Thermal Stability of Caffeine Molecules and Thermodynamics of High-Temperature Sublimation

1. Governing Equations of Heat Transfer and Energy Balance in the Roasting Process

Coffee roasting is a highly complex thermodynamic process, where physicochemical changes within the green coffee beans are determined by the efficiency of energy transfer inside the drum. The total heat absorbed by the beans during roasting is defined as the sum of conduction, convection, and radiation. The energy balance equation that determines the Rate of Rise (RoR) at the core of the bean is expressed as follows:

$ m C_p \frac{dT_s}{dt} = q_{cond} + q_{conv} + q_{rad} - Q_{evap} + Q_{rxn} $

Here, each term represents the following physical meanings:

• $q_{cond} = -k A abla T$: Direct conductive heat transfer between the drum surface and the coffee bean particles.
• $q_{conv} = h A (T_g - T_s)$: Convective heat transfer between the airflow and the bean surface, where the convection coefficient $h$ acts as the driving force in the latter stage of roasting.
• $q_{rad} = \epsilon \sigma A (T_{surr}^4 - T_s^4)$: The process of radiant energy emitted from the heated drum walls being absorbed by the beans.
• $Q_{evap} = \frac{dm_w}{dt} \Delta H_{vap}$: The massive latent heat consumed for water evaporation during the initial drying phase.
• $Q_{rxn}$: The enthalpy change occurring during Maillard reactions and chlorogenic acid thermal decomposition; precise control is required, especially in the exothermic reaction zone near 200°C.

2. Modeling the Glass Transition Temperature $(T_g)$ and Cell Wall Structure Phase Transition

Green beans maintain a glassy state in a dry environment and transition into a rubbery state as moisture acts as a plasticizer. At this point, the glass transition temperature $(T_g)$ can be predicted by the Gordon-Taylor relation:

$ \frac{1}{T_g} = \frac{w_1}{T_{g1}} + \frac{w_2}{T_{g2}} $

At the beginning of roasting, when the moisture content $(w)$ is high, $T_g$ remains low, facilitating plastic deformation of the cell walls. However, as roasting progresses and moisture evaporates rapidly, $T_g$ increases, and the structure becomes highly brittle. The porous structure formed at this point is within the range of approximately $\epsilon \approx 0.3 \sim 0.5$, which plays a decisive role in the diffusion path of chlorogenic acid and the release of final flavor compounds.

3. Thermal Decomposition Pathways of Chlorogenic Acid (CGA) and Chemical Products

Chlorogenic acid (CGA), which modulates the acidity and bitterness of coffee, undergoes its most active decomposition between 160°C and 200°C during roasting. The thermal decomposition of CGA proceeds through the following pathway, converting into quinic acid and caffeic acid. This process is sensitive to temperature changes, and the spectrum of acidity changes as the roasting time increases.

Temperature Range	Major Chemical Reaction	Product Characteristics
160°C ~ 180°C	CGA Hydrolysis	Quinic acid (Acidity) and Caffeic acid (Body) generation
190°C ~ 210°C	Lactonization	Quinic acid lactones (Moderate bitterness)
210°C and above	Phenylindane polymerization	Phenylindanes (Very strong, unpleasant bitterness)

Phenylindanes generated during the dark roast stage are condensed structures resulting from the thermal decomposition of quinic acid lactones, making bitterness perceptible even at very low thresholds. Consequently, the core of roasting science lies in controlling the $Q_{rxn}$ of the energy balance equation to guide CGA toward the quinic acid range for optimal acidity and sweetness, or applying physical temperature profiling to suppress the excessive formation of phenylindanes. Since heat transfer efficiency varies with internal porosity changes after the first crack—the point where cell structure brittleness is maximized—the precise control of the convective heat transfer coefficient to regulate the speed of thermal decomposition is essential for high-quality roasting.