A NEW METHOD FOR DETERMINING THE SIZE OF LARGE MOLECULES AND POLYMER PARTICLES

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A NEW METHOD FOR DETERMINING THE SIZE OF LARGE MOLECULES AND POLYMER PARTICLES

A Dissertation SUBMITTED TO THE GRADUATE COUNCIL OP WAYNE UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE DEPARTMENT OF CHEMISTRY

by Kermit Herrington "Mr**"

Detroit, Michigan 1950

ACKNOWLEDGMENT

In addition to those individuals whose kind and generous assistance I have acknowledged in the body of this report I wish to include Professor J. J. Jasper of Wayne University whose encouragement and interest was deeply appreciated. Thanks are also due to the Research Corporation, without whose financial aid this project could not have been accomplished. Above all, thanks are due to professor Wilfried Heller, whose generous and invaluable assistance and guidance are gratefully appreciated.

TABLE OP CONTENTS Page ACKNOWLEDGEMENT

ii

CHAPTER I. INTRODUCTION II. DESCRIPTION OP THE APPARATUS

1 11

A. The Illuminating Unit

12

B.

The Monochromating Unit

13

C.

The Apparatus for Measuring Light Scattered under 90°

16

D. The Apparatus Modified for Transmission Measurements

19

E. The Apparatus Modified for Determining Anisotropic Scattering from Opaque Surfaces

25

P. The Apparatus Modified for Determining the Shape the Particles from Dityndallism.

26

G. The Apparatus Modified for Determining the Absolute Dimensions of Non-spherical Particles from Dityndallism

28

H.

29

The Recording Instruments

III. Experimental Results...............

33

A. Transmission Measurements

34

B.

36

90° Measurements

C. The Multiplier Photocell Photometer ...... D.

Tabular Compilation of Experimental Measurements «...

IV. SUMMARY AND CONCLUSIONS FIGURES BIBLIOGRAPHY

37 40 52

CHAPTER I INTRODUCTION The determination of molecular dimensions and masses has always been a fundamental problem In physical chemistry. In recent years there has been a rapid expansion in the fields of polymer science and biological chemistry; or in terms of a common property, the chemistry of macromolecules. The classical methods, so successfully employed in the molecular weight and size determinations of small, simple molecular species were found to be, in many ways, in­ applicable in dealing with the determination of the same properties for this ever growing group of Industrially and biologically Important macromolecules.

Of the new

methods devised for studying these large colloidal parti­ cles, the one which will be the subject of this thesis is the relationship between the size of the particle and the amount of light that this particle is capable of scattering, under certain conditions.

In the early years

of World War II Professor W. Heller"*" at the University of O Chicago, and shortly thereafter, Professor P. Debye at Cornell University, both working under the auspices of the Rubber Reserve Program independently enunciated the 1. Heller, W. and associates, Rubber Reserve Program Reports, 1943 and later. 2. Debye, P. and associates, Rubber Reserve Program Reports, 1943 and later.

2 possibility of utilizing light scattering for the deter­ mination of particle sizes of synthetic rubber polymer particles.

In subsequent years the methods have been

used extensively in the determination of the sizes, shapes, and particle weights of a great variety of macromolecules•1 The theory underlying the phenomena of light scatter­ ing is not, however, of particularly recent origin. The very common example of light scattering, the Tyndall p effect, receives its name from John Tyndall, who in 1869 presented a paper at the Royal Society of London describing the relation between suspended particles in the sky and the intensity and polarization of the observed scattered light*

The classical theory of light scattering can be 'Z

attributed to Lord Rayleigh,

who first developed the

theory on the basis of the elastic solid theory of light and later showed that Maxwell's electromagnetic theory can account equally well for the observed scattering of light by the molecules of a gas#

He considered isolated

particles which were negligibly small compared to the 1. An excellent review on light scattering is found in Chemical Reviews, 45, 319 (1948) by Gerald Oster. 2. Tyndall, J., Phil. Mag., 37, 384 (1869). 3. Lord Rayleigh, Phil, Mag., 41, 447 (1871); 12, 81, (1881).

5 wavelengths of light used, and showed that the oscillating electric field of the incident light induced in the particle an oscillating electric moment®

The particle

behaves like an electric dipole, radiating light in all directions except the direction of the vibrations.

An

immediate consequence of this is that the scattered light is completely polarized under an angle of 90° with respect to the direction of the incident, which is substantiated by the experimental evidence given by Tyndall.

On the

basis of electromagnetic theory Rayleigh has shown that the intensity of scattered light for small isolated spheres is given by; (1)

i =

8

n"*v> a' I

(1 + c03e g

)

A4 where:

1 = intensity of the scattered light per unit volume ^ = number of independent,small isotropic spheres per unit volume ^ = polarizability of the spheres (or their in­ duced dipole moment) I = intensity of the unpolarized incident beam /\ = wavelength of light r = distance between the sphere and observer & - angle between observer and the proceeding incident beam.

The unity term in parenthesis refers to the component of scattered light whose electric vector is perpendicular to

4 the plane defined by the incident beam and the scattered beam, and the cos%0 term refers to that component whose electric vector lies in this plane. From equation (1) it is seen that;

(a) the intensity of the scattered light

is proportional to the reciprocal fourth power of the wavelength; and (b) the light scattered at 90° is com­ pletely polarized with the electric vector vibrating perpendicular to the plane of observation. The following diagram shows the intensities of the components of the scattered light. The distance from the origin to any point on the curve indicates the intensity of the scat­ tered light in that direction.

The origin is the center

of the scattering sphere.

where:

lx is the curve for the light vibrating perpen dicularly to the plane of the paper

5 ls i

is the horizontal component is the relative sum of the two components.

Prom the diagram it is also apparent that as much light is scattered forward as backward. As the beam of light traverses the solution it becomes weakened in intensity due to the light scattered by the particles. This fractional decrease in intensity of the transmitted beam is formally defined as the turbidity, % as follows: (2)

- c?'i I = i0e

where I0 is the original intensity and I is the intensity after it has traversed 1 cm through the solution.

This

has been expressed by Rayleigh as follows; (3)

r= 8TT ( x A Z

In order to use this equation to solve for T, the polarizability must be known. It can be correlated with the refractive index as follows: (4) where np

2 77^ ^ = np -1 is the refractive index of the particle. For

particles in dilute solution the turbidity has been ex­ pressed by W. Heller"*" as: (5)

where:

C

=

24 77"s

(npg -

A

(np® + 2nm&)£

(j/iT

nra = refractive index of the medium