Method for estimating conversion values ​​of polymeric materials and use of conversion values

Abstract

The present invention relates to a method for estimating a degree of conversion value (α) of a polymeric material, the method comprising the steps of heating the polymeric material at a predetermined heating rate (β), obtaining at least one first measured value from the polymeric material at a given temperature (T), the first measured value relating to a specific type of degree of conversion, determining a fixed value (QI) related to the inverse of the temperature (1 / T) and the heating rate (β), the fixed value (QI) being independent of the degree of conversion value (α) of the polymeric material, and estimating the degree of conversion value (α) of the polymeric material based on the first measured value and the fixed value (QI).

Description

[Technical Field]

[0001] The present invention relates to a method for estimating a degree of conversion value of the degree of conversion of a polymeric material and to the use of the degree of conversion value. [Background technology]

[0002] Generally, polymeric materials may contain one or more polymers or a mixture of one or more polymers and one or more fillers. Polymeric materials, such as prepregs, solder masks, glues, and ABFs, are important substrates for electronic devices and / or components thereof, such as PCBs, ECPs, and substrates. In addition, polymeric materials are widely used as coatings, such as paints, for fabrics. Furthermore, polymeric materials may contain one or more monomers and / or oligomers; for example, some glues and / or paints may contain high amounts of these structures. Understanding the behavior of these materials in terms of curing, aging, and / or degradation can enable the production of high-quality and / or low-cost electronic devices. Therefore, the curing kinetics of polymeric materials is tested during the material qualification stage, for example, to determine whether a production process or a step in the production process is suitable for processing the corresponding polymeric material. For example, it can be determined in advance whether a given polymeric material can be fully cured after a certain duration and / or at a given temperature.

[0003] To study the curing kinetics of polymeric materials, thermal kinetic analysis (TKA) can be performed on probes of polymeric materials, where kinetics deals with measuring and parameterizing the process rate and thermal analysis concerns the thermally stimulated process. TKA is widely used for the curing and decomposition processes of polymeric materials in all polymer-related industries.

[0004] Furthermore, Model Free Kinetics (MFK) is a well-known and widely used method for characterizing various polymeric materials such as EMCs (Epoxy Molding Compounds), prepregs, and SMs (Solder Masks), as it allows predicting the thermal behavior of materials such as crystallization, melting, crosslinking, and decomposition behavior.

[0005] However, due to limitations imposed by the current MFK theory, the prediction accuracy and range are heavily influenced by experimental data. Summary of the Invention [Means for solving the problem]

[0006] It is an object of the present invention to overcome at least some of the above problems.

[0007] This object is achieved by the subject matter of the independent claims. Further exemplary embodiments are evident from the dependent claims and the following description.

[0008] One aspect of the present invention relates to a method for estimating a degree of conversion value of a polymeric material, the method comprising the steps of heating the polymeric material at a predetermined heating rate; obtaining at least one first measured value from the polymeric material at a given temperature, the first measured value relating to a particular type of degree of conversion; determining a fixed value related to the inverse of the temperature and the heating rate, the fixed value being independent of the degree of conversion value of the polymeric material; and estimating a degree of conversion value (α) of the polymeric material based on the first measured value and the fixed value (QI).

[0009] The polymeric material may include one or more polymers or a mixture of one or more polymers and one or more fillers. Furthermore, the polymeric material may include one or more monomers and / or oligomers; for example, some glues and / or paints may contain a high content of such structures. The first measured value may be a first degree of cure value at a given temperature. The first measured value may be measured directly or may be determined from measurements, such as TKA or DSC analysis, as described below. While the first degree of cure value may be determined by measurements at a specific temperature and a specific heating rate, the degree of cure value to be estimated may indicate a temperature corresponding to a specific degree of cure value at a specific heating rate. This degree of cure value may be estimated without a separate measurement. The fixed value may be referred to as the Qi point. The Qi point may be predetermined, as described below.

[0010] The above method using the Qi point can be called model-free kinetics (MFKq) using the Qi point. MFKq provides guidelines for better control and processing of polymeric materials. Additionally, MFKq improves the accuracy of the traditional MFK method and expands the prediction range, especially for non-isothermal and isothermal predictions. On the other hand, MFKq provides a means to determine the quality of measurement data, especially before making any predictions, to ensure high quality predictions. Furthermore, due to its expanded prediction range, MFKq enables additional applications compared to traditional MFK. For example, MFKq can be used to predict the state of an incompletely cured polymeric material at a certain environmental temperature, e.g., for shelf life prediction. The shelf life prediction can be used as a guideline for the storage time and / or temperature of the polymeric material in a corresponding warehouse.

[0011] Thus, an advantage of the present invention is that the use of the Qi point in estimating the degree of conversion allows for a more precise estimation of values ​​related to a particular degree of conversion, e.g., degree of cure, at a particular temperature and heating rate. In other words, thanks to the adjustment of the estimate through the use of the Qi point, the estimation of a particular degree of conversion, e.g., degree of cure, of a polymeric material resulting from a particular temperature and a particular heating rate can be closer to the actual degree of conversion, e.g., degree of cure, as disclosed below with respect to preferred embodiments.

[0012] According to one embodiment, the method further includes a step of estimating the slope of a Qi curve by performing a thermokinetic analysis (TKA) specific to the conversion value to be estimated based on the first measured value, where the estimation of the conversion value of the polymeric material is based on the first measured value, a fixed value, and the estimated slope. This conversion conversion may be performed to linearize the dependence of the heating rate on temperature. This may facilitate a simple graphical analysis of the adjusted estimated conversion value. When the first measured value, i.e., the first cure value, and the fixed value, i.e., the Qi point, are connected in a Qi curve diagram, the slope of the resulting line corresponds to the slope. The Qi curve diagram shows one or more Qi curves. Each Qi curve shows the dependence of the natural logarithm of the heating rate on the inverse of the temperature, with one Qi curve for each measured cure value.

[0013] According to one embodiment, the method further comprises a step of adjusting the estimated slope based on a fixed value, and the estimation of the degree of conversion of the polymeric material is based on the measured value, the fixed value (Qi point), and the adjusted slope, which can be useful for a simple and reliable estimation of the degree of conversion.

[0014] According to one embodiment, the acquisition of measured values ​​from the polymeric material is performed for at least two values ​​of degree of conversion, which may allow the definition of a specific temperature / heating rate and the Qi point to be determined in a very precise manner, for example through interception of a graph of the estimated line resulting from two specific estimated degree of conversion values.

[0015] According to one embodiment, the at least two measured values ​​include a minimum and a maximum value for a particular degree of conversion of the polymeric material. For example, if the degree of conversion is the cure rate, the minimum value may refer to an uncured polymeric material, and the maximum value may refer to a fully cured polymeric material. This may help to precisely define the estimated trend, and hence the Qi point, resulting from the two specific estimated degree of conversion values.

[0016] According to one embodiment, a third measured value is obtained from the polymeric material, the third measured value being related to a type of conversion degree and being for a further value of the conversion degree, and the estimation of the conversion value of the polymeric material is based on the third measured value and the fixed value, which can facilitate a very accurate and easy estimation of the conversion value, for example through interception of the further conversion degree graph by the Qi point.

[0017] According to one embodiment, obtaining a third measured value from the polymeric material for a further degree of conversion value related to the type of degree of conversion is performed independently from obtaining measured values ​​for at least two values ​​of degree of conversion required to make the TKA, which can facilitate a highly efficient estimation of the degree of conversion value.

[0018] According to one embodiment, the fixed value (QI) corresponds to a value based on a specific temperature range at several or any conversion degree values. In particular, depending on the size of the temperature value range considered for the calculation of the fixed value, the estimation of the fixed value (QI) occurs with different accuracy. In other words, the wider the temperature range considered for the calculation, the more accurately the fixed value (QI) is determined (and therefore the more accurately the estimation of the conversion degree is provided).

[0019] According to a preferred embodiment, a finite temperature range at several conversion values ​​is used for the determination of the fixed value (QI) to yield a specific value, where the range of temperature values ​​is selected taking into account the desired level of precision of the conversion estimation.

[0020] According to a further preferred embodiment, the entire possible temperature range at any conversion value is used to determine the fixed value (QI), resulting in infinity ∞, in which case the result of the conversion estimation is made as precise as possible.

[0021] According to one embodiment, one or more of the measured values ​​of the polymeric material and / or the TKA are obtained under at least one of isothermal and non-isothermal conditions, which may aid in accurate derivation of the present MFKq theory.

[0022] According to one embodiment, obtaining one or more measured values ​​of a polymeric material includes measuring corresponding measured values ​​at a specific position of the change in value along at least one of time and temperature. The specific position may be a peak, e.g., a maximum value. The shift of the peak, e.g., the maximum value, may be related to the corresponding thermodynamic theory. This may facilitate highly accurate obtaining of one or more measured values ​​of a polymeric material.

[0023] According to one embodiment, TKA is based on one or more measured values ​​at specific peaks of change in value over time and / or temperature, which can make for a highly accurate TKA.

[0024] According to one embodiment, the type of conversion relates to the degradation of the polymer of the polymeric material, and each TKA includes a TGA (Thermogravimetric Analysis), which can be useful for very accurate TKA.

[0025] According to one embodiment, the type of conversion is related to the viscosity (change) of the polymer, and each TKA includes a rheological measurement. The rheological measurement can be useful for a highly accurate TKA. The rheological measurement can be performed using a rheometer.

[0026] According to one embodiment, the type of conversion is related to the change in cure rate, and each TKA includes a DSC analysis. Alternatively, each TKA can include a DTA (Differential Thermal Analysis). DSC analysis or DTA can be useful for very accurate TKA.

[0027] According to one embodiment, the type of conversion is related to the change in elastic modulus, and each TKA includes a rheological measurement, such as a DMA measurement.

[0028] According to one embodiment, the type of conversion is related to the uptake of one or more fluids, and each TKA includes a TMA (Thermomechanical Analysis) / humidity chamber and TGA analysis-measurement. The fluids can be liquid, e.g., water, or gaseous, e.g., water vapor, ammonia, and / or CO2.

[0029] According to one embodiment, the type of conversion is related to the change in CTE / shrinkage, and each TKA includes a TMA measurement.

[0030] One aspect of the present invention relates to the use of the degree of conversion values ​​estimated according to the above method for the simulation and / or production and / or application and / or use definition of polymeric materials.

[0031] These and other aspects of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter. [Brief explanation of the drawings]

[0032] In the following, embodiments of the invention will be described in more detail with reference to the accompanying drawings. [Figure 1] 1 shows a flowchart of an exemplary embodiment of a method for estimating the QI point of a given polymeric material. [Figure 2] Examples of DSC thermograms of polymeric materials under different heating rates are shown. [Figure 3]1 shows an example of a diagram showing the degree of cure of a polymeric material as a function of temperature at different heating rates under non-isothermal conditions. [Figure 4] An example of an Ozawa-Flynn-Wall diagram is shown below. [Figure 5] Some examples of intersection distributions are shown below. [Figure 6] A detailed view of the intersection between 10% and 90% according to FIG. 5 is shown. [Figure 7] An example of a Qi curve in a Qi curve diagram is shown. [Figure 8] A detailed view of the QI curve according to FIG. 7 is shown. [Figure 9] 1 shows a flowchart of an exemplary embodiment of a method for determining a graph for estimating a conversion value of a degree of conversion of a polymeric material under isothermal conditions. [Figure 10] 1 shows a diagram containing an exemplary graph of the degree of conversion as a function of time under isothermal conditions. [Figure 11] 1 shows a flowchart of an exemplary embodiment of a method for determining a graph for estimating a conversion value of a degree of conversion of a polymeric material under non-isothermal conditions. [Figure 12] 1 shows a diagram containing an exemplary graph of conversion values ​​as a function of temperature under non-isothermal conditions. [Figure 13] 1 shows a flowchart of an exemplary embodiment of a method for determining a graph for estimating a conversion value of the degree of conversion of a polymeric material under isothermal or non-isothermal conditions. [Figure 14] Further examples of Qi curves are shown in the Qi curve diagram.

[0033] The reference symbols used in the drawings and their meanings are listed in summary form in the legends. As a rule, identical parts in the drawings are provided with the same reference symbols. DETAILED DESCRIPTION OF THE INVENTION

[0034] FIG. 1 shows a flow chart of an exemplary embodiment of a method for estimating the Qi point QI (see FIG. 7) of a given polymeric material.

[0035] In step S2, differential scanning calorimetry (DSC) of the polymeric material probe is performed at n different heating rates β n °=°[β0,β1,...,β n-1 ], where n is a natural number. For example, n can be in the range of 1 to 20, such as 1 to 10, such as 3 to 6.

[0036] 2 shows an example of a DSC thermogram 20 of a polymeric material determined by DSC measurement. The DSC thermogram 20 includes one graph for each heating rate β. n is given in K / min. Alternatively, the heating rate β may be given in any other possible temperature versus time relationship, for example in °C / sec or °F / hr. The degree of cure value α can be determined from the DSC thermogram 20, and is calculated by the formula

number

[0037] In step S4, each temperature rise rate β i For each hardening value α°=°[0,0.01,...,100] (a total of 10001 elements) and the corresponding temperature T i =[T i,0 ,T i,1 ,...,T i,1000 ] is determined, where i°=°0,°1,°...,°m-1 are natural numbers.

[0038] 3 shows an example of a diagram, which may be referred to hereinafter as the first diagram 22. The first diagram 22 shows the relationship between the heating rate β n Temperature T i 3 shows the determined degree of cure value α of the polymeric material as a function of the heating rate β and the temperature T.

number

[0039] For example, the horizontal dashed line in the first diagram 22 may correspond to a degree of cure value α of 50%, i.e., α°=°50°%, and the intersection of the graph of degree of cure α with that horizontal dashed line provides the temperature T at which the degree of cure value α is 50% under the corresponding heating rate β.

[0040] Figure 4 shows an example of an Ozawa-Flynn-Wall diagram, which may be referred to as the second diagram 24. The second diagram 24 may be achieved by Ozawa-Flynn-Wall analysis, as known in the art. The Ozawa-Flynn-Wall diagram of Figure 4 shows the heating rate β extracted by the corresponding horizontal line from the diagram of Figure 3 for a degree of cure α = 50%, as explained above. n and temperature T.

[0041] The Ozawa-Flynn-Wall diagram may also include correspondingly constructed graphs for other degrees of cure α = ° [0, 0.01, ..., 100]. However, corresponding graphs constructed according to conventional Ozawa-Flynn-Wall analysis may intersect with each other in the region of the Ozawa-Flynn-Wall diagram (not shown), which is unreasonable from a physical point of view and shows the shortcomings of conventional Ozawa-Flynn-Wall analysis. Therefore, instead of using conventional Ozawa-Flynn-Wall analysis, the inventors have found a more accurate approach to constructing graphs for predicting the degree of cure α of a given polymeric material, as described below.

[0042] In step S6, the graph of the Ozawa-Flynn-Wall diagram is i , heating rate β n , and the hardening degree (α°=°[0,°0.01,°...,°100],

number

[0043] In step S8, the graph of the Qi curve diagram is linearly fitted, and the slope and y-axis intercept of the corresponding fitted graph, i.e., Qi curve, are extracted to obtain the slope K°=°[k0,k1,...,k 10000 ] and the intercept B°=°[b0,b1,...,b 10000 ] may occur.

[0044] In step S10, the intersections of the fitted graph for the degree of cure value α between 1% and 30%, for example between 5% and 15%, e.g., α°=°10°%, with all other fitted graphs are calculated, e.g.,

number

[0045] In step S12, the intersection points of the fitted graph for the degree of cure value α between 30% and 60%, for example between 40% and 55%, e.g., α°=°50°%, with all other fitted graphs are calculated, e.g.,

number

[0046] In step S14, the intersection points of the fitted graph for the degree of cure value α between 70% and 99%, for example between 85% and 95%, e.g., α°=°90°%, with all other fitted graphs are determined, e.g.,

number

[0047] In step S16, the intersection points determined in steps S10-S14 may be plotted in a third diagram 26, for example as shown in FIG.

[0048] Figure 5 shows an example of the distribution of some of the above intersection points. The distribution of the intersection points is shown in the third diagram 26. From Figure 5 it can be seen that 80% of the intersection points are around the inverse of temperature 0, which can only be achieved at temperatures T tending to infinity.

[0049] FIG. 6 shows a detailed view of the intersection between 10% and 90% in the fourth diagram 36.

[0050] In step S18, the intersection point of the fitted graph with 1 / T°=°0 can be determined as the Qi point QI, where QI°=°(0,lnβ).

[0051] 7 shows in a fifth diagram 38 an example of Qi curves, all of which include the Qi point QI. The Qi curves do not cross each other except at the Qi point QI, which makes perfect sense from a physical point of view.

[0052] FIG. 8 shows a detailed view of the QI curve according to FIG. 7, in particular the view of the lower area 28 of the fifth diagram 38.

[0053] The Qi curves of Figures 7 and 8 can be determined by steps S20 and S22.

[0054] In step S20, the graph, i.e., the Qi curve, is calculated according to the Ozawa-Flynn-Wall formula:

number

number

[0055] In step S22, the graph can be linearly fitted again in the Qi diagram to obtain a Qi curve corresponding to the Ozawa-Flynn-Wall curve containing the Qi points QI, and the corresponding fitted slope K' = °[k'0, °k'1, °..., °k' 10000 ] and the intercept B'=°[b'0,b'1,...,b' 10000 ] can be extracted.

[0056] FIG. 9 shows a flowchart of an exemplary embodiment of a method for determining a graph for estimating a conversion value α of a polymeric material under isothermal conditions. The conversion degree may be the curing degree. Alternatively, the conversion degree may be different from the curing degree. In general, the conversion degree may represent the proportion of reactants that have already reacted. The type of conversion degree may depend on the type of the corresponding reaction. For example, if the reaction is a polymerization process, the conversion degree may be the curing degree. If the reaction is a decomposition process, the conversion degree may be the decomposition degree. Furthermore, the conversion degree may be at least one of polymer degradation, polymer viscosity, curing rate, change in modulus, uptake of one or more fluids, and CTE / shrinkage.

[0057] The method further comprises: i, the heating rate β and the determined Qi points QI can be used to calculate the temperature T in the form of a mathematical function and / or a corresponding graph as a function of time, so that one or more desired and / or optional hardening values ​​α can be extracted later by the mathematical function and / or from the corresponding graph. iso a predetermined hardness value α for estimating the continuous progression and / or behavior of the hardness value α below; i The corresponding time t at which

[0058] In step S30, a graph showing the hardness value α of the hardness of the polymer material as a function of time t is generated based on the temperature T iso The temperature T is received by the device for determining the graph for estimating the cure value α. iso can be input, and the device can be driven at temperature T iso The device may receive a temperature T iso may be received from an external device or from the memory of a general-purpose computer.

[0059] In step S32, the index i and the hardness value α i and time t i are set to 0, and the above cure value α°=°[0,0.01,...,100] and the above Qi point QI°=°(0,lnβ) are received by the device. Furthermore, the slope of the graph is calculated as a function of the cure α, e.g.,

number

[0060] In step S34, the index i is incremented by 1, i.e., i°=°i°+°1, and the next conversion frequency α i But, for example, α i °=°α i-1 It is chosen as °+°δα.

[0061] In step S36, the current conversion degree value α i It is checked whether is greater than 100. If the condition of step S36 is not met, the method may proceed to step S38. If the condition of step S36 is met, the method may proceed to step S44.

[0062] In step S38, ΔT is

number

[0063] In step S40, Δt is

number

[0064] In step S42, t i But, t i °=°t i-1 °+°Δt.

[0065] The method then proceeds to step S34.

[0066] In step S44, a graph representing the behavior of the degree of cure value α versus time t may be plotted, for example as shown in Figure 10, and / or the method for determining a graph for estimating the degree of conversion value α of the degree of conversion of the polymeric material under isothermal conditions may be terminated, which may have the advantage of more accurately predicting the curing time of the polymeric material.

[0067] The above-described method for determining a graph for estimating a conversion value α of a polymeric material under isothermal conditions can be used as a subroutine of a method for estimating a conversion value α of a polymeric material under isothermal conditions, which can estimate one or more conversion values ​​α at a desired time t by extracting the corresponding conversion values ​​α from the determined graph.

[0068] 10 shows a diagram including an exemplary graph of the degree of conversion α as a function of time t under isothermal conditions. This diagram may be referred to as the sixth diagram 40. The sixth diagram 40 may be determined by the above-described method for determining a graph for estimating the degree of conversion value α of the degree of conversion of a polymeric material under isothermal conditions. The graph may be used by the method for estimating the degree of conversion value α of the degree of conversion of a polymeric material under isothermal conditions.

[0069] 11 shows a flowchart of an exemplary embodiment of a method for determining a graph for estimating a degree of conversion value of a polymeric material under non-isothermal conditions. The degree of conversion can be a degree of cure. This method involves using the predetermined degree of cure value α i , the heating rate β and the determined Qi points QI can be used to calculate the hardening degree values ​​α in the form of a mathematical function and / or a corresponding graph depending on the temperature T, so that one or more hardening degree values ​​α at one or more desired and / or arbitrary temperatures T can be extracted by the mathematical function and / or from a corresponding graph. i a predetermined hardening value α for estimating the continuous progression and / or behavior of i The corresponding temperature T reached can be determined.

[0070] In step S50, a given heating rate β is received for which a graph representing a degree of cure value α of the degree of cure of the polymeric material as a function of temperature T is to be estimated. The heating rate β can be input to a device for determining a graph for estimating the degree of cure value α, and the device can receive the heating rate β.

[0071] In step S52, the index i and the hardness value α iare set to 0, and the hardness value α i °=°[0,0.01,...,100] and the above Qi point QI°=°(0,lnβ) is received by the device. Furthermore, the slope of the graph can be given as the above function f(α).

[0072] In step S54, T i but

number

[0073] In step S56, the index i is incremented by 1, i.e., i°=°i°+°1, and the next conversion frequency α i But, for example, α i °=°α i-1 °+°δα, where δα can be 1 for example.

[0074] In step S58, the current conversion degree value α i It is checked whether is greater than 100. If the condition of step S58 is not met, the method may proceed to step S54. If the condition of step S58 is met, the method may proceed to step S60.

[0075] In step S60, a graph representing the degree of cure α versus temperature T may be plotted, for example as shown in FIG. 12, and / or the method for determining a graph for estimating the degree of conversion value α of the degree of conversion of a polymeric material under non-isothermal conditions may be terminated.

[0076] The above-described method for determining a graph for estimating a conversion value α of a polymeric material under non-isothermal conditions can be used as a subroutine of a method for estimating a conversion value α of a polymeric material under non-isothermal conditions, which can correspondingly estimate one or more conversion values ​​α at one or more desired temperatures T by extracting the corresponding conversion values ​​α from the determined graph.

[0077] 12 shows a diagram including an exemplary graph of the degree of conversion α as a function of temperature T under non-isothermal conditions, particularly at different given heating rates β. This diagram may be referred to as seventh diagram 42. Seventh diagram 42 may be determined by the above-described method for determining a graph for estimating the degree of conversion value α of the degree of conversion of a polymeric material under non-isothermal conditions. The graph may be used by the method for estimating the degree of conversion value α of the degree of conversion of a polymeric material under non-isothermal conditions.

[0078] 13 shows a flowchart of an exemplary embodiment of a method for determining a graph for estimating a degree of conversion value of a polymeric material under isothermal or non-isothermal conditions. The degree of conversion can be a degree of cure. This method involves using the predetermined degree of cure value α i , the heating rate β and the determined Qi points QI can be used to estimate the continuous progression and / or behavior of the hardening value α at a given time t and / or temperature T in the form of a mathematical function and / or a corresponding graph depending on the time t and / or temperature T, such that one or more hardening values ​​α at desired and / or arbitrary one or more times t and / or temperatures T can be extracted by the mathematical function and / or from a corresponding graph. i The corresponding time t and / or temperature T at which

[0079] In step S70, a predetermined temperature T i =[T0,T1,...,T n ] and time t i° =°[t0,T1,...,T n ] may be received by the device performing the method. Further, the hardness value α is set to 0, δT is set to 0.1, δα is set to 0.001, and the index i°=°0,°1,°...,°m-1 is a natural number.

[0080] In step S72, the index i is set to 1, and the above Qi point QI and slope f(α) are received by the device.

[0081] In step S74, the hardness value α is set to α=α i-1 is set to

[0082] In step S76, the current conversion degree value α i It is checked whether is less than 100. If the condition of step S76 is not met, the method may proceed to step S112. If the condition of step S76 is met, the method may proceed to step S78.

[0083] In step S78, the temperature T s But, for example, T s °=°T i-1 By T i-1 where s is a natural number.

[0084] In step S80, Δt1 is set to 0.

[0085] In step S82,

number

[0086] If the conditions of step S82 are met, the method may proceed to step S84. If the conditions of step S82 are not met, the method may proceed to step S86.

[0087] In step S84, T e T i is set to

[0088] In step S86, T e but

number

[0089] In step S88, Δt is

number

[0090] In step S90, T iso but

number

[0091] In step S92, ΔT is

number

[0092] In step S94, Δt0 is

number

[0093] In step S96, Δt1 is

number

[0094] In step S98,

number

[0095] If the conditions of step S98 are met, the method may proceed to step S100. If the conditions of step S98 are not met, the method may proceed to step S102.

[0096] In step S100, the hardness value α is

number

[0097] In step S102, the hardness value α is

number

[0098] In step S104,

number

[0099] If the conditions of step S104 are met, the method may proceed to step S108. If the conditions of step S104 are not met, the method may proceed to step S106.

[0100] In step S106, the temperature T s T e is set to

[0101] In step S108, the hardness value α i is set to α.

[0102] In step S110,

number

[0103] If the conditions of step S110 are met, the method may proceed to step S112. If the conditions of step S110 are not met, the method may proceed to step S114.

[0104] In step S112, the hardness value α i is set to 100.

[0105] In step S114, the function α.append(α i) can be used for the corresponding program code, and α can be an array and can start with one element, i.e., α=[0]. When the corresponding loop starts, α evolves from 0 to 100, which is the case when the array is α i This means that you need to add them one by one.

[0106] In step S116, the index i is incremented by one.

[0107] The above-mentioned method allows for plotting graphs for degree of cure values ​​under isothermal and non-isothermal conditions. In particular, the MFKq theory presented in this application allows for finding the correct degree of cure value α with a given time t and temperature T. If the input of time t and temperature T is for the non-isothermal case, the output of degree of cure value α is for the non-isothermal case. If the input of time t and temperature T is isothermal, the output of degree of cure α can represent that of isothermal curing conditions.

[0108] FIG. 14 shows an alternative way of estimating the degree of conversion through the relationship between temperature (1 / T) and heating rate (lnβ) over the entire temperature range at any given degree of conversion α.

[0109] According to this alternative embodiment, the curve, in particular from lower to higher temperatures, eventually converges to an infinite point on the y-axis, representing the Qi point QI. According to the embodiment shown, all segments of the curve can be straight lines. Its boundary on the x-axis is predefined according to the application, preferably in two steps. a. Define the division points of x in the temperature integral p(x) according to your application: [x0, x1, ..., x n ] b.1 / T=xR / E α Define division points on the x-axis according to: [1 / T 0,α ,1 / T 1,α ,...,1 / T n,α ] The slope of each line k i,α is the corresponding slope d in a plot of lnp(x) versus x.i This is preferably calculated based on the following two steps: ad i =ln[p(x i ) / p(x i+1 )] / (x i -x i+1 ) is calculated as follows: [d0,d1,...,d n ] bk i,α =d i E α Calculate / R: [k 0,α ,k 1,α ,...,k n-1,α ].

[0110] Intercept b of each line i,α is the first intercept b calculated from the experimental data m,α Preferably, it is solved by recursion using First intercept b m,α Preferably, there are three steps to obtain 1. Average logarithmic heating rate lnβ at α based on experimental inputs avg and the reciprocal of the average temperature, 1 / T avg,α Calculate. 2. The reciprocal of the average temperature [1 / T 0,α ,1 / T 1,α ,...,1 / T n,α ] in 1 / T m,α ≦1 / T avg,α ≦1 / T m+1,α Find the index m such that 3. Calculate the intercept based on the known index m and the linear equation: b m,α =lnβ avg -k m,α / T avg,α . The remaining intercepts can be solved according to the following formula: ib i-1,α =b i,α +(k i,α -k i-1,α ) / T i,α ,i∈[1,m] ii.b i+1,α =b i,α +(ki,α -k i+1,α ) / T i+1,α ,i∈[m,n-2]

[0111] While the present invention has been illustrated and described in detail in the drawings and the foregoing description, such illustrations and descriptions are to be considered illustrative or exemplary and not restrictive, and the invention is not limited to the disclosed embodiments. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art and practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite articles "a" or "an" do not exclude a plurality. A single processor or controller or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope. [Explanation of symbols]

[0112] 20 DSC thermograph 22 First Diagram 24 Second Diagram 26 Third Diagram 28 Lower Area 30 Isotherms 32 Non-isotherms 36 Fourth Diagram 38 The Fifth Diagram 40 Sixth Diagram 42 Seventh Diagram QI Qi point S2~S86 Steps 2~68

Claims

1. 1. A method for estimating a degree of conversion value (α) of a polymeric material, comprising: - heating the polymeric material at a predetermined heating rate (β); - obtaining at least one first measured value at a given temperature (T) from said polymeric material, said first measured value relating to a particular type of said degree of conversion; - determination of a fixed value (QI) related to the inverse of the temperature (1 / T) and the heating rate (β), said fixed value (QI) being independent of the degree of conversion value (α) of said polymeric material; - estimating the degree of conversion value (α) of the polymeric material at a specific heating rate based on the first measured value and the fixed value (QI); A method comprising:

2. 10. The method of claim 1, Based on the first measured value, a thermal kinetic analysis (TKA) specific to the conversion value (α) from which the estimation is made is performed to estimate the slope of the Qi curve. further comprising the estimation of the degree of conversion value (α) of the polymeric material is based on the first measured value, the fixed value (QI), and the estimated slope; method.

3. 3. The method of claim 2, - Adjustment of the estimated slope based on the fixed value (QI) The method further includes the steps of: the estimation of the degree of conversion value of the polymeric material is based on the first measured value, the fixed value (QI), and the adjusted slope; method.

4. 4. The method according to claim 1, wherein the obtaining of the measured value from the polymeric material is performed for at least two values ​​of the degree of conversion.

5. 5. The method of claim 4, wherein the at least two measured values ​​include a minimum value and a maximum value for the particular degree of conversion of the polymeric material.

6. 5. The method of claim 4, wherein a third measured value is obtained from the polymeric material, the third measured value being related to the type of degree of conversion and for a further value of the degree of conversion, and the estimation of the degree of conversion value of the polymeric material is based on the third measured value and the fixed value (QI).

7. 7. The method of claim 6, wherein the obtaining of the third measured value from the polymeric material for the additional value of degree of conversion related to the type of degree of conversion is performed independently from the obtaining of the measured values ​​for the at least two values ​​of degree of conversion required to produce TKA.

8. 4. The method according to any one of claims 1 to 3, wherein said fixed value (QI) corresponds to a value based on a specific temperature range at some or any degree of conversion value.

9. 4. The method of claim 1, wherein the obtaining of one or more of the measured values ​​of at least one of the polymeric material and the TKA is performed under at least one of isothermal and non-isothermal conditions.

10. 4. The method of claim 1, wherein the obtaining of one or more of the measured values ​​of the polymeric material comprises measuring corresponding measured values ​​at specific positions of corresponding curves along at least one of time and temperature.

11. 11. The method of claim 10 when dependent on claim 2, wherein the TKA is based on one or more of the measured values ​​at particular peaks of a change in value along at least one of time and temperature (T).

12. 4. The method of claim 1, wherein the type of degree of conversion relates to degradation of a polymer of the polymeric material, and each TKA comprises a TGA analysis.

13. 4. The method of claim 1, wherein the type of degree of conversion is related to the viscosity of the polymer, and each TKA comprises a rheological measurement.

14. 4. The method of claim 1, wherein the type of degree of conversion relates to a change in cure rate, and each TKA comprises a DSC analysis.

15. 4. The method of claim 1, wherein the type of degree of conversion relates to a change in elastic modulus, and each TKA comprises a DMA measurement.

16. 4. The method of claim 1, wherein the type of degree of conversion is related to the uptake of one or more fluids, and each TKA includes a TMA / humidity chamber and a TGA analysis-measurement.

17. 4. The method of any one of claims 1 to 3, wherein the type of degree of conversion relates to a change in CTE / shrinkage, and each TKA comprises a TMA measurement.

18. Use of the estimated degree of conversion value (α) in all steps of the method according to any one of claims 1 to 3 for the simulation and / or production and / or application and / or use definition of the polymeric material.

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