Kaiser Andreas, Babel Sonja, ten Hagen Borge, von Ferber Christian, Löwen Hartmut
Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany.
J Chem Phys. 2015 Mar 28;142(12):124905. doi: 10.1063/1.4916134.
We study the swelling of a flexible linear chain composed of active particles by analytical theory and computer simulation. Three different situations are considered: a free chain, a chain confined to an external harmonic trap, and a chain dragged at one end. First, we consider an ideal chain with harmonic springs and no excluded volume between the monomers. The Rouse model of polymers is generalized to the case of self-propelled monomers and solved analytically. The swelling, as characterized by the spatial extension of the chain, scales with the monomer number defining a Flory exponent ν which is ν = 1/2, 0, 1 in the three different situations. As a result, we find that activity does not change the Flory exponent but affects the prefactor of the scaling law. This can be quantitatively understood by mapping the system onto an equilibrium chain with a higher effective temperature such that the chain swells under an increase of the self-propulsion strength. We then use computer simulations to study the effect of self-avoidance on active polymer swelling. In the three different situations, the Flory exponent is now ν = 3/4, 1/4, 1 and again unchanged under self-propulsion. However, the chain extension behaves non-monotonic in the self-propulsion strength.
我们通过解析理论和计算机模拟研究了由活性粒子组成的柔性线性链的膨胀情况。考虑了三种不同的情形：自由链、限制在外部简谐势阱中的链以及一端被拖动的链。首先，我们考虑一个具有简谐弹簧且单体之间无排除体积的理想链。聚合物的Rouse模型被推广到自推进单体的情形并进行了解析求解。以链的空间伸展来表征的膨胀，与定义弗洛里指数ν的单体数成比例，在三种不同情形下，ν分别为1/2、0、1。结果，我们发现活性并不改变弗洛里指数，但会影响标度律的前置因子。通过将该系统映射到具有更高有效温度的平衡链上，可以定量地理解这一点，使得链在自推进强度增加时膨胀。然后，我们使用计算机模拟来研究自回避对活性聚合物膨胀的影响。在这三种不同情形下，弗洛里指数现在分别为ν = 3/4、1/4、1，并且在自推进下再次保持不变。然而，链的伸展在自推进强度方面表现出非单调行为。
