Calorimetric and Microstructural Investigation of Frozen Hydrated Gluten

Abstract

The thermal and microstructural properties of frozen hydrated gluten were studied by using differential scanning calorimetry (DSC), modulated DSC, and low-temperature scanning electron microscopy (cryo-SEM). This work was undertaken to investigate the thermal transitions observed in frozen hydrated gluten and relate them to its microstructure. The minor peak that is observed just before the major endotherm (melting of bulk ice) was assigned to the melting of ice that is confined to capillaries formed by gluten. The Defay–Prigogine theory for the depression of melting point of fluids confined in capillaries was put forward in order to explain the calorimetric results. The pore radius size of the capillaries was calculated by using four different empirical models. Kinetic analysis of the growth of the pore radius size revealed that it follows first-order kinetics. Cryo-SEM observations revealed that gluten forms a continuous homogeneous and not fibrous network. Results of the present investigation showed that is impossible to assign a T _g value for hydrated frozen gluten because of the wide temperature range over which the gluten matrix vitrifies, and therefore the construction of state diagrams is not feasible at subzero temperatures for this material. Furthermore, the gluten matrix is deteriorated with two different mechanisms from ice recrystallization, one that results from the growth of ice that is confined in capillaries and the other from the growth of bulk ice.

Appendix

In the following, a modification of the Kelvin equation for the case of water that is confined in a pore and is surrounded by ice will be derived. The subscripts refer to Figure 1.

For a system in equilibrium with flat surfaces, the Gibbs–Duhem equation for each phase is:

$$ - S_{i} {\text{d}}T + V_{i} {\text{d}}P_{i} + n_{i} {\text{d}}\mu _{i} = 0 $$

(A1)

where S _i , V _i , n _i , and μ _i are the entropy, volume, number of moles, and chemical potential of phase i [where i designates gas (g), liquid (l) or solid (s)].

The system must also be in mechanical equilibrium and therefore the Laplace equation for the solid liquid interface is:

$$P_{{\text{s}}} - P_{{\text{l}}} = \kappa _{{{\text{sl}}}} \gamma _{{{\text{sl}}}} $$

(A2)

where κ _sl is a shape factor that relates to the interface curvature between solid and liquid phases and γ _sl the interfacial tension between the solid and liquid interfaces.

Because the solid–gas interface is flat the pressures on each side of the interface will be equal:

$$ P_{{\text{g}}} = P_{{\text{s}}} $$

(A3)

It is also known that at equilibrium the chemical potentials of each phase are equal:

$$ n_{{\text{s}}} \mu _{{\text{s}}} = n_{{\text{l}}} \mu _{{\text{l}}} = n_{{\text{g}}} \mu _{{\text{g}}} $$

(A4)

If the system passes from one equilibrium state to another neighboring equilibrium state, then:

$${\text{d}}P_{{\text{s}}} - {\text{d}}P_{{\text{l}}} = {\text{d}}{\left( {\kappa _{{{\text{sl}}}} \gamma _{{{\text{sl}}}} } \right)}{\text{ }}\,{\text{or }}\,{\text{d}}P_{{\text{l}}} = {\text{d}}P_{{\text{s}}} - {\text{d}}{\left( {\kappa _{{{\text{sl}}}} \gamma _{{{\text{sl}}}} } \right)}$$

(A5)

$$ {\text{d}}P_{{\text{g}}} = {\text{d}}P_{{\text{s}}} $$

(A6)

$$ n_{{\text{s}}} {\text{d}}\mu _{{\text{s}}} = n_{{\text{l}}} {\text{d}}\mu _{{\text{l}}} = n_{{\text{g}}} {\text{d}}\mu _{{\text{g}}} $$

(A7)

It is necessary to find a relation between the thermodynamic parameters that describe the system where all the above equations can be used in the analysis. Since the Gibbs–Duhem (GD) equations for each phase equal to zero at equilibrium, then it is valid to subtract GD_solid − GD_liquid and GD_gas − GD_solid. The first subtraction and use of Eqs. (A5), (A6), and (A7) gives:

$${\left( {\frac{{S_{{\text{l}}} - S_{{\text{s}}} }} {{V_{{\text{s}}} - V_{{\text{l}}} }}} \right)}{\text{d}}T + {\text{d}}P_{{\text{s}}} + \frac{{V_{{\text{l}}} }} {{V_{{\text{s}}} - V_{{\text{l}}} }}{\text{d}}{\left( {\kappa _{{{\text{sl}}}} \gamma _{{{\text{sl}}}} } \right)} = 0$$

(A8)

After the second subtraction:

$$ \frac{{S_{{\text{s}}} - S_{{\text{g}}} }} {{V_{{\text{g}}} - V_{{\text{s}}} }}{\text{d}}T + {\text{d}}P_{s} = 0 $$

(A9)

A third subtraction of Eqs. (A8) and (A9) yields:

$${\left[ {{\left( {S_{{\text{l}}} - S_{{\text{s}}} } \right)} - \frac{{V_{{\text{s}}} - V_{{\text{l}}} }} {{V_{{\text{g}}} - V_{{\text{s}}} }}{\left( {S_{{\text{s}}} - S_{{\text{g}}} } \right)}} \right]}{\text{d}}T = - V_{{\text{l}}} {\text{d}}{\left( {\kappa _{{{\text{sl}}}} \gamma _{{{\text{sl}}}} } \right)}$$

(A10)

Since $V_{{\text{g}}} \gg V_{{\text{s}}} {\text{, }}V_{{\text{l}}} {\text{, and }}\,\,V_{{\text{s}}} - V_{{\text{l}}} \ll V_{{\text{g}}}$, the second term in the square brackets can be neglected. On melting $\Delta S_{{{\text{s}} \to {\text{l}}}} = S_{{\text{l}}} - S_{{\text{s}}}$. The entropy change at equilibrium is $\Delta S_{{{\text{s}} \to {\text{l}}}} = {\Delta H_{{\text{f}}} } \mathord{\left/ {\vphantom {{\Delta H_{{\text{f}}} } {T_{0} }}} \right. \kern-\nulldelimiterspace} {T_{0} }$, where ΔH _f is the heat of fusion of ice and T ₀ is the equilibrium melting point of bulk water. By utilizing all of the above, one finally arrives at:

$$\frac{{{\text{d}}T}} {T} = - \frac{{V_{{\text{l}}} {\text{d}}{\left( {\kappa _{{{\text{sl}}}} \gamma _{{{\text{sl}}}} } \right)}}} {{\Delta H_{{\text{f}}} }}$$

(A11)

Equation (A11) with integration from T ₀ to T and from 0 to κ _sl γ _sl yields:

$${\text{In}}\frac{T} {{T_{0} }} = - \frac{{V_{{\text{l}}} \kappa _{{{\text{sl}}}} \gamma _{{{\text{sl}}}} }} {{\Delta H_{{\text{f}}} }}$$

(A12)

Equation (A12) can also be found with a positive sign. This depends on the choice of the curvature (wetting or not wetting of the walls), and the change in curvature remedies this discrepancy. The shape factor can be taken as 2/r _sl if it is assumed that the surface is hemispherical.

The logarithm in Eq. (A12) can be approximated by using:

$$ {\text{ln}}\frac{T} {{T_{0} }} = {\text{ln}}{\left( {1 + \frac{{T - T_{0} }} {{T_{0} }}} \right)} \approx \frac{{T - T_{0} }} {{T_{0} }} $$

(A13)

And finally, Eq. (A12) can be rearranged to:

$$T = T_{0} - \frac{{V_{{\text{l}}} \kappa _{{{\text{sl}}}} \gamma _{{{\text{sl}}}} }} {{\Delta H_{{\text{f}}} }}T_{0}$$

(A14)