Data-efficient methods for determining Flory–Huggins χ parameters in multicomponent polymer formulations

Polymer formulations are essential in diverse applications, including personal care products, coatings, paints, adhesives, and plastic materials. Designing these formulations requires navigating large, complex design spaces, where phase and self-assembly behavior critically impact performance. The Flory-Huggins $\chi$ parameter, which quantifies segmental miscibility, is widely used to parameterize the excess free energy of mixing in formulation models. In this work, we introduce two data-efficient, top-down methods for estimating $\chi$ parameters using the Random Phase Approximation (RPA): (i) Boundary Nonlinear Regression (Boundary-NLR), which fits theoretical spinodal boundaries to experimental phase boundaries, and (ii) Surrogate Model Inverse Parameter Estimation (SMIPE), which uses a Gaussian Process Classifier to fit sparse phase maps via a surrogate model. Both methods allow rapid parameterization of polymer field-theoretic models without the need for additional experiments. We..., , # Data from: Data-efficient methods for determining Flory–Huggins χ parameters in multicomponent polymer formulations

Dataset DOI: [10.5061/dryad.s1rn8pkmt](https://doi.org/10.5061/dryad.s1rn8pkmt)

## Description of the data and file structure

No experiments were conducted, and all results are from numerical computations. Experimental data that is included has been published elsewhere.

#### Files and variables

**Figure 1**

\* **`SK_data.csv`**: Data for the plot of inverse structure factors.

\* `k`: Wavevector in units of $1/R_g$, where $R_g$ is the radius of gyration.

\* `invdetSK_{x}`: The inverse of the determinant of the structure factor matrix (unitless).

\* `x`: The Flory-Huggins interaction parameter, $\chi$, which ranges from 0.06 to 0.12 in this dataset (unitless).

\* **`Ternary_data.csv`**: Data for the ternary phase diagram, showing the spinodal curve for a polymer-solvent-nonsolvent system.

\* `phiS`: Volume fraction of the solvent, $\phi_S$.

\* `phiP`: Volume fr...,

聚合物配方在个人护理产品、涂料、油漆、胶粘剂以及塑料材料等众多领域中均具有至关重要的应用价值。这类配方的开发需要在庞大且复杂的设计空间中进行探索，而相行为与自组装行为对最终性能具有决定性影响。弗洛里-哈金斯（Flory-Huggins）$chi$参数用于量化链段间的相容性，是配方模型中表征混合过剩自由能的常用参数。本研究提出了两种基于随机相近似（Random Phase Approximation, RPA）的高效数据驱动自上而下方法，用于估算$chi$参数：(i) 边界非线性回归（Boundary-NLR）：将理论旋节线边界拟合至实验相边界；(ii) 代理模型逆参数估计（SMIPE）：通过高斯过程分类器，借助代理模型对稀疏相图进行拟合。本研究提出的两种方法均无需开展额外实验，即可快速完成聚合物场论模型的参数化工作。[数据来源：多组分聚合物配方中弗洛里-哈金斯$chi$参数的高效测定方法]
数据集DOI：[10.5061/dryad.s1rn8pkmt](https://doi.org/10.5061/dryad.s1rn8pkmt)

### 数据与文件结构说明
本研究未开展任何实验，所有结果均来自数值计算；所包含的实验数据已在其他文献中发表。

#### 文件与变量说明
**图1**
* **`SK_data.csv`**：用于绘制逆结构因子曲线的数据集。
* `k`：以$1/R_g$为单位的波矢，其中$R_g$为回转半径。
* `invdetSK_{x}`：结构因子矩阵行列式的逆（无量纲）。
* `x`：弗洛里-哈金斯相互作用参数$chi$，本数据集内取值范围为0.06至0.12（无量纲）。
* **`Ternary_data.csv`**：用于绘制三元相图的数据集，展示了聚合物-溶剂-非溶剂体系的旋节线曲线。
* `phiS`：溶剂的体积分数$phi_S$。
* `phiP`：体积分...