Colorimetric Quick Response (QR) Tags and Other Time-Temperature Indicators (TTIs) for Remote Quality Assessment: Theoretical Kinetics Aspects

Abstract

The fast-growing use of quick-response tags (QRs), advances in colored inks synthesis for time-temperature integrators (TTIs), and spread of cloud computing, create new opportunities for remote in-situ quality assessments. If a color irreversible intensification or fading can be represented by a single colorimetric measure, such as Hue or vector in a color space, and if this transformation temperature-dependent kinetics and its parameters are also known, then a scanned and transmitted tag’s color coordinates at any time can be used to construct a single equivalent constant-temperature history and an infinite number of equivalent varying-temperature histories that would have produced the same colorimetric reading. A way to test such temperature histories equivalency is to have, at least initially, two different colors following two different transformation kinetics, and use one to predict, or at least approximate, the other’s reading. This is demonstrated with simulated colorimetric changes that follow zero-order kinetics, representing fixed order intensification, and Weibull (stretched exponential) intensification and fading, representing nonlinear kinetics. Both were tested by predicting readings not used in their equivalent temperature history construction. The simulations indicate that the traditional notion of a meaningful constant temperature equivalent existence might need reconsideration, especially for nonlinear color transformation kinetics. It is proposed to try low-degree polynomials as equivalent temperature profile model equations first, replaced by elaborate algebraic expressions or stochastic models if needed. Also demonstrated is how successive colorimetric readings from the same lot can be used to construct its almost-true external temperature history as judged by fit criteria.