A method and system for rapid determination of rubber crosslinking density and chain segment molecular weight based on dynamic mechanical analysis

Abstract

This invention relates to the field of rubber performance testing technology, and particularly to a method and system for rapid determination of rubber crosslinking density and segment molecular weight based on dynamic mechanical analysis. The procedure is as follows: sample drying and cutting; determining the linear viscoelastic region at 1 Hz; heating at 3 ℃ / min, isolating at a high-elasticity plateau of 90±2 ℃ and recording E′ using steady-state criteria; performing a single 5–10% large strain pretreatment or Kraus correction to subtract filler stiffness for the filled system; calculating and outputting quality control conclusions based on G′=E′ / 3, Ve=G′ / (RT), and Me=ρ / Ve. This method can be completed within 30 minutes, requires no organic solvents, and is applicable to NR, SBR, BR, EPDM and their blends. It shows good consistency with the swelling method and is suitable for rapid laboratory screening and near-line quality control in production.

Description

Technical Field

[0001] This invention relates to the field of rubber performance testing technology, and in particular to a method and system for rapid determination of rubber crosslinking density and segment molecular weight based on dynamic mechanical analysis. Background Technology

[0002] The three-dimensional network structure formed during the vulcanization process of rubber products (especially tires) determines key properties such as hardness, elasticity, compression set, abrasion resistance, and heat generation. Among these, "crosslinking density (or equivalent number of network segments)" and "average molecular weight of segments between two crosslinking points" are the most critical structural characterization parameters. Therefore, the ability to quickly and reproducibly obtain crosslinking density / segment molecular weight in the R&D and production stages is fundamental for formulation screening, vulcanization process window setting, and quality control. Currently, the most commonly used industrial method is the equilibrium swelling-Flory-Rehner approach: the vulcanized rubber is swollen in a good solvent for a long time, the equilibrium volume fraction is measured, and then the crosslinking density is calculated by substituting it into the equation. To adapt to foamed rubber or special systems, some schemes empirically modify the swelling mass term or volume fraction, but overall, it is still an offline method with "long cycle and high solvent consumption". Taking Chinese patents CN105388081A and CN105547896A as examples, the calculation accuracy of the crosslinking density of foamed materials is improved by modifying the mass parameters in the Flory-Rehner formula. However, their testing process still requires several hours to tens of hours of swelling and equilibrium determination, which is difficult to meet the needs of rapid quality control and online processing.

[0003] In addition to the swelling method, some patents also use scattering methods (SAXS / SANS) to estimate the crosslinking concentration. For example, CN106198585B uses small-angle X-ray or neutron scattering to fit samples with different swelling degrees to evaluate the crosslinking concentration. Such methods require expensive equipment and complex sample pretreatment, and are more used in research scenarios rather than in rapid workshop-level detection.

[0004] Dynamic mechanical analysis (DMA) can provide viscoelastic spectra such as storage modulus E′, loss modulus E″, and loss factor tanδ in the temperature / frequency dimension. Several Chinese patents mention in material performance evaluations that in the "high-elasticity plateau" region above the glass transition temperature (Tg) and below the material's melting point, the modulus of a compound is proportional to its crosslinking density, and the plateau modulus can be used to characterize the degree of curing or relative crosslinking level. For example, CN111526750A and CN111491788A state that "DMA can be used to determine the modulus plateau, and the crosslinking density within the plateau region is proportional to the modulus," for determining the curing / partial curing of shoe outsole elastomers; CN102838701A, in discussing ethylene propylene rubber systems, also gives the correlation that "the rubber plateau storage modulus increases with increasing crosslinking degree." These disclosures indicate that, from both theoretical and practical perspectives, there is a usable correspondence between DMA plateau modulus and network structure.

[0005] However, there are still several key challenges in truly applying "DMA platform modulus and crosslinking density / segment molecular weight" to reproducible quantitative determination in industry. This has resulted in existing publications mostly remaining at the level of "relative judgment or performance correlation," lacking directly applicable conversion processes and standardized conditions:

[0006] 1) Selection of platform temperature and steady-state determination. If the value is too close to Tg, the glass transition relaxation effect is significant; if the temperature is too high, it may introduce secondary crosslinking or thermo-oxidative reactions, causing E′ drift. Existing publications usually generalize the description to "perform DMA testing over a wide temperature range", which is difficult to support consistent conversion across laboratories.

[0007] 2) Unification of Linear Viscoelastic Region (LVR) and Strain Amplitude. Filled rubber exhibits small strain nonlinearity (Payne effect), and improper selection of strain amplitude can introduce E′ bias caused by the construction / destruction of the filler network. Although some existing technologies define the Payne index ΔG′ (e.g., the 0.1%–25% strain range) and its physical meaning in the material characterization section, they do not provide a standardized procedure for "LVR dual threshold / steady-state criterion for crosslinking density conversion".

[0008] 3) Separation of filler stiffening and polymer network contribution. The stiffening effect of fillers such as silica and carbon black can increase the plateau modulus. If the data is not corrected, directly applying it to rubber elasticity theory will systematically overestimate the network chain density. Although literature and patents generally discuss formulation strategies to "reduce the Payne effect / improve dispersion", there is still a lack of unified and operable regulations in existing Chinese patent texts for filler correction models (such as corrections based on filler volume fraction) for "quantitative conversion of crosslinking density".

[0009] 4) Parameter matching and result output. The conversion of DMA to Ve / Me requires the use of parameters such as real-time temperature, density, and Poisson's ratio and they need to be consistent. However, most of the existing public reports only "report DMA indicators for performance comparison" and rarely provide complete processes for factory quality control, such as density measurement temperature matching, plateau steady-state determination, error control and result classification (under-sulfur / appropriate sulfur / over-sulfur).

[0010] In summary, existing technologies have fully demonstrated that while the equilibrium swelling method can theoretically calculate crosslinking density, it suffers from common problems such as long testing cycles, high solvent consumption, and the need for specific corrections for foaming / filling systems. Although the scattering method can characterize network structures, it is difficult to use as a routine QC tool. Meanwhile, the qualitative or semi-quantitative correlation between DMA (Digital Crosslinking Modulus) and the degree of crosslinking has been used in multiple patents for material performance evaluation. The industry still urgently needs a standardized and rapid determination method to achieve green, rapid, reproducible, and comparable quantitative output of crosslinking density and segment molecular weight, serving rubber formulation optimization and production process control. Summary of the Invention

[0011] This invention aims to address the problems of existing methods for determining rubber crosslinking density, such as long processing time, cumbersome operation, high solvent consumption, and inapplicability to filled systems. It provides a rapid method for determining rubber crosslinking density and segment molecular weight based on dynamic mechanical analysis (DMA). This method measures the storage modulus E' in the rubber's high-elasticity plateau region and calculates the crosslinking density Ve and segment molecular weight Me using rubber elasticity theory formulas. This method can shorten the traditional three-day swelling test to less than 30 minutes, eliminates the need for organic solvents, and is suitable for rapid laboratory preparation and online monitoring of production processes.

[0012] To achieve the above objectives, the present invention adopts the following technical solution:

[0013] A rapid method for determining the crosslinking density and segment molecular weight of rubber based on dynamic mechanical analysis, comprising the following steps:

[0014] S1) Sample preparation: Cut samples according to standard, with a thickness of 1.5–3.0 mm, and vacuum dry at 60–80℃ for 2–4 h;

[0015] S2) Linear viscoelastic region (LVR) determination: Strain scan is performed at 1 Hz, and the strain amplitude is selected as 0.10–0.20% based on the slope threshold of the E′–ε curve and the tanδ change threshold.

[0016] S3) Temperature program: Increase the temperature at 3℃ / min from Tg+30℃ to 120℃;

[0017] S4) Steady-state value of the high-elasticity platform: When the temperature reaches 90±2℃, hold the temperature for 2–3 min, and determine the steady state by the combination of the absolute value of dE′ / dt ≤ preset threshold and tanδ ≤ preset threshold, and record the steady state E′.

[0018] S5) Filler system calibration: For samples containing high levels of filler, choose one of the following to perform:

[0019] S5-1) First, perform a single cycle with a large strain of 5–10% to destroy the weak packing network, and then take the values ​​according to S2–S4.

[0020] or,

[0021] S5-2) Apply the Kraus-type modified model to deduct the stiffening contribution of the filler based on the filler volume fraction;

[0022] S6) Parameter Conversion and Output: According to... Given the shear storage modulus, and taking R as the gas constant and T as the Kelvin temperature, calculate the crosslinking density. And according to Me=ρ / Ve, the average molecular weight of the chain segment between the two crosslinking points is obtained, where ρ is the density of the vulcanized rubber;

[0023] S7) Quality control judgment: Compare {Ve,Me} with the target range or historical database. When Ve deviates from the target upper limit by more than 10% and Me is lower than the target lower limit by more than 10%, output "over-sulfur" prompt; when Ve is lower than the target lower limit by more than 10% and tanδ@90℃>0.12, output "under-sulfur" prompt.

[0024] Preferably, the steady-state discrimination uses a joint threshold: And tanδ≤0.10, both of which must be satisfied to determine the recording platform E′.

[0025] Preferably, the dual thresholds selected by the LVR include: The curve has a relative slope change of <2% and the increment of tanδ with increasing strain is <0.01. It is preferred to test at 0.15% strain and 1Hz.

[0026] Preferably, the Kraus-type correction uses a filler volume fraction. Subtracting the relationship with the unfilled reference sample E′0, we obtain the contribution of the polymer network. According to Perform Ve calculations.

[0027] Preferably, the DMA mode is tension or three-point bending, and the equivalent E′ is obtained through geometric conversion; the sample width is 4–10 mm and the length is 8–20 mm, and mechanical pre-stabilization is performed for 2–5 min after clamping to eliminate clamping slack.

[0028] Preferably, ρ is determined by density gradient liquid or Archimedes method, and the temperature and density correction is used to calculate Me based on the actual density at the test temperature of 90°C.

[0029] As a preferred option, the system automatically searches for a platform temperature window: within the range of Tg+30℃ to 120℃, the variance of E′ and the mean of tanδ are calculated using a sliding window, and the center temperature of the window that satisfies both the minimum variance and the minimum tanδ is selected as the platform temperature, with a default value of 90±2℃.

[0030] Furthermore, the present invention also provides a rapid crosslinking density determination system for implementing the method, comprising:

[0031] —A DMA main unit with a temperature-controlled chamber and a tension / bending fixture;

[0032] —Test control module, used to perform LVR scanning, temperature programming and steady-state discrimination;

[0033] —The filler correction module is used to perform large strain preprocessing or Kraus-type calculation correction;

[0034] —Parameter conversion and quality control module, used to calculate G′, Ve, and Me, classify the results, and generate reports;

[0035] — Database module, used to store historical {E′,Ve,Me} and formulation / vulcanization parameters to enable batch-to-batch comparison and trend analysis.

[0036] Furthermore, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method.

[0037] Furthermore, the present invention also provides a computer program product, including a computer program or instructions that, when executed by a processor, implement the method.

[0038] This invention, by employing the aforementioned technical solution, introduces a synergistic mechanism of high-elasticity plateau steady-state discrimination, linear viscoelastic region dual-threshold selection, and filler stiffening correction into dynamic mechanical analysis (DMA). This allows the storage modulus E′ to accurately reflect the elastic contribution of the rubber molecular network, thereby enabling rapid and accurate calculation of crosslinking density Ve and segment molecular weight Me. Verification shows that this method can complete testing and conversion within 30 minutes, shortening the testing cycle by approximately 95% compared to the traditional swelling method, and completely avoiding the use of organic solvents. The results show a high linear correlation with Ve and Me measured by the equilibrium swelling method. The repeatability deviation is less than ±3%. Furthermore, by applying Kraus correction or strain pretreatment to the filler system, this method significantly reduces the interference of the filler network on the modulus, enabling different rubber types (natural rubber, styrene-butadiene rubber, cis-butadiene rubber, and their blends) to obtain consistent crosslinking structure parameters under the same testing conditions. Therefore, this invention not only possesses the advantages of being environmentally friendly and highly efficient, but also sensitively captures changes in crosslinking density caused by formulation fine-tuning or vulcanization process differences, providing a reliable quantitative means for online quality control and rapid formulation optimization of rubber materials. Attached Figure Description

[0039] Figure 1 These are the energy storage modulus diagrams for Embodiments 1-4 of this application.

[0040] Figure 2 This is a crosslinking density diagram of Examples 1-4 of this application.

[0041] Figure 3 This is a molecular weight diagram of the chain segments in Examples 1-4 of this application. Detailed Implementation

[0042] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present invention.

[0043] I. Testing Apparatus and General Requirements

[0044] Apparatus: A dynamic mechanical analyzer (DMA) equipped with a temperature-controlled chamber and a tension / bending fixture, featuring strain control, constant temperature maintenance, and data export functions; temperature control accuracy is not less than ±0.5℃.

[0045] Sample: Vulcanized rubber sheet, preferably 1.5–3.0 mm thick; cut with clean, burr-free edges. Typical dimensions for the tensile test are... The three-point bending mode should be performed according to the equipment's recommended dimensions.

[0046] Drying and pre-stabilization: Before loading the sample, dry it in a vacuum oven at 60–80℃ for 2–4 hours, and then cool it to room temperature before testing; after clamping, perform a mechanical pre-stabilization for 2–5 minutes to eliminate clamping slack.

[0047] Density measurement: The sample density ρ is preferably measured by Archimedes method or density gradient liquid. If the density is measured at 23℃, it can be converted to 90℃ according to the material's volumetric thermal expansion coefficient, or ρ can be directly measured at 90℃ and used in the calculation.

[0048] Symbols and calculation formulas:

[0049] Storage modulus: E′; Shear storage modulus: Since rubber is approximately incompressible, we take ν = 0.5. ;

[0050] Crosslinking density: ;

[0051] Average molecular weight of chain segments: ;

[0052] Where R is the gas constant. T is the absolute temperature (K), and ρ is the sample density (g·cm³). −3 (When converting, the unit of volume must be consistent with the actual unit of volume. The SI system should be used in actual conversions to ensure unit consistency.)

[0053] II. General Method and Procedure (Applicable to Unfilled or Low-Filled Systems)

[0054] S1 linear viscoelastic region (LVR) selection: Strain scanning is performed at 1 Hz (0.05% → 0.50%, step size 0.01% or minimum step size of the device), and the strain amplitude is determined by a combination of two criteria:

[0055] The relative slope change of the E′–strain curve is <2%;

[0056] The increment of tanδ with increasing strain is <0.01.

[0057] Combining the two thresholds, the preferred strain amplitude is 0.10–0.20%, with the default being 0.15%.

[0058] S2 temperature program setting: heating rate 3℃ / min, from Tg+30 to 120℃.

[0059] Steady-state values ​​for the S3 high-elasticity platform: Maintain a constant temperature of 90±2℃ for 2–3 minutes, and monitor E′ and tanδ in real time. When the joint steady-state criterion is met... Record platform E′E′E′ when tanδ≤0.10; if not satisfied, the isothermal period can be extended (total holding time not exceeding 5min).

[0060] S4 Calculation and Output: G′, Ve, and Me are obtained sequentially according to the formula in the previous section, and compared with the historical database / target range to output assessments and suggestions such as "under-sulfurized / appropriate-sulfurized / over-sulfurized" (e.g., extending / shortening the vulcanization time, fine-tuning the accelerator ratio, etc.).

[0061] Note: The above 90±2℃ is located in the high elasticity plateau region of most tire rubbers. This avoids the relaxation effect near Tg and suppresses the secondary crosslinking or modulus drift caused by heat and oxygen that may occur above 100℃, ensuring stable and reproducible results.

[0062] III. Data Correction of the Filling System and Two Implementation Approaches

[0063] For systems containing medium to high filler content such as silica / carbon black, the filler network will increase the small strain E′ and introduce the Payne effect. To ensure that E′ primarily reflects the elastic contribution of the polymer network, the following methods can be chosen:

[0064] Approach A: Large strain single-cycle pretreatment

[0065] A1) At 90℃ and 1Hz, perform a single loading-unloading cycle with a strain of 5–10% to destroy the weak packing network; A2) Return to LVR (0.10–0.20%) and 90±2℃, and repeat “S3 high elasticity platform steady state value”.

[0066] Advantages: Simple operation, no additional modeling required; suitable for rapid judgment in production sites.

[0067] Note: Excessive cycling of thermally sensitive or weakly networked systems is not recommended to avoid introducing irreversible structural changes.

[0068] Approach B: Kraus-type correction based on volume fraction

[0069] B1) Determine the packing volume fraction ϕ;

[0070] B2) Establish an internal standard curve using the same matrix rubber (without filler or with low filler), or use a verified empirical relationship to obtain the modulus increase caused by filler stiffening. ;

[0071] B3) Platform modulus correction to Calculated based on this and .

[0072] Advantages: Does not alter the sample structure; suitable for batch comparison in R&D laboratories.

[0073] Notice: Data must be established or updated under the same frequency, temperature, and LVR conditions to ensure comparability.

[0074] IV. Automated Measurement System (Optional)

[0075] To reduce discrepancies in human judgment, the following algorithms can be embedded in the software:

[0076] LVR Automatic Determination: Calculated using sliding linear regression Strain slope, combined The strain amplitude is automatically selected in increments;

[0077] Platform steady-state determination: The first derivative and... Threshold joint judgment;

[0078] Packing calibration module: Call internal standard Functions or triggers large strain preprocessing procedures;

[0079] Parameter self-consistency: Check the unit / temperature consistency of ρ, T, and ν;

[0080] Report generation: Output E′@90℃, Ve, Me, judgment level and trend chart.

[0081] V. Examples

[0082] Example 1 (Rapid determination of unfilled or low-filled systems)

[0083] (1) Sample: vulcanized rubber sheet, cut into 10mm×5mm×2mm, vacuum dried at 70℃ for 3h.

[0084] (2) LVR: The optimal strain amplitude is 0.15% obtained by strain scanning at 1Hz.

[0085] (3) Temperature program: 3℃ / min from T_g+30℃ to 120℃.

[0086] (4) Platform value: 90±2℃ constant temperature for 3min, record E′ after the steady state criterion is met.

[0087] (5) Calculation: The parameters are obtained by G′=E′ / 3, Ve=G′ / (RT), and Me=ρ / Ve.

[0088] (6) Results: See Table 1. (Temperature T is taken as 363K; density ρ is calculated using measured values.)

[0089] Example 2 (Medium-filling system: Approach A)

[0090] (1)–(3) Same as Example 1.

[0091] (4) Pretreatment: 90℃, 1Hz, 8% single-cycle loading-unloading once;

[0092] (5) Platform value: Return to 0.15% strain, maintain constant temperature at 90±2℃ until steady state, and record E′;

[0093] (6) Calculation: Same as in Example 1.

[0094] (7) Note: Compared with no pretreatment, As the value decreases, the platform E′ becomes more stable, and the calculated Ve fluctuations decrease.

[0095] Example 3 (Medium-filling system: Pathway B)

[0096] (1)–(3) Same as Example 1.

[0097] (4) Kraus type correction: Determine And call internal standard (5) Calculation: according to Convert Ve,p and Me,p. (6) Note: Suitable for horizontal comparison between series of samples under R&D conditions.

[0098] Table 1. Parameters of representative samples on the 90℃ platform (examples)

[0099]

[0100] Note: Based on E′=3RTVe, the E′ of samples 1–4 at 90℃ is approximately 6.97–8.11 MPa (the specific value varies slightly depending on ρ, ν and the steady state of the plateau), which is consistent with the actual readings.

[0101] VI. Quality Control and Result Grading (Optional)

[0102] If Ve is more than 10% higher than the target upper limit and Me is more than 10% lower than the target lower limit, it is judged as "oversulfurized";

[0103] If Ve is more than 10% below the target lower limit and It was judged to be "sulfur deficient";

[0104] Based on historical data, we provide suggestions for fine-tuning vulcanization time / temperature and accelerator ratio.

[0105] VII. Scope and Boundaries

[0106] This method is applicable to vulcanization systems of natural rubber (NR), butadiene rubber (BR), styrene-butadiene rubber (SBR), nitrile rubber (NBR), ethylene propylene diene monomer (EPDM), and their blends; for heat-sensitive or special systems containing active fillers, the platform temperature window can be automatically searched. Internally, through "minimum variance" The "minimum" criterion is used to determine the temperature at the center of the platform.

[0107] The foregoing description of embodiments of the present invention, through which those skilled in the art are able to implement or use the present invention, will be readily apparent to those skilled in the art. Various modifications to these embodiments will be readily apparent to those skilled in the art. The general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novelty disclosed herein.

Claims

1. A rapid method for determining the crosslinking density and segment molecular weight of rubber based on dynamic mechanical analysis, characterized in that, The method includes the following steps: S1) Sample preparation: cut samples according to standard cutting standards, with a thickness of 1.5–3.0 mm, and vacuum dry at 60–80℃ for 2–4 h; S2) Linear viscoelastic region (LVR) determination: perform strain scanning at 1 Hz, and select a strain amplitude of 0.10–0.20% based on the slope threshold of the E′-ε curve and the tanδ change threshold simultaneously; S3) Temperature program: increase the temperature at 3℃ / min from Tg+30℃ to 120℃; S4) Steady-state determination of the high-elasticity plateau: hold the temperature at 90±2℃ for 2–3 min, and determine the steady state based on the combination of the absolute value of dE′ / dt ≤ preset threshold and tanδ ≤ preset threshold, and record the steady-state E′; S5) Filler system correction: for samples containing high filler content, choose one of the following steps: S5-1) First, perform a single cycle with a large strain of 5–10% to destroy the weak packing network, and then take the values ​​according to S2–S4. or, S5-2) Apply the Kraus-type correction model to deduct the stiffening contribution of the filler based on the filler volume fraction; S6) Parameter conversion and output: Obtain the shear storage modulus according to G′=E′ / 3, take R as the gas constant and T as the Kelvin temperature, calculate the crosslinking density Ve=G′ / (RT), and obtain the average molecular weight of the chain segment between two crosslinking points according to Me=ρ / Ve, where ρ is the density of the vulcanized rubber; S7) Quality control judgment: Compare {Ve,Me} with the target range or historical database. When Ve deviates from the target upper limit by more than 10% and Me is lower than the target lower limit by more than 10%, output "over-sulfurization" prompt; when Ve is lower than the target lower limit by more than 10% and tanδ@90℃>0.12, output "under-sulfurization" prompt.

2. The method according to claim 1, characterized in that, The steady-state discrimination uses a joint threshold: And tanδ≤0.10, both of which must be satisfied to determine the recording platform E′.

3. The method according to claim 1, characterized in that, The dual thresholds selected by the LVR include: The curve has a relative slope change of <2% and the increment of tanδ with increasing strain is <0.

01. It is preferred to test at 0.15% strain and 1Hz.

4. The method according to claim 1, characterized in that, The Kraus-type correction uses the filler volume fraction ϕ and an unfilled reference sample. Subtracting the relationship, we obtain the contribution of the polymer network. According to = Perform Ve calculations.

5. The method according to claim 1, characterized in that, The DMA mode is tension or three-point bending, and the equivalent E′ is obtained through geometric conversion; the sample width is 4–10 mm and the length is 8–20 mm, and mechanical pre-stabilization is performed for 2–5 min after clamping to eliminate clamping slack.

6. The method according to claim 1, characterized in that, ρ is determined by density gradient liquid or Archimedes method, and temperature and density corrections are made based on the actual density at the test temperature of 90°C in the Me calculation.

7. The method according to claim 1, characterized in that, The system automatically searches for the platform temperature window: within the range of Tg+30℃ to 120℃, it calculates the variance of E′ and the mean of tanδ using a sliding window, and selects the center temperature of the window that satisfies both the minimum variance and the minimum tanδ as the platform temperature. The default value is 90±2℃.

8. A rapid crosslinking density determination system for implementing the method of any one of claims 1-8, characterized in that, include: —A DMA main unit with a temperature-controlled chamber and a tension / bending fixture; —Test control module, used to perform LVR scanning, temperature programming and steady-state discrimination; — Filler calibration module, used to perform large strain pretreatment or Kraus-type calculation correction; — Parameter conversion and quality control module, used to complete the calculation and result classification of G′, Ve, and Me, and generate reports; — Database module, used to store historical {E′, Ve, Me} and formulation / vulcanization parameters, and realize batch-to-batch comparison and trend analysis.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by a processor, it implements the method of any one of claims 1–7.

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the method of any one of claims 1–7.

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