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Team:KULeuven/Thermodynamics
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∆G*= 16 π σ ³/(3(∆Gp)²) <br><br> | ∆G*= 16 π σ ³/(3(∆Gp)²) <br><br> | ||
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FIGURE 2: The Gibbs free energy in relation to the radius of nuclei.<br><br> | FIGURE 2: The Gibbs free energy in relation to the radius of nuclei.<br><br> | ||
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In this equation, θ represents the contact angle (figure 3) between the water impurity and the forming crystal. f(θ) in the formulas above is smaller than 1, consequently the Gibbs free energy for the formation of a crystal in heterogeneous nucleation is smaller than for the Gibbs free energy in homogenous nucleation and crystals will form more easily. The smaller the contact angle between the impurity and ice, the lower the Gibbs free energy. For a graphical representation of the different Gibbs free energies, take a look at figure 3. <br><br> | In this equation, θ represents the contact angle (figure 3) between the water impurity and the forming crystal. f(θ) in the formulas above is smaller than 1, consequently the Gibbs free energy for the formation of a crystal in heterogeneous nucleation is smaller than for the Gibbs free energy in homogenous nucleation and crystals will form more easily. The smaller the contact angle between the impurity and ice, the lower the Gibbs free energy. For a graphical representation of the different Gibbs free energies, take a look at figure 3. <br><br> | ||
| - | <img src="http://homes.esat.kuleuven.be/~igemwiki/images/ | + | <img src="http://homes.esat.kuleuven.be/~igemwiki/images/thermodynamics/thermo_fig3.jpg"> |
FIGURE 3: contact angle θ <br><br> | FIGURE 3: contact angle θ <br><br> | ||
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FIGURE 4: Gibbs free energies of heterogeneous nucleation compared to homogenous nucleation.<br><br> | FIGURE 4: Gibbs free energies of heterogeneous nucleation compared to homogenous nucleation.<br><br> | ||
Revision as of 00:16, 29 October 2011
Thermodynamics
Water crystallization
Crystallization exists of two different successive stages: nucleation and crystal growth. The interaction between these two steps determines the crystal characteristics, i.e. , size, distribution and morphology of the crystals. When crystallization happens in a crystal-free solution, the process is called primary nucleation. When crystals form at the presence of formerly created crystals, the process is called secondary nucleation. Primary nucleation can be divided in homogenous nucleation and heterogeneous nucleation. Homogenous nucleation takes place when primary nucleation proceeds in a nucleation free solution; this is when the solution contains no foreign particles. Heterogeneous nucleation takes place if primary nucleation proceeds when foreign particles are present in the solution. In biological systems, water is never free of particles, consequently only heterogeneous nucleation is possible. [1]Water crystallization, how does it Work?
NucleationThe driving force for nucleation in water is the degree of supercooling (figure 1). In the case of primary nucleation and especially for the homogenous type, large supercooling driving force is required. When water contains impurities (heterogeneous nucleation), the required supercooling is smaller. [1]
FIGURE 1: Degree of supercooling is determined as the temperature difference between the freezing point (A) and the nucleation point (B).Crystal growth
After the formation of the nuclei, the next step is crystal growth. The initially formed nuclei serve as a template for depositing material upon, so bigger crystals start to grow. [1]
Mathematical models
Several mathematical models have been developed to describe the nucleation and crystal growth. For primary nucleation the change in Gibbs free energy exhibits a volume term and a surface term:
∆G = 4/3πr³∆Gp + 4πr²σ
∆G is the overall excess free energy between a small solid particle of solute and the solute in solution, ∆Gp is the free energy change of the transformation per unit volume and is a negative quantity, σ is the surface free energy.
The volume term is negative below the freezing point. This term is the driving force for nucleus formation. The surface term is always positive and counteracts the ice forming process. Particles with a radius bigger than the critical radius (r*), will enlarge spontaneously. These particles have passed the activation energy “mountain”. These particles are the so-called nuclei. Particles with a radius below the critical radius will spontaneously disintegrate.
∆G*= 16 π σ ³/(3(∆Gp)²)
FIGURE 2: The Gibbs free energy in relation to the radius of nuclei.In analogy with homogenous nucleation, equations can be described for heterogeneous nucleation:
∆Ghet = ∆Ghom . f(θ)
f(θ) = (1-cosθ)²(2+cosθ )/4
∆G*het= ∆Ghom * . f(θ)
In this equation, θ represents the contact angle (figure 3) between the water impurity and the forming crystal. f(θ) in the formulas above is smaller than 1, consequently the Gibbs free energy for the formation of a crystal in heterogeneous nucleation is smaller than for the Gibbs free energy in homogenous nucleation and crystals will form more easily. The smaller the contact angle between the impurity and ice, the lower the Gibbs free energy. For a graphical representation of the different Gibbs free energies, take a look at figure 3.
FIGURE 3: contact angle θ 
FIGURE 4: Gibbs free energies of heterogeneous nucleation compared to homogenous nucleation.Water crystallization: ice nucleating proteins and antifreeze proteins
Ice nucleating proteins (INPs) are able to induce ice nucleation in liquids at temperatures significantly higher than liquids without INPs, due to the ordination of ice crystals. INPs can create large and long ice crystals in ordered directions. For food materials INPs can be of great advantage. They elevate the nucleation point to higher temperature, shorten freezing time, increase freezing rate and change the texture of frozen foods, thus decreasing refrigeration cost and improving the quality [1].Antifreeze proteins (AFPs) have the opposite effect of INPs, they lower the nucleation temperature in heterogeneous solutions. The decrease of nucleation temperature is believed to be the result of binding of ice nucleating agents to the ice surface by blocking off certain sites of the ice nucleating agents such that the fast-growing prismatic facet is no longer favored to grow. In homogenous solutions AFP is not further depressing the nucleation temperature significantly [2].
Measuring effects of ice nucleating proteins and antifreeze proteins
The most important thing we measured is the difference in the degree of supercooling necessary to crystallize E. coli coated with INPs or AFPs and compare this with E. coli without INP (or AFP) and with deionized water (E. coli is in both cases dissolved in deionized water).We can try to estimate the refrigeration costs which can be saved by using INP. To estimate this cost we take into account the difference in supercooling and the possibly difference in energy release. Crystallization is an exothermic process, which means that during crystallization, heat will be released. It is possible to determine the difference in energy released for freezing pure water compared to water containing INPs and AFPs.
Determining nucleation point and difference in energy released
To examine the nucleation point, differential scanning calorimetry (DSC) can be applied. Also an automated lag-time apparatus (ALTA) can be used, which repeatedly supercools the same sample linearly as a function of time many times [3]. Besides determining the nucleation point of a sample, DSC makes it also possible to calculate the difference in the energy released. DSC also generates the amount of heat which should be removed for each sample compared to a reference sample.References
[1] Kiani H., Sun D.W., Water crystallization and its importance to freezing of foods: A review. Trends in Food Science & Technology 22 (2011) 407- 426.[2] Yeh Y., Feeny R.E., Antifreeze proteins: Structures and Mechanisms of Function. Chemical Reviews 96 (1996) 601-618
[3] Wilson P.W., et al. Ice nucleation in nature: supercooling point (SCP) measurements and the role of heterogeneous nucleation. Cryobiology 46 (2003) 88–98.
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