Method for predicting the properties of a semiconductive composition

Abstract

A method for designing an electrical heater comprising a layer of an electrically semiconductive composition with a positive temperature coefficient comprising a polyethylene, polypropylene or a mixture thereof and a conductive filler; wherein the layer has a substantially uniform thickness; wherein said electrical heater comprises a plurality of evenly spaced conductors in contact with or at least partially embedded within the layer of an electrically semiconductive composition and arranged to apply a voltage to the electrically semiconductive composition, and wherein the performance of the electrical heater can be described by a performance index defined as a function of a spacing between the evenly spaced conductors, the thickness of the layer of the electrically semiconductive composition and the applied voltage; said method comprising: identifying a target steady state temperature for the heater; determining a value for the performance index of the electrical heater that corresponds to the target steady state temperature; and selecting the spacing between the evenly spaced conductors, the thickness of the layer of the electrically semiconductive composition, and the applied voltage based on the value of the performance index that corresponds to the target steady state temperature.

Description

[0001] Method for predicting the properties of a semiconductive composition

[0002] This invention relates to a method for designing a self-regulating flat sheet heater comprising a semiconductive composition in order to ensure that the heater develops a preferred target temperature. In particular, the invention demonstrates that through the use of a performance index, certain variables can be manipulated in order to target a flat sheet heater with particular properties. The performance of the self-regulating flat sheet heater can therefore be predicted through analysis of the film thickness, applied voltage, electrical conductivity and spacing between conductors.

[0003] Background of Invention

[0004] Self-regulating heaters are known in the art. Self-regulating heaters utilise a conversion from electrical to thermal energy by allowing a current to pass through a semiconductive medium with positive temperature coefficient (PTC) characteristics, which elevates the object temperature above that of its surroundings, until a steady state is reached (self-regulation). A material with a PTC has an electrical resistance that increases with temperature and is the mechanism behind the self-regulating function. These PTC products are often used in underfloor heating or wrapped around pipes for e.g. anti-freeze purposes.

[0005] The use of flat sheet self-regulating heaters is known therefore. In W02014 / 188190, an electrical heater is described that comprises conductors and a heating element disposed between the conductors wherein the heating element comprises an electrically conductive material distributed within a first electrically insulating material. The insulating material separates the conductor from the electrically conductive material.

[0006] US7250586 describes a surface heating system for a car seat or the like comprising a support and a heating layer that contains an electrically conductive plastic, which is characterized by the fact that the heating layer is formed by a flexible film and that the support is flexible. US4247756 describes a heated floor mat in which two inner electrically conductive inner layers sandwich conductors. These conductors are adhered to the inner layers.

[0007] US7053344 describes a flexible heater for a fabric.

[0008] US2021112631 describes a heating element that has at least one film of an electrically conductive polymer material.

[0009] US5451747 discloses a heat mat with PTC material.

[0010] WO2008 / 133562 describes a heating device comprising two elongated electrodes arranged at a distance and being inter-connected by a semiconducting heat generating member of a polymer based material having positive temperature coefficient regarding resistivity (PTC-material), wherein the heat generating member comprises electrode interconnection sections of a low resistivity PTC material compared with the PTC material of intermediate section.

[0011] EP1275274 describes a device for floor heating comprising a bendable, electrically conductive, thermoplastic mat. The device is provided with at least two electrodes. Current is conducted through the device, which heats up and emits heat.

[0012] WO2021 / 188595 describes a blanket comprising a first outer panel, a selfregulating heating element proximate to said first outer panel and a second outer panel proximate to said self-regulating heating element joined to said first outer panel wherein said first outer panel and said second outer panel contain said selfregulating heating elements.

[0013] WO2022 / 129251 describes a self-regulating flat sheet heater prepared by coextrusion where conductors are embedded within the semiconductive composition, and discloses that the heating power of the flat sheet heater can be controlled through the thickness of the sheet, separation of the conductors, conductive filler content and applied voltage.

[0014] EP4294122 describes a flat sheet electrical heater whose heating power can be controlled through the thickness of the sheet, separation of the conductors, conductive filler content and applied voltage.

[0015] In a conventional flat sheet heater, a flat sheet or film of semiconductive composition is provided and attached thereto are a plurality of conductors to provide power to the flat sheet heater. It would be useful if the skilled person could readily predict how a particular design of flat sheet heater will perform, e.g. in terms of the temperature at which a steady state will be reached. There are many variables that will affect the steady state temperature such as the thickness of the semi conductive layer which is heated, the distance between conductors present, the voltage applied to the semi conductive material and the nature of the semiconductive composition, e.g. in terms of the amount of conductive filler present. The present inventors have determined that there is a non-trivial relationship between certain parameters of a flat sheet heater and hence that it is possible to predict certain properties of a flat sheet heater, such as the temperature to which a semiconductive composition within a flat sheet heater will reach, based on the relationship between these parameters.

[0016] Summary of Invention

[0017] Viewed from one aspect the invention provides a process in which the performance index of a flat sheet electrical heater is determined, wherein said flat sheet heater comprises a layer of an electrically semiconductive composition with a positive temperature coefficient comprising a polyethylene, polypropylene or a mixture thereof and a conductive filler; wherein the layer has a substantially uniform thickness; said heater comprises a plurality of evenly spaced conductors in contact with or at least partially embedded within the layer of an electrically semiconductive composition and arranged to apply a voltage to the electrically semiconductive composition; wherein the performance index is defined as a function of a spacing between the evenly spaced conductors, the thickness of the layer of the electrically semiconductive composition and the applied voltage.

[0018] Viewed from another aspect the invention provides a method for designing an electrical heater comprising a layer of an electrically semiconductive composition with a positive temperature coefficient comprising a polyethylene, polypropylene or a mixture thereof and a conductive filler; wherein the layer has a substantially uniform thickness; wherein said electrical heater comprises a plurality of evenly spaced conductors in contact with or at least partially embedded within the layer of an electrically semi conductive composition and arranged to apply a voltage to the electrically semi conductive composition, and wherein the performance of the electrical heater can be described by a performance index defined as a function of a spacing between the evenly spaced conductors, the thickness of the layer of the electrically semi conductive composition and the applied voltage; said method comprising: identifying a target steady state temperature for the heater; determining a value for the performance index of the electrical heater that corresponds to the target steady state temperature; and selecting the spacing between the evenly spaced conductors, the thickness of the layer of the electrically semi conductive composition, and the applied voltage based on the value of the performance index that corresponds to the target steady state temperature.

[0019] Viewed from another aspect, the invention provides a method of manufacturing an electrical heater, the heater comprising: a layer of an electrically semi conductive composition with a positive temperature coefficient comprising a polyethylene, polypropylene or a mixture thereof and a conductive filler; wherein the layer has a substantially uniform thickness; and a plurality of evenly spaced conductors in contact with or at least partially embedded within the layer of an electrically semiconductive composition and arranged to apply a voltage to the electrically semiconductive composition; wherein the performance of the electrical heater can be described by a performance index defined as a function of a spacing between the evenly spaced conductors, the thickness of the layer of the electrically semiconductive composition and the applied voltage; wherein the method comprises: identifying a target steady state temperature for the electrical heater; determining a value for the performance index of the electrical heater that corresponds to the target steady state temperature; selecting values for the spacing between the evenly spaced conductors, the thickness of the layer of the electrically semi conductive composition, and the applied voltage based on the value of the performance index that corresponds to the target steady state temperature; and manufacturing the heater to have the determined spacing and thickness, and to be configured to apply the voltage.

[0020] In other words, this aspect relates to a method of manufacturing an electrical heater which comprises designing the electrical heater according to the aforementioned aspect and then manufacturing the heater accordingly.

[0021] It will be recognised that the use of the performance index in designing or manufacturing the heater allows the person skilled in the art to design the dimensions, conductor arrangements and / or operational voltage of the heater to achieve a desired performance, e.g. such that it has the same performance as another given design.

[0022] The performance index may be defined as any function of the spacing between the evenly spaced conductors, the thickness of the layer of the electrically semiconductive composition and the voltage applied to the electrically semiconductive composition that has a one-to-one relationship with the steady state temperature of the heater (e.g. over a feasible operational range of temperatures).

[0023] In other words, the performance index may comprise any function whose value is determined by the spacing, thickness and voltage and which varies monotonically with the steady state temperature of the heater.

[0024] Conventionally, designing a heater to have a desired steady state temperature can involve a resource-intensive iterative process, in which one or more parameters of the heater (e.g. the spacing, thickness or voltage mentioned above) are varied and the effects on the steady state temperature identified by experiment or computer simulation. This process can be time consuming and inefficient, because the effect on temperature has to be re-calculated by physical experiment or computer simulation for each change to a heater parameter.

[0025] In contrast, utilising a performance index that has a one-to-one relationship with the steady state temperature can allow the design and manufacturing processes to be simplified. A designer may simply identify the value of the performance index which corresponds to the target temperature. Because the performance index is a (known) function of the spacing, thickness and voltage, identifying the value of the performance index that corresponds to the target temperature effectively identifies a solution space of suitable combinations of spacing, thickness and voltage that will deliver the desired temperature (i.e. a set of designs which would reach the same working temperature). A designer can then simply select one of these combinations (e.g. the combination that is most appropriate in light of other design constraints) in a single step without needing to perform iterative experiments or simulations.

[0026] In some embodiments, one or two of the spacing, thickness and voltage may be fixed (e.g. by other design considerations). In such embodiments, selecting the values for the spacing between the evenly spaced conductors, the thickness of the layer of the electrically semi conductive composition, and the voltage applied to the electrically semi conductive composition based on the value of the performance index that corresponds to the target steady state temperature may comprise finding values for the one or two non-fixed parameters which achieve the performance index value when combined with the fixed values(s).

[0027] In a set of embodiments, the performance index is defined by a function that is a linear with respect to the thickness of the layer of the electrically semiconductive composition. For instance, the performance index may be proportional to the thickness of the layer of the electrically semiconductive composition.

[0028] In a set of embodiments, the performance index is defined by a function that is non-linear with respect to the spacing between the evenly spaced conductors and / or the voltage applied to the electrically semiconductive composition. For instance, the performance index may be proportional to the square of the applied voltage and / or inversely proportional to the square of the spacing between the evenly spaced conductors.

[0029] In a set of embodiments, the performance index, PI, is defined as: wherein dcis the spacing between the evenly spaced conductors (i.e. the distance between neighboring conductors, e.g. measured in cm), th is the thickness of the semi conductive layer (e.g. measured in micrometers), A His the voltage applied to the electrically semiconductive composition (e.g. measured in volts), A is a number between 0.5 and 1.5 (e.g., 1), and B is a number between 1.5 and 2.5 (e.g., 2).

[0030] In some embodiments, a value for the performance index of the electrical heater that corresponds to the target steady state temperature may be determined using a predetermined relationship between performance index and steady state temperature. This relationship may be determined by measuring experimentally the steady state temperature achieved in electrical heaters with different combinations of thickness, voltage and spacing (e.g. combinations of up to 5 layer thicknesses, up to 5 applied voltages and up to 5 conductor spacings).

[0031] Additionally or alternatively, the relationship between temperature and PI may be determined by simulating (e.g. with an appropriate computer model), the steady state temperature achieved in electrical heaters with different combinations of thickness, voltage and spacing (e.g. combinations of at least 3 layer thicknesses, at least 3 applied voltages and at least 3 conductor spacings). In a set of embodiments, said simulation comprises finite element analysis.

[0032] In some embodiments the experimenting and / or simulating forms part of the method of designing or manufacturing the electrical heater.

[0033] In some examples, the predetermined relationship is represented by entries in a look-up table (i.e. comprising a set of temperatures and a corresponding set of performance index values, e.g. determined by experiment and / or simulation). In such examples, determining a value for the performance index of the electrical heater that corresponds to the target steady state temperature may comprise identifying a performance index value in the look up table that corresponds to a temperature in the look up table equal or closest to the target temperature. In some embodiments, the performance index value may be determined by interpolating between values in the look-up table (e.g. to estimate an appropriate PI value for a temperature between two entries in the look-up table).

[0034] A look-up table may be a relatively straightforward approach for representing the predetermined relationship (e.g. being simple to populate with experimental or simulated data). However, in some embodiments the predetermined relationship is represented by a correlation curve, i.e. a mathematical relation between performance index value and temperature. The correlation curve may be determined by fitting a curve to experimental and / or simulated data, e.g. using any appropriate technique known in the art per se (e.g. least squares).

[0035] In some embodiments populating a look-up table and / or calculating a correlation curve from experimental and / or simulated data forms part of the method of designing or manufacturing the electrical heater.

[0036] In a specific embodiment, the invention concerns a method for predicting the steady state temperature that can be achieved by an electrical heater comprising a layer of an electrically semiconductive composition with a positive temperature coefficient comprising a polyethylene, polypropylene or a mixture thereof and a conductive filler; wherein the layer has the a substantially uniform thickness; wherein said electrical heater comprises a plurality of evenly spaced conductors in contact with or at least partially embedded within the layer of an electrically semiconductive composition and arranged to apply a voltage to the electrically semiconductive composition; said method comprising determining the performance index of the electrical heater where the performance index is defined as a function of the spacing between the evenly spaced conductors, the thickness of the layer of the electrically semiconductive composition and the applied voltage; and based on the determined PI value, predicting the steady state temperature based on a predetermined relationship between temperature and PI.

[0037] The temperature performance of a flat heater in practice may not depend exclusively on the thickness, spacing and voltage discussed above. For instance, the steady state temperature reached by a heater may depend on the particular semiconductive material used, because different materials can have different conductivity vs temperature relationship, in a set of embodiments, determining a value for the performance index of the electrical heater that corresponds to the target steady state temperature comprises taking into account the semiconductive material used. This may comprise using a predetermined relationship between the temperature and performance index (e.g. represented by a look-up table or a correlation curve) that corresponds to said semi conductive material to determine the value for the performance index.

[0038] For instance, multiple look-up tables and / or correlation curves may be determined for different semiconductive materials. This may be done by performing dedicated experiments and / or simulations for different semiconductive materials, or by modifying existing results to account for different semiconductive materials (e.g. scaling existing results based on a known conductivities of the different materials).

[0039] Moreover, the steady state temperature reached by a heater may depend on the environment in which it is used (e.g. on boundary conditions for the heater). For instance, the steady state temperature of the heater may be effected by environmental factors such as the local temperature or climate, the presence and properties of adjacent objects (e.g. human users) or materials, a level of ventilation near the heater (i.e. indicative of airflow over the heater).

[0040] In many situations, the effect of these environmental factors on heater performance may be sufficiently small that it is acceptable to manufacture the heater (i.e. to select parameters for the thickness, spacing and voltage) without specifically taking into account an expected environment in which the heater is to be used (e.g. with the value of the performance index determined based on a set of standard or nominal environmental conditions). However, in a set of embodiments, determining a value for the performance index of the electrical heater that corresponds to the target steady state temperature comprises taking into account one or more expected environmental factors for the heater. This may comprise using a predetermined relationship between the temperature and performance index (e.g. represented by a look-up table or a correlation curve) that corresponds to said one or more expected environmental factors to determine the value for the performance index. For instance, multiple look-up tables and / or correlation curves may be determined for different environmental conditions (e.g. by performing dedicated experiments and / or simulations for different conditions, or by modifying existing results to account for different conditions). A designer can then consult the appropriate look-up table or correlation curve for the conditions expected for the heater being designed / manufactured. In a set of embodiments, the steady state temperature discussed herein is the maximum steady state temperature attained at any point accrossthe heater. However, any specific temperature across the surface may be used in other embodiments. In some embodiments, the steady state temperature is an average steady state temperature of the heater.

[0041] The invention also relates to a method for predicting the properties of a flat sheet heater as hereinbefore defined wherein the spacing between the evenly spaced conductors in cm, the thickness of the semi conductive layer in micrometers, and the applied voltage are selected so as to enable the formation of a heater having a target PI value wherein the performance index is a function of the spacing between the evenly spaced conductors, the thickness of the layer of the electrically semiconductive composition and the voltage applied to the heater.

[0042] Some or all of the steps of the methods described herein may be performed by a computer. In other words, the methods of designing and / or manufacturing an electrical heater invention disclosed herein may be at least partially computer- implemented.

[0043] The invention extends to computer software that, when executed by a suitable computer system, causes the computer system to perform the method of designing an electrical heater disclosed herein. The invention also extends to a computer system storing computer software that, when executed, causes the computer system to perform the method of designing an electrical heater disclosed herein. The computer system may comprise one or more standard components appropriate for implementing the method known in the art per se, e.g. a memory, a processor, a user I / O device or a network interface. For instance, identifying a target steady state temperature for the heater may comprise the computer system receiving user input specifying the target temperature from a user I / O device.

[0044] The computer system may comprise a personal computer or a smartphone. In some embodiments the computer system may be distributed, i.e. with at least two different computing devices performing different steps. For instance, identifying a target steady state temperature may be performed on a user device (e.g. a smartphone) whilst determining a value for the performance index of the electrical heater that corresponds to the target steady state temperature may be performed on a remote device (e.g. remote server). This may, in relevant embodiments, mitigate the need to send full details of the predetermined relationship between the performance index and steady state temperature to a user device (e.g. allowing the underlying look-up table(s) and / or correlation curve(s) to remain secret).

[0045] Detailed Description of Invention

[0046] The invention will now be described with reference to the following nonlimiting examples and figures.

[0047] Figure l is a graph of electrical conductivity vs temperature for a first semiconductive composition.

[0048] Figure 2 is a theoretical extrapolation of the graph of figure 1 in which conductivities that are 0.75x and 1.25x the value in figure 1 are drawn.

[0049] Figure 3 illustrates a correlation curve between temperature and PI for the semiconductive composition of example 1.

[0050] Figure 4 illustrates a correlation curve for temperature and PI for a semiconductive composition having a conductivity of 1.25x times the value of example 1.

[0051] Figure 5 illustrates a correlation curve for temperature and PI for a semiconductive composition having a conductivity of 0.75x times the value of example 1.

[0052] The present invention relates to a method for designing self-regulating flat sheet heaters, e.g. to have a target maximum heating temperature or to adjust the thickness, voltage or conductor separation to achieve a desired target. The electrical heater of the invention is in the form of a flat sheet or film. The film or sheet (these terms are used interchangeably to define a flat sheet or film of semiconductive composition) of the invention relies on the principle of positive temperature coefficient (PTC). To avoid overheating and potential destruction of the film, the heat generated in the film is self-limiting and requires no regulating electronics. As temperature increases within the film caused by the power applied to the film, resistance within the semiconductive film increases until a steady state is reached and no further heating takes place. The heat within the semiconductive composition is limited therefore by its resistivity.

[0053] In one embodiment therefore, the heater of the invention contains no regulating electronics, e.g. a heat cut off to prevent overheating.

[0054] The electrically semiconductive composition cannot overheat and requires no overheat protection. The technical solution in this particular invention utilises conversion from electrical to thermal energy by allowing a current to pass through a semiconductive medium with PTC characteristics, which elevates the object temperature above that of its surroundings, until a steady state is reached (selfregulation).

[0055] The flat sheet heater of the invention may be multilayer or monolayer. The film contains a single semiconductive layer however comprising (or consisting of) a semiconductive composition. Any other layers present are preferably not semiconductive layers such as insulation layers or decorative layers.

[0056] The flat sheet heater therefore contains a layer of semiconductive composition and it is the thickness of this layer that is important for the PI calculation. The semiconductive composition comprises a polyolefin and conductive filler. The polyolefin may be a polyethylene, polypropylene or mixture thereof. The nature of the semiconductive composition is not critical in this case and the method described herein can be adapted to design / predict the temperature in a wide variety of semiconductive compositions.

[0057] In one embodiment the electrically semiconductive composition comprises a polyethylene or polypropylene and a conductive filler (e.g. carbon black). The selfregulating thermal phenomenon occurs due to two parallel antagonistic processes: a. Poor conduction of electrons through the semiconductive composition generates electrical losses, manifested in heat emission. b. Thermal expansion of the non-conductive part of the semiconductive composition leads to further decrease of the conductivity of the semiconductive composition by separation of the conductive filler particles. Once the two processes have equalised, a steady elevated temperature plateau is reached.

[0058] The temperature increase in the electrically semi conductive composition is governed mainly by the spacing between the conductors present, the thickness of the electrically semi conductive layer, the amount of conductive filler present and the applied voltage.

[0059] Closer conductors increase the temperature at which a steady elevated temperature plateau is reached.

[0060] A thicker semi conductive layer increases the temperature at which a steady elevated temperature plateau is reached.

[0061] Increases in conductive filler content increases the temperature at which a steady elevated temperature plateau is reached.

[0062] Higher voltage causes an increase to the temperature at which a steady elevated temperature plateau is reached.

[0063] The present method is designed to allow the skilled person to design the heater to have a target temperature. The skilled person can adjust the thickness, voltage or conductor separation to target a particular PI value corresponding to a desired temperature.

[0064] It is preferred that the steady state elevated temperature is no more than 50°C, such as no more than 45°C. The heater should ideally achieve a temperature of at least 30 °C.

[0065] The method gives the product designer freedom to alter the parameters above to target a given target temperature, e.g. through the thickness of the semiconductive layer, the location of the conductors or applied voltage.

[0066] Electrically semiconductive composition

[0067] The flat sheet heater of the invention will contain a semiconductive layer. The semiconductive layer comprises, such as consists of, an electrically semiconductive composition. The electrically semiconductive composition comprises a polyethylene or polypropylene and a conductive filler. It preferred if the polyolefin is a polypropylene copolymer or a polyethylene, especially one prepared in a high temperature autoclave or tubular process such as a LDPE homopolymer or copolymer.

[0068] Although the term LDPE is an abbreviation for low density polyethylene, the term is understood not to limit the density range, but covers the LDPE-like high pressure (HP) polyethylenes. The term LDPE describes and distinguishes only the nature of HP polyethylene with typical features, such as different branching architecture, compared to the polyethylene produced in the presence of an olefin polymerisation catalyst.

[0069] The LDPE as said polyolefin means a low density homopolymer of ethylene (referred herein as LDPE homopolymer) or a low density copolymer of ethylene with one or more comonomer(s) (referred herein as LDPE copolymer).

[0070] It is preferred if the electrically semi conductive composition comprises an LDPE copolymer. The one or more comonomers of LDPE copolymer are preferably selected from the polar comonomer(s), non-polar comonomer(s) or from a mixture of the polar comonomer(s) and non-polar comonomer(s). Moreover, said LDPE homopolymer or LDPE copolymer may optionally be unsaturated.

[0071] As a polar comonomer for the LDPE copolymer, comonomer(s) containing carboxyl and / or ester group(s) are used as said polar comonomer. Still more preferably, the polar comonomer(s) of LDPE copolymer is selected from the groups of acrylate(s), methacrylate(s) or acetate(s), or any mixtures thereof.

[0072] If present in said LDPE copolymer, the polar comonomer(s) is preferably selected from the group of alkyl acrylates, alkyl methacrylates or vinyl acetate, or a mixture thereof. The use of ethylene alkyl acylates or ethylene vinyl acetate is preferred.

[0073] Further preferably, said polar comonomers are selected from Ci- to Ce-alkyl acrylates, Ci- to Ce-alkyl methacrylates or vinyl acetate. Still more preferably, said LDPE copolymer is a copolymer of ethylene with Ci- to C4-alkyl (meth)acrylate, such as methyl, ethyl, propyl or butyl acrylate, or vinyl acetate, or any mixture thereof. The use of ethylene methyl acrylate (EMA), ethylene ethyl acrylate (EEA), ethylene butyl acrylate (EBA) or ethylene vinyl acetate (EVA) is preferred.

[0074] As the non-polar comonomer(s) for the LDPE copolymer preferred options are polyunsaturated comonomers comprising C and H atoms only. In a preferred embodiment, the polyunsaturated comonomer consists of a straight carbon chain with at least 8 carbon atoms and at least 4 carbon atoms between the non-conjugated double bonds, of which at least one is terminal.

[0075] A preferred diene compound is 1,7-octadiene, 1,9-decadiene, 1,11- dodecadiene, 1,13 -tetradecadiene, or mixtures thereof. Furthermore, dienes like 7- methyl-l,6-octadiene, 9-methyl-l,8-decadiene, or mixtures thereof can be mentioned.

[0076] If the LDPE polymer is a copolymer, it preferably comprises 1.0 to 40 wt.- %, more preferably 5.0 to 35 wt.-%, still more preferably 10 to 30 wt%, of one or more comonomer(s).

[0077] Where there is a polar comonomer, the comonomer content is preferably 5.0 to 30 wt%, such as 7.5 to 20 wt% in the polymer. The use of ethylene methyl acrylate (EMA), ethylene ethyl acrylate (EEA), ethylene butyl acrylate (EBA) or ethylene vinyl acetate (EVA) is preferred especially where there is 5 to 30 wt%, such as 7.5 to 20 wt% comonomer present.

[0078] MFR21 values of 4.0 g / lOmin or more are required, such as at least 6.0 g / 10 min, even more preferably 8.0 to 15 g / 10 min, and most preferably at least 10.0 g / 10 min when measured under a load of 21.6 kg / 125°C.

[0079] An upper limit of 25 g / lOmin is preferred, such as 18 g / lOmin when measured under a load of 21.6 kg / 125°C.

[0080] Using higher MFR values appears to give more uniform layer thicknesses and allows higher extrusion output without changing the ability of the polyethylene to act as a heater through PTC principles.

[0081] Any LDPE homopolymer or copolymer may have a density of 905 to 935 kg / m3, such as 910 to 925 kg / m3.

[0082] The polyolefin can be produced by any conventional polymerisation process. Preferably, it is an LDPE and is produced by radical polymerisation, such as high pressure radical polymerisation. High pressure polymerisation can be effected in a tubular reactor or an autoclave reactor. Preferably, it is a tubular reactor. In general, the pressure can be within the range of 1200-3500 bars and the temperature can be within the range of 150°C-350°C. Further details about high pressure radical polymerisation are given in WO93 / 08222, which is herewith incorporated by reference. The polymers of the semi conductive composition are well known and are commercially available.

[0083] The polyolefin may also be a polypropylene. Polypropylenes of interest are polypropylene copolymers, such as random propylene copolymers

[0084] The semi conductive composition may comprise at least 50 wt% of the polyolefin, such as at least 60 wt%. Any layer in which the electrically semiconductive composition is present may consist of the electrically semiconductive composition. Thus, any layer in which the electrically semiconductive composition is present may comprise at least 50 wt% of the polyolefin, such as at least 60 wt%. The polyolefin will form the balance of the electrically semiconductive composition once all other components are determined.

[0085] The use of EVA is especially preferred.

[0086] Conductive Filler

[0087] According to the present invention, the semiconductive composition further comprises a conductive filler such as carbon black.

[0088] Suitable conductive fillers include graphite, graphene, carbon fibres, carbon nanotubes, metal powders, metal strands or carbon black. The use of carbon black is preferred.

[0089] The semiconductive properties result from the conductive filler added. Thus, the amount of conductive filler is at least such that a semiconducting composition is obtained. Depending on the desired use and conductivity of the composition, the amount of conductive filler can vary. Preferably, the electrically semiconductive composition comprises 5-50 wt% conductive filler, such as 15 to 50 wt%. In other preferred embodiments, the amount of conductive filler is 5-48 wt.-%, 10-45 wt%, 20-45 wt%, 25-45 wt% or 30-41 wt%, based on the weight of the electrically semiconductive composition.

[0090] It also follows that the semiconductive composition may comprise 5-50 wt% conductive filler, such as 15 to 50 wt%. In other preferred embodiments, the amount of conductive filler in the semiconductive composition is 5-48 wt.%, 10-45 wt%, 20-45 wt%, 25-45 wt% or 30-41 wt%, based on the weight of the semiconductive composition. Any carbon black can be used which is electrically conductive. Examples of suitable carbon blacks include furnace blacks, channel blacks, gas blacks, lamp blacks, thermal blacks and acetylene blacks. Additionally, graphitised furnace blacks (as produced by Imerys) and high structure blacks (known as Ketjenblacks produced by Nouryon) may also be used. Mixtures may also be used. Where a blend of carbon blacks is used then this percentage refers to the sum of the carbon blacks present.

[0091] The carbon black may have a nitrogen surface area (BET) of 5 to 1500 m2 / g, for example of 10 to 300 m2 / g, e.g. of 30 to 200 m2 / g, when determined according to ASTM D3037-93. Further, the carbon black may have one or more of the following properties: i) a primary particle size of at least 5 nm which is defined as the number average particle diameter according to ASTM D3849-95a, ii) iodine adsorption number (IAN) of at least lOmg / g, for example 10 to 300 mg / g, e.g. 30 to 200 mg / g, when determined according to ASTM D-1510; and / or iii) DBP (dibutyl phthalate) absorption number (= oil absorption number) of at least 30 cm3 / 100g, for example 60 to 300 cm3 / 100g, e.g. 70 to 250 cm3 / 100g, for example 80 to 200 cm3 / 100g, e.g. 90 to 180 cm3 / 100g, when measured according to ASTM D 2414.

[0092] Furthermore, the carbon black may have one or more of the following properties: a) a primary particle size of at least 15 nm which is defined as the number average particle diameter according ASTM D3849-95a; b) iodine number of at least 30 mg / g according to ASTM DI 510; c) oil absorption number of at least 30 ml / lOOg which is measured according to ASTM D2414.

[0093] Furnace carbon blacks are preferred. This is a generally acknowledged term for the well-known carbon black type that is produced continuously in a furnacetype reactor. As examples of carbon blacks, the preparation process thereof and the reactors, reference can be made to i.a. EP-A-0629222 of Cabot, US 4,391,789, US 3,922,335 and US 3,401,020. As an example of commercial furnace carbon black grades described in ASTM D 1765-98b i.a. N351, N293 and N550, can be mentioned.

[0094] Other components

[0095] The semi conductive composition may be crosslinked using peroxide or silane moisture curing systems. Crosslinking may also be effected using irradiation to avoid the need for a crosslinking agent.

[0096] Preferably, crosslinking is avoided and the resulting film is a more recyclable product. The semi conductive composition of the invention is preferably not crosslinked.

[0097] Antioxidant

[0098] The semi conductive composition may contain an antioxidant. As antioxidant, sterically hindered or semi-hindered phenols, aromatic amines, aliphatic sterically hindered amines, organic phosphates, thio compounds, polymerized 2,2,4- trimethyl-l,2-dihydroquinoline and mixtures thereof, can be mentioned.

[0099] More preferred, the antioxidant is selected from the group of 4,4'- bis(l,l'dimethylbenzyl)diphenylamine, para-oriented styrenated diphenylamines, 4,4’-thiobis (2 -tert, butyl-5-methylphenol), polymerized 2,2,4-trimethyl-l,2- dihydroquinoline, 4-( 1 -methyl- 1 -phenylethyl )N-[4-( 1 -methyl- 1 -phenylethyl)phenyl] aniline or derivatives thereof.

[0100] More preferred, the antioxidant is selected from the group (but not limited to) of 4,4'- bis(l,l'dimethylbenzyl)diphenylamine, para-oriented styrenated diphenylamines, 4,4’-thiobis (2-tert. butyl-5-methylphenol), 2,2’ - thiobis(6-t-butyl-4-methylphenol), distearylthiodipropionate, 2,2’-thio-diethyl- bis-(3-(3,5-di-tertbutyl-4-hydroxyphenyl)propionate, polymerized 2,2,4- trimethyl-l,2-dihydroquinoline, or derivatives thereof. Of course, not only one of the above-described antioxidants may be used but also any mixture thereof.

[0101] The amount of antioxidant, optionally a mixture of two or more antioxidants, can range from 0.005 to 2.5 wt-%, such as 0.01 to 2.5 wt-%, preferably 0.01 to 2.0 wt-%, more preferably 0.03 to 2.0 wt-%, especially 0.03 to 1.5 wt-%, more especially 0.05 to 1.5 wt%, or 0.1 to 1.5 wt% based on the weight of the semi conductive composition.

[0102] The semi conductive composition may comprise further additives. As possible additives stabilisers, processing aids, flame retardant additives, acid scavengers, inorganic fillers, voltage stabilizers, or mixtures thereof can be mentioned.

[0103] Flat sheet

[0104] The semi conductive layer may have a thickness of 50 to 3000 pm, such as 75 to 2000 pm, especially 100 to 1000 pm. The layer (e.g. the whole layer) has a substantially uniform thickness (e.g. a thickness which varies by less than 50%, less than 25%, less than 10% or less than 5% from an average thickness).

[0105] Conductors

[0106] The flat sheet heater of the invention comprises a plurality of evenly spaced conductors. The term plurality is used herein to imply at least 2, preferably at least 4 conductors. Ideally, the flat sheet heater of the invention comprises an even number of conductors although an odd number will also work. In use, the conductors have alternate polarity.

[0107] The conductors can be made from any suitable conductive metal, typically copper or aluminium. Conductors may have a diameter or thickness of 1.0 pm to 2.0 mm, such as 5.0 pm to 1.0 mm. Conductors can be spherical in cross-section in which case the diameter is given above. Some conductors may have a width of 0.5 to 15 mm, such as 1.0 to 10 mm. The length of the conductor is governed by the size of the heater into which the film will be incorporated.

[0108] The conductors can be at least partially embedded within or in contact with the semiconductive layer. One, some or all of the conductors may be fully embedded within the semiconductive layer. The conductors should preferably pass through the majority, such as the whole, of the heater. The conductor thickness will be adjusted therefore based on the semiconductive layer thickness. The conductors are elongate which implies that the conductors are long and thin compared to their width and thickness. The conductors are often wires or tapes. Each conductor may be provided with an electrode to allow the plurality of conductors to be interconnected and to allow the application of an external power source to create a circuit and hence heat. The conductors may be designed to be directly solderable for ease of installation.

[0109] The heater may comprise a minimum of 2 separate conductors but it may contain many more conductors. The conductors are evenly spaced apart from each and hence do not touch. The conductors are preferably substantially parallel to each other. All conductors should be evenly spaced from each other to ensure an even temperature on application of power. By evenly spaced means that the distance between adjacent conductors is always the same. The conductors are preferably linear. In theory however the conductors might be curved (SS shaped for example) such that they remain equidistant from each other at all times. We regard this as being “parallel”.

[0110] In one embodiment, the spacing between the conductors is 20 to 150 mm, preferably 30 to 90 mm, such as 40 to 80 mm. The spacing between the conductors may be measured from the nearest edges of two adjacent conductors.

[0111] The heater comprises a plurality of conductors that are evenly spaced apart from and substantially parallel to each other, e.g. wherein the spacing between conductors is 20 to 150 mm.

[0112] The conductors are in direct contact with the electrically semiconductive composition. There should not therefore be a layer separating the electrically semiconductive composition from the conductor although an adhesive might be present. The conductors may be attached to the outside of the semiconductive layer or be at least partially embedded within the electrically semiconductive layer. The latter option is preferred. This can be achieved if the conductors are coextruded with two identical layers of the electrically semi-conductive composition. It might also be achieved by sandwiching the conductors between two layers of identical electrically semiconductive composition, e.g. using well known lamination techniques. If two layers of identical semiconductive composition are co-extruded or laminated together, we regard the resulting structure as containing one layer.

[0113] Alternatively, an adhesive layer may be provided on at least a part the conductors. In effect therefore the conductors may be coated (at least partially) with an adhesive layer. This adhesive layer partially or completely covers the conductor and not only adheres to the semi conductive composition but provides an electrical contact with the semi conductive composition.

[0114] Suitable adhesives are conductive adhesives such as those comprising silicone or epoxy resins filled with metallics or conductive carbon fragments.

[0115] It is preferred therefore if the plurality of conductors are at least partially embedded within the semiconductive composition layer, e.g. wherein the semiconductive composition layer is provided as two separate sub layers such that said plurality of conductors are sandwiched between and in contact with said sub layers.

[0116] Where the conductors are coextruded with the semiconductive composition, it is preferred that the conductors are a parallel with the machine direction of the film. It is however possible that the conductors are oriented in the transverse direction in particular if these are retrofitted to the heater after formation or if the semiconductive composition layer is prepared by lamination.

[0117] One arrangement of conductors within the semiconductive layer is shown in scheme 1 : thickness semiconductive layer in crosssection with embedded conductors

[0118] Scheme 1

[0119] Production

[0120] It is possible for the claimed heater to be prepared by colamination. In such a process, two electrically semiconductive layers can be prepared, e.g. via extrusion. These may be allowed to cool before colamination occurs. The layers may be the same. These layers are preferably the same thickness. These layers can then be used to sandwich a layer of the conductors. One layer is therefore placed above and one layer placed below the conductors and the ensemble compressed together. The gaps between the conductors are therefore filled by the electrically semi conductive layers. It will be appreciated that the conductor layer is often very thin compared to the electrically semi conductive layers.

[0121] It is possible to heat one surface of one or both electrically semiconductive layers before colamination such that when colaminated together, the electrically semiconductive layers adhere to the conductors and adhere to the other electrically semiconductive layer without the use of a separate adhesive. In this way, the conductor layer becomes embedded within an electrically semiconductive composition. Alternatively an adhesive can be used.

[0122] A preferred aspect of the invention is that the claimed heater can be prepared using coextrusion. The semiconductive composition layer of the invention is preferably not therefore a typical laminate where the various layers are prepared separately and laminated together, perhaps using an adhesive. We do not require adhesive in our product to form the required heater.

[0123] The heater of the invention can therefore be prepared continuously.

[0124] Importantly, the semiconductive composition can be extruded onto the conductors and hence these are embedded within the semiconductive composition during the extrusion process rather than separately adhered to the semiconductive composition. The semiconductive composition that forms the layer above and below the plurality of conductors can therefore be extruded continuously onto those conductors.

[0125] The process described herein is therefore one that can be operated continuously maximising the value of the formed product. The heater of the invention is cheap. It is also thin and flexible.

[0126] It is preferred therefore if two identical semi-conductive layers are coextruded to encompass the central conductors.

[0127] A coextrusion process can be readily adapted to include further layers above or below the semiconductive layers. In particular, a second layer can also be coextruded above or below the electrically semi- conductive composition layer. Alternatively, the second layer can be laminated above or below the electrically semiconductive composition layer.

[0128] In one embodiment, crosslinking conditions can then be applied to cause a crosslinking reaction. It is preferred however if no crosslinking reaction is used.

[0129] The term coextrusion means herein that two or more layers are extruded in the same extrusion step. The term coextrusion means that all or part of the layer(s) are formed simultaneously using one or more extrusion heads.

[0130] Flat sheet Heater

[0131] The flat sheet heater of the invention is flexible. The heater of the invention may be provided with one or more additional layers to protect the semiconductive composition from damage. For example, an aesthetic top layer can be textile fabric, non-woven or solid sheet (rubber, plastic, paper, wood, metal, etc.). Optionally, no top layer(s) are used.

[0132] The top layer may be extrudable, e.g. a polyolefin layer.

[0133] In a preferred embodiment the heater is provided with an insulation layer or heat reflective layer at the base of the heater. Such an insulation layer may be electrically insulating, thermally insulating or both. Such a layer increases the heating effectiveness of the film. Such a layer may comprise a polyolefin such as a polyethylene, especially an LLDPE, MDPE, HDPE or polypropylene copolymer layer. The polymer of this layer has a higher melting point than the semiconductive polymer.

[0134] The use of LDPE, e.g. an LDPE homopolymer is also possible. Preferred insulation layers use LDPE as the only polymer component. Such a layer is preferably one that can be coextruded although lamination of this layer is also an option.

[0135] The heater may be provided with a support to provide mechanical strength to the heater.

[0136] In use, a voltage is applied to the electrically semiconductive composition via the conductors to generate heat. Typically voltages are 10 to 70 V, such as 12 to 30 V. The heater may comprise a power supply apparatus arranged to produce the voltage. The power supply apparatus may comprise a power source (e.g. one or more batteries) and / or means for connecting the heater to an external power supply (e.g. a mains supply). The power supply apparatus may comprise a voltage converter for converting a supply voltage from a power source to the voltage for applying to the electrically semi conductive composition (e.g. a transformer). The application of the power to the heater leads to almost instant heat. There is no risk of electrocution as the voltage used does not need to be high.

[0137] The heater can be prepared in any desired dimensions. The width of the heater can be adjusted readily to any possible use. The width may be a function of the coextrusion apparatus and sheets from 5 cm to 5 metres can be produced readily.

[0138] As previously discussed, the heating power of the film can be controlled through the thickness of the sheet, separation of the conductors, conductive filler content and applied voltage. Moving the conductors closer together increases the wattage and hence the heat generated.

[0139] Thicker semiconductive layers tend to increase the power output.

[0140] Applications

[0141] The heater of the invention can be utilised in many fields. Applications of the technology described herein are therefore widespread.

[0142] We often provide thermal comfort in winter by heating the entire volume of air in a room or building. In earlier times, our ancestor’s concept of heating was more localized: heating people, not places. They used radiant heat sources that warmed only certain parts of a room, creating micro-climates of comfort. These people countered the large temperature differences with insulating furniture, such as hooded chairs and folding screens, and they made use of additional, personal heating sources that warmed specific body parts. It would make a lot of sense to restore this old way of warming, especially since modern technology has made it so much more practical, safe and efficient.

[0143] The heater of the invention may therefore be employed within an item of furniture such as a screen, chair or sofa.

[0144] In one embodiment the film of the invention might be used in a heated garment. Heated garments available today have small wires (often made of brittle carbon fibres) built into them. They heat up when a low voltage electric current is passed through. There are two main types of heated clothing, battery powered or powered by a vehicle (e.g. heated gloves on a motorcycle). The heaters of the invention are ideally suited for use in both these applications.

[0145] The heater may also be used in a blanket. A major concern with electric heating blankets on the market today is fire risk. These blankets tend to overheat. Using the heater of the present invention that risk is eliminated.

[0146] Radiators are large, immobile and often unattractive. In many parts of the world, radiators are hidden behind more aesthetically pleasing covers of various designs. These covers may also reduce noise or protect against the touching of radiators that get excessively hot. But hiding the radiator is not efficient because adding a radiator cover slows the movement of heat out of the radiator and into the room. The rate of heat loss out through the building’s exterior wall is likely to be increased.

[0147] The heaters of the invention can replace radiators or be used in walls, under floors, in ceilings as heaters. The heaters could even be included within a carpet or rug or other floor covering.

[0148] Electric cars generate next to no heat as opposed to conventional passenger vehicles, which produce more than enough engine heat to heat the interior. An additional electric heater is therefore required in an electric vehicle to heat the interior.

[0149] This heater is supplied with power by the same battery that provides the engine with energy. This can reduce the maximum possible drive distance by a considerable amount.

[0150] Thus, there is a need for heating e-vehicles as efficiently as possible. The present invention might be used to heat inner contact surfaces such as steering wheel, armrest, door panels, seats within the vehicle. More efficient heating can be envisaged compared to heating the entire inner volume of the car, especially for short journeys.

[0151] The heater of the invention could be used to prevent ice or snow build up on a critical surface such as a solar panel. Films might therefore have utility in deicing operations. Other surfaces might be wing mirrors. The heaters are flexible and might be wrapped around pipes to prevent liquid freezing therein. Films can furthermore be used to keep fluids heated e.g. in swimming pools or liquid containers. The skilled person can device many applications of these versatile heating heaters.

[0152] Design Control

[0153] The invention primarily relates to the ability to manipulate the flat sheet heater to have desired properties. Flat sheet heaters can be designed to have particular PI values. We are the first to realise that there is a complex relationship between the applied voltage, layer thickness and the conductor separation - the PI. This PI value correlates to the temperature that the semiconductive layer will reach.

[0154] PI values can be correlated to a particular temperature which the heater will achieve. The invention therefore offers the ability to manipulate the design parameters to achieve that temperature.

[0155] The performance index can be defined as: wherein dcis the spacing between the evenly spaced conductors in the semiconductive layer (i.e. the distance between neighboring conductors) in cm, th is the thickness of the semiconductive layer in micrometers, zlKis the applied voltage to the semiconductive layer in volts.

[0156] In one embodiment, the invention teaches that for a given semiconductive composition a relationship between maximum temperature and PI can be determined by experimentally measuring the maximum temperature or by simulating the maximum temperature achieved in a semiconductive composition layer as a function of the layer thickness, applied voltage and 5 conductor spacings. Obviously, the more measurements / simulations that are taken the more reliable the determined relationship. It is suggested that a minimum of 3 layer thicknesses, up to 3 applied voltages and up to 3 conductor spacings is appropriate.

[0157] Experimentally therefore, the skilled person can prepare a semi conductive layer using a defined semi conductive composition having a defined thickness with defined conductor separation and measure the maximum temperature that is achieved when a defined voltage is applied. This gives a first data point regarding the PI vs temperature relationship.

[0158] A second semiconductive layer can then be produced in which one or more of the variables is changed. Each time, a new data point regarding the PI vs temperature relationship is generated.

[0159] As the skilled person knows the temperature that is achieved in the semiconductive composition through measurement and knows dcthe spacing between the conductors in cm, th the thickness of the layer of the electrically semiconductive composition in micrometers, and AV the applied voltage to the heater in volts, a graph of PI vs temperature can be plotted.

[0160] Once a sufficient number of points are generated, (perhaps a minimum of 9), a correlation curve may be generated (e.g .by least-squares fitting). This curve represents the relationship between the PI and temperature and therefore enables the skilled person to predict for any dcth and AV values what temperature will be achieved for that semiconductive composition. Conversely, the correlation curve enables a user to establish a PI that will generate a given temperature, which can in turn be used to determine suitable values for dcth and AV without out the need for specific investigation of a heater having those values. This already therefore provides the skilled person with a valuable design tool. No one before has realized the correlation between PI and temperature and hence between the parameters in the PI calculation and temperature.

[0161] Different semiconductive compositions have different conductivity properties. Figure 1 shows a conductivity vs temperature curve generated experimentally for a first material. A polypropylene copolymer BC918CF: density 905 kg / m3and MFR2 of 3.0 g / lOmin (Commercial polymer from Borealis AG - PP) and 38 wt% carbon black (the semiconductive composition) was prepared and was formed into sheets of thickness 125 to 1000 microns. From an extruded film, a specimen was punched out having a 25 mm width (w) and a 160 mm length. The specimen was oven dried for ~5h at 60°C and subsequently kept in a desiccator for a minimum of 16h. For the actual conductivity measurement, electrodes were attached to the sample with a 130 mm gap. In order to compensate for so called contact resistance, two more electrodes were attached 10 mm further out from the measurement electrodes. The electrodes were connected to an apparatus that can provide the resistance (R) between the electrodes (e.g. multimeter or VOM-device). The resistance R was measured in ohms. The volume resistivity (VR) was then calculated by multiplying the resistance (R) with the cross- sectional area (A) wherein A = h*w (3*25 mm) of the specimen, divided by the length (L) between the electrodes (130 mm) or VR=R *A / L / The electrical conductivity c is then calculated as o = 1 / VR.

[0162] The conductivity of this semi conductive composition was measured following the protocol above as a function of temperature from 22°C to 80°C. The resulting curve is shown in figure 1.

[0163] Figure 2 shows temperature vs conductivity curves for theoretical semiconductive compositions which have 0.75x or 1.25x the conductivity of the semiconductive composition of figure 1. The skilled person might also want to be able to predict the properties of heaters based on these other semiconductive compositions without having to carry out numerous experiments to prepare a correlation curve each time. Alternatively or in addition to experiments, therefore, computer simulation may be used to predict the steady state temperature in an electrical heater. The simulation may involve calculating the effect of the following physical phenomena: o Electrical current resulting from the applied voltage o Electromagnetic heating (Joule's heating) resulting from the electrical current and the material's resistivity o Heat transfer via conduction (across the heater film, the electrodes and, e.g., an idealized 8mm foam layer sitting below the heater) o Heat transfer via convection (with the surrounding media, in this case assuming it be still air at room temperature natural convection) o Heat transfer via surface-to-ambient radiation The model solves the following general physical laws in a 3D domain (the heater film): o Conservation of energy o Conservation of electrical charge o Maxwell's Equations o Ohm’s Law o Joule's Heating

[0164] These laws are formulated in differential form and the computer solves them by using the finite element method (FEM), an efficient and relatively fast approach for this task. FEM software packages are commercially available, which allow users to set up a problem, design a geometry, impose boundary conditions (like applied voltage or initial temperature), set material properties (like the conductivity vs. temperature relationship) and solve the equations in a relatively straight-forward and user-friendly manner.

[0165] One option is to use Comsol Multiphysics software package and set up the problem using the “Electric currents”, “Heat Transfer in Solids” and “Multiphysics - Electromagnetic Heating” interfaces in the program.

[0166] The model produces as an output the prediction of the temperature at every point in the geometry.

[0167] Various (e.g. 100 or more) simulations can be run of heaters with different values of thickness (th), electrode spacing (de) and applied voltage (V), to build up a data set of temperatures for various combinations of thickness (th), electrode spacing (de) and applied voltage (V)). This set of simulations is for a heater that uses a first semiconductive material having the the electrical conductivity vs. temperature relationship depicted in Figure 1 (the simulation needs this relationship to predict the temperature evolution in the films).

[0168] When solving Maxwell's Equations and the conservation of charge, two additional relationships need to be provided to 1) relate the electric field in a material and the corresponding current density; and 2) relate this current density with the heat generated by it. For 1) the relationship is called “Ohm's Law” and has the electrical conductivity as a coefficient; for 2) the relationship is called “Joule's Heating” and also uses the electrical conductivity as coefficient.

[0169] For each simulation the PI was calculated directly from PI=th*(V / d)2. The PI and temperature for each simulation was plotted, with the result shown in Figure 3. A correlation curve fit to these points may then be used to design heaters as described herein.

[0170] Other sets of simulations can be performed for other semi conductive materials to build up a collection of correlation curves for heaters made using different materials. Figures 4 and 5 show correlation curves of PI vs maximum temperature for semiconductive compositions which respectively have 1.25x and 0.75x the theoretical conductivity as a function of temperature of the semiconductive material used to prepare the correlation curve in figure 3 (i.e. the upper and lower conductivity relationships shown in Figure 2).

[0171] The correlation surves shown in Figures 3-5 illustrate the different performance of different materials. For instance, for a PI of 60, the maximum temperature achieved is higher in figure 5 than figure 4 reflecting therefore the lower conductivity.

[0172] The person skilled in the art can produce a series of correlation curves for use in designing heaters with a range of semiconductive compositions. The person skilled in the art need only use the curve which is most appropriate for the semiconductive composition being considered.

[0173] If the skilled person wishes to use a semiconductive composition for which a correlation curve has not already been generated, such as one in which the conductive filler content is changed, then the skilled person only has to determine the conductivity of the different semiconductive composition at a given temperature and compare that to figure 2 (or a similar curve) in order to establish how the conductivity of that semiconductive composition varies relative to that of figure 1. Based on how it varies, the appropriate correlation curve of PI vs temperature can be used, e.g. the 0.75x or 1.25x correlation curves of figure 4 and 5.

[0174] The method therefore provides a straight-forward and non-trivial tool that allows the skilled person to identify variables to guarantee a specific performance of the heater, e.g., to tailor the design of the semiconductive composition to reach a target temperature.

[0175] The method allows therefore the development of a flexible self-regulating flat sheet heater comprising parallel conductors in contact with or at least partially embedded within a semiconductive composition where target properties can be achieved by choosing combinations of sheet thickness, conductor spacing and applied voltage that lead to a desired target temperature.

[0176] Whilst the invention has primarily been described in terms of using the defined method to predict the temperature within the semiconductive layer it will be appreciated that further applications of the PI equation are possible. For a given semiconductive composition, the maximum temperature achieved is directly related to the PI value. Thus, if the skilled person is looking to redesign a heater to maintain a certain temperature, the PI equation enables that.

[0177] The skilled person could redesign the dimensions, thickness and / or operational voltage of the heater so that is has the same performance index as another given design. In other words, two designs using the same semiconductive composition with the same PI value would reach the same working temperature.

Claims

Claims1. A method for designing an electrical heater comprising a layer of an electrically semi conductive composition with a positive temperature coefficient comprising a polyethylene, polypropylene or a mixture thereof and a conductive filler; wherein the layer has a substantially uniform thickness; wherein said electrical heater comprises a plurality of evenly spaced conductors in contact with or at least partially embedded within the layer of an electrically semi conductive composition and arranged to apply a voltage to the electrically semi conductive composition, and wherein the performance of the electrical heater can be described by a performance index defined as a function of a spacing between the evenly spaced conductors, the thickness of the layer of the electrically semi conductive composition and the applied voltage ; said method comprising: identifying a target steady state temperature for the heater; determining a value for the performance index of the electrical heater that corresponds to the target steady state temperature; and selecting the spacing between the evenly spaced conductors, the thickness of the layer of the electrically semiconductive composition, and the applied voltage based on the value of the performance index that corresponds to the target steady state temperature.

2. A method of manufacturing an electrical heater, the heater comprising: a layer of an electrically semiconductive composition with a positive temperature coefficient comprising a polyethylene, polypropylene or a mixture thereof and a conductive filler; wherein the layer has a substantially uniform thickness; and a plurality of evenly spaced conductors in contact with or at least partially embedded within the layer of an electrically semiconductive composition and arranged to apply a voltage to the electrically semiconductive composition; wherein the performance of the electrical heater can be described by a performance index defined as a function of a spacing between the evenly spacedconductors, the thickness of the layer of the electrically semi conductive composition and the applied voltage; wherein the method comprises: identifying a target steady state temperature for the electrical heater; determining a value for the performance index of the electrical heater that corresponds to the target steady state temperature; selecting values for the spacing between the evenly spaced conductors, the thickness of the layer of the electrically semi conductive composition, and the applied voltage based on the value of the performance index that corresponds to the target steady state temperature; and manufacturing the heater to have the determined spacing and thickness, and to be configured to apply the voltage.

3. The method of claim 1 or 2, wherein the performance index is defined by a function that is a linear with respect to the thickness of the layer of the electrically semiconductive composition.

4. The method of any preceding claim, wherein the performance index is defined by a function that is non-linear with respect to the spacing between the evenly spaced conductors and / or the voltage applied to the electrically semiconductive composition.

5. The method of claim 4, wherein the performance index is proportional to the square of the applied voltage and / or inversely proportional to the square of the spacing between the evenly spaced conductors.

6. The method of any preceding claim wherein the performance index, PI, is defined as:wherein dcis the spacing between the evenly spaced conductors in cm, th is the thickness of the semiconductive layer in micrometers and A V is the voltage applied to the electrically semiconductive compositionin volts.

7. The method of any preceding claim wherein the value for the performance index of the electrical heater that corresponds to the target steady state temperature is determined using a predetermined relationship between performance index and steady state temperature.

8. The method of claim 7, wherein the predetermined relationship is determined by measuring experimentally the steady state temperature achieved in electrical heaters with different combinations of thickness, voltage and spacing.

9. The method of claim 7 or 8, wherein the predetermined relationship is determined by simulating the steady state temperature achieved in electrical heaters with different combinations of thickness, voltage and spacing.

10. The method of any of claims 7-10, wherein the predetermined relationship is represented by entries in a look-up table or a correlation curve.

11. A method as claimed in any preceding claim wherein the flat sheet heater comprises a single layer of semiconductive composition and said semiconductive composition consists of a polyethylene, polypropylene or a mixture thereof and a conductive filler and one or more additives.

12. A method as claimed in any preceding claim wherein the conductor spacing is 20 to 150 mm, the applied voltage is 10 to 70 V and the thickness of the semiconductive layer is 50 to 900 pm.

13. A method as claimed in any preceding claim wherein the semiconductive composition comprises a LDPE homopolymer or LDPE copolymer, such as anethylene alkyl acrylate or ethylene vinyl acetate polymer, or a polypropylene copolymer.

14. A computer readable medium storing computer software that, when executed by a computer system, causes the computer system to perform the method of claim 1.

15. A method for predicting the steady state temperature that can be achieved by an electrical heater comprising a layer of an electrically semi conductive composition with a positive temperature coefficient comprising a polyethylene, polypropylene or a mixture thereof and a conductive filler; wherein the layer has a substantially uniform thickness; wherein said electrical heater comprises a plurality of evenly spaced conductors in contact with or at least partially embedded within the layer of an electrically semi conductive composition and arranged to apply a voltage to the electrically semi conductive composition; said method comprising determining the performance index of the electrical heater where the performance index is defined as a function of a spacing between the evenly spaced conductors, the thickness of the layer of the electrically semiconductive composition and the applied voltage; and based on the determined PI value, predicting the steady state temperature based on a predetermined relationship between temperature and PI.

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