Chemistry Versus Physics: Chemical Reactions Near Critical Points

144 Pages·2009·1.614 MB·English

by  Moshe Gitterman

CHEMISTRY
VERSUS
PHYSICS
Chemical Reactions Near Critical Points
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
CHEMISTRY
VERSUS
PHYSICS
Chemical Reactions Near Critical Points
Moshe Gitterman
Bar-Ilan University, Israel
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
CHEMISTRY VERSUS PHYSICS
Chemical Reactions Near Critical Points
Copyright © 2010 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to
photocopy is not required from the publisher.
ISBN-13 978-981-4291-20-0
ISBN-10 981-4291-20-X
Printed in Singapore.
ZhangFang - Chemistry vs Physics.pmd 1 9/10/2009, 7:09 PM
September14,2009 16:24 WorldScienti(cid:12)cBook-9inx6in General-nn
Preface
Inthisbookweattempttotracetheconnectionbetweenchemicalreactions
and the physical forces of interaction manifested in critical phenomena.
Thephysicalandchemicaldescriptionsofmatterareintimatelyrelated. In
fact, the division of forces into \physical" and \chemical" is arbitrary. It
is convenient [1] to distinguish between strong attractive (chemical) forces
leadingtotheformationofchemicalspecies,andweakattractive(physical)
forces, called van der Waals forces. It should be remembered, therefore,
when one considers the \ideal" ternary mixture A, B and A B ; that the
m n
strong chemical bonding interaction between A and B atoms has already
been takeninto account viathe formationof the chemical complexA B ,
m n
andtheterm\ideal"onlymeansthatthereareno\physical"forcespresent.
The growth of clusters in a metastable state is an example of the fuzzy
distinction between physicaland chemical forces. In numericalsimulations
aratherarbitrarydecisionhastobemadewhetheragivenparticlebelongs
to a \chemical" cluster.
The usefulness of a \chemical" approach to physical problems can be
seen from the mean-(cid:12)eld theory of the phase transition on an Ising lattice
of non-stoichiometric AB alloys [2]. The temperature dependence of the
long-rangeandshort-rangeorderparametersisfoundfromthe\lawofmass
action" for the appropriatelychosen \chemical reaction." The latter is the
exchange of position of an atom A from one sublattice and an atom B
fromthesecondsublattice. Thechangeoftheinteractionenergyforsucha
transitionwhenbothatomsareorarenotnearestneighborsdeterminesthe
\constant of chemical reaction." Such an approachallows one to avoid the
calculation of entropy provided that one is interested only in the value of
the critical temperature, ratherthan in the behavior of allthermodynamic
quantities, which are determined by the same classical critical indices in
v
September14,2009 16:24 WorldScienti(cid:12)cBook-9inx6in General-nn
vi Chemistryversus Physics: Chemical Reactions near Critical Points
all versions of mean-(cid:12)eld theory. The latter example is, in fact, a special
case of chapter 15 in [3], where the typical \physical" process of di(cid:11)usion
is considered as a \chemical reaction" in which some amount of substance
A passes from volume element a to b while a di(cid:11)erent amount of B passes
from b to a.
The\chemical"method, in which agivenatomwith allits neighborsis
consideredasthebasicgroup,givesbetterresultsthantheBragg-Williams
or Bethe-Peierls method. In the Bragg-Williams method, each atom is
exposedtothe(self-consistent)averagein(cid:13)uenceofallotheratoms,whereas
in the Bethe-Peierls method, a pair of adjacent atoms is considered as the
basic group.
Even though the border between chemical and physical forces is arbi-
trary, one usually considers (cid:12)rst the \physical" forces in the equation of
state, and then the \chemical" forces in the law of mass action based on
the non-ideal equation of state. I shall follow this approach.
Onecanalsotracethe commonfeaturesof phasetransitionsandchem-
ical reactions by analyzing the time evolution of the state variables de-
scribed by the equation
d =dt=F [ ;(cid:21)]; (0.1)
where(cid:21)isthesetofinternalandexternalparameters,andF isanonlinear
functional in . In the case of a phase transition, Eq. (0.1) may be the
Landau-Ginzburg equation for the order parameter, while in the case of
a chemical reaction | the equation for the rate of reaction. The steady
state of the system is described by 0((cid:21)) which is the solution of equation
F 0;(cid:21) =0:FornonlinearF, morethanonesteadystatesolutionispos-
sible, andforsomevaluesof(cid:21);attheso-calledtransitionpoint,bifurcation
(cid:2) (cid:3)
may occur, when a system goes from the original steady state to the new
steadystate. Suchatransitionmightbe of(cid:12)rstorsecondorderinthecase
of a phase transition, and, analogously, the hard or soft transition for a
chemical reaction.
I have kept this book as simple as possible, so that it will be useful
for a wide range of researchers, both physicists and chemists, as well as
teachers and students. No preliminary knowledge is assumed, other than
undergraduate courses in general physics and chemistry. In line with this
approach, I have favored a phenomenological presentation, thus avoiding
the details of both microscopic and numerical approaches. There are a
tremendous number of published articles devoted to this subject, and it
provedimpossibletoincludemanyofthem inthisbookof smallsize. Iask
September14,2009 16:24 WorldScienti(cid:12)cBook-9inx6in General-nn
Preface vii
the forgivenessof the authorswhosepublications werebeyondthe scopeof
this book.
The organizationof the book is as follows.
AftertheIntroduction,Chapter1containsashortreviewofphasetran-
sitions and chemical reactions and their interconnection, which is needed
to understand the ensuing material. Chapter 2 is devoted to the speci(cid:12)c
changesin a chemical reactionoccurringnearthe critical point. The e(cid:11)ect
of pressureand phase transformationon the equilibrium constantand rate
ofreactionisthesubjectofSecs.2.1{2.2. Thehallmarkofcriticalphenom-
ena|theslowingdownofallprocesses|leadsalsototheslowing-downof
the rates of chemical reactions. This phenomenon is described in Sec. 2.3,
while the opposite peculiar phenomenon of speeding-up of a chemical re-
action near the critical point provides the subject matter for Sec. 2.4. It
is shown that all three types of behavior (slowing-down, speeding-up and
unchanged) are possible depending on the given experiment. In Sec. 2.5,
we consider another in(cid:13)uence of criticality | the anomalies in chemical
equilibria including supercritical extraction. The appropriate experiments
are described in Sec. 2.6.
The reverse process | in(cid:13)uence of chemistry on critical phenomena |
formsthe contentof Chapter3, includingthe changein the criticalparam-
eters (Sec. 3.1), critical indices (Sec. 3.2), transport coe(cid:14)cients (Sec. 3.5)
and degree of dissociation (Sec. 3.3). Section 3.4 is devoted to the isotope
exchange reaction in near-critical systems.
Chapter 4 deals with the problem of the phase separation in reactive
systems. The occurrence of multiple solutions of the law of mass action
is described in Sec. 4.1. The mechanism of phase separation depends on
whetheritstartsfromametastableoranon-stablestate. Theformercase,
where phase separation takes place through nucleation, and the spinodal
decompositionforthelattercaseareconsideredinSecs.4.2and4.3,respec-
tively. Section 4.4 is devoted to the special case of a dissociation reaction
in a ternary mixture.
Chapter5containsadescriptionofchemicalreactionsnearsomespeci(cid:12)c
regionsofthephasediagram. Anaccountofthesupercritical(cid:13)uidsisgiven
inSec.5.1,whilethevicinitiesoftheazeotrope,meltinganddoublecritical
points are considered in Secs. 5.2, 5.3 and 5.4, respectively. The main ex-
perimentalmethods of analysisof near-critical(cid:13)uids |soundpropagation
and light scattering | are considered in Chapter 6. Finally, in Chapter 7
we present our conclusions.
September14,2009 16:24 WorldScienti(cid:12)cBook-9inx6in General-nn
Contents
Preface v
1. Criticality and Chemistry 1
1.1 Critical phenomena. . . . . . . . . . . . . . . . . . . . . . 1
1.2 Chemical reactions . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Analogybetweencriticalphenomenaandthe instabilityof
chemical reactions . . . . . . . . . . . . . . . . . . . . . . 12
2. E(cid:11)ect of Criticality on Chemical Reaction 15
2.1 Thee(cid:11)ectofpressureontheequilibriumconstantandrate
of reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 E(cid:11)ect of phase transformations on chemistry . . . . . . . 17
2.3 Critical slowing-downof chemical reactions . . . . . . . . 19
2.4 Hydrodynamic equations of reactive binary mixture:
piston e(cid:11)ect . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4.1 Heterogeneous reactions in near-critical systems . 26
2.4.2 Dynamics of chemical reactions . . . . . . . . . . 27
2.4.3 Relaxation time of reactions . . . . . . . . . . . . 29
2.4.4 Hydrodynamic equations of a reactive binary
mixtures . . . . . . . . . . . . . . . . . . . . . . . 32
2.4.5 Hydrodynamic equations with statistically
independent variables . . . . . . . . . . . . . . . 38
2.5 Critical anomalies of chemical equilibria . . . . . . . . . . 46
2.6 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3. E(cid:11)ect of Chemistry on Critical Phenomena 53
ix
September14,2009 16:24 WorldScienti(cid:12)cBook-9inx6in General-nn
x Chemistryversus Physics: Chemical Reactions near Critical Points
3.1 Change of critical parameters due to a chemical reaction . 53
3.2 Modi(cid:12)cation of the critical indices . . . . . . . . . . . . . 55
3.3 Singularity in the degree of dissociation near a critical point 60
3.4 Isotope exchange reaction in near-critical systems . . . . . 62
3.5 Singularities of transport coe(cid:14)cients in reactive systems . 63
3.5.1 Mode-coupling analysis . . . . . . . . . . . . . . . 63
3.5.2 Renormalization group methods . . . . . . . . . . 65
4. Phase Separation in Reactive Systems 67
4.1 Multiple solutions of the law of mass action . . . . . . . . 67
4.2 Phase equilibrium in reactive binary mixtures quenched
into a metastable state . . . . . . . . . . . . . . . . . . . . 69
4.2.1 Thermodynamic analysis of reactive binary
mixtures . . . . . . . . . . . . . . . . . . . . . . . 69
4.2.2 Thermodynamic analysis of reactive ternary
mixtures . . . . . . . . . . . . . . . . . . . . . . . 72
4.2.3 Kinetics of phase separation . . . . . . . . . . . . 75
4.3 Phase equilibrium in reactive mixtures quenched into an
unstable state . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.4 Thermodynamics of a three-component plasma with a
dissociative chemical reaction . . . . . . . . . . . . . . . . 89
5. Comments on the Geometry of the Phase Diagram of a
Reaction Mixture 93
5.1 Solubility in supercritical (cid:13)uids . . . . . . . . . . . . . . . 93
5.2 Azeotropic points in reactive many-component systems. . 100
5.3 Melting point of reactive binary mixtures . . . . . . . . . 101
5.4 Double critical point . . . . . . . . . . . . . . . . . . . . . 105
6. Sound Propagation and Light Scattering in Chemically
Reactive Systems 111
6.1 Ultrasound attenuation in near-criticalreactive mixtures . 111
6.2 Hydrodynamicanalysisofthedispersionrelationforsound
waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.3 Light scattering from reactive systems . . . . . . . . . . . 118
6.4 Inhomogeneous structure of near-critical reactive systems 121
7. Conclusions 125