CHEMICAL SENSORS WITH NON-COVALENT SURFACE MODIFICATION OF GRAPHENE

Abstract

Embodiments herein relate to chemical sensors, devices and systems including the same, and related methods. In an embodiment, a medical device is included. The medical device can include a graphene varactor. The graphene varactor can include a graphene layer and a self-assembled monolayer disposed on an outer surface of the graphene layer through π-π stacking interactions. The self-assembled monolayer can provide a Langmuir theta value of at least 0.9. The self-assembled monolayer can include polycyclic aromatic hydrocarbons, tetraphenylporphyrins or derivatives thereof, metallotetraphenylporphyrins, or aromatic cyclodextrins. Other embodiments are also included herein.

Description

FIELD

Embodiments herein relate to chemical sensors, devices and systems including the same, and related methods. More specifically, embodiments herein relate to chemical sensors based on the non-covalent surface modification of graphene.

BACKGROUND

The accurate detection of diseases can allow clinicians to provide appropriate therapeutic interventions. The early detection of diseases can lead to better treatment outcomes. Diseases can be detected using many different techniques including analyzing tissue samples, analyzing various bodily fluids, diagnostic scans, genetic sequencing, and the like.

Some disease states result in the production of specific chemical compounds. In some cases, volatile organic compounds (VOCs) released into a gaseous sample of a patient can be hallmarks of certain diseases. The detection of these compounds or differential sensing of the same can allow for the early detection of particular disease states.

SUMMARY

In a first aspect, a medical device is included. The medical device can include a graphene varactor. The graphene varactor can include a graphene layer and a self-assembled monolayer disposed on an outer surface of the graphene layer through π-π stacking interactions. The self-assembled monolayer can provide a Langmuir theta value of at least 0.9.

In a second aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the self-assembled monolayer can include one or more polycyclic aromatic hydrocarbons having 3 to 10 aromatic rings.

In a third aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the polycyclic aromatic hydrocarbons can include one or more of anthracene, benzoanthracene, phenanthrene, phenalene, naphthacene, benzanthracene, chrysene, pentacene, dibenzanthracene, triphenylene, pyrene, benzopyrene, picene, perylene, benzoperylene, pentaphene, pentacene, anthanthrene, coronene, ovalene, or derivatives thereof.

In a fourth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the polycyclic aromatic hydrocarbons can include one or more hydroxyl, carboxyl, ester, ammonium, amino, diethylamino, or boronic acid functional groups.

In a fifth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the self-assembled monolayer can include one or more of perbenzylated α-cyclodextrin, perbenzylated β-cyclodextrin, or perbenzylated γ-cyclodextrin, or derivatives thereof.

In a sixth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the self-assembled monolayer can include one or more tetraphenylporphyrins, or derivatives thereof.

In a seventh aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the self-assembled monolayer can include one or more metallotetraphenylporphyrins, or derivatives thereof.

In an eighth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the medical device can include a plurality of graphene varactors configured in an array.

In a ninth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the plurality of graphene varactors can be configured to detect the same analyte in a gaseous sample.

In a tenth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the plurality of graphene varactors can be configured to detect different analytes in a gaseous sample.

In an eleventh aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the self-assembled monolayer can provide a Langmuir theta value of at least 0.95.

In a twelfth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the self-assembled monolayer can provide a Langmuir theta value of at least 0.98.

In a thirteenth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the self-assembled monolayer can be homogeneous.

In a fourteenth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the self-assembled monolayer can be heterogeneous.

In a fifteenth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the medical device can include an endoscope, a bronchoscope, or tracheoscope.

In a sixteenth aspect, a method of modifying a surface of graphene to create a graphene varactor, the method is included. The method can include forming a self-assembled monolayer on an outer surface of a graphene layer of the graphene varactor through π-π stacking interactions. The method can include quantifying the extent of surface coverage of the self-assembled monolayer using contact angle goniometry, Raman spectroscopy, or X-Ray photoelectron spectroscopy. The method can include selecting derivatized graphene layers that exhibit a Langmuir theta value of at least 0.9.

In a seventeenth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the step of selecting derivatized graphene layers can include selecting derivatized graphene layers that exhibit a Langmuir theta value of at least 0.95.

In an eighteenth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the step of selecting derivatized graphene layers can include selecting derivatized graphene layers that exhibit a Langmuir theta value of at least 0.98.

In a nineteenth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the self-assembled monolayer can include one or more polycyclic aromatic hydrocarbons having 3 to 10 aromatic rings.

In a twentieth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the polycyclic aromatic hydrocarbons can include one or more of anthracene, benzoanthracene, phenanthrene, phenalene, naphthacene, benzanthracene, chrysene, pentacene, dibenzanthracene, triphenylene, pyrene, benzopyrene, picene, perylene, benzoperylene, pentaphene, pentacene, anthanthrene, coronene, ovalene, or derivatives thereof.

In a twenty-first aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the polycyclic aromatic hydrocarbons can include one or more hydroxyl, carboxyl, ester, ammonium, amino, diethylamino, or boronic acid functional groups.

In a twenty-second aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the self-assembled monolayer can include one or more of perbenzylated α-cyclodextrin, perbenzylated β-cyclodextrin, or perbenzylated γ-cyclodextrin, or derivatives thereof.

In a twenty-third aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the self-assembled monolayer can include one or more tetraphenylporphyrins, or derivatives thereof.

In a twenty-fourth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the self-assembled monolayer can include one or more metallotetraphenylporphyrins, or derivatives thereof.

In a twenty-fifth aspect, a method for detecting an analyte is included. The method can include collecting a gaseous sample from a patient and contacting the gaseous sample with one or more graphene varactors. Each graphene varactor can include a graphene layer and a self-assembled monolayer disposed on an outer surface of the graphene layer through π-π stacking interactions. The self-assembled monolayer can provide a Langmuir theta value of at least 0.9.

In a twenty-sixth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the method can further include measuring a differential response in a capacitance of the one or more graphene varactors due to the binding of one or more analytes present in the gaseous sample.

In a twenty-seventh aspect, a medical device is included. The medical device can include a chemical sensor element. The chemical sensor element can include a first measurement zone, where the first measurement zone can include a graphene varactor including a graphene layer and a self-assembled monolayer disposed on an outer surface of the graphene layer through π-π stacking interactions. The self-assembled monolayer can cover at least 90% of the surface of the graphene layer.

In a twenty-eighth aspect, in addition to one or more of the preceding or following aspects, or in the alternative to some aspects, the chemical sensor element can include a second measurement zone.

This summary is an overview of some of the teachings of the present application and is not intended to be an exclusive or exhaustive treatment of the present subject matter. Further details are found in the detailed description and appended claims. Other aspects will be apparent to persons skilled in the art upon reading and understanding the following detailed description and viewing the drawings that form a part thereof, each of which is not to be taken in a limiting sense. The scope herein is defined by the appended claims and their legal equivalents.

BRIEF DESCRIPTION OF THE FIGURES

Aspects may be more completely understood in connection with the following drawings, in which:

FIG. 1 is a schematic perspective view of a graphene varactor in accordance with various embodiments herein.

FIG. 2 is a schematic cross-sectional view of a portion of a graphene varactor in accordance with various embodiments herein.

FIG. 3 is a schematic top plan view of a chemical sensor element in accordance with various embodiments herein.

FIG. 4 is a schematic diagram of a portion of a measurement zone in accordance with various embodiments herein.

FIG. 5 is a circuit diagram of a passive sensor circuit and a portion of a reading circuit in accordance with various embodiments herein.

FIG. 6 is a schematic view of a system for sensing gaseous analytes in accordance with various embodiments herein.

FIG. 7 is a schematic view of a system for sensing gaseous analytes in accordance with various embodiments herein.

FIG. 8 is a schematic cross-sectional view of a portion of a chemical sensor element in accordance with various embodiments herein.

FIG. 9 is a representative plot of relative surface coverage as a function of concentration in accordance with various embodiments herein.

FIG. 10 is a representative plot of relative surface coverage as a function of the logarithm of concentration presented in FIG. 9, in accordance with various embodiments herein.

FIG. 11 is a representative high-resolution XPS spectrum and fits in accordance with various embodiments herein.

FIG. 12 is a representative high-resolution XPS spectrum and fits in accordance with various embodiments herein.

FIG. 13 is a representative high-resolution XPS spectrum and fits in accordance with various embodiments herein.

FIG. 14 is a representative high-resolution XPS spectrum and fits in accordance with various embodiments herein.

FIG. 15 is a representative plot of relative surface coverage as a function of concentration in accordance with various embodiments herein.

FIG. 16 is a representative plot of relative surface coverage as a function of the logarithm of concentration presented in FIG. 15, in accordance with various embodiments herein.

FIG. 17 is a reaction pathway for the synthesis of pyrene derivatives in accordance with various embodiments herein.

FIG. 18 is a reaction pathway for the synthesis of pyrene derivatives in accordance with various embodiments herein.

FIG. 19 is a reaction pathway for the synthesis of cyclodextrin derivatives in accordance with various embodiments herein.

FIG. 20 is a representative plot of relative surface coverage as a function of concentration in accordance with various embodiments herein.

FIG. 21 is a representative plot of relative surface coverage as a function of the logarithm of concentration presented in FIG. 20, in accordance with various embodiments herein.

FIG. 22 is a representative plot of relative surface coverage as a function of concentration in accordance with various embodiments herein.

FIG. 23 is a representative plot of relative surface coverage as a function of the logarithm of concentration presented in FIG. 22, in accordance with various embodiments herein.

FIG. 24 is a representative plot of relative surface coverage as a function of concentration in accordance with various embodiments herein.

FIG. 25 is a representative plot of relative surface coverage as a function of the logarithm of concentration presented in FIG. 24, in accordance with various embodiments herein.

FIG. 26 is a representative plot of relative surface coverage as a function of concentration in accordance with various embodiments herein.

FIG. 27 is a representative plot of relative surface coverage as a function of the logarithm of concentration presented in FIG. 26, in accordance with various embodiments herein.

FIG. 28 is a representative plot of Raman spectra in accordance with various embodiments herein.

While embodiments are susceptible to various modifications and alternative forms, specifics thereof have been shown by way of example and drawings, and will be described in detail. It should be understood, however, that the scope herein is not limited to the particular embodiments described. On the contrary, the intention is to cover modifications, equivalents, and alternatives falling within the spirit and scope herein.

DETAILED DESCRIPTION

Embodiments herein relate to chemical sensors, medical devices and systems including the same, and related methods for detecting chemical compounds in gaseous samples, such as, but not limited to, the breath of a patient. In some embodiments, the chemical sensors herein can be based on the non-covalent surface modification of graphene.

Graphene is a form of carbon containing a single layer of carbon atoms in a hexagonal lattice. Graphene has a high strength and stability due to its tightly packed sp² hybridized orbitals, where each carbon atom forms one sigma (σ) bond each with its three neighboring carbon atoms and has one p orbital projected out of the hexagonal plane. The p orbitals of the hexagonal lattice can hybridize to form a π band suitable for non-covalent π-π stacking interactions with other π-electron rich molecules.

The non-covalent functionalization of graphene with a self-assembled monolayer does not significantly affect the atomic structure of graphene, and provides a stable graphene-based sensor with high sensitivity towards a number of volatile organic compounds (VOCs) in the parts-per-billion (ppb) or parts-per-million (ppm) levels. As such, the embodiments herein can be used to detect VOCs and/or differential binding patterns of the same that, in turn, can be used to identify disease states.

Referring now to FIG. 1, a schematic view of a graphene-based variable capacitor (or graphene varactor) 100 is shown in accordance with the embodiments herein. It will be appreciated that graphene varactors can be prepared in various ways with various geometries, and that the graphene varactor shown in FIG. 1 is just one example in accordance with the embodiments herein.

Graphene varactor 100 can include an insulator layer 102, a gate electrode 104 (or “gate contact”), a dielectric layer (not shown in FIG. 1), one or more graphene layers, such as graphene layers 108a and 108b, and a contact electrode 110 (or “graphene contact”). In some embodiments, the graphene layer(s) 108a-b can be contiguous, while in other embodiments the graphene layer(s) 108a-b can be non-contiguous. Gate electrode 104 can be deposited within one or more depressions formed in insulator layer 102. Insulator layer 102 can be formed from an insulative material such as silicon dioxide, formed on a silicon substrate (wafer), and the like. Gate electrode 104 can be formed by an electrically conductive material such as chromium, copper, gold, silver, tungsten, aluminum, titanium, palladium, platinum, iridium, and any combinations or alloys thereof, which can be deposited on top of or embedded within the insulator layer 102. The dielectric layer can be disposed on a surface of the insulator layer 102 and the gate electrode 104. The graphene layer(s) 108a-b can be disposed on the dielectric layer. The dielectric layer will be discussed in more detail below in reference to FIG. 2.

Graphene varactor 100 includes eight gate electrode fingers 106a-106h. It will be appreciated that while graphene varactor 100 shows eight gate electrode fingers 106a-106h, any number of gate electrode finger configurations can be contemplated. In some embodiments, an individual graphene varactor can include fewer than eight gate electrode fingers. In some embodiments, an individual graphene varactor can include more than eight gate electrode fingers. In other embodiments, an individual graphene varactor can include two gate electrode fingers. In some embodiments, an individual graphene varactor can include 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more gate electrode fingers.

Graphene varactor 100 can include one or more contact electrodes 110 disposed on portions of the graphene layers 108a and 108b. Contact electrode 110 can be formed from an electrically conductive material such as chromium, copper, gold, silver, tungsten, aluminum, titanium, palladium, platinum, iridium, and any combinations or alloys thereof. Further aspects of exemplary graphene varactors can be found in U.S. Pat. No. 9,513,244, the content of which is herein incorporated by reference in its entirety.

The graphene varactors described herein can include those in which a single graphene layer has been surface-modified through non-covalent π-π stacking interactions between graphene and π-electron-rich molecules, such as, for example, pyrene, pyrene derivatives, and other compounds with aryl groups. In some embodiments, the surface of a single graphene layer can be surface-modified through non-covalent π-π stacking interactions between graphene and any one of a number of cyclodextrins and derivatives thereof. In some embodiments, the surface of a single graphene layer can be surface-modified through non-covalent π-π stacking interactions between graphene and any one of a number of tetraphenylporphyrins and derivatives thereof. Details regarding the graphene varactors and π-electron-rich molecules suitable for use herein will be discussed more fully below.

Referring now to FIG. 2, a schematic cross-sectional view of a portion of a graphene varactor 200 is shown in accordance with various embodiments herein. The graphene varactor 200 can include an insulator layer 102 and a gate electrode 104 recessed into the insulator layer 102. The gate electrode 104 can be formed by depositing an electrically conductive material in the depression in the insulator layer 102, as discussed above in reference to FIG. 1. A dielectric layer 202 can be formed on a surface of the insulator layer 102 and the gate electrode 104. In some examples, the dielectric layer 202 can be formed of a material, such as, silicon dioxide, aluminum oxide, hafnium dioxide, zirconium dioxide, hafnium silicate, or zirconium silicate.

The graphene varactor 200 can include a single graphene layer 204 that can be disposed on a surface of the dielectric layer 202. The graphene layer 204 can be surface-modified with a self-assembled monolayer 206. The self-assembled monolayer 206 can be formed of a homogenous population of n-electron-rich molecules disposed on an outer surface of the graphene layer 204 through non-covalent π-π stacking interactions. Exemplary π-electron-rich molecules are described more fully below. The self-assembled monolayer 206 can provide at least 90% surface coverage (by area) of the graphene layer 204. In some embodiments, the self-assembled monolayer 206 can provide at least 95% surface coverage of the graphene layer 204. In other embodiments, the self-assembled monolayer 206 can provide at least 98% surface coverage of the graphene layer 204.

In some embodiments, the self-assembled monolayer can provide at least 50%, 60%, 70%, 80%, 81%, 82%, 83%, 84%, 85%, 86%, 87%, 88%, 89%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, or 100% surface coverage (by area) of the graphene layer. It will be appreciated that the self-assembled monolayer can provide surface coverage falling within a range wherein any of the forgoing percentages can serve as the lower or upper bound of the range, provided that the lower bound of the range is a value less than the upper bound of the range.

In some embodiments, it will be appreciated that the self-assembly of π-electron-rich molecules on the surface of the graphene layer can include the self-assembly into more than a monolayer, such as a multilayer. Multilayers can be detected and quantified by techniques such as scanning tunneling microscopy (STM) and other scanning probe microscopies. References herein to a percentage of coverage greater than 100% shall refer to the circumstance where a portion of the surface area is covered by more than a monolayer, such as covered by two, three or potentially more layers of the compound used. Thus, a reference to 105% coverage herein shall indicate that approximately 5% of the surface area includes more than monolayer coverage over the graphene layer. In some embodiments, graphene surfaces can include 101%, 102%, 103%, 104%, 105%, 110%, 120%, 130%, 140%, 150%, or 175% surface coverage of the graphene layer. It will be appreciated that multilayer surface coverage of the graphene layer can fall within a range of surface coverages, wherein any of the forgoing percentages can serve as the lower or upper bound of the range, provided that the lower bound of the range is a value less than the upper bound of the range. For example, ranges of coverage can include, but are not limited to, 50% to 150% by surface area, 80% to 120% by surface area, 90% to 110%, or 99% to 120% by surface area.

In some embodiments, the self-assembled monolayers suitable for use herein can provide coverage of the graphene surface with a monolayer as quantified by the Langmuir theta value of at least some minimum threshold value, but avoid covering the majority of the surface of the graphene with a multilayer thicker than a monolayer. Details about the Langmuir theta values and determination of thereof for a particular self-assembled monolayer using Langmuir adsorption theory is described more fully below. In some embodiments, the self-assembled monolayers suitable for use herein provide a Langmuir theta value of at least 0.95. In some embodiments, the self-assembled monolayers suitable for use herein provide a Langmuir theta value of at least 0.98. In some embodiments, the self-assembled monolayers can provide a Langmuir theta value of at least 0.85, 0.86, 0.87, 0.88, 0.89, 0.90, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99, or 1.0. It will be appreciated that the self-assembled monolayer can provide a range of Langmuir theta values, wherein any of the forgoing Langmuir theta values can serve as the lower or upper bound of the range, provided that the lower bound of the range is a value less than the upper bound of the range.

Referring now to FIG. 3, a schematic top plan view of a chemical sensor element 300 is shown in accordance with various embodiments herein. The chemical sensor element 300 can include a substrate 302. It will be appreciated that the substrate can be formed from many different materials. By way of example, the substrate can be formed from silicon, glass, quartz, sapphire, polymers, metals, glasses, ceramics, cellulosic materials, composites, metal oxides, and the like. The thickness of the substrate can vary. In some embodiments, the substrate has sufficient structural integrity to be handled without undue flexure that could damage components thereon. In some embodiments, the substrate can have a thickness of about 0.05 mm to about 5 mm. The length and width of the substrate can also vary. In some embodiments, the length (or major axis) can be from about 0.2 cm to about 10 cm. In some embodiments, the length (or major axis) can be from about 20 μm to about 1 cm. In some embodiments, the width (perpendicular to the major axis) can be from about 0.2 cm to about 8 cm. In some embodiments, the width (perpendicular to the major axis) can be from about 20 μm to about 0.8 cm. In some embodiments, the graphene-based chemical sensor can be disposable.

A first measurement zone 304 can be disposed on the substrate 302. In some embodiments, the first measurement zone 304 can define a portion of a first gas flow path. The first measurement zone (or gas sample zone) 304 can include a plurality of discrete graphene-based variable capacitors (or graphene varactors) that can sense analytes in a gaseous sample, such as a breath sample. A second measurement zone (or environment sample zone) 306, separate from the first measurement zone 304, can also be disposed on the substrate 302. The second measurement zone 306 can also include a plurality of discrete graphene varactors. In some embodiments, the second measurement zone 306 can include the same (in type and/or number) discrete graphene varactors that are within the first measurement zone 304. In some embodiments, the second measurement zone 306 can include only a subset of the discrete graphene varactors that are within the first measurement zone 304. In operation, the data gathered from the first measurement zone, which can be reflective of the gaseous sample analyzed, can be corrected or normalized based on the data gathered from the second measurement zone, which can be reflective of analytes present in the environment.

In some embodiments, a third measurement zone (drift control or witness zone) 308 can also be disposed on the substrate. The third measurement zone 308 can include a plurality of discrete graphene varactors. In some embodiments, the third measurement zone 308 can include the same (in type and/or number) discrete graphene varactors that are within the first measurement zone 304. In some embodiments, the third measurement zone 308 can include only a subset of the discrete graphene varactors that are within the first measurement zone 304. In some embodiments, the third measurement zone 308 can include discrete graphene varactors that are different than those of the first measurement zone 304 and the second measurement zone 306. Aspects of the third measurement zone are described in greater detail below.

The first measurement zone, the second measurement zone, and the third measurement zone can be the same size or can be of different sizes. The chemical sensor element 300 can also include a component 310 to store reference data. The component 310 to store reference data can be an electronic data storage device, an optical data storage device, a printed data storage device (such as a printed code), or the like. The reference data can include, but is not limited to, data regarding the third measurement zone (described in greater detail below).

In some embodiments, chemical sensor elements embodied herein can include electrical contacts (not shown) that can be used to provide power to components on the chemical sensor element 300 and/or can be used to read data regarding the measurement zones and/or data from the stored in component 310. However, in other embodiments there are no external electrical contacts on the chemical sensor element 300.

It will be appreciated that the chemical sensor elements embodied herein can include those that are compatible with passive wireless sensing. A schematic diagram of a passive sensor circuit 502 and a portion of a reading circuit 522 is shown in FIG. 5 and discussed in more detail below. In the passive wireless sensing arrangement, the graphene varactor(s) can be integrated with an inductor such that one terminal of the graphene varactor contacts one end of the inductor, and a second terminal of the graphene varactor contacts a second terminal of the inductor. In some embodiments, the inductor can be located on the same substrate as the graphene varactor, while in other embodiments, the inductor could be located in an off-chip location.

Referring now to FIG. 4, a schematic diagram of a portion of a measurement zone 400 is shown in accordance with various embodiments herein. A plurality of discrete graphene varactors 402 can be disposed within the measurement zone 400 in an array. In some embodiments, a chemical sensor element can include a plurality of graphene varactors configured in an array within a measurement zone. In some embodiments, the plurality of graphene varactors can be identical, while in other embodiments the plurality of graphene varactors can be different from one another.

In some embodiments, the discrete graphene varactors can be heterogeneous in that they are all different from one another in terms of their binding behavior or specificity with regard to a particular analyte. In some embodiments, some discrete graphene varactors can be duplicated for validation purposes, but are otherwise heterogeneous from other discrete graphene varactors. Yet in other embodiments, the discrete graphene varactors can be homogeneous. While the discrete graphene varactors 402 of FIG. 4 are shown as boxes organized into a grid, it will be appreciated that the discrete graphene varactors can take on many different shapes (including, but not limited to, various polygons, circles, ovals, irregular shapes, and the like) and, in turn, the groups of discrete graphene varactors can be arranged into many different patterns (including, but not limited to, star patterns, zig-zag patterns, radial patterns, symbolic patterns, and the like).

In some embodiments, the order of specific discrete graphene varactors 402 across the length 412 and width 414 of the measurement zone can be substantially random. In other embodiments, the order can be specific. For example, in some embodiments, a measurement zone can be ordered so that the specific discrete graphene varactors 402 for analytes having a lower molecular weight are located farther away from the incoming gas flow relative to specific discrete graphene varactors 402 for analytes having a higher molecular weight which are located closer to the incoming gas flow. As such, chromatographic effects which may serve to provide separation between chemical compounds of different molecular weight can be taken advantage of to provide for optimal binding of chemical compounds to corresponding discrete graphene varactors.

The number of discrete graphene varactors within a particular measurement zone can be from about 1 to about 100,000. In some embodiments, the number of discrete graphene varactors can be from about 1 to about 10,000. In some embodiments, the number of discrete graphene varactors can be from about 1 to about 1,000. In some embodiments, the number of discrete graphene varactors can be from about 2 to about 500. In some embodiments, the number of discrete graphene varactors can be from about 10 to about 500. In some embodiments, the number of discrete graphene varactors can be from about 50 to about 500. In some embodiments, the number of discrete graphene varactors can be from about 1 to about 250. In some embodiments, the number of discrete graphene varactors can be from about 1 to about 50.

Each of the discrete graphene varactors suitable for use herein can include at least a portion of one or more electrical circuits. By way of example, in some embodiments, each of the discrete graphene varactors can include one or more passive electrical circuits. In some embodiments, the graphene varactors can be included such that they are integrated directly on an electronic circuit. In some embodiments, the graphene varactors can be included such that they are wafer bonded to the circuit. In some embodiments, the graphene varactors can include integrated readout electronics, such as a readout integrated circuit (ROIC). The electrical properties of the electrical circuit, including resistance or capacitance, can change upon binding, such as specific and/or non-specific binding, with a component from a gas sample.

Referring now to FIG. 5, a schematic diagram of a passive sensor circuit 502 and a portion of a reading circuit 522 is shown in accordance with various aspects herein. In some embodiments, the passive sensor circuit 502 can include a metal-oxide-graphene varactor 504 (wherein RS represents the series resistance and CG represents the varactor capacitor) coupled to an inductor 510. Graphene varactors can be prepared in various ways and with various geometries. By way of example, in some aspects, a gate electrode can be recessed into an insulator layer as shown as gate electrode 104 in FIG. 1. A gate electrode can be formed by etching a depression into the insulator layer and then depositing an electrically conductive material in the depression to form the gate electrode. A dielectric layer can be formed on a surface of the insulator layer and the gate electrode. In some examples, the dielectric layer can be formed of a metal oxide such as, aluminum oxide, hafnium dioxide, zirconium dioxide, silicon dioxide, or of another material such as hafnium silicate or zirconium silicate. A surface-modified graphene layer can be disposed on the dielectric layer. Contact electrodes can also be disposed on a surface of the surface-modified graphene layer, also shown in FIG. 1 as contact electrode 110.

Further aspects of exemplary graphene varactor construction can be found in U.S. Pat. No. 9,513,244, the content of which is herein incorporated by reference in its entirety.

In various embodiments, the functionalized graphene layer (e.g., functionalized to include analyte binding receptors), which is part of the graphene varactor and thus part of a sensor circuit, such as a passive sensor circuit, is exposed to the gas sample flowing over the surface of the measurement zone. The passive sensor circuit 502 can also include an inductor 510. In some embodiments, only a single varactor is included with each passive sensor circuit 502. In other embodiments, multiple varactors are included, such as in parallel, with each passive sensor circuit 502.

In the passive sensor circuit 502, the capacitance of the electrical circuit changes upon binding of an analyte in the gas sample and the graphene varactor. The passive sensor circuit 502 can function as an LRC resonator circuit, wherein the resonant frequency of the LRC resonator circuit changes upon binding with a component from a gas sample.

The reading circuit 522 can be used to detect the electrical properties of the passive sensor circuit 502. By way of example, the reading circuit 522 can be used to detect the resonant frequency of the LRC resonator circuit and/or changes in the same. In some embodiments, the reading circuit 522 can include a reading coil having a resistance 524 and an inductance 526. When the sensor-side LRC circuit is at its resonant frequency, a plot of the phase of the impedance of the reading circuit versus the frequency has a minimum (or phase dip frequency). Sensing can occur when the varactor capacitance varies in response to binding of analytes, which changes the resonant frequency, and/or the value of the phase dip frequency.

Referring now to FIG. 6, a schematic view of a system 600 for sensing gaseous analytes in accordance with various embodiments herein is shown. The system 600 can include a housing 618. The system 600 can include a mouthpiece 602 into which a subject to be evaluated can blow a breath sample. The gaseous breath sample can pass through an inflow conduit 604 and pass through an evaluation sample (patient sample) input port 606. The system 600 can also include a control sample (environment) input port 608. The system 600 can also include a sensor element chamber 610, into which disposable sensor elements can be placed. The system 600 can also include a display screen 614 and a user input device 616, such as a keyboard. The system can also include a gas outflow port 612. The system 600 can also include flow sensors in fluid communication with the gas flow associated with one or more of the evaluation sample input port 606 and control sample input port 608. It will be appreciated that many different types of flow sensors can be used. In some embodiments, a hot-wire anemometer can be used to measure the flow of air. In some embodiments, the system can include a CO₂ sensor in fluid communication with the gas flow associated with one or more of the evaluation sample input port 606 and control sample input port 608.

In various embodiments, the system 600 can also include other functional components. By way of example, the system 600 can include a humidity control module 640 and/or a temperature control module 642. The humidity control module can be in fluid communication with the gas flow associated with one or more of the evaluation sample input port 606 and control sample input port 608 in order to adjust the humidity of one or both gas flow streams in order to make the relative humidity of the two streams substantially the same in order to prevent an adverse impact on the readings obtained by the system. The temperature control module can be in fluid communication with the gas flow associated with one or more of the evaluation sample input port 606 and control sample input port 608 in order to adjust the temperature of one or both gas flow streams in order to make the temperature of the two streams substantially the same in order to prevent an adverse impact on the readings obtained by the system. By way of example, the air flowing into the control sample input port can be brought up to 37 degrees Celsius or higher in order to match or exceed the temperature of air coming from a patient. The humidity control module and the temperature control module can be upstream from the input ports, within the input ports, or downstream from the input ports in the housing 618 of the system 600. In some embodiments, the humidity control module 640 and the temperature control module 642 can be integrated.

In some embodiments (not shown), the control sample input port 608 of system 600 can also be connected to a mouthpiece 602. In some embodiments, the mouthpiece 602 can include a switching airflow valve such that when the patient is drawing in breath, air flows from the control sample input port 608 to the mouthpiece, and the system is configured so that this causes ambient air to flow across the appropriate control measurement zone (such as the second measurement zone). Then when the patient exhales, the switching airflow valve can switch so that a breath sample from the patient flows from the mouthpiece 602 through the inflow conduit 604 and into the evaluation sample input port 606 and across the appropriate sample (patient sample) measurement zone (such as the first measurement zone) on the disposable sensor element.

In an embodiment, a method of making a chemical sensor element is included. The method can include depositing one or more measurement zones onto a substrate. The method can further include depositing a plurality of discrete graphene varactors within the measurement zones on the substrate. The method can include generating one or more discrete graphene varactors by modifying a surface of a graphene layer with π-electron-rich molecules to form a self-assembled monolayer on an outer surface of the graphene layer through π-π stacking interactions. The method can include quantifying the extent of surface coverage of the self-assembled monolayer using contact angle goniometry, Raman spectroscopy, or X-Ray photoelectron spectroscopy. The method can include selecting derivatized graphene layers that exhibit a Langmuir theta value of at least 0.9, as will be discussed more fully below. The method can further include depositing a component to store reference data onto the substrate. In some embodiments, the measurement zones can all be placed on the same side of the substrate. In other embodiments, the measurement zones can be placed onto different sides of the substrate.

In an embodiment, a method of assaying one or more gas samples is included. The method can include inserting a chemical sensor element into a sensing machine. The chemical sensor element can include a substrate and a first measurement zone comprising a plurality of discrete graphene varactors. The first measurement zone can define a portion of a first gas flow path. The chemical sensor element can further include a second measurement zone separate from the first measurement zone. The second measurement zone can also include a plurality of discrete graphene varactors. The second measurement zone can be disposed outside of the first gas flow path.

The method can further include prompting a subject to blow air into the sensing machine to follow the first gas flow path. In some embodiments, the CO₂ content of the air from the subject is monitored and sampling with the disposable sensor element is conducted during the plateau of CO₂ content, as it is believed that the air originating from the alveoli of the patient has the richest content of chemical compounds for analysis, such as volatile organic compounds. In some embodiments, the method can include monitoring the total mass flow of the breath sample and the control (or environmental) air sample using flow sensors. The method can further include interrogating the discrete graphene varactors to determine their analyte binding status. The method can further include discarding the disposable sensor element upon completion of sampling.

Referring now to FIG. 7, a schematic view of a system 700 for sensing gaseous analytes in accordance with various embodiments herein is shown. In this embodiment, the system is in a hand-held format. The system 700 can include a housing 718. The system 700 can include a mouthpiece 702 into which a subject to be evaluated can blow a breath sample. The system 700 can also include a display screen 714 and a user input device 716, such as a keyboard. The system can also include a gas outflow port 712. The system can also include various other components such as those described with reference to FIG. 6 above.

In some embodiments, one of the measurement zones can be configured to indicate changes (or drift) in the chemical sensor element that could occur as a result of aging and exposure to varying conditions (such as heat exposure, light exposure, molecular oxygen exposure, humidity exposure, etc.) during storage and handling prior to use. In some embodiments, the third measurement zone can be configured for this purpose.

Referring now to FIG. 8, a schematic cross-sectional view is shown of a portion of a chemical sensor element 800 in accordance with various embodiments herein. The chemical sensor element 800 can include a substrate 802 and a discrete graphene varactor 804 disposed thereon that is part of a measurement zone. Optionally, in some embodiments the discrete graphene varactor 804 can be encapsulated by an inert material 806, such as nitrogen gas, or an inert liquid or solid. In this manner, the discrete graphene varactor 804 for the third measurement zone can be shielded from contact with gas samples and can therefore be used as a control or reference to specifically control for sensor drift which may occur between the time of manufacturing and the time of use of the disposable sensor element. In some embodiments, such as in the case of the use of an inert gas or liquid, the discrete binding detector can also include a barrier layer 808, which can be a layer of a polymeric material, a foil, or the like. In some cases, the barrier layer 808 can be removed just prior to use.

In an embodiment, method for detecting one or more analytes is included. The method can include collecting a gaseous sample from a patient. In some embodiments the gaseous sample can include exhaled breath. In other embodiments, the gaseous sample can include breath removed from the lungs of a patient via a catheter or other similar extraction device. In some embodiments, the extraction device can include an endoscope, a bronchoscope, or tracheoscope. The method can also include contacting a graphene varactor with the gaseous sample, where the graphene varactor includes a graphene layer and a self-assembled monolayer disposed on an outer surface of the graphene layer through π-π stacking interactions. In some embodiments, the self-assembled monolayer can provide a Langmuir theta value of at least 0.9. Langmuir theta values will be discussed more fully below. In some embodiments, the method can include measuring a differential response in a capacitance of the graphene reactor due to the binding of one or more analytes present in the gaseous sample, which in turn can be used to identify disease states.

Graphene Varactors

The graphene varactors described herein can be used to sense one or more analytes in a gaseous sample, such as, for example, the breath of a patient. Graphene varactors embodied herein can exhibit a high sensitivity for volatile organic compounds (VOCs) found in gaseous samples at or near parts-per-million (ppm) or parts-per-billion (ppb) levels. The adsorption of VOCs onto the surface of graphene varactors can change the resistance, capacitance, or quantum capacitance of such devices, and can be used to detect the VOCs and/or patterns of binding by the same that, in turn, can be used to identify disease states such as cancer, cardiac diseases, infections, multiple sclerosis, Alzheimer's disease, Parkinson's disease, and the like. The graphene varactors can be used to detect individual analytes in gas mixtures, as well as patterns of responses in highly complex mixtures. In some embodiments, one or more graphene varactors can be included to detect the same analyte in a gaseous sample. In some embodiments, one or more graphene varactors can be included to detect different analytes in a gaseous sample. In some embodiments, one or more graphene varactors can be included to detect a multitude of analytes in a gaseous sample.

An exemplary graphene varactor can include a graphene layer and a self-assembled monolayer disposed on an outer surface of the graphene layer, interacting with the latter through π-π stacking interactions, as shown and discussed above in reference to FIG. 2. The self-assembled monolayers suitable for use herein can provide a Langmuir theta value of at least 0.9. Determination of the Langmuir theta value for a particular self-assembled monolayer using Langmuir adsorption theory is described more fully below. In some embodiments, the self-assembled monolayers suitable for use herein provide a Langmuir theta value of at least 0.95. In some embodiments, the self-assembled monolayers suitable for use herein provide a Langmuir theta value of at least 0.98.

The graphene varactors described herein can include those in which a single graphene layer has been surface-modified through non-covalent π-π stacking interactions between the graphene layer and π-electron-rich molecules.

One exemplary class of π-electron electron-rich molecules includes polycyclic aromatic hydrocarbons. Examples of polycyclic aromatic hydrocarbons suitable for use in the graphene varactors described herein can include, but are not limited to those having from 3 to 10 aromatic rings. For example, polycyclic aromatic hydrocarbons having from 3 to 10 aromatic rings can include anthracene, benzoanthracene, phenanthrene, phenalene, naphthacene, benzanthracene, chrysene, pentacene, dibenzanthracene, triphenylene, pyrene, benzopyrene, picene, perylene, benzoperylene, pentaphene, pentacene, anthanthrene, coronene, or ovalene. In some embodiments, the polycyclic aromatic hydrocarbons can further include derivatives thereof, including those having one or more of a hydroxyl, carboxyl, ester, ammonium, amino, diethylamino, or boronic acid functional group. In some embodiments, polycyclic aromatic hydrocarbons having from 10 to 20 aromatic rings are also contemplated.

As described herein, a polycyclic aromatic hydrocarbon can be described by the formula:

where X¹ can be any substitution, including, but not limited to, any linear, branched, or cyclic C₁-C₁₀ alkyl covalently bound directly to the base aromatic ring structure, —H, —R¹OH, —R²COOH, —R³COOR⁴, ≤R⁵NH₃⁺, —R⁶NH₂, —R⁷NR⁸, —R⁹NR¹⁰R¹¹⁺, —R¹²B(OH)₂, or any combination thereof; n is any integer from 3 to 10, from 3 to 15, or from 3 to 20; and R¹ through R¹² can include, but are not to be limited to, any linear, branched, or cyclic C₁-C₁₀ alkyl, or a combination thereof, or absent such that the remaining portion of the functional group is covalently bound directly to one or more carbon atoms of the base aromatic ring structure.

In some embodiments, the polycyclic aromatic hydrocarbon can include pyrene and pyrene derivatives described by the formula:

where X¹, X², X³, and X⁴ can be any substitution, including, but not limited to, any linear, branched, or cyclic C₁-C₁₀ alkyl covalently bound directly to the base aromatic ring structure, —H, —R¹OH, —R²COOH, —R³COOR⁴, —R⁵NH₃⁺, —R⁶NH₂, —R⁷NR⁸, —R⁹NR¹⁰R¹¹⁺, —R¹²B(OH)₂, or any combination thereof; and R¹ through R¹² can include, but are not to be limited to, any linear, branched, or cyclic C₁-C₁₀ alkyl, or a combination thereof, or absent such that the remaining portion of the functional group is covalently bound directly to one or more carbon atoms of the base aromatic ring structure. In some embodiments, the pyrene (Pyr) derivatives suitable for use herein include, but are not to be limited to, Pyr-CH₂OH, Pyr-CH₂COOH, Pyr-CH₂COOCH₃, Pyr-CH₂NH₂, Pyr-CH₂NH₂.HCl, Pyr-CH₂N(CH₂CH₃)₂, and Pyr-B(OH)₂.

In some embodiments, the functional groups suitable for use herein can include polar functional groups containing at least one oxygen atom, including but not limited to —R¹OH, —R²COOH, and —R³COOR⁴, or any combination thereof, where R¹, R², R³, and R⁴, can include, but are not to be limited to, any linear, branched, or cyclic C₁-C₁₀ alkyl or combination thereof, or absent such that the remaining portion of the functional group is covalently bound directly to one or more carbon atoms of the base aromatic ring structure. In some embodiments, the functional groups suitable for use herein can include polar functional groups containing at least one nitrogen atom, including but not limited to —R⁵NH₃⁺, —R⁶NH₂, —R⁷NR⁸, —R⁹NR¹⁰R¹¹⁺, —R¹²B(OH)₂, or any combination thereof, where R⁵, R⁶, R⁷, R⁸, R⁹, R¹⁰, R¹¹, and R¹² can include, but are not to be limited to, any linear, branched, or cyclic C₁-C₁₀ alkyl or combination thereof, or absent such that the remaining portion of the functional group is covalently bound directly to one or more carbon atoms of the base aromatic ring structure. In other embodiments, the functional group can include combinations of polar functional groups containing at least one oxygen atom and polar functional groups containing at least one nitrogen atom.

Another class of π-electron electron-rich molecules suitable for modifying a surface of graphene through non-covalent π-π stacking interactions includes molecules with multiple aromatic groups, such as the polycyclic groups mentioned above, and also aromatic groups with one or more aromatic rings, such as phenyl, benzyl, or naphthyl groups, and their derivatives. Examples of such molecules for use herein are aromatic cyclodextrins, such as benzylated cyclodextrins and include, but are not limited to α-, β- and γ-cyclodextrins derivatives. In some embodiments, the cyclodextrins can include perbenzylated α-, β- and γ-cyclodextrins. In some embodiments, the cyclodextrins can include partially benzylated α-, β- and γ-cyclodextrins.

In some embodiments, the perbenzylated cyclodextrins and their derivatives can include, but not be limited to those having the formula:

where n can be an integer from 5-10, or any integer from 6 to 8, and X can include, but is not be limited to, any combination of —H, hydroxyl, amino, any linear, branched, or cyclic C₁-C₁₀ alcohol, any linear, branched, or cyclic C₁-C₁₀ amines, phenyl, benzyl, or naphthyl groups, and any of their derivatives, provided that each repeating unit in the structure above includes at least one X that is an aromatic functional group. In some embodiments, the presence of one or more hydroxyl groups or amino groups can contribute to hydrogen bonding between the cyclodextrin molecules and the graphene layer.

Another class of π-electron electron-rich molecules suitable for modifying a surface of graphene through non-covalent π-π stacking interactions includes tetraphenylporphyrin (TPP), and derivatives thereof. A structure for tetraphenylporphyrin is as follows:

In various embodiments herein, tetraphenylporphyrins can be derivatized with various functional groups. As such, in some embodiments, a tetraphenylporphyrin here can be described by the formula:

where n can be any integer from 1 to 5; m can be 1 or 2; R¹ through R⁸ can be any substitution, including, but not limited to, —H; —X, where X includes any halogen atom; —R⁹; —R¹⁰OH; —R¹¹COOH; —R¹²COOR¹³; —R¹⁴OR¹⁵; —R¹⁶COH; —R¹⁷COR¹⁸; —R¹⁹NH₃⁺; —R²⁰NH₂; —R²¹NR²²; —R²³NR²⁴R²⁵⁺; —R²⁶X or —R²⁷COX, where X can be any halogen atom; —R²⁸SH or any combination thereof; and R⁹ through R²⁸ can include, but are not to be limited to, any linear or branched C₁-C₁₂ alkyl, C₁-C₁₂ alkenyl, C₁-C₁₂ alkynyl, or any combination thereof, or absent such that the remaining portion of the functional group is covalently bound directly to one or more carbon atoms of the base aromatic ring structure.

In some embodiments, the tetraphenylporphyrin is a metallotetraphenylporphyrin. A structure for a metallotetraphenylporphyrins is as follows:

In various embodiments herein, metallotetraphenylporphyrin can be derivatized with various functional groups. As such, in some embodiments, a metallotetraphenylporphyrin can be described by the formula:

where M is any metal atom, including but not limited to aluminum, calcium, magnesium, manganese, iron, cobalt, nickel, zinc, ruthenium, palladium, or derivatives thereof; where n can be any integer from 1 to 5; m can be 1 or 2; R¹ through R⁸ can be any substitution, including, but not limited to, —H; —X, where X includes any halogen atom; —R⁹; —R¹⁰OH; —R¹¹COOH; —R¹²COOR¹³; —R¹⁴OR¹⁵; —R¹⁶COH; —R¹⁷COR¹⁸; —R¹⁹NH₃⁺; —R²⁰NH₂; —R²¹NR²²; —R²³NR²⁴R²⁵⁺; —R²⁶X or —R²⁷COX, where X can be any halogen atom; —R²⁸SH or any combination thereof; and R⁹, through R²⁸ can include, but not be limited to, any linear or branched C₁-C₁₂ alkyl, C₁-C₁₂ alkenyl, C₁-C₁₂ alkynyl, or any combination thereof, or absent such that the remaining portion of the functional group is covalently bound directly to one or more carbon atoms of the base aromatic ring structure.

The self-assembled monolayers can include those that are homogeneous and those that are heterogeneous (e.g., they can include a layer of more than one type of compound). In some embodiments a self-assembled monolayer can be monofunctional and in other embodiments a self-assembled monolayer can be bifunctional, trifunctional, etc. In some embodiments, the self-assembled monolayer can include at least about 5%, 10%, 15%, 20%, 25%, 30%, 40%, or 50% of a secondary compound (or an amount falling within a range between any of these amounts), which can be any of the compounds described herein, but different than a primary compound which accounts for the substantial balance of the coverage of the graphene layer.

In some embodiments, the graphene layer can be disposed on the surface of a substrate. Substrate materials suitable for use herein can include metals such as copper, nickel, ruthenium, platinum, iridium, and the like, and metal oxides such as copper oxide, zinc oxide, magnesium oxide, and the like. Substrate materials can also include silicon, quartz, sapphire, glass, ceramic, polymers, etc.

Further aspects of exemplary graphene varactors can be found in U.S. Pat. No. 9,513,244, the content of which is herein incorporated by reference in its entirety.

Contact Angle Goniometry

Contact angle goniometry can be used to determine the wettability of a solid surface by a liquid. Wettability, or wetting, can result from the intermolecular forces at the contact area between a liquid and a solid surface. The degree of wetting can be described by the value of the contact angle Φ formed between the area of contact between the liquid and the solid surface and a line tangent to the liquid-vapor interface. When a surface of a solid is hydrophilic and water is used as the test liquid, (i.e., a high degree of wettability), the value for c can fall within a range of 0 to 90 degrees. When a surface of a solid is moderately hydrophilic to hydrophobic, (i.e., a medium degree of wettability), the value for Φ for water as the test liquid can fall within a range of 85 to 105 degrees. When the surface of a solid is highly hydrophobic, (i.e., a low degree of wettability), the value for Φ with water as the test liquid can fall within a range of 90 to 180 degrees. Thus, a change in contact angle can be reflective of a change in the surface chemistry of a substrate.

Graphene surfaces and modifications made to graphene surfaces can be characterized using contact angle goniometry. Contact angle goniometry can provide quantitative information regarding the degree of modification of the graphene surface. Contact angle measurements are highly sensitive to the functional groups present on sample surfaces and can be used to determine the formation and extent of surface coverage of self-assembled monolayers. A change in the contact angle from a bare graphene surface as compared to one that has been immersed into a self-assembly solution containing π-electron-rich molecules, can be used to confirm the formation of the self-assembled monolayer on the surface of the graphene.

The types of solvents suitable for use in determining contact angle measurements, also called wetting solutions, are those that maximize the difference between the contact angle of the solution on bare graphene and the contact angle on the modified graphene, thereby improving data accuracy for measurements of binding isotherms. In some embodiments, the wetting solutions can include, but are not limited to, deionized (DI) water, NaOH aqueous solution, borate buffer (pH 9.0), other pH buffers, CF₃CH₂OH, and the like. In some embodiments, the wetting solutions are polar. In some embodiments, the wetting solutions are non-polar.

Langmuir Adsorption Theory

Without wishing to be bound by any particular theory, it is believed that according to Langmuir adsorption theory, monolayer modification of graphene can be controlled by varying the concentration of the adsorbate in the bulk of the self-assembly solution according to:

$\begin{array}{cc}\theta =\frac{K*C}{1+K*C}& \left(1\right)\end{array}$

where θ is the fractional surface coverage, C is the concentration of the adsorbate in the bulk of the self-assembly solution, and K is the equilibrium constant for adsorption of the adsorbate to graphene. Experimentally, the surface coverage can be expressed by the change in contact angle between bare graphene and modified graphene according to:

$\begin{array}{cc}\theta =\frac{\Phi \left(i\right)-\Phi \left(\mathrm{bare}\right)}{\Phi \left(sat.\right)-\Phi \left(\mathrm{bare}\right)}& \left(2\right)\end{array}$

where Φ(i) is the contact angle of the modified graphene as a function of the concentration in the self-assembly solution, Φ(bare) is the contact angle of bare graphene, and Φ(sat.) is the contact angle of graphene modified with a complete monolayer of receptor molecules (i.e., 100% surface coverage or θ=1.0). Insertion of θ from eq (2) into eq (1) and solving for Φ(i) gives eq (3)

$\begin{array}{cc}\Phi \left(i\right)=\Phi \left(\mathrm{bare}\right)+\frac{K*C\left[\Phi \left(sat.\right)-\Phi \left(\mathrm{bare}\right)\right]}{1+K*C}& \left(3\right)\end{array}$

Thus, the experimentally observed Φ(i) values can be fitted as a function of receptor concentration in the self-assembly solution, using the two fitting parameters K and Φ(sat.). Once these two parameters have been determined, relative surface coverages at different self-assembly concentrations can be predicted from eq (1), using K.

Data can be fitted with the Langmuir adsorption model to determine the equilibrium constants for surface adsorption and the concentrations of self-assembly solutions needed to form dense monolayers having 90% or greater surface coverage (i.e., θ>0.9) on graphene. In some embodiments, a surface coverage of at least 90% or greater is desired. In some embodiments, a surface coverage of at least 95% or greater is desired. In some embodiments, a surface coverage of at least 98% or greater is desired.

A representative Langmuir adsorption isotherm for the adsorption of Pyr-CH₂OH to graphene is shown in FIG. 9 and described more fully in Example 8 below. The data show the relative monolayer coverage (dots) along with a fit based on Langmuir adsorption theory (solid line) for the adsorption of Pyr-CH₂OH to graphene, as determined by contact angle measurements. The logarithm of the concentration as a function of relative surface coverage for the adsorption of Pyr-CH₂OH to graphene is shown in FIG. 10.

In the above example, the Langmuir model is used to determine K from contact angle data. Instead of contact angle data, the intensity of bands in spectra from surface spectroscopy may be used, such as data obtained with infrared spectroscopy or Raman spectroscopy.

X-Ray Photoelectron Spectroscopy

X-ray photoelectron spectroscopy (XPS) is a highly sensitive spectroscopic technique that can quantitatively measure the elemental composition of a surface of a material. The process of XPS involves irradiation of a surface with X-rays under a vacuum, while measuring the kinetic energy and electron release within the top 0 to 10 nm of a material. Without wishing to be bound by any particular theory, it is believed that XPS can be used to confirm the presence of a self-assembled monolayer formed on the surface of graphene.

The surface concentrations of the types of atoms that the monolayer, graphene, and the underlying substrate consist of (as determined from XPS) depends on the Langmuir theta value of the monolayer or, in other words, the surface density of the monolayer molecules on the graphene. For example, the surface concentrations of carbon, oxygen, and copper (i.e., C %, O %, and Cu %, as determined from XPS) for the monolayers of any given cyclodextrin on a copper substrate depends on the concentration of that cyclodextrin in the self-assembly solution. Due to experimental error, a slightly different value of the equilibrium constant, K, for surface adsorption will result when either the C %, O %, or Cu % data are fitted separately. However, because the C %, O %, or Cu % data characterize the same equilibrium, there is only one true value for K. Therefore, the XPS data can not only be fitted separately for the C %, O %, and Cu % data but also as one combined set of data. Fitting of the combined data for several types of atoms that the monolayer, graphene, and the underlying substrate consist of gives more accurate estimates of the true value of K. For this purpose, the following equation can be used, where each data point consists of a vector comprising (i) an index, (ii) the concentration of the self-assembly solution, and (iii) the carbon, oxygen, or copper concentration as determined by XPS.

$\mathrm{KroneckerDelta}\left[1-index\right]*\left\{C\%\left(bare\right)+\frac{K*Conc*\left[C\%\left(sat.\right)-C\%\left(bare\right)\right]}{1+K*Conc}\right\}+\mathrm{KroneckerDelta}\left[2-\mathrm{index}\right]*\left\{O\%\left(\mathrm{bare}\right)+\frac{K*Conc*\left[O\%\left(sat.\right)-O\%\left(\mathrm{bare}\right)\right]}{1+K*Conc}\right\}+\mathrm{KroneneckerDelta}\left[3-\mathrm{index}\right]*\left\{\mathrm{Cu}\%\left(\mathrm{bare}\right)+\frac{K*Conc*\left[\mathrm{Cu}\%\left(sat.\right)-\mathrm{Cu}\%\left(\mathrm{bare}\right)\right]}{1+K*Conc}\right\}$

The index 1 was used for the C % data, 2 for the 0% data, and 3 for the Cu % data. The output of the Kronecker delta for the input of 0 is 1, and it is 0 for any other input. This fitting procedure provides in one step the maximum surface concentrations of carbon, oxygen, and copper (i.e., C % (sat.), O % (sat.), and Cu % (sat.), respectively) along with one single value for K for all three adsorption isotherms.

In the example above, the K value is fitted from 3 adsorption isotherms, that is, the surface concentrations of 3 types of atoms. The same type of fit may also be performed for adsorption isotherms of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or more different types of atoms.

Representative C1s and O1s spectra for bare graphene and graphene modified with α-CDBn₁₈ are shown in FIGS. 10-13 and are described further below in Example 14. The equilibrium constant K, as determined by the fit of the XPS data, can be used in the Langmuir adsorption model to determine the θ value for graphene surfaces modified with various molecules forming monolayers on graphene, such as cyclodextrins and cyclodextrin derivatives. A representative Langmuir adsorption isotherm for the adsorption of perbenzylated β-cyclodextrin (β-CDBn₂₁) modified graphene is shown in FIG. 15. The data show the relative monolayer coverage (dots) along with a fit (solid line) based on Langmuir adsorption theory for the adsorption of graphene modified with β-CDBn₂₁, as determined by XPS data. The relative surface coverage for the adsorption of β-CDBn₂₁ to graphene as a function of the logarithm of the β-CDBn₂₁ concentration in the self-assembly solution is shown in FIG. 16.

Aspects may be better understood with reference to the following examples. These examples are intended to be representative of specific embodiments, but are not intended as limiting the overall scope of embodiments herein.

EXAMPLES

Example 1: Experimental Materials

Experimental materials suitable for use in the synthesis of reagents described in Examples 2-6 are provided. For the self-assembly of the perbenzylated α-, β- and γ-cyclodextrins, monolayer graphene on Cu foil was purchased from Graphenea (Donostia, Spain). For all other self-assembly, monolayer graphene was grown on 25-μm-thick Cu foils (No. 46365, Alfa Aesar, Tewksbury, Mass.) by chemical vapor deposition using hydrogen and methane flow rates of 21 sccm and 0.105 sccm, respectively, at 1050° C. Pyrene, 1-pyreneacetic acid, 1-pyrenemethylammonium chloride, 1-pyreneboronic acid, β-cyclodextrin, PBr₃, and NaH (60% w/w dispersion in mineral oil) were obtained from Aldrich (St. Louis, Mo.). 1-Pyrenemethanol and α- and γ-cyclodextrin were purchased from TCI (Cambridge, Mass.). The α-, β- and γ-cyclodextrins were dried in a vacuum overnight before use. Toluene, methanol, and dimethyl sulfoxide (DMSO) were dried over molecular sieves overnight before use. Deionized water (DI water, 0.18 MΩ m specific resistance) was obtained by purification with a Milli-Q PLUS reagent grade water system (Millipore, Billerica, Mass.). Borate buffer (pH=9) was prepared from 50 mL aqueous solution containing 0.1 M boric acid and 0.1 M KCl, 20.8 mL 0.1 M NaOH (aq), and 29.2 mL DI water.

Example 2: Graphene Surface Modification Through Self-Assembly

Graphene substrates were immersed overnight into solutions containing the pyrene or cyclodextrin derivatives at various concentrations (0, 0.03, 0.10, 0.30, 1.0, 3.0, or 10 mM). The modified graphene substrates were then washed 3 times with small portions of the solvent to remove excess self-assembly solution. For the Pyr-CH₂COOH, Pyr-CH₂COOCH₃, Pyr-CH₂NH₂—HCl, Pyr-CH₂NH₂, and Pyr-CH₂N(CH₂CH₃)₂ modifications, ethanol was used as the self-assembly solvent. For modifications with pyrene, Pyr-CH₂OH, Pyr-B(OH)₂, α-CDBn₁₈, β-CDBn₂₁, and γ-CDBn₂₄, acetonitrile was used instead, because pyrene and Pyr-CH₂OH could not be assembled well on graphene from ethanol, and the perbenzylated cyclodextrins were not soluble in ethanol.

The concentrations needed for 90% monolayer coverage for all pyrene derivatives are estimated to be in the range of 0.30-3.6 mM, independently of whether self-assembly was performed form acetonitrile or ethanol solution. The equilibrium constants (K) for all pyrene derivatives varied between 10^3.4 and 10^4.6M⁻¹. The equilibrium constants (K) for the cyclodextrins were found to be 10^3.24, 10^2.97, and 10^2.95 M⁻¹ for α-CDBn₁₈, β-CDBn₂₁, and γ-CDBn₂₄, respectively. The equilibrium constants and monolayer concentrations required for 90% surface coverage are reported in Table 1.

TABLE 1
Equilibrium constants and monolayer concentrations for adsorption
of receptors with a pyrene group or benzyl groups to graphene.
			Concentration of
			self-assembly
			solution needed
	Log K	Self-assembly	for 90% surface
Receptors	(Log M−1)	solvent	coverage (mM)
Pyrene	3.87 (3.76-3.96)	Acetonitrile	1.2
Pyr—CH2OH	3.76 (3.69-3.83)	Acetonitrile	1.3
Pyr—CH2COOH	4.49 (4.28-4.63)	Ethanol	0.30
Pyr—CH2COOOCH3	3.79 (3.66-3.90)	Ethanol	1.5
Pyr—CH2NH2•HCl	4.13 (4.03-4.21)	Ethanol	0.70
Pyr—CH2NH2	3.81 (3.72-3.89)	Ethanol	1.4
Pyr—CH2N(CH2CH3)2	4.60 (4.47-4.70)	Ethanol	0.30
Pyr—B(OH)2	3.40 (2.97-3.61)	Acetonitrile	3.6
α-CDBn18	3.24 (3.09-3.36)	Acetonitrile	5.2
β-CDBn21	2.97 (2.86-3.05)	Acetonitrile	9.6
γ-CDBn24	2.95 (2.84-3.04)	Acetonitrile	10.0

Example 3: Preparation of Pyr-CH₂NH₂.HCl

Experimental materials suitable for the synthesis of Pyr-CH₂NH₂.HCl are described above in Example 1. Briefly, 50 mg Pyr-CH₂NH₂.HCl was dissolved in 10 mL CH₂Cl₂ and washed three times each with 10 mM NaOH (aq; 3×10 mL) and DI water (3×10 mL). The CH₂Cl₂ phase was collected and dried over anhydrous Na₂SO₄, giving upon solvent evaporation under a vacuum a yellow solid (yield 50% by weight). ¹H NMR (δ, ppm, deuterated dimethyl sulfoxide (DMSO-d₆): 4.483 (s, 2H, Ar—CH₂); 8.048-8.444 (m, 11H, Ar—H, NH₂).

Example 4: Synthesis of Pyr-CH₂COOCH₃

Experimental materials suitable for the synthesis of Pyr-CH₂COOCH₃ are described above in Example 1. Briefly, 0.25 mL concentrated sulfuric acid was added into 5 mL dried methanol. 150 mg Pyr-CH₂COOH was added, and the resulting solution was refluxed for 24 h. Upon methanol evaporation, the suspension that remained was added into 20 mL ice-cold DI water. The resulting suspension was extracted with diethyl ether (3×20 mL). The combined ether phases were washed with DI water (3×60 mL) and dried over anhydrous Na₂SO₄. Solvent evaporation on a vacuum gave a yellow solid (yield 66% by weight). ¹H NMR (δ, ppm, DMSO-d₆): 3.645 (s, 3H, CH₃); 4.476 (s, 2H, Ar—CH₂); 8.014-8.329 (m, 9H, Ar—H). Mass spectrometry (ESI-TOF, MeOH), m/z: 297.0961 (Pyr-CH₂COOCH₃.Na⁺). The synthesis of Pyr-CH₂COOCH₃ is shown in FIG. 17.

Example 5: Synthesis of Pyr-CH₂N(CH₂CH₃)₂

Experimental materials suitable for the synthesis of Pyr-CH₂N(CH₂CH₃)₂ are described above in Example 1. Pyr-CH₂Br was prepared first. 250 mg Pyr-CH₂OH was added to 5.35 mL dried toluene. The suspension was cooled to 0° C., and 125 μL PBr₃ was added dropwise with a syringe. The mixture was stirred at 0° C. for 1 h, and at room temperature overnight. Then, 5 mL saturated Na₂CO₃ aqueous solution was added slowly under ice-cold conditions. The solid and the toluene layer were combined and dried over Na₂SO₄. Upon removal of the solids by filtration, the solvent was evaporated from the liquid phase using a vacuum, giving a yellow solid (Pyr-CH₂Br, yield 75% by weight). ¹H NMR (δ, ppm, CDCl₃): 5.295 (s, 2H, Ar—CH₂); 8.0-8.5 (m, 9H, Ar—H).

125 mg Pyr-CH₂Br and 0.2 mL diethylamine were added to 3 mL toluene in an N₂ atmosphere. The mixture was refluxed overnight. Toluene was evaporated, and the solid obtained was added into 20 mL of a CH₂Cl₂/10 mM NaOH (aq) mixture (1:1, v/v), followed by stirring of the mixture overnight. The CH₂Cl₂ phase was collected, washed with DI water (3×10 mL), and dried over anhydrous Na₂SO₄. Solvent evaporation under vacuum gave a yellow solid (Pyr-CH₂N(CH₂CH₃)₂, yield 66% by weight). ¹H NMR (δ, ppm, DMSO-d₆): 1.037-1.072 (t, 6H, CH₃); 2.562-2.615 (m, 4H, CH₂); 4.229 (s, 2H, Ar—CH₂); 8.053-8.602 (m, 9H, Ar—H). Mass spectrometry (ESI-TOF, MeOH), m/z: 215.1125, 288.2231 (Pyr-CH₂N(CH₂CH₃)₂.H⁺). The synthesis of Pyr-CH₂N(CH₂CH₃)₂ is shown in FIG. 18.

Example 6: Synthesis of Perbenzylated α-, β-, and γ-Cyclodextrins

Experimental materials suitable for the synthesis of perbenzylated α-, β-, and γ-cyclodextrins are described above in Example 1. Briefly, 915 mg NaH (60 wt % in mineral oil, 4 equivalents with respect to the hydroxyl groups on the cyclodextrin) was added to a 2-neck round bottom flask. The NaH was washed 5 times with hexane under N₂ protection to remove the mineral oil. Then, 300 mg cyclodextrin was dissolved in 10 mL DMSO, and the solution was degassed for 20 min and transferred into the round bottom flask. After 2 h stirring to allow the NaH to react with the hydroxyl groups of the cyclodextrin, 2.62 mL benzyl chloride (4 equivalents with respect to the hydroxyl groups on cyclodextrins) was added dropwise to the mixture. The reaction was stirred at room temperature for 24 h under N₂ protection. Then, 15 mL water was added to the reaction mixture to neutralize excess NaH. The resulting suspension was extracted with dichloromethane (4×30 mL). Then, the combined dichloromethane phases were washed with water (1×120 mL) and dried over anhydrous Na₂SO₄. Solvent evaporation with a vacuum was performed overnight. The synthesis of perbenzylated α-, β-, and γ-cyclodextrins is shown in FIG. 19.

The yellow liquid raw product was washed with hexane to remove most of the remaining benzyl chloride, followed by purification chromatography on alumina (using first ethyl acetate/hexanes, 1:6, as eluent, later switching over to 1:3), giving a white solid foam (yield 40% by weight). ¹H NMR (β-CDBn₂₁, δ, ppm, CDCl₃): 7.233-7.020 (m, 105H, aromatic H), 5.174 (d, 7H, H1), 5.069-4.335 (m, 42H, CH₂-Ph), 4.034-3.957 (m, 28H, H3, H4, H5, H6), 3.551-3.454 (m, 14H, H2, H6). ¹³C NMR (β-CDBn₂₁, δ, ppm, CDCl₃): 139.268, 138.341, 138.197 (3×C aromatic without H substituents), 128.291-126.913 (CH aromatic), 98.443 (C1), 80.900 (C3), 78.797 (C2), 78.678 (C4), 75.441, 73.273, 72.641 (3×CH₂-Ph), 71.438 (C5), 69.294 (C6). Mass spectrometry (MALDI, 50 mM 2,5-dihydroxybenzoic acid as matrix), m/z: 3048.0449 (β-CDBn₂₁.Na⁺). Elemental analysis (β-CDBn₂₁): calculated C, 74.98%, H, 6.53%. Found C, 74.53%, H, 6.48%. ¹H NMR (α-CDBn₁₈, δ, ppm, CDCl₃): 7.256-7.021 (m, 90H, aromatic H), 5.171 (d, 6H, H1), 5.097-4.303 (m, 36H, CH₂-Ph), 4.166-3.894 (m, 24H, H3, H4, H5, H6), 3.498-3.452 (m, 12H, H2, H6). ¹H NMR (γ-CDBn₂₄, δ, ppm, CDCl₃): 7.396-7.081 (m, 120H, aromatic H), 5.214 (d, 8H, H1), 5.139-4.322 (m, 48H, CH₂-Ph), 4.042-3.893 (m, 32H, H3, H4, H5, H6), 3.490-3.469 (m, 16H, H2, H6).

Example 7: Graphene Modified with Pyr-CH₂NH₂.HCl, Pyr-CH₂NH₂, and Pyr-CH₂COOCH₃

Contact angle measurements of bare graphene and graphene modified with Pyr-CH₂NH₂.HCl, Pyr-CH₂NH₂, and Pyr-CH₂COOCH₃ were performed with a contact angle goniometer (Erma, Tokyo, Japan). A drop of 4, 8, or 12 μL of an appropriate solvent was placed onto the graphene surface, and the average contact angle was obtained from 6 advancing contact angle readings at two spots. The results of the contact angle measurements for bare graphene and graphene modified with Pyr-CH₂NH₂.HCl, Pyr-CH₂NH₂, and Pyr-CH₂COOCH₃ are shown in Table 2.

The contact angle of bare graphene was obtained after the immersion of graphene into pure solvent. The contact angle for bare graphene was found to be 90-92° with DI water as the wetting liquid. A change in the contact angle after the graphene was immersed into self-assembly solutions containing pyrene derivatives, confirming the formation of the self-assembly monolayer on the surface of the graphene. For example, the contact angle of graphene decreased to 74.0° after exposure to 10 mM Pyr-CH₂NH₂.HCl solution.

The relative monolayer coverage as a function of concentration of the self-assembly (mM) solution was fitted to the Langmuir adsorption model for graphene modified independently with Pyr-CH₂COOCH₃, Pyr-CH₂NH₂.HCl, and Pyr-CH₂NH₂. Individual data points (dots) and a fit (solid line) based on Langmuir adsorption theory for Pyr-CH₂COOCH₃ is shown in FIG. 22. The relative surface coverage for the adsorption of Pyr-CH₂COOCH₃ to graphene as a function of the logarithm of the concentration of Pyr-CH₂COOCH₃ in the self-assembly solution is shown in FIG. 23. Individual data points (dots) and a fit (solid line) based on Langmuir adsorption theory for Pyr-CH₂NH₂.HCl is shown in FIG. 24. The relative surface coverage for the adsorption of Pyr-CH₂NH₂.HCl to graphene as a function of the logarithm of the concentration of Pyr-CH₂NH₂.HCl in the self-assembly solution is shown in FIG. 25. Individual data points (dots) and a fit (solid line) based on Langmuir adsorption theory for Pyr-CH₂NH₂ is shown in FIG. 26. The relative surface coverage for the adsorption of Pyr-CH₂NH₂ to graphene as a function of the logarithm of the concentration of Pyr-CH₂NH₂ in the self-assembly solution is shown in FIG. 27.

TABLE 2
Contact angle of DI water on bare graphene and graphene modified with
Pyr—CH2NH2•HCl, Pyr—CH2NH2, or Pyr—CH2COOCH3.
Concentration of
self-assembly	Contact angle (°) in DI water
solution (mM)	Pyr—CH2NH2•HCl	Pyr—CH2NH2	Pyr—CH2COOCH3
0	92.0 ± 1.2	90.7 ± 3.9	90.7 ± 3.9
0.03	88.0 ± 2.2	89.3 ± 3.1	90.3 ± 2.2
0.10	81 ± 1.4	86.5 ± 1.2	85.7 ± 1.0
0.30	76.8 ± 2.2	81.8 ± 4.2	84.0 ± 2.3
1.0	76.6 ± 2.3	80.0 ± 4.3	81.7 ± 1.9
10	74.0 ± 1.2	79.2 ± 3.4	80.2 ± 2.6

Example 8: Graphene Modified with Pyr-CH₂COOH, Pyrene, Pyr-CH₂OH, or Pyr-CH₂N(CH₂CH₃)₂

Contact angle measurements of graphene modified with Pyr-CH₂COOH, pyrene, Pyr-CH₂OH, and Pyr-CH₂N(CH₂CH₃)₂ were performed with a contact angle goniometer (Erma, Tokyo, Japan). A drop of 4, 8, or 12 μL of an appropriate solvent was placed onto the graphene surface, and the average contact angle was obtained from 6 advancing contact angle readings at two spots. The results of the contact angle measurements for graphene modified with Pyr-CH₂COOH, pyrene, Pyr-CH₂OH, and Pyr-CH₂N(CH₂CH₃)₂ are shown Table 3.

The relative monolayer coverage as a function of concentration of the self-assembly (mM) solution was fitted to the Langmuir adsorption model for graphene modified independently with Pyr-CH₂COOH, pyrene, Pyr-CH₂OH, or Pyr-CH₂N(CH₂CH₃)₂. Individual data points (dots) and a fit (solid line) based on Langmuir adsorption theory for pyrene is shown in FIG. 20. The logarithm of the concentration as a function of relative surface coverage for the adsorption of pyrene to graphene is shown in FIG. 21. Individual data points (dots) and a fit (solid line) based on Langmuir adsorption theory for Pyr-CH₂OH is shown in FIG. 9. The relative surface coverage for the adsorption of Pyr-CH₂OH to graphene as a function of the logarithm of the concentration of Pyr-CH₂OH in the self-assembly solution is shown in FIG. 10.

TABLE 3
Contact angle measurements of graphene modified with
Pyr—CH2COOH, pyrene, Pyr—CH2OH, and Pyr—CH2N(CH2CH3)
Concentration of	Contact angle (°) (aqueous solutions used for contact angle measurements)
self-assembly	Pyr—CH2COOH	Pyrene	Pyr—CH2OH	Pyr—CH2N(CH2CH3)2
solution (mM)	(10 mM NaOH)	(10 mM NaOH)	(borate buffer)	(10% CF3CH2 OH)
0	91.3 ± 1.2	82.5 ± 3.9	92.8 ± 1.9	74.3 ± 2.5
0.0001	88.8 ± 1.2	—	—	—
0.001	88.8 ± 1.5	—	—	—
0.003	89.4 ± 1.4	—	—	—
0.01	88.2 ± 1.0	—	—	—
0.03	85.0 ± 1.4	84.3 ± 1.8	91.8 ± 3.1	81.7 ± 2.7
0.10	83.1 ± 1.6	87.3 ± 2.2	89.5 ± 2.9	85.3 ± 2.2
0.30	—	88.5 ± 1.9	86.5 ± 3.1	85.2 ± 2.6
1.0	80.2 ± 1.9	92.0 ± 0.7	85.5 ± 3.9	87.2 ± 2.6
10	77.6 ± 2.0	92.2 ± 1.5	83.7 ± 4.4	88.5 ± 4.0

Example 9: Graphene Modified with Pyr-B(OH)₂

X-ray photoelectron spectroscopy (XPS) spectra of graphene modified with Pyr-B(OH)₂ were collected on a VersaProbe III Scanning XPS Microprobe (PHI 5000, Physical Electronics, Chanhassen, Minn.). The results for the elemental surface composition of graphene modified with Pyr-B(OH)₂ are shown in Table 4.

TABLE 4
Elemental surface composition of graphene modified
with Pyr—B(OH)2, as determined by XPS
	Concentration of
	self-assembly
	solution (mM)	C %	O %	Si %
	0	54.7 ± 1.2	33.3 ± 0.6	12.4 ± 0.2
	0.01	53.1 ± 0.1	34.1 ± 0.1	12.1 ± 0.1
	0.10	56.9 ± 0.9	31.8 ± 0.1	11.3 ± 0.8
	0.40	56.2 ± 2.2	30.8 ± 1.2	13 ± 1.0
	1.0	60.2 ± 1.6	28.4 ± 1.4	11.3 ± 0.3
	2.0	60.4 ± 0.1	28.7 ± 0.6	10.7 ± 0.2

Example 10: Graphene Modified with Perbenzylated α-Cyclodextrin (α-CDBn₁₈)

X-ray photoelectron spectroscopy (XPS) spectra of graphene modified with perbenzylated α-cyclodextrin (α-CDBn₁₈) were collected on a VersaProbe III Scanning XPS Microprobe (PHI 5000, Physical Electronics, Chanhassen, Minn.). The results for the elemental surface composition of graphene modified with α-CDBn₁₈ are shown in Table 5.

TABLE 5
Elemental surface composition of graphene modified with perbenzylated
α-cyclodextrin (α-CDBn18), as determined by XPS
	Concentration of
	self-assembly
	solution (mM)	C %	O %	Si %
	0	56.3 ± 0.4	11.0 ± 1.5	32.6 ± 1.4
	0.03	54.7 ± 1.1	12.8 ± 1.3	32.5 ± 1.7
	0.10	57.3 ± 2.3	14.7 ± 1.4	28.1 ± 3.3
	0.30	62.4 ± 0.5	15.0 ± 0.5	22.7 ± 0.2
	1.0	62.8 ± 1.1	16.3 ± 0.1	20.9 ± 1.0
	3.0	69.0 ± 0.7	19.0 ± 0.4	12.0 ± 0.3

Example 11: Graphene Modified with Perbenzylated β-Cyclodextrin (β-CDBn₂₁)

XPS spectra of graphene modified with perbenzylated β-cyclodextrin (β-CDBn₂₁) were collected on a VersaProbe III Scanning XPS Microprobe (PHI 5000, Physical Electronics, Chanhassen, Minn.). The results for the elemental surface composition of graphene modified with β-CDBn₂₁ are shown in Table 6.

TABLE 6
Elemental surface composition of graphene modified with perbenzylated
β-cyclodextrin (β -CDBn21), as determined by XPS
	Concentration of
	self-assembly
	solution (mM)	C %	O %	Si %
	0	56.3 ± 0.4	11.0 ± 1.5	32.6 ± 1.4
	0.03	56.0 ± 0.8	11.7 ± 0.7	32.2 ± 0.4
	0.10	59.5 ± 0.1	13.8 ± 1.0	26.7 ± 0.9
	0.30	59.9 ± 1.0	14.1 ± 0.4	26.0 ± 0.6
	1.0	62.4 ± 1.1	19.0 ± 1.9	18.5 ± 2.0
	3.0	66.9 ± 1.6	24.4 ± 2.1	8.7 ± 0.6

Example 12: Graphene Modified with Perbenzylated γ-Cyclodextrin (γ-CDBn₂₄)

XPS spectra of graphene modified with perbenzylated γ-cyclodextrin (γ-CDBn₂₄) were collected on a VersaProbe III Scanning XPS Microprobe (PHI 5000, Physical Electronics, Chanhassen, Minn.). The results for the elemental surface composition of graphene modified with β-CDBn₂₄ are shown in Table 7.

TABLE 7
Elemental surface composition of graphene modified with perbenzylated
γ-cyclodextrin (γ -CDBn24), as determined by XPS
	Concentration of
	self-assembly
	solution (mM)	C %	O %	Si %
	0	58.2 ± 0.5	10.5 ± 0.7	31.3 ± 1.1
	0.03	57.4 ± 1.3	10.5 ± 1.2	32.0 ± 2.5
	0.10	59.0 ± 0.9	12.1 ± 1.8	28.9 ± 1.4
	0.30	62.2 ± 0.1	12.3 ± 1.4	25.4 ± 1.5
	1.0	61.6 ± 1.0	13.5 ± 0.4	24.9 ± 0.8
	3.0	66.7 ± 2.4	15.8 ± 0.7	17.6 ± 3.0

Example 13: XPS of Bare Graphene

X-ray photoelectron spectroscopy (XPS) spectra of bare graphene on a copper substrate were collected on a VersaProbe III Scanning XPS Microprobe (PHI 5000, Physical Electronics, Chanhassen, Minn.). The observed elemental surface composition of bare graphene on a copper substrate was found to be 56.3 mol % carbon, 11.0 mol % oxygen, and 32.6 mol % copper. The high resolution C1s XPS spectrum of bare graphene (FIG. 11) reveals five types of carbon atoms, which can be assigned to C═C (284.5 eV), C—OH (285.4 eV), C—O—C (286.4 eV), C═O (287.4 eV) and O—C═O (288.9 eV). As shown in the high resolution O1s XPS spectrum (FIG. 12), four types of oxygen were observed, i.e., Cu—O (530.4 eV), C—O (531.4 eV), C═O (532.1 eV), and O—C═O (532.9 eV). The Cu—O peak was the largest, and integration of these peaks suggested that 61.2% oxygen came from the underlying copper substrate (Cu—O).

Example 14: XPS of Surface Modified Graphene

Graphene samples modified either with α-CDBn₁₈, β-CDBn₂₁, or γ-CDBn₂₄ were characterized by XPS. XPS spectra of graphene modified with either perbenzylated α-cyclodextrin (α-CDBn₁₈), perbenzylated β-cyclodextrin (β-CDBn₂₁), or perbenzylated γ-cyclodextrin (γ-CDBn₂₄) were collected on a VersaProbe III Scanning XPS Microprobe (PHI 5000, Physical Electronics, Chanhassen, Minn.).

After the self-assembly of the perbenzylated cyclodextrins, the Cu percentage was reduced significantly, and the C and O percentages increased. This trend is consistent with the composition of the cyclodextrin monolayers, which is 84.4 mol % carbon and 15.6 mol % oxygen for all three cyclodextrins (See Tables 5-7). The high resolution XPS spectra for C1s and O1s confirmed the surface modification with α-CDBn₁₈ by showing a much smaller Cu—O peak as compared to bare graphene and much larger peaks for the sp3 carbon and C—O—C carbon and oxygen atoms pertaining to the perbenzylated cyclodextrins (FIGS. 13-14).

Example 15: Stability and Reversibility of the Surface Modification to Heat and Vacuum

To ensure the stability of the surface modification of graphene under heating or vacuum, graphene modified with Pyr-CH₂NH₂.HCl was baked overnight in a high vacuum (2×10⁻⁵ Torr) at 100° C. This was followed by contact angle measurements with DI water as the wetting liquid. Table 8 shows that the contact angle of graphene substrates modified with Pyr-CH₂NH₂.HCl did not change measurably as a result of the heat and vacuum exposure, suggesting that the Pyr-CH₂NH₂.HCl monolayer on graphene is not damaged under these conditions.

TABLE 8
Stability of graphene modified with Pyr—CH2NH2 •HCl
towards heat and vacuum treatments
	Water Contact Angle (°)
		After heating in a vacuum
Modification Conditions	No heating/vacuum	(100° C., 2 × 10−5 Torr)
Graphene immerged into	92.0 ± 1.0	N/A
ethanol overnight
Graphene immerged into	81.0 ± 1.4	81.4 ± 2.6
0.10 mM Pyr—CH2NH2•HCl
overnight
Graphene immerged into	76.6 ± 2.3	77.2 ± 1.6
1.0 mM Pyr—CH2NH2•HCl
overnight

Example 16: Stability and Reversibility of the Surface Modification to Toluene

Pyr-CH₂NH₂.HCl modified graphene was immersed into toluene for 1 h (replacing the toluene once after 0.5 h). Contact angle measurements were recorded before and after the toluene immersion. The increase in contact angle from 85.5°±1.4° with the monolayer modification to 91.6°±0.5° after toluene immersion shows that, as expected, the toluene removed the receptor monolayer from graphene, exposing again the bare graphene surface. A control experiment was also performed immersing bare graphene into ethanol overnight and subsequently into toluene for 1 h. The contact angles were found to be 91.3°±1.5° and 92.5°±1.9° after the ethanol immersion and the toluene immersion, respectively, confirming that toluene did not damage the graphene-coated Cu substrates.

Example 17: Self-Assembly of 5,10,15,20-Tetraphenyl-21H,23H-Porphine Manganese(III) Chloride (Mn(III)TPPCl) on Graphene

The metallotetraphenylporphyrin, 5,10,15,20-tetraphenyl-21H,23H-porphine manganese(III) chloride (Mn(III)TPPCl), was purchased from Aldrich (St. Louis, Mo.). The chemical structure of Mn(III)TPPCl can be described by the following formula:

where R is a phenyl group at each location on the molecule.

For the self-assembly of Mn(III)TPPCl on graphene, graphene substrates grown on copper were immersed overnight into ethanol solutions containing Mn(III)TPPCl at various concentrations (0, 0.128, 0.64, 1.28, 3.0, or 10 mM). The modified graphene substrates were then washed 3 times with small portions of ethanol to remove excess self-assembly solution. XPS was performed to determine the C %, 0%, N % and Cu % of the modified surface. A summary of the surface compositions as determined by XPS is presented in Table 9.

TABLE 9
Elemental surface composition of graphene modified
with Mn(III)TPPCl, as determined by XPS
Concentration of
self-assembly
solution (mM)	C %	Cu %	N %	O %
0	55.8 ± 1.5	33.2 ± 1.9	—	11.0 ± 0.5
0.128	56.2 ± 0.5	34.6 ± 0.6	—	9.0 ± 1.0
0.64	61.7 ± 1.5	28.4 ± 0.4	1.5 ± 0.8	8.4 ± 1.6
1.28	76.5 ± 2.2	9.2 ± 2.5	4.8 ± 1.0	9.5 ± 1.1
3.0	81.8 ± 0.9	4.2 ± 0.8	5.8 ± 0.4	8.3 ± 0.7
10	79.0 ± 0.4	0.8 ± 0.1	5.5 ± 0.6	14.7 ± 0.7

The C % and Cu % data were fitted simultaneously, as described above, to determine the equilibrium constant K. N % and O % data were not included into the fitting because the maximum changes in O % and N % fell within the background noise of the experiment. The equilibrium constant, K, and concentration of self-assembly solution needed for at least 90% monolayer formation with Mn(III)TPPCl are shown in Table 10.

TABLE 10
Equilibrium constants and monolayer concentrations for
adsorption of Mn(III)TPPCl and β-CDBn19(OH)2 on graphene
			Concentration of
			self-assembly
			solution needed
Self-Assembly	Log K	Self-assembly	for 90% surface
Molecule	(Log M−1)	solvent	coverage (mM)
β-CDBn19(OH)2	3.38 (3.23-3.50)	Acetonitrile	3.8
Mn(III)TPP	2.99 (2.71-3.16)	ethanol	9.5

Example 18: Self-Assembly of 6^A,6^D-Dihydroxyl Benzylated β-Cyclodextrin (β-CDBn₁₉(OH)₂) on Graphene

The 6^A,6^D-dihydroxyl benzylated β-cyclodextrin (β-CDBn₁₉(OH)₂) was synthesized as follows: 325 mg perbenzylated β-cyclodextrin (β-CDBn₂₁) was dissolved in 10 mL anhydrous toluene. The solution was degassed for 20 min with argon and transferred into a 2-neck round bottom flask with the protection of nitrogen. Then, 6.5 mL of diisobutylaluminum hydride solution (1M in toluene, Aldrich) was added dropwise into the flask, and the solution was heated to 50° C. After 2 h, another 6.5 mL of diisobutylaluminum hydride solution (1M in toluene, Aldrich) was added into the solution and allowed to react for another 5.5 h. Then, 20 mL 1 M HCl (aq) was added slowly into the mixture while in an ice bath. The resulting suspension was extracted with ethyl acetate (4×30 mL). The combined ethyl acetate phases were washed with water (1×120 mL) and dried over anhydrous Na₂SO₄. Solvent evaporation with a vacuum was performed overnight. Afterwards, the white raw product was purified with chromatography on silica (using first ethyl acetate/hexanes, 1:4, as eluent, later switching over to 1:2). The yield was 37%. Mass spectrometry (MALDI, 50 mM 2,5-dihydroxybenzoic acid as matrix) was performed to give m/z: 2868.2 (β-CDBn₁₉(OH)₂.Na⁺). Elemental analysis (β-CDBn₁₉(OH)₂): calculated C, 73.82%, H, 6.51%. Found C, 73.57%, H, 6.48%.

For the self-assembly of β-CDBn₁₉(OH)₂ on graphene, graphene substrates grown on copper were immersed overnight into acetonitrile solutions containing 13-CDBn₁₉(OH)₂ at various concentrations (0, 0.03, 0.1, 0.3, 1.0, or 3.0 mM). The modified graphene substrates were then washed 3 times with small portions of acetonitrile to remove excess self-assembly solution. XPS was perform to determine the C %, O % and Cu % of the modified surface. A summary of the surface compositions as determined by XPS is presented in Table 11.

TABLE 11
Elemental surface composition of graphene modified
with β-CDBn19(OH)2, as determined by XPS
	Concentration of
	self-assembly
	solution (mM)	C %	Cu %	O %
	0	63.2 ± 0.4	25.1 ± 1.0	11.4 ± 0.8
	0.03	64.5 ± 2.6	24.2 ± 3.3	11.3 ± 0.8
	0.1	63.0 ± 1.5	25.6 ± 1.5	11.3 ± 1.2
	0.3	74.1 ± 1.0	12.1 ± 0.6	13.8 ± 0.5
	1.0	76.5 ± 1.1	6.8 ± 1.7	16.7 ± 0.8
	3.0	81.1 ± 1.0	3.0 ± 0.6	15.9 ± 0.8

The C %, O % and Cu % data were fitted simultaneously, as described above, to determine the equilibrium constant K. The equilibrium constant, K, and concentration of self-assembly solution needed for at least 90% monolayer formation with β-CDBn₁₉(OH)₂ is shown in Table 10.

Example 19: Raman Spectroscopy of Graphene Modified with Pyr-B(OH)₂

Raman spectroscopy was performed on graphene modified with Pyr-B(OH)₂. To estimate the surface coverage, graphene was modified in Pyr-B(OH)₂ solutions at different concentrations, including 1 mM and 2 mM. Peaks at around 1286 cm⁻¹ and 1378 cm⁻¹ were observed in the Raman spectra of the modified graphene surfaces, which correspond to the B—OH bending and B—O stretching vibration, respectively. The results of the Raman spectroscopy are shown in FIG. 28.

The peak height ratios for the B—OH peak (1283 cm⁻¹) to graphene G peak (˜1600 cm⁻¹) were 0.048 and 0.083 for the 1 mM and 2 mM Pyr-B(OH)₂ solutions, respectively. The peak height ratios of the B—OH (1283 cm⁻¹) to graphene 2D peaks (2692 cm⁻¹) were 0.045 and 0.098 for the 1 mM and 2 mM Pyr-B(OH)₂ solutions, respectively. The peak height ratio of the B—OH peak to the G/2D peak increased as the self-assembly concentration increased from 1.0 mM to 2.0 mM, which, without wishing to be bound by any particular theory, is believed to indicate that the graphene surface was not fully saturated with the 1.0 mM self-assembly solution.

It should be noted that, as used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the content clearly dictates otherwise. Thus, for example, reference to a composition containing “a compound” includes a mixture of two or more compounds. It should also be noted that the term “or” is generally employed in its sense including “and/or” unless the content clearly dictates otherwise.

It should also be noted that, as used in this specification and the appended claims, the phrase “configured” describes a system, apparatus, or other structure that is constructed or configured to perform a particular task or adopt a particular configuration to. The phrase “configured” can be used interchangeably with other similar phrases such as arranged and configured, constructed and arranged, constructed, manufactured and arranged, and the like.

All publications and patent applications in this specification are indicative of the level of ordinary skill in the art to which this invention pertains. All publications and patent applications are herein incorporated by reference to the same extent as if each individual publication or patent application was specifically and individually indicated by reference.

The embodiments described herein are not intended to be exhaustive or to limit the invention to the precise forms disclosed in the following detailed description. Rather, the embodiments are chosen and described so that others skilled in the art can appreciate and understand the principles and practices. As such, aspects have been described with reference to various specific and preferred embodiments and techniques. However, it should be understood that many variations and modifications may be made while remaining within the spirit and scope herein.

Claims

1. A medical device comprising: a graphene varactor comprising: a graphene layer;a self-assembled monolayer disposed on an outer surface of the graphene layer through π-π stacking interactions; andwherein the self-assembled monolayer provides a Langmuir theta value of at least 0.9.

2. The medical device of claim 1, the self-assembled monolayer comprising one or more tetraphenylporphyrins, or derivatives thereof.

3. The medical device of claim 1, the self-assembled monolayer comprising:

4. The medical device of claim 1, comprising a plurality of graphene varactors configured in an array on the medical device.

5. The medical device of claim 1, wherein the self-assembled monolayer provides a Langmuir theta value of at least 0.98.

6. The medical device of claim 1, wherein the self-assembled monolayer provides coverage over the graphene from 50% to 150% by surface area.

7. The medical device of claim 1, wherein the self-assembled monolayer provides coverage over the graphene from 99% to 120% by surface area.

8. A method of modifying a surface of graphene to create a graphene varactor, the method comprising: forming a self-assembled monolayer on an outer surface of a graphene layer of the graphene varactor through π-π stacking interactions;quantifying the extent of surface coverage of the self-assembled monolayer using contact angle goniometry, Raman spectroscopy, or X-Ray photoelectron spectroscopy;selecting derivatized graphene layers that exhibit a Langmuir theta value of at least 0.9.

9. The method of claim 8, wherein selecting derivatized graphene layers includes selecting derivatized graphene layers that exhibit a Langmuir theta value of at least 0.98.

10. The method of claim 8, wherein the self-assembled monolayer provides coverage over the graphene from 50% to 150% by surface area.

11. The method of claim 8, wherein the self-assembled monolayer provides coverage over the graphene from 99% to 120% by surface area.

12. The method of claim 8, wherein the self-assembled monolayer comprises at least one selected from the group consisting of polycyclic aromatic hydrocarbons comprising 3 to 10 aromatic rings; tetraphenylporphyrins or derivatives thereof; metallotetraphenylporphyrins or derivatives thereof; and aromatic cyclodextrins.

13. A method for detecting an analyte comprising: collecting a gaseous sample from a patient;contacting the gaseous sample with one or more graphene varactors, each of the one or more graphene varactors comprising: a graphene layer;a self-assembled monolayer disposed on an outer surface of the graphene layer through π-π stacking interactions; andwherein the self-assembled monolayer provides a Langmuir theta value of at least 0.9.

14. The method of claim 13, further comprising measuring a differential response in a capacitance of the one or more graphene varactors due to the binding of one or more analytes present in the gaseous sample.

15. The method of claim 13, wherein the self-assembled monolayer comprises at least one selected from the group consisting of polycyclic aromatic hydrocarbons comprising 3 to 10 aromatic rings; tetraphenylporphyrins or derivatives thereof; metallotetraphenylporphyrins or derivatives thereof; and aromatic cyclodextrins.

16. The method of claim 13, wherein selecting derivatized graphene layers includes selecting derivatized graphene layers that exhibit a Langmuir theta value of at least 0.98.

17. The method of claim 13, wherein the self-assembled monolayer provides coverage over the graphene from 50% to 150% by surface area.

18. The method of claim 13, wherein the self-assembled monolayer provides coverage over the graphene from 99% to 120% by surface area.