Particle and field-theoretic simulations are both commonly used methods to study the equilibrium properties of polymeric materials. Yet despite the formal equivalence of the two methods, no comprehensive comparisons of particle and field-theoretic simulations exist in the literature. In this work, we seek to fill this gap by performing a systematic and quantitative comparison of particle and field-theoretic simulations. In our comparison, we consider four representative polymeric systems: a homopolymer melt/solution, a diblock copolymer melt, a polyampholyte solution, and a polyelectrolyte gel. For each of these systems, we first demonstrate that particle and field-theoretic simulations are equivalent and yield exactly the same results for the pressure and the chemical potential. We next quantify the performance of each method across a range of different conditions including variations in chain length, system density, interaction strength, system size, and polymer volume fraction. The outcome of these calculations is a comprehensive look into the performance of each method and the systems and conditions when either particle or field-theoretic simulations are preferred. We find that field-theoretic simulations are equal to or faster than particle simulations for nearly all of the systems and conditions examined. In many situations, field-theoretic simulations are several orders of magnitude faster than particle simulations, especially if the polymer chains are long, the system density is high, and long-range Coulombic interactions are present. We also demonstrate that field-theoretic simulations are considerably faster at calculating the chemical potential and bypass the challenges associated with particle-based Widom insertion techniques. Taken together, our results provide quantitative evidence that field-theoretic simulations can reach and sample equilibrium considerably faster than particle simulations while simultaneously producing equivalent results.

中文翻译：

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粒子和场论模拟的定量等效性和性能比较


粒子模拟和场论模拟都是研究聚合物材料平衡特性的常用方法。然而，尽管这两种方法在形式上等效，但文献中并不存在粒子和场论模拟的全面比较。在这项工作中，我们试图通过对粒子和场论模拟进行系统和定量的比较来填补这一空白。在我们的比较中，我们考虑了四种具有代表性的聚合物系统：均聚物熔体/溶液、二嵌段共聚物熔体、聚两性电解质溶液和聚电解质凝胶。对于这些系统中的每一个，我们首先证明粒子和场论模拟是等效的，并且对压力和化学势产生完全相同的结果。接下来，我们量化了每种方法在一系列不同条件下的性能，包括链长、系统密度、相互作用强度、系统尺寸和聚合物体积分数的变化。这些计算的结果是全面了解每种方法的性能以及首选粒子或场论模拟的系统和条件。我们发现，对于几乎所有所研究的系统和条件，场论模拟等于或更快于粒子模拟。在许多情况下，场论模拟比粒子模拟快几个数量级，尤其是在聚合物链很长、系统密度高并且存在长程库仑相互作用的情况下。我们还证明，场论模拟在计算化学势方面要快得多，并绕过了与基于粒子的 Widom 插入技术相关的挑战。 综上所述，我们的结果提供了定量证据，证明场论模拟可以比粒子模拟更快地达到和采样平衡，同时产生等效的结果。