## Using DSC for determination of heatinduced calorimetric parameters

DSC PRINCIPLE

DSC is powerful for monitoring physical state changes (liquid/solid) or molecular conformation or structural perturbations through the change of one thermo -dynamic parameter: temperature. Commercially available calorimeters working on the basis of different measuring principles (power compensation or heat flux calorimeters) measure a temperature difference that is linked to the energy changes involved during heat-induced reactions in sample materials .

In DSC, the furnace provides the same temperature programme to a sample pan (containing the material to be studied) and to a reference pan (containing a non-reacting material). If T0 is the starting temperature, the programmed temperature Tat time t, and constant heating rate, dT/ dt = P (°C s-1) is:

For ideally symmetri cal sample and reference pans this results in equality between the heat that flows through the instrument source to the sample and reference pans. If an endothermic or exothermic reaction occurs in the sample pan, the symmetry is disturbed, and there is a temperature difference (AT= Ts-Tr) between the reacting sample and non-reacting reference. The DSC measured signal, AT is proportional to the heat flow rates between the instrument source and sample (to be studied) and reference. Following Newton's law the rate at which heat is transferred from the instrument source, at temperature T, to the sample or to the reference is:

Where Tsr is the temperature of the sample (or reference), R is the thermal resistance (°C W-1), between symmetrical samples and holders. The rate of heat flow between the furnace and the sample pan when an exothermic (dH/dt < 0) or en-dothermic (dH/dt > 0) reaction occurs in the sample pan with heat capacity at constant pressure equal to Cs is:

dH/dt being the instantaneous heat absorbed (dH/dt > 0) or generated (dH/dt <0) by the reaction. The rate of heat flow between the furnace and reference with heat capacity at constant pressure equal to Cr, and for which dH/dt = 0 by definition, and dTr/dt = dT/dt = P (steady-state heating mode) is

Therefore, the relation between the reaction heat flow rate (dH/dt) and the measurement signal (AT = Ts-Tr) is dH/dt= - (AT/R) - (Cs-Cr) P - Cs d(A T) /dt (7)

This expression links the heat flow rate (dH/dt) caused by the temperature difference (AT) between the reacting sample and the non-reacting reference. It contains a first term assigned to this temperature difference, a second term due to differences between the heat capacities of sample and reference materials (initial deviation of the signal after reaching its quasi-steady state in scanning mode), and a third term taking into account the thermal inertia (x = RCs) of the sys tem when AT is detected.

In heat flux DSC system, operating with cylinder-type containers, thermocouples connected in series between the containers and the furnace measure the differential signal, AT as a voltage. In power compensation DSC, the temperature difference is 'compensated' by an additional increasing (endothermic reaction) or decreasing (exothermic reaction) heating power. In both DSC systems the measured temperatures and sample temperatures are different. There is a systematic temperature lag occurring in non steady-state condition and depending on instrument characteristics and operating conditions (temperature scanning rate, sample weight and heat capacity). The sample temperature is related to the programmed temperature and characteristic time constant (x):

R and x = RC are determined by calibration measurements from melting curves of pure standards. During melting of a pure standard:

Ts is constant dTJdt = 0 d(Ts-Tr)/dt = - dTJdt = p d2(Ts-Tr)/di2 = 0

Therefore, the thermal conductance (1/R) between sample holder and sample is deduced by application of Eq. 7, from melting curves of pure materials. It is determined from the slope of the linear increase in the heat flow rate with temperature. The determination of the sample heat capacity (mCs), before and after a thermal transition, may be performed  relatively to the heat capacity of a different sample with known heat capacity (mC). Pure water or synthetic sapphire is used for determination of sample heat capacity, following a three-step method, where calorimetric heat flow rates obtained from samples of known and unknown heat capacity (dH/dts and dH/dt') are determined after subtraction of the zero base line (two-empty pans):

In non steady-state conditions (AT # 0) the asymmetry between sample and reference sides introduces a complex dependence of heat capacities, scanning rates, and thermal resistances on the shape of DSC signal. From Eq. (7), the effects on dH/dt of DSC experimental conditions (scan rate, sample weight, thermal inertia) can be minimized by using sample and reference as similar as possible, in regards with their heat capacities and thermal resistances, and also a scanning rate as low as possible.

### DSC PARAMETERS

Calorimetric parameters associated with a thermal transition occurring in the sample pan are extracted from DSC signals after subtraction of zero DSC signal, obtained by using two pans filled with reference materials (buffer for study of transitions in protein solutions, or empty pans for fat samples). Temperature of transition mostly used is that of extrapolated peak onset (Textr), or peak maximum (Tmax), the temperature of the observed maximum deviation of the heat-flow signal, corresponding to approximatively 50% denaturation reaction. The area between the peak and a sample baseline drawn from temperatures corresponding to pre- and post-transitions (maximum amount sample materials in initial and final states, respectively), divided by the amount of reacting materials in the sample pan, is used to determine the apparent heat of reaction, Qcal, involved during the thermal transition. In the physico-chemical environmental conditions used for food preparation, thermal transitions observed for protein conformational changes occur without a significant shift between the pre- and

post-transition region, and approximation of a straight baseline drawn by interpolation between the beginning and the end points of the transition is mostly used.

Due to its relatively low characteristic time constants (<few seconds), power compensation DSC is used for determination of the fractional completion of reaction x (T), as a function of temperature T, from the pattern analysis of the heat flow involded during the scanning mode:

AT, is the apparent heat of reaction at temperature T, calculated from the partial area under the exothermal heat flow curve), and Qcal the calorimetric heat of reaction, calculated by using a straight base-line sample drawn between the initial and final deviations of the heat flow.

In the present study, this methodology is used to compare the growing-up of fat cryst als in non-emulsified fat samples and in emulsions which differed only by the nature of adsorbed proteins. 