Image and video-capturing technologies have permeated our every-day life. Such technologies can continuously monitor individuals' expressions in real-life settings, affording us new insights into their emotional states and transitions, thus paving the way to novel well-being and healthcare applications. Yet, due to the strong privacy concerns, the use of such technologies is met with strong skepticism, since current face-based emotion recognition systems relying on deep learning techniques tend to preserve substantial information related to the identity of the user, apart from the emotion-specific information. This paper proposes an adversarial learning framework which relies on a convolutional neural network (CNN) architecture trained through an iterative procedure for minimizing identity-specific information and maximizing emotion-dependent information. The proposed approach is evaluated through emotion classification and face identification metrics, and is compared against two CNNs, one trained solely for emotion recognition and the other trained solely for face identification. Experiments are performed using the Yale Face Dataset and Japanese Female Facial Expression Database. Results indicate that the proposed approach can learn a convolutional transformation for preserving emotion recognition accuracy and degrading face identity recognition, providing a foundation toward privacy-aware emotion recognition technologies.