Departamento de Física, Universidade Federal do Ceará, Fortaleza, Ceará, Brazil.
Laboratório de Ciência de Dados e Inteligência Artificial, Universidade de Fortaleza, Fortaleza, Ceará, Brazil.
PLoS One. 2024 Mar 7;19(3):e0299296. doi: 10.1371/journal.pone.0299296. eCollection 2024.
Stressed soft materials commonly present viscoelastic signatures in the form of power-law or exponential decay. Although exponential responses are the most common, power-law time dependencies arise peculiarly in complex soft materials such as living cells. Understanding the microscale mechanisms that drive rheologic behaviors at the macroscale shall be transformative in fields such as material design and bioengineering. Using an elastic network model of macromolecules immersed in a viscous fluid, we numerically reproduce those characteristic viscoelastic relaxations and show how the microscopic interactions determine the rheologic response. The macromolecules, represented by particles in the network, interact with neighbors through a spring constant k and with fluid through a non-linear drag regime. The dissipative force is given by γvα, where v is the particle's velocity, and γ and α are mesoscopic parameters. Physically, the sublinear regime of the drag forces is related to micro-deformations of the macromolecules, while α ≥ 1 represents rigid cases. We obtain exponential or power-law relaxations or a transitional behavior between them by changing k, γ, and α. We find that exponential decays are indeed the most common behavior. However, power laws may arise when forces between the macromolecules and the fluid are sublinear. Our findings show that in materials not too soft not too elastic, the rheological responses are entirely controlled by α in the sublinear regime. More specifically, power-law responses arise for 0.3 ⪅ α ⪅ 0.45, while exponential responses for small and large values of α, namely, 0.0 ⪅ α ⪅ 0.2 and 0.55 ⪅ α ⪅ 1.0.
受应力的软物质通常表现出黏弹性特征，其形式为幂律或指数衰减。尽管指数响应最为常见，但幂律时间依赖性却在复杂软物质中奇特地出现，例如活细胞。理解在宏观尺度上驱动流变行为的微观机制，在材料设计和生物工程等领域将具有变革性。我们使用浸入粘性流体中的大分子的弹性网络模型，数值再现了这些特征黏弹性松弛，并展示了微观相互作用如何决定流变响应。大分子由网络中的粒子表示，通过弹簧常数 k 与相邻分子相互作用，并通过非线性阻力模式与流体相互作用。耗散力由γvα给出，其中 v 是粒子的速度，γ和α是介观参数。从物理上讲，阻力的次线性区域与大分子的微观变形有关，而α≥1 代表刚性情况。通过改变 k、γ和α，我们得到了指数或幂律松弛或它们之间的过渡行为。我们发现指数衰减确实是最常见的行为。然而，当大分子与流体之间的力是次线性时，可能会出现幂律。我们的研究结果表明，在不太软也不太硬的材料中，在次线性区域，流变响应完全由α控制。更具体地说，当 0.3 ⪅ α ⪅ 0.45 时，会出现幂律响应，而当 α 的值较小或较大时，即 0.0 ⪅ α ⪅ 0.2 和 0.55 ⪅ α ⪅ 1.0 时，会出现指数响应。
