Una legió d’individus: «Perquè som molts»

452ºF

3. Una legió d’individus: «Perquè som molts»

A catalyst is a substance that accelerates the rate of a reaction but is not consumed by it. The cata-lyst has the effect of stabilizing the intermediate and lowering its energy (Fig. 3.7). A higher pro-portion of molecules are able to form the lower energy intermediate and so the rate of the for-ward and reverse reaction is accelerated. Impor-tantly the catalyst does not affect the energies of the reagents or products, so the equilibrium posi-tion of the reacposi-tion is unaffected.

An enzyme is a protein that can very specifi-cally bind certain compounds and catalyze their transformation. Enzymes are essential to life as they enable cells to regulate their chemistry by controlling the kinetices. For example, high-en-ergy chemicals (e.g., fats, starch) can be stored for long periods and then broken down when

re-quired by controlling the release of an enzymatic catalyst. Enzymes can remain active in fresh foods but as the plant or animal that made the tissue is dead and has lost control of the cellu-lar processes, they can sometimes react in unex-pected and undesirable ways. For example, lipase enzymes are important in lipid digestion, where they catalyze the removal of fatty acids from the glycerol backbone of a triacylglycerol. They are also present in unpasteurized milk, and if the milk is mixed vigorously, the membrane surrounding the fat globules can be damaged, allowing the en-zyme access to the lipid and very quickly produc-ing a characteristic off-flavor due to the release of butyric acid. Enzymes are also used in food processing (e.g., amylase enzymes used to hydro-lyze starch to form corn syrup, chymosin used to cleaving κ-casein to form a yogurt gel from milk) and of course in the digestion of foods.

The mode of action of most enzymes involves a two stage process (i) binding the substrate and (ii) facilitating the chemical transformation and releasing the product:

Enzyme Substrate Enzyme-Substrate Enzyme + Product

→

+ ←

→

Uncatalyzed intermediate

Catalyzed intermediate

Energy

Reagents ∆E

Products

∆Er‡

∆Ef‡

Fig. 3.7 Effect of a catalyst on a reaction surface: The rate of the forward and reverse reaction is increased while the equilibrium distribution is unaffected

To analyze this mechanism, the rate of the reac-tion ( v) is measured as a funcreac-tion of substrate concentration ([S], Fig. 3.8a):

• When there is no substrate, the reaction does not take place so rate is zero.

• At low substrate concentrations, the enzyme is able to catalyze the chemical change faster than it can bind more substrate. The overall rate is limited by the first step of mechanism and the increases with increasing substrate concentration. The capacity of the enzyme to bind limited substrate is the binding coef-ficient ( K_m).

• At high substrate concentrations, the enzyme is saturated. The overall rate of the reaction depends on the second step of the mechanism and adding more substrate makes little dif-ference. The maximum rate possible ( V_max) is seen when the enzyme is saturated with enzyme.

The overall dependency of rate on substrate con-centration is given by the Michaelis–Menten equation:

(3.7) Equation 3.6 is more commonly seen in its linear form:

(3.8)

and plots of reciprocal rate against reciprocal concentration can be used to calculate K_m and V_max (i.e., a Lineweaver–Burk plot, Fig. 3.8b).

Nonenzymatic catalysts are important in in-dustrial chemistry; for example liquid oils are hydrogenated to form solid fats by reaction with hydrogen under high pressures in the presence of a Raney nickel catalyst is very slow. Raney nickel is treated to produce a very high surface area per unit mass (~ 100 m² g⁻¹) that can adsorb the re-agents and lower the free energy required to form the intermediate and thus catalyze the reaction.

Purely physical transformations can also be cata-lyzed. For example, a glass of a carbonated drink will bubble slowly because the chemical poten-tial of carbon dioxide is lower in the atmosphere than in the solution. The process is slow because of a free energy barrier associated with forming a small bubble. The reaction can be catalyzed with a spoonful of sugar or salt that will cause the drink to fizz spectacularly as the formation of small bubbles is catalyzed at the solid surface. (It is easy to show that the solid surface is important, as a spoonful of sugar solution has no comparable effect.)

3.7 Summary

Kinetics is distinct but complementary subject to thermodynamics. It postulates the existence of a high-energy intermediate state that react-ing molecules must overcome to form products.

The energy barrier slows down change and even stops the system reaching equilibrium, but has no affect on the final composition at equilibrium.

Reactions in living systems are very tightly

ki-max[ ]

1/[Substrate] (µM^-1)

K_m/V_max

1/V_max -1/K_m

Fig. 3.8 (a) Rate of lipase catalyzed hydrolysis of a tria-cylglycerol as a function of substrate concentration. (b) Lineweaver–Burk plot of the same data. (Unpublished data courtesy of Dr. Josh Lambert (Penn State Univer-sity))

3.7 Summary

netically regulated and nonequilibrium states are the rule rather than the exception. Similarly few foods are consumed in their equilibrium states.

The empirical rates of reaction are propor-tional to the concentrations of reagents raised to a power and the integral form of this relationship can be used to model changes in concentration with time. The proportionality constant (the rate constant) usually increases with temperature ac-cording to the Arrhenius equation, which itself is similar to the Boltzmann distribution in that it provides a measure of the proportional of mol-ecules with sufficient energy to react at a given temperature. Catalysts, particularly enzymes, can be used to increase the rate of biological reac-tions by lowering the activation energy needed to produce the intermediate.

In the next chapter, we will bring together the laws of thermodynamics, the properties of

molecules, and the kinetic theory studied here to investigate the general phenomena of why some food ingredients mix and others will more or less quickly separate into two phases.

3.8 Bibliography

This very introductory description of kinetics is readily extended by most physical chemistry textbooks (Atkins and De Paula 2006; Tinoco et al. 2002) and I have found “Reaction Kinet-ics and Mechanism” (Avery 1974) particularly helpful. Dill et al. (2003) cover much of the same material in Chap. 18 and 19 of “Molecular Driv-ing Forces” but use a more intuitive, molecular approach. Walstra considers similar material with a focus on foods in Chap. 4 of “Food Physical Chemistry” (Walstra 2003).

4 Phase Behavior

J. N. Coupland, An Introduction to the Physical Chemistry of Food, Food Science Text Series, DOI 10.1007/978-1-4939-0761-8_4, © Springer Science+Business Media New York 2014

4.1 Introduction

Some ingredients will dissolve in one another while others do not, or at least not completely.

For example, ethanol and water can be blended at all proportions, as can olive oil and canola oil. On the other hand, while oil and water can be com-bined to make a salad dressing, they do not actu-ally dissolve in one another. Often the tendency to dissolve depends on the conditions; if you add sugar to iced tea, the first few crystals will dis-solve, sweetening the drink, but sugar added be-yond a certain limit will sink to the bottom of the pitcher and not be tasted. It is possible to make much sweeter hot tea as the solubility limit of su-crose in water increases with temperature.

If ingredients do not dissolve, they must form separate phases within the food. In the language of physical chemistry, a phase is a region where at least some of the properties (e.g., chemical composition, density, viscosity) change abruptly at the boundary. The change in properties must persist over several molecular dimensions; while the dissolved lactose molecules in cream are not each treated as separate phases but as part of an aqueous solution phase, the oil in micrometer-sized droplets is an independent liquid phase (Fig. 4.1). While cream appears to the naked eye to be a homogeneous fluid, it is microscopi-cally a two-phase system. The presence of fine oil droplets affects the texture of the product, for example higher fat creams are more viscous than lower fat ones (Chapter 8) The phase behavior of real foods can be very complex. For example, if

cream is sweetened, whipped, and frozen to form ice cream, the final product we eat has a crys-talline ice phase, a concentrated sugar solution phase, a lipid phase (in droplets), and some bub-bles of an entrained gas phase (Fig. 4.2). Once more, the properties of the product depend on the proportions of each phase present, for example, if too much of the water is frozen into ice or too little air whipped in, then the product would be hard and difficult to scoop. The balance of phases present depends on the conditions (i.e., tempera-ture), and the ingredients used (e.g., an ice cream formulated with high sugar content will tend to be softer and have less ice).

The goal of this chapter is to first understand how to use phase behavior to understand and pre-dict the properties of a food and second to under-stand phase behavior in terms of molecular in-teractions and the laws of thermodynamics. It is usually productive to start with a simple system, understand it thoroughly, and then add complex-ity later. With that in mind, we will consider the phase behavior of the simplest of foods—water.

4.2 Single-Component Phase Diagrams

Water is a unique material as it occurs on our planet and in our food in abundant quantities in its solid, liquid, and gaseous phases. We could make experimental measurements of the freezing point and boiling point of water and plot them on a line to show the conditions at which the

dif-ferent phases are seen: Above 100 °C steam is the stable form of water and the liquid will boil, below 0 °C ice is the stable form and water will crystallize. Precisely at 100 °C and 0 °C, we can say water is in equilibrium with steam and ice respectively and we can see two phases together.

Alternatively, if we have a glass of iced water or a pan of boiling water, we know the tempera-ture of the water, precisely because there are two phases present simultaneously.

The boiling point of water is also a function of pressure (water boils at only about 69 °C at the top of Mount Everest). We can show the effects of temperature and pressure on the phase behav-ior of water by using them as the axes of a phase diagram (Fig. 4.3). The labeled regions show the conditions where the different phases of water (ice, water, and steam) are seen. For example, under ambient conditions ( p = 1 atm, T = 25 °C) water is liquid but at − 10 °C it is solid. We can freely vary temperature and pressure within one of these regions so long as we do not cross one of the lines that represent the conditions for a phase transition (i.e., boiling, freezing, or sublimation).

Along the lines, two phases are at equilibrium with one another and if we want to maintain this equilibrium, we are not free to independently change temperature and pressure. For example, if we have boiling water and we want to raise the temperature to 121 °C, the pressure must increase to 2 atm to stay on the line. If water is boiling at 69 °C, the pressure must be 0.28 atm because of the phase line. The point where the boiling and freezing lines intersect is the triple point of water (0.01 °C, 0.006 atm) and these are the

      

3DWP

7 .

ZDWHU

VWHDP

Fig. 4.3 Phase diagram of pure water (NIST 2014)

Fig. 4.2 Electron micrograph showing the different phases present in ice cream: ice crystals ( C), air bubbles ( A), unfrozen serum phase ( S), partly crystalline fat drop-lets ( F). (Image courtesy Dr. Douglas Goff, University of Guelph)

[oil]

distance

A B

Fig. 4.1 Optical micrograph showing the oil and water present as separate phases in a model cream. The concen-tration of oil changes abruptly at the oil–water interface, justifying us describing it as a separate phase

53 4.2 Single-Component Phase Diagrams

only conditions where it is possible to see steam, water, and ice are at equilibrium.

A practical application of the water phase dia-gram is seen in operation of the retorts used to cook canned foods. A retort is an industrial pres-sure cooker; the cans of food are sealed into a container partly filled with water and heated. In an open container, the water would boil at a con-stant temperature until all the water had evapo-rated before the pan itself would begin to heat further. However, inside a sealed retort, the water would initially boil at 100 °C but as soon as some steam was generated, the pressure would increase and the boiling would stop. The retort would then have to be heated a little further to reach the boil-ing point of water at the higher pressure but as soon as it boiled again, the pressure and hence the temperature required for further boiling would increase. In practice, the temperature and pres-sure inside the retort would increase together—

so long as there was water and steam present to-gether. We are used to cooking times in domestic recipes being specified in terms of time and oven temperature but retorting processes are usually specified in terms of a cooking time and a retort pressure which fixes the temperature according

to the phase diagram (and has the additional ad-vantage of being easier to measure inside a sealed container).

What is it about water molecules that cause them to behave in this way? We can go some way to understanding this using a simple car-toon representation of the crystalline, liquid, and gaseous states (Fig. 4.4a). In a crystalline solid, the molecules are regularly packed and strongly associated with their neighbors. Each molecule may vibrate about its position but not diffuse away from it. In a liquid, the molecules are still closely packed, but now free to diffuse from their starting positions and there is no persistent regu-lar arrangement of the molecules. In a gas, the molecules are no longer closely packed, and can diffuse freely. The overall free energy of a phase is a combination of enthalpy terms (bonding) and entropy terms (“disorganization”) i.e.: G = H−TS (Eq. 1.10). In a crystal, there are many strong bonds so the energy term is large but as the struc-ture is regular, the entropy is small. In a gas, there are few bonds so bonding energy is low and but the entropy high. The properties of a liquid lie between these extremes, but are usually closer to those of a crystal than those of a gas.

The effect of temperature on the free energy of a gaseous, liquid, and crystal phase is shown schematically in Fig. 4.4b. At low temperatures, the entropy term is relatively unimportant so the free energy is dominated by the bonds pres-ent and the strong bonds in the crystalline phase means it has a lower free energy than the gas (with the liquid as an intermediate state). The stable phase will be the one with the lowest free energy so materials tend to crystallize when cooled. Free energy decreases with temperature for all materials (again see Eq. 1.10, G = H − TS), but as the entropy of the gas phase is greater than the crystal phase, the rate of decrease is greater (with the liquid somewhere between the two).

The temperatures where the free energy curve for the liquid phase intersects with those of the solid and gaseous phases correspond to the melting and boiling points respectively.

Another way of looking at boiling and freez-ing would be to say that higher temperatures give the molecules sufficient thermal energy to break

Crystal Liquid Gas

Free energy

Temperature b

melting boiling

Fig. 4.4 a A cartoon representation of the arrangement of molecules in a crystalline solid, a liquid, and a gas phase.

b The free energy of the different phases as a function of temperature

the bonds holding them together. Similar think-ing can help understand the effects of pressure:

Compression forces the molecules together into more condensed phases. Because increasing tem-perature and pressure have opposing effects on phase behavior, we are free to use changes in one to compensate for changes in the other. In effect, that is what is happening in the retort example earlier: Water boils at 100 °C at atmospheric pres-sure but we can make it boil at a higher tempera-ture by using increased pressure to hold the high-er enhigh-ergy molecules togethhigh-er in a dense phase.

Applying too much pressure and the steam would condense into the water phase—too little pres-sure and all the water would boil off into steam.

The one-component system was helpful to understand phase transitions in terms of mo-lecular interactions and entropy but to begin to understand foods we must now add more com-ponents and look at the phase behavior of mix-tures. In this case, we will encounter additional complications due to the entropy effect of mixing (favoring miscibility) and the different types of possible molecular interactions. We will begin by examining phase diagrams as practical descrip-tions of the behavior of mixtures and then try to provide some sort of theoretical framework.

4.3 Multicomponent Phase Diagrams

The first challenge in drawing a multicompo-nent phase diagram is to represent composi-tion as an axis on the plot. We can succinctly express the composition of a two-component mixture on a phase diagram as a mass or mole fraction. For example dissolving 2 g of sugar in 10 g of water would produce a 16.7 wt % (i.e., 2/

(2 + 10) × 100 %) solution. Knowing the fraction of one component fixes the other (i.e., 83.3 wt % water) and so we can describe the overall compo-sition of a mixture using only this one number. If we use one axis for composition, then the remain-ing one can be either temperature or pressure but we cannot show the effects of both parameters simultaneously. Temperature is usually more rel-evant to foods so a typical two-component phase

diagram represents experimental measurements of the phase(s) present in a mixture as a function of temperature and composition. It is possible to draw phase diagrams for more complex mixture of ingredients but in practice it is unusual to see data for more than a ternary mixture. For a three-component mixture A + B + solvent, one axis rep-resents the mass fraction of A and the second the mass fraction of B.

A phase diagram shows the phases at equilib-rium with one another under given conditions.

How the data is generated depends on the nature of the system but as an example consider how we might form a sugar–water phase diagram. We could just add sugar to the water until no more dissolves, and mark that concentration as the solubility limit. In practice, the process of dis-solution can be prohibitively slow and it works better to just add an excess of sucrose, let the undissolved crystals sediment out, and measure the concentration of the saturated sucrose solu-tion (Fig. 4.5a). Repeating the experiment over a range of temperatures, we could generate a phase boundary in the sucrose–water phase diagram (Fig. 4.5b). Any point on the phase line shows the composition of the sucrose solution at equi-librium with sucrose crystals. Mixtures more

In document Vista de 'MI NOMBRE ES LEGIÓN' LITERATURA Y GENEALOGÍA EN ANTÓNIO LOBO ANTUNES (página 36-40)