Science of the Physical Universe 27. Science and Cooking: From Haute Cuisine to Soft Matter Science. Final Review

Transcription

1 Science of the Physical Universe 27 Science and Cooking: From Haute Cuisine to Soft Matter Science Final Review

2 Week 1: Phases of Matter Readings: 1. On Food and Cooking, Introduction pgs On Food and Cooking, A chemistry primer pgs Learning objectives of the week: I. Scientific principles can be used to explain all of the phenomena in cooking; some are complicated and others are not. II. III. IV. Understand what phase behavior is, and how to read a phase diagram. Understand how chefs use phase diagrams to manipulate foods. Understand the connection between phase boundaries and microscopic structure of materials

3 Equation of the Week [Week 1] This equation describes the connection between melting temperatures and bond energies. Increasing temperature results in higher jiggling motion of the molecules. U interaction = 3 2 k B T Here, U interaction is the interaction energy between the molecules in a material, k B is Boltzmann s constant, and T is the temperature. U interaction has units of Joules, T has units of degrees Kelvin (remember that you must add 273 to the Celsius temperature scale to get Kelvin) and k B has units of Joules/degree Kelvin. Below is a chart of the approximate interaction energy per mole for different types of bonds. To find the interaction energy per mole, multiply by Avogadro s number. Type of Interaction Hydrogen bonds Van der Waals Electrostatic Covalent bonds Interaction Energy ~5 kj/mol ~2 kj/mol ~20 kj/mol ~330 kj/mol

4 Week 2: Food Components Readings: 1. On Food and Cooking, The Four Basic Food Molecules (pgs ) Learning objectives of the week: Understand the major characteristics of the three essential components of food (carbohydrates, proteins and fats). Food contains energy. The energy is stored in high energy molecular bonds that are broken down when food is digested. The bonds that are broken down during digestion have much higher energy than those that are manipulated when cooking. Understand the connection between cooking induced phase changes and molecular structure.

5 Equation of the Week [Week 2] This emphasizes the connection between the caloric content of foods (measured in Calories) and the energy stored in bonds (typically measured in kj). Here Calorie is the dietary calorie the quantity that is written on food labels; calories are scientific calories; 1 kj=1000 Joules, the same unit of energy discussed in the first equation of the week. The caloric content of foods can be approximated by the rule: add 4 Calories per gram of sugars and proteins and 9 Calories per gram of fat to find the total value. The energy content of food is contained in its bond energies. The energy released from metabolizing a certain food can be found from: 1. Adding together the total energy of the bonds in the food (sugars, fats, and amino acids) 2. Adding together the total energy of the bonds in the product (water and carbon dioxide) The difference between these is equal to the caloric content of the food.

6 Week 3: Viscosity and Elasticity Readings: 1. On Food and Cooking, Sauces (pgs , optional: ) Meat (pgs ) Learning objectives of the week: The ability of a material to flow is quantified by its viscosity. For simple fluids (fats and oils), viscosity increases with increasing molecular size. Thickeners and food additives are used to control viscosity. A sufficient amount of thickener causes the thickener molecules to interact with each other, causing a dramatic increase in viscosity. The amount of thickener required can be very small. The ability of a material to resist compression is quantified by its elasticity. Food additives can be used to make a liquid (e.g. water at room temperature) have elastic properties, or exhibit elastic behavior.

7 Equation of the Week [Week 3] The equations this week that you are responsible for are best organized in the following table. The first column of the table refers to the measurements you made in the laboratory; the second column explains the connection between the measurements and the molecular structure of the material. Measurement Molecular origin Viscosity ν = B t ν = l c Elasticity E = (F / A 0 ) / (DL/L 0 ) E = k B T / l 3 In the first row, the viscosity equations, ν is the kinematic viscosity, measured in cm 2 /sec. The quantity t is the time that you measured in laboratory for how long a fixed volume of fluid drained through a funnel (measured in seconds), and B is a calibration constant (measured in cm 2 /sec 2 ) we measured for you in the lab. In the molecular origin equation, lower case l is the molecular scale (measured in centimeters), and c is the speed of molecules in the liquid (measured in cm/sec). As emphasized on the homework, the velocity of the molecules at atmospheric pressure and room temperature is always about 1500 m/sec= cm/sec. In the second row, the elasticity equations: E is the elastic modulus (or elastic constant), measured in Joules/m 3. In the lab, F is the force exerted on the material by a fixed weight. This force is measured in Newtons (kg m/sec 2 ). L 0 is the initial thickness of the material that the weight is sitting on (measured in meters), and A 0 is the area of the weight (measured in meters 2 ). The quantity ΔL is what you actually measure how far the material deforms due to the weight (in meters). In the molecular origin equation, k is Boltzmann s constant (identical to that in the first equation of the week); T is the temperature measured in Kelvin, and lower case l is the molecular length scale, measured in meters. You should understand that whereas the elasticity formula applies quite generally to elastic materials that arise when cooking, the viscosity formula only applies to

8 simple liquids. Food additives are more complicated, since they can interact with each other.

9 Week 4: Heating, Cooling Readings: 1. On Food and Cooking, Cooking Methods and Utensil Materials (pgs , ) Learning objectives of the week: Different foods (Meat, fish, eggs, chocolate, etc.) require different target temperatures for the cooking to be successful, depending on the molecular transitions that must occur. Controlling these phase transformations requires precise temperature control. Different heating methods (baking, frying, microwaving, etc.) require different heating protocols for optimal cooking, since they cause different temperature distributions within the food during cooking. Heat is transferred through food by diffusion. Since the dominant component of all foods is water, the characteristic law for a food to be heated or cooled is the same as heat transfer through quiescent water, and is thus identical in essentially all foods.

10 Equation of the Week [Week 4] The equations that you are responsible include the equation of the week, and the ways in which it is used to understand heating and cooling times during cooking. In addition to the main form we presented in lecture, where T(t) = (T initial T external )e ( t /τ ) + T external τ = 1 π L 2 D The equation of the week can be rewritten as: t cook = τ log T initial T external T target T external This equation is extremely useful for computing the cooking times of foods. You should understand how to apply this equation. Namely, how to take the initial temperature of a food, together with the desired target temperature and oven temperature (T external ) to arrive at the required cooking time.. Note that in both of these equations, T initial is the initial temperature of the food; this is usually room temperature = 20 C. T external is the temperature of the cooking medium; i.e. the temperature of the oven or the temperature of a pan. T(t) is the temperature in the food a time t after heating begins. Here t is measured in seconds. τ is the timescale over which the food heats up. This is measured in seconds. Note that e 0 =1 and e -t/τ goes to zero as t becomes large. Thus this equation starts out with T(t)=T initial and at very long times T(t) goes to T external, the oven temperature. D is the diffusion constant of food. In class we emphasized that since food is mainly water, the diffusion constant is the same as the diffusion constant in water. This is D=1.4 x 10-7 m 2 /sec, or D=1.4 x 10-3 cm 2 /sec.

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12 It is helpful to consider two different categories: 1. A thin layer around the surface of the food is being cooked. An example would be searing a steak, in which L is the penetration of the heat into the food. The penetration of the cooked layer is roughly equal to (π D t). This comes from the fact that heat is diffusing inwards in a random walk. 2. The entire volume of the food is being cooked. In this situation, there are two sub-cases, depending on the geometry of the food: a. A thin, flat object (like a pizza crust): in this case L is the thickness of the object. If the food is being heated from both sides, then L is half the thickness. b. A roughly spherical object (like a turkey): in this case L is approximately the radius of a sphere of the same volume. To find the equivalent radius, use M = (4/3) π ρ L 3, where M is the mass of the food and ρ is the density (roughly equal to water).

13 Week 5: Protein Folding and Unfolding Reading for the week: On Food and Cooking; Milk and dairy products, pgs 16-21, Learning objectives of the week: I. Modifying the interactions within and between proteins is central to cooking. II. The dominant forces leading to protein folding and unfolding are hydrophobicity, electrostatic interactions and entropy. III. The propensity of a protein to unfold during cooking is catalyzed by changing temperature (entropy), ph and salt concentration (electrostatic interactions). IV. After unfolding, hydrophobic regions of proteins bind to each other, causing coagulation. This coagulation is usually (but not always) irreversible.

14 Equation of the Week [Week 5] The equations that you are responsible include the equation of the week, and the ways in which it is used to understand This equation of the week represents the competition between three different driving forces for protein unfolding hydrophobicity (leading to energy U hydrophobicity (or U(hydro)), entropy (N k B T) and electrostatic (U electrostatics or U(electro)). These are three dominant forces that drive both protein unfolding (denaturation) and the subsequent coagulation. However, the equation of the week was invented to represent the competition during protein unfolding/denaturation. The equation (and the logic that was applied using this equation) only applies to denaturation, not coagulation. The same physical forces apply to coagulation as well, but there are subtleties that the way we told you to use the equation is not capturing. U(hydro) is the energy required to break the hydrophobic 'bonds' within one folded protein, in order to expose the hydrophobic regions to the water. It is very like U(electro) in the equation of the first week. This type of energy is often referred to as a binding energy. Note that a larger U(hydro) means a more stable configuration (more thermal energy required to unfold the protein); this is how a binding energy is different from other ways of measuring energy, where we have told you that the lowest-energy state is the most favorable. Here, U(hydro) is larger the more hydrophobic interactions there are within the protein, and is smaller when more of the hydrophobic regions are exposed to water instead of interacting with one another. A normal folded protein has hydrophobic parts in the center, touching each other and avoiding water, hence it has a high U(hydro). The entropy (represented by N kb T) is not large enough to overcome this stable configuration. The protein is 'happy' and stays folded. But when you add something (heat, acid, salt, etc), the configurations of the protein are disturbed. You can increase N kb T by adding heat, you can change U(electro) by changing the charge state of the protein, or you can change U(hydro) by putting the protein in a different solvent (i.e. oil) or by otherwise causing hydrophobic parts to contact with water. Unfolding or denaturation occurs when new forces cause the protein to expand and fill space. The two

15 knobs that are most accessible in the kitchen are temperature (entropy) and electrostatics (ph). By either increasing the temperature or increasing the charge on the protein, the scale is tilted towards electrostatics and entropy beating hydrophobicity, promoting unfolding. You should understand how to reason qualitatively with this equation as it applies to protein unfolding. You should also understand that the same forces act during coagulation (i.e. in a gelation reaction strands can stick to each other because of hydrophobic forces) but we won t ask you (and didn t teach you) to use an equation to quantify this.

16 Week 6: Foams and Emulsions Reading for the week: On Food and Cooking, Emulsions and Mayonnaise pgs The Curious Cook, Mayonnaise, doing more with Lecithin (posted on course web site) Learning objectives of the week: I. An emulsion is mixture of droplets of one liquid dispersed within another liquid. A foam is a mixture of air bubbles dispersed within a liquid. II. Energy is required to form new interfaces. III. Stabilizing the interfaces requires a coating with surfactants. IV. The tendency to reduce the surface area of each droplet requires an internal energy within the drops. V. Foams and emulsions can become solids when the concentration of droplets becomes sufficiently high.

17 Equation of the Week [Week 6] There are two equations for this week the first represents the surface energy that is required to create an interface: this is the surface tension σ ( sigma ), multiplied by the surface area of the interface (4 π R 2 ). The second equation is the pressure difference (Δp) across a bubble surface. We asked you two types of questions for using these equations: The first question gave you an amount of surfactant (i.e. 1 gram of lecithin) and asked whether the amount was sufficient to cover all of the surface area present in an emulsion. If you multiply this surface area by the surface tension of the interface (without surfactant covering it), that uses the first equation. Secondly, we gave you the pressure difference across an interface of a droplet and asked you to compute the droplet size. The point here is that smaller droplets lead to larger pressure differences and hence they are stiffer!

18 Week 7: Gelation Reading for the week: 1. On Food and Cooking, Sauces pgs Learning objectives of the week: I. Gelation is a phase transition that turns a liquid into a solid, by forming a cross-linked network. II. A critical density of cross links is needed for this phase transition to occur. III. The cross links can form through a variety of different processes, including physical (e.g. entanglement of polymers) or chemical (bond formation). IV. In normal spherification, calcium must move into the alginate containing droplet. The molecules move through diffusion, precisely analogous to the diffusion of heat.

19 Equation of the Week There are two equations for this week the first is our elasticity equation which we discussed in detail in week 3. The point here of course is that a measurement of the elastic modulus (E), when coupled with this equation, gives you an estimate for the distance between the cross links in the gel (symbolized by l). The second equation is the spherification equation it gives you the thickness of the alginate shell (L shell ) when a droplet of alginate is put into a bath of calcium, or vice versa, as a function of time (t). D Ca is the diffusion constant of Calcium. This equation should remind you of the similar equation we used during heat transfer week both heat, and calcium ions in solution, diffuse---with the same physical process! Indeed, the science fair was full of diffusion! Note that the other quantitative exercise we asked you to do this week was the measurement of the thickness of the spherification shells in the lab. You should review how this thickness measurement was made.

20 Week 8: Complex Phase Changes: Advanced concepts Reading for the week: 1. On Food and Cooking, Browning Reactions and Flavors (pgs ). 2. The Physiology of Flavor: Mediation II, on Taste. See (search for the Meditation on Taste). 3. Herve This, The Science of the Oven, excerpt on Course web site on flavor: see Readings section of the web site. Learning objectives of the week: I. The Maillard reaction involves the reaction of a carbohydrate molecule with an amino acid, requiring temperatures in excess of 120 C. II. Caramelization reacts sugar molecules, requiring temperatures in excess of 165 C. III. Temperatures above boiling in food can only be achieved by evaporating off the liquid component of the food. IV. Transglutaminase binds together protein molecules with a covalent bond between two specific amino acids.

21 Equation of the Week The equation this week was the same as the equation during the heat transfer week. This is because the Maillard reaction is temperature-dependent and how far it proceeds depends on how hot the food becomes (defined by T(t)). This is what our equation of the week describes! One important aspect of the Maillard reaction that this equation does not capture is that creating flavor compounds is NOT a phase transition. Namely there is not a critical temperature at which the compounds are produced. Instead, the rate of production of flavor compounds and the browning reactions increases as the temperature goes up. This is why books (e.g. On food and cooking) just report a range for when the reaction happens.

22 Week 9: Soil and Microbes Reading for the week: 1. J. E. Cohen How many people can the earth support?,, pgs. 5-45; this excerpt covers the human population growth of the planet and how changes in farming practices have influenced this. Excerpt can be found at Google books: #v=onepage&q&f=false 2. On Food and Cooking: a. The preservation of meats: pgs b. Microbes and alcohol: pgs c. Wine making: pgs d. Bread and yeast: pgs Learning objectives of the week: I. Biological populations human, animal, bacterial, or plant, increase in size exponentially in time in the absence of constraints. This creates a tremendous demand for resources. Changes in food production and water availability have historically led to dramatic changes in the growth of human populations. II. Microbes play a critical role in food production, regulating soil quality in farming, as well as serving as a critical link in the nitrogen cycle. III. Microbes also play innumerable roles in food preparation itself, ranging from the curing meats, to the making of wine and bread. IV. Preventing food spoilage primarily requires inhibiting microbial growth. V. Microbes are essential for our gaining nourishment from food.

23 Equation of the Week [Week 9] We used this equation to quantify the exponential growth of bacteria over time. The number of bacteria is defined by N(t), starting from an initial population N 0 and growing with a time constant k. The time constant is related to the doubling time (τ) by: k = ln(2)/τ. You can check this by substituting t = τ into the equation of the week and noting that N(τ) = 2 N 0.

24 Week 10 Dessert! Reading for the week: On Food and Cooking, Candy pgs On Food and Cooking, Cakes and Breads, pgs Learning objectives of the week: I. Phase Change: Sugar candies form from crystallization of dissolved sugar in water. The characteristics of the crystals depend critically on temperature, ph. II. III. IV. Elasticity: The structure and elasticity of cakes, breads and pastries can be attributed through the remarkable properties of gluten networks. The texture and elasticity of the network can be modified by controlling the cross-linking strength and density of the gluten, leading to the rich variety of textures in cakes and breads. Heat Transfer: Recipes for pies, cakes and cookies have very different heating protocols, due to the different requirements and compositions of these desserts. Foams and Emulsions: Bread, meringues and cakes are solid foams. The air bubbles are produced by the growth of CO2 bubbles during baking, caused by leavening agents. V. Gelation: Gelling agents can be used to stabilize foams like marshmallow and mousse.