Panyukov Sergey, Zhulina Ekaterina B, Sheiko Sergei S, Randall Greg C, Brock James, Rubinstein Michael
P. N. Lebedev Physics Institute, Russian Academy of Sciences, Moscow, Russia.
J Phys Chem B. 2009 Mar 26;113(12):3750-68. doi: 10.1021/jp807671b.
Molecular bottle-brushes are highly branched macromolecules with side chains densely grafted to a long polymer backbone. The brush-like architecture allows focusing of the side-chain tension to the backbone and its amplification from the pico-Newton to nano-Newton range. The backbone tension depends on the overall molecular conformation and the surrounding environment. Here we study the relation between the tension and conformation of the molecular brushes in solutions, melts, and on substrates. In solutions, we find that the backbone tension in dense brushes with side chains attached to every backbone monomer is on the order of f(0)N(3/8) in athermal solvents, f(0)N(1/3) in theta solvents, and f(0) in poor solvents and melts, where N is the degree of polymerization of side chains, f(0) approximately equal k(B)T/b is the maximum tension in side chains, b is the Kuhn length, k(B) is Boltzmann's constant, and T is the absolute temperature. Depending on the side chain length and solvent quality, molecular brushes develop tension on the order of 10-100 pN, which is sufficient to break hydrogen bonds. Significant amplification of tension occurs upon adsorption of brushes onto a substrate. On a strongly attractive substrate, maximum tension in the brush backbone is approximately f(0)N, reaching values on the order of several nano-Newtons, which exceeds the strength of a typical covalent bond. At low grafting density and high spreading parameter, the cross-sectional profile of an adsorbed molecular brush is approximately rectangular with a thickness approximately b (A/S)1/2, where A is the Hamaker constant, and S is the spreading parameter. At a very high spreading parameter (S > A), the brush thickness saturates at monolayer approximately b. At a low spreading parameter, the cross-sectional profile of adsorbed molecular brush has a triangular tent-like shape. In the cross-over between these two opposite cases, covering a wide range of parameter space, the adsorbed molecular brush consists of two layers. Side chains in the lower layer gain surface energy due to the direct interaction with the substrate, while the second layer spreads on the top of the first layer. Scaling theory predicts that this second layer has a triangular cross-section with width R approximately N(3/5) and height h approximately N(2/5). Using self-consistent field theory we calculate the cap profile y(x) = h(1 - x2/R2)2, where x is the transverse distance from the backbone. The predicted cap shape is in excellent agreement with both computer simulation and experiment.
分子刷是高度支化的大分子，其侧链密集地接枝到一条长聚合物主链上。刷状结构允许将侧链张力集中到主链上，并将其从皮牛顿范围放大到纳牛顿范围。主链张力取决于整体分子构象和周围环境。在此，我们研究了分子刷在溶液、熔体和基底上的张力与构象之间的关系。在溶液中，我们发现，对于侧链连接到每个主链单体的致密刷，在无热溶剂中主链张力约为(f(0)N^{3/8})，在(\theta)溶剂中约为(f(0)N^{1/3})，在不良溶剂和熔体中约为(f(0))，其中(N)是侧链的聚合度，(f(0)\approx k_{B}T/b)是侧链中的最大张力，(b)是库恩长度，(k_{B})是玻尔兹曼常数，(T)是绝对温度。根据侧链长度和溶剂性质，分子刷产生的张力在(10 - 100)皮牛顿量级，这足以破坏氢键。当刷吸附到基底上时，张力会显著放大。在强吸引性基底上，刷主链中的最大张力约为(f(0)N)，达到几纳牛顿量级的值，这超过了典型共价键的强度。在低接枝密度和高铺展参数下，吸附分子刷的横截面轮廓近似为矩形，厚度约为(b(A/S)^{1/2})，其中(A)是哈梅克常数，(S)是铺展参数。在非常高的铺展参数((S > A))下，刷的厚度在单层时饱和，约为(b)。在低铺展参数下，吸附分子刷的横截面轮廓呈三角形帐篷状。在这两种相反情况之间的过渡区域，涵盖了广泛的参数空间，吸附的分子刷由两层组成。下层的侧链由于与基底的直接相互作用而获得表面能，而第二层则铺展在第一层之上。标度理论预测，这第二层具有三角形横截面，宽度(R)约为(N^{3/5})，高度(h)约为(N^{2/5})。使用自洽场理论，我们计算出帽状轮廓(y(x)=h(1 - x^{2}/R^{2})^{2})，其中(x)是距主链的横向距离。预测的帽状形状与计算机模拟和实验结果都非常吻合。
