Molecular dynamics simulation method and system for screening polymer blend compatibility

Abstract

The application discloses a kind of molecular dynamics simulation polymer blend compatibility screening method and system.Method includes: at least two polymer chain molecular model is constructed and is modeled according to multiple different blend composition;Molecular dynamics simulation is carried out to each composition, calculates the florey-hacking interaction parameter χ, obtains the composition dependence relationship of this parameter;By trajectory statistics hetero-chain local interaction spatial distribution, obtain the unevenness of distribution metric;According to the coupling relationship of composition dependence morphology and distribution unevenness metric, determine compatible interval and phase separation tendency;When the parameter is within compatible threshold value, composition dependence morphology satisfies non-monotonic condition, and distribution unevenness metric exceeds unevenness threshold value, determine metastable compatibility and output phase separation early warning, to screen formula.The application overcomes the compatibility missed judgment caused by single parameter criterion, improves the reliability of blend formula compatibility screening, and can be used for polymer alloy and blend material formula development.

Description

Technical Field

[0001] This invention relates to the field of polymer blending modification technology, specifically to a method and system for screening the compatibility of polymer blends using molecular dynamics simulation. Background Technology

[0002] Polymer blending modification is an important approach for preparing polymer alloys and expanding the properties of polymer materials. Whether blending two or more polymers can yield a stable homogeneous material depends on their compatibility. Systems with insufficient compatibility are prone to phase separation during processing or use, leading to deterioration in the material's mechanical properties and appearance. Therefore, in polymer alloy formulation development, how to quickly determine the compatibility of a large number of candidate polymer combinations and screen out compatible blend formulations has long been a practical need in this field.

[0003] In traditional R&D models, compatibility is mainly determined through repeated blending experiments, supplemented by characterization methods such as differential scanning calorimetry, electron microscopy, and scattering. This trial-and-error approach is time-consuming and costly, and the workload increases dramatically with the number of candidate components and combinations, making it difficult to meet the needs of high-throughput formulation screening.

[0004] To improve screening efficiency, molecular simulation techniques have been introduced to predict the compatibility of blends at the molecular level. One common approach involves constructing molecular models of the polymer chains involved in the blend, establishing a molecular simulation model of the blend system, and performing molecular dynamics simulations. The mixing energy is calculated from the cohesive energy density obtained from the simulation, and then the Florey-Hutchins interaction parameter χ is calculated based on the Florey-Hutchins theory. This parameter is then compared with a critical value to determine compatibility. For example, patent application CN121687271A discloses a method for calculating the phase diagram of a homopolymer rubber binary blend system using computer simulation. This method introduces structural parameters such as crosslinking density and molecular chain entanglement into a coarse-grained model, and combines force field correction to calculate the phase separation temperature and phase boundary of the blend system. This method of predicting compatibility using molecular simulation improves screening efficiency to some extent compared to pure experimental trial and error.

[0005] However, the aforementioned existing technologies generally use a single interaction parameter value calculated under a single representative blend composition when determining compatibility, and use whether this value is below a critical value as the compatibility criterion. This approach implicitly assumes that the interaction parameter value under a single composition is sufficient to characterize the compatibility behavior across the entire blend composition range. Based on this premise, existing methods tend to ignore two objectively existing situations: First, the interaction parameter itself can vary with the blend composition. Related studies have shown that the interaction parameter of some blend systems exhibits non-monotonic changes with composition, and the value under a single composition is difficult to reflect its compatibility behavior under other compositions. Second, the local interactions between dissimilar polymer chains can exhibit spatial non-uniformity in the blend system. When strong local specific interactions (such as hydrogen bonds) exist, local aggregates or microregions may form within the system, and a single interaction parameter based on the average amount of the system is insufficient to reflect this local non-uniformity.

[0006] The resulting structural consequence is that when the interaction parameters of a blend system fall within the compatibility threshold, but the interaction parameters change non-monotonically with the composition, or the spatial distribution of its local interactions is highly uneven, relying solely on the interaction parameter values ​​of a single component can easily lead to the failure to classify systems that are actually metastable or have a tendency to phase separation as compatible. Consequently, the blend formulations selected in this way may experience phase separation during subsequent processing or use. It should be noted that the aforementioned omissions are not accidental errors of existing methods on individual systems, but rather an inevitable consequence of two simplification premises inherent in their criterion structure: First, treating the interaction parameter as a scalar independent of composition is equivalent to replacing the composition-varying interaction parameter with a constant in the Florey-Hutchins free energy description, thus mathematically erasing the curvature information carried by the interaction parameter as a function of composition. This curvature information determines whether the second derivative of the mixing free energy with respect to composition turns negative in a certain composition interval, i.e., whether the system becomes unstable in that interval. Second, using the system's average quantity as a compatibility criterion is equivalent to ignoring local compositional fluctuations. However, this neglect does not hold when there are strong local specific interactions between dissimilar chains. In other words, even if the scalar interaction parameter at a representative composition is below the critical value, as long as the interaction parameter is not monotonic with composition or the local interaction space is significantly non-uniform, the system may still exhibit a tendency towards phase separation locally, which a single scalar criterion cannot reflect in principle. In other words, both the traditional approach that relies on experimental trial and error and the existing molecular simulation approach that uses a single component and a single interaction parameter as the criterion are insufficient in the key dimension of "characterizing the composition dependence and local spatial inhomogeneity of the interaction parameters". Reliable screening of polymer alloy formulations requires a more accurate determination of compatibility in this dimension.

[0007] Therefore, there is an urgent technical problem to be solved in this field: how to overcome the misjudgment of compatibility caused by using a single interaction parameter under a single composition as the criterion (that is, judging a system that actually has a tendency to phase separation as compatible) when screening the compatibility of polymer blends with molecular dynamics simulation without relying on repeated blending experiments, so that the determination of compatibility range and phase separation tendency can take into account the composition dependence of interaction parameters and the spatial inhomogeneity of local interactions, thereby more reliably screening out compatible blend formulations. Summary of the Invention

[0008] The purpose of this invention is to overcome the problem of misjudgment of polymer blend compatibility caused by the single interaction parameter criterion in the prior art, and to provide a method and system for screening polymer blend compatibility using molecular dynamics simulation. This method further identifies metastable compatible systems that actually have a tendency to phase separation and provides early warnings in systems that are deemed compatible by the existing scalar χ criterion, thereby providing a more reliable high-throughput calculation and screening basis for the development of polymer alloy blend formulations.

[0009] To clarify the technical contribution of this invention, it is necessary to first point out a long-held, but deviated, understanding in the field. In existing methods for screening the compatibility of polymer blends using molecular dynamics simulations, in pursuit of high throughput and computational simplicity, it is generally assumed that "a scalar Florey-Hutchins interaction parameter χ calculated under a single representative composition is sufficient to characterize the compatibility of the entire blend system across the entire composition range." However, this assumption deviates systematically from objective reality: First, χ is not a constant, but varies with blend composition, degree of polymerization, dispersion, etc. Two polymers may only be compatible within a certain composition range or at certain molecular weights, and similar χ values ​​can correspond to drastically different phase separation behaviors. Second, even if macroscopic characterization (such as a single glass transition temperature or a scalar χ that meets the standard) shows that the system is compatible, there may still be localized inhomogeneities at the nanoscale that are strongly influenced by composition and temperature. In other words, a scalar χ falling within the compatibility threshold cannot rule out the possibility that the system is actually metastable and compatible, and has a tendency to phase separation—this is precisely the failure mode of the single χ criterion "missing detection."

[0010] This invention identifies and targets this neglected failure mode: instead of simply stating "compatibility is determined by χ²," it constructs a composite criterion that can further identify metastable compatibility under the premise that χ² is met. It is important to emphasize that the failure mode addressed by this invention is not an isolated case observation, but rather an inherent consequence of the Florey-Hutchins free energy description when interaction parameters vary with composition and the local interaction space is non-uniformly distributed: when constant interaction parameters replace composition-varying interaction parameters, the term contributed by the curvature of the interaction parameters in the second derivative of the mixing free energy with respect to composition is neglected, causing instability that should occur in a certain composition interval to be unreflected by a single scalar criterion; its theoretical analysis is detailed in Example 6 of the specific implementation of this specification. Because this failure mode is rooted in the simplified structure of existing criteria, this invention covers it with a criterion that couples composition-dependent morphology with a measure of non-uniform distribution, which is necessary to overcome this failure mode, rather than a simple superposition of conventional calculation operations.

[0011] To achieve the above objectives, the technical solution of the present invention includes the following three aspects.

[0012] In a first aspect, a method for screening the compatibility of polymer blends using molecular dynamics simulations is provided, the method comprising the following steps: Construct molecular models of at least two polymer chains, and establish molecular simulation models of the blending systems under each blending composition according to multiple different blending compositions; Molecular dynamics simulations were performed on the molecular simulation models of each blend system. The mixing free energy and Florey-Hutchins interaction parameter χ of the blend system under each blend composition were calculated from the simulation trajectory to obtain the composition dependence of the Florey-Hutchins interaction parameter χ with the blend composition. Based on the trajectories simulated by molecular dynamics, the spatial distribution of local interactions between dissimilar polymer chains in each blend system is statistically analyzed, and a distribution non-uniformity metric characterizing the degree of non-uniformity in the spatial distribution of the local interactions is determined. Based on the coupling relationship between the composition dependence pattern reflected by the composition dependence relationship and the distribution non-uniformity measure, the compatibility range and phase separation tendency of the blend system are determined, and the blend formulation is screened accordingly. Specifically, when the Florey-Huggins interaction parameter χ is within a preset compatibility determination threshold, the composition-dependent morphology satisfies a preset non-monotonic condition, and the distribution non-uniformity measure exceeds a preset non-uniformity threshold, the corresponding blend composition is determined to be metastable and compatible, and a phase separation tendency warning is output.

[0013] Here, it is necessary to explain the essential difference between this technical solution and conventional calculation operations. While the operations of "calculating χ² by multi-component sampling" and "statistically analyzing the spatial distribution of local interactions" are, individually, within the conventional capabilities of molecular dynamics simulations, those skilled in the art, given the prevailing understanding that "χ² compliance equates to compatibility," have no motivation to combine these two results to overturn a compatibility determination that has already met the χ² standard. The core of this invention lies not in performing the aforementioned two operations themselves, but in establishing a reversal criterion: using the coupling of "composition-dependent morphological non-monotonicity" and "local distribution inhomogeneity exceeding the threshold" as the triggering condition, reversing the conclusion, determining metastable compatibility, and issuing a warning when the scalar χ² determination is compatible. This reversal criterion and its triggering condition are not naturally derived from conventional calculation operations; their basis comes from the identification of the aforementioned failure modes, i.e., χ² compliance but still exhibiting nanoscale local inhomogeneity or composition-dependent phase separation. This load-bearing criterion corresponds to the characteristic portion of claim 1 and is implemented by the compatibility determination module of claim 9 and the storage medium of claim 10.

[0014] For ease of description, the term "compatibility threshold" in the following text and the term "compatibility determination threshold" in the claims refer to the same threshold and have the same meaning. In some embodiments, the composition-dependent morphology is characterized by at least one of the following: the minimum value of the composition-dependent relationship χ, the curvature sign, or the difference between the two end compositions and the middle composition; the non-monotonic condition is the occurrence of a minimum value or the reversal of the curvature sign within the compatibility threshold range; the local interactions include at least one of contact, hydrogen bonding, and electrostatics; the distribution non-uniformity measure is characterized by at least one of variance, coefficient of variation, or cluster size distribution, and can be obtained by partitioning the simulation box and counting the number or intensity of local interactions in each local region; the mixing free energy can be calculated from the cohesive energy density through the mixing energy relationship, and χ can be converted from the mixing energy with characteristic volume and temperature; the plurality of The blend composition takes at least 3 points in the range of 0 to 1 and includes the enriched components at both ends and at least one intermediate component; the molecular model is an all-atom model or a coarse-grained model. When using a coarse-grained model, the local interaction is characterized by the number of bead contacts; the coupling relationship determination can weight and combine composition-dependent morphological characteristics and distribution non-uniformity measures into a composite compatibility index, compare it with the classification threshold, and output the classification results of compatibility, metastable compatibility, or incompatibility. After calculating the composite index, candidate compatible formulations can be screened, composition and temperature boundaries of the compatibility range can be determined by changing the composition or temperature, and chain structure, chain length, or ratio can be adjusted and recalculated after determining metastable compatibility to form a closed loop.

[0015] Secondly, a molecular dynamics simulation-based polymer blend compatibility screening system is provided, see [link to relevant documentation]. Figure 3The system 100 includes: a modeling module 10 for constructing molecular models of at least two polymer chains and modeling multiple blend compositions; a simulation and parameter calculation module 20 for performing molecular dynamics simulations on each composition and calculating χ and its compositional dependence; a distribution statistics module 30 for statistically analyzing the spatial distribution of local interactions between heterogeneous chains and obtaining a distribution non-uniformity metric; and a compatibility determination module 40 for determining the compatibility range and phase separation tendency based on the coupling relationship between compositional dependence morphology and distribution non-uniformity metric, and determining metastable compatibility and outputting a phase separation warning when χ is within the compatibility threshold, the compositional dependence morphology satisfies the non-monotonic condition, and the distribution non-uniformity metric exceeds the non-uniformity threshold.

[0016] Thirdly, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the method described in the first aspect above.

[0017] Compared with the prior art, the present invention is expected to achieve the following beneficial effects: Firstly, this invention replaces the scalar χ under a single composition with the composition-dependent form of χ, which is expected to reflect the partial compatibility of two polymers that are only compatible in a certain composition range. In principle, this overcomes the tendency of misjudgment of compatibility caused by the inability of the existing single-point scalar χ to express composition dependence.

[0018] Secondly, this invention introduces a measure of the spatial distribution non-uniformity of local interactions between heterogeneous chains, which is expected to characterize the nanoscale local non-uniformity masked by macroscopic criteria, thereby distinguishing between macroscopically compatible but locally non-uniform systems.

[0019] Third, this invention uses a coupled criterion of composition-dependent morphology and distribution non-uniformity measurement to further identify metastable compatibility and output phase separation warning when the scalar χ is determined to be compatible. It is expected to reduce the risk of misjudging metastable compatible systems as stable compatible systems by existing methods, and provide early indications of phase separation tendency for blend formulation screening.

[0020] Fourth, the present invention can weight and combine the above-mentioned characteristic quantities into a composite compatibility index and classify it, which is expected to be beneficial for the rapid classification and sorting of a large number of candidate systems for compatibility, metastable compatibility and incompatibility in high-throughput computational screening of blend formulations, and to help narrow the scope of subsequent experimental verification by determining the composition and temperature boundaries and metastable feedback recalculation closed loop.

[0021] It should be noted that the above-mentioned beneficial effects, such as the accuracy of compatibility determination and the reduction of the risk of missed determination, are related to the performance of specific systems and are expected descriptions based on the criterion mechanism of this invention and existing technical literature. The specific numerical performance needs to be determined by experiments or further simulation verification in combination with specific polymer systems. This specification does not limit the scope of protection of this invention with specific measured data. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the overall process of the polymer blend compatibility screening method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the compatibility determination logic of an embodiment of the present invention, which shows the coupled determination process based on the Flory-Hutchins interaction parameter χ, composition-dependent morphology and distribution non-uniformity measure; Figure 3 This is a schematic diagram of the module structure of the polymer blend compatibility screening system according to an embodiment of the present invention.

[0023] In the diagram: S1 to S6 are Figure 1 The steps of the method shown; R1 to R3 are Figure 2 The judgment steps in the shown judgment logic are as follows: R4 is the comprehensive judgment and early warning output step; 100 is... Figure 3 The polymer blend compatibility screening system shown is divided into three modules: 10 is the modeling module, 20 is the simulation and parameter calculation module, 30 is the distribution statistics module, and 40 is the compatibility determination module. X represents the Florey-Hutchins interaction parameter χ, which is indicated by the Latin letter X for clarity in the accompanying figures. Detailed Implementation

[0024] The present invention will be further described below with reference to the embodiments. It should be understood that the embodiments described herein are only for explaining the present invention and not for limiting the present invention; the specific polymer types, parameter values ​​and numerical results involved in the embodiments are all exemplary and are used to illustrate how the steps of the present invention are implemented and how the criteria are calculated, and do not constitute a limitation on the scope of protection of the present invention.

[0025] Example 1: Full Atom Model - Best Implementation Covering the Independent Claims This embodiment takes a binary blend system composed of polymer A and polymer B as an example and uses a full-atom model to illustrate the complete implementation process of the compatibility screening method of the present invention.

[0026] Step 1: Construct molecular models and set multiple compositions. Establish all-atom chain models for polymers A and B, respectively, with chain lengths taken as several repeating units as an example. Model multiple distinct blend compositions. In this embodiment, five composition points are selected in the volume fraction range of A, φ_A = 0 to 1, including end-enriched compositions such as φ_A = 0.1 and 0.9, and intermediate compositions such as φ_A = 0.3, 0.5, and 0.7. Simulation boxes for the corresponding blend systems are constructed, ensuring the chain number within each box matches the target composition.

[0027] Step two: Molecular dynamics simulation and parameter calculation. For each composition, energy minimization and pre-equilibrium are first performed. Then, molecular dynamics simulation is conducted until the system reaches equilibrium under a set temperature and ensemble, such as an isothermal and isobaric ensemble. The cohesive energy density of the pure component and the blend system is calculated from the equilibrium trajectory. The mixing energy of the composition is obtained through the mixing energy relation. Then, the Florey-Hutchins interaction parameter χ of the composition is obtained by combining the characteristic volume and temperature. The above calculation is repeated for all five compositions to obtain discrete data points of χ as a function of composition φ_A. The composition dependence χ(φ_A) of χ is obtained by interpolation or fitting.

[0028] Step 3: Statistical analysis of the spatial distribution of local interactions. Based on the equilibrium trajectories of each component system, the local interactions between heterogeneous chain segments A and B are statistically analyzed. In this embodiment, the number of contacts between chain segments A and B is used to characterize local interactions. The simulation box is divided into several spatial sub-regions, and the number of heterogeneous chain contacts in each sub-region is counted to obtain the spatial distribution of the contact numbers. The coefficient of variation of this distribution is used as a measure of distribution non-uniformity; a larger coefficient of variation indicates that the local interactions are more spatially non-uniform and more prone to local enrichment or segregation.

[0029] Step 4: Coupling Determination and Load-Bearing Criterion. Let the compatibility threshold be χ_c; values ​​below this threshold are typically considered compatible by existing methods. Let the non-uniformity threshold be CV_th. In this embodiment, for each candidate component, a determination is made based on the coupling relationship between the composition-dependent morphology and the distribution non-uniformity metric of χ(φ_A): —If χ is higher than χ_c, it is judged as incompatible, which is consistent with the existing criteria; —If χ is lower than χ_c, and χ(φ_A) is monotonic within the compatibility threshold range and the non-uniformity of distribution does not exceed CV_th, it is considered compatible; —If χ is lower than χ_c, it should be considered compatible according to the scalar χ. However, if the composition-dependent morphology of χ(φ_A) satisfies the non-monotonic condition, that is, a minimum value or curvature sign reversal occurs within the threshold range, and the uneven distribution measure exceeds CV_th, then this invention determines that the system is metastable and compatible, and outputs a phase separation warning.

[0030] To illustrate how the load-bearing criterion is calculated, a set of exemplary values ​​is provided to demonstrate the judgment logic. The following values ​​are example values ​​used to demonstrate the calculation of the criterion, not actual test results of a specific real system. Suppose that χ = ​​0.35 is calculated for a certain composition, which is lower than the compatibility threshold χ_c = 0.5. According to the single scalar χ criterion, it should be judged as compatible. However, this embodiment further finds that the system χ(φ_A) has a minimum value within the threshold range, satisfying the non-monotonic condition, and the coefficient of variation of the contact number distribution CV = 0.6, exceeding the non-uniformity threshold CV_th = 0.4—all three conditions are met simultaneously. Therefore, this invention determines that the system is metastable and compatible and outputs a phase separation warning. It can be seen that for a system that would be judged as compatible according to the scalar χ criterion, this invention can further identify its phase separation tendency based on the coupling of composition-dependent morphology and local non-uniform distribution.

[0031] This embodiment covers all the necessary technical features of independent claim 1, including multi-component modeling, calculation of χ composition dependency relationship, statistics of non-uniformity measurement of local interaction spatial distribution, coupling determination of composition dependency morphology and non-uniformity measurement, and load-bearing criterion of "χ meets the standard but judges metastable compatibility and gives early warning".

[0032] Example 2: Coarse-grained Model - Sub-example This embodiment uses a coarse-grained model to implement the method of the present invention, in order to illustrate the implementation of the "coarse-grained model" in claim 6, and the substitutability of different distribution non-uniformity measures.

[0033] Polymers A and B were mapped to coarse-grained bead chain models, and multiple blend compositions were set up as in Example 1, followed by coarse-grained molecular dynamics simulations. The calculation of χ and its composition dependence was similar to that in Example 1, and in the coarse-grained model, it could be obtained from the interaction energy or mixing energy relationship between beads. Local interactions were characterized by the number of contacts between dissimilar beads, and the number of contacts between dissimilar beads in each spatial sub-region was counted. In this embodiment, the cluster size distribution of the contact number distribution was used as a measure of distribution non-uniformity, for example, by the maximum cluster size or the statistical moments of the cluster size. A larger cluster size indicates that the dissimilar interactions tend to aggregate and the space is more non-uniform. Coupling and load-bearing criteria were the same as in Example 1: when χ is below the compatibility threshold, the composition-dependent morphology is non-monotonic, and the cluster size exceeds the corresponding threshold, metastable compatibility was determined, and a phase separation warning was output. This embodiment illustrates that the molecular model of the present invention can be a coarse-grained model, and the distribution non-uniformity can be characterized by various methods such as cluster size distribution, all of which can achieve the purpose of the present invention.

[0034] Example 3: Composite Compatibility Index Classification and High-Throughput Screening – Closed-Loop Implementation This embodiment illustrates the implementation of claims 7 and 8, namely, using composite compatibility indexes for classification and applying them to high-throughput calculation and screening of blend formulations.

[0035] Following the method described in Example 1 or 2, composition-dependent morphological features, such as the curvature or minimum depth of χ(φ_A), and a measure of distribution inhomogeneity, such as the coefficient of variation, are calculated for each candidate system. These features are then weighted and combined into a composite compatibility index, for example, by linearly combining composition-dependent morphological features and a measure of distribution inhomogeneity with predetermined weights. These weights can be adjusted based on system experience or verification. A tiered threshold is set, and the composite index is compared with the tiered threshold to output a three-level classification: compatible, metastable compatible, and incompatible.

[0036] In high-throughput screening applications, a batch of candidate polymer formulations are evaluated for composite compatibility indices, graded, and ranked, with priority given to formulations deemed compatible. For formulations deemed metastable and compatible, phase separation warnings are issued. Further, the composite indices are recalculated by changing the blending composition or temperature of the selected formulations to determine the compositional and temperature boundaries of the compatibility range. For formulations deemed metastable and compatible, the chain structure, chain length, or A / B ratio is adjusted, and feedback is used for recalculation, forming a closed loop of "judgment-adjustment-recalculation," gradually approaching the design of stable and compatible formulations. This embodiment illustrates that the present invention can rapidly grade and screen a large number of candidate systems, and narrows the scope of subsequent experimental verification through boundary determination and a metastable feedback loop.

[0037] Example 4: Formal Explanation of Criterion Calculation – Supporting Reproducibility This embodiment further formalizes the calculation methods of the Florey-Hutchins interaction parameter χ, the distribution non-uniformity measure, and the composite compatibility index involved in the foregoing embodiments, so that those skilled in the art can reproduce the criterion calculation of the present invention at once. The meanings of the symbols and the methods of taking values ​​in the following formulas are all known in the art or can be directly obtained from the simulation trajectory. The numerical examples given are for demonstration purposes only and are not the experimental results of specific real systems.

[0038] First, the calculation of the Florey-Hutchins interaction parameter χ. For a system with a given blend composition, the cohesive energy densities of pure component A, pure component B, and blend system AB are calculated using molecular dynamics simulations of equilibrium trajectories, denoted as CED_A, CED_B, and CED_AB, respectively. The mixing energy density Δe_mix = (φ_A·CED_A + φ_B·CED_B) - CED_AB is calculated according to the mixing energy relationship, where φ_A and φ_B are the volume fractions of components A and B, respectively, and φ_A + φ_B = 1. Then, the Florey-Hutchins interaction parameter χ under this composition is obtained by converting it using the formula χ = V_ref·Δe_mix / (R·T), where V_ref is the reference molar volume, which is taken as the characteristic volume of the blend system, R is the gas constant, and T is the molecular dynamics simulation temperature. Calculate χ for at least three component points within the 0 to 1 component interval to obtain a discrete data sequence {χ(φ_A)} of χ as a function of component φ_A. Interpolate or fit this sequence to obtain the component dependency χ(φ_A).

[0039] Second, the calculation of composition-dependent morphological features. The composition-dependent morphology can be characterized by at least one of the following features of χ(φ_A): (a) Minimum depth Δχ_min = χ_end - χ_min, where χ_min is the minimum value of χ(φ_A) within the compatibility threshold range, and χ_end is the mean value of χ at the enriched components at both ends; (b) Curvature, derived from the second difference d of χ(φ_A). 2 χ / dφ_A 2 The approximation is used to determine the curvature reversal; when the minimum value corresponding to χ_min appears within the compatibility threshold range (Δχ_min>0) or the curvature sign is reversed, it is determined that the non-monotonic condition is met.

[0040] Third, the calculation of the distribution non-uniformity metric. The simulation box is divided into N equal-volume spatial sub-regions. The number of local interactions between dissimilar polymer chains, such as contacts between dissimilar chain segments, is counted in the i-th sub-region: n_i (i=1,2,…,N). The mean μ=(1 / N)·Σn_i of the contact number in each sub-region is calculated as follows: μ = (1 / N)·Σ(n_i-μ) 2 ]^(1 / 2), and the coefficient of variation CV=σ / μ is obtained as a measure of distribution non-uniformity. The larger the CV, the more spatially non-uniform the local interactions are. When using cluster size distribution to characterize, the number of sub-regions or beads contained in the largest cluster formed by spatially connected contacts is taken as the maximum cluster size, or the statistical moments of the cluster size are taken as a measure of distribution non-uniformity.

[0041] Fourth, composite compatibility index and grading judgment. The normalized composition-dependent morphological feature quantity f_shape, which is obtained by normalization with Δχ_min for example, and the normalized distribution non-uniformity metric g_hetero, which is obtained by normalization with CV for example, are linearly combined according to set weights to obtain the composite compatibility index I=w1·f_shape+w2·g_hetero, where w1 and w2 are weights greater than 0 and can be adjusted based on system experience or verification; I is compared with preset grading thresholds I_th1 and I_th2 (I_th1<I_th2), and a grading result of compatible, metastable compatible or incompatible is output.

[0042] Fifth, formal expression of the load-bearing criterion. Let the compatibility threshold be χ_c and the non-uniformity threshold be CV_th, the load-bearing criterion of the present invention can be expressed as: when the three conditions that χ<χ_c, i.e., it should be judged as compatible according to the scalar χ, the composition-dependent morphology satisfies the non-monotonic condition (Δχ_min>0 or curvature sign reversal), and CV>CV_th are satisfied at the same time, the corresponding blend composition is judged as metastable compatible and an early warning of phase separation tendency is output; when χ≥χ_c, it is judged as incompatible; the rest of the cases are judged as compatible. Using the exemplary values of Example 1, χ=0.35<χ_c=0.5, χ(φ_A) has a minimum value within the threshold range, and CV=0.6>CV_th=0.4, the three conditions are satisfied at the same time, so it is judged as metastable compatible and an early warning is issued, which is consistent with the judgment result of Example 1.

[0043] It should be noted that the distribution non-uniformity metric described in the present invention characterizes the spatial distribution non-uniformity degree of local interactions between dissimilar polymer chains, such as contacts, hydrogen bonds, and electrostatic interactions between dissimilar chain segments, which reflects the spatial segregation of dissimilar components at the nanoscale; this is different from the method that only uses the local fluctuation of the total density of the blend system, for example, the standard deviation of the density of local regions to characterize whether macroscopic phase separation has occurred. The former is obtained from the spatial distribution of specific interactions between dissimilar chains, and serves as a criterion dimension coupled with the composition-dependent morphology to participate in the identification of metastable compatibility; the latter is a statistic at the total density level of the system, and is usually used as a single indicator for whether phase separation has occurred. Therefore, the distribution non-uniformity metric of the present invention is not a simple replacement or equivalent expression for the total density fluctuation of the system, but a criterion dimension oriented to the spatial distribution of local interactions between dissimilar chains and jointly forming a coupled criterion with the composition-dependent morphology.

[0044] This example illustrates that each calculation step and its load-bearing criterion described in independent claim 1 of the present invention can be calculated at one time from the simulation trajectory through the above formal relational expressions, and those skilled in the art can reproduce the criterion calculation and judgment logic of the present invention without creative labor based on this.

[0045] Example 5 Compatibility Screening System · Corresponding to Claim 9 See Figure 3 This embodiment provides a polymer blend compatibility screening system 100 for implementing the above method, including a modeling module 10, a simulation and parameter calculation module 20, a distribution statistics module 30 and a compatibility determination module 40 connected in sequence.

[0046] Modeling module 10 constructs molecular models of at least two polymer chains, wherein the molecular models are either all-atom models or coarse-grained models, and establishes molecular simulation models of the blending system under each blending composition according to multiple different blending compositions, and outputs each model to simulation and parameter calculation module 20.

[0047] The simulation and parameter calculation module 20 performs molecular dynamics simulations on the molecular simulation models of each blend system. The simulation trajectory is used to calculate the mixing free energy and the Florey-Hutchins interaction parameter χ under each composition according to the method described in one of Examples 4. The composition dependence of χ as a function of the blend composition is obtained, and the simulation trajectory and the composition dependence of χ are output to the distribution statistics module 30 and the compatibility determination module 40, respectively.

[0048] The distribution statistics module 30 uses the simulated trajectory to statistically analyze the spatial distribution of local interactions between dissimilar polymer chains in the manner described in Example 4, third, to determine the distribution non-uniformity measure and output it to the compatibility determination module 40.

[0049] The compatibility determination module 40, in accordance with the manner described in the fourth and fifth embodiments of Example 4, determines the compatibility range and phase separation tendency based on the coupling relationship between composition-dependent morphology and distribution non-uniformity measurement, and screens blending formulations; when χ is within the compatibility threshold, the composition-dependent morphology satisfies the non-monotonic condition, and the distribution non-uniformity measurement exceeds the non-uniformity threshold, the corresponding blending composition is determined to be metastable and compatible, and a phase separation tendency warning is output.

[0050] Each of the above modules can be implemented by a computer program and stored in a computer-readable storage medium. When executed by a processor, it implements the method described in the first aspect of the present invention, namely, the computer-readable storage medium described in claim 10. The system of this embodiment corresponds to claim 9, and each of its modules corresponds one-to-one with each step of the method of the present invention.

[0051] Example 6: Theoretical Analysis of the Mechanism of Action – Non-obviousness of the Support Load-Bearing Criterion To facilitate understanding of the mechanism of action of this invention and its difference from existing single χ criteria, a theoretical analysis of this invention is conducted below under idealized assumptions. The following analysis is based on idealized assumptions made for ease of theoretical explanation and aims to elucidate the concept and mechanism of action of this invention. It does not constitute a limitation on the scope of protection of this invention, nor does it represent the precise quantitative performance of actual systems. This embodiment does not introduce any measured data; all related relationships are thermodynamic descriptions well-known in the art.

[0052] Assumption 1: The system under consideration is a binary blend system composed of component A and component B, described by the Florey-Hutchins free energy; Assumption 2: The Florey-Hutchins interaction parameter χ is a continuous function of the blend composition φ, χ(φ), where φ is the volume fraction of component A, 0 < φ < 1; Assumption 3: Local interactions between dissimilar chains can be spatially non-uniformly distributed, and the degree of non-uniformity is characterized by the aforementioned distribution non-uniformity measure.

[0053] Corollary 1: Under what circumstances will the existing single-point χ² criterion inevitably miss a case? Within the Florey-Hutchins framework, the mixing free energy at a unit lattice point in a binary blend system can be written as ΔG_mix(φ) / (R·T)=(φ / N_A)·lnφ+((1-φ) / N_B)·ln(1-φ)+χ(φ)·φ·(1-φ), where N_A and N_B are the degrees of polymerization of components A and B, respectively, R is the gas constant, and T is the temperature. The local stability of the system to small compositional fluctuations is determined by the second derivative of the mixing free energy with respect to the composition: g″(φ)= ΔG_mix / The sign of g″(φ) determines the local stability of the composition: when g″(φ)>0, the composition is locally stable; when g″(φ)<0, the composition is unstable due to composition fluctuations, i.e., it enters the unstable region defined by the spindle line; g″(φ)=0 is the boundary between stability and instability. Existing single-point χ criteria, in calculation and comparison, essentially replaces the composition-varying χ(φ) with a single constant χ0, i.e., letting χ(φ)≡χ0. Under this substitution, compatibility is determined solely by the relationship between χ0 and the critical value χ_c, while all the information carried by χ(φ) with compositional variation, especially its curvature contribution to g″(φ), is structurally erased. However, as can be seen from the above equation, g″(φ) contains contributions from the term χ(φ)·φ·(1-φ), related to the first and second compositional derivatives of χ(φ); when χ(φ) is non-monotonic with composition, i.e. When the sign changes within the examined interval, this contribution can cause g″(φ) to take a negative value in a certain composition interval, thus causing local instability in that interval. This situation can occur even when the scalar value χ0 at the representative composition of the system is still below the critical value χ_c, i.e., it should be considered compatible according to the single-point criterion. Therefore, it is theoretically inevitable that for a system where χ(φ) is not monotonic, the existing criterion of comparing a single constant χ0 with a threshold will miss the system that has actually entered instability or metastability in a local composition interval and fail to be considered compatible. Furthermore, this missed judgment stems from the loss of χ(φ) curvature information, not from the value of the threshold χ_c; therefore, simply tightening the threshold χ_c will only change the boundary between compatibility and incompatibility, and cannot restore the erased second-order composition information, thus failing to correct the above-mentioned missed judgment. This closes off the conventional improvement path of "avoiding missed judgment by making the compatibility threshold more stringent".

[0054] Inference 2: Why do well-known simple substitutions fail to solve the problem, and why is the coupling criterion of this invention necessary? Consider several readily conceivable alternatives in the art: Alternative 1: Calculate χ for multiple compositions and average them to obtain an average scalar χ; however, this method still yields a single scalar and does not retain the curvature information of χ(φ), failing to reflect the local instability caused by the non-monotonicity of χ(φ), thus failing to resolve the missed detection. Alternative 2: Only track the lowest point or minimum value of the χ(φ) curve to determine whether composition-dependent phase separation exists; while this method can reflect composition dependence to some extent, it only characterizes this one failure path and is not sensitive to the uneven distribution of local interactions between dissimilar chains in real space—when the system's χ meets the standard for all compositions, but forms local aggregates or micro-regions at the nanoscale due to strong local specific interactions such as hydrogen bonds, simply looking at the minimum value of χ(φ) will still classify it as compatible, thus still resulting in missed detection. Therefore, metastable compatibility has two physically independent failure paths: one is composition-dependent instability, corresponding to the negative transformation of g″(φ) in a certain composition interval, characterized by the composition-dependent form of χ(φ), i.e., its curvature; the other is micro-region segregation due to local spatial inhomogeneity, corresponding to the local failure of the mean-field description based on the system's average quantity, characterized by the spatial distribution inhomogeneity of local interactions between dissimilar chains. The key constraint of this invention is that the above two failure paths are characterized by two different types of physical quantities, and any single physical quantity can only cover one path, not both simultaneously. Therefore, only by coupling the composition-dependent form with the distribution inhomogeneity measure and using their joint condition as a trigger can both failure paths be covered without omission. This shows that the coupling load-bearing criterion of this invention is not a simple superposition of several known computational quantities, but rather, under the constraint of "covering two independent failure paths with two independent types of physical quantities respectively," it achieves the necessary criterion structure for complete identification of metastable compatibility. If any physical quantity is removed, an uncovered failure path will be left behind, thus restoring the missed detection.

[0055] Inference 3 supports the relevant limitations of the claims. As can be seen from Inference 1, the physical basis for the limitation in the independent claim of this invention, namely, that "the composition-dependent form satisfies a preset non-monotonic condition," lies in the non-monotonicity of χ(φ), i.e. The sign change is a necessary prerequisite for g″(φ) to turn negative within the threshold range, meaning the system can locally enter instability. Therefore, using "non-monotonic conditions" as one of the conditions for triggering metastable compatibility determination has a clear thermodynamic basis. Similarly, the limitation that "the Florey-Hutchins interaction parameter χ is within the preset compatibility determination threshold" corresponds to the situation where the scalar χ at the representative composition of the system is still below the critical value χ_c, meaning that it should be judged as compatible according to existing criteria. This is precisely the target range that this invention needs to further identify. "The distribution non-uniformity exceeds the preset non-uniformity threshold" corresponds to the condition for triggering the second failure path. The three are independent of each other but together constitute the coupled triggering conditions, corresponding one-to-one with the coverage relationship of the above two failure paths.

[0056] The above theoretical analysis, under idealized assumptions, shows that existing single χ criteria have a fundamental omission for systems where χ(φ) is not monotonic or locally spatially inhomogeneous. This omission cannot be eliminated by conventional methods such as averaging more composition points, only tracking the minimum value of χ, or tightening the threshold. In contrast, the load-bearing criterion of this invention, which couples composition-dependent morphology with a measure of distribution inhomogeneity, is necessary to achieve complete coverage of two independent failure pathways in metastable compatibility. It should be noted that this theoretical analysis aims to explain the mechanism and non-obviousness of the criterion of this invention and does not represent a quantitative conclusion for any specific real system. In practice, for specific blend systems, the above mechanism and effects can be further verified through molecular dynamics simulations and criterion calculations described in the foregoing embodiments of this invention, supplemented by corresponding experimental controls.

[0057] Comparison of the single χ² criterion in Example 1 and the composite criterion of this invention – demonstrating inventiveness This comparative example is used to illustrate the differences and functions of the present invention compared to the existing single χ criterion.

[0058] For the same blend system as in Example 1, existing methods typically calculate a scalar χ value under a single representative composition, such as an equal proportion composition φ_A=0.5, and compare this scalar χ with a compatibility threshold: if χ is lower than the threshold, it is considered compatible. Using the exemplary value obtained in step four of Example 1, the system calculates χ=0.35 under the examined composition, which is lower than the compatibility threshold χ_c=0.5. Therefore, according to the existing single χ criterion, it will be considered compatible, and no phase separation indication will be given.

[0059] In Example 1 of this invention, for the same system, while χ meets the standard (χ=0.35<χ_c), the composition-dependent morphology of χ(φ_A) is further examined. It is found that it has a minimum value within the threshold range and satisfies the non-monotonic condition. It is also a measure of the non-uniformity of the local contact number distribution, with a coefficient of variation CV=0.6>CV_th=0.4. According to the coupling criterion, the system is determined to be metastable and compatible, and a phase separation warning is output.

[0060] As can be seen from this comparison, for systems that might be deemed compatible by existing single χ² criteria and thus potentially missed, this invention can further identify their phase separation tendency and provide early warning based on the coupling of composition-dependent morphology and local spatial inhomogeneity. It should be noted that the numerical values ​​used for comparison are exemplary values ​​demonstrating the differences in the criteria. The compatibility determination results for specific systems need to be determined in conjunction with actual calculations and experimental verification of that system. This comparative example aims to illustrate the difference in the determination logic between the two criteria, rather than providing measured comparison data for a specific system.

[0061] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for screening the compatibility of polymer blends using molecular dynamics simulations, characterized in that, The method includes the following steps: Construct molecular models of at least two polymer chains, and establish molecular simulation models of the blending systems under each blending composition according to multiple different blending compositions; Molecular dynamics simulations were performed on the molecular simulation models of each blend system. The mixing free energy and Florey-Hutchins interaction parameter χ of the blend system under each blend composition were calculated from the simulation trajectory to obtain the composition dependence of the Florey-Hutchins interaction parameter χ with the blend composition. Based on the trajectories simulated by molecular dynamics, the spatial distribution of local interactions between dissimilar polymer chains in each blend system is statistically analyzed, and a distribution non-uniformity metric characterizing the degree of non-uniformity in the spatial distribution of the local interactions is determined. Based on the coupling relationship between the composition dependence pattern reflected by the composition dependence relationship and the distribution non-uniformity measure, the compatibility range and phase separation tendency of the blend system are determined, and the blend formulation is screened accordingly. Specifically, when the Florey-Huggins interaction parameter χ is within a preset compatibility determination threshold, the composition-dependent morphology satisfies a preset non-monotonic condition, and the distribution non-uniformity measure exceeds a preset non-uniformity threshold, the corresponding blend composition is determined to be metastable and compatible, and a phase separation tendency warning is output.

2. The method according to claim 1, characterized in that, The composition-dependent morphology includes at least one of the following: whether the curve of the Florey-Hutchins interaction parameter χ as a function of blend composition reaches a minimum, the sign of the curvature of the curve, and the difference between the Florey-Hutchins interaction parameter χ at the two end compositions and the middle composition. The non-monotonic condition is that the curve exhibits a minimum value or the curvature sign reverses when the Florey-Hutchins interaction parameter χ is within the blend composition range that is within the compatibility determination threshold.

3. The method according to claim 1, characterized in that, The local interactions include at least one of the following: contact between heterogeneous polymer chain segments, hydrogen bonding, and electrostatic interactions; The measure of uneven distribution is obtained by statistically analyzing the spatial dispersion of the number or intensity of the local interactions in each local region, and includes at least one of the following: the variance of the number or intensity, the coefficient of variation, and the cluster size distribution.

4. The method according to claim 3, characterized in that, The method of statistically analyzing the spatial distribution of local interactions between dissimilar polymer chains in each blend system includes: dividing the simulation box of the molecular simulation model into multiple local regions, statistically analyzing the number or intensity of local interactions between dissimilar polymer chains in each local region, and obtaining the spatial distribution of the local interactions in each local region.

5. The method according to claim 1, characterized in that, The mixing free energy is calculated from the cohesive energy density of each blend system and each pure component system using the mixing energy relationship; the Florey-Hutchins interaction parameter χ is calculated from the mixing energy, the characteristic volume of the blend system, and the temperature of the molecular dynamics simulation; the multiple distinct blend compositions take at least three composition points within the composition range of 0 to 1, and the at least three composition points include the end-enriched compositions and at least one intermediate composition.

6. The method according to claim 1, characterized in that, The molecular model can be an all-atom model or a coarse-grained model; when the molecular model is a coarse-grained model, the spatial distribution of the local interactions is characterized by the number of contacts between the coarse-grained beads.

7. The method according to claim 1, characterized in that, The determination based on the coupling relationship between the composition-dependent morphology and the distribution non-uniformity metric includes: The feature quantity of the composition-dependent morphology is weighted and combined with the distribution non-uniformity measure to form a composite compatibility index; The composite compatibility index is compared with a preset grading threshold, and the grading result of compatibility, metastable compatibility, or incompatibility is output.

8. The method according to claim 7, characterized in that, The method further includes: For the blend formulation to be screened, the composite compatibility index of the blend formulation to be screened is calculated according to the steps described in claim 1, and the blend formulations whose composite compatibility index reaches the preset compatibility criterion are output as candidate compatible formulations. For the candidate compatible formulation, the blending composition or molecular dynamics simulation temperature is changed in the molecular simulation model, the composite compatibility index is recalculated, and the composition boundary and temperature boundary of the compatibility range of the candidate compatible formulation are determined. For blends that are determined to be metastable and compatible, the chemical structure, chain length, or blending ratio of at least one of the at least two polymer chains is adjusted, and the steps are repeated until the composite compatibility index reaches the preset compatibility criterion, and the adjusted blend formulation is output.

9. A polymer blend compatibility screening system based on molecular dynamics simulation, characterized in that, The system includes: The modeling module is used to construct molecular models of at least two polymer chains and to establish molecular simulation models of blending systems under each blending composition according to multiple different blending compositions. The simulation and parameter calculation module is used to perform molecular dynamics simulations on the molecular simulation models of each of the blend systems, calculate the mixing free energy and Florey-Hutchins interaction parameter χ of the blend system under each blend composition from the simulation trajectory, and obtain the composition dependence of the Florey-Hutchins interaction parameter χ with the blend composition. The distribution statistics module is used to statistically analyze the spatial distribution of local interactions between dissimilar polymer chains in each blend system based on the trajectories simulated by the molecular dynamics, and to determine a distribution non-uniformity metric that characterizes the degree of non-uniformity in the spatial distribution of the local interactions. The compatibility determination module is used to determine the compatibility range and phase separation tendency of the blend system and screen the blend formulation based on the coupling relationship between the composition dependence mode reflected by the composition dependence relationship and the distribution non-uniformity measure; and when the Florey-Hutchins interaction parameter χ is within a preset compatibility determination threshold, the composition dependence mode satisfies a preset non-monotonic condition, and the distribution non-uniformity measure exceeds a preset non-uniformity threshold, the corresponding blend composition is determined to be metastable and compatible, and a phase separation tendency warning is output.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the polymer blend compatibility screening method based on molecular dynamics simulation as described in any one of claims 1 to 8.

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