Samuel A. Safran
Addison-Weslev, Reading, Mass.,
1994. 270 pp.' $55.95 he
ISBN 0-201-62633-0
Only recently has soft condensed mat-
ter physics—an area dealing with such
diverse materials as polymers, am-
phiphiles, liquid crystals and mem-
branes—been recognized by the phys-
ics community as an area of study in
its own right. The materials embraced
share a tendency to self-assemble into
aggregates such as lamellae and cylin-
drical or spherical micelles. These ag-
gregates may themselves assemble,
producing either ordered phases whose
symmetries range from the pedestrian
to the bizarre or disordered fluids
whose structures range from the trivial
to the complex.
The growth of interest in this non-
traditional area is fed not simply by
the inherent interest of such systems
but also by their enormous technologi-
cal importance and the increased
stimulation arising from the area's
overlap with biological subdisciplines.
Indeed, the model of biological mem-
branes as a bilayer ofamphiphilic phos-
pholipids, undergirded by an elastic
network of specialized proteins (them-
selves polymers of amino acids) and
incorporating other biologically active
proteins, serves as a paradigm of the
overlap of interests. This intersection
of physics, chemistry, biology and ma-
terials science is most likely to be one
of the areas of greatest excitement and
growth in the next decade.
A small indication of the activity in
this field was the publication in late
1994 of three books on the subject,
including Samuel Safran's Statistical
Thermodynamics of Surfaces, Inter-
faces, and Membranes. All three deal
with similar material but each presents
it very differently and to a somewhat
different audience. The other two
books are the multiauthor collection
Micelles, Membranes, Microemulsions
and Monolayers, edited by William Gel-
bart, Avinoam Ben-Shaul and Didier
Roux (Springer-Verlag) and the mono-
graph Self-Assembling Amphiphilic
Systems by Gerhard Gompper and me
(Academic) (See PHYSICS TODAY, March
1995, page 91). Whereas the latter two
are more narrowly intended for re-
searchers and their students, Safran's
book is broadly targeted at first-year
graduate students in any number ofdis-
ciplines and assumes only a rudimentary
knowledge of statistical mechanics.
One of the most laudable aspects of
Safran's presentation is the methodical
way he proceeds from simple to com-
plex systems. He first considers a sin-
gle isolated and static interface. The
effects of thermal fluctuations on the
interface are then considered in a dis-
cussion that culminates in a particu-
larly simple variational treatment of
the roughening transition first given
by Yukio Saito. Interactions between
rigid interfaces are considered next. I
was surprised and pleased to find here
a nice presentation of the theory of van
der Waals interactions due to Igor
Dzyaloshinskii, Evgenii Lifshitz and
Lev Pitaevskii; such a presentation is
unusual in a book aimed at beginning
graduate students. Fluctuations are
then added to the interfaces, which
leads to the discussion of bending en-
ergies and curvature moduli. This sec-
tion provides a nice example of the
benefits of a well-thought-out incre-
mental approach. Having previously
calculated the pressure between
charged plates immersed in solvent,
Safran can now use it to obtain the
saddle-splay modulus of a collection of
charged membranes. Finally, systems
of extensive amounts of interface are
treated, starting with colloids, whose
surfaces are given and rigid, and con-
cluding with self-assembling systems
consisting of fluctuating interfaces, as
exemplified by microemulsions.
While the systems studied get pro-
gressively more complex, the methods
employed do not. Safran consistently
applies variational methods wherever
possible. If this approach causes him
to sacrifice a treatment of the Koster-
litz-Thouless recursion relations when
discussing roughening, it nonetheless
enables him to tie this discussion to a
later one devoted to fluctuations in
bicontinuous phases. The presenta-
tion also benefits greatly from stimu-
lating and challenging problems.
The book has one major weakness:
There is almost no discussion ofexperi-
ment or its connection to theory. Were
I to teach a course using Safran's book,
I would certainly have to supplement
it with much discussion of physical
phenomena. Following my own preju-
dices, I would also broaden the cover-
age of the last chapter on self-assem-
bling systems, which now builds only
on the elastic description of interfaces
in earlier chapters, to include a Landau
description, which would also use
methods presented earlier. But it is a
tribute to this delightful book that,
after reading it, I would like to teach
a course based upon it. And I would
advertise it widely, not only in my own
department, but in biology, chemistry
and materials science as well.