Table Of ContentProgress in Colloid & Polymer Science. LoV 77
PROGRESS IN COLLOID & POLYMER SCIENCE
Editors: H.-G. Kilian (Ulm) and G. Lagaly (Kiel)
Volume 77 (1988)
desrepsiD smetsyS
Guest Editors: K. Hummel and .J Schurz (Graz)
0
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Preface
The 33rd meeting of the "Kolloid-Gesellschaft" was mers, optical investigation methods, pharmaceutical
held September 1987, in Graz, Austria. Graz holds a systems, adsorption processes, clay minerals and relat-
long tradition of work in colloid science. R. Zsigmon- ed topics. The program was well-balanced and includ-
dy, later Nobel prize winner for his work in this field, ed theoretical and practical aspects of today's colloid
was a lecturer at Graz University. G.E Hi)ttig's in- science. Scientists from eastern European countries,
vestigations into disperse systems and interfaces are especially Hungary, Yugoslavia, and Bulgaria, par-
well remembered. O. Kratky developed the application ticipated along with those from other European and
of x-ray small angle scattering to colloidal systems and foreign countries, making the meeting a truly interna-
we were honored that Prof. Kratky delivered the open- tional event.
ing lecture of the 1987C onference. This Progress Volume contains a selection of the
More than 160 active participants attended and the papers presented at the 1987 Conference. We hope it
scientific program included 55 lectures and 24 posters. will demonstrate the manifold nature and the diversity
The Conference covered colloids, latices, interface, of modern colloid science as an interdisciplinary field.
and surface films, surfactants, membranes, liquid
crystalline systems, emulsions, microemulsions, mi- Klaus Hummel
celles, lipids, polymeric structures, properties of poly- Josef Schurz
Contents
General
Kratky O: The importance of X-ray small-angle scattering in colloid research ................................ 1
Hosemann R: The a*-law in colloid and polymer science .................................................. 51
Spelt JK, Neumann AW: The theory of surface tension components and the equation of state approach ........ 26
Jacobasch H-J, Schurz J: Characterization of polymer surfaces by means of electrokinetic measurements ....... 40
Ribitsch ,V Jorde Ch, Schurz J, Jacobasch H J: Measuring the zeta-potential of fibers, films and granulates ..... 49
Surfactant Aggregation
Moroi :Y Relationship between solubility and micellization of surfactants: the temperature range of micellization 55
Anghel DE Balcan M: Critical micelle concentration of some homogeneously ethoxylated nonylphenols ........ 62
Ebert G, Plachky M, Sen0 M, Noritomi H: Studies on the conformation of polypeptides in reverse micelles .... 67
Kretzschmar G: Phase transitions in phospholipid monolayers and rheological properties of corresponding membrane
model ............................................................................................ 72
Heusch R, Kopp F: Structures in aqueous solutions of nonionic tensides .................................... 77
Te~ak D, Heimer S, Popovi6 S, Cerovec-Kostani6 B: Phase equilibria and thermodynamics of liquid and solid crystal
phases: formation of transition metal dodecyl benzenesulfonates ......................................... 86
Hinke E, Laslop D, Staude E: The influence of charged surfactants upon reverse osmosis ..................... 94
Emulsions and Microemulsions
Wielebinski D, Findenegg GH: Measurement of low interfacial tensions by capillary wave spectroscopy. Study of an
oil-water-surfactant system near its phase inversion ..................................................... 100
Sax B-M, SchOn G, Paasch S, Schwuger M "J Dielectric spectroscopy - a method of investigating the stability of
water-oil-emulsions ................................................................................. 109
Robertus C, Joosten JGH, Levine YK: Porod's limit of small angle-x-ray scattering from AOT/H20 isooctane
microemulsions .................................................................................... 115
Tondre C, Burger-Guerrisi C: Kinetics of phase transformations in a fluorinated microemulsion system ......... 120
Neumann H-J, Paczyfiska-Lahme B: Petroleum emulsions, microemulsions and micellar solutions .............. 321
Anghel DF, Balcan M, Donescu D: Phase equilibria in the systems used for vinyl acetate microemulsion
polymerization .................................................................................... 721
Tiemessen HLGM, Bodd6 HE, van Mourik C, Junginger HE: In vitro drug release from liquid cristalline creams;
cream structure dependence ......................................................................... 131
Dispersed Systems
Sakai M: Physico-chemical properties of small bubbles in liquids .......................................... 136
Mehandjiev MR: Thermodynamics of accumulation processes applied to colloidal systems .................... 341
Ludwig P, Peschel G: Evidence for secondary minimum coagulation in a silic hydrosol obtained by dynamic light
scattering ......................................................................................... 146
Pitsch M, Heckmann K, Kohler H-H, Strnad J: Sharp maxima in the flotation rate .......................... 152
Liphard M, yon Rybinski W: Pigment dispersion in organic solvents ....................................... 851
Zrinyi M, Kabai-Faix M, Horkay F: On the sediment volume of colloidal aggregates. .1 A. Fractal approach to the
problem .......................................................................................... 561
Hilbert F, Schweiger H, Huber I: Application of bentonite suspensions as supporting media in foundation engineer-
ing and other underground workings ................................................................. 171
Pfragner J: Effective volume and immobilization concentration of dispersed particles ......................... 771
Fischer JP, N61ken E: Correlation between latex stability data determined by practical and colloid chemistry-based
methods ....... _ .................................................................................. 180
Fiiredi-Milhofer H, Skrti6 D, Markovi6 M, Komunjer Lj: Kinetic analysis of the influence of additives on spontaneous
precipitation from electrolytic solutions ............................................................... 591
Stubi~ar N, (~avar M, Skrti6 D: Crystal growth of lead fluoride using constant composition method. I. The effect
of Pb/F activity Ratio on the solubility of solid phase ................................................. 102
Sperka G: Crystal growth in gels - a survey ............................................................ 207
VIII Contents
Polymer Solutions and Polymers
Tricot M: Electro-optical study of a polyelectrolytic graft copolymer ....................................... 211
Steiner E, Divjak H, Steiner W, Lafferty RM, Esterbauer H: Rheological properties of solutions of a colloidally
dispersed homoglucan from schizophyllum commune ................................................... 217
Lap~ik L, Valko L, Mikula M, Jan~ovi~ovd ,V Pan~ik J: Kinetics of swollen surface layer formation in the diffusion
process of polymer dissolution ...................................................................... 221
Ferdinand A, Springer J: Investigations of the permselectivity of styrene-butadiene block copolymer membranes. 227
Kanig G: Further electronmicroscope observations on polyethylene II. An artifact makes amorphous surface layers
visible on crystal lamellae in melts ................................................................... 234
Kunz M, Heinrich U-R, MOiler M, Cantow H-J: Element specific electron microscopy of polymeric materials ... 238
Author Index ........................................................................................ 242
Subject Index ....................................................................................... 243
Progress in Colloid & remyloP ecneicS rgorP & Colloid remyloP icS 77:1-14 )8891(
lareneG
The importance of x-ray small-angle scattering in colloid research
.O Kratky
yeK :sdrow ssaM_ determination, epah_s determination, radial density distribu-
length, tion, persistence s'doroP_ relations, scattering rewop
Introduction Of all the systems that can be approached by small
angle scattering we first describe the analysis of
When ew ask about possibilities to study the
monodisperse solutions of biological macromolecules,
geometric structure of colloidal and macromolecular
because they demonstrate the possibilities of the meth-
systems we can mention a number of methods which
od best.
provide one or two parameters; in addition, three
Why small-angle scattering? According to the law
methods exist which lead to much more substantial in-
of reciprocity in optics, diffraction occurs at smaller
formation:
angles the larger the structural dimensions are. Now,
)1 x-ray crystal structure analysis
since colloidal particles are huge as compared with the
2) electron microscopy
wave length of x-rays (approximately ,~), 1 scattering
)3 small-angle scattering of x-rays and neutrons
occurs at correspondingly small angles. In a
Even though crystal structure analysis exceeds all
monodisperse solution which is sufficiently dilute so
other methods in terms of resolution, there exists a
that the average distances between the particles are
limitation in its applicability through the requirement
large as compared with the particle size, the scattering
for crystals which must be not only of macroscopic
intensities from the individual particles simply add,
size but also largely free of defects: these requirements
and the effective scattering curve corresponds to that
are currently met only for part of all macromolecular
of one particle averaged over allp ossible spatial orien-
substances.
tations: in this case ew speak of particle scattering.
Electron microscopy has the undoubted advantage
of providing immediately comprehensible pictures;
however, the method is far from being non-invasive. A) Parameters
Moreover, because of the necessity of separating the
From certain characteristic features of particle scat-
particles from a solution, it is impossible, for instance,
tering a number of parameters can be obtained unam-
to study biological molecules in their natural sur-
biguously. eW shall discuss some of them in the
roundings. Considering the limitations of the other
following.
two methods, x-ray small angle scattering has certain
distinct advantages:
)1 Radius of gyration
a) x-ray small-angle scattering offers the possibility of
studying macromolecules in their natural sur- Just 50 years ago, Guinier [30] showed that the in-
roundings, i.e., in aqueous solution. nermost part of any particle scattering curve of
b) it is practically a non-destructive method. monodisperse particles is a Gaussian curve. Allow me
c) it does not require crystals. then to show a photograph of this pioneer of small-
d) it provides information on intermediate states in angle scattering: Guinier and the author in discussion
solution which are likely to be lost during crystalli- at the 2nd International Conference on X-ray Small-
zation or in the preparation steps necessary for Angle Scattering in Graz, 1970 (Fig. .)1
electron microscopic investigation. The following relation 1( a) describes the Gaussian
Therefore, x-ray small-angle scattering si an ideal course of a small-angle scattering curve in its inner-
supplement to the other two techniques. most part.
2 P: rogress R2 in Colloid & Polymer Science, Iiol. 77 (1988)
o T
H
e--
~. (2e) 2
Fig. .2 Schematic course of a particle scattering curve at very
small angles
Fig. .1 Andrd Guinier and the author in discussion at the
2nd International Conference on X-Ray Small-Angle Scat-
tering, Graz, 1970
I= Io.e -KR2(20)z K = 1 __ 1( a)
3
;1
In I = In Io-KR2(20) 2 I( )b
It contains the scattering angle 20, the scattering in-
tensity I and its value at zero angle I0, and, most im-
portantly, the parameter R, the radius of gyration. It 15p
represents the root mean square distance of all elec-
N¢
trons within one particle from the common electronic
center of gravity, and is, therefore, an illustrative mea- s~
sure fort he spatial dimension of particles. Plotting the
logarithm of the intensity, ln I versus (20) 2 (Guinier
plot) (I b), a curve is obtained (Fig. 2) in which the
61
tangent of the linear course in its innermost part yields O
the radius of gyration directly. R is a most important S~
parameter, not only as a measure for the size of a par-
ticle but also as a very useful indicator for structural
changes in a substance. An important field of shape
information is opened if we consider the behavior of
very anisotropic structures.
2) Rod-like particles [1] I 2 3
(20)2X 01 ~
Let us first consider a solution of infinitely thin and
infinitely long particles. This system of needles has a Fig. .3 Changes in cross section factor of malatsynthase with
scattering function represented by 1/20. In reality, increasing x-ray irradiation time in the Guinier plot ]2[
however, particles always have a finite thickness. This
leads to the function Ic, the cross section factor,
which depends on the size and shape of the cross sec- Analogous with the determination of the radius of
tion and by which the needle-scattering curve must be gyration R from the intensity in the case of cor-
multiplied: puscular particles, the radius of gyration of the cross
section R c in the case of elongated particles can be
1 evaluated from the cross section factor I¢ by a Guinier
I= c I :---- ; c I = I×(20) . (2)
02 plot.
Kratky, The importance of x-ray small-angle scattering in colloid hcraeser 3
In reality the particles also have a finite length, i.e., small-angle scattering. In addition if offers the
the maximum dimensions are lacking in comparison possibility of weighing particles [4]. According to
to infinitely long particles. According to the law of Thomson the ratio of scattering of the single electron
reciprocity these distances would scatter to the to the primary energy is known. Hence one can
smallest angles; if they are lacking, a deficit in intensi- calculate the ratio of scattering to primary energy for
ty at the smallest angle will occur, and, consequently, all electrons within one particle of the mass M, and
the cross section factor shows a falling tendency in its determine the molecular weight from the experimen-
innermost part. tally observed ratio of 0 I to P0. The following equa-
A very instructive example for these relationships is tion describes this relationship
givenb y the enzyme malatsynthase, which has been in-
M= 21"0"I°'a2 21.0- 1 (4)
vestigated by Zipper and Durchschlag [2]. Figure 3
shows the cross section factor for a series of solutions P0[Z2- 02~oI]2d'c NL Te
which have been exposed to increasing x-ray doses,
from bottom to top; this treatment leads to an associa-
The primary energy P0 is so exceedingly large that
tion of the particles. If one neglects the innermost
it cannot be measured with the same detector as the
part, the same cross section factor is observed in all
scattered energy I .0 However, this experimental prob-
cases; hence aggregation takes place in the longitudi-
lem is solved and we shall not discuss this here in any
nal direction.
detail. The symbols in Eq. (4) have the following
The original particles are initially short, and
meanings: a - sample-detector distance; d[cm] -
therefore, one observes at the beginning a strong de-
sample thickness; c[g/ml] - concentration; 2z -
crease of the cross section factor towards the angle
number of mole electrons per gram of dissolved sub-
zero. With increasing duration of irradiation this ef-
stance; 1Q - electron density of the solvent; 20 -
fect decreases and the shape approaches that of a long
partial specific volume of the dissolved substance; e T
rod. For the longest irradiation period finally, one - 7.9×1026 (Thomson's constant); n N - Avogadro's
observes in the innermost parts of the curves an in-
number.
creased cross section factor, which can be easily inter-
Hundreds of molecular weights of macromolecules
preted in terms of lateral aggregation of two rods.
have been measured according to Eq. (4). Of course,
there are other techniques for the same purpose,
3) Lamellar particles ]1[
especially ultracentrifugation. A unique possibility of
An analogous treatment applies to two-dimen- the small-angle method, however, is given by the fact
sional, lamellar particles, only that in this case the that it can determine the mass per unit length for
square of the scattering angle (20) 2 takes the place of elongated particles, it can, hence, quasi-weigh the slice
0 2 in all the formulas. Since we shall be concerned in of a sausage in molecular dimensions (5 a); likewise, in
the following mainly with the cross section factor, we the case of lamellar particles the mass per unit area
have limited ourselves to its discussion. can be determined (5b) .151 The corresponding rela-
tions
4) Particle volume
A further important parameter which can be ob- 6.68 [I(h h × ) 01 2 a
(5a)
tained from particle scattering is the volume. Accord- Mc = ~0 2Z[ - ]1Q20 2d'c
ing to Porod ]3[ the following equation holds
23"10 3.34[I(h )×h2]o az
= V (3) )bS(
- M t ~, 2p0 2Z[ - 02Q112d'c
4n ~ I×(20)2d(20) .
o
The integral in the denominator is frequently assigned contain the factors [I(h) h × 0] and [I(h) × h 012 , re-
the symbol Q and is called the invariant because it is spectively, wherein
independent of the degree of dispersion. This quantity
will be used repeatedly in the following discussion. h = n 4 sin 0/2 . (6)
5) Mass determination
These expressions hence are proportional to the cross
The determination of sizes and shapes of dissolved section factor [lo(20)]o and the thickness factor
macromolecules is not the only possibility offered by [1(20)21o at the angle zero.
4 ssergorP ni Polymer Colloid & Science, LoV 77 )8891(
B) General scattering theory 147] If we know the shape of a body, we can calculate
p(r) (this is a merely geometrical task, relatively easy
)1 Homogeneous particles to solve for all tri-axial symmetrical bodies as for in-
stance tri-axial ellipsoids, but it is more difficult for
We have derived certain parameters from the scat-
complex particles which are composed of several sym-
tering curve. In the following we shall attempt to
metric parts). We have only to insert the result into Eq.
describe the entire shape of the particle as precisely as
(7a) to obtain the corresponding scattering curve.
possible. This requires a quantitative relation such as
However, we intend to go the opposite way: we know
the following (7 a):
the scattering curve and want to evaluate the shape of
the body. The only possibility that remains is the trial
~sin hr'~
I(h)=4/r 0~ p(r) \---~r J dr; h = n 4 sin 0/2 and error approach, i.e., to try assumed structures un-
til one finds one that closely approximates the ob-
(7a)
served distance distribution function p(r) obtained by
and by Fourier transformation
Fourier transformation (7 b) of the measured scatter-
ing curve.
r 2 I(h)×h 2 sinhr.dh (7b) Frequently this task can be facilitated by auxilliary
p(r) -= ---z~2 ~ o hr
information from other sources. An example is given
by Immunoglobulin [6]. From the scattering curve a
sin h r . cross section factor is obtained, shown in its Guinier
The term- is the scattering of a dumbbell ac-
hr representation in Fig. 4. This plot shows three charac-
cording to Debye, hence the scattering of a body con- teristic properties:
sisting of two point masses separated by the distance
)1 the substance is composed from rod-like particles,
r, averaged over all orientations in space. If a structure
otherwise no straight section in the Guinier plot of
has the distance distribution function p(r) (which is
the cross section could be observed (the measure-
the number distribution of distances r between any
ments are shown by the points at the bottom
two volume elements within one particle), we have on-
curve).
ly to perform the above integration in order to obtain 2) the decay of the cross section factor in the Guinier
the entire scattering curve I(h). plot in the innermost part shows that the rods are
short.
3) the curve has two branches, which means that there
are two cross sections prevailing. In good agree-
ment with this, the biochemical investigations by
F
Edelman ]7[ have provided evidence for the ex-
istence of three subunits. Of the possible con-
figurations following from these facts the one with
fully stretched arms (assigned no. 4) leads to the
best agreement between experiment (points in
curve 5) and theory (curve 4).
Frequently, the power of the trial and error method
is amazing. As an example, the comparison of the ex-
perimental distance distribution function of the lac
repressor to the theoretical curves, which correspond
to the models, is shown in Fig. 5 (in collaboration with
$: O. Jardetzky [8]). This model has been formed by 600
I0, -... [ ,
small spheres which do not represent subunits but
serve for the simulation of the shape only. In the same
way a major number of trial and error developments
• ( 20} 2 2] {radians
has been carried out by Pilz, a former collaborator of
2 • 10 -z' /, .10 -/" 6 .10 -t' ~o mine. This kind of research requires three distinct fac-
Fig. .4 Guinipelro t of the theoretical cross section scattering tors: )1 diligence and patience, 2) access to a powerful
curves (1-4) of the -Y and X-shaped models shown in the
computer, 3) a feeling for the manifold variations, one
right part of the figure (1-4) of IgG in solution. The -xe
perimental curve ]5[ shows the best fit to model ,4 ]6[ of which finally leads to success.
