For a 5 m column, membrane thickness varied from 34 nm to 241 nm (forward mode from inlet to outlet, reverse mode from outlet to inlet). A vector of concentration versus time was obtained by observing the concentration along the second dimension (i.e., in time), corresponding to the signal obtained from the detector at the outlet. The maximum value (as a function of time) corresponds to the elution/retention time, and the FWHM can be measured by observing the concentration at half the time of the peak. The resolution (R) between adjacent peaks can be additionally calculated using a formula.

Where _t1 and _t2 are the retention times of the two peaks, and _w1 and _w2 are the corresponding FWHM.

Peak retention time and full width at half maximum (FWHM) can be measured at the column outlet (i.e., x = L) and are provided in Table 1. Table 1 shows the programmed temperature profiles and pressure heads used for simulation, uniform thickness control, separation of alkanes from _C7 to _C16 , separation of aromatic compounds, and separation of highly volatile alkanes ( _C5 and _C6 ).

Table 1

Table 2 shows the simulated retention time (RT) and full width at half maximum (FWHM) for _C8 to _C15 in both forward and reverse modes. RT and FWHM for uniform coating thickness are also provided for reference. The temperature was increased from 40°C at a rate of 30°C/min, and the pressure head was 3.45 psi. The column length was 5 m. All values are provided in minutes. Further analyses are provided in Table 3.

Table 2

<![CDATA[RT_fwd]]> <![CDATA[FWHM_fwd]]> <![CDATA[RT_uni]]> <![CDATA[FWHM_uni]]> <![CDATA[RT_bkwd]]> <![CDATA[FWHM_bkwd]]> <![CDATA[C₈]]> 0.460 0.0382 0.449 0.0519 0.439 0.0684 <![CDATA[C₉]]> 0.731 0.0473 0.714 0.0704 0.697 0.0995 <![CDATA[C₁₀]]> 1.157 0.0574 1.136 0.0885 1.113 0.1296 <![CDATA[C₁₁]]> 1.639 0.0656 1.615 0.1005 1.560 0.1487 <![CDATA[C₁₂]]> 2.106 0.0713 2.082 0.1073 2.055 0.1584 <![CDATA[C₁₃]]> 2.591 0.0763 2.568 0.1120 2.541 0.1640 <![CDATA[C₁₄]]> 3.050 0.0807 3.027 0.1158 3.001 0.1679 <![CDATA[C₁₅]]> 3.460 0.0842 3.437 0.1186 3.411 0.1708

Table 3 shows the simulated resolution (R) between adjacent peaks _C8 to _C15 in both forward and reverse modes, as well as in uniform thickness. The resolution in the forward mode is greater than that in both the reverse mode and uniform thickness. The difference in resolution is defined as R _{_diff} = R _{_fwd} - R_{_bkwd} .

Table 3

Table 1 shows the analyte peaks eluted at different times in forward and reverse modes; this is because the separation conditions for a given analyte differ between the two modes. In forward mode, the analyte is first exposed to a thinner film at a lower temperature and then reaches a thicker film at a higher temperature, which is the exact opposite of the analyte's experience in reverse mode. Therefore, the retention times for the analyte differ between the two modes when evaluating column performance, and the full width at half maximum (FWHM) cannot be directly compared. Instead, the resolution R is used between the two peaks to analyze the separation performance (see Table 2), as given by Equation 23.

Table 2 shows that the forward mode produces higher resolution between adjacent peaks compared to the inverse mode, meaning that the forward mode can contain more peaks in the same time interval than the inverse mode. The uniform thickness resolution is greater than that of the inverse mode but consistently less than that of the forward mode, indicating that peak focusing is achieved in the forward mode. Further analysis of the resolution between adjacent peaks shows that the resolution difference between the forward and inverse modes (i.e., R- _difference = R- _forward - R- _inverse ) decreases with increasing analyte retention. This is likely due to slower mass transfer (i.e., lateral diffusion) in thicker film regions—more pronounced for heavier compounds. In the forward mode, this effect causes lower volatile compounds to broaden closer to the column outlet, thus offsetting the focusing provided by the column. Conversely, in the inverse mode, the thinner film at the outlet results in smaller broadening, which offsets the defocusing from the inverse gradient. Therefore, the resolution difference between the forward and inverse modes is reduced for lower volatile compounds.

Peak focusing was performed on the alkane mixture. The peak focusing capability of FTGC was evaluated by separating a mixture of _C7 to _C16 alkanes. 0.025 μL of liquid was injected at a split ratio of 5:1. The same separation conditions were used for forward mode, uniform thickness column, and reverse mode (denoted as "Same Parameters Reverse Mode", see Table 1 – Alkane Mixtures). Example chromatograms are shown in Figures 5A-5D.

Figure 6 shows the analyte peaks eluted at different times in both forward and reverse modes with the same parameters for a uniform thickness column, consistent with the simulation (Table 2). This is because the separation conditions for a given analyte differ between the two modes, which in turn differs from the uniform thickness column. In forward mode, the analyte is first exposed to a thinner film at a lower temperature and then reaches a thicker film at a higher temperature, which is the exact opposite of the analyte's experience in reverse mode. In a uniform thickness column, the analyte experiences the same film thickness at all temperatures. Therefore, when evaluating column performance, the retention times for the analyte differ between these two modes and the uniform column, and the full width at half maximum (FWHM) cannot be directly compared. Instead, the resolution between adjacent peaks (e.g., _C7 and _C8 , _C8 and _C9 , etc.) is used to analyze separation performance. The resolution of the same-parameter inverse mode and the uniform column were subtracted from the corresponding resolution in the forward mode; the resolution difference (i.e., R _{_forward} - R_{_{same-parameter inverse}} or R_{_forward} - R_{_uniform}) between all adjacent peak pairs (average of 5 runs) is plotted in Figure 6. The p-values for the resolution difference were calculated using a paired “Student” t-test (5 runs in the forward mode, same-parameter inverse mode, and uniform column), and the resulting T-scores were converted to p-values (see Table 3). Significance was found at p = 0.05, indicating that the forward mode has significantly higher resolution between all adjacent peak pairs compared to the same-parameter inverse mode. Simulations confirmed this (Table 3), also demonstrating higher resolution in the forward mode, meaning that the forward mode can contain more peaks than the inverse mode within the same time interval. The uniform thickness column resolution was lower than the forward mode resolution up to C _₁₀ /C _₁₁ , but higher for the C _₁₅/C_₁ pair. Overall performance analysis is provided below.

Table 4 shows the p-values for the separation of _C7 to _C16 alkanes between the forward mode and uniform thickness, the inverse mode with the same parameter (IP), and the inverse mode with equal time (ET). Significance is indicated at p = 0.05. All p-values are significant between the forward mode and the IP inverse mode, while for the ET inverse mode, the p-values for _C7 to _C13 are significant. The significance of the forward mode resolution is higher than that of the uniform thickness resolution up to _C10 / _C11 , and even higher for _C15 / _C16 .

Table 4

To further explain the differences in retention times, a second set of chromatograms was obtained by reducing the temperature ramp rate in the reverse mode to ensure that _C16 (the last eluted analyte) eluted simultaneously with the forward mode (this is referred to as "isochronous reverse mode," see Table 1 – Separation Conditions, Figures 5A-5D Chromatograms, Figure 6 – Resolution Differences, Table 4 – p-values). Similarly, the forward mode provided significantly higher resolution for alkane pairs between _C7 and _C13 (results obtained from 5 runs), but a similar approach to the isochronous reverse mode was performed for _C13 to _C16 . While the forward mode was not superior to the isochronous reverse mode (or uniform thickness column) for all local resolutions (i.e., between adjacent alkane pairs), it exhibited a significantly higher peak capacity (PC) compared to all other modes, defined as the sum of all resolutions.

(Table 5). Focusing rate analysis, defined as...

This indicates that, compared to a uniform thickness column, a reverse mode with the same parameters, and an isochronous reverse mode, the forward mode shows total focus rates of approximately 11.7%, 26.8%, and 29.8%, respectively.

Table 5

Positive peak capacity 49.34±0.841 Reverse peak capacity (IP) 38.90±0.831 p-value 1.73e-4 Focusing rate (IP) 26.84% Inverse peak capacity (ET) 38.02±2.400 p-value (ET) 4.62e-4 Focusing rate (ET) 29.76% Uniform peak capacity 44.18±0.483 p-value (uniform) 1.63e-4 Focusing rate (uniformity) 11.67%

Table 5. For the separation of _C7 to _C16 alkanes in Figures 5A-5D, peak capacity, total resolution, p-value, and focusing efficiency are compared between the forward mode, the inverse mode with the same parameters (IP), the inverse mode with isochronous (ET), and the uniform thickness. Significance is observed at p = 0.05. The peak capacity in the forward mode is significantly better than that of all other modes.

Peak focusing of aromatic compound mixtures

FTGC peak focusing was also used to analyze the separation of a mixture of aromatic compounds containing benzene, toluene, ethylbenzene, o-xylene, and 1,3-dichlorobenzene. 0.025 μL of the mixed liquid was injected at a split ratio of 5:1 (separation conditions are provided in Table 1 – Aromatic Compound Mixtures). Example chromatograms are shown in Figures 7A-7D, and resolution differences are shown in Figure 8. Local resolution difference p-values (calculated from 5 runs) are provided in Table 6. Peak capacity, p-values, and focusing efficiency are provided in Table 7, showing that the forward mode has significantly higher peak capacity compared to all other modes. Therefore, regardless of whether the separation parameters are kept constant (and the analyte elutes faster in the reverse mode with the same parameters) or changed to ensure simultaneous elution of the final compounds (in both forward and isochronous reverse modes), the separation performance in the forward mode is always better than in any of the reverse modes. The forward mode also outperforms uniform thickness columns, indicating a focusing efficiency of 28.2% (Table 7). Therefore, overall, the forward mode (i.e., positive film thickness gradient) demonstrates the ability to improve the separation peak capacity.

Table 6 shows the p-values for the forward mode versus the uniform thickness, identical parameter (IP) reverse mode, and equal time (ET) reverse mode used for the separation of aromatic compounds. See Figures 7A–7D for elution order and abbreviations. Significance is observed at p = 0.05. All p-values show a significant improvement in resolution under the forward mode.

Table 6

p-value p-value (IP) p-value (ET) p-value (uniform) B/T 3.08e-7 5.56e-7 1.83e-5 T/E 3.84e-7 9.28e-7 4.20e-6 E/X 9.32e-6 8.28e-5 0.012 X/DCB 5.95e-6 2.06e-5 2.28e-5

Table 7 shows the peak capacity, p-value, and focusing efficiency for the forward mode, the inverse mode with the same parameters (IP), the isochronous (ET) inverse mode, and the uniform thickness for the separation of aromatic compounds in Figures 7A-7D. Significance is observed at p = 0.05. The forward mode significantly outperforms all other modes in terms of separation.

Table 7

Positive peak capacity 13.47±0.089 Reverse peak capacity (IP) 9.59±0.060 p-value 1.60e-7 Focusing rate (IP) 40.35% Inverse peak capacity (ET) 9.85±0.093 p-value (ET) 1.56e-6 Focusing efficiency (ET) 36.73% Uniform peak capacity 10.50±0.146 p-value (uniform) 1.13e-5 Focusing rate (uniformity) 28.22%

warming effect

To demonstrate how heating rate affects peak focusing, separations of C7 through _C10 were performed in forward mode, reverse mode with the same parameters, and using a column of uniform thickness at four different heating rates (0, 10, 20, and 30 °C/min, from ₆₀ °C without holding). The pressure was 3.45 psi (2.7 mL/min at 60 °C), and the split ratio for all separations was 15:1 (0.025 μL of mixed liquid injected). Blank time was measured by methane injection and found to be 0.36 min for all heating rates. Resolution and focusing efficiency for each temperature distribution are provided in Table 8 (values provided as averages of 5 runs). In forward mode, at higher heating rates, the analyte encounters a relatively higher temperature as it reaches the thicker stationary phase closer to the column outlet. Therefore, the analyte spends less time in the thicker film, resulting in less peak broadening. In reverse mode, the analyte first encounters the thicker stationary phase at a lower temperature and then flows to the thinner stationary phase at a higher temperature. Peak broadening from the low-thickness stationary phase is already minimal; therefore, in the reverse mode, peak broadening due to temperature increase is generally reduced. Consequently, the focusing efficiency increases with the rate of temperature increase, reaching as high as 61.9% compared to both forward and reverse modes at a rate of 30 °C/min, and as high as 68.1% compared to the forward mode and uniform thickness.

Table 8 shows the resolution (R), peak capacity (PC), and focusing efficiency for forward, reverse, and uniform thickness separations of C7 to C10 at different heating rates. The initial temperature for all separations was 60 °C, and the carrier gas head was 3.45 psi (2.7 mL/min at 60 °C). 0.025 μL of the mixed liquid was injected using a split ratio of 15:1.

Table 8

Focusing for highly volatile compounds

Unlike NTGS, FTGC gradients can focus peaks at low temperatures where temperature gradients are difficult to generate (provided these peaks are reasonably preserved at these temperatures). To demonstrate this, room temperature isothermal separations were performed for _C5 and _C6 (Table 1) (Figures 9A-9C). Resolution, p-values, and focusing efficiency (average of 5 runs) are provided in Table 9. The focusing efficiency reached 40.2%, with an average forward mode resolution of 2.97 and a uniform thickness resolution of 2.12. It is noteworthy that for NTGS, highly volatile compounds are difficult to focus with the same peak performance because only a small temperature gradient is generated at low operating temperatures.

Table 9 shows the resolution, p-value, and focusing efficiency for forward mode, reverse mode, and uniform thickness separation of _C5 and _C6 at room temperature (26°C). Significance is observed at p = 0.05.

Table 9

Forward resolution 2.97±0.140 Reverse resolution 1.85±0.055 p-value (inverse) 1.17e-4 Focusing rate (inverse) 60.4% Uniform resolution 2.12±0.049 p-value (uniform) 4.87e-4 Focusing rate (uniformity) 40.2%

This paper details the development and evaluation of a stationary phase thickness gradient column technique capable of peak focusing. Experimental results, confirmed by theoretical analysis and simulation, demonstrate increased separation performance for various compounds in forward mode, including focused separation of highly volatile compounds at room temperature. Compared to NTGS, FTGC offers advantages such as a wider applicable temperature and compound volatility range, simple operation without auxiliary equipment, less dependence on environmental conditions, and better compactness. This stationary phase thickness gradient technique can be readily applied to a wide range of GC applications and can be used with stationary phases of any material or thickness, as long as a gradient can be generated. Furthermore, it is applicable to both capillary columns with regular circular cross-sections and microcolumns with rectangular cross-sections. For illustrative and descriptive purposes, the foregoing description of embodiments has been provided. This description is not intended to be exhaustive or limiting of this disclosure. Various elements or features of a particular embodiment are generally not limited to that particular embodiment, but are interchangeable and can be used in selected embodiments where applicable, even if not specifically shown or described. The same parts may also be varied in various ways. These variations should not be considered as departing from this disclosure, and all such modifications are intended to be included within the scope of this disclosure.

Claims (28)

1. A gas chromatographic apparatus, said gas chromatographic apparatus being used for peak focusing of one or more target analytes, said gas chromatographic apparatus comprising: A chromatographic column having an inlet and an outlet, wherein the inlet receives a sample, the sample comprising one or more target analytes exiting the column at the outlet; and A stationary phase is deposited within the chromatographic column and has a positive thickness gradient, wherein the stationary phase extends from the inlet to the outlet and has a first thickness at the inlet of the chromatographic column and a second thickness at the outlet of the chromatographic column, wherein the second thickness is at least 10% greater than the first thickness. 2. The gas chromatography apparatus according to claim 1, wherein the first thickness is greater than or equal to 10 nm to less than or equal to 10 micrometers, and the second thickness is greater than or equal to 30 nm to less than or equal to 30 micrometers. 3. The gas chromatography apparatus according to claim 1, wherein the second thickness is greater than or equal to the first thickness by at least 100%. 4. The gas chromatography apparatus according to claim 1, wherein the second thickness is greater than or equal to the first thickness by at least 300%. 5. The gas chromatography apparatus according to claim 1, wherein the chromatographic column is a micro gas chromatography column. 6. The gas chromatography apparatus according to claim 1, wherein the stationary phase comprises a siloxane polymer. 7. The gas chromatography apparatus according to claim 6, wherein the siloxane polymer comprises at least one alkyl or aryl group, the alkyl or aryl group comprising 1 to 30 carbon atoms. 8. The gas chromatography apparatus according to claim 1, wherein the cross-sectional shape of the chromatographic column is selected from the group consisting of: circular, elliptical, rectangular and triangular. 9. A peak focusing method in a gas chromatograph, the method comprising: Two or more target analytes are introduced into the inlet of a chromatographic column, the column comprising: a stationary phase deposited inside the column and having a positive thickness gradient, wherein the stationary phase extends from the inlet to the outlet and has a first thickness at the inlet of the column and a second thickness at the outlet of the column, wherein the second thickness is at least 10% greater than the first thickness; Separating the two or more target analytes in the chromatographic column; and The two or more target analytes are eluted from the outlet of the chromatographic column. 10. The method of claim 9, wherein the two or more target analytes are volatile organic compounds (VOCs). 11. The method of claim 9, wherein at least one of the two or more target analytes comprises an aromatic compound, and the total peak focusing efficiency for the aromatic compound is greater than or equal to 25%. 12. The method of claim 9, wherein at least one of the two or more target analytes comprises an alkane compound, and the total peak focusing rate for the alkane compound is greater than or equal to 10%. 13. The method of claim 9, wherein the first thickness is greater than or equal to 10 nm to less than or equal to 10 micrometers, and the second thickness is greater than or equal to 30 nm to less than or equal to 30 micrometers. 14. The method of claim 9, wherein the second thickness is greater than or equal to the first thickness by at least 300%. 15. The method according to claim 9, wherein the chromatographic column is a micro gas chromatography column. 16. The method of claim 9, wherein the stationary phase comprises a siloxane polymer, the siloxane polymer comprising at least one alkyl or aryl group, the alkyl or aryl group comprising 1 to 30 carbon atoms. 17. The method of claim 9, wherein the cross-sectional shape of the chromatographic column is selected from the group consisting of: circular, elliptical, rectangular and triangular. 18. A method for verifying peak focusing in a gas chromatograph, the method comprising: Forward operation is performed by introducing two or more target analytes into the inlet of a chromatographic column, the chromatographic column comprising: a stationary phase deposited inside the chromatographic column and having a positive thickness gradient, wherein the stationary phase extends from the inlet of the chromatographic column to the outlet and has a first thickness at the inlet of the chromatographic column and a second thickness at the outlet of the chromatographic column, wherein the second thickness is at least 10% greater than the first thickness; Separate the two or more target analytes in the chromatographic column; The two or more target analytes are eluted from the outlet of the chromatographic column; The reverse operation is performed by introducing two or more target analytes into the outlet of the chromatographic column, the column comprising a stationary phase; Separate the two or more target analytes in the chromatographic column; Elute the two or more target analytes from the inlet of the chromatographic column; and Compare the chromatographic resolutions from the forward operation and the reverse operation, wherein the peak focusing rates of at least one pair of corresponding peaks from the two target analytes are greater than 5%. 19. A method of manufacturing a gas chromatographic apparatus, the gas chromatographic apparatus having a chromatographic column having a positive thickness gradient, the method comprising: A precursor liquid is introduced into the chromatographic column, wherein the precursor liquid comprises a stationary phase precursor and a low-boiling-point solvent, the low-boiling-point solvent evaporating along the length of the chromatographic column to increase the concentration of the stationary phase precursor as it moves along the column; and The stationary phase precursor is reacted or crosslinked to form the positive thickness gradient stationary phase, which extends from the inlet of the chromatographic column to the outlet of the chromatographic column and has a first thickness at the inlet of the chromatographic column and a second thickness at the outlet of the chromatographic column, wherein the second thickness is at least 10% greater than the first thickness. 20. The method of claim 19, wherein the inner surface of the chromatographic column is silanized prior to the introduction of the precursor liquid. 21. The method of claim 20, wherein the silanization comprises passing a reactive silane in the gas phase through the chromatographic column. 22. The method of claim 19, wherein the chromatographic column includes an inlet and an outlet, and the introduction, reaction, or crosslinking comprises: dynamically coating the inner surface of the chromatographic column by partially filling the chromatographic column with the precursor liquid, applying pressure at the inlet to force the precursor liquid downward along the length of the chromatographic column, and applying a vacuum at the outlet to evaporate the low-boiling solvent. 23. The method of claim 19, wherein the first thickness is greater than or equal to 10 nm to less than or equal to 10 micrometers, and the second thickness is greater than or equal to 30 nm to less than or equal to 30 micrometers. 24. The method of claim 19, wherein the second thickness is greater than or equal to the first thickness by at least 100%. 25. The method of claim 19, wherein the second thickness is greater than or equal to the first thickness by at least 300%. 26. The method according to claim 19, wherein the chromatographic column is a micro gas chromatography column. 27. The method of claim 19, wherein the positive thickness gradient stationary phase comprises a siloxane polymer. 28. The method of claim 27, wherein the siloxane polymer comprises at least one alkyl or aryl group, the alkyl or aryl group comprising 1 to 30 carbon atoms.