作为一种重要的材料形式，薄膜材料在科研和日常生活中均有着广泛的应用。薄膜材料最显著的几何特征是一个维度的尺寸远小于另外两个维度，这也使其具有较小的弯曲刚度，在面外载荷作用下极易变形。石墨烯等二维材料和磷脂分子层等生物材料的表观厚度较小且比表面积较大，因此也被视作重要的薄膜材料。然而由于其厚度方向原子层数较少，它们的表面形貌和变形还会受到温度等热力学因素的影响，进而使物理性质发生相应的改变。为了减少环境因素对于薄膜性能的影响，它们的使用经常需要衬底材料作为支撑。由于薄膜的比表面积较大，薄膜与衬底间结合和黏附的能量将成为调控其行为的重要因素。因此，针对薄膜与衬底间界面作用的研究是非常必要的。本文基于此，以石墨烯和磷脂分子层作为薄膜材料的代表，开展了以下几个方面的研究：

（1）石墨烯的弯曲刚度较小，因此在温度和载荷的影响下表面会产生褶皱。本文通过分子动力学模拟和统计力学分析，研究了温度对于支撑石墨烯表面波动的影响。同时结合模拟与理论分析可知，由温度带来的形貌改变会影响石墨烯与衬底间的平衡距离，进而影响石墨烯与衬底间黏附的强度和作用的范围。由于磷脂分子层表面也存在热波动，表面形貌的影响也可延伸至磷脂分子层与衬底间的黏附过程。

（2）鼓泡测试是测定石墨烯与衬底间黏附强度的重要方法，该方法通过测定石墨烯鼓泡的特征尺寸来获取界面黏附能。基于此测试方法，本文首先建立了考虑边缘黏附与滑移的薄膜鼓泡方程，并通过有限差分方法进行求解。之后借助该数值解，建立石墨烯鼓泡前后衬底空腔内压强的关系，并最终预测了更为精确的石墨烯鼓泡的几何特征。

（3）界面上的黏附与结合对于石墨烯的制备有重要作用。具有高指数晶面的单晶铜箔是制备优质石墨烯的重要衬底材料，本文首先研究了界面作用对于其可控制备的意义。当以石墨为衬底对多晶铜箔进行高温退火时，由于铜箔与石墨衬底的热膨胀系数存在差异，在界面的束缚作用下，铜箔内部会产生热应力。通过理论分析可知，此时靠近Cu(100)晶面的高指数晶面晶粒具有能量优势，更容易发生长大。本文从理论计算的角度阐述了对石墨上多晶铜箔进行高温退火，制备高指数晶面单晶铜箔这一方法的可行性。制备得到的高指数晶面单晶铜箔表面不仅存在本征的铜原子台阶，还会存在滑移线。这些滑移线与石墨烯晶畴边缘的相互作用也会影响石墨烯的生长取向，从而说明石墨烯的生长方向一致性不仅取决于衬底的晶面取向和对称性，还会受到晶体表面缺陷的影响。

As an important form of materials, membranes are widely used during scientific researches and our daily lives. The most distinguishing geometric feature of membranes is that the size of one dimension is much smaller than the others, which consequently lowers their bending stiffness. And, as a result, it is easier for them to deform under the loads normal to their surfaces. Two-dimensional materials and biological membranes, including graphene and lipid bilayers, are also considered membranes owing to their small apparent thickness and large specific area. However, as they are composed merely of a few atomic layers, their morphologies often change along with the temperature variation in the environment, which will further induce changes of their physical properties. In order to reduce the influence of environmental conditions on the membranes, they are often supported by a substrate when put into application. The interfacial interactions between a membrane and the supporting substrate are important factors manipulating its mechanical behavior and physical properties, which makes it of great significance to look into the interactions at their interface. Consequently, taking graphene and lipid bilayers as representatives of membranes, the researches were mainly focused on the following issues:

(1) Due to the low bending stiffness, graphene ripples under the influence of temperature and loads. In the current work, the influence of temperature on the surface fluctuation of a supported graphene was studied by molecular dynamics simulations and statistical mechanics analysis. It was also found that the thermally induced morphological changes will affect the average distance between a graphene sheet and its substrate, and as a result, will further affect the strength and range of the adhesion at the interface. Thermal fluctuations also exist on the surface of lipid bilayers. The adhesion between lipid bilayers and their substrates could also be modulated by their morphologies.

(2) Blister test is an important method to measure the adhesion between graphene and the substrate. The typical sizes of a graphene blister are measured and used to determine the interfacial interaction strength. To improve the accuracy of the method, equations of a blistered membrane were established, considering both the adhesion and the sliding at the blister edge. The equations were solved by finite difference method, with which the pressure within the caivities in the substrate before and after the blistering process were acquired. Finally, a more precise morphology of a graphene blister could be predicted.

(3) The interfacial interaction and binding are also crucial for the preparation of graphene. In this part, we first demonstrated the importance of interfacial interactions on the controllable preparation of single crystal copper foils with high index crystal facets, which are of great importance for preparing graphene of high-quality. When a polycrystalline copper foil, supported by a graphite substrate, is annealed at a high temperature, thermal stress will be induced. This is a comprehensive effect of their different thermal expansion coefficients and interfacial interaction. It can be inferred from the theoretical analysis that single crystals with high index facets close to Cu(100) crystal plane retain an advantage of lower strain energy density and are more likely to grow continuously. Here we took out theoretical analysis to prove that it is feasible to prepare a single crystal copper foil with high index facets by annealing a polycrystalline copper foil supported by a graphite substrate. It should be noted that on the high index facets, there exist not only intrinsic steps, but also slip lines. These slip lines are able to guide the growth of graphene as well, which is resulted from the binding between the atomic steps and the edges of the graphene domain. The orientation of the graphene prepared depends on both the symmetry and the defects on the surfaces of the substrates.