Vaporizer including heating element with positive temperature coefficient of resistivity (PTCR)

Abstract

To provide a portable personal vaporizer device including a PTCR heating element utilizing a semiconductive material with a nonlinear positive temperature coefficient of resistivity, for generating an inhalable aerosol from one or more vaporizable materials.SOLUTION: An apparatus includes: a housing including a power source; a reservoir including an inlet and an outlet and configured to contain a vaporizable material and to couple to the housing; and a PTCR heating element configured to electrically couple to the power source and heat the vaporizable material to form aerosol. The PTCR heating element includes an electrical resistivity that varies based on temperature. The electrical resistivity includes an electrical resistivity transition zone including an increase in electrical resistivity over a temperature range, so that, when the PTCR heating element is heated to a first temperature within the transition zone, a current flow from the power source is reduced to a level that limits a further temperature rise of the PTCR heating element.SELECTED DRAWING: Figure 3F

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Provisional Patent Application No. 62 / 730,257, filed September 12, 2018, entitled “Vaporizer Including Positive Temperature Coefficient of Resistivity Heater”, which claims priority to U.S. Provisional Patent Application No. 62 / 897,229, filed September 6, 2019, entitled “Vaporizer Including (PTCR) Positive Temperature Coefficient of Resistivity Heating Element”, the contents of all of which are incorporated herein by reference in their entireties to the extent permitted by law.

[0002] Technical Field The subject matter described herein relates to vaporizer devices, for example, portable personal vaporizer devices for generating inhalable aerosols from one or more vaporizable materials, the portable personal vaporizer devices including a PTCR heating element that utilizes a semiconductor material having a nonlinear positive temperature coefficient of resistance.

[0003] 2. Background of the Invention Vaporizer devices, which may also be referred to as vaporizers, electronic vaporizer devices, or e-vaporizer devices, can be used to deliver an aerosol (e.g., a gas-phase and / or condensed-phase material suspended in a body of still or moving air or other gas carrier) containing one or more active ingredients through inhalation of the aerosol by a user of the vaporizer device. For example, electronic nicotine delivery systems (ENDS) include certain vaporizer devices that are battery-powered and can be used to simulate the smoking experience without burning tobacco or other substances. Vaporizers have become increasingly popular in both medical prescription applications in the delivery of medicines and the consumption of tobacco, nicotine, and other botanical materials. Vaporizer devices are portable, self-contained, and / or convenient to use.

[0004] In using a vaporizer device, a user inhales an aerosol, commonly referred to as "vapor," which may be generated by a PTCR heating element that vaporizes the vaporizable material (e.g., transitions a liquid or solid at least partially to the gas phase). The vaporizable material may be a liquid, solution, solid, paste, wax, and / or any other form that may be compatible with the use of a particular vaporizer device. The vaporizable material used in a vaporizer may be provided in a cartridge (e.g., a separable portion of the vaporizer device that contains the vaporizable material) that includes an inlet and an outlet (e.g., a mouthpiece) for inhalation of the aerosol by the user.

[0005] To receive the inhalable aerosol generated by the vaporizer device, a user can activate the vaporizer device by taking a puff, which in certain examples is detected by a pressure sensor that turns on a PTCR heating element and / or by some other approach, such as a simple user-operated push button switch. A puff, as used herein, can refer to an inhalation by a user that draws a predetermined amount of air into the vaporizer device such that an inhalable aerosol is generated by combination of the vaporized vaporizable material and the predetermined amount of air.

[0006] Approaches by which vaporizer devices generate inhalable aerosols from vaporizable materials include heating the vaporizable material in a vaporization chamber (e.g., a heater chamber) to convert the vaporizable material to a gas phase (or vapor). A vaporization chamber may refer to an area or volume within a vaporizer device in which a heat source (e.g., a conductive, convective, and / or radiative heat source) causes the vaporizable material to heat, generating a mixture of air and vaporized vaporizable material, forming a vapor through which a user of the vaporizer device inhales the vaporizable material.

[0007] Certain components of the gas-phase vaporizable material may condense after vaporization due to cooling and / or pressure changes, thereby forming an aerosol that includes particles of the condensed phase (e.g., liquid and / or solid) suspended in at least a portion of the air drawn into the vaporizer device by the puff. When the vaporizable material includes a semi-volatile compound (e.g., a compound such as nicotine that has a relatively low vapor pressure under inhalation temperatures and pressures), the inhalable aerosol may include the semi-volatile compound in local equilibrium between the gas and condensed phases.

[0008] Typically, the vaporizable material may be drawn from the reservoir through a wicking element (e.g., a wick) into the vaporization chamber. The drawing of the vaporizable material into the vaporization chamber may be at least partially due to capillary action provided by the wick as it draws the vaporizable material along the wick toward the vaporization chamber. However, as the vaporizable material is drawn from the reservoir, the pressure in the reservoir decreases, which creates a vacuum and acts against the capillary action. This may reduce the effectiveness of the wick to draw the vaporizable material into the vaporization chamber, thereby reducing the effectiveness of the vaporization device to vaporize a desired amount of the vaporizable material. Furthermore, the vacuum created in the reservoir may ultimately result in not all of the vaporizable material being drawn into the vaporization chamber, thereby wasting the vaporizable material. Thus, it is desirable to improve vaporizer devices and / or vaporizer cartridges to improve or overcome these problems.

[0009] The vaporizer device can be controlled by one or more on-the-vaporizer controllers, electronic circuitry (e.g., sensors, heating elements), etc. The vaporizer device can also communicate wirelessly with an external controller (e.g., a computing device such as a smartphone).

[0010] Summary of the Invention In certain aspects of the present subject matter, challenges associated with heating devices for vaporizers can be addressed by including one or more of the features described herein or equivalent or comparable approaches, as will be appreciated by those of skill in the art. Aspects of the present subject matter relate to methods and systems for utilizing PTCR (Positive Temperature Coefficient of Resistance) heating elements, also referred to as PTCR heaters, which are characterized by electrical resistivity that changes based on temperature within a vaporizer device.

[0011] In some implementations, the device includes a power source configured to provide a current flow at a predetermined voltage, a reservoir configured to contain a vaporizable material, and a PTCR (Positive Temperature Coefficient of Resistance) heating element configured to electrically couple to the power source to receive a current flow from the power source and heat the vaporizable material to form an aerosol. The PTCR heating element includes a PTCR material having an electrical resistivity that varies based on temperature. The electrical resistivity includes an electrical resistivity transition region where the electrical resistivity increases over a predetermined temperature range, such that when the PTCR heating element is heated beyond a first temperature within the transition region, the flow of current from the power source is reduced to a level that limits further temperature increase of the PTCR heating element.

[0012] In some implementations, the device includes a power source configured to provide a current flow at a predetermined voltage, a reservoir configured to contain a vaporizable material, and an atomizer coupled to the reservoir to receive the vaporizable material. The atomizer includes a PTCR (Positive Temperature Coefficient of Resistance) heating element electrically coupled to the power source and configured to receive a current flow from the power source and vaporize the vaporizable material. The PTCR heating element is configured to be heated to an operating temperature at which its resistivity reduces the flow of current such that an increase in operating temperature is prevented.

[0013] In some implementations, the apparatus includes a power source configured to provide a current flow at a predetermined voltage, a receptacle configured to receive a vaporizable material, and a PTCR (Positive Temperature Coefficient of Resistance) heating element configured to be electrically coupled to the power source to receive the current flow from the power source and vaporize the vaporizable material. The PTCR heating element is configured to be heated to an operating temperature at which its resistivity reduces the flow of current such that an increase in operating temperature is prevented.

[0014] In some implementations, the apparatus includes a power source configured to provide a current flow at a predetermined voltage, a receptacle configured to receive a vaporizable material, and a PTCR (Positive Temperature Coefficient of Resistance) heating element configured to be electrically coupled to the power source to receive the current flow from the power source and vaporize the vaporizable material. The PTCR heating element has a first resistivity of between 10 Ωcm and 100 Ωcm at 100° C. and a second resistivity of between 50,000 Ωcm and 150,000 Ωcm at 260° C.

[0015] In some variations, one or more of the following features may be optionally included in any workable combination. In one aspect, the device includes a housing including a power source, a fluid reservoir including an inlet, an outlet, containing a fluid, and configured to be coupled to the housing, and a PTCR heating element electrically coupled to the power source and configured to heat the fluid to form an aerosol. The PTCR heating element includes an electrical resistivity that varies based on temperature. The electrical resistivity includes an electrical resistivity transition region that includes an increase in electrical resistivity over a temperature range, such that when the PTCR heating element is heated to a first temperature within the transition region, the flow of electrical current from the power source is reduced to a level that limits further temperature increase of the PTCR heating element due to the flow of electrical current.

[0016] One or more of the following features may be included in any operable combination. For example, the PTCR heating element may be disposed between the inlet and the outlet. The device may include a cartridge including a fluid reservoir, a fluid in the fluid reservoir, a PTCR heating element, a wick configured to transport the fluid to a vaporization location, and electrical contacts electrically coupled to the PTCR heating element and configured to provide electrical current from a power source to the PTCR heating element. The PTCR heating element may be configured to heat the fluid at the vaporization location.

[0017] The device can include an input configured to electrically connect a power source to the PTCR heating element in response to a user input. The input can include a push button. The PTCR heating element of the device is self-regulating to maintain a predetermined temperature when activated. The device does not require a pressure sensor and / or a controller coupled to the pressure sensor to electrically connect a power source to the PTCR heating element and regulate its temperature.

[0018] The electrical resistivity transition region may begin at a first temperature between 150° C. and 350° C. The electrical resistivity transition region may begin at a first temperature between 220° C. and 300° C. The electrical resistivity transition region may begin at a first temperature between 240° C. and 280° C.

[0019] The increase in electrical resistivity over the temperature range of the electrical resistivity transition region may include an increase factor of at least 10, the increase factor characterizing the relative change in electrical resistivity between the electrical resistivity at a first temperature associated with the beginning of the electrical resistivity transition region and the electrical resistivity at a second temperature associated with the end of the electrical resistivity transition region. The increase in electrical resistivity over the temperature range of the electrical resistivity transition region may include an increase factor of at least 100, the increase factor characterizing the relative change in electrical resistivity between the electrical resistivity at a first temperature associated with the beginning of the electrical resistivity transition region and the electrical resistivity at a second temperature associated with the end of the electrical resistivity transition region. The increase in electrical resistivity over the temperature range of the electrical resistivity transition region may include an increase factor of at least 1000, the increase factor characterizing the relative change in electrical resistivity between the electrical resistivity at a first temperature associated with the beginning of the electrical resistivity transition region and the electrical resistivity at a second temperature associated with the end of the electrical resistivity transition region.

[0020] The electrical resistivity transition region can begin at a first temperature and end at a second temperature. The difference between the first and second temperatures can be 500° C. or less. The difference between the first and second temperatures can be 200° C. or less. The difference between the first and second temperatures can be 100° C. or less. The difference between the first and second temperatures can be 50° C. or less.

[0021] The electrical resistivity transition region may begin at a first temperature, and the electrical resistivity of the PTCR heating element below the first temperature may be between 20 Ωcm and 200 Ωcm. Ωcm and Ωm are units of electrical resistivity of the PTCR material, which is directly proportional to its resistance and cross-sectional area and inversely proportional to its length. The electrical resistivity of the PTCR heating element below the first temperature may be between 2.0 Ωcm and 20 Ωcm. The electrical resistivity of the PTCR heating element below the first temperature may be between 0.2 Ωcm and 2.0 Ωcm.

[0022] The increase in electrical resistivity over the temperature range of the electrical resistivity transition region includes an enhancement factor of at least 100, the enhancement factor characterizing the relative change in electrical resistivity between the electrical resistivity at a first temperature associated with the beginning of the electrical resistivity transition region and the electrical resistivity at a second temperature associated with the end of the electrical resistivity transition region. The first temperature may be between 200° C. and 350° C., the difference between the first and second temperatures may be less than or equal to 200° C., and the electrical resistivity of the PTCR heating element at temperatures below the first temperature may be between 20 Ω cm and 200 Ω cm.

[0023] The PTCR heating element may include a plate shape, a polygonal shape, and / or a circular shape, including a height, a width, and a length. If the PTCR heating element includes a plate shape, the height may be 0.5 mm, the length may be 5.0 mm, and the width may be 5.0 mm. The plate shape may include two parallel sides with conductive leads attached to them.

[0024] The PTCR heating element may include a layer of material having a positive temperature coefficient of resistance between a first conductive layer and a second conductive layer, the first conductive layer being coupled to a first conductive lead and the second conductive layer being coupled to a second conductive lead. The PTCR heating element may include a hole feature extending through the PTCR heating element. The PTCR heating element may include an aspect ratio of 1-50.

[0025] The PTCR heating element comprises a composition, the composition being selected from the group consisting of: a ceramic; a mixed metal oxide; two or more mixed metal oxides; one or more mixed metal oxides and one or more elemental metals, MO x One or more binary metal oxides having the MN type phase x One or more binary metal nitrides having the type phase, MC x One or more bimetallic carbides with MB type phases x One or more bimetallic borides having the type phase, and / or MSi xcomposite mixtures of two or more binary metal oxides; composite mixtures of two or more binary metal oxides with one or more elemental metals, one or more binary metal nitrides, one or more binary metal carbides, one or more binary metal borides, and / or one or more binary metal silicides; and / or crosslinked polymer composites of one or more elemental metals with one or more binary metal oxides, one or more binary metal nitrides, one or more binary metal carbides, one or more binary metal borides, and / or one or more binary metal silicides; and / or any combination thereof.

[0026] The PTCR heating element may include a composition, the composition being an ABO3 type compound, where the element A includes Li, Na, K, Rb, Mg, Ca, Sr, Ba, Y, La, Ce, Pb, Bi, or a mixture thereof, and the element B includes Mg, Al, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Nb, Hf, Ta, or a mixture thereof; barium titanate (BaTiO3); lead titanate (PbTiO3); lead zirconate (PbZrO3); bismuth aluminate (BiAlO3); alkali niobate (ANbO3, A=Li, Na, K, Rb), alkali tantalate (ATaO3, A=Li, Na, K, Rb), or a solid solution thereof; main group alkali zirconate (Bi 0.5 A 0.5 ZrO3, A=Li, Na, K); main group titanate-zirconates (PbTi 1-x Zr x O3), rare earth substituted variants, and / or Ba 1-x RE x Solid solutions containing TiO3 (RE=La, Ce); alkaline earth niobates (Sr 1-x Ba x Nb2O6), general formula [Bi2O2][A n-1 BnO 3n+1 ] Aurivillius-type phase of Bi4Ti3O 12, and substitutional, solid solution, non-stoichiometric and intergrowth phases thereof; elemental metals including C, Al, Si, Ti, Fe, Zn, Ag and / or Bi; binary metal oxides including MgO, Al2O3, SiO2, TiO2, Ti2O3, Cr2O3, MnO, FeO, CoO, NiO, CuO, ZnO and / or SnO2; binary metal nitrides including TiN, Mn3N2, Co2N, Ni3N and / or Zn3N2; binary metal carbides including TiC; binary metal borides including ZrB2 and / or NbB2; binary metal silicides including NbSi2, WSi2 and / or MoSi2; polyethylene; polyamide; kynar; polytetrafluoroethylene; and / or any combination thereof.

[0027] The PTCR heating element may include a composition, which may be an ABO3 type compound, where the element A includes Li, Na, K, Rb, Mg, Ca, Sr, Ba, Y, La, Ce, Pb, Bi, or mixtures thereof, and the element B includes Mg, Al, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Nb, Hf, Ta, or mixtures thereof. Examples of such compositions include barium titanate (BaTiO3); lead titanate (PbTiO3); lead zirconate (PbZrO3); bismuth aluminate (BiAlO3); alkali niobate (ANbO3, A=Li, Na, K, Rb), alkali tantalate (ATaO3, A=Li, Na, K, Rb), or solid solutions thereof; main group alkali zirconate (Bi 0.5 A 0.5 ZrO3, A=Li, Na, K); main group titanate-zirconates (PbTi 1-x Zr x O3), rare earth substituted variants, and / or Ba 1-x RE x Additionally or alternatively, compositions such as alkaline earth niobates (Sr 1-x Ba x Nb2O6), general formula [Bi2O2][A n-1 BnO 3n+1] or Bi4Ti3O 12 may be included or used. The compounds may be non-stoichiometric or intergrowth phases and are not constrained to nominal stoichiometry. The compositions may include elemental metals including C, Al, Si, Ti, Fe, Zn, Ag, and / or Bi; binary metal oxides including MgO, Al2O3, SiO2, TiO2, Ti2O3, Cr2O3, MnO, FeO, CoO, NiO, CuO, ZnO, and / or SnO2; binary metal nitrides including TiN, Mn3N2, Co2N, Ni3N, and / or Zn3N2; binary metal carbides including TiC; binary metal borides including ZrB2 and / or NbB2; binary metal silicides including NbSi2, WSi2, and / or MoSi2; polyethylene; polyamide; kynar; polytetrafluoroethylene; and / or any combination thereof.

[0028] The device can include a wick adjacent to the PTCR heating element, the wick configured to transport the fluid to a vaporization location. The PTCR heating element can be configured to heat the fluid at the vaporization location. The device can include a second heating element, the second heating element adjacent to a second side of the wick and the first heating element adjacent to a first side of the wick. The wick can include an open weave configuration. The open weave configuration can be adjacent to the first heating element, the second heating element, and / or a cylindrical end of the wick.

[0029] The power source can be configured to provide a voltage between 3V and 6V. In some implementations, the power source can be a battery, such as a rechargeable battery. In some implementations, the power source can provide a voltage between 3V and 10V, 3V and 50V, or 3V and 100V, among others. The power source can provide either direct current (DC) or alternating current (AC).

[0030] The method includes receiving, by a vaporizer device, a user input and heating a vaporizable fluid using a PTCR heating element of the vaporizer device, the PTCR heating element being electrically coupled to a power source and configured to heat the vaporizable fluid to form an aerosol. The PTCR heating element includes an electrical resistivity that varies based on temperature, the electrical resistivity including an electrical resistivity transition region including an increase in electrical resistivity over a temperature range, such that when the PTCR heating element is heated to a first temperature within the transition region, a flow of electrical current from the power source is reduced to a level that limits further temperature increase of the PTCR heating element due to current flow. The method may further include generating a vapor by heating the vaporizable fluid.

[0031] In some implementations, the device includes a housing including a power source, a fluid reservoir including an inlet, an outlet, containing a fluid, and configured to be coupled to the housing, and a PTCR heating element electrically coupled to the power source and configured to heat the fluid to form an aerosol. The PTCR heating element includes an electrical resistivity that changes based on temperature. The electrical resistivity includes an electrical resistivity transition region that includes an increase in electrical resistivity over a temperature range, such that when the PTCR heating element reaches a temperature within the transition region, the resistivity of the element increases to a level that limits the flow of electrical current from the battery, limiting further temperature increase of the PTCR heating element.

[0032] The details of one or more variations of the subject matter described herein are set forth in the accompanying drawings and the description below. Other features and advantages of the subject matter described herein will become apparent from the description and drawings, and from the claims. The claims following this disclosure are intended to define the scope of the protected subject matter.

[0033] The patent or application file contains at least one drawing executed in color. Copies of any color drawing(s) in this patent or patent application publication will be provided by the Office upon request and payment of the necessary fee.

[0034] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate certain aspects of the subject matter disclosed herein and, together with the description, serve to explain some of the basic schemes associated with the disclosed implementations. [Brief description of the drawings]

[0035] [Figure 1A] FIG. 1 illustrates the behavior of thermal power generation in an isotropic PTCR material. [Figure 1B] FIG. 2 is a plot illustrating an example resistivity versus temperature curve for a semiconductor material having a nonlinear positive temperature coefficient of resistance, consistent with an implementation of the present subject matter. [Figure 1C] FIG. 1C presents a table of resistivity versus temperature curve data for the nonlinear PTCR semiconductor material shown in FIG. 1B, consistent with an implementation of the present subject matter. [Figure 2A] FIG. 13 shows a diagram of an example heating element that may enable improved vaporizer heating consistent with implementations of the present subject matter. [Figure 2B] 2B is a diagram showing a cross-section of an exemplary heating element shown in FIG. 2A consistent with an implementation of the present subject matter. [Figure 3A] FIG. 2 illustrates modeled temperatures for an exemplary heater consistent with implementations of the present subject matter. [Figure 3B] FIG. 2 illustrates modeled temperatures for an exemplary heater consistent with implementations of the present subject matter. [Figure 3C] FIG. 2 illustrates modeled temperatures for an exemplary heater consistent with implementations of the present subject matter. [Figure 3D] FIG. 2 illustrates modeled temperatures for an exemplary heater consistent with implementations of the present subject matter. [Figure 3E] FIG. 2 illustrates modeled temperatures for an exemplary heater consistent with implementations of the present subject matter. [Figure 3F] FIG. 2 illustrates a resistivity vs. temperature curve of an exemplary nonlinear PTCR consistent with implementations of the present subject matter. [Figure 3G] FIG. 2 shows another exemplary PTCR resistivity versus temperature curve consistent with implementations of the present subject matter. [Figure 4] FIG. 2 illustrates an exemplary positive temperature coefficient resistivity heater including a material having a positive temperature coefficient of resistance sandwiched between conductive layers, consistent with an implementation of the present subject matter. [Diagram 5] 5 is a diagram illustrating the temperature of the example heater of FIG. 4, consistent with an implementation of the present subject matter. [Figure 6] FIG. 2 illustrates an exemplary vaporization assembly including a fibrous wick with an exemplary heater mounted on one flat side of the fibrous wick, consistent with an implementation of the present subject matter. [Figure 7] FIG. 13 illustrates another exemplary implementation of a vaporization assembly with a heater surrounded by an open weave wicking material consistent with implementations of the present subject matter. [Figure 8] 1 is a block diagram illustrating an example vaporizer consistent with implementations of the present subject matter. [Figure 9] FIG. 2 illustrates a process flow chart of an exemplary process for operating an exemplary vaporizer device utilizing a heating element having a positive temperature coefficient of resistance, consistent with implementations of the present subject matter. [Figure 10A] FIG. 2 illustrates modeled temperatures of an exemplary PTCR heater consistent with implementations of the present subject matter. [Figure 10B] FIG. 2 illustrates modeled temperatures of an exemplary PTCR heater consistent with implementations of the present subject matter. [Figure 10C] FIG. 2 illustrates modeled temperatures of an exemplary PTCR heater consistent with implementations of the present subject matter. [Figure 10D] FIG. 2 illustrates modeled temperatures of an exemplary PTCR heater consistent with implementations of the present subject matter. [Figure 10E] FIG. 2 illustrates modeled temperatures of an exemplary PTCR heater consistent with implementations of the present subject matter. [Figure 10F] FIG. 2 illustrates modeled temperatures of an exemplary PTCR heater consistent with implementations of the present subject matter. [Figure 11A] FIG. 2 illustrates modeled surface temperature as a function of time for an exemplary PTCR heater consistent with implementations of the present subject matter. [Figure 11B] FIG. 13 illustrates modeled and measured maximum surface temperatures as a function of time for an exemplary PTCR heater consistent with implementations of the present subject matter. [Figure 11C] FIG. 1 illustrates modeled and measured average surface temperature as a function of time for an exemplary PTCR heater consistent with implementations of the present subject matter. [Figure 12] FIG. 2 illustrates the transient current response as a function of time of an exemplary PTCR heater consistent with implementations of the present subject matter.

[0036] Wherever practical, like reference numerals refer to like structures, features, or elements.

[0037] Detailed Description Implementations of the present subject matter include methods, apparatus, articles of manufacture, and systems related to vaporizer heaters that utilize heating elements with a nonlinear positive temperature coefficient of resistance (PTCR), also referred to as PTCR heaters. It should be noted that "nonlinear" refers to a PTCR heating element over its operating range. Some operating ranges may exhibit a linear resistivity coefficient, but at transition temperatures where the rate of change of the resistivity coefficient becomes significant, the resistivity coefficient changes significantly. In this manner, the PTCR heating element may be self-limiting in temperature, and given a known range of applied voltages, a rapid increase in resistance limits current flow so that the PTCR heating element does not heat beyond a certain operating temperature. Some aspects of the present subject matter may enable a vaporizer device that utilizes a PTCR heating element to provide inherent temperature control of the PTCR heating element at or near a desired operating temperature. Temperature can be controlled over a range of applied voltages without the need for temperature sensors, electronic circuitry, controllers, microprocessors, and / or algorithms to provide power control to the PTCR heating element. Utilizing a PTCR heating element with inherent temperature control can prevent overheating (e.g., combustion) of a vaporizable material (e.g., a vaporizable fluid or other material), thereby avoiding the formation of undesirable and potentially hazardous chemical by-products.

[0038] One type of heating element can include a resistive heating element, which can be constructed of or at least include a material (e.g., a metal or alloy such as a nickel-chromium alloy, or a non-metallic resistor) configured to dissipate power in the form of heat when an electrical current is passed through one or more resistive segments of the PTCR heating element.

[0039] Vaporizer devices can typically be divided into two classes. One class of vaporizer devices may be more advanced in that they utilize relatively strict temperature control to prevent overheating and the formation of unwanted and potentially dangerous chemical by-products. Such temperature control may require hardware and / or software to measure temperature, such as one or more temperature sensors and electronic circuitry, which is generally expensive. The electronic circuitry may include a microprocessor that may provide the ability to control power to the PTCR heating element at the point of vaporization.

[0040] Another class of vaporizer device may be simpler in that no temperature control is provided, resulting in a cheaper vaporizer device to build, but this may carry the risk of overheating the vaporizable material and / or various components of the vaporizer device, which may permanently damage the vaporizer device and / or produce undesirable chemical by-products.

[0041] In some implementations, the present subject matter may enable vaporizer devices with PTCR heating elements, including simpler electronics, lower cost, and unique and precise temperature control.

[0042] The resistivity coefficient of a material characterizes the change in resistivity of a PTCR heating element in response to a change in temperature. Some implementations of the present subject matter include a PTCR heating element having a nonlinear positive temperature coefficient of resistance (PTCR), which may include a material (e.g., a semiconductor) having an electrical resistivity (also referred to as resistivity) that changes nonlinearly with increasing temperature. For example, a PTCR heating element may include a material having a resistivity that is temperature-dependent, which may be referred to as a nonlinear PTCR material because the resistivity includes a region (e.g., a transition region) where the resistivity increases relatively greatly over a relatively short period of temperature change. Such a PTCR heating element with a nonlinear PTCR material may simply be referred to as a PTCR heating element.

[0043] In such a PTCR heating element, the resistivity of the PTCR material may be relatively low while the temperature remains below the temperature transition region. Once above the temperature transition region, the resistivity of the PTCR material may be significantly higher than the resistivity of the same PTCR material at temperatures below the temperature transition region. For example, the change in resistivity may be orders of magnitude greater in the temperature transition region below 50 degrees Celsius.

[0044] PTCR heating elements utilize a nonlinear PTCR material to provide inherent temperature control. For example, a PTCR heating element at ambient temperature can be connected to a power source to provide a voltage gradient and resulting current flow. The resistivity of the PTCR heating element is relatively low at ambient temperature (e.g., ambient temperature is below the transition region), so current flows through the PTCR heating element. As current flows through the nonlinear PTCR material, heat is generated (e.g., by dissipating power) due to the resistance. The generated heat increases the temperature of the PTCR heating element, causing a change in the resistivity of the PTCR heating element. When the temperature of the PTCR heating element reaches the transition region (i.e., the transition temperature), the resistivity increases significantly over a narrow temperature range. The change in resistivity can be caused by a change in the physical properties of the material. For example, a phase transition may occur within the material. Such an increase in resistivity (resulting in an overall increase in resistance) reduces the flow of current and reduces the amount of heat generated. The transition region includes the temperature at which there is an inflection point, and insufficient heat is generated to further increase the temperature of the PTCR heating element. This limits the temperature of the PTCR heating element. As long as the power source is connected and current is applied, the PTCR heating element will maintain a uniform temperature with minimal temperature change. In this case, the power applied to the PTCR heating element is given by the formula P I =Volts 2 The heat loss of the PTCR heating element can be expressed as P L and includes any combination of conductive, convective, radiative, and latent heat. During steady-state operation, P I =P L It is. L As P increases, the temperature of the PTCR heating element decreases, which decreases the resistance and increases the current through the PTCR heating element. L As P decreases, the temperature of the PTCR heating element increases, which increases its resistance and reduces the current flowing through the PTCR heating element. LThe resistance of a PTCR heating element increases logarithmically as approaches 0. The limited operating temperature of a PTCR heating element can be influenced by the element material, element geometry, element resistivity as a function of temperature characteristics, power supply, and circuit characteristics (e.g., voltage gradient, current, time-varying characteristics), etc.

[0045] The material structure of a PTCR heating element consistent with the present disclosure may be composed of many individual crystallites. At the edges of these individual crystallites are grain boundaries where potential barriers are formed, preventing free electrons from diffusing to adjacent regions. This means that the grain boundaries result in high resistance. However, at low temperatures there is no effect. Without being bound to a particular theory, it is believed that the high dielectric constant and the rapid polarization at the grain boundaries prevents the formation of potential barriers at low temperatures and allows the flow of free electrons (i.e., current flow). The higher temperature is known as the Curie temperature, above which the dielectric constant and polarization decrease to a point where the potential barrier grows so large that electrical resistance rises. At a certain temperature range above the Curie temperature, the resistance of the PTCR heating element increases exponentially.

[0046] As shown in FIG. 1A, the thermal power generation in an isotropic PTCR material can be characterized as follows: for every control volume ∂x, ∂y, ∂z in an isotropic PTCR material subjected to a voltage gradient ∇V, the control volume ∂x, ∂y, ∂z heats to a temperature within the PTCR transition region and maintains that temperature within a wide range of ∇V. The thermal power generation is

number

[0047] FIG. 1B is a plot showing an exemplary resistivity vs. temperature curve of a nonlinear PTCR material. The vertical axis is logarithmic. A PTCR heating element (referred to as a PTCR heater) constructed (e.g., formed) of a nonlinear PTCR material may include advantageous properties. For example, upon application of a sufficient voltage gradient (e.g., ∇V), the PTCR heater heats up and the temperature increases until a transition region is reached. In the curve shown in FIG. 1B, the transition region extends from temperature T1 to T2. In the curve shown in FIG. 1B, the resistivity vs. temperature curve appears nonlinear between T1 and T2, but in other embodiments, the resistivity vs. temperature curve may be approximately linear or linear or of other shapes. At temperatures above T1, the resistivity of the nonlinear PTCR material increases to a point where further temperature increase stops. This is because the overall resistance increases to a point where current flow is limited. In other words, in a PTCR heater implementation, the temperature can be considered self-limiting and will not heat up beyond just above a low point T1 in the temperature transition region given a known range of applied voltage. In the curve shown in Figure 1B, the resistivity decreases as the temperature increases to T1, but in other embodiments the resistivity may be more plateaued or increase as the temperature increases to T1.

[0048] FIG. 1C presents a table of resistivity versus temperature curve data for the nonlinear PTCR semiconductor material shown in FIG. 1B. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 100 Ωcm at 100° C. and a resistivity of 50,000 Ωcm to 150,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 20 Ωcm to 200 Ωcm at 100° C. and a resistivity of 100,000 Ωcm to 200,000 Ωcm at 265° C. In some implementations, the PTCR heating element has a resistivity of less than 100 Ωcm at 100° C. and a resistivity of more than 100,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of less than 100 Ωcm at 100° C. and a resistivity of more than 250,000 Ωcm at 275° C. In some implementations, the PTCR heating element has a resistivity of less than 100 Ωcm at 100° C. and greater than 300,000 Ωcm at 295° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 110 Ωcm at 25° C., a resistivity of 10 Ωcm to 110 Ωcm at 100° C., and a resistivity of 100,000 Ωcm to 325,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 150 Ωcm at 25° C., a resistivity of 10 Ωcm to 150 Ωcm at 100° C., and a resistivity of 100,000 Ωcm to 350,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 200 Ωcm at 25° C., a resistivity of 10 Ωcm to 200 Ωcm at 100° C., and a resistivity of 100,000 Ωcm to 375,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 300 Ωcm at 25° C., a resistivity of 10 Ωcm to 300 Ωcm at 100° C., and a resistivity of 100,000 Ωcm to 400,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 400 Ωcm at 25° C., a resistivity of 10 Ωcm to 400 Ωcm at 100° C., and a resistivity of 100,000 Ωcm to 450,000 Ωcm at 280° C.In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 500 Ωcm at 25° C., a resistivity of 10 Ωcm to 500 Ωcm at 100° C., and a resistivity of 100,000 Ωcm to 500,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 110 Ωcm at 25° C., a resistivity of 50 Ωcm to 110 Ωcm at 100° C., and a resistivity of 150,000 Ωcm to 325,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 150 Ωcm at 25° C., a resistivity of 50 Ωcm to 150 Ωcm at 100° C., and a resistivity of 150,000 Ωcm to 350,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 200 Ωcm at 25° C., a resistivity of 50 Ωcm to 200 Ωcm at 100° C., and a resistivity of 150,000 Ωcm to 375,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 300 Ωcm at 25° C., a resistivity of 50 Ωcm to 300 Ωcm at 100° C., and a resistivity of 150,000 Ωcm to 400,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 400 Ωcm at 25° C., a resistivity of 50 Ωcm to 400 Ωcm at 100° C., and a resistivity of 150,000 Ωcm to 450,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 500 Ωcm at 25° C., a resistivity of 50 Ωcm to 500 Ωcm at 100° C., and a resistivity of 150,000 Ωcm to 500,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 90 Ωcm to 110 Ωcm at 25° C., a resistivity of 90 Ωcm to 110 Ωcm at 100° C., and a resistivity of 200,000 Ωcm to 325,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 90 Ωcm to 150 Ωcm at 25° C., a resistivity of 90 Ωcm to 150 Ωcm at 100° C., and a resistivity of 200,000 Ωcm to 350,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 90 Ωcm to 200 Ωcm at 25°C, a resistivity of 90 Ωcm to 200 Ωcm at 100°C, and a resistivity of 200,000 Ωcm to 375,000 Ωcm at 280°C.In some implementations, the PTCR heating element has a resistivity of 90 Ωcm to 300 Ωcm at 25° C., a resistivity of 90 Ωcm to 300 Ωcm at 100° C., and a resistivity of 200,000 Ωcm to 400,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 90 Ωcm to 400 Ωcm at 25° C., a resistivity of 90 Ωcm to 400 Ωcm at 100° C., and a resistivity of 200,000 Ωcm to 450,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 90 Ωcm to 500 Ωcm at 25° C., a resistivity of 90 Ωcm to 500 Ωcm at 100° C., and a resistivity of 200,000 Ωcm to 500,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 110 Ωcm at 50° C., a resistivity of 10 Ωcm to 50 Ωcm at 150° C., and a resistivity of 50,000 Ωcm to 125,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 150 Ωcm at 50° C., a resistivity of 10 Ωcm to 100 Ωcm at 150° C., and a resistivity of 50,000 Ωcm to 150,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 200 Ωcm at 50° C., a resistivity of 10 Ωcm to 150 Ωcm at 150° C., and a resistivity of 50,000 Ωcm to 175,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 300 Ωcm at 50° C., a resistivity of 10 Ωcm to 200 Ωcm at 150° C., and a resistivity of 50,000 Ωcm to 200,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 400 Ωcm at 50° C., a resistivity of 10 Ωcm to 250 Ωcm at 150° C., and a resistivity of 50,000 Ωcm to 250,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 500 Ωcm at 50° C., a resistivity of 10 Ωcm to 300 Ωcm at 150° C., and a resistivity of 50,000 Ωcm to 300,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 110 Ωcm at 50° C., a resistivity of 20 Ωcm to 50 Ωcm at 150° C., and a resistivity of 75000 Ωcm to 125000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 150 Ωcm at 50° C., a resistivity of 20 Ωcm to 100 Ωcm at 150° C., and a resistivity of 75000 Ωcm to 150000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 200 Ωcm at 50° C., a resistivity of 20 Ωcm to 150 Ωcm at 150° C., and a resistivity of 75000 Ωcm to 175000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 300 Ωcm at 50° C., a resistivity of 20 Ωcm to 200 Ωcm at 150° C., and a resistivity of 75000 Ωcm to 200000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 400 Ωcm at 50° C., a resistivity of 20 Ωcm to 250 Ωcm at 150° C., and a resistivity of 75000 Ωcm to 250000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 500 Ωcm at 50° C., a resistivity of 20 Ωcm to 300 Ωcm at 150° C., and a resistivity of 75000 Ωcm to 300000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 75 Ωcm to 110 Ωcm at 50° C., a resistivity of 30 Ωcm to 50 Ωcm at 150° C., and a resistivity of 100,000 Ωcm to 125,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 75 Ωcm to 150 Ωcm at 50° C., a resistivity of 30 Ωcm to 100 Ωcm at 150° C., and a resistivity of 100,000 Ωcm to 150,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 75 Ωcm to 200 Ωcm at 50° C., a resistivity of 30 Ωcm to 150 Ωcm at 150° C., and a resistivity of 100,000 Ωcm to 175,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 75 Ωcm to 300 Ωcm at 50°C, a resistivity of 30 Ωcm to 200 Ωcm at 150°C, and a resistivity of 100,000 Ωcm to 200,000 Ωcm at 260°C.In some implementations, the PTCR heating element has a resistivity of 75 Ωcm to 400 Ωcm at 50° C., a resistivity of 30 Ωcm to 250 Ωcm at 150° C., and a resistivity of 100,000 Ωcm to 250,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 75 Ωcm to 500 Ωcm at 50° C., a resistivity of 30 Ωcm to 300 Ωcm at 150° C., and a resistivity of 100,000 Ωcm to 300,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 110 Ωcm at 25° C., a resistivity of 10 Ωcm to 50 Ωcm at 150° C., and a resistivity of 100,000 Ωcm to 325,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 150 Ωcm at 25° C., a resistivity of 10 Ωcm to 100 Ωcm at 150° C., and a resistivity of 100,000 Ωcm to 350,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 200 Ωcm at 25° C., a resistivity of 10 Ωcm to 150 Ωcm at 150° C., and a resistivity of 100,000 Ωcm to 375,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 300 Ωcm at 25° C., a resistivity of 10 Ωcm to 200 Ωcm at 150° C., and a resistivity of 100,000 Ωcm to 400,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 400 Ωcm at 25° C., a resistivity of 10 Ωcm to 250 Ωcm at 150° C., and a resistivity of 100,000 Ωcm to 450,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 500 Ωcm at 25° C., a resistivity of 10 Ωcm to 300 Ωcm at 150° C., and a resistivity of 100,000 Ωcm to 500,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 110 Ωcm at 25° C., a resistivity of 20 Ωcm to 50 Ωcm at 150° C., and a resistivity of 150,000 Ωcm to 325,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 150 Ωcm at 25°C, a resistivity of 20 Ωcm to 100 Ωcm at 150°C, and a resistivity of 150,000 Ωcm to 350,000 Ωcm at 280°C.In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 200 Ωcm at 25° C., a resistivity of 20 Ωcm to 150 Ωcm at 150° C., and a resistivity of 150,000 Ωcm to 375,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 300 Ωcm at 25° C., a resistivity of 20 Ωcm to 200 Ωcm at 150° C., and a resistivity of 150,000 Ωcm to 400,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 400 Ωcm at 25° C., a resistivity of 20 Ωcm to 250 Ωcm at 150° C., and a resistivity of 150,000 Ωcm to 450,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 500 Ωcm at 25° C., a resistivity of 20 Ωcm to 300 Ωcm at 150° C., and a resistivity of 150,000 Ωcm to 500,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 90 Ωcm to 110 Ωcm at 25° C., a resistivity of 30 Ωcm to 50 Ωcm at 150° C., and a resistivity of 200,000 Ωcm to 325,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 90 Ωcm to 150 Ωcm at 25° C., a resistivity of 30 Ωcm to 100 Ωcm at 150° C., and a resistivity of 200,000 Ωcm to 350,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 90 Ωcm to 200 Ωcm at 25° C., a resistivity of 30 Ωcm to 150 Ωcm at 150° C., and a resistivity of 200,000 Ωcm to 375,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 90 Ωcm to 300 Ωcm at 25° C., a resistivity of 30 Ωcm to 200 Ωcm at 150° C., and a resistivity of 200,000 Ωcm to 400,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 90 Ωcm to 400 Ωcm at 25° C., a resistivity of 30 Ωcm to 250 Ωcm at 150° C., and a resistivity of 200,000 Ωcm to 450,000 Ωcm at 280° C. In some implementations, the PTCR heating element has a resistivity of 90 Ωcm to 500 Ωcm at 25°C, a resistivity of 30 Ωcm to 300 Ωcm at 150°C, and a resistivity of 200,000 Ωcm to 500,000 Ωcm at 280°C.In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 110 Ωcm at 50° C., a resistivity of 10 Ωcm to 110 Ωcm at 100° C., and a resistivity of 50,000 Ωcm to 125,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 150 Ωcm at 50° C., a resistivity of 10 Ωcm to 150 Ωcm at 100° C., and a resistivity of 50,000 Ωcm to 150,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 200 Ωcm at 50° C., a resistivity of 10 Ωcm to 200 Ωcm at 100° C., and a resistivity of 50,000 Ωcm to 175,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 300 Ωcm at 50° C., a resistivity of 10 Ωcm to 300 Ωcm at 100° C., and a resistivity of 50,000 Ωcm to 200,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 400 Ωcm at 50° C., a resistivity of 10 Ωcm to 400 Ωcm at 100° C., and a resistivity of 50,000 Ωcm to 250,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 10 Ωcm to 500 Ωcm at 50° C., a resistivity of 10 Ωcm to 500 Ωcm at 100° C., and a resistivity of 50,000 Ωcm to 300,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 110 Ωcm at 50° C., a resistivity of 50 Ωcm to 110 Ωcm at 100° C., and a resistivity of 75000 Ωcm to 125000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 150 Ωcm at 50° C., a resistivity of 50 Ωcm to 150 Ωcm at 100° C., and a resistivity of 75000 Ωcm to 150000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 200 Ωcm at 50° C., a resistivity of 50 Ωcm to 200 Ωcm at 100° C., and a resistivity of 75000 Ωcm to 175000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 300 Ωcm at 50°C, a resistivity of 50 Ωcm to 300 Ωcm at 100°C, and a resistivity of 75000 Ωcm to 200000 Ωcm at 260°C.In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 400 Ωcm at 50° C., a resistivity of 50 Ωcm to 400 Ωcm at 100° C., and a resistivity of 75000 Ωcm to 250000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 50 Ωcm to 500 Ωcm at 50° C., a resistivity of 50 Ωcm to 500 Ωcm at 100° C., and a resistivity of 75000 Ωcm to 300000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 75 Ωcm to 110 Ωcm at 50° C., a resistivity of 90 Ωcm to 110 Ωcm at 100° C., and a resistivity of 100000 Ωcm to 125000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 75 Ωcm to 150 Ωcm at 50° C., a resistivity of 90 Ωcm to 150 Ωcm at 100° C., and a resistivity of 100,000 Ωcm to 150,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 75 Ωcm to 200 Ωcm at 50° C., a resistivity of 90 Ωcm to 200 Ωcm at 100° C., and a resistivity of 100,000 Ωcm to 175,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 75 Ωcm to 300 Ωcm at 50° C., a resistivity of 90 Ωcm to 300 Ωcm at 100° C., and a resistivity of 100,000 Ωcm to 200,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 75 Ωcm to 400 Ωcm at 50° C., a resistivity of 90 Ωcm to 400 Ωcm at 100° C., and a resistivity of 100,000 Ωcm to 250,000 Ωcm at 260° C. In some implementations, the PTCR heating element has a resistivity of 75 Ωcm to 500 Ωcm at 50° C., a resistivity of 90 Ωcm to 500 Ωcm at 100° C., and a resistivity of 100,000 Ωcm to 300,000 Ωcm at 260° C.

[0049] The performance of a PTCR heater may depend on the PTCR behavior and the heater geometry as shown in FIG. 1B. A PTCR heater with a relatively long and narrow geometry with electrical contacts across the long dimension of the PTCR heater for applying a differential voltage may generally be ineffective because the resistivity of the nonlinear PTCR material is too high at temperatures below T1. A nonlinear PTCR material with a steep transition region where the temperature difference between T1 and T2 is less than 10° C. may have all of the voltage drop within a small portion of the length of the elongated geometry, and any material will inevitably have spatial nonuniformity. Therefore, some implementations of PTCR heaters include electrode structures for PTCR heaters where the nonlinear PTCR material is provided in a parallel circuit. This can improve the uniformity of heating in some implementations. The geometry of the PTCR heater may include a thin piece of nonlinear PTCR material sandwiched between conductors or conductive coatings, between which a differential voltage can be applied.

[0050] FIG. 2A illustrates an exemplary PTCR heating element 50 that may improve the heating of a vaporizer. A thin piece of nonlinear PTCR material 10 (e.g., a PTCR ceramic material) is shown in FIG. 2, where the nonlinear PTCR material 10 is sandwiched between conductive layers 20 and is further attached to conductive leads 30 such that a differential voltage may be applied from the conductive leads 30. In some implementations, a single conductive lead 30 is attached to each conductive layer 20 of the PTCR heating element 50. In some implementations, two or more conductive leads 30 are attached to each conductive layer 20 of the PTCR heating element 50. FIG. 2B illustrates a cross-sectional view of the exemplary PTCR heating element 50 shown in FIG. 2A.

[0051] In some implementations, which may be effective in vaporizer devices using vaporizable materials, the fluid may be a combination including propylene glycol and glycerol, for example. In some implementations, the fluid is a vaporizable material including a nicotine formulation. In some implementations, the PTCR heating element 50 includes the shape shown in FIG. 2A, with other dimensions of 0.5 mm thickness (height) and 5.0 mm (length and width) of nonlinear PTCR material. In some exemplary embodiments, the thickness of the PTCR material may be about 0.2 mm to about 0.5 mm. Electrical properties of the nonlinear PTCR material include the following values: That is, the T1 value is between 150°C and 300°C, for example between 220°C and 280°C, the resistivity at temperatures below T1 is between 0.1 Ωm and 100 Ωm, for example between 1 Ωm and 10 Ωm, the change in resistivity between T1 and T2 is an enhancement factor of more than 100, for example an enhancement factor of more than 1000, and the temperature difference between T1 and T2 is less than 200°C, for example less than 50°C.

[0052] 3A-3E show modeled temperatures for an example of a PTCR heating element 50. In the illustrated example, the nonlinear PTCR material 10 includes a plate shape with dimensions of 5 mm×5 mm×0.5 mm. The conductive layer 20 was formed of silver (Ag) with dimensions of 5 mm×5 mm×0.025 mm. The conductive leads 30 were formed of copper (Cu) with dimensions of 12 mm×2 mm×0.2 mm. The plate shape may include two parallel sides with conductive leads attached. The nonlinear PTCR material 10 included a PTCR resistivity vs. temperature curve with a nonlinear transition region from about 240° C. to about 300° C., as shown in FIG. 3F. A voltage of 3V-6V was applied across the conductive leads 30 of the exemplary PTCR heating element 50. Other configurations may apply different voltage ranges, such as, for example, 3V-10V, 3V-50V, etc. Under these conditions, an exemplary PTCR heating element 50 outdoors with free convection airflow will increase in temperature as shown in the modeled sequence of Figures 3A-3E, which show 0.0, 0.2, 0.5, 1.0, and 2.0 seconds, respectively, after application of the differential voltage. As shown, beyond 1.0 second, the temperature is relatively uniform, with a peak temperature at the surface of the conductive layer 20 below 270°C.

[0053] FIG. 3G shows another exemplary PTCR resistivity versus temperature curve. In this example, the density of the PTCR material is 5700 kg / m 3 , heat capacity of 520 J / kgK, and thermal conductivity of 2.1 W / mK. The resistivity first begins to increase at temperatures above about 440 K, then increases sharply between 503 K and 518 K. At 298 K, the resistivity of the PTCR material forming the PTCR heating element is 0.168 Ωm, at 373 K, the resistivity of the PTCR material forming the PTCR heating element is 0.105 Ωm, and at 518 K, the resistivity of the PTCR material forming the PTCR heating element is 3.669 Ωm. In some example implementations, the density of the PTCR material is 5000 kg / m 3 ~7000kg / m 3 , the heat capacity is 450J / kgK~600J / kgK, and the thermal conductivity is 1.5W / mK~3.0W / mK.

[0054] Uniform temperature is a desirable performance attribute of PTCR heaters and gives them a distinct advantage over series coil heaters, such as series heaters where the power input is controlled by temperature sensors, microprocessor-equipped electronics, and advanced algorithms dedicated to temperature control. Existing series heaters can adjust the overall power in response to temperature measurements at one point, or by the average temperature estimated by the overall electrical resistivity combined with the TCR (temperature coefficient of resistivity) of a typical series heating element. However, in some series heaters, the overall power is adjusted such that local temperature variations due to local resistivity variations, for example, can cause the temperature within the series heater to vary by more than 40°C.

[0055] In some implementations, the PTCR heating element 50 can be constructed using materials with the same or similar non-linear PTCR resistivity vs. temperature curve as shown in FIG. 1B, in a parallel geometry as shown in FIG. 2A and FIG. 2B, and with an appropriate (e.g., 3V-6V) differential voltage applied to the conductive leads 30. Each given control volume within such a PTCR heater has a temperature within a narrow range, typically less than 10° C. This can also be achieved using a differential heat load. The less than 10° C. range can be tailored for vaporization by controlling the material and geometric configuration of the PTCR heating element.

[0056] PTCR heaters can be formed in any of a number of geometric shapes. For example, FIG. 4 shows an exemplary PTCR heater 460 that includes a PTCR material 410 sandwiched between conductive layers 420. The PTCR material 410 includes a rectangular hole 440. The conductive layers 420 are attached to the conductive leads 430 such that a differential voltage can be applied to the conductive leads 430. The rectangular hole 440 provides a path for vapor to escape in one example where the PTCR heater 460 is in contact with a material that is pre-saturated with the liquid to be vaporized.

[0057] The shape and size of the holes in the PTCR heater 460 may be of any size, spacing and shape, including any polygonal or circular shape that may be configured for vaporization.

[0058] FIG. 5 shows the temperature of an exemplary PTCR heater 460 modeled with applied voltage, with the temperature after 2.0 seconds exhibiting a temperature of 265±1.0° C. as shown in FIG.

[0059] FIG. 6 shows an exemplary vaporizer assembly 100 including a fibrous wick 90 with an exemplary PTCR heater 460 mounted on one flat side of the fibrous wick 90 (e.g., the broad surface of the wick 90). In some implementations, the PTCR heater 460 can be mounted on both flat surfaces of the fibrous wick 90. ​​In some implementations, the vaporizer assembly 100 can be positioned within a vaporizer device such that the inflow of air (typically generated by a user of the vaporizer device) is oriented parallel to the broad surface of the vaporizer assembly 100, as shown by the arrows. Such a vaporizer assembly configuration can ensure that vapor is generated primarily in the area heated by the PTCR heater 460 with a directed airflow. The parallel airflow can generate appropriate (e.g., maximum) surface shear stress in the primary vapor generation area, which can improve the operation of the vaporizer device.

[0060] 7 shows another exemplary implementation of a vaporization assembly 200 with a PTCR heating element 50 having conductive leads 30 surrounded by an open weave wicking material 220 whose ends are rolled into a cylindrical shape 210 to receive a vaporizable material (not shown). The exemplary configuration of FIG. 7 allows the end of the wick to be smaller than the PTCR heating element while still taking advantage of the large surface area of ​​the PTCR heating element to improve heating. Other vaporization assembly configurations are possible.

[0061] The PTCR heating element can be implemented in a vaporizer device. Referring to the block diagram of FIG. 8, an exemplary vaporizer 810 includes a housing 812 containing a power source 822 (such as a battery, which may be a rechargeable battery) for providing a current flow at a predetermined voltage, and optionally a controller 824 (e.g., a processor, circuitry, etc. capable of executing logic) for controlling the delivery of heat to a vaporizer 826 to convert the vaporizable material from a condensed form (e.g., a solid, liquid, solution, suspension, at least partially unprocessed part of plant material, etc.) to a gas phase. The optional controller 824 may be part of one or more printed circuit boards (PCBs) consistent with a particular implementation of the present subject matter. The vaporizer 826 includes a wicking element (also referred to herein as a wicking element (not shown in FIG. 8)) and a PTCR heating element 828. The wicking element allows air to enter the reservoir to replace the volume of liquid that is removed. In other words, by capillary action, vaporization by the PTCR heating element draws the liquid vaporizable material into the wicking element (discussed below). Air, in some implementations of the present subject matter, can return through the wicking element to the reservoir to at least partially equalize pressure within the reservoir. Other approaches that allow air to return to the reservoir to equalize pressure are also within the scope of the present subject matter.

[0062] The PTCR heating element 828 includes a PTCR material. In some implementations, the PTCR heating element can be or include one or more of a conductive heater, a radiative heater, and a convective heater. In some implementations of the present subject matter, the vaporizer can include a PTCR heating element that can be wrapped around or disposed within the wicking element, or integrated into the wicking element in bulk form, or pressed into thermal contact with the wicking element, or otherwise arranged to deliver heat to the wicking element, such that liquid vaporizable material drawn from the reservoir into the wicking element is vaporized for subsequent inhalation by the user in the gas phase and / or condensed (e.g., aerosol particles or droplets) phase. As described herein, other wicking element, heating element, and / or vaporizer assembly configurations are also possible.

[0063] Additionally or alternatively, certain vaporizers can be configured to generate inhalable intakes of gas and / or aerosol phase vaporizable material, for example, via heating of a non-liquid vaporizable material, such as a solid-phase vaporizable material (e.g., wax) or a plant material containing vaporizable material (e.g., tobacco leaves and / or portions thereof). In such vaporizers, the PTCR heating element may be part of, or otherwise integrated into, or in thermal contact with, the wall of the oven or other heating chamber in which the non-liquid vaporizable material is placed. Alternatively, one or more PTCR heating elements may be used to heat air that has passed or passed through the non-liquid vaporizable material, resulting in convective heating of the non-liquid vaporizable material. In yet other examples, the PTCR heating element or elements may be disposed in intimate contact with the plant material such that direct conductive heating of the plant material occurs from within a given mass of the plant material (e.g., not just inwardly from the walls of the oven).

[0064] The PTCR heating element can be actuated (e.g., by a controller, which may be part of the vaporizer body, as described below, and by a controller, which may pass current from a power source through a circuit including the PTCR heating element, which may be part of the vaporizer cartridge, as described below) in association with a user's puff (e.g., inhalation, inhalation, etc.) on the vaporizer mouthpiece 830 to flow air from the air inlet, along an airflow path that passes through the vaporizer 826 (e.g., the wicking element and the PTCR heating element 828), and in some implementations through one or more condensation areas or chambers, to an air outlet of the mouthpiece. The incoming air along the airflow path passes over or through the vaporizer, etc., entraining gas-phase vaporizable material into the air. As described above, the entrained gas-phase vaporizable material condenses as it passes through the remainder of the airflow path, such that an inhalable intake of the vaporizable material in aerosol form can be delivered from the air outlet (e.g., into the mouthpiece 830 for inhalation by the user).

[0065] Activation of the PTCR heating element 828 is triggered by closing a circuit between the power source and the PTCR heating element using an input device 833. In some implementations, the input device 833 is a switch and may be used to electrically complete the circuit between the power source and the PTCR heating element. In some implementations, the input device 833 includes a relay, a solenoid, and / or a solid state device and may be used to electrically complete the circuit between the power source and the PTCR heating element.

[0066] Activation of the PTCR heating element 828 may optionally be triggered by automatic detection of a puff based on one or more of signals generated by one or more sensors 832, such as, for example, one or more pressure sensors arranged to detect pressure along the airflow path relative to ambient pressure (or optionally to measure changes in absolute pressure), one or more motion sensors in the vaporizer 810, one or more flow sensors in the vaporizer 810, a capacitive lip sensor in the vaporizer 810, as an optional means, may be triggered by receipt of a signal from a computing device in communication with the vaporizer 810 in response to detection of a user interaction with one or more input devices 833 (e.g., a button or other tactile control device on the vaporizer 810), and / or via other approaches to determine that a puff has occurred or is imminent.

[0067] As mentioned in the previous paragraph, a vaporizer consistent with implementations of the present subject matter may be optionally configured to connect (e.g., via wireless or wired connections) to a computing device (or optionally two or more devices) that communicates with the vaporizer 810. To this end, the optional controller 824 may include communications hardware 834. The optional controller 824 may also include memory 836. The computing device may be a component of a vaporizer system that includes the vaporizer 810 and may include its own communications hardware that may establish a wireless communications channel with the communications hardware 834 of the vaporizer 810. For example, a computing device used as part of a vaporizer system may include a general-purpose computing device (e.g., a smartphone, tablet, personal computer, some other portable device such as a smart watch) that executes software to generate a user interface to allow a user of the device to interact with the vaporizer. In other implementations of the present subject matter, devices used as part of such vaporizer systems may be dedicated pieces of hardware, such as a remote control or other wireless or wired device having one or more physical or software-based interface controls (e.g., configurable on a screen or other display device and selectable via user interaction with a touch-sensitive screen or other input device such as a mouse, pointer, trackball, cursor buttons, etc.). The vaporizer 810 may also include one or more output 838 features or devices for providing information to a user.

[0068] A computing device that is part of a vaporizer system as defined above may be used for any of one or more functions, such as controlling intake (e.g., intake monitoring, intake setting, intake limiting, user tracking, etc.), controlling sessioning (e.g., session monitoring, session setting, session limiting, user tracking, etc.), controlling nicotine delivery (e.g., switching between nicotine and non-nicotine vaporizable materials, adjusting the amount of nicotine delivery, etc.), obtaining location information (e.g., location of other users, location of a retailer / commercial establishment, location of vaping, relative or absolute location of the vaporizer itself, etc.), personalizing the vaporizer (e.g., naming the vaporizer, locking / password protecting the vaporizer, adjusting one or more parental controls, associating the vaporizer with a user group, registering the vaporizer with a manufacturer or warranty maintenance organization, etc.), participating in social activities with other users (e.g., games, social media communications, interacting with one or more groups, etc.). The terms "sessioning," "session," "vaporizer session," or "vaporization session" are used generally to refer to a period of time dedicated to the use of a vaporizer, which may include a period of time, number of ingestions, amount of vaporizable material, etc.

[0069] In examples where a computing device provides signals related to the actuation of the PTCR heating element, or in other examples of coupling of a vaporizer and a computing device for the implementation of various control or other functions, the computing device executes one or more sets of computer instructions to provide a user interface and underlying data processing. In one example, upon detection by the computing device of user interaction with one or more user interface elements, the computing device can send a signal to the vaporizer 810 to activate the PTCR heating element 828 to the full operating temperature for generating an inhalable dose of vapor / aerosol. Other functions of the vaporizer 810 may be controlled by user interaction with a user interface on a computing device in communication with the vaporizer.

[0070] The temperature of the PTCR heating element of the vaporizer may depend on several factors, including conductive heat transfer to other parts of the electronic vaporizer and / or to the environment, latent heat loss from the vaporization of the vaporizable material from the wicking element and / or the entire atomizer, and convective heat loss due to airflow (e.g., air moving across the PTCR heating element or the entire atomizer as the user inhales on the electronic vaporizer). As described above, to ensure that the PTCR heating element is activated or heated to a desired temperature, the vaporizer, in some implementations of the present subject matter, may utilize a signal from a pressure sensor to determine when the user is inhaling. The optional pressure sensor may be located in the airflow path and / or connected (e.g., by a passageway or other path) to the airflow path connecting the inlet for air entering the device and the outlet for the user to inhale the resulting vapor and / or aerosol. As a result, the pressure sensor experiences pressure changes as air passes through the vaporizer device from the air inlet to the air outlet. In some implementations of the present subject matter, the PTCR heating element may be associated with a user's puff and activated, for example, by automatic detection of a puff, for example, by a pressure sensor detecting a pressure change in the airflow path.

[0071] Typically, the optional pressure sensor (as well as the other optional sensors 832) is located on the optional controller 824 or can be coupled (e.g., electrically or electronically connected via a physical or wireless connection) to the optional controller 824 (e.g., a printed circuit board assembly or other type of circuit board). To ensure accurate measurements and to maintain the durability of the vaporizer, it is beneficial to provide an optional resilient seal 842 to isolate the airflow path from other parts of the vaporizer 810. The optional seal 842, which may be a gasket, can be configured to at least partially surround the optional pressure sensor such that the connection of the optional pressure sensor to the internal circuitry of the vaporizer 810 is isolated from the portion of the optional pressure sensor exposed to the airflow path. In one embodiment of a cartridge-based vaporizer, the optional seal or gasket 842 can isolate one or more electrical connections between the vaporizer body 850 and the vaporizer cartridge 852. Such configuration of any gasket or seal 842 in the vaporizer 810 may help mitigate potentially destructive effects on the vaporizer components resulting from interaction with environmental factors such as water in the vapor or liquid phase, other fluids such as vaporizable materials, and / or may help reduce deviation of air from the designed airflow path within the vaporizer 810. The passage and / or contact of unwanted air, liquids, or other fluids through the vaporizer circuitry may cause various undesirable effects such as altering pressure measurements and / or causing the accumulation of undesirable materials such as moisture, vaporizable materials, etc. in portions of the vaporizer 810, which may result in poor pressure signals, degradation of pressure sensors or other components, and / or shortened life of the vaporizer 810. Also, leakage of any seal or gasket 842 may result in a user inhaling air that has passed through portions of the vaporizer device 810 that contain or are configured with materials that may be undesirable to inhale.

[0072] A common class of vaporizers that has gained popularity in recent years includes a vaporizer body 850 that includes an optional controller 824, a power source 822 (e.g., a battery), one or more optional sensors 832, charging contacts, optional gaskets or seals 842, and a cartridge receptacle 854 configured to receive a vaporizer cartridge 852 that is coupled to the vaporizer body 850 via one or more of a variety of attachment structures. In some embodiments, the vaporizer cartridge 852 includes a reservoir 856 that includes an inlet (not shown) for receiving liquid vaporizable material and an outlet (not shown) for releasing the vaporizable material, and a mouthpiece 830 for delivering an inhalable intake of the vaporizable material to a user. The vaporizer cartridge 852 can include a sprayer 826 having a wicking element and a PTCR heating element 828, or alternatively, one or both of the wicking element and the PTCR heating element 828 can be part of the vaporizer body 850. In implementations in which any portion of the sprayer 826 (e.g., the heating element 828 and / or the wicking element) is part of the vaporizer body 850, the vaporizer 810 can be configured to supply liquid vaporizer material from a reservoir 856 in the vaporizer cartridge 852 to a portion of the sprayer 826 contained in the vaporizer body 850.

[0073] Cartridge-based configurations for vaporizers that generate inhalable doses of non-liquid vaporizable materials through heating of the non-liquid vaporizable material are also within the scope of the present subject matter. For example, a vaporizer cartridge may include a mass of plant material that has been processed and formed to directly contact portions of one or more PTCR heating elements, and such a vaporizer cartridge may be configured to be mechanically and electrically coupled to a vaporizer body that includes a processor, a power source, and electrical contacts for connecting to corresponding cartridge contacts to complete a circuit with one or more PTCR heating elements.

[0074] In a vaporizer in which the power supply 822 is part of the vaporizer body 850 and the PTCR heating element 828 is disposed within a vaporizer cartridge 852 configured to be coupled to the vaporizer body 850, the vaporizer 810 may include electrical connection features (e.g., means for completing a circuit) to complete a circuit including the optional controller 824 (e.g., a printed circuit board, a microcontroller, etc.), the power supply 822, and the PTCR heating element 828. These features may include at least two contacts on a bottom surface of the vaporizer cartridge 852 (referred to herein as cartridge contacts 860) and at least two contacts disposed near the base of the cartridge receptacle of the vaporizer 810 (referred to herein as receptacle contacts 862) such that the cartridge contacts 860 and the receptacle contacts 862 make electrical connection when the vaporizer cartridge 852 is inserted into and coupled to the cartridge receptacle 854. The circuit completed by these electrical connections allows for the supply of current to the PTCR heating element 828 and may be used for additional functions, such as, for example, to identify the cartridge based on one or more electrical characteristics of the PTCR heating element 828 or other circuitry of the vaporizer cartridge 852.

[0075] In some embodiments of the present subject matter, the at least two cartridge contacts 860 and the at least two receptacle contacts 862 can be configured to be electrically connected in either of at least two orientations. In other words, one or more circuits required for operation of the vaporizer 810 can be completed by inserting the vaporizer cartridge 852 into the cartridge receptacle 854 in a first rotational orientation (about an axis where an end of the vaporizer cartridge 852 having a cartridge is inserted into the cartridge receptacle 854 of the vaporizer body 850). As a result, a first cartridge contact of the at least two cartridge contacts 860 is electrically connected to a first receptacle contact of the at least two receptacle contacts 862, and a second cartridge contact of the at least two cartridge contacts 860 is electrically connected to a second receptacle contact of the at least two receptacle contacts 862. Furthermore, one or more circuits required for operation of the vaporizer can be completed by inserting the vaporizer cartridge 852 into the cartridge receptacle 854 in a second rotational orientation. As a result, a first cartridge contact of the at least two cartridge contacts 860 is electrically connected to a second receptacle contact of the at least two receptacle contacts 862, and a second cartridge contact of the at least two cartridge contacts 860 is electrically connected to a first receptacle contact of the at least two receptacle contacts 862. This feature of the vaporizer cartridge 852 being reversibly insertable into the cartridge receptacle 854 of the vaporizer body 850 is described further below.

[0076] The at least two cartridge contacts 860 and the at least two receptacle contacts 862 may take a variety of forms. For example, one or both sets of contacts may include conductive pins, tabs, posts, receiving holes for pins or posts, etc. Some types of contacts may include springs or other biasing features to create better physical and electrical contact between the contacts on the vaporizer cartridge 852 and the vaporizer body 850. The electrical contacts may optionally be gold plated and / or include other materials.

[0077] 9 is a process flow diagram illustrating an example process 900 for operating an example vaporizer device utilizing a PTCR heating element. The vaporizer utilizes a PTCR heating element, which provides inherent temperature control, eliminates the need for feedback temperature sensors and power duty cycles, and provides more uniform heating.

[0078] At 910, the vaporizer (e.g., a controller) can determine if an input has been provided by a user. The input can be via a pressure sensor that senses inhalation, against a push button, or the like. The input can include an open push button or other means that completes a circuit between the battery and the PTCR heater. If no input has been provided at 910, the process waits until an input is provided. Once an input is provided, the process proceeds to step 920.

[0079] At 920, the electrical circuit connecting the PTCR heating element to the power source is closed, allowing current to flow through the PTCR heating element. The PTCR heating element increases in temperature as current flows through it. When the temperature of the PTCR heating element reaches an electrical resistivity transition region, the resistivity of the PTCR heating element increases until an equilibrium state is reached when the current flow is reduced and the PTCR heating element maintains a uniform temperature without active control by the vaporizer (e.g., the temperature is maintained at a value based on the material properties of the PTCR heating element). In other words, the vaporizer controller does not need to perform temperature sensing or duty cycle the power source to maintain the desired temperature. Thus, the PTCR heating element provides heating and self-regulation at the desired temperature. In some implementations, the push button can be replaced with a mechanical switch triggered by a snap-through threshold pressure valve with hysteresis or other means.

[0080] Heating produces vapor at 930. Utilizing a PTCR heating element with inherent temperature control avoids overheating (e.g., burning) the vaporizer fluid (or other material), thereby avoiding the formation of undesirable and potentially dangerous chemical by-products.

[0081] 10A-10F show modeled temperatures for different embodiments of a PTCR heating element 50. A gradient temperature scale is shown on the left side of each figure, with red representing the hottest temperature of about 255° C. and the colors of the visible light spectrum (i.e., red, orange, yellow, green, blue, and purple) shown, down to the coldest temperature of about 23° C. In each illustrated embodiment, the nonlinear PTCR material 10 includes a plate shape with dimensions of about 5 mm×5 mm×0.5 mm. The conductive layer 20 was formed of silver (Ag) with dimensions of about 5 mm×5 mm×0.025 mm. The conductive leads 30 were formed of copper (Cu) with dimensions of about 12 mm×2 mm×0.2 mm. The plate shape can include two parallel sides including a conductive layer 20 with conductive leads 30 attached. The conductive leads 30 are attached to the center of the conductive layer 20 on each side of the PTCR heating element 50 using connections 40. In some implementations, the connections 40 are clamps, clips, conductive pastes, high temperature solders, lead-free solders, and / or combinations thereof.

[0082] 10A shows the temperature 1.0 second after current is applied to activate the PTCR heating element 50. The purple conductive lead 30 is still at about 25° C. The majority of the PTCR material 10 and conductive layer 20 have risen in temperature to about 120° C., with the area containing the central connection 40 at a slightly cooler temperature of about 80° C.

[0083] 10B shows the temperature 2.0 seconds after current is applied to activate the PTCR heating element 50. The blue / green colored conductive leads 30 have risen in temperature to approximately 90° C. The majority of the PTCR material 10 and conductive layer 20 have risen in temperature to approximately 210° C., with the area containing the central connection 40 at a cooler temperature of approximately 160° C.

[0084] 10C shows the temperature 3.0 seconds after current is applied to activate the PTCR heating element 50. The conductive leads 30, which are colored green, have risen in temperature to approximately 140° C. The majority of the PTCR material 10 and conductive layer 20 have risen in temperature to approximately 250° C., with the area containing the central connection 40 at a cooler temperature of approximately 200° C.

[0085] 10D shows the temperature 4.0 seconds after current is applied to activate the PTCR heating element 50. The conductive leads 30, which are colored green, have risen in temperature to approximately 160° C. The majority of the PTCR material 10 and conductive layer 20 remain at a temperature of up to approximately 250° C., with the area containing the central connection 40 at a cooler temperature of approximately 215° C.

[0086] 10E shows the temperature 5.0 seconds after current is applied to activate the PTCR heater 50. The conductive leads 30, colored green / yellow, have risen in temperature to approximately 180° C. The PTCR material 10 and the bulk of the conductive layer 20 remain at a temperature of up to approximately 250° C., with the area containing the central connection 40 at a cooler temperature of approximately 225° C.

[0087] 10F shows the temperature 6.0 seconds after current is applied to activate the PTCR heating element 50. The conductive leads 30, which are colored yellow, have risen in temperature to approximately 200° C. The PTCR material 10 and the bulk of the conductive layer 20 remain at a temperature of up to approximately 250° C., with the area containing the central connection 40 being only slightly cooler at approximately 235° C.

[0088] FIG. 11A shows the modeled surface temperature as a function of time for an exemplary PTCR heating element. In the model, the surface temperature of the PTCR heater starts at time zero at 25° C. (i.e., room temperature). After applying the current, the surface temperature rises linearly for about 2 seconds to a temperature of about 225° C. After about 2 seconds, the rate of temperature rise gradually decreases to a steady-state operating temperature of about 250° C. The steady-state of about 250° C. is achieved about 3 seconds after actuation. The model assumes that the nonlinear PTCR material is in a non-contact, free convection state, and the emitted radiation is measured from a distance. In some implementations, the PTCR heating element is heated to an operating temperature of 240° C. to 280° C. In some implementations, the PTCR heating element is heated to an operating temperature of 245° C. to 255° C. In some implementations, the PTCR heating element is heated to an operating temperature of about 250° C.

[0089] FIG. 11B shows the modeled and measured maximum surface temperature as a function of time for an exemplary PTCR heater. Using an infrared camera, the maximum surface temperature of the PTCR heater was measured as a function of time over four repeated measurements and plotted against a model of the maximum surface temperature. The model assumes that the nonlinear PTCR material is in a non-contact free convection state and the emitted radiation was measured from a distance. In both cases, the maximum surface temperature of the PTCR heating element starts at time zero at about 25° C. (i.e., room temperature). After applying the current, the maximum surface temperature increases linearly for about 2 seconds to a temperature of about 225° C. After about 2 seconds, the rate of temperature increase gradually decreases to a steady-state operating temperature of about 250° C. The steady-state of about 250° C. is achieved about 3 seconds after activation. In some implementations, the PTCR heating element is heated to an operating temperature of 240° C. to 280° C. In some implementations, the PTCR heating element is heated to an operating temperature of 245° C. to 255° C. In some implementations, the PTCR heating element is heated to an operating temperature of about 250°C.

[0090] FIG. 11C shows the modeled and measured average surface temperature as a function of time for an exemplary PTCR heating element. Four measurements were repeated using an infrared camera to measure the average surface temperature of the PTCR heating element as a function of time and plotted against a model of the average surface temperature. The model assumes that the nonlinear PTCR material is in a non-contact, free convection state and the emitted radiation was measured from a distance. In both cases, the average surface temperature of the PTCR heating element starts at time zero at about 25° C. (i.e., room temperature). After the current is applied, the maximum surface temperature increases linearly for about 2 seconds to a temperature of about 225° C. After about 2 seconds, the rate of temperature increase gradually decreases to a steady-state operating temperature of about 250° C. The steady-state of about 250° C. is achieved about 3 seconds after activation. In some implementations, the PTCR heating element is heated to an operating temperature of 240° C. to 280° C. In some implementations, the PTCR heating element is heated to an operating temperature of 245° C. to 255° C. In some implementations, the PTCR heating element is heated to an operating temperature of about 250°C.

[0091] 12 illustrates the transient current response as a function of time for an exemplary heater consistent with implementations of the present subject matter. In the graph, the current, measured in amperes, increases at a nearly linear rate, reaching peak draw approximately 1.5 seconds after actuation. Thereafter, as the PTCR heater reaches its self-regulating operating temperature, the resistance increases rapidly and the current draw drops.

[0092] Although some variations have been described in detail above, other modifications or additions are possible. For example, the present subject matter may include a vaporizer with a PTCR heating element that allows for a heated tobacco product (HNB). The heated tobacco product (HNB) may include an actual tobacco product to improve flavor. In some implementations, the actual tobacco product is solid or semi-solid.

[0093] In some implementations, the PTCR heating element includes an aspect ratio between 1 and 50. For example, the PTCR heating element can include an aspect ratio between 1 and 5, 5 and 10, 10 and 15, 15 and 20, 20 and 25, 25 and 30, 30 and 35, 35 and 40, 40 and 45, or 45 and 50. Other aspect ratios are possible.

[0094] In some implementations, the PTCR heating element includes a composition, the composition being a mixed metal oxide; or a complex mixture of two or more mixed metal oxides; or one or more mixed metal oxides and one or more elemental metals, or alternatively one or more binary metal oxides (MOs). x type phase), or alternatively one or more binary metal nitrides (MN x type phase), or alternatively one or more bimetallic carbides (MC x type phase), or alternatively one or more bimetallic borides (MB x type phase), or alternatively one or more binary metal silicides (MSi xor a composite mixture of two or more binary metal oxides; or a composite mixture of two or more binary metal oxides with one or more elemental metals, or alternatively one or more binary metal nitrides, or alternatively one or more binary metal carbides, or alternatively one or more binary metal borides, or alternatively one or more binary metal silicides; or a crosslinked polymer composite of one or more elemental metals, or alternatively one or more binary metal oxides, or alternatively one or more binary metal nitrides, or alternatively one or more binary metal carbides, or alternatively one or more binary metal borides, or alternatively one or more binary metal silicides. The composition may include components such as ABO3 type compounds, where the element A may be, but is not limited to, Li, Na, K, Rb, Mg, Ca, Sr, Ba, Y, La, Ce, Pb, Bi, or mixtures thereof, and the element B may be, but is not limited to, Mg, Al, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Nb, Hf, Ta, or mixtures thereof. The composition may include components such as barium titanate (BaTiO3), lead titanate (PbTiO3), lead zirconate (PbZrO3), bismuth aluminate (BiAlO3), alkali niobate (ANbO3, A=Li, Na, K, Rb), alkali tantalate (ATaO3, A=Li, Na, K, Rb), or solid solutions thereof, or main group alkali zirconate (Bi 0.5 A 0.5 ZrO3, A=Li, Na, K) or as main group titanate-zirconates (PbTi 1-x Zr x O3), or Ba 1-x RE x The composition may include rare earth substituted variants such as TiO3 (RE=La, Ce). Such compositions are not limited to being explicitly defined by their stoichiometry and therefore may be non-stoichiometric or intergrowth materials. Alternative or additional compositions include, for example, alkaline earth niobates (Sr 1-x Ba x Nb2O6), general formula [Bi2O2][A n-1 BnO 3n+1 ] Aurivillius-type phase of Bi4Ti3O12 , substitutional phases thereof, solid solution phases, non-stoichiometric phases, and intergrowth phases. The components may alternatively or additionally include elemental metals, such as C, Al, Si, Ti, Fe, Zn, Ag, or Bi, among others; binary metal oxides, such as MgO, Al2O3, SiO2, TiO2, Ti2O3, Cr2O3, MnO, FeO, CoO, NiO, CuO, ZnO, or SnO2, among others; binary metal nitrides, such as TiN, Mn3N2, Co2N, Ni3N, or Zn3N2, among others; binary metal carbides, such as TiC, among others; binary metal borides, such as ZrB2, NbB2, among others; and binary metal silicides, such as NbSi2, WSi2, MoSi2, among others. The components may alternatively or additionally include polymers, such as polyethylene, polyamide, kynar, polytetrafluoroethylene, among others, and combinations thereof.

[0095] In some implementations, the PTCR heating element is electrically coupled to a power source and configured to heat the fluid to form an aerosol, the PTCR heating element comprising an electrical resistivity that varies based on temperature, the electrical resistivity comprising a transition region comprising an increase in electrical resistivity across a temperature range. In some implementations, the electrical resistivity transition region begins at a first temperature (e.g., T1) between 150° C. and 350° C., or the electrical resistivity transition region begins at a first temperature between 200° C. and 300° C., or the electrical resistivity transition region begins at a first temperature between 220° C. and 290° C., or the electrical resistivity transition region begins at a first temperature between 240° C. and 280° C. In some implementations, the increase in electrical resistivity across a temperature range (e.g., from T1 to T2) of the electrical resistivity transition region comprises an increase factor of at least 10 (e.g., the resistivity at T2 is at least 10 times greater than the resistivity at T1). The enhancement factor characterizes the relative change in electrical resistivity between the electrical resistivity at a first temperature (e.g., T1) associated with the beginning of the transition region and the electrical resistivity at a second temperature (e.g., T2) associated with the end of the transition region. Other factors are possible, for example, the factor can be at least 100, 1000, or more.

[0096] In some implementations, the difference between the start temperature (e.g., T1) of the transition region and the end temperature (e.g., T2) of the transition region can be 500° C. or less. Other temperature ranges are possible, for example, the difference between the start temperature (e.g., T1) of the transition region and the end temperature (e.g., T2) of the transition region can be 200° C. or less, 100° C. or less, 50° C. or less, or less.

[0097] In some implementations, the electrical resistivity of the PTCR heating element at temperatures below the transition region (e.g., below T1) is between 2 Ωcm and 2000 Ωcm. Other resistivities are possible, for example, the electrical resistivity of the PTCR heating element at temperatures below the transition region (e.g., below T1) can be between 0.2 Ωcm and 20 Ωcm, between 2.0 Ωcm and 20 Ωcm, between 0.2 Ωcm and 2.0 Ωcm, between 2 Ωcm and 200 Ωcm, between 20 Ωcm and 200 Ωcm, or between 2 Ωcm and 20 Ωcm.

[0098] The subject matter described herein provides many technical advantages. For example, the PTCR heating element ensures inherent temperature control of the vaporizer at the point of vaporization over a range of applied voltages without the need for a temperature sensor or electronic circuitry or microprocessor or algorithms that provide a means of controlling power to the PTCR heating element at the point of vaporization. In some implementations, the inherent temperature control of the PTCR heating element ensures that thermal runaway does not occur under conditions in which no vaporizable material is present, without the need for additional components such as fuses, sensors, or other shutoff mechanisms that may be required or desired in the absence of temperature control circuitry.

[0099] term The term "vaporizer device" refers to either a self-contained device, a device that includes two or more separable parts (e.g., a vaporizer body that includes a battery and other hardware, and a cartridge that includes a vaporizable material), and the like. Examples of vaporizer devices consistent with implementations of the present subject matter include electronic vaporizers, electronic nicotine delivery systems (ENDS), and the like. Generally, such vaporizer devices are handheld devices that heat a vaporizable material (e.g., by convection, conduction, radiation, and / or some combination thereof) to provide an inhalable intake of the material. The vaporizable material used in a vaporizer device can be provided in a cartridge (e.g., a portion of a vaporizer that contains the vaporizable material in a reservoir or other container), which may be refillable when empty, or disposable so that a new cartridge containing the same or different type of additional vaporizable material can be used. The vaporizer device can be a cartridge-based vaporizer device, a cartridge-less vaporizer device, or a multi-use vaporizer device that can be used with or without a cartridge. For example, the vaporizer device may include a heating chamber configured to directly receive the vaporizable material into the heating chamber (e.g., an oven or other area where the material is heated by a PTCR heating element), and / or a reservoir for containing the vaporizable material, etc. In some implementations, the vaporizer device may be configured for use with liquid vaporizable material (e.g., a carrier solution in which active and / or non-active ingredients are suspended or held in solution, or a liquid form of the vaporizable material itself), paste, wax, and / or solid vaporizable material. The solid vaporizable material may include plant material that releases a portion of the plant material as vaporizable material (e.g., such that after the material is vaporized for inhalation by the user, a portion of the plant material remains as waste), or optionally, may be a solid form of the vaporizable material itself such that all of the solid material may ultimately be vaporized for inhalation. The liquid vaporizable material may similarly be completely vaporized, or may include a portion of the liquid material that remains after all of the material suitable for inhalation has been vaporized. As used herein, a "vaporizer system" may include one or more components, such as a vaporizer device.

[0100] As used herein, the term "wick" or "wicking element" includes any material capable of inducing fluid movement via capillary pressure.

[0101] As used herein, when a feature or element is referred to as "on" another feature or element, it may be directly on the other feature or element, or there may be intervening features and / or elements present. In contrast, when a feature or element is referred to as "directly on" another feature or element, there are no intervening features or elements present. Also, when a feature or element is referred to as being "connected," "attached," or "coupled" to another feature or element, it will be understood that it may be directly connected, attached, or coupled to the other feature or element, or there may be intervening features or elements present. In contrast, when a feature or element is referred to as being "directly connected," "directly attached," or "directly coupled" to another feature or element, there are no intervening features or elements present.

[0102] Although described or illustrated with respect to one embodiment, the features and elements described or illustrated may be applicable to other embodiments, and those skilled in the art will understand that a reference to a structure or feature being disposed "adjacent" to another feature may have overlapping or underlying portions of the adjacent feature.

[0103] The terminology used herein is for the purpose of describing particular embodiments and embodiments only and is not intended to be limiting. For example, as used herein, the singular forms "a," "an," and "the" are intended to include the plural forms as well unless the context clearly indicates otherwise.

[0104] In the above description and in the claims, phrases such as "at least one of" or "one or more of" may occur following a conjunction list of elements or features. The term "and / or" may also occur in a list of two or more elements or features. Unless otherwise implicitly or explicitly contradicted by the context in which it is used, such phrases are intended to mean any of the listed elements or features individually, or any of the listed elements or features in combination with any of the other listed elements or features. For example, the phrases "at least one of A and B," "one or more of A and B," and "A and / or B" are intended to mean "A only, B only, or A and B together," respectively. A similar interpretation is intended for lists containing more than two items. For example, the phrases "at least one of A, B, and C," "one or more of A, B, and C," and "A, B, and / or C" are intended to mean "A only, B only, C only, A and B together, A and C together, B and C together, or A and B and C together," respectively. Use of the term "based on" above and in the claims is intended to mean "based at least in part on," allowing for unrecited features or elements.

[0105] Spatially relative terms such as "front", "back", "under", "below", "lower", "over", "upper" and the like may be used herein to describe the relationship of one element or feature to another element or feature for ease of description as shown in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device during use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is inverted, an element described as "under" or "beneath" the other element or feature would be oriented "over" the other element or feature. Thus, the exemplary term "under" can encompass both an upward and downward orientation. The device may be in other orientations (rotated 90 degrees or other orientations) and the spatially relative word forms used herein will be interpreted accordingly. Similarly, terms such as "upward", "downward", "vertical", "horizontal", and the like are used herein for descriptive purposes only, unless otherwise noted.

[0106] In this specification, the terms "first" and "second" may be used to describe various features / elements (including steps), but these features / elements should not be limited by these terms unless the context indicates otherwise. These terms may be used to distinguish one feature / element from another feature / element. Thus, without departing from the teachings provided herein, a first feature / element described below may be referred to as a second feature / element, and similarly, a second feature / element described below may be referred to as a first feature / element.

[0107] As used herein, including in the examples, and in the claims, unless expressly specified otherwise, all numbers may be read as if preceded by the word "about" or "approximately", even if the word is not expressly recited. In describing a size and / or location, the phrase "about" or "approximately" may be used to indicate that the stated value and / or location is within a reasonably expected range of values ​​and / or locations. For example, a numerical value may have a value of ±0.1% of the stated value (or numerical range), ±1% of the stated value (or numerical range), ±2% of the stated value (or numerical range), ±5% of the stated value (or numerical range), ±10% of the stated value (or numerical range), etc. Additionally, numerical values ​​recited herein should be understood to include exactly that value or approximately that value, unless the context indicates otherwise. For example, if a value of "10" is disclosed, then "about 10" is also disclosed. Numeric ranges recited herein are intended to include all subranges contained therein. It is understood that when a value is disclosed, "less than or equal to that value," "greater than or equal to that value," and possible ranges between the values ​​are also disclosed, as would be understood by one of ordinary skill in the art. For example, if a value of "X" is disclosed, "less than or equal to X" and "greater than or equal to X" (e.g., X is a numeric value) are also disclosed. It is understood that data is provided in many different formats throughout the application, and that this data represents endpoints, starting points, and ranges for any combination of data points. For example, if a specific data point "10" and a specific data point "15" are disclosed, it is understood that not only is between 10 and 15 disclosed, but also data points greater than 10 and greater than or equal to 10, less than 15 and less than or equal to 15, and equal to 10 and 15 are considered to be disclosed. The disclosure of each unit between two specific units is also understood. For example, if 10 and 15 are disclosed, then 11, 12, 13, and 14 are also disclosed.

[0108] Although various exemplary embodiments have been described above, any number of modifications may be made to the various embodiments without departing from the teachings herein. For example, the order in which the various method steps described are performed may often be changed in alternative embodiments, and in other alternative embodiments, one or more method steps may be skipped entirely. Any feature of the various device and system embodiments may be included in some embodiments and not included in other embodiments. Thus, the foregoing description has been provided primarily for illustrative purposes and should not be construed as limiting the scope of the claims.

[0109] One or more aspects or features of the subject matter described herein may be implemented in digital electronic circuitry, integrated circuits, specially designed application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs) computer hardware, firmware, software, and / or combinations thereof. These various aspects or features may include implementation into one or more computer programs executable and / or interpretable on a programmable system including at least one programmable processor, which may be special or general purpose, coupled to receive data and instructions from and transmit data and instructions to a storage system, at least one input device, and at least one output device. The programmable system or computing system may include clients and servers. The clients and servers are typically remote from each other and typically have an interaction through a communications network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.

[0110] These computer programs may also be referred to as programs, software, software applications, applications, components, or codes. These computer programs may include machine instructions for a programmable processor and may be implemented in high-level procedural languages, object-oriented programming languages, functional programming languages, logic programming languages, and / or assembly / machine languages. As used herein, the term "machine-readable medium" refers to any computer program product, apparatus, and / or device used to provide machine instructions and / or data to a programmable processor, such as, for example, magnetic disks, optical disks, memories, and programmable logic devices (PLDs), including machine-readable media that receive machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal used to provide machine instructions and / or data to a programmable processor. Machine-readable media may store such machine instructions non-transitory, such as, for example, a non-transitory solid-state memory or a magnetic hard drive or any equivalent storage medium. Machine-readable media may alternatively or additionally store such machine instructions in a transitory manner, such as, for example, a processor cache or other random access memory associated with one or more physical processor cores.

[0111] The examples and figures contained herein illustrate, by way of illustration and not limitation, specific embodiments in which the subject matter may be practiced. As previously mentioned, other embodiments may be utilized and derived therefrom, such that structural and logical substitutions and changes may be made without departing from the scope of the present disclosure. Such embodiments of the subject matter of the present invention may be referred to herein, individually or collectively, by the term "invention" for convenience only, without any voluntary intention to limit the scope of the present application to any single invention or inventive concept, where substantially more than one invention or inventive concept is disclosed. Thus, although specific embodiments have been shown and described herein, any configuration calculated to achieve the same purpose may be substituted for the specific embodiment shown. The present disclosure is intended to cover any and all adaptations or variations of the various embodiments. Combinations of the above embodiments, and other embodiments not specifically described herein, will be apparent to one of ordinary skill in the art upon reviewing the above description. The use of the term "based on" in this specification and claims is intended to mean "based at least in part on," with unrecited features or elements also being allowed for.

[0112] The subject matter described herein may be embodied in systems, devices, methods, and / or articles, depending on the desired configuration. The implementations described in the foregoing description do not represent all implementations consistent with the subject matter described herein. Instead, these are merely some examples consistent with aspects related to the described subject matter. Although some variations have been described in detail herein, other modifications or additional forms are possible. In particular, further features and / or variations may be provided in addition to those described herein. For example, the implementations described herein may be directed to various combinations and subcombinations of the disclosed features, and / or combinations and subcombinations of some further features disclosed herein. Furthermore, the logic flow depicted in the accompanying figures and / or described herein does not necessarily require the particular order shown or sequential order to achieve the desired results. Other implementations may be within the scope of the following claims.

Claims

1. a power source configured to provide a flow of current at a predetermined voltage; a reservoir configured to contain a vaporizable material; a PTCR (positive temperature coefficient of resistance) heating element configured to be electrically coupled to the power source to receive the flow of electrical current and to heat the vaporizable material to form an aerosol, the PTCR heating element comprising a PTCR material having an electrical resistivity that varies based on temperature, the electrical resistivity including an electrical resistivity transition region where the electrical resistivity increases over a predetermined temperature range, and when the PTCR heating element is heated above a first temperature within the transition region, the flow of electrical current from the power source is reduced to a level that limits further temperature increase of the PTCR heating element; 13. An apparatus comprising:

2. The apparatus of claim 1 , further comprising a housing, the power source being contained within the housing.

3. The device of claim 2 , wherein the reservoir includes an inlet and an outlet and is configured to be coupled to the housing.

4. The apparatus of claim 3 , wherein the PTCR heating element is disposed between the inlet and the outlet.

5. The device of claim 1 , further comprising a cartridge containing the reservoir.

6. The apparatus, a cartridge including the reservoir and the PTCR heating element, the vaporizable material being a fluid in the reservoir; a wick configured to transport the fluid to a vaporization location; an electrical contact electrically coupled to the PTCR heating element and configured to provide the flow of electrical current from the power source to the PTCR heating element, the PTCR heating element configured to heat the fluid at the vaporization location; and The apparatus of claim 1 , further comprising:

7. 7. The apparatus of claim 1, wherein the vaporizable material is a liquid.

8. 7. The device of claim 1, wherein the vaporizable material is a tobacco product.

9. 10. The device of claim 8, wherein the tobacco product is a solid or semi-solid.

10. The apparatus of claim 1 , further comprising an input configured to electrically connect the power source to the PTCR heating element in response to a user input.

11. The device of claim 10 , wherein the input comprises a push button.

12. The apparatus of claim 1 , wherein the apparatus does not include a controller.

13. 13. The apparatus of claim 1, wherein the apparatus does not include a pressure sensor.

14. The apparatus, A pressure sensor; a controller coupled to the pressure sensor and configured to detect inhalation and, in response, electrically connect the power source to the PTCR heating element; The apparatus of claim 1 , further comprising:

15. The apparatus of any one of claims 1 to 14, wherein the electrical resistivity transition region begins at the first temperature between 150°C and 350°C.

16. The device of any one of claims 1 to 15, wherein the electrical resistivity transition region begins at the first temperature between 220°C and 300°C.

17. 17. The device of any one of claims 1 to 16, wherein the electrical resistivity transition region begins at the first temperature between 240°C and 280°C.

18. 18. The apparatus of claim 1, wherein the first temperature is greater than 225°C.

19. 19. Apparatus according to any one of the preceding claims, wherein the PTCR heating element is heated to an operating temperature of between 240°C and 280°C.

20. 20. The apparatus of any one of claims 1 to 19, wherein the PTCR heating element is heated to an operating temperature of between 245°C and 255°C.

21. 21. The apparatus of claim 1, wherein the PTCR heating element is heated to an operating temperature of about 250°C.

22. 22. The device of claim 1, wherein the increase in electrical resistivity over the temperature range of the electrical resistivity transition region includes an increase factor of at least 10, the increase factor characterizing a relative change in electrical resistivity between the electrical resistivity at the first temperature associated with a start of the electrical resistivity transition region and the electrical resistivity at a second temperature associated with an end of the electrical resistivity transition region.

23. 23. The apparatus of claim 1, wherein the increase in electrical resistivity over the temperature range of the electrical resistivity transition region includes an increase factor of at least 100, the increase factor characterizing a relative change in electrical resistivity between the electrical resistivity at the first temperature associated with a start of the electrical resistivity transition region and the electrical resistivity at a second temperature associated with an end of the electrical resistivity transition region.

24. 24. The apparatus of claim 1, wherein the increase in electrical resistivity over the temperature range of the electrical resistivity transition region includes an increase factor of at least 1000, the increase factor characterizing a relative change in electrical resistivity between the electrical resistivity at the first temperature associated with a start of the electrical resistivity transition region and the electrical resistivity at a second temperature associated with an end of the electrical resistivity transition region.

25. 25. The apparatus of claim 1, wherein the electrical resistivity transition region begins at the first temperature and ends at a second temperature, the difference between the first temperature and the second temperature being 500° C. or less.

26. 26. The apparatus of claim 1, wherein the electrical resistivity transition region begins at the first temperature and ends at a second temperature, the difference between the first temperature and the second temperature being 200° C. or less.

27. 27. The apparatus of claim 1, wherein the electrical resistivity transition region begins at the first temperature and ends at a second temperature, the difference between the first temperature and the second temperature being 100° C. or less.

28. 28. The apparatus of claim 1, wherein the electrical resistivity transition region begins at the first temperature and ends at a second temperature, the difference between the first temperature and the second temperature being 50° C. or less.

29. 29. The apparatus of any one of claims 1 to 28, wherein the electrical resistivity transition region begins at the first temperature, and the electrical resistivity of the PTCR heating element at temperatures below the first temperature is between 20 Ω cm and 200 Ω cm.

30. 29. The apparatus of any one of claims 1 to 28, wherein the electrical resistivity transition region begins at the first temperature, and the electrical resistivity of the PTCR heating element at temperatures below the first temperature is between 2.0 Ω cm and 20 Ω cm.

31. 29. The apparatus of any one of claims 1 to 28, wherein the electrical resistivity transition region begins at the first temperature, and the electrical resistivity of the PTCR heating element at temperatures below the first temperature is between 0.2 Ω cm and 2.0 Ω cm.

32. the increase in electrical resistivity over the temperature range of the electrical resistivity transition region includes an increase factor of at least 100, the increase factor characterizing a relative change in electrical resistivity between an electrical resistivity at the first temperature associated with a start of the electrical resistivity transition region and an electrical resistivity at a second temperature associated with an end of the electrical resistivity transition region; the first temperature is between 150° C. and 350° C.; the PTCR heating element is heated above the first temperature to an operating temperature of between 240° C. and 280° C.; the difference between the first temperature and the second temperature is less than or equal to 200° C.; the electrical resistivity of the PTCR heating element at a temperature lower than the first temperature is between 2 Ω cm and 200 Ω cm; 15. Apparatus according to any one of claims 1 to 14.

33. 33. The apparatus of any one of claims 1 to 32, wherein the PTCR heating element comprises a plate shape, a polygonal shape and / or a circular shape having a height, a width and a length.

34. 34. The device of claim 33, wherein the height is 0.5 mm, the length is 5.0 mm, and the width is 5.0 mm.

35. 34. The apparatus of claim 33, wherein the plate shape includes two parallel sides having conductive leads attached thereto.

36. 36. The device of claim 1, wherein the PTCR heating element includes a layer of material having a positive temperature coefficient of resistance between a first conductive layer and a second conductive layer, the first conductive layer being coupled to a first conductive lead and the second conductive layer being coupled to a second conductive lead.

37. 37. The apparatus of any one of claims 1 to 36, wherein the PTCR heating element includes a pit feature extending through the PTCR heating element.

38. The apparatus of any one of claims 1 to 37, wherein the PTCR heating element comprises an aspect ratio of 1-50.

39. The PTCR heating element comprises a composition, the composition comprising: ceramic; mixed metal oxide; Two or more mixed metal oxides; One or more mixed metal oxides and one or more elemental metals, MO ｘ One or more binary metal oxides having a phase of the MN type ｘ One or more binary metal nitrides having a phase of the type MC ｘ One or more bimetallic metal carbides having a phase of the MB type. ｘ One or more bimetallic borides having a phase of the type MSi ｘ complex mixtures with one or more binary metal silicides having the same type phase; A complex mixture of two or more binary metal oxides; a complex mixture of two or more binary metal oxides with one or more elemental metals, one or more binary metal nitrides, one or more binary metal carbides, one or more binary metal borides, and / or one or more binary metal silicides; and / or crosslinked polymer composites of one or more elemental metals and one or more binary metal oxides, one or more binary metal nitrides, one or more binary metal carbides, one or more binary metal borides, and / or one or more binary metal silicides; and / or any combination thereof; Including, 39. Apparatus according to any one of claims 1 to 38.

40. The composition, A.B.O. ３ ABO type compounds, in which the element A includes Li, Na, K, Rb, Mg, Ca, Sr, Ba, Y, La, Ce, Pb, Bi or a mixture thereof, and the element B includes Mg, Al, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Nb, Hf, Ta or a mixture thereof. ３ type compound; Barium titanate (BaTiO ３ ). Lead titanate (PbTiO ３ ). Lead zirconate (PbZrO ３ ). Bismuth aluminate (BiAlO ３ ). Alkali niobate (ANbO ３ , A = Li, Na, K, Rb), alkali tantalate (ATaO ３ , A=Li, Na, K, Rb), or a solid solution thereof; Main group alkali zirconate (Bi ０．５ A ０．５ ZrO ３ , A=Li, Na, K); Main group titanate-zirconates (PbTi １－ｘ Zr ｘ O ３ ), rare earth substituted variants, and / or Ba １－ｘ R.E. ｘ TiO ３ (RE=La, Ce) Alkaline earth niobate (Sr １－ｘ Ba ｘ Nb ２ O ６ ), general formula [Bi ２ O ２ ][A ｎ－１ BnO ３ｎ＋１ ] Aurivillius-type phase, Bi ４ Ti ３ O １２ , and their substitutional, solid solution, non-stoichiometric and intergrowth phases; Elemental metals including C, Al, Si, Ti, Fe, Zn, Ag and / or Bi; MgO, Al ２ O ３ , SiO ２ , TiO ２ , Ti ２ O ３ , Cr ２ O ３ , MnO, FeO, CoO, NiO, CuO, ZnO and / or SnO ２ Binary metal oxides comprising: TiN, Mn ３ N ２ , Co ２ N, Ni ３ N and / or Zn ３ N ２ Binary metal nitrides including Binary metal carbides including TiC; ZrB ２ and / or NbB ２ Binary metal borides including: NbSi ２ , WSi ２ and / or MoSi ２ Binary metal silicides including: polyethylene; polyamide; Kynar; Polytetrafluoroethylene; and / or any combination thereof; 40. The apparatus of claim 39, comprising:

41. the device further comprising a wick adjacent to the PTCR heating element and configured to transport the vaporizable material to a vaporization location; the PTCR heating element is configured to heat the vaporizable material at the vaporization location; 41. Apparatus according to any one of claims 1 to 40.

42. 42. The device of claim 41, further comprising a second heating element, the second heating element adjacent a second side of the wick and the PTCR heating element adjacent a first side of the wick.

43. 42. The device of claim 41, wherein the wick includes an open weave configuration adjacent the PTCR heating element and a cylindrical end.

44. 44. Apparatus according to any one of claims 1 to 43, wherein the power supply is configured to provide the voltage between 3V and 6V.

45. 45. The apparatus of any one of claims 1 to 44, wherein the power source is a battery.

46. 46. ​​The device of any one of claims 1 to 45, wherein the vaporizable material comprises a nicotine formulation.

47. receiving, by the vaporizer device, a user input; heating a vaporizable material using a PTCR heating element of the vaporizer device, the PTCR heating element being electrically coupled to a power source and configured to heat the vaporizable material to form an aerosol, the PTCR heating element having an electrical resistivity that varies based on temperature, the electrical resistivity including an electrical resistivity transition region that includes an increase in electrical resistivity over a temperature range from a first temperature to a second temperature, and when the PTCR heating element is heated between the first temperature and the second temperature, a flow of electrical current from the power source is reduced to a level that limits further temperature increase of the PTCR heating element due to current flow; generating vapor by heating a vaporizable fluid; A method comprising:

48. 48. The method of claim 47, wherein the vaporizable fluid comprises a nicotine formulation.

49. a power source configured to provide a flow of current at a predetermined voltage; a reservoir configured to contain a vaporizable material; a vaporizer coupled to the reservoir to receive the vaporizable material, the vaporizer including a PTCR (Positive Temperature Coefficient of Resistance) heating element electrically coupled to the power source to receive a flow of electrical current from the power source and configured to vaporize the vaporizable material, the PTCR heating element configured to be heated to an operating temperature at which its resistivity reduces the flow of electrical current such that an increase in operating temperature is prevented; 13. An apparatus comprising:

50. 50. The apparatus of claim 49, further comprising a housing, the power source being contained within the housing.

51. 51. The device of claim 50, wherein the reservoir is configured to be coupled to the housing.

52. 52. The apparatus of any one of claims 49 to 51, wherein the atomizer includes an inlet and an outlet, and the PTCR heating element is disposed between the inlet and the outlet.

53. 53. The device of any one of claims 49 to 52, wherein the device further comprises a cartridge containing the reservoir and the sprayer.

54. The apparatus, a cartridge including the reservoir and the PTCR heating element, the vaporizable material being a fluid in the reservoir; a wick configured to transport the fluid to a vaporization location; an electrical contact electrically coupled to the PTCR heating element and configured to provide the flow of electrical current from the power source to the PTCR heating element, the PTCR heating element configured to heat the fluid at the vaporization location; and 53. The apparatus of any one of claims 49 to 52, further comprising:

55. 55. The apparatus of any one of claims 49 to 54, wherein the vaporizable material is a liquid.

56. 55. The device of any one of claims 49 to 54, wherein the vaporizable material is a tobacco product.

57. 57. The device of claim 56, wherein the tobacco product is a solid or semi-solid.

58. 58. The apparatus of any one of claims 49 to 57, wherein the apparatus further comprises an input configured to electrically connect the power source to the PTCR heating element in response to a user input.

59. 60. The device of claim 58, wherein the input comprises a push button.

60. 60. The apparatus of any one of claims 49 to 59, wherein the apparatus does not include a controller.

61. 61. The apparatus of any one of claims 49 to 60, wherein the apparatus does not include a pressure sensor.

62. The apparatus, A pressure sensor; a controller coupled to the pressure sensor and configured to detect inhalation and, in response, electrically connect the power source to the PTCR heating element; 60. The apparatus of any one of claims 49 to 59, further comprising:

63. 63. The apparatus of any one of claims 49 to 62, wherein the operating temperature is between 240°C and 280°C.

64. 64. The apparatus of any one of claims 49 to 63, wherein the operating temperature is between 245°C and 255°C.

65. 65. The apparatus of any one of claims 49 to 64, wherein the operating temperature is about 250°C.

66. 66. The apparatus of any one of claims 49 to 65, wherein the resistivity is greater than 500 ohm-cm.

67. 67. The apparatus of any one of claims 49 to 66, wherein the resistivity is greater than 5000 ohm-cm.

68. 68. The apparatus of any one of claims 49 to 67, wherein the resistivity is greater than 15000 Ω cm.

69. 69. The apparatus of any one of claims 49 to 68, wherein the resistivity is greater than 20,000 ohm-cm.

70. 70. The apparatus of any one of claims 49 to 69, wherein the PTCR heating element comprises a plate shape, a polygonal shape and / or a circular shape having a height, a width and a length.

71. 71. The device of claim 70, wherein the height is 0.5 mm, the length is 5.0 mm, and the width is 5.0 mm.

72. 71. The apparatus of claim 70, wherein the plate shape includes two parallel sides having conductive leads attached thereto.

73. 73. The device of any one of claims 49 to 72, wherein the PTCR heating element includes a layer of material having a positive temperature coefficient of resistance between a first conductive layer and a second conductive layer, the first conductive layer being coupled to a first conductive lead and the second conductive layer being coupled to a second conductive lead.

74. 74. The apparatus of any one of claims 49 to 73, wherein the PTCR heating element includes a pit feature extending through the PTCR heating element.

75. 75. The apparatus of any one of claims 49 to 74, wherein the PTCR heating element comprises an aspect ratio of 1-50.

76. The PTCR heating element comprises a composition, the composition comprising: ceramic; mixed metal oxide; Two or more mixed metal oxides; One or more mixed metal oxides and one or more elemental metals, MO ｘ One or more binary metal oxides having a phase of the MN type ｘ One or more binary metal nitrides having a phase of the type MC ｘ One or more bimetallic metal carbides having a phase of the MB type. ｘ One or more bimetallic borides having a phase of the type MSi ｘ complex mixtures with one or more binary metal silicides having the same type phase; A complex mixture of two or more binary metal oxides; a complex mixture of two or more binary metal oxides with one or more elemental metals, one or more binary metal nitrides, one or more binary metal carbides, one or more binary metal borides, and / or one or more binary metal silicides; and / or crosslinked polymer composites of one or more elemental metals and one or more binary metal oxides, one or more binary metal nitrides, one or more binary metal carbides, one or more binary metal borides, and / or one or more binary metal silicides; and / or any combination thereof; 76. The apparatus of any one of claims 49 to 75, comprising:

77. The composition, A.B.O. ３ ABO type compounds, in which the element A includes Li, Na, K, Rb, Mg, Ca, Sr, Ba, Y, La, Ce, Pb, Bi or a mixture thereof, and the element B includes Mg, Al, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Nb, Hf, Ta or a mixture thereof. ３ type compound; Barium titanate (BaTiO ３ ). Lead titanate (PbTiO ３ ). Lead zirconate (PbZrO ３ ). Bismuth aluminate (BiAlO ３ ). Alkali niobate (ANbO ３ , A = Li, Na, K, Rb), alkali tantalate (ATaO ３ , A=Li, Na, K, Rb), or a solid solution thereof; Main group alkali zirconate (Bi ０．５ A ０．５ ZrO ３ , A=Li, Na, K); Main group titanate-zirconates (PbTi １－ｘ Zr ｘ O ３ ), rare earth substituted variants, and / or Ba １－ｘ R.E. ｘ TiO ３ (RE=La, Ce) Alkaline earth niobate (Sr １－ｘ Ba ｘ Nb ２ O ６ ), general formula [Bi ２ O ２ ][A ｎ－１ BnO ３ｎ＋１ ] Aurivillius-type phase, Bi ４ Ti ３ O １２ , and their substitutional, solid solution, non-stoichiometric and intergrowth phases; Elemental metals including C, Al, Si, Ti, Fe, Zn, Ag and / or Bi; MgO, Al ２ O ３ , SiO ２ , TiO ２ , Ti ２ O ３ , Cr ２ O ３ , MnO, FeO, CoO, NiO, CuO, ZnO and / or SnO ２ Binary metal oxides comprising: TiN, Mn ３ N ２ , Co ２ N, Ni ３ N and / or Zn ３ N ２ Binary metal nitrides including Binary metal carbides including TiC; ZrB ２ and / or NbB ２ Binary metal borides including: NbSi ２ , WSi ２ and / or MoSi ２ Binary metal silicides including: polyethylene; polyamide; Kynar; Polytetrafluoroethylene; and / or any combination thereof; 77. The apparatus of claim 76, comprising:

78. the device further comprising a wick adjacent the PTCR heating element, the wick configured to transport the vaporizable material to a vaporization location; the PTCR heating element is configured to heat the vaporizable material at the vaporization location; 78. Apparatus according to any one of claims 49 to 77.

79. 80. The device of claim 78, further comprising a second heating element, the second heating element adjacent a second side of the wick and the PTCR heating element adjacent a first side of the wick.

80. 80. The device of claim 78, wherein the wick includes an open weave configuration adjacent the PTCR heating element and a cylindrical end.

81. 81. Apparatus according to any one of claims 49 to 80, wherein the power supply is configured to provide the voltage between 3V and 6V.

82. 82. The apparatus of any one of claims 49 to 81, wherein the power source is a battery.

83. 83. The device of any one of claims 49 to 82, wherein the vaporizable material comprises a nicotine formulation.

84. a power source configured to provide a flow of current at a predetermined voltage; a receptacle configured to receive a vaporizable material; a PTCR (positive temperature coefficient of resistance) heating element electrically coupled to the power source to receive a flow of current from the power source and configured to vaporize the vaporizable material, and configured to be heated to an operating temperature whose resistivity reduces the flow of current such that an increase in operating temperature is prevented; 13. An apparatus comprising:

85. 85. The apparatus of claim 84, further comprising a housing, the power source being contained within the housing.

86. 86. The device of claim 85, wherein the device further comprises a reservoir configured to contain the vaporizable material and to be coupled to the housing.

87. 87. The apparatus of any one of claims 84 to 86, wherein the apparatus further comprises a sprayer including an inlet and an outlet, the PTCR heating element being disposed between the inlet and the outlet.

88. 88. The device of claim 87, wherein the device further comprises a cartridge containing the reservoir and the sprayer.

89. The apparatus, a cartridge including a reservoir containing the vaporizable material and the PTCR heating element, the vaporizable material being a fluid within the reservoir; a wick configured to transport the fluid to a vaporization location; an electrical contact electrically coupled to the PTCR heating element and configured to provide the flow of electrical current from the power source to the PTCR heating element, the PTCR heating element configured to heat the fluid at the vaporization location; and 86. The apparatus of claim 84 or 85, further comprising:

90. 90. The apparatus of any one of claims 84 to 89, wherein the vaporizable material is a liquid.

91. 90. The device of any one of claims 84 to 89, wherein the vaporizable material is a tobacco product.

92. 92. The device of claim 91, wherein the tobacco product is a solid or semi-solid.

93. 93. The apparatus of any one of claims 84 to 92, wherein the apparatus further comprises an input configured to electrically connect the power source to the PTCR heating element in response to a user input.

94. 94. The device of claim 93, wherein the input comprises a push button.

95. 95. The apparatus of any one of claims 84 to 94, wherein the apparatus does not include a controller.

96. 96. The apparatus of any one of claims 84 to 95, wherein the apparatus does not include a pressure sensor.

97. The apparatus, A pressure sensor; a controller coupled to the pressure sensor and configured to detect inhalation and, in response, electrically connect the power source to the PTCR heating element; 95. The apparatus of any one of claims 84 to 94, further comprising:

98. 98. The apparatus of any one of claims 84 to 97, wherein the operating temperature is between 240°C and 280°C.

99. 99. The apparatus of any one of claims 84 to 98, wherein the operating temperature is between 245°C and 255°C.

100. 100. The apparatus of any one of claims 84 to 99, wherein the operating temperature is about 250°C.

101. 101. The apparatus of any one of claims 84 to 100, wherein the resistivity is greater than 500 Ω cm.

102. 102. The apparatus of any one of claims 84 to 101, wherein the resistivity is greater than 5000 Ω cm.

103. 103. The apparatus of any one of claims 84 to 102, wherein the resistivity is greater than 15000 Ω cm.

104. 104. The apparatus of any one of claims 84 to 103, wherein the resistivity is greater than 20,000 Ω cm.

105. 105. The apparatus of any one of claims 84 to 104, wherein the PTCR heating element comprises a plate shape, a polygonal shape and / or a circular shape having a height, a width and a length.

106. 106. The device of claim 105, wherein the height is 0.5 mm, the length is 5.0 mm, and the width is 5.0 mm.

107. 106. The apparatus of claim 105, wherein the plate shape includes two parallel sides having conductive leads attached thereto.

108. 108. The device of any one of claims 84 to 107, wherein the PTCR heating element includes a layer of material having a positive temperature coefficient of resistance between a first conductive layer and a second conductive layer, the first conductive layer being coupled to a first conductive lead and the second conductive layer being coupled to a second conductive lead.

109. 109. The apparatus of any one of claims 84 to 108, wherein the PTCR heating element includes a pit feature extending through the PTCR heating element.

110. 110. The apparatus of any one of claims 84 to 109, wherein the PTCR heating element comprises an aspect ratio of 1-50.

111. The PTCR heating element comprises a composition, the composition comprising: ceramic; mixed metal oxide; Two or more mixed metal oxides; One or more mixed metal oxides and one or more elemental metals, MO ｘ One or more binary metal oxides having a phase of the MN type ｘ One or more binary metal nitrides having a phase of the type MC ｘ One or more bimetallic metal carbides having a phase of the MB type. ｘ One or more bimetallic borides having a phase of the type MSi ｘ complex mixtures with one or more binary metal silicides having the same type phase; A complex mixture of two or more binary metal oxides; a complex mixture of two or more binary metal oxides with one or more elemental metals, one or more binary metal nitrides, one or more binary metal carbides, one or more binary metal borides, and / or one or more binary metal silicides; and / or crosslinked polymer composites of one or more elemental metals and one or more binary metal oxides, one or more binary metal nitrides, one or more binary metal carbides, one or more binary metal borides, and / or one or more binary metal silicides; and / or any combination thereof; 111. The apparatus of any one of claims 84 to 110, comprising:

112. The composition, A.B.O. ３ ABO type compounds, in which the element A includes Li, Na, K, Rb, Mg, Ca, Sr, Ba, Y, La, Ce, Pb, Bi or a mixture thereof, and the element B includes Mg, Al, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Nb, Hf, Ta or a mixture thereof. ３ type compound; Barium titanate (BaTiO ３ ). Lead titanate (PbTiO ３ ). Lead zirconate (PbZrO ３ ). Bismuth aluminate (BiAlO ３ ). Alkali niobate (ANbO ３ , A = Li, Na, K, Rb), alkali tantalate (ATaO ３ , A=Li, Na, K, Rb), or a solid solution thereof; Main group alkali zirconate (Bi ０．５ A ０．５ ZrO ３ , A=Li, Na, K); Main group titanate-zirconates (PbTi １－ｘ Zr ｘ O ３ ), rare earth substituted variants, and / or Ba １－ｘ R.E. ｘ TiO ３ (RE=La, Ce) Alkaline earth niobate (Sr １－ｘ Ba ｘ Nb ２ O ６ ), general formula [Bi ２ O ２ ][A ｎ－１ BnO ３ｎ＋１ ] Aurivillius-type phase, Bi ４ Ti ３ O １２ , and their substitutional, solid solution, non-stoichiometric and intergrowth phases; Elemental metals including C, Al, Si, Ti, Fe, Zn, Ag and / or Bi; MgO, Al ２ O ３ , SiO ２ , TiO ２ , Ti ２ O ３ , Cr ２ O ３ , MnO, FeO, CoO, NiO, CuO, ZnO and / or SnO ２ Binary metal oxides comprising: TiN, Mn ３ N ２ , Co ２ N, Ni ３ N and / or Zn ３ N ２ Binary metal nitrides including Binary metal carbides including TiC; ZrB ２ and / or NbB ２ Binary metal borides including: NbSi ２ , WSi ２ and / or MoSi ２ Binary metal silicides including: polyethylene; Polyamide; Kynar; Polytetrafluoroethylene; and / or any combination thereof; 112. The apparatus of claim 111, comprising:

113. the device further comprising a wick adjacent to the PTCR heating element and configured to transport the vaporizable material to a vaporization location; the PTCR heating element is configured to heat the vaporizable material at the vaporization location; 13. Apparatus according to any one of claims 84 to 112.

114. 114. The device of claim 113, further comprising a second heating element, the second heating element adjacent a second side of the wick and the PTCR heating element adjacent a first side of the wick.

115. 114. The device of claim 113, wherein the wick includes an open weave configuration adjacent the PTCR heating element and a cylindrical end.

116. 116. Apparatus according to any one of claims 84 to 115, wherein the power supply is configured to provide the voltage between 3V and 6V.

117. 117. The apparatus of any one of claims 84 to 116, wherein the power source is a battery.

118. 118. The device of any one of claims 84 to 117, wherein the vaporizable material comprises a nicotine formulation.

119. a power source configured to provide a flow of current at a predetermined voltage; a receptacle configured to receive a vaporizable material; a PTCR (Positive Temperature Coefficient of Resistance) heating element electrically coupled to the power source to receive a flow of electrical current from the power source and configured to vaporize the vaporizable material, the heating element having a first resistivity of 10 Ωcm to 100 Ωcm at 100° C. and a second resistivity of 50,000 Ωcm to 150,000 Ωcm at 260° C.; 13. An apparatus comprising:

120. 120. The apparatus of claim 119, further comprising a housing, the power source being contained within the housing.

121. 121. The device of claim 120, wherein the device further comprises a reservoir configured to contain the vaporizable material and to be coupled to the housing.

122. 122. The apparatus of any one of claims 119 to 121, wherein the apparatus further comprises a sprayer including an inlet and an outlet, the PTCR heating element being disposed between the inlet and the outlet.

123. 123. The device of claim 122, wherein the device further comprises a cartridge containing the reservoir and the sprayer.

124. The apparatus, a cartridge including a reservoir containing the vaporizable material and the PTCR heating element, the vaporizable material being a fluid within the reservoir; a wick configured to transport the fluid to a vaporization location; an electrical contact electrically coupled to the PTCR heating element and configured to provide the flow of electrical current from the power source to the PTCR heating element, the PTCR heating element configured to heat the fluid at the vaporization location; and 121. The apparatus of claim 119 or 120, further comprising:

125. 125. The apparatus of any one of claims 119 to 124, wherein the vaporizable material is a liquid.

126. 125. The device of any one of claims 119 to 124, wherein the vaporizable material is a tobacco product.

127. 127. The device of claim 126, wherein the tobacco product is a solid or semi-solid.

128. 128. The apparatus of any one of claims 119 to 127, further comprising an input configured to electrically connect the power source to the PTCR heating element in response to a user input.

129. 129. The device of claim 128, wherein the input comprises a push button.

130. 130. Apparatus according to any one of claims 119 to 129, wherein the apparatus does not include a controller.

131. 131. The apparatus of any one of claims 119 to 130, wherein the apparatus does not include a pressure sensor.

132. The apparatus, A pressure sensor; a controller coupled to the pressure sensor and configured to detect inhalation and, in response, electrically connect the power source to the PTCR heating element; 130. The apparatus of any one of claims 119 to 129, further comprising:

133. 133. Apparatus according to any one of claims 119 to 132, wherein the PTCR heating element has an operating temperature of between 240°C and 280°C.

134. 134. The apparatus of any one of claims 119 to 133, wherein the PTCR heating element has an operating temperature of 245°C to 255°C.

135. 135. The apparatus of any one of claims 119 to 134, wherein the PTCR heating element has an operating temperature of approximately 250°C.

136. 136. The apparatus of any one of claims 119 to 135, wherein the PTCR heating element comprises a plate shape, a polygonal shape and / or a circular shape having a height, a width and a length.

137. 137. The device of claim 136, wherein the height is 0.5 mm, the length is 5.0 mm, and the width is 5.0 mm.

138. 137. The apparatus of claim 136, wherein the plate shape includes two parallel sides having conductive leads attached thereto.

139. 139. The device of any one of claims 119 to 138, wherein the PTCR heating element includes a layer of material having a positive temperature coefficient of resistance between a first conductive layer and a second conductive layer, the first conductive layer being coupled to a first conductive lead and the second conductive layer being coupled to a second conductive lead.

140. 140. The apparatus of any one of claims 119 to 139, wherein the PTCR heating element includes a hole feature extending through the PTCR heating element.

141. 141. The apparatus of any one of claims 119 to 140, wherein the PTCR heating element comprises an aspect ratio of 1-50.

142. The PTCR heating element comprises a composition, the composition comprising: ceramic; mixed metal oxide; Two or more mixed metal oxides; One or more mixed metal oxides and one or more elemental metals, MO ｘ One or more binary metal oxides having a phase of the MN type ｘ One or more binary metal nitrides having a phase of the type MC ｘ One or more bimetallic metal carbides having a phase of the MB type. ｘ One or more bimetallic borides having a phase of the type MSi ｘ complex mixtures with one or more binary metal silicides having the same type phase; A complex mixture of two or more binary metal oxides; a complex mixture of two or more binary metal oxides with one or more elemental metals, one or more binary metal nitrides, one or more binary metal carbides, one or more binary metal borides, and / or one or more binary metal silicides; and / or crosslinked polymer composites of one or more elemental metals and one or more binary metal oxides, one or more binary metal nitrides, one or more binary metal carbides, one or more binary metal borides, and / or one or more binary metal silicides; and / or any combination thereof; 142. The apparatus of any one of claims 119 to 141, comprising:

143. The composition, A.B.O. ３ ABO type compounds, in which the element A includes Li, Na, K, Rb, Mg, Ca, Sr, Ba, Y, La, Ce, Pb, Bi or a mixture thereof, and the element B includes Mg, Al, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Nb, Hf, Ta or a mixture thereof. ３ type compound; Barium titanate (BaTiO ３ ). Lead titanate (PbTiO ３ ). Lead zirconate (PbZrO ３ ). Bismuth aluminate (BiAlO ３ ). Alkali niobate (ANbO ３ , A = Li, Na, K, Rb), alkali tantalate (ATaO ３ , A=Li, Na, K, Rb), or a solid solution thereof; Main group alkali zirconate (Bi ０．５ A ０．５ ZrO ３ , A=Li, Na, K); Main group titanate-zirconates (PbTi １－ｘ Zr ｘ O ３ ), rare earth substituted variants, and / or Ba １－ｘ R.E. ｘ TiO ３ (RE=La, Ce) Alkaline earth niobate (Sr １－ｘ Ba ｘ Nb ２ O ６ ), general formula [Bi ２ O ２ ][A ｎ－１ BnO ３ｎ＋１ ] Aurivillius-type phase, Bi ４ Ti ３ O １２ , and their substitutional, solid solution, non-stoichiometric and intergrowth phases; Elemental metals including C, Al, Si, Ti, Fe, Zn, Ag and / or Bi; MgO, Al ２ O ３ , SiO ２ , TiO ２ , Ti ２ O ３ , Cr ２ O ３ , MnO, FeO, CoO, NiO, CuO, ZnO and / or SnO ２ Binary metal oxides comprising: TiN, Mn ３ N ２ , Co ２ N, Ni ３ N and / or Zn ３ N ２ Binary metal nitrides including Binary metal carbides including TiC; ZrB ２ and / or NbB ２ Binary metal borides including: NbSi ２ , WSi ２ and / or MoSi ２ Binary metal silicides including: polyethylene; polyamide; Kynar; Polytetrafluoroethylene; and / or any combination thereof; 143. The apparatus of claim 142, comprising:

144. the device further comprising a wick adjacent to the PTCR heating element and configured to transport the vaporizable material to a vaporization location; the PTCR heating element is configured to heat the vaporizable material at the vaporization location; 144. Apparatus according to any one of claims 119 to 143.

145. 145. The device of claim 144, further comprising a second heating element, the second heating element adjacent a second side of the wick and the PTCR heating element adjacent a first side of the wick.

146. 145. The device of claim 144, wherein the wick includes an open weave configuration adjacent the PTCR heating element and a cylindrical end.

147. 147. Apparatus according to any one of claims 119 to 146, wherein the power supply is configured to provide the voltage between 3V and 6V.

148. 148. The device of any one of claims 119 to 147, wherein the power source is a battery.

149. 149. The device of any one of claims 119 to 148, wherein the vaporizable material comprises a nicotine formulation.

150. 150. The apparatus of any one of claims 119 to 149, wherein the first resistivity is between 25 Ωcm and 75 Ωcm and the second resistivity is between 75000 Ωcm and 125000 Ωcm.

151. 151. The apparatus of any one of claims 119 to 150, wherein the first resistivity is between 40 Ωcm and 60 Ωcm and the second resistivity is between 100,000 Ωcm and 120,000 Ωcm.

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