Shape variation of linear polymers upon phase separation in a ternary solution
Shape variation of linear polymers upon phase separation in a ternary solution
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DOI：
10.1021/ma034506o
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发表时间：
2003-10-21
期刊：
影响因子：
5.5
通讯作者：
Luijten, E
中科院分区：
文献类型：
--
作者：
Guo, L;Luijten, E
库恩在70年前就认识到柔性聚合物链的典型形状是椭圆形而不是球形。 1 这种形状各向异性除了是一种基本性质外，还具有相当大的科学和技术重要性，影响着多种聚合物性质。例如，有人提出它会影响聚合物流体的流动特性2，并且最近证明3聚合物非球面性可以解释在胶体-聚合物混合物中观察到的聚合物诱导的耗尽电势。 4 因此，无规行走 (RW) 和自避行走 (SAW) 聚合物的形状已通过分析和模拟进行了广泛研究。 5-9 最近，在实验中实际上观察到了不对称形状。 10, 11 然而，应该指出的是，实验以及绝大多数理论工作都集中在高度稀溶液中单个线圈的形状。对浓度作用的研究很少，并且基本上表明，对于非热链的均匀溶液，随着浓度的增加，非球面性仅非常缓慢地减小。 12, 13 在不良溶剂中，观察到相反的效果， 14 这主要是由于在贫聚合物相中发生了卷曲-球状转变。显然，结构和热力学性质密切相关，这促使我们研究更复杂的相图中的形状变化。在本说明中，我们讨论了三元溶液中聚合物的线圈形状，该三元溶液由两种聚合物物质（用 A 和 B 表示）和溶剂 (S) 组成。我们特别关注该系统中聚合物-聚合物分离的影响，并通过蒙特卡罗模拟对其进行了研究。研究发现，这种相变确实对聚合物的形状有显着的影响，其特征在于回转半径张量Q的特征值λ1 e λ2 e λ3，定义为5, 15，其中ri代表链上第i个单体的位置，R,) 1, 2, 3表示笛卡尔分量，N是聚合物的聚合度。三个特征值之和等于回转半径 Rg 2 的平方。一个重要的度量是非球面度 A6、9、16、17，其中括号表示整体平均值。 18 A 取0（球体）和1（棒）之间的值。在稀释极限下，它接近 N f∞ 的通用值，根据一阶 ϵ 展开估计为 0.415，根据模拟估计为 0.431。 9, 19, 20 在熔体极限下，链表现理想，该值预计会降低到（确切已知的）RW 值 0.39427.... 17
It was recognized by Kuhn 70 years ago that the typical shape of a flexible polymer chain is ellipsoidal rather than spherical. 1 This shape anisotropy, besides being a fundamental property, is of considerable scientific and technological importance, affecting a variety of polymer properties. For example, it has been proposed that it influences the flow properties of polymeric fluids, 2 and recently it was demonstrated3 that the polymer asphericity can account for the polymer-induced depletion potential observed in colloid-polymer mixtures. 4 Accordingly, the shape of random-walk (RW) and selfavoiding-walk (SAW) polymers has been studied extensively both analytically and by simulations. 5-9 Very recently, the asymmetric shape has actually been observed in experiments. 10, 11 However, it should be noted that the experiments, as well as the vast majority of the theoretical work, focus on the shape of a single coil in a highly dilute solution. Studies of the role of concentration are rare and have essentially shown that, for a homogeneous solution of athermal chains, the asphericity diminishes only very slowly upon increasing concentration. 12, 13 In a poor solvent, the reverse effect was observed, 14 which is essentially due to the coil-globule transition taking place in the polymer-lean phase. Clearly, structural and thermodynamic properties are intimately connected, which has motivated us to investigate shape variations within a more complicated phase diagram. In this Note, we discuss the coil shapes of polymers in a ternary solution, consisting of two polymer species (denoted by A and B) and a solvent (S). In particular, we focus on the effect of polymer-polymer separation in this system, which we have investigated by means of Monte Carlo simulations. It is found that this phase transition indeed has a dramatic effect on the polymer shape, which is characterized by the eigenvalues λ1 e λ2 e λ3 of the radius-of-gyration tensor Q, defined as5, 15 where ri represents the position of the ith monomer along the chain, R,) 1, 2, 3 denote Cartesian components, and N is the degree of polymerization of the polymer. The sum of the three eigenvalues equals the squared radius of gyration Rg 2. An important measure is the asphericity A6, 9, 16, 17 where the brackets indicate the ensemble average. 18 A takes values between 0 (sphere) and 1 (rod). In the dilute limit it approaches a universal value for N f∞, estimated as 0.415 from first-order ϵ expansions and as 0.431 from simulations. 9, 19, 20 In the melt limit, where the chains behave ideally, this value is anticipated to decrease to the (exactly known) RW value 0.39427.... 17