DETERMINATION OF PARTICLE SHAPE

CHAPTER 10

DETERMINATION OF PARTICLE

SHAPE

COLLOIDAL particles may possess very different shapes. The most common shapes are shown in Fig. 91. It is very difficult to give a complete classification of colloids based on particle shape. Proposals have been made to classify the particles as linear, laminar, or corpuscular, or as one-, two- or three-dimensional. In linear particles the atoms are lined up in one dimension, in laminar particles they form leaflets (two dimensions), in a corpuscular particle there are three-dimensional units. However, an atom itself is three-dimensional, and consequently any linear or laminar particle is three-dimensional. Moreover, a linear molecule, e.g. of polystyrene, may contain laminar units, as the benzene rings in this polymer. Further, a linear molecule can be coiled. The coil may be very loose or quite compact. The linear molecule can be so slightly kinked and loose that it is almost like a thread ; but it can be also coiled to such a degree that it is actually a three-dimensional body. There are many other possibilities of various intermediate shapes and secondary structures. A complete classification is impossible and would be useless. Very useful, however, is the simple classification into spherocolloids and linear colloids, as proposed by STAUDINGER. The particles of the former need not necessarily have the shape of a ball, but they may be shaped like an egg, a short rod, or a thick leaflet. The linear colloids, on the other hand, may have particles like long rods, coiled or branched threads. The principal particle shapes are best distinguished by viscosity measurements. A 1% solution of a spherocolloid has a low viscosity, whereas such solutions of linear colloids are very viscous.

F I G . 9 1 . The most common shapes of colloidal particles.

Sometimes it is useful to classify the particles as isometric and anisometric. The former have approximately the same dimensions in all directions in space (ball, polyhedron), the latter, however, are extended in one or two directions, and can be rods, leaflets, threads, etc. A 217

218

DETERMINATION

OF

PARTICLE

SHAPE

moderately coiled linear molecule may form an isometric unit, and thus the colloids with isometric particles are not necessarily spherocolloids. On the other hand, a colloid containing anisometric rods or leaflets may possess the properties of a spherocolloid (low viscosity), if the particles are not greatly extended in one direction. This classification principle is illustrated in the scheme : - Colloidal

Particles

Isometric<

/ ν

Polyhedric units

Compact spheres

Loose coils

^ Short rods

Long rods

Leaflets

Linear molecules Loose Branched anisometric threads loops

Instead of ' isometric ' the words isodiametric, isodimensional, or simply symmetric can be used ; accordingly, instead of ' anisometric ' one may say anisodiametric, anisodimensional, or asymmetric. The optical anisotropy (see p. 125), however, must not be confused with the terms denoting the mere geometrical shape (asymmetry, anisometry, etc.), as an optically anisotropic particle may be isometric, and a geometrically asymmetric particle may be optically isotropic. All emulsions, as well as most of the metal sols, sulphide sols and sulphur colloids have isometric (or isodimensional) particles. Molecules of many proteins, e.g. egg albumin, serum globulin and insulin, have shapes like short rods or egg-shaped bodies. Vanadium pentoxide sols, and some proteins (myosin of muscle, tobacco mosaic virus) have long rods. Graphite sols, some clays, and some hydroxide colloids possess laminar particles. Starch has branched threads. The macromolecules of the synthetic polymers have in most instances the shapes of more or less kinked threads The particles in different kinds of clays have very interesting shapes. As an example may be mentioned the attapulgite (Georgia, U.S.A.). It is a strongly hydrated magnesium aluminium silicate composed of long particles. According to the electron micrographs taken by ( 1) MARSHALL and CALDWELL the particles are about 6,400 to 12,000 À long and 170 to 630 Â wide. They are lath-shaped. The electron ( 1)

C. E . MARSHALL and O . G . C A L D W E L L ;

/ . Phys. Colloid

Chem. 5 1 , 3 1 1 (1947).

IMPORTANCE OF PARTICLE

SHAPE

219

micrographs show that single particles of appreciable width are of a faint optical density, whereas narrower particles are much blacker, suggesting that they are laths seen on edge. It is noteworthy that suspensions of attapulgite are very sensitive to coagulation a n d readily form temporary associations of particles which can be broken u p by shaking (thixotropy). The flat leaf-shaped particles of graphite are important in improving lubricating greases and oils. The so called ' Oildag ' is a trade name of an about 1 5 % dispersion of finely dispersed graphite in oil which is added to lubricants. In addition to the lubricating effects of the oil, the friction between the surfaces is reduced by a layer of the laminar graphite that precipitates on the bearings. The mechanical properties of a colloidal material depend primarily on the molecular shape. N o rayon with sufficient tensile strength can be made of a cellulose derivative with short molecules. N o durable structures can be made of round-shaped particles. This is especially important in considering biological structures. It is now universally admitted that all structural tissues are built of linear colloids. Cellulose is the most important linear colloid in plants, whereas in animals the same functions are performed by various linear proteins—collagen in skin, sinews and bone ; myosin in muscle ; keratin in nails, horn, and hair. The proteins circulating in the bodily fluids, however, have globular molecules, since thread-like units would increase the viscosity too much. Spheres are thus much better for such transportation than threads or branched rods, which might even clog the capillaries dangerously. In the important process of blood clotting, however, some of the blood proteins are converted into linear proteins which then can form a solid jelly. Important changes have also occurred in the general concepts concerning the structure of protoplasm. While some decades ago the concept prevailed that the semi-solid structure and high V I S -

FIG. 92. The formation of structures with fibrous and with globular particles.

cosity of protoplasm was caused by a very high degree of hydration of the cell colloids, it is now generally recognised that protoplasm contains linear colloids which are responsible for the peculiar behaviour of ( 2) In a solution of a linear colloid fewer junctions are these systems. ^ A. FREY-WYSSLING, translated by J. H E R M A N S and M. H O L L A N D E R ; Submicroscopic Morphology of Protoplasm and its Derivatives (Elsevier Publ.,

Amsterdam, 2nd ed., 1953).

220

DETERMINATION

OF PARTICLE

SHAPE

needed to build u p a framework than in the case of spherical particles (Fig. 92). Linear molecules have also a much larger surface than the same quantity of a substance with spherical particles. Because of the larger surface linear molecules are capable of all kind of interactions, both with the water and with other macromolecules. Biological objects are known which contain 9 7 % or more water, and yet they possess a structure. Several exact methods are now available for the determination of particle shapes: (1) double refraction of flow, (2) light scattering, (3) sedimentation and diffusion measurements, (4) the viscosimetric method, (5) X-ray analysis, and (6) electron microscopy. Methods (5) and (6) will be discussed in the next chapter. Double refraction of flow, depolarisation, and other optical phenomena There are several simple methods by means of which it is possible to draw qualitative conclusions concerning particle shape, if the particles are sufficiently large and are sufficiently different from the medium in their optical properties. Thus it is possible to obtain a definite optical effect from aged vanadium pentoxide colloids. If this yellow, clear sol is slowly stirred, the path of the stirring r o d lightens up. The effect is explained by the orientation of the rod-like particles of vanadium pentoxide along the stream lines; the oriented particles reflect a n d scatter the light more than the unoriented particles which, because of the Brownian movement, are moving and rotating at random. The same optical effect can be observed in several other colloids possessing rod-like particles, but never in spherocolloids. Rod-like particles can also be distinguished from spherical particles by means of the ultramicroscope. Rod-like particles 'twinkle' if observed in the ultramicroscope, whereas the light coming from isometric particles is uniform. The twinkling of rod-like particles is explained by the change in their positions in respect to the light beam by the Brownian movement. In positions parallel to the beam the particles will influence the beam less than if they move across it. A step forward toward the quantitative investigation of particle shape by optical methods was taken by DIESSELHORST a n d FREUNDLICH

in 1916. They observed the light scattered by colloids flowing through

F I G . 93. Rodlike particles streaming in a rectangular tube.

DOUBLE

REFRACTION

OF FLOW

221

narrow rectangular tubes. The scatter did not change with the rate of flow when a sol possessing spherical particles flowed through such a tube. Asymmetric particles, however, behave quite differently: firstly, the scattering depends on whether the sol rests or moves, and secondly, the intensity of the scattered light depends on the direction of observation (Fig. 9 3 ) . These differences are caused by the anisometric shape of the particles. When the sol rests in the tube, the particles are randomly distributed not only in respect to their concentration, but also in respect to their relative geometrical positions. Under the influence of flow, however, rod-like particles are oriented along the stream lines, and the whole solution behaves like a crystal. The above-mentioned authors were also able to distinguish by this method between rod-like and laminar particles. Moreover, it is obvious that the longer the rods the more easily they will be oriented in the stream, which behaviour may serve as a basis for a quantitative method. The oriented particles in a rectangular tube behave like an anisotropic system, i.e. show the phenomenon of double refraction. The so-called double refraction of flow or streaming birefringence is a very important property in the investigation of particle shape. Assume, for example, that a colloid possessing rod-like particles, such as those of vanadium pentoxide or myosin, is observed in a rectangular tube between two crossed Nicol prisms. When the colloid is undisturbed, the field of vision will be dark. If, however, the colloid is forced to flow, the field of vision will lighten up. The brightness of the field can be measured quantitatively by means of a photoelectric cell. The brightness is proportional to the double refraction of flow. By means of this method LAUFFER a n d STANLEY ( 3) investigated the asymmetry of the particles of the tobacco mosaic virus. It must be pointed out that the double refraction of flow depends on the shape of the particles as well as on the flow rate, but it is independent of the optical anisotropy of the individual particles. A colloid possessing optically anisotropic particles, either rod-like or of any other shape, if n o t flowing, will show n o double refraction at all. The double refraction will appear only in flow. The same phenomenon of double refraction of flow is shown by all those colloids whose particles are asymmetrical, but n o t necessarily optically anisotropic. F o r instance, a kinked linear molecule of polyvinyl chloride is asymmetric but not anisotropic ; it will be oriented in flow, a n d will show the phenomenon of streaming birefringence. The most efficient experimental method to investigate double refraction of flow is that of MAXWELL. F o r this purpose an apparatus like that of the viscometer of COUETTE (p. 1 6 1 ) is used. The colloid is placed between two cylinders, a n d it can be observed through two Niçois (Fig. 9 4 ) . One of the cylinders can be rotated, thus causing 3

<> M . A . L A U F F E R and W . M . S T A N L E Y ;

/ . Biol. Chem.

123, 507 (1938).

222

DETERMINATION OF PARTICLE SHAPE

flow and orientation of the particles along the stream lines. Colloids possessing isometric particles, when observed in this instrument between crossed Niçois, will show no change, either in the solution at

F I G . 94. Schematic drawing of the Maxwell device.

FIG. 95. Schematic view of the biréfringent medium in the gap between the concentric cylinders. The cross of isoclyne is shown at an angle X, the so-called extinction angle, with respect to the plane of the polariser for a rotating outer cylinder. The angle is determined experimentally. It is equal to the angle formed between an oriented rod-like particle a and the stream lines of high velocity gradient. The angle X varies between 0 and 45°. If the rod-like particle is fully oriented, the angle is zero. In the case of a complete disorientation the average position of the particles with respect to the stream lines will be 45°. The angle X decreases with increasing angular velocity of the rotating cylinder and with the orientation of the particles.

rest or in motion. Colloids with anisometric particles, however, will behave quite differently. T h e originally dark field of vision, after the rotation starts, will lighten up, leaving only a cross-shaped shadow. When the rate of rotation of the cylinder is increased, the position of the arms of the cross change. It is then possible to relate this change to the angular velocity, and to the axial ratio of the oriented particles. The calculations are based on the relation existing between the double refraction of flow and the rotational diffusion constant F. The meaning of the latter can be explained as follows. Suppose that all the rod-like particles in a linear colloid are oriented by means of some external force and that this force is then suddenly removed. Because of Brownian movement the rods now will be disoriented, and after a certain time they will be quite randomly distributed in the solution. This relaxation time t is related to F by F= \ t. The measured extinction angle X is related to F by the equation : tan 2 ^ = 6 / 7 6 , (1) where G, the flow gradient, is determined by the speed and dimensions of the rotating cylinders. F i s related to the length of the rods L by the following approximated equation : F=3kTI\67TVL\

(2)

DOUBLE

REFRACTION

A N D VISCOSITY

223

where k is the Boltzmann constant, Τ the absolute temperature, and η the absolute viscosity of the solution. The rotatory diffusion constant thus is inversely proportional to the cube of the length of the rods. If the angle X is measured, F and L ( )4 can be calculated. Another method of measuring the double refraction is by means of a compensator which is placed in the path of the beam passing the Maxwell device. This compensator is a biréfringent plate. It is placed with its optical axis parallel or perpendicular to Ρ or Px (Fig. 95), and the analyser Nicol is rotated until the light is extinguished. This angle of rotation A is the measure of the double refraction ne - n0 of the oriented colloid. SIGNER, M U R A L T , EDSALL

( 5 )

a n d others showed in 1 9 3 0 - 1 9 3 9 that

linear colloids show the phenomenon of double refraction of flow. Conclusions regarding the length of the particles, e.g. their axial ratio have been drawn; the estimates were in some cases confirmed by direct observations in the electron microscope. ROBINSON in 1 9 3 9 made a very interesting study of the simultaneous streaming birefringence a n d viscosity properties of the tobacco mosaic virus protein. The colloid was observed in a Couette viscometer (see p. 1 6 1 ) . U p o n rotating the outer cylinder the long rod-like particles of the virus became oriented along the stream lines, a n d by means of Nicol prisms the orientation could be measured. A t the same time the inner cylinder started to turn because of the viscosity. The higher the viscosity the more the inner cylinder was rotated. ROBINSON found that with increasing speeds of rotation of the outer cylinder the double ( 6) refraction of flow increased but the viscosity decreased. The latter is in complete agreement with the concept that orientated rods show less resistance to flow than randomly distributed rods. The theoretical treatment relating the streaming birefringence to the asymmetry of the particles is very complex. Moreover, the whole problem is complicated by the fact that most of the colloids are poly( 7) disperse systems. Generally the rods are of the same thickness, but

F I G . 96. The stretching of matted coils under the influence of shear stress. ( 4)

J. T. E D S A L L in C O H N and E D S A L L ; Proteins, Amino Acids and Peptides (Reinhold, New York, 1943), Chap. 21. ( 5 ) R . S I G N E R and H . G R O S S ; Z . physik. Chem. 165, 161 (1933); J. T . E D S A L L ; Advances in Colloid Science (edited bv E . K R A E M E R ) , 1, 269 (1942); J. T . E D S A L L and J. F . F O S T E R ; / . Amer. Chem. Soc. 70, 1860 (1948) ; R. C E R F and H. S C H E R A G A ; Chem. Revs. 51, 185 (1952). (e > J. R . R O B I N S O N ; Proc. Roy. Soc. {London), A 170, 519 (1939). ( 7) A . E . A L E X A N D E R and P. J O H N S O N ; Colloid Science (Clarendon Press, Oxford 1949), pp. 380-^12. C H . S A D R O N ; / . Phys. Radium 9, 381 (1938), and I.e. 5.

224

DETERMINATION

OF PARTICLE

SHAPE

they have different lengths. Further, if the particles are not rigid rods or leaflets but flexible chains, their shape can be changed under the influence of the shear stress. Suppose a macromolecule in solution exists as a kinked thread (Fig. 96) ; in the case of a solution at rest the parts of the chain under the influence of Brownian motion will change their positions, but the overall molecule shape will remain the same. A sufficiently strong shear stress, however, may force the thread to stretch out. The faster the cylinder rotates in the Maxwell apparatus, the more the threads will be stretched. In the case of rigid rods under a gradually increased shear stress (rotation rate of the cylinder in the Maxwell apparatus) the double refraction will approach a limit. This ' saturation value ' corresponds to the full orientation of the rigid rods. In the case of flexible macromolecules such a limit or saturation has not been reached, but the double refraction steadily increases with increasing shear stress. This fact is explained by the assumption that the kinked chains are more and more extended by the increasing shearing force. This was shown quite convincingly, for instance, with solutions of polyisobutylene (in petroleum ether) subjected to very high shear ( 8) For high molecular fractions of the polymer the double stress. refraction increased with increasing shear stress much more than for the low molecular fractions (Fig. 97). These facts confirm the assump-

Ν

Shear stress

F I G . 97. The increase of the double refraction of flow with increasing shear stress. Curve 1—a high molecular fraction of polyisobutylene; curve 2 —a lower molecular fraction of polyisobutylene.

F I G . 98. The observation of the double refraction in ferric hydroxide sols placed in a magnetic field. Ρλ and P2 are two Nicol prisms. The sol is placed in the container a.

tion that kinked chains are somewhat extended if subjected to a sufficiently intense orientating force. There are several other ways of investigating particle shapes by optical means. The phenomenon of depolarisation is important in light scattering. The light scattered by small spherical particles is polarised in various degrees depending on the angle of observation. The light observed at 90° in respect to the illuminating beam is com( 8)

V. N. T S V E T K O V and E. F R I S M A N ; Acta Physicochim. U.R.S.S. 20, 61 (1945); C.A. 40, 788 (1946); V. Ν. T S V E T K O V ; / . Polymer Sei. 23, 151 (1957).

LIGHT

SCATTERING

AND

PARTICLE

SHAPE

225

pletely polarised. (If the size of the spherical particles is of the order of one wavelength, the maximum polarisation is not found at right angles to the entering beam, but at a different angle, e.g. 110°.) If the solution, however, contains small optically anisotropic particles, the light scattered in the direction perpendicular to the illuminating beam is not completely polarised. The amount of depolarisation can be determined, and the measurements thus provide a means of determining the optical anisotropy of the particles. Finally, it should be pointed out that double refraction in a number of colloids possessing asymmetric particles can be produced by the action of electrical or magnetic fields. It was shown by MAJORANA as early as 1 9 0 2 that ferric hydroxide sols, when placed between sufficiently strong magnets (Fig. 9 8 ) , may become anisotropic. The same phenomenon occurs if instead of ferric hydroxide, colloidal vanadium pentoxide is investigated. The magnet obviously produces some orientation of the asymmetric particles. If these colloids are mixed with hot gelatin solution, and the mixture is allowed to set in the magnetic field, the jelly acquires permanent optical anisotropy. The gelatin jelly is isotropic, but it holds the oriented particles of ferric hydroxide or vanadium pentoxide in oriented positions. (In a liquid medium the orientation caused by flow, or by a magnetic field, is temporary, and disappears gradually, because of the Brownian motion, when the stress ceases.) The shape of colloidal particles from the anisotropy of conductivity This new method is based on the fact that the conductivity of a colloid containing asymmetric electrically charged particles depends on ( 8 a) A theoretical treatment of this the orientation of the p a r t i c l e s . ( 8 b) effect has also been given r e c e n t l y . When a colloid containing asymmetric particles is oriented in a Couette concentric cylinder device (see p. 1 6 1 ) , the electrical conductivity is different in different directions, and it is possible in this way to distinguish rod-shaped particles from ( 8 c) In other words: the conductivity of such systems oriented in disks. flow gradient becomes anisotropic. Measurement in direction perpendicular to the plane of flow enables rod-shaped and disk-shaped particles to be distinguished simply by the arithmetical sign of the change of conductivity. If the conductivity is plotted against velocity gradient, which can be conveniently varied by changing the speed of rotation of one of the cylinders, the conductivity of disks increases with increasing

8A

( ) K . H E C K M A N N ; Naturwiss. 40, 41$ (1953); U . S C H I N D E W O L F ; ibid. 40, 4 3 5 (1953); B . JACOBSON; Rev. Sei. Instrum. 24, 949 (1953). 8B ( > G . S C H W A R Z ; Z. Phys. 145, 563 (1956). 8C < ) K . G . G Ö T Z and Κ . H E C K M A N N ; / . Colloid Sei. 13, 266 (1958). Ρ

ce.

226

DETERMINATION

OF

PARTICLE

SHAPE

gradient, whereas for rods it decreases. The theory was tested by investigating colloids of known particle shape, such as the polyphosphate ( 8 d) colloid (rods) and graphite acid sol (disks), and confirmed. Moreover, the new method was recently applied to such micellar colloids as cetyl trimethylammonium bromide and sodium oleate sols, and it was clearly demonstrated that in both instances the micelles are rod( 8 c) This is in agreement also with recent results of light shaped. ( 9) scattering studies. The optical dissymmetry in light scattering and particle shape In the previous treatment of light scattering on p. 112 simple cases of solutions containing very small spherical or nearly symmetrical particles have been considered. In such cases the scattered light is polarised and is found to be of the same intensity at different angles. F o r small particles, such as protein molecules, only a small correction factor for depolarisation need be introduced in the final calculation of ( 1 0) the molecular w e i g h t . The matter becomes much more complicated if the particles are large or asymmetric. Owing to interference effects, caused by reflection at different points on the surface of the particles, the scattered light will be of different intensity if measured at different angles to the incident beam (see p. 117). For large particles the intensity of the light scattered at an angle of, for example, 40° will differ considerably from the intensity at an angle of, say, 120°. The ratio of the intensities of the light scattered at two different angles (usually 45° and 135°) is called the dissymmetry. This dissymmetry of scattering is observed in linear colloids, and also in spherocolloids possessing large particles. The following questions can now be raised : (1), H o w does the scattering dissymmetry depend on particle shape? (2), Is it possible to relate the dissymmetry to the axial ratio of rod-like particles? (3), Is it possible to relate the coiling of flexible linear macromolecules to the scattering dissymmetry? These problems were approached by both theoretical and experimental means. Various model structures were postulated ; the scattering at various angles was calculated and compared with the observed data. Special attention was given to the most frequently occurring shapes of spheres, rigid rods, and randomly kinked coils. The theoretical treatment is complicated, and a number of simplifications are necessary to achieve a practically convenient mathematical solution. 8D

(9 ) H . M A L M G R E N and O. L A M M ; Z. anorg. Chem. 252, 256 (1944). ( 10) P. DEBYE and E. W. A N A C K E R ; / . Phys. Colloid Chem. 55, 644 (1951). ( > M . H A L W E R , G . C. N U T T I N G and B . A . B R I C E ; / . Amer. Chem. Soc. 73, 2 7 8 6 (1951); P . D O T Y and J. T. E D S A L L ; Advances in Protein Chemistry, 6, 4 6 (1951). B. H . ZIMM, R . S. STEIN and P . D O T Y ; Polymer Bull. 1, 90 (1945).

LIGHT SCATTERING

AND

PARTICLE

SHAPE

227

F o r instance, the following equations were derived on the assumption that the difference between the refractive index of the particle and of the solvent is very small, and that there is no secondary, intermolecular interference in the solution. The intensity of the scattered light at an angle θ is denoted by Ιθ ; λ is the wavelength of the light in solution, D is the diameter of the spheres, L the length of rigid rods or the mean diameter of a randomly kinked coil.

[

3

"Ί

2

^ ( s i n χ -x cos x)J ,

Ι

Rod: Coil:

1C

2x

=- \

θ

{unxjx)dx

-(sin

X J0

2TT

(3A)

χ = ^^ΰη\θ.

x/x) , 2

ITTL

x = -r—sinJ0.

(3B)

A

*= | s i n

i t = ^[e-'-(i-x)],

Ifl)*.

(3c)

F r o m these equations theoretical values for Ie were calculated, assuming certain values of L or D for definite θ and λ. Then the scattering at different angles was measured, and compared with the calculated ( 1 2) values. Of course, the values of the particle dimensions L can also be evaluated from the scattering dissymmetry measurements. In Table 28 the results obtained by STEIN and D O T Y for several fractions of cellulose acetate solutions in acetone are presented. In the third column are given the lengths of the molecules calculated from scattering dissymmetry measurements assuming that the molecules are rigid rods. In the fourth column are shown data calculated from the same scattering measurements, but considering the molecules as random coils. In the last column is presented the calculated length of completely extended chains, computed from the molecular weight of the particular TABLE

28.

Fraction 8B

23B 18B 32B 31B

Dimensions of cellulose acetate molecules in acetone

Molecular weight

Length for rods

Length for random coils

Length from mol. weight

163,000 135,000 75,000 65,000 52,000

1900 Â 1900 1550 1550 1380

1340 Â 1340 1120 1120 960

3100 Â 2400 1440 1250 1000

fraction of the polymer. The results show that for the high molecular fractions of cellulose acetate the measured length of the linear molecules is much less than the calculated length for an extended chain. They must therefore be bent in loops or spirals. The smaller molecules, however, seem to be completely extended. ο β a n The dependence between the scattering dissymmetry / 4 5 / Λ 3 5 d the 12

< > R . S.

STEIN

and P .

DOTY;

/.

Amer. Chem. Soc. 68, 159 (1946).

228

DETERMINATION

OF PARTICLE

SHAPE

length of the rods L or the diameter of kinked coils can best be illustrated graphically. In Fig. 9 9 , the dissymmetry is plotted versus LjX for spheres, random coils, a n d for stiff rods. An important paper on the study of particle shape by light scattering was published in 1 9 4 7 by OSTER, D O T Y a n d Z I M M .

( 1 3)

They chose

tobacco mosaic virus as an example of their study. T h e size a n d shape of the particles in this case are well known from electron micrographs.

F I G . 99. The dependence of the scattering dissymmetry on the particle shape.

the scattering dissymmetry on concentration for tobacco mosaic virus (OSTER, D O T Y and ZIMM).

Tobacco mosaic virus particles are thin rigid rods. Their length is about half the wavelength of the visible light. Therefore they serve as excellent models for testing the theory of light scattering from thin rod-like particles. The light scattering was measured at the angles of 4 2 - 5 ° a n d 1 3 7 - 5 ° as a function of concentration of the virus, a n d the dissymmetry w as ^42.5/^137.5 plotted versus concentration. The intrinsic dissymmetry then is obtained by extrapolation to zero concentration (Fig. 1 0 0 ) . F r o m this value, which was 1 -94, a n d the theoretical curve (that in Fig. 9 9 for rods), the length of the scattering particles was obtained. (From the point 1-94 on the ordinate a line parallel to the abscissa is drawn to the curve, a n d from the point of intersection a perpendicular line is extended to the abscissa. Thus the value of LjX is obtained. Since the wavelength λ is known, the length L is calculated easily.) I n this way the length of the virus particles was found t o be 2 7 0 millimicrons ( 2 7 0 0 Â ) in excellent agreement with the electron microscopy, viscosity and sedimentation data. This agreement clearly confirms the validity of the light scattering method for the determination of particle shapes. 18

< > G . OSTER, P . M . D O T Y and Β . H . Z I M M ; / . Amer. Chem. Soc. 69, 1193 (1947),

SEDIMENTATION

AND DIFFUSION

MEASUREMENTS

229

The determination of particle shape from sedimentation and diffusion measurements The sedimentation of colloidal particles in the cell of an ultracentrifuge is the result of the mutual interaction of two forces : the centrifugal force of rotation and the frictional force. The latter is, according to SVEDBERG, a product of the frictional coefficient/and the sedimentation velocity dxjdt. The frictional coefficient is related to the sedimentation constant s and to the molecular weight by the simple equation : f=M(l-VP)ls9 where V is the partial specific volume (p. 187) and ρ the density of the solvent. If the latter values were known, the frictional coefficientcould be calculated (per mole). On the other hand, the frictional coefficient can be calculated from STOKES'S law (p. 184), according to which the frictional coefficient for a single particle or molecule is 6πψ, or 6πψΝ for a mole, where η is the absolute viscosity of the medium in poises. Assuming that the molecules are non-solvated spheres, the frictional coefficient fQ can be calculated from : /0 = 6πψΝ,

or /0 =

6πηΝ(3Μν/4πΝ)Κ

The comparison of / with f0 permits us to draw conclusions about the shape of the molecules or micelles. If the particles really are nonsolvated s p h e r e s , / = / 0 . Usually, however, fis larger than f0. The value f/f0 is called the molar frictional ratio. In the ideal case in which the sedimenting particles are compact spheres, and if they are not hydrated, / / / o = 1. Since there is always a certain deviation of the ideal spherical shape and also certain hydration, the frictional ratio is larger than 1. T h e / v a l u e s can be determined not only from sedimentation measurements by means of the ultracentrifuge, but also from diffusion measurements : f=RT/D; f can be easily calculated if the diffusion coefficient D for the particular substance is known. In Table 29 are compiled f/f0 values for some proteins. TABLE

29.

The molar frictional ratio for several proteins

///· Lactalbumin Gliadin (wheat) Insulin Ovalbumin Serum albumin (human) Fibrinogen (human plasma) Tobacco mosaic virus

1-16 1-60 1-13 1-16 1 -28 1 -98 3*12

230

DETERMINATION

OF PARTICLE

SHAPE

The f/f0 values only partially express the true asymmetry of the particles. For instance, the frictional ratio for tobacco mosaic virus (Table 29) is 3-12, but actually the particles are long rods ; the ratio of the length to the thickness is about 34 or 40 to 1, as confirmed by direct observations in the electron microscope. T h e molar frictional ratio f/f0 does not represent the axial ratio of particles, b u t it characterises the resistance properties of them against the displacement in a liquid. F o r example, kinked coils may be approximately spherical, i.e. the axial ratio = 1, but the frictional ratio will be much larger, because the coils may encompass much liquid. Such particles cannot be moved about in solution as easily as if they were compact spheres. The viscosity of the solutions of such coils is thus also higher than the viscosity of spherocolloids. The ratio of the measured molar frictional coefficient / to that for unsolvated spheres fQ (of the same mass) is a measure of the combined effect of shape and of solvation. Attempts have been made to determine ( 1 4) the shape factor a n d the solvation separately. However, only in a few cases is such separation possible. The main reason for these difficulties is the lack of a reliable method for measuring solvation. Sometimes the shape of the particles is known by other methods (e.g. tobacco mosaic virus can be seen directly in the electron microscope), and then the / / / 0 values provide data for evaluating hydration. The particle shape and viscosity of solutions; rigid particles Solutions of the spherocolloids have low viscosities, which d o not depend greatly on particle size. F o r instance, all gold sols, independently of their colour and particle size, have very low viscosities. That these sols contain corpuscular a n d more or less spherical particles (though their surface is rough) can be directly seen in the electron microscope. The particles also have the same shape in the sulphide sols, in glycogen sols, a n d in many other colloids. A highly-disperse arsenious trisulphide sol is of about the same viscosity as a coarse ( 1 5) The low molecular glycogens have the same viscosities as the one. ( 1 6) high molecular o n e s . The viscosity of linear colloids, however, is high, and it increases with particle size (p. 168). An important question can now be raised: is there a quantitative relation between the viscosity and axial ratio of the particles? Numerous attempts have been made to answer this question, assuming that the (L4

> J. L . O N C L E Y ; Ann. N.Y. Acad. Sei. 41, 121 (1941).

(L5

> A B O U T A R I C and R . S I M O N E T ; Bull. Acad. Roy. Belg. (5), 10, 150 (1924). Η . S T A U D I N G E R and E. H U S E M A N N ; Ann. 530, 1 (1937). E. H U S E M A N N ;

( Ι Β )

prakt.

Chem. 158, 163 (1941).

J.

PARTICLE

SHAPE

AND

VISCOSITY

231

particles have the shapes of rigid rods, of lamellar discs, of more or less flexible strings, and so on. If L is the length of the long axis of an asymmetric particle and D is the length of the short axis, LjD is the axial ratio. For a long cylindrical particle, L is the length of the cylinder and D is its diameter. Complicated theoretical calculations, based on the laws of hydrodynamics, have been made in order to correlate the viscosity with the axial ratio for several shapes. Cylindrical rigid rods, as well as ellipsoids of revolution, and flat discs have been investigated in detail. A separate problem is that of the relation between the viscosity and the mean diameter of the loose coils and loops of linear macromolecules. In this latter case one has to deal with changing shapes, whereas the above-mentioned cylinders, rods and discs are supposed to be rigid. Of the several equations which correlate the axial ratio of rods with ( 1 7) viscosity, that of SIMHA seems to be in the best agreement with the facts. The theoretically derived equation is as follows : JL * _ o 9

255 =

φ

( ^ )

2

15 (In 2L/D - 3/2)

.

2

WD)

5 (In 2L/D

) - J)

, 14 15 '

( 1 8)

According to NEURATH and associates, this equation gives reasonable values for the axial ratios of proteins. Assuming 3 3 % hydration, the LjD value for serum albumin is then 3-3, and that for pepsin is 3Ό. This means that the pepsin molecules are roughly egg-shaped or that they have a shape like that of a jelly jar. ONCLEY, SCATCHARD and ( 1 9) BROWN obtained for the axial ratio of gamma-globulin from viscosity and sedimentation data the value 5-3. It should be borne in mind that these axial ratios are not rigorous measures for the actual shapes, since the obtained numbers depend on the choice of a certain model. Prolate ellipsoids of revolution have been considered by most authors, though nobody ever has proved that protein molecules have the form of ellipsoids. On the contrary, recent X-ray structural studies on wet crystals of myoglobin, a red globular muscle protein, have revealed the ( 1 9 a) molecules as something like folded s a u s a g e s . Recent electron micrographs of very gently handled preparations of fibrinogen show a macromolecule as composed of three nodules linked by a thin 1 9 b) thread. < (17

> R. S I M H A ; / . Phys. Chem. 44, 25 (1940). A. POLSON, Kolloid-Z. 88, 51 (1939). 18 ( )H. N E U R A T H , G. R. COOPER and J. O . E R I C K S O N ; / . Biol. Chem. 138, 411 (1941); J. T. EDSALL, / . Polymer. Sei. 12, 253 (1954). ( l 9)

J. L. ONCLEY, G. S C A T C H A R D and A. B R O W N ; / . Phys. Colloid Chem. 51, 184

(1947); H. SCHERAGA and L. M A N D E L K E R N ; / . Amer. Chem. Soc. 75, 179 (1953). 19a

( ) J. C K E N D R E W , G. BODO, H. M . D I N T Z I S , R. G. PARRISH, H. W Y C K O F F , and Congress of Biochem. (Pergamon, London 1960), vol. VIII, p. 1. 19B < ) C E. H A L L and H . S . SLAYTER, / . Biophys. Biochem. Cytol. 5, 11 (1959).

and D . C PHILLIPS, Nature 181,662 (1958) ; J. C K E N D R E W in Proc. 4th Int. * φ is the volume fraction occupied by the particles.

232

DETERMINATION

OF PARTICLE

SHAPE

For lamellar, disc-shaped particles PETERLIN and STUART presented the following equation: ^sp_4 c 9

jnD L

(D is the diameter of the disc, L its thickness.) The validity of this equation was tested by FEITKNECHT, SIGNER and ( 2 0) BERGER. They prepared a nickel hydroxide colloid a n d studied it by means of viscosity, electron microscopy, X-ray analysis, etc. They showed that the particles have a lamellar shape. T h e D\L values cal( 2 1) culated from the above-mentioned equation of PETERLIN and STUART agreed well with the data obtained by other exact methods. The rod-like particles of tobacco mosaic virus, and especially those of the muscle protein" myosin, are very long a n d thin. According to ( 2 2 ) , the myosin particles (or molecules) are about 2300 Â PORTZEHL long and only 23 Â thick. Nevertheless, these long rods are n o t very flexible, a remarkable property which will be discussed in another section in this chapter. The colloidal particles of the deoxyribonucleic acid and its salts represent a similar example. These colloids are highly viscous, and there is evidence that this high viscosity is due to the presence of extremely long and thin particles. Each of these is composed of two linear chains wound around each other, and the so-formed double chain is of a limited flexibility, and in a solution it is only gently coiled. The molecular weight of 7,400,000 was found in a recent study ( 2 2 a) for a deoxyribonucleate, and the intrinsic viscosity of it was 6 9 . By exposing the solutions to ultrasonic waves, the linear particles were degraded through double-chain scission, producing shorter fragments 1

2

3

\ D

ΰ <= Û S û ^ Β 0 ff Œ

F I G . 101.

(20)

W

Glass rods of various axial ratios. The reduced viscosity increases with increasing axial ratio.

F E I T K N E C H T , R . S I G N E R and A . B E R G E R ;

Kolloid-Z.

101, 1 2 (1942).

A.

B E R( 2G1)E R ; Kolloid-Z. 103, 185 (1943); 104, 2 4 (1943). A . PETERLIN and A . H . S T U A R T ; Z . Physik. I l l , 2 3 2 (1938); 112, 129 (1939). 22 < >H. P O R T Z E H L ; Z . Naturforsch. 5 Β, 75 (1950). (22a) ρ D O T Y , Β. B U N C E M C G I L L and S. A . R I C E ; Proc. Natl. Acad. Sei., Wash 44, 4 3 2 (1958).

LINEAR

MACROMOLECULES

IN

SOLUTION

233

For instance, a 5 min exposure to the radiation yielded a degradation product with an average molecular weight of 7 0 0 , 0 0 0 , whereby the ( 2 2 A) intrinsic viscosity decreased to 5 - 3 . A very convincing proof that the viscosity really increases with an increasing axial ratio of rigid rods is the result obtained from experi( 2 3) ments with models. EIRICH and associates prepared uniform suspensions of glass fibre and measured the viscosity. With the same amount of fibre of the same concentration (in grams per litre) the shorter fibre always gave a lower viscosity. The viscosity thus increased with increasing LjD of the fine glass rods (Fig. 1 0 1 ) . The shapes of linear macromolecules in solution Colloidal particles which have the shape of an egg, coin or cigar are generally rigid and do not change shape in solution. It is obvious that such change is impossible simply because of the many true chemical bonds (primary valences) which hold the atoms together in a rigid unit. A quite different situation is encountered in solutions of linear macromolecules. H o w flexible really are these linear macromolecules? To what degree can coiling take place? On p. 2 2 7 were reported the results of STEIN and D O T Y on cellulose acetate in acetone. N o t much coiling was found in this example. Similar statements were ( 2 4) made by M O S I M A N N , who worked with nitrocellulose, and by ( 2 5) WISSLER, investigating methylcellulose. MOSIMANN studied several well-fractionated samples of nitrocellulose by means of the ultracentrifuge, double refraction of flow, and viscosity. The lengths of the stretched linear molecules of the various fractions of nitrocellulose were calculated, and these lengths were compared with the axial ratios as estimated experimentally from the above-mentioned properties. The axial ratio from sedimentation in the ultracentrifuge was estimated from the f/f0 values. The axial ratio from the viscosity and streaming birefringence data was calculated according to theoretical relations ( 2 6) developed by B U R G E R S . The results are reported in Table 3 0 . The data of Table 3 0 show that the values of L/D are very high. The nitrocellulose molecules are thus long and thin. Moreover, they are not strongly coiled. In the very high molecular fractions I and II the calculated length for straight rods is only some two or three times greater than the measured length. In the low molecular fractions the calculated length for wholly straightened molecules is about 23

< 24> F. E I R I C H , H. M A R G A R E T H A and M . B U N Z L ; Kolloid-Z. <25 >H. M O S I M A N N ; Helv. Chim. Acta 26, 61 (1943). <2 6> A. W I S S L E R ; Kunststoffe 34, 220 (1944).

( ) J. M . B U R G E R S ; Second Report on Viscosity and Plasticity

Chap. 3.

7 5 , 20 (1936).

(Amsterdam 1938),

234

DETERMINATION TABLE 30.

Sample

OF

PARTICLE

The axial ratio of nitrocellulose in acetone

Calculated for

Sedimentation in F r o m viscosity F r o m streaming

straight rods ultracentrifuge L/D L in  L/D L in Â

I. Mol. wt. 613,000 II. Mol. wt. 199,000 III. Mol. wt. 80,200 IV. Mol. wt. 30,000 V. Mol. wt. 6,200

SHAPE

LID

L in Â

birefringence LID L in A

1083

1190

290

435

560

675

222

365

352

386

188

224

300

306

150

198

140

153

144

138

160

148

90

105

53

58

57

54

95

75

12

13

16

14

18

15

the same as the experimentally estimated length. Consequently, the small molecules, of molecular weight 6,000-30,000, are completely extended. They have the shape of a bristle hair. The molecules in the fractions I and II seem to have the shapes of loops or spirals. The stiffness is probably caused by steric hindrance in the molecule. A certain influence on the rigidity may also be exerted by solvation, i.e. the binding of acetone around and between the glucose radicals in the molecular chain. All this makes the originally thread-like macromolecule thicker, like a stiff rope (Fig. 102).

®Η,® n«H)«n« Η,® π ® ®

®

®

C H 2- 0 p — \

@ = Acetone

• = The - 0 - N 0 2 group

=

" ° ^ %

Η

^

Η

^

I

F I G . 102. The stiffness of the linear molecules of nitrocellulose dissolved in acetone. The chains are stiffened by the acetone molecules A bound at the chain.

The behaviour of the linear macromolecules of vinyl polymers in solution is quite different. The linear molecules of polystyrene, polyvinyl chloride, or of polyvinylpyrrolidone are not like stiff strings, but rather do they resemble matted coils. Various degrees of compactness of such coils are possible, and have indeed been found. Since the linear macromolecules are more or less flexible, their shapes in solution are continually changing. N o t only the whole molecule, but also its segments perform movements in quite a chaotic fashion (see p . 37). It is consequently impossible to ascribe any definite,

LINEAR MACROMOLECULES IN

SOLUTION

235

constant values to the axial ratio, length or diameter of the coil. These flexible coils are characterised by a mean diameter, or by the root mean square distance between the ends of the chain. K U H N and K U H N

( 2 7 )

( 2 )8

( 2 )9

and others have tried to correlate exactly the experimentally measurable quantities, chiefly viscosity and double refraction of flow, with the shape of linear macromolecules in solutions. Since the viscosity is the most conveniently measurable quantity, most of the efforts were directed towards relating the intrinsic viscosity to the mean diameter of the coils and to the so-called interaction constant a. Values for the mean diameter can now also be obtained from light scattering measurements (see p. 227). The mean distance between the ends of a kinked linear macromolecule in solutions is most conveniently evaluated from viscosity measurements, using the equations of F L O R Y and Fox (p. 176) : [η]

, HUGGINS,

12

=KM ' oc\

FLORY

2

3

and K=F(L IM) I\

F=2l

21

χ 10 .

The expansion constant can be determined easily (see p. 176), and the molecular weight M for any particular linear polymer can be obtained by precise viscosity measurements in dilute solutions. Furthermore, as F is a constant for all polymers in all solvents, and its value is known, the mean square distance between the chain 2 3 2 2 ends, L , can be calculated easily from K=F(L /M) I . F L O R Y and Fox presented such calculations for polyisobutylene and polystyrene : CH 3 I

CH 3 I

CH 3 I

CH 3 I

...—C — CH 2— C —CH 2—C —CH 2—C —CH 2—.. .Polyisobutylene I

CH 3

I

CH 3

I

CH 3

I

CH 3

-CH—CH 2—CH—CH 2—CH—CH 2—CH—CH 2—... Polystyrene I I

6

The L values were calculated from viscosity data obtained for fractions with M= 10 . For polyisobutylene in cyclohexane solution at 25°, L was estimated to be 1220 Â ; in benzene it was 795 Â. If the bonds were completely free to rotate and the chain could coil up completely, the mean distance would be only 412 Â. For polystyrene the coiling is still more restricted, probably due to steric hindrance by the benzene rings. Assuming complete flexibility and the formation of compact coils, the mean 6 distance L (M= 10 ) should be 302 Â, but actually values of 703 and 725 Â, or even 1100Â (in good solvent) have been found. The reported values, 703 to 1100Â, agree fairly well with those obtained from light scattering measurements. 27

< > W. K U H N and H. K U H N ; Helv. Chim. Acta 26, 1394 (1943); / . Colloid Sei. 3, 11 (1948). 28 < 29> M . L . H U G G I N S ; / . Phys. Chem. 43, 439 (1939). < > P. J. F L O R Y and T. G. Fox; / . Polymer Sei. 5, 745 (1950); / . Amer. Chem. Soc. 73, 1904, 1909, 1915 (1951).

236

DETERMINATION (3

OF PARTICLE

SHAPE

3 l)

S C H O L T A N ° ) , and HENGSTENBERG and S C H U C H ^ have recently investigated solutions of well-fractionated samples of polyvinylpyrrolidone ( P V P ) by the means of viscosity, osmotic pressure and light scattering measurements. They came to the conclusion that P V P molecules in solution are randomly kinked chains encompassing immobilised solvent. For a sample with a mean molecular weight of 249,000 the mean molecular diameter was found to be 360 Â. For another sample of M=1,116,000 the mean diameter obtained was 930 Â. It should be pointed out that the F L O R Y - F O X treatment is valid only for linear macromolecules of considerable length, i.e. for polymer fractions with a mean molecular weight not below 50,000. Further, it is of interest to discuss the meaning of a According to the the constant a in the modified Staudinger equation [η] =KM . ( 3 2) theoretical considerations of K U H N and others, a = \ for coils in which the solvent is not bound : a = £ for coiled macromolecules which carry adsorbed solvent inside the coil. Further, the constant a decreases with increasing M. Since very long chains of either kind are prone to coiling, the decrease of a with increasing M is reasonable. At this point a very interesting problem concerning solvation becomes evident : one has to deal with two kinds of binding of the liquid by the macromolecules. In good solvents, true solvation predominates and very little liquid is mechanically bound in the loose coils and loops. In bad solvents, mechanical inclusion of liquid predominates and the chemical solvation is insignificant. Finally, it should be pointed out that the problems discussed in this section are far from being completely solved. The theoretical calculations of K U H N and K U H N , D E B YE and ( 3 )8 34 and K I R K W O O D and R I E S E M A N / ^ were all worked out on the basis of a BUECHE,

number of simplifying assumptions. Very interesting results have been obtained recently with the synthetic ( 3 4) a which showed different shapes in different poly-y-benzyl-L-glutamate (35) solvents. Light scattering a n d viscosity measurements indicated that in dichloroacetic acid the polymer behaved normally, i.e. the macromolecules showed the behaviour of r a n d o m coils. However, the same polymer in cresol or dimethyl formamide seemed to possess rodshaped particles. Various specimens of the polymer were investigated, the average molecular weight ranging from 21,400 u p to 336,000, a n d higher, a n d the light scattering disymmetry was determined. Most interesting, of course, was the finding that such a polymer can have a rod-configuration in certain solvents, as the polymer chain molecules are k n o w n t o be very flexible. Careful light scattering a n d viscosity studies were then made on a large n u m b e r of specimens in many solvents, and, firstly, all cases were excluded in which association of the m a c r o ( 3 )0

W . S C H O L T A N ; Makromol. Chem. 7, 209 (1952). 81 (3 2) J. HENGSTENBERG and E. S C H U C K ; ibid. 7, 236 (1952). ) W . K U H N and H . K U H N ; Helv. Chim. Acta, 26, 1394 (1943) ; 30, 1233 (1947). os ρ DEBYE and A. M. B U E C H E ; / . Chem. Phys. 16, 573 (1948). ' J- G . K I R K W O O D and J. R I E S E M A N ; / . Chem. Phys. 16, 565 (1948): ibid. 17, 34a

( 3 5) E. R . B L O U T and R . H . K A R L S O N ; / . Amer. Chem. Soc. 78, 941 (1956).

( ) P . D O T Y , J. H . B R A D B U R Y and A . M . H O L T Z E R ;

/ . Amer.

Chem.

Soc. 78,

LINEAR

MACROMOLECULES

IN

237

SOLUTION

molecules occurred. A particularly suitable solvent in which no association occurred, and in which rod-shaped macromolecules were detected, was chloroform saturated with formamide. The angular scattering distribution data indicated that rod-shaped units are present even in the very high molecular specimens of M = 336,000. The dimensions of the macromolecular rods, however, were incompatible with the dimensions of a fully extended chain, but they fitted well with a stiff cylindrical spiral (helix). The configuration in this solvent seems to be ( 3 6) the same as in the solid polymer, namely the α-helical configuration. With M = 262,000, for example, a length of 1825 Â was calculated for the rod-shaped spirals, and their diameter was estimated to be only 15-18 Â, hence the axial ratio in this case is 1: 100. This is schematically

(a)

(b)

F I G . 103. Two different configurations of the linear colloid poly-ybenzyl-L-glutamate in two different solvents. The particles assume the shape of helical rods in such solvents as cresol (case A ) , while in dichloroacetic acid (case B ) they appear as random coils.

illustrated in Fig. 103. This helical configuration appears to be rigid and rod-like up to molecular weights of 300,000; when the rods become (35) extremely long, they acquire a slight flexibility. These different shapes of the same colloid in various solvents are explained as caused by different affinity of the solvent to the solute; the randomly coiled configuration in dichloroacetic acid is due to strong secondary bonding (solvation) of this solvent with the polypeptide chain. Charged linear macromolecules If the macromolecules are ionised, the relations become still more complex, because of the interaction between the segments of the chain, 36

( ) L. P A U L I N G , R. B . COREY and H. R. B R A N S O N ; Proc.

37, 205 (1951).

Natl. Acad. Sei.,

Wash.

238

DETERMINATION

OF PARTICLE

SHAPE

as well as between solute a n d solvent. Since, for example, the negatively charged carboxyl groups of a polyacrylic acid molecule will repel each other, it is obvious that this will cause stretching of the chain. The higher the degree of dissociation the more extensively will the segments of the chain be charged, a n d the more the chain will uncoil. Further, the interaction between the charged macromolecule and the molecules of a polar solvent (such as water) will increase with increasing charge on the chain: highly charged macromolecules will be more solvated than the uncharged ones. Hence the Huggins constant k, which depends on such interactions as well as on molecular shape, should be different for solutions of linear macromolecules which are ( 3 7) have thoroughly investigated charged. EIRICH a n d associates polyvinyl pyridinium bromide, a linear vinyl polymer which carries positive charges on the pyridinium radicals of the chain. Viscosity, streaming birefrigence, sedimentation, diffusion and electrophoretic mobility measurements were made in aqueous solution, a n d the influence of added electrolyte on the various properties was determined. The Huggins k values were found to be very high (2-7-5-2), which suggests a different type of interaction for these systems. The frictional r a t i o / / / 0 for this polyelectrolyte was estimated as 2-38. A strong con( 3 8) traction or coiling u p occurs upon adding s a l t s . Contractile muscle proteins ( 3 9)

WEBER, M U R A L T and EDSALL a n d others have shown that muscle contains a fibrous protein whose solutions possess very high viscosities and double refractions of flow. The protein they called myosin. Its particles have proved t o be comparatively stiff filaments which nevertheless may change their shape quite regularly. It must be emphasised that the myosin particle differs considerably from a macromolecule of a linear polyelectrolyte. Myosin, like all proteins, is a colloidal electrolyte, but, contrary to the synthetic polyelectrolytes, myosin is amphoteric. Furthermore, myosin filaments are thicker than molecular chains, e.g. of polyvinyl chloride, which have the thickness of a few angstroms only. Important contributions to the problem of muscle contraction have been made by SZENT-GYÖRGYI

( 4 )0

and M O M M E R T S .

C 4 1)

SZENT-GYÖRGYI

has brought forward evidence that myosin is a complex protein; it is composed of the so-called actin and myosin. The complex which was formerly called myosin is now renamed actomyosin. Actin ( 3 )7

Β. R O S E N , P. K A M A T H and F . E I R I C H ; Discuss. Faraday Soc. 11, 135 (1951). > P. A L E X A N D E R and S. F . H I T C H ; Biochim. Biophys. Acta 9, 229 (1952). > A. L. v. M U R A L T and J. Τ. E D S A L L ; / . Biol. Chem. 89, 322 (1930). ( 4 0) A. S Z E N T - G Y Ö R G Y I ; The Chemistry of Muscular Contraction (Academic Press, (38 (39

New York 1947); Discuss. Faraday Soc. 11, 199 (1951). (41) ψ ρ H. M O M M E R T S ; Muscular Contraction (Interscience, New York 1950).

CONTRACTILE

MUSCLE

PROTEINS

239

is composed of globular molecules of weight about 60,000. In the presence of certain salts the latter become adlineated into filaments. This process is strongly catalysed by myosin. Myosin itself is a linear protein composed of stiff filaments with a diameter of 20-25 Â, and a length of about 2,300 Â. Since the filaments are composed not of single peptide chains, but are thicker than one of these, the linear particles are not coiled. Moreover, the filaments are stiffened by the relatively ( 4 2) high charge density on their surfaces. According to SZENT-GYÖRGYI, in resting muscle actin and myosin are separated by repulsive electro-

F I G . 104 Actin and myosin rodlets in a muscle fibre.

static forces. On excitation, actin combines with myosin, causing the myosin filaments to undergo contraction. The mechanism of muscular contraction is not yet fully explained. Other mechanisms, instead of the contraction and stretching due to charge effects, have been proposed. For example, there is some evidence that changes of the length of striated muscle occur not by folding of certain linear particles, but by (42a) their sliding past one another. This is illustrated in Fig. 104, where (42

> J . R I E S E M A N and J. G . K I R K W O O D ; / . Amer. Chem. Soc. 70, 2820 (1948); H . B . B U L L ; / . Amer. Chem. Soc. 67, 2047 (1945). ( 4 2 a ) A. F . H U X L E Y ; Prog. Biophys. Biophys. Chem. 7, 257 (1957); see also A. E N G S T R Ö M and J. B . F I N E A N ; Biological Ultrastructure (Academic Press, New

York 1958).

240

DETERMINATION OF PARTICLE SHAPE

the thicker rodlets represent myosin and the thinner actin. U p o n muscular movement, the actin filaments are thought to slide between the myosin rodlets. A very interesting experiment was described by KATCHALSKY and ( 4 3) EISENBERG. Polyvinylphosphate, a linear colloidal electrolyte, was used as a model of myosin, and it was shown that this fibrous substance contracts rapidly when dipped into acid. ... — C H 2 — C H — C H 2 — C H — C H 2 — C H — C H 2 — C H — C H 2 — C H — . . .

I

ο I ο=ρ ο_ο_ Λ

Η+Η+

I

I

ο I

I

ο

I

I

Ο = Ρ

Ο=Ρ

Ο = Ρ

ο_ο_

ο_ο_

ο_ο_

Η+Η+

Η+Η+

Η+Η+

Λ

I

ο

Λ

Λ

ο I

Ο=Ρ

ο_ο_ Λ

Η+Η+

Polyvinylphosphoric acid

The fibrous substance was prepared by phosphorylation of fibrous polyvinyl alcohol. At nearly neutral reaction the free phosphate groups of the fibre are ionised and the fibre is highly swollen and elongated. When it is dipped into concentrated hydrochloric acid, the ionisation is suppressed, and it contracts in a fraction of a second to about one-half of its length and to one-third of its thickness in the swollen state. When the fibre is again immersed in distilled water or dilute alkali, it expands rapidly to its original length. This reversible process may be repeated many times. This analogy supports the view that the reversible contractions of muscle fibre may be caused by changes in ionisation of the fibrous myosin molecules (see ref. 42). Finally, it must be emphasised that the mentioned ideas do not fully explain the structural and functional aspects of muscle. There is a wide gap between the various in vitro observations and the functionation of living muscle. A unifying theory which gives a logical explanation of all the facts of energetics, chemistry, and submicroscopic morphology of muscle proteins and their changes is still lacking. The picture is confused also by several recent discoveries, such as the complex nature of myosin, and its possible dissociation into small subunits of relatively ( 4 4) low molecular weight by the action of u r e a . 43

( ) A . KATCHALSKY and H . EISENBERG; Nature, Lond. 166, 267 (1950). 44 ( ) A . G . S Z E N T - G Y Ö R G Y I ; Advances in Enzymology 16, 3 1 3 (1955).