Graphene has exceptional electronic, mechanical, and thermal properties, and it is expected to have important applications in integrated circuits and other microelectronic fields. Its performances are greatly affected by surface adhesion force when it is used in a humid environment. In this paper, based on the law of variable water contact angle changing in the process of water vapor condensation, we established a cone−plane contact model, which is related to relative humidity and dwell time, to reveal the internal mechanism of the influence of relative humidity and dwell time on silica/graphene adhesion force. First, the silica/graphene adhesion force dependence of dwell time was measured by atomic force microscopy (AFM) at 45−85% RH. Then, the changing process of the meniscus between the AFM tip and the graphene surface was discussed, and the function of adhesion force with variables of dwell time and contact angle was established. Furthermore, the theoretical and experimental results were compared and analyzed. The results show that with the increase of relative humidity and dwell time, the capillary condensation increases, but the water contact angle of the cone material decreases. This causes the adhesion force to increase first and then decrease after it reaches a threshold value. Furthermore, the variable water contact angle of the graphene surface increases, but the adhesion force decreases gradually with the increase of surface water film. The theoretical results are in good agreement with the experimental results.

There are many cylinder–plane contacts in microaccelerators, microgyroscopes, and RF switches. Adhesion is one of the main factors affecting the manufacture and use of these micro–nano devices, but its research is insufficient. Graphene is expected to be used in these fields due to its excellent electrical and mechanical properties. Therefore, it is significant to research the adhesion force of graphene under cylinder–plane. Firstly, the meniscus formation process was introduced using the variable-water-contact-angle method. Secondly, the adhesion force of the graphene surface was measured with a cylindrical atomic-force-microscope probe. Finally, the contact area was considered as a number of nanoscale cylinders in contact with the plane, and the adhesion force of the cylinder–plane model was obtained. The results showed that there was a maximum adhesion force at a relative humidity of 65%. The adhesion force was evidently not time-dependent when the relative humidity was below 45%, because the meniscus cannot be formed on the graphene surface at low relative humidity. While the graphene contact surface formed a meniscus for higher relative humidity, and the adhesion force-versus-time curves first increased and then decreased to stability. Moreover, the relationship between adhesion force and substrate contact angle, roughness, relative humidity, and dwell time was established, and the number of cylinders was determined. The error between the modified theoretical model and the experimental values was only 6%.