Thermodynamics of surface and interfaces

Slides:



Advertisements
Similar presentations
The thermodynamics of phase transformations
Advertisements

Diffusion (continued)
Learning Objectives and Fundamental Questions What is thermodynamics and how are its concepts used in petrology? How can heat and mass flux be predicted.
The Second Law of Thermodynamics
Department of Civil & Environmental Engineering
Real Solutions Lecture 7.
Solutions Lecture 6. Clapeyron Equation Consider two phases - graphite & diamond–of one component, C. Under what conditions does one change into the other?
For a closed system consists of n moles, eq. (1.14) becomes: (2.1) This equation may be applied to a single-phase fluid in a closed system wherein no.
(Q and/or W) A closed system is one that does not exchange matter with its surroundings, although it may exchange energy. dn i = 0(i = 1, 2, …..)(1.1)
First Law of Thermodynamics
8.5 The Helmholtz Function The change in internal energy is the heat flow in an isochoric reversible process. The change in enthalpy H is the heat flow.
Entropy Cengel & Boles, Chapter 6 ME 152.
Thermodynamic relations for dielectrics in an electric field Section 10.
MSEG 803 Equilibria in Material Systems 4: Formal Structure of TD Prof. Juejun (JJ) Hu
Lecture 18Multicomponent Phase Equilibrium1 Theories of Solution The Gibbs energy of mixing is given by: And the chemical potential is: For ideal gases,
1 Thermodynamics of Interfaces And you thought this was just for the chemists...
Solution thermodynamics theory—Part IV
P v Surface Effects in Condensation If we compress a gas isothermally condensation is suppose to start at point O, and if we compress further the pressure.
Heat Capacity Amount of energy required to raise the temperature of a substance by 1C (extensive property) For 1 mol of substance: molar heat capacity.
ESS 材料熱力學 3 Units (Thermodynamics of Materials)
Chapter 2 Matter and Change Section 2.1 Properties of Matter.
1 The Laws of Thermodynamics in Review 1.The internal energy* of an isolated system is constant. There are only two ways to change internal energy – heat.
Notation convention Let G' stand for total free energy and in a similar fashion S', V', H', etc. Then we will let = G'/n represent the free energy per.
Chemical Thermodynamics II Phase Equilibria
1 Lecture 2 Summary Summary 1) The Zeroth Law: Systems that have no tendency to transfer heat are at the same temperature. 2) Work: A process which transfers.
11111 Chemistry 132 NT It takes a big man to cry, but it takes a bigger man to laugh at that man. Jack Handey.
Thermodynamics Chapter 19 Brown-LeMay. I. Review of Concepts Thermodynamics – area dealing with energy and relationships First Law of Thermo – law of.
Spontaneity, Entropy, and Free Energy
The Thermodynamic Potentials Four Fundamental Thermodynamic Potentials dU = TdS - pdV dH = TdS + Vdp dG = Vdp - SdT dA = -pdV - SdT The appropriate thermodynamic.
Chapter 19 Chemical Thermodynamics HW:
Chemical thermodynamics I. Medical Chemistry László Csanády Department of Medical Biochemistry.
Chapter 19 Chemical Thermodynamics Lecture Presentation John D. Bookstaver St. Charles Community College Cottleville, MO © 2012 Pearson Education, Inc.
Dr.Salwa Al Saleh Lecture 11 Thermodynamic Systems Specific Heat Capacities Zeroth Law First Law.
33.1 Temperature Dependence of Gibbs’ Free Energy Methods of evaluating the temperature dependence of the Gibbs’ free energy can be developed by beginning.
1. (1.3) (1.8) (1.11) (1.14) Fundamental equations for homogeneous closed system consisting of 1 mole:
The Second Law of Thermodynamics
Partial Molar Quantities and the Chemical Potential Lecture 6.
1 Chapter 7. Applications of the Second Law. 2 Consider entropy changes in various reversible (!!!) processes We have: (a) Adiabatic process Hence a reversible.
6. Coping with Non-Ideality SVNA 10.3
Thermodynamics Thermodynamics Thermodynamics Way to calculate if a reaction will occur Way to calculate if a reaction will occur Kinetics Kinetics Way.
Thermodynamics and Equilibrium Chapter Copyright © by Houghton Mifflin Company. All rights reserved. Thermodynamics Thermodynamics is the study.
1 Chemical thermodynamics. The first law of thermodynamics. Plan 1 The basic concepts of thermodynamics 2. First law of thermodynamics. Heat (Q) and Work.
Chemical Equilibrium By Doba Jackson, Ph.D.. Outline of Chpt 5 Gibbs Energy and Helmholtz Energy Gibbs energy of a reaction mixture (Chemical Potential)
Solution thermodynamics theory—Part IV
Chapter 2 Matter and Change Section 2.1 Properties of Matter.
Solution thermodynamics theory
Thermodynamics of surface and interfaces – (Gibbs ) Define : Consider to be a force / unit length of surface perimeter. (fluid systems) If a portion.
Thermodynamics and the Phase Rule
Clapeyron and Clausius Clapeyron Equations
SOLUTION THERMODYNAMICS:
Imperfections in Solids
j a g g c h d j a b.
Classical Thermodynamics of Solutions
Chemical Thermodynamics  2009, Prentice-Hall, Inc. First Law of Thermodynamics You will recall that energy cannot be created nor destroyed. Therefore,
THEME: Theoretic bases of bioenergetics. LECTURE 6 ass. prof. Yeugenia B. Dmukhalska.
Energy Changes in Chemical Reactions -- Chapter First Law of Thermodynamics (Conservation of energy)  E = q + w where, q = heat absorbed by system.
Electric Forces and Fields AP Physics C. Electrostatic Forces (F) (measured in Newtons) q1q1 q2q2 k = 9 x 10 9 N*m 2 /C 2 This is known as “Coulomb’s.
Thermodynamics Thermodynamics Thermodynamics Way to calculate if a reaction will occur Way to calculate if a reaction will occur Kinetics Kinetics Way.
Surface Effects in Condensation
Exam #3 1. You should know from memory:
Chemical Potential Combining the First and Second Laws for a closed system, Considering Hence For an open system, that is, one that can gain or lose mass,
Sorption Properties of Food
Solution of Thermodynamics: Theory and applications
Fundamental Property Relation,The Chemical
Figure 6.2 Comparison among the Debye heat capacity, the Einstein heat capacity, and the actual heat capacity of aluminum.
Classical Thermodynamics of Multicomponent Systems
Don’t be in a such a hurry to condemn a person because he doesn’t do what you do, or think as you think. There was a time when you didn’t know what you.
Thermodynamic Potentials
Presentation transcript:

Thermodynamics of surface and interfaces Define : Consider to be a force / unit length of surface perimeter. (fluid systems) If a portion of the perimeter moves an infinitesimal of distance in the plane of the surface of area A, the area change dA is a product of that portion of perimeter and the length moved. Work term - dA; force x distance, and appears in the combined 1st and 2nd laws of thermodynamics as

Strictly speaking , is defined as the change in internal energy when the area is reversibly increased at constant S, V and Ni (i.e., closed system). For a system containing a plane surface this equation can be readily integrated : and rearranging for yields. where U – TS + PV is the Gibbs free energy of the system, i.e., the actual energy of the system

And is the Gibbs free energy of the materials comprising the system, i.e., the energy of the system as if it were uniform ignoring any variations associated with the surface Thus is an excess free energy due to the presence of the surface. def Surface Excess Quantities Macroscopic extensive properties of an interface separating bulk phases are defined as a surface excess.

There is a hypothetical 2D “dividing surface” defined for which the parameters of the bulk phases change discontinuously at the dividing surface. def The excess is defined as the difference between the actual value of the extensive quantity in the system and that which would have been present in the same volume if the phases were homogeneous right up to the “ Dividing Surface ” i.e., The real value of x in the system The values of x in the homogeneous and phases

Concept of the Gibbs Dividing Surface Extensive property Density Distance perpendicular to the surface For a 1 component system the position of the dividing surface is chosen such that the two shared areas in the figure are equal. This yields a consistent value (equal to zero ) for the surface excess.

For a multicomponent system the position of the dividing surface that makes some Ni equal to zero will be unlikely to make all the other Nj ≠i = 0. By convention, N1, the surface excess of the component present in the largest amount (i.e., the solvent) is made zero by appropriate choice of dividing surface. Alternatively if we consider a large homogeneous crystalline body containing N atoms surrounded by plane surfaces then if U0 and S0 are the energy and entropy / per atom, the surface energy per unit area Us is defined by where U is the total energy of the system.

Similarly Consider once again the combined form of 1st and 2nd laws including the surface work term. Substitution of the definition of G leads to

If the surface is reversibly created in a closed system (Ni fixed) at constant T and P. is always the free energy change appropriate to the constraints imposed on the system.

Since for the bulk phases a and b the surface terms vanish, the combined 1st and 2nd law take the form and and for the total system From the definition of surface excess: By Def.

Integration yields, Forming the Gibbs-Duhem relation : so Gibbs-Adsorption Equation where

Solid and liquid Surfaces In a nn pair potential model of a solid, the surface free energy can be thought of as the energy/ unit -area associated with bond breaking. : work/ unit area to create new surface = where n/A is the # of broken bonds / unit-area and the is the energy per bond i.e., the well depth in the pair-potential. Then letting A = a2 where a lattice spacing

pair potential If the solid is sketched such that the surface area is altered the energy r U(r) The total energy of the surface is changed by an amount. and

Surface Stress and Surface Energy Unit Cube 1 The difference in the work per unit area required for the constrained stretching (fix dimension in the y direction while stretching along the x-direction) is defined as the surface stress, fxx. This is the excess work owing to the presence of the surfaces. fxx W1=2g Split Stretch W2 w1 1+dx fxx w2=2(g+dg)(1+dx) Shuttleworth cycle relating surface stress, f and surface energy, g.

Relation between fij and g Surface Stress and Surface Energy Relation between fij and g Consider 2 paths to get to the same final state of the deformed halves. Path I - The cube is first stretched and then separated. WI = w1 + w2 = w1 + 2(1+dx) (g + Dg) = w1 + 2 g + 2 Dg + 2 g dx where xx (= dx/1) has caused a change Dg in g. Path II - The cube is first separated and then stretched. WII = W1 + W2 = 2 g + W2 Since WI = WII, w1 + 2 g + 2 Dg + 2 g xx = 2 g + W2 work/unit area = (W2 - w1)/2xx = fxx =  + D /Dxx

Surface stress, surface free energy and chemical equilibrium of small crystals Recall that for finite-size liquid drops in equilibrium with the vapor. (see condensation discussion) Equil. cond. where Vl is the molar vol. of the liquid. For a finite-size solid of radius r the internal pressure is a function of the size owing to the surface stress {isotropic surface stress}.

The pressure difference between the finite-size solid in equil The pressure difference between the finite-size solid in equil. with the liquid is Consider the equilibrium between a solid sphere and a fluid containing the dissolved solid. r

The total energy of the system is given by =0 Gibbs dividing surface set for component 1, other components are not allowed to cause area changes.

Consider the variation dU = 0 under the indicated constraints, Making the substitutions and for a sphere, gdA = (2g/r)dVs

Now consider an N component solid of which components 1, … Now consider an N component solid of which components 1, ….. k are substitutional and k +1, …. N are interstitial. Note that the addition or removal of interstitial atoms leaves AL unchanged. Then and

For interstitial exchange : fluid --interstitial--- solid ⓐ For substitutional exchange : fluid -- substitutional --- solid and defining and as the molar volume. ⓑ

Examples of how finite – size effects alter equilibria (1) Vapor pressure of a single – component solid using ⓑ same result as earlier

(2) Solubility of a sparingly soluble single component solid : using ⓑ (3) Melting point of a single component solid : see Clausius – Clapyron Equation where Sl and Ss are molar entropies.

using ⓑ (4) Vapor pressure of a dilute interstitial component in a non-volatile matrix ( H in Fe….) If the interstitial vaporizes as a molecule: or if it reacts with a vapor species, A, forming a compound AmXn

The chemical potential of X in the vapor is related to the partial pressure P of Xn or AmXn by and for the solid when Vx is the molar volume of X in the solid. Using ⓐ indicating that f determines the change in vapor pressure