Method for estimating degree of conversion value of degree of conversion of polymer material and use of degree of conversion value

Abstract

The invention relates to a method of estimating a degree of conversion value (alpha) of a polymeric material, wherein the method comprises the steps of: heating the polymeric material at a predetermined heating rate (beta); acquiring at least one first measurement of the polymer material at a current temperature (T), said first measurement relating to a specific type of degree of conversion; determining a fixed value (QI) associated with the reciprocal of temperature (1 / T) and the heating rate (beta), the fixed value (QI) being independent of the degree of conversion value (alpha) of the polymeric material; and estimating the degree of conversion value (alpha) 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 conversion value of a polymer material and a use of the conversion value. Background of the Invention

[0003] Typically, polymer materials may include one or more polymers, or a mixture of one or more polymers and one or more fillers. Polymer materials, such as prepregs, solder masks, glues, ABFs, etc., are important base materials for electronic devices and / or electronic device components (e.g., PCBs, ECPs, and / or substrates). In addition, polymer materials are widely used in coatings as paints, for cloth fabrics, and the like. In addition, polymer materials may also include one or more monomers and / or oligomers, wherein, for example, certain glues and / or paints may contain a high content of the structure. Understanding the behavior of these materials with respect to curing, aging, and / or decomposition can produce high-quality and / or low-priced electronic devices. Therefore, the curing kinetics of polymer materials are studied at the material identification stage, for example, in order to check whether the production process or the steps of the production process are suitable for processing the corresponding polymer materials. For example, it is possible to check in advance whether a given polymer material can be fully cured within a certain time and / or at a given temperature.

[0004] To study the curing kinetics of polymer materials, thermokinetic analysis (TKA) can be performed on polymer material probes, where kinetics involves the measurement and parameterization of process rates and where thermal analysis involves thermal stimulation of the process. TKA is widely used in all polymer-related industries for curing and decomposition processes of polymer materials.

[0005] In addition, model-free kinetics (MFK) is a well-known and widely used method to characterize various polymer materials (e.g., EMC (epoxy molding compound), prepreg, SM (solder mask)) because it can predict the thermal properties of the materials, such as crystallization, melting, cross-linking and decomposition properties, etc.

[0006] However, due to the limitations of the current MFK theory, the prediction accuracy and prediction range are greatly affected by experimental data. Summary of the invention

[0007] It is an object of the present invention to overcome at least some of the above problems.

[0008] 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.

[0009] One aspect of the present invention relates to a method for estimating a conversion degree value of a polymer material, the method comprising the following steps: heating the polymer material at a predetermined heating rate; obtaining at least one first measurement value of the polymer material at a given temperature, the first measurement value being related to a specific type of conversion degree; determining a fixed value associated with the inverse of the temperature and the heating rate, the fixed value being independent of the conversion degree value of the polymer material; and estimating the conversion degree value of the polymer material based on the first measurement value and the fixed value.

[0010] The polymer material may include one or more polymers, or a mixture of one or more polymers and one or more fillers. In addition, the polymer material may include one or more monomers and / or oligomers, wherein for example, some glues and / or paints may contain high levels of the structure. The first measured value may be a first degree of cure value at a given temperature. Wherein, the first measured value may be measured directly or determined based on measurement, for example, determined based on TKA or DSC analysis, as described below. Although the first degree of cure value may be determined by measurement at a specific temperature and with a specific heating rate, the conversion value to be estimated may indicate a temperature corresponding to a specific degree of cure value at a specific heating rate. The degree of cure value may be estimated without measuring again. A fixed value may be referred to as a Qi-point. As described below, the Qi-point may be predetermined.

[0011] The above-mentioned method using Qi-point can be called model-free dynamics using Qi-point (MFKq). MFKq provides guidance for better control and processing of polymer materials. In addition, MFKq improves the accuracy of the traditional MFK method and expands the prediction range, especially for non-isothermal predictions and isothermal predictions. At the same time, a method for measuring and judging data quality is also provided, especially before making any predictions, to ensure high-quality predictions. In addition, compared with traditional MFK, MFKq can achieve more applications due to the expanded prediction range. For example, MFKq can be used to predict the state of polymer materials that are not fully cured at a specific ambient temperature, for example, it can be used for shelf life prediction. The shelf life prediction can be used to guide the storage time and / or temperature of the polymer material in the corresponding warehouse.

[0012] Therefore, the advantage of the present invention is that the use of the Qi-point in the estimation of the degree of conversion can more accurately estimate the relevant value of the specific degree of conversion (e.g., degree of curing) at the corresponding temperature and heating rate. In other words, since the estimated value is adjusted by the participation of the Qi-point, the estimated value of the specific degree of conversion (e.g., degree of curing) of the polymer material obtained according to the specific temperature and the specific heating rate may be closer to the true degree of conversion, as described below (e.g., with reference to the preferred embodiments).

[0013] According to one embodiment, the method further comprises the following steps: performing a thermodynamic analysis (TKA) for the conversion degree value being estimated based on the first measurement value to estimate the slope of the Qi-curve, wherein the estimated conversion degree value (α) of the polymer material is based on the first measurement value, the fixed value, and the estimated slope. These values ​​can be converted to linearize the relationship between the heating rate and the temperature. This can facilitate a simple graphical analysis of the adjusted estimated conversion degree value. If the first measurement value (i.e., the first degree of cure value) and the fixed value (i.e., the Qi-point) are connected in the Qi-curve diagram, the slope of the resulting line corresponds to the above slope. The Qi-curve diagram shows one or more Qi-curves. Each Qi-curve shows the relationship between the natural logarithm of the heating rate and the inverse of the temperature, wherein there is one Qi-curve for each measured degree of cure value.

[0014] According to one embodiment, the method further comprises the step of: adjusting the estimated slope according to the fixed value; wherein the estimated degree of conversion of the polymer material is based on the measured value, the fixed value (QI-point) and the adjusted slope. This can help to easily and reliably estimate the degree of conversion.

[0015] According to one embodiment, measurements of the polymer material are obtained for at least two conversion degree values. In this way, a specific temperature / heating rate can be defined very accurately and the Qi-point determined, for example, by graphically intercepting the resulting estimated line for two specific estimated conversion degree values.

[0016] According to one embodiment, the at least two measured values ​​include a minimum and a maximum value of a specific degree of conversion of the polymer material. For example, in the case of a curing rate as the degree of conversion, the minimum value may relate to an uncured polymer material and the maximum value may relate to a fully cured polymer material. This may help to precisely define the resulting estimated trends of two specific estimated conversion degree values, and thus define the Qi-point.

[0017] According to one embodiment, a third measurement value is obtained from the polymer material, the third measurement value is related to the type of conversion degree and is used for another value of the conversion degree, and the conversion degree value of the polymer material is estimated based on the third measurement value and the fixed value. This can help to estimate the conversion degree value very accurately and conveniently, for example, by using Qi-points to perform a graphical interception of another conversion degree.

[0018] According to one embodiment, the third measurement value for obtaining a further value of the degree of conversion related to the type of degree of conversion from the polymer material is performed separately from the measurements for obtaining at least two values ​​of the degree of conversion required for creating a TKA. This facilitates very simple estimation of the value of the degree of conversion.

[0019] According to one embodiment, the fixed value (QI) corresponds to a value based on a specific temperature range at some or any conversion degree value. In particular, depending on the magnitude of the temperature value range considered when calculating the fixed value, the fixed value (QI) estimate will result in different accuracy. In other words, the larger the magnitude of the temperature range considered when calculating, the more accurate the determined fixed value (QI) (and therefore the more accurate the conversion degree estimate provided).

[0020] According to a preferred embodiment, a limited range of temperatures at certain conversion degree values ​​is used for determination of the fixed value (QI), resulting in a specific value. In this case, the range of temperature values ​​is selected according to the desired level of accuracy of the conversion degree estimation.

[0021] According to another preferred embodiment, the entire possible temperature range at any value of the degree of conversion is used for the determination of the fixed value (QI), resulting in infinity. In this case, the result of the degree of conversion estimation has the highest possible accuracy.

[0022] According to one embodiment, obtaining one or more measurements of the polymer material and / or TKA is performed under isothermal and / or non-isothermal conditions. This may help to accurately derive the existing MFKq theory.

[0023] According to one embodiment, obtaining one or more measurements of the polymer material includes measuring corresponding measurements at a specific location as a function of time and / or temperature. The specific location may be a peak, e.g., a maximum. The movement of the peak (e.g., maximum) may be related to corresponding thermodynamic theory. This may help to obtain one or more measurements of the polymer material very accurately.

[0024] According to one embodiment, TKA is based on one or more measurements along time and / or temperature at a specific peak in the change in value. This can help to achieve a very accurate TKA.

[0025] According to one embodiment, the type of conversion degree is related to polymer degradation of the polymer material and the corresponding TKA comprises TGA (thermogravimetric analysis). TGA can help to achieve a very accurate TKA.

[0026] According to one embodiment, the type of conversion degree is related to polymer viscosity (change) and the corresponding TKA includes rheological measurements. Rheological measurements can help to achieve a very accurate TKA. Rheological measurements can be performed with the aid of a rheometer.

[0027] According to one embodiment, the conversion rate profile is related to the curing rate change, and the corresponding TKA includes DSC analysis. Alternatively, the corresponding TKA may include DTA (differential thermal analysis). DSC analysis or DTA may help to achieve a very accurate TKA.

[0028] According to one embodiment, the type of transformation degree is related to modulus change and the corresponding TKA includes rheological measurements, such as DMA measurements.

[0029] According to one embodiment, the conversion degree type is related to the absorption of one or more fluids, and the corresponding TKA includes TMA (thermomechanical analysis) / humidity chamber and TGA analysis measurement. The fluid can be a liquid (e.g., water), or a gas (e.g., water vapor, ammonia and / or CO2).

[0030] According to one embodiment, the conversion type is related to CTE / contraction changes and the corresponding TKA includes TMA measurements.

[0031] One aspect of the present invention relates to the use of the conversion degree value estimated according to the above method for the simulation and / or production and / or application and / or use definition of the polymer material.

[0032] These and other aspects of the invention will be apparent from and elucidated with reference to the embodiments described hereinafter. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The embodiments of the present invention are further described in detail below with reference to the accompanying drawings.

[0034] Figure 1 A flow chart showing an exemplary embodiment of a method for estimating the QI-point of a given polymer material;

[0035] Figure 2 shows examples of DSC thermograms of polymer materials at different heating rates;

[0036] Figure 3 An example of a graph showing the degree of cure of a polymer material as a function of temperature at different heating rates under non-isothermal conditions is shown;

[0037] Figure 4 An example of an Ozawa-Flynn-Wall plot is shown;

[0038] Figure 5 An example of the distribution of several intersections is shown;

[0039] Figure 6 Shown according to Figure 5 A detailed view of the intersection between 10% and 90%;

[0040] Figure 7 An example of a Qi curve in a Qi curve diagram is shown;

[0041] Figure 8 Shown according to Figure 7 Detailed view of the QI curve;

[0042] Fig. 9 A flow chart illustrating an exemplary embodiment of a method of determining a graph of degree of conversion values ​​for estimating the degree of conversion of a polymer material under isothermal conditions;

[0043] Fig.10 shows a graph including an exemplary graph of degree of conversion versus time under isothermal conditions;

[0044] Fig.11 A flow chart illustrating an exemplary embodiment of a method of determining a graph of degree of conversion values ​​for estimating the degree of conversion of a polymer material under non-isothermal conditions;

[0045] Fig.12 shows a graph including an exemplary plot of degree of conversion values ​​as a function of temperature under non-isothermal conditions;

[0046] Fig.13 A flow chart illustrating an exemplary embodiment of a method of determining a graph of degree of conversion values ​​for estimating the degree of conversion of a polymer material under isothermal or non-isothermal conditions;

[0047] Fig.14 A further example of a Qi curve is shown in the Qi curve diagram.

[0048] The reference symbols used in the drawings and their meanings are listed in summary form in the reference symbol list. In principle, identical components in the figures are provided with the same reference symbols. DETAILED DESCRIPTION

[0049] Figure 1 The estimated Qi-point QI for a given polymer material is shown in Figure 7 ) is a flowchart of an exemplary embodiment of a method.

[0050] In step S2, at n different heating rates β n =[β0,β1,…,β n-1 ] Perform differential scanning calorimetry (DSC) measurement on the probe of the polymer material under , wherein n is a natural number. For example, n can be 1 to 20, such as 1 to 10, such as 3 to 6.

[0051] Figure 2 An example of a DSC thermogram 20 of a polymer material determined by a DSC measurement is shown. The DSC thermogram 20 contains one plot for each heating rate β, where the heating rate β n The unit is K / min. Alternatively, the heating rate β can be given in any other possible temperature-time relationship, such as °C / s or °F / h.

[0052] The degree of cure value α of the degree of cure can be determined based on the DSC thermogram 20, wherein the degree of cure value α can be determined by the following formula:

[0053]

[0054] Among them, H Total is the energy absorbed by the polymer material until the solidification of the polymer material is completed, H Total Corresponds to Figure 2 The area below the corresponding figure in H T is the energy absorbed by the polymer material until it reaches temperature T, H T Corresponds to Figure 2 The area from the leftmost side to temperature T below the corresponding graph.

[0055] In step S4, for each heating rate β i Determine the curing degree 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 ], where i=0, 1,…, m-1 are natural numbers.

[0056] Figure 3 An example of a graph is shown, which may be referred to hereinafter as a first graph 22. The first graph 22 shows the heating rate β under non-isothermal conditions. n , according to the temperature T i Determine the value of the degree of solidification of the polymer material α. Figure 3 It can be seen that the degree of curing is a function of the heating rate β and the temperature T.

[0057] ∝=∝(β,T).

[0058] For example, the dashed horizontal line in the first graph 22 may correspond to a curing degree value α of 50%, ie α=50%, wherein the intersection of the graph of the curing degree α and the dashed horizontal line represents the temperature T at which the curing degree value is 50% at the corresponding heating rate β.

[0059] Figure 4 An example of an Ozawa-Flynn-Wall graph is shown, which may be referred to as a second graph 24. The second graph 24 may be implemented by Ozawa-Flynn-Wall analysis known in the art. Figure 4 The Ozawa-Flynn-Wall diagram can be obtained from Figure 3 The heating rate β is extracted from the diagram by the corresponding horizontal line n and temperature T are constructed for a degree of curing α=50%.

[0060] The Ozawa-Flynn-Wall diagram may also include correspondingly constructed diagrams for other degrees of cure α = [0, 0.01, ..., 100]. However, the corresponding diagrams constructed according to the traditional Ozawa-Flynn-Wall analysis may intersect each other in a certain area of ​​the Ozawa-Flynn-Wall diagram (not shown in the figure), which is meaningless from a physical point of view, indicating the defects of the traditional Ozawa-Flynn-Wall analysis. Therefore, instead of using the traditional Ozawa-Flynn-Wall analysis, the inventors have found a more accurate method for constructing a diagram for predicting the degree of cure α of a given polymer material, as described below.

[0061] In step S6, according to all the above temperatures T i , heating rate β n and curing degree α = [0,0.01,…,100] to draw the graph in the Ozawa-Flynn-Wall diagram

[0062]

[0063] For example, j = 0, 1, ..., 10000. Therefore, the corresponding graph (which may be called Qi curve graph) may contain 10001 graphs, for example.

[0064] In step S8, a linear fit can be performed on the graph of the Qi curve, and the slope and intercept of the corresponding fitted graph (i.e., the Qi curve) relative to the y-axis can be extracted to obtain a slope K=[k0, k1, ..., k 10000 ] and the intercept B = [b0, b1, ..., b 10000 ].

[0065] In step S10, the intersection point of the fitted graph with a curing degree value α between 1% and 30% (e.g., between 5% and 15%, e.g., α=10%) and all other fitted graphs can be determined, for example, by the following formula:

[0066]

[0067] In step S12, the intersection of the fitting graph with a curing degree value α between 30% and 60% (e.g., between 40% and 55%, e.g., α=50%) and all other fitting graphs can be determined, for example, by the following formula:

[0068]

[0069] In step S14, the intersection of the fitting graph with a curing degree value α between 70% and 99% (e.g., between 85% and 95%, e.g., α=90%) and all other fitting graphs can be determined, for example, by the following formula:

[0070]

[0071] In step S16, the intersection points determined in steps S10 to S14 may be plotted in a third diagram 26, for example as shown in FIG. Figure 5 shown.

[0072] Figure 5 The distribution of the above-mentioned intersections is shown in the third diagram 26. Figure 5 It can be seen that 80% of the crossover points are located near the temperature inverse 0, where the temperature inverse 0 can only be achieved when the temperature T tends to infinity.

[0073] Figure 6 A detailed view of the intersection point between 10% and 90% is shown in a fourth diagram 36 .

[0074] In step S18, the intersection point of the fitting graph at 1 / T=0 may be determined as the Qi point QI, where QI=(0, lnβ).

[0075] Figure 7 An example of Qi curves is shown in the fifth graph 38, all of which include a Qi point QI. Except for the Qi point QI, the Qi curves do not intersect each other, which is completely reasonable from a physical point of view.

[0076] Figure 8 Shown according to Figure 7 Detailed view of the QI curve of FIG. 38 , in particular a view of the lower region 28 of the fifth graph 38 .

[0077] Figure 7 and Figure 8 The Qi-curve can be determined through steps S20 and S22.

[0078] In step S20, the Qi point QI is used and according to the Ozawa-Flynn-Wall equation

[0079]

[0080] Draw the graph again (i.e., the Qi curve), where the term (-E α / R) defines the slope, R is the ideal gas constant, and the term The intercept of the corresponding curve is defined, and A is the pre-index factor with the unit of [1 / s].

[0081]

[0082] For example, j=0,1,...,10000.

[0083] In step S22, a linear fit can be performed again on the Qi graph to obtain a Qi curve corresponding to the Ozawa-Flynn-Wall curve including the Qi point QI, and the corresponding adjusted slope K'=[k'0, k'1, ..., k' 10000 ] and the intercept B' = [b'0, b'1, ..., b' 10000 ].

[0084] Fig. 9 A flow chart of an exemplary embodiment of a method for determining a graph of a degree of conversion value α for estimating the degree of conversion of a polymer material under isothermal conditions is shown. The degree of conversion can be a degree of cure. Alternatively, the degree of conversion is different from the degree of cure. In general, the degree of conversion can describe the portion of the reactant that has reacted. The degree of conversion type can depend on the corresponding reaction type. For example, if the reaction is a polymerization process, the degree of conversion can be a degree of cure. If the reaction is a decomposition process, the degree of conversion can be a degree of decomposition. In addition, the degree of conversion can also be a polymer degradation degree, a polymer viscosity, a cure rate, a modulus change, an absorption of one or more fluids, and / or a CET / shrinkage rate.

[0085] The method can use the above-mentioned predetermined curing degree value α i , heating rate β and the determined Qi-point QI, and it can be determined that the predetermined curing degree value α is reached i The corresponding time t of the temperature T is estimated in the form of a mathematical function based on time and / or a corresponding diagram. iso The continuous progression and / or progression of the degree of hardening values ​​α makes it possible to subsequently extract one or more desired and / or arbitrary degree of hardening values ​​α by means of mathematical functions and / or from corresponding diagrams.

[0086] In step S30, the temperature T is received. iso , for temperature T iso , a graph showing the degree of curing of the polymer material as a function of time t should be estimated. The temperature T iso is input into a device for determining a map of estimated curing degree values ​​α, and the device can receive a temperature T iso The device may be a processor of a general purpose computer. Temperature T iso It may be received from an external device or from the memory of a general purpose computer.

[0087] In step S32, the index i and the curing degree value α are i and time t i are set to 0 respectively, the device receives the above curing degree value α i = [0, 0.01, ..., 100] and the above Qi-point QI = (0, lnβ). In addition, the slope of the graph can be given as a function of the degree of cure α, for example by the following formula

[0088]

[0089] where c3 and c4 can be determined by fitting the graph with an sigmoid curve, and where the value of α is between predefined values ​​different from α min =0 and α max = the minimum value of 100 (α min ) and the maximum value (α max ) (for example, α min =2.5 and α max =97.5).

[0090] In step S34, the index i is increased by 1, that is, i=i+1, and the next conversion degree value α is selected. i , for example, by α i =α i-1 +δα to select.

[0091] In step S36, check the current conversion degree value α i Is it greater than 100. If the condition of step S36 is not met, the method can proceed to step S38. If the condition of step S36 is met, the method can proceed to step S44.

[0092] In step S38, ΔT can be determined by the following formula:

[0093]

[0094] In step S40, Δt may be determined by the following formula:

[0095]

[0096] In step S42, t i =t i-1 +Δt to determine t i .

[0097] Then, the method proceeds to step S34.

[0098] In step S44, a graph showing the change of the curing degree α with time t may be drawn, for example, Fig.10 As shown, and / or the method for determining a graph of conversion value α for estimating the conversion degree of the polymer material under isothermal conditions can be terminated. The advantage of doing so is that the curing time of the polymer material can be predicted more accurately.

[0099] The above method for determining a graph of conversion degree values ​​α for estimating the conversion degree of a polymer material under isothermal conditions can be used as a subroutine of a method for estimating conversion degree values ​​α for the conversion degree of a polymer material under isothermal conditions. The latter method can estimate one or more conversion degree values ​​α at a desired time t by extracting the corresponding conversion degree values ​​α from the determined graph.

[0100] Fig.10 A graph including an exemplary graph of the degree of conversion α changing with time t under isothermal conditions is shown. This graph may be referred to as a sixth graph 40. The sixth graph 40 may be determined by the above-described method for determining a graph of a degree of conversion value α for estimating the degree of conversion of a polymer material under isothermal conditions. The method for estimating a degree of conversion value α for the degree of conversion of a polymer material under isothermal conditions may use this graph.

[0101] Fig.11 A flow chart showing an exemplary embodiment of a method for determining a graph of a degree of conversion value for estimating the degree of conversion of a polymer material under non-isothermal conditions. The degree of conversion may be a degree of curing. The method may use the predetermined degree of curing value α i , heating rate β and the determined Qi point QI, and it can be determined to reach the predetermined curing degree value α i The corresponding temperature T of the solidification degree is estimated in the form of a mathematical function based on the temperature T and / or a corresponding diagram. i The continuous progression and / or trend of one or more degree of solidification values ​​α at one or more desired and / or arbitrary temperatures T can then be extracted by means of mathematical functions and / or from corresponding diagrams.

[0102] In step S50, a given heating rate β is received for which a graph of curing degree values ​​α representing the curing degree of the polymer material versus temperature T is estimated. The heating rate β may be input into a device for determining a graph estimating the curing degree values ​​α, which may receive the heating rate β.

[0103] In step S52, the index i and the curing degree value α are i are set to 0 respectively, the device receives the above-mentioned curing degree value α i = [0, 0.01, ..., 100] and the above Qi point QI = (0, lnβ). In addition, the slope of the graph can be given as the above function f(α).

[0104] In step S54, T i It can be determined by the following formula

[0105]

[0106] In step S56, the index i is increased by 1, that is, i=i+1, and the next conversion degree value α is selected. i , for example, by αi =α i-1 +δα is selected, where δα can be 1, for example.

[0107] In step S58, check the current conversion degree value α i Is it 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.

[0108] In step S60, a graph showing the change of the curing degree α with the temperature T may be drawn, for example, Fig.12 As shown, and / or the method for determining a graph of a degree of conversion value α for estimating a degree of conversion of a polymer material under non-isothermal conditions may be terminated.

[0109] The above method for determining a graph for estimating a conversion value α for a polymer material under non-isothermal conditions can be used as a subroutine of a method for estimating a conversion value α for a polymer material under non-isothermal conditions. The latter method can estimate one or more conversion value α at the corresponding one or more desired temperatures T by extracting the corresponding conversion value α from the determined graph.

[0110] Fig.12 A graph including an exemplary graph of degree of conversion values ​​α varying with temperature T under non-isothermal conditions, in particular for different given heating rates β, is shown. The graph may be referred to as the seventh graph 42. The seventh graph 42 may be determined by the above-described method for determining a graph of degree of conversion values ​​α for estimating the degree of conversion of a polymer material under non-isothermal conditions. The method for estimating degree of conversion values ​​α for estimating the degree of conversion of a polymer material under non-isothermal conditions may use the graph.

[0111] Fig.13 A flow chart showing an exemplary embodiment of a method for determining a graph of a degree of conversion value for estimating the degree of conversion of a polymer material under isothermal or non-isothermal conditions. The degree of conversion may be a degree of curing. The method may use the predetermined degree of curing value α i , heating rate β and the determined Qi-point QI, and it can be determined that the predetermined curing degree value α is reached i corresponding time t and / or temperature T, so as to estimate the continuous progress and / or trend of the degree of cure value α at a given time t and / or temperature T in the form of a mathematical function and / or a corresponding graph based on the time t and / or temperature T, so that one or more degree of cure values ​​α at one or more desired and / or arbitrary time t and / or temperature T can then be extracted by a mathematical function and / or from the corresponding graph.

[0112] In step S70, the device executing the method may receive a predetermined temperature T i =[T0, T1, ..., T n ] and time ti =[t0, T1, ..., T n ]. In addition, the curing degree value α is set to 0, δT is set to 0.1, and δα is set to 0.001, wherein the index i=0, 1, ..., m-1 is a natural number.

[0113] In step S72, the index i is set to 1, and the device receives the above-mentioned Qi-point QI and slope f(α).

[0114] In step S74, the curing degree value α is set to α=α i-1 .

[0115] In step S76, check the current conversion degree value α i Is it 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.

[0116] In step S78, for example, by T s =T i-1 Set the temperature T s Set to T i-1 , where s is a natural number.

[0117] In step S80 , Δt1 is set to zero.

[0118] In step S82, check whether there is |T i -T e |<δT.

[0119] If the condition of step S82 is met, the method may proceed to step S84. If the condition of step S82 is not met, the method may proceed to step S86.

[0120] In step S84, T e Set to T i .

[0121] In step S86, T is set according to the following formula e

[0122] T e =T s +sign(T i -T i-1 )δT

[0123] The sign() function can be used to select the sign of the real number in the brackets. This makes it possible to handle not only heating applications but also cooling applications.

[0124] In step S88, Δt is set according to the following formula:

[0125]

[0126] In step S90, T is set according to the following formula iso

[0127]

[0128] In step S92, ΔT is set according to the following formula:

[0129]

[0130] In step S94, Δt0 is set according to the following formula:

[0131]

[0132] In step S96, Δt1 is set according to the following formula:

[0133] Δt1=Δt1+Δt0.

[0134] In step S98, it is checked whether Δt1 ≥ Δt.

[0135] If the condition of step S98 is met, the method may proceed to step S100. If the condition of step S98 is not met, the method may proceed to step S102.

[0136] In step S100, the curing degree value α is set according to the following formula:

[0137]

[0138] In step S102, the curing degree value α is set according to the following formula:

[0139] ∝=∝+δα.

[0140] In step S104, check whether there is T e =T i .

[0141] If the condition of step S104 is met, the method may proceed to step S108. If the condition of step S104 is not met, the method may proceed to step S106.

[0142] In step S106, the temperature T s Set to T e .

[0143] In step S108, the curing degree value α i Set to α.

[0144] In step S110, check whether there is ∝ i >100.

[0145] If the condition of step S110 is met, the method may proceed to step S112. If the condition of step S110 is not met, the method may proceed to step S114.

[0146] In step S112, the curing degree value α i Set to 100.

[0147] In step S114, the function α.append(α i ) can be used for the corresponding program code, where α can be an array and can start with one element, that is, α=[0]. When the corresponding loop starts, α is from 0 to 100, which means that the array needs to be appended with α one by one i .

[0148] In step S116, the index i is incremented by 1.

[0149] The above method enables plotting of the degree of cure values ​​under isothermal and non-isothermal conditions. In particular, the MFKq theory proposed in the present application enables finding the correct degree of cure value α at a given time t and temperature T. If the input of time t and temperature T is for a non-isothermal situation, the output of the degree of cure value α is for a non-isothermal situation. If the input of time t and temperature T is for an isothermal relationship, the output of the degree of cure α can represent isothermal curing conditions.

[0150] Fig.14 Another method of estimating the degree of conversion is shown by the relationship between temperature (1 / T) and heating rate (lnβ) over the full temperature range for any given degree of conversion α.

[0151] According to this alternative embodiment, the curve, in particular the curve from lower temperature to higher temperature, eventually converges to an infinite point on the y-axis representing the Qi point QI. According to the illustrated embodiment, each segment of the curve can be a straight line. Its boundaries on the x-axis are predefined according to the application, preferably consisting of two steps:

[0152] a. Predefine the split points of x in the temperature integral p(x) according to the application: [x0, x1, …, x n ],

[0153] b. Define the split point on the x-axis according to 1 / T = xR / Eα: [1 / T 0,α ,1 / T 1,α ,…,1 / T n,α ].

[0154] The slope k of each straight line i,α The preferred value is based on its corresponding slope d in the plot of lnp(x) versus x. i To calculate, it includes the following two steps:

[0155] a. Calculate d i =ln[p(x i ) / p(x i+1 )] / (x i -x i+1 ):[d0,d1,…,d n ],

[0156] b. Calculate k i,α =d i Eα / R:[k 0,α ,k 1,α ,…,k n-1,α ].

[0157] The intercept b of each line i,α Preferably, the solution is obtained recursively, where the first b m,α It is calculated based on experimental data.

[0158] Preferably, there are three steps for obtaining the first intercept b m,α :

[0159] 1. Based on the experimental input, calculate the average logarithmic heating rate lnβ at α avg and the inverse of the average temperature 1 / T avg,α .

[0160] 2. In [1 / T 0,α ,1 / T 1,α ,…,1 / T n,α ] to find the index m of the reciprocal of the average temperature so that 1 / T m,α ≤1 / T avg,α ≤1 / T m+1,α .

[0161] 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 .

[0162] The remaining intercepts can be solved according to the following equations:

[0163] ib i-1,α =b i,α +(k i,α -k i-1,α ) / T i,α ,i∈[1,m],

[0164] ii.b i+1,α =b i,α +(k i,α -k i+1,α ) / T i+1,α,i∈[m,n-2].

[0165] Although the present invention has been elaborated and described in detail in the drawings and the above description, these illustrations and descriptions should be regarded as illustrative or exemplary rather than restrictive; the present invention is not limited to the disclosed embodiments. Other variations of the disclosed embodiments can be understood and implemented by those skilled in the art and those practicing the claimed invention by studying the drawings, the disclosure and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" / "an" does not exclude a plurality. A single processor or controller or other unit may perform the functions of several items described in the claims. The fact that certain measures are cited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference symbols in the claims should not be interpreted as limiting the scope.

[0166] Reference Symbols List

[0167] 20 DSC thermogram

[0168] 22 First Chart

[0169] 24 Second Chart

[0170] 26 Third Chart

[0171] 28 Lower area

[0172] 30 Isotherms

[0173] 32 Non-isothermal

[0174] 36 Fourth Chart

[0175] 38 Fifth Chart

[0176] 40 Sixth Chart

[0177] 42 Seventh Chart

[0178] QI Qi point

[0179] S2-S86 Step 2 to step 86.

Claims

1. A method for estimating a conversion value (α) of a polymer material, the method comprising the following steps: - heating the polymer material at a predetermined heating rate (β); - obtaining at least one first measurement of said polymeric material at a given temperature (T), said first measurement being related to a specific type of degree of conversion; - determining a fixed value (QI) associated with the inverse temperature (1 / T) and said heating rate (β), said fixed value (QI) being independent of said conversion degree value (α) of said polymer material; as well as - estimating the conversion degree value (a) of the polymer material based on the first measured value and the fixed value (QI).

2. The method according to claim 1, further comprising the steps of: performing a thermodynamic analysis TKA for the conversion degree value (α) being estimated, based on the first measured value, to estimate the slope of the Qi-curve, The estimated conversion degree value (α) of the polymer material is based on the first measured value, the fixed value (QI) and the estimated slope.

3. The method according to claim 2, further comprising the steps of: - adjusting the estimated slope according to said fixed value (QI); The estimated conversion degree value of the polymer material is based on the first measured value, the fixed value (QI) and the adjusted slope.

4. A method according to any one of the preceding claims, wherein: Measurements of the polymeric material are obtained for at least two degrees of conversion values.

5. The method according to claim 4, wherein: The at least two measurements include a minimum value and a maximum value for a particular degree of conversion of the polymeric material.

6. The method according to claim 4 or 5, wherein: A third measurement value is obtained from the polymer material, the third measurement value being associated with a type of degree of conversion and being used for another value of the degree of conversion, and estimating the value of the degree of conversion of the polymer material is based on the third measurement value and the fixed value (QI).

7. The method of claim 6, wherein the third measurement value for obtaining a type of degree of conversion and another value of the degree of conversion from the polymer material is performed separately from the measurements for obtaining at least two values ​​of the degree of conversion required to create a TKA.

8. A method according to any one of the preceding claims, wherein: The fixed value (QI) corresponds to a value based on a specific temperature range at some or any conversion degree value.

9. A method according to any one of the preceding claims, wherein: Obtaining one or more measurements of the polymer material and / or TKA is performed under isothermal and / or non-isothermal conditions.

10. A method according to any one of the preceding claims, wherein: Obtaining one or more measurements of the polymer material includes measuring corresponding measurements along time and / or temperature (T) at specific locations on corresponding curves.

11. The method according to claim 10 as dependent on claim 2, wherein: TKA is based on one or more measurements along time and / or temperature (T) at a specific peak in the change in value.

12. The method according to any one of claims 1 to 11, wherein: The conversion degree type is related to polymer degradation of the polymer material, and the corresponding TKA includes TGA analysis.

13. The method according to any one of claims 1 to 11, wherein: The type of conversion degree is related to polymer viscosity and the corresponding TKA includes rheological measurements.

14. The method according to any one of claims 1 to 11, wherein: The type of conversion degree is related to the change in cure rate and the corresponding TKA includes DSC analysis.

15. The method according to any one of claims 1 to 11, wherein: The type of transformation degree is related to modulus change and the corresponding TKA includes DMA measurement.

16. The method according to any one of claims 1 to 11, wherein: The conversion type is related to the absorption of one or more fluids and the corresponding TKA includes TMA / humidity chamber and TGA analysis measurements.

17. The method according to any one of claims 1 to 11, wherein: The degree of conversion type is related to CTE / contraction changes and the corresponding TKA includes TMA measurements.

18. Use of the conversion degree value (a) estimated according to the method of any one of claims 1 to 17 for simulation and / or production and / or application and / or use definition of the polymer material.

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