Physical Methods in Chemical Analysis. Volume IV

480 Pages·1961·8.389 MB·English

by  Walter G. Berl (Eds.)

PHYSICAL METHODS
IN
CHEMICAL ANALYSIS
Edited by
WALTER G. BERL
Applied Physics Laboratory, Johns Hopkins University, Silver Spring, Maryland
VOLUME IV
1961
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Contributors to Volume IV
MAXIMO BARON, Scientific Department, ATANOR S.A.M., Munro (Buenos
Aires), Argentina
A. E. CAMERON, Oak Ridge National Laboratory, Union Carbide Nuclear
Company, Oak Ridge, Tennessee
CHARLES W. CARR, Department of Physiological Chemistry, University of
Minnesota, Minneapolis, Minnesota
G. DICKEL, Physical-Chemistry Institute, University of Munich, West
Germany
ROLLAND L. MAYS, Linde Company, Division of Union Carbide Corporation,
Tonawanda, New York
WILLIAM EIEMAN, III, Rutgers, The State University, New Brunswick, New
Jersey
ROGER SARGENT, The Dow Chemical Company, Midland, Michigan
TUDOR L. THOMAS, Linde Company, Division of Union Carbide Corporation,
Tonawanda, New York
F. A. VON METZSCH, Th. Goldschmidt A.G., Essen, West Germany
MILTON E. WADSWORTH, Department of Metallurgy, University of Utah,
Salt Lake City, Utah
PREFACE
This, the fourth volume in the series on "Physical Methods in Chemical
Analysis", deals exclusively with Separation Methods. The importance of
these operations will be appreciated by anyone who, in dealing with complex
mixtures, wishes to apply the most advanced techniques of qualitative or
quantitative analysis or who is concerned with isolating components in a
state of high purity. Eefinements in the available physical analytical tools
have by no means eliminated the need for equally refined means of separation.
Taken hand-in-hand, they supply powerful aids to the analytical chemist.
The methods of separation discussed in this volume fall into four groups—
those depending on differences in rates of transport (dialysis, thermal
diffusion), on differences in electrical or magnetic properties, on differences
in phase equilibria (solvent extraction, adsorption, ion exchange), and on the
utilization of specific geometrical factors (inclusion compounds, molecular
sieves).
Although the discovery of dialysis goes back to 1861, exciting progress in
this field is now made by the availability of improved membranes, par-
ticularly those in which the electrical charge can be adjusted to suit the
specific separations. A similar major advance in adsorption techniques has
come about through the use of adsorbents with controlled porosity (molecular
sieves). Novel separations are made possible by the fact that adsorption
sites can be chosen of such a size that the "fitting" of one component is
possible but not of another of different size. A similar use is made of the
phenomenon of co-crystallization by inclusion compounds where the physical
dimensions of the precipitates are such as to carry along only those com-
pounds that fit the available dimensions.
Differences in phase equilibria are exploited in the technique of solvent
extraction which is of outstanding importance and usefulness in the
laboratory as well as in industry. The construction of multistep and auto-
matic apparatus has produced a veritable revolution in the application of
this method, particularly to biochemical problems. Another equilibrium
effect is exploited in ion exchange, which, together with Chromatographie
methods, represent one of the most widely used techniques at present.
Adsorption on interfaces (foams) is primarily of interest in mineralogical
problems although the application to other systems may well prove of
importance in the future.
While the above separation techniques are well established in most
laboratories, two methods are discussed here which have more specialized
vii
vin PREFACE
application and also require equipment of rather subtle design. Separation
of measurable quantities of electrically charged substances by deflection of
ion beams in a magnetic field is carried out in establishments where the pro-
duction of isotopes is carried out on a relatively large scale. An entirely
different method, also applied to isotope separation, is based on the thermal
diffusion properties of gases and of liquids.
The aim of the individual chapters is to review the theory and practical
aspects of the various techniques, to indicate their range of application in
the analytical laboratory, and to explain the scientific foundation upon which
they are built.
The chapters entitled "Separation of Gases and Liquids by Thermal
Diffusion" and "Solvent Extraction" were translated from the original
German by the Editor.
To the authors, above all, and to the publisher the Editor extends his
profound thanks for their exemplary cooperation.
WALTER G. BERL
April 1961
Dialysis
CHARLES W. CARR
Department of Physiological Chemistry, University of Minnesota,
Minneapolis, Minnesota
CONTENTS
Page
1. Introduction 1
2. General Theory and Background 2
2.1. Mechanism of Dialysis 2
2.2. Factors Affecting Dialysis 7
3. Membranes for Dialysis 12
3.1. Characterization of Membrane Porosity 12
3.2. Membrane Materials .. 16
4. Apparatus and Techniques 25
4.1. Introduction 25
4.2. Batch Dialysis 26
4.3. Semicontinuous Dialysis 28
4.4. Continuous Dialysis 29
5. Applications 30
5.1. Conventional Dialysis 30
5.2. Fractional Dialysis 33
5.3. Dialysis with Highly Charged Membranes 35
5.4. Diasolysis 37
5.5. Estimation of Molecular Sizes 37
5.6. Equilibrium Dialysis 38
References 40
1. Introduction
Dialysis as a method of separation is based on the relative rates of
diffusion of substances through membranes. It is generally considered to
have been first described in the literature by Thomas Graham in 1861 (59).
As a result of his observations, he classified solutes into two groups, the
crystalloids, which passed through parchment membranes and the colloids
which would not pass through. Thus, if two substances are to be separated
by a given membrane, the one substance should diffuse readily through the
membrane, and the other substance should be held back completely or almost
completely. If the smaller substance which permeates the membrane is
continually removed from the outside compartment, the substance being
retained inside will eventually be completely separated from the other sub-
1
2 CHARLES W. CARR
stance. This procedure, or modifications of it, has been used for a long time
for the separation of very small molecules from large molecules or particles.
Through the development of our chemical knowledge it is now clear
that there is no sharp dividing line that separates one group of substances
from another on the basis of their permeability through membranes. There
is a complete spectrum of solutes ranging in size from that of the smallest
molecules to that of substances having particle weights of several million.
It is also possible to have a complete spectrum of membrane porositites,
ranging from membranes which are scarcely permeable to water to mem-
branes which will allow substances as large as viruses to pass through. It
has now become possible to make separations of a much finer degree than
heretofore had been considered.
It will be the purpose of this chapter to show how dialysis has been used
in the laboratory in its conventional form for the separation of various sub-
stances and to indicate some of the less well-known possibilities in this area.
The emphasis will be mainly on the theory of dialysis, the nature of mem-
branes, and the various applications of the process. There are other methods
of separation that are closely related to simple dialysis that will not be dis-
cussed in this chapter. Electrodialysis is dialysis carried out in the presence
of an electrical field. Ultrafiltration is filtration under pressure through
larger-pored dialyzing membranes. What is written here concerning the
properties of membranes and their preparation is, of course, applicable to
these other two techniques.
2* General Theory and Background
2.1. MECHANISM OF DIALYSIS
2.1.1. Description of the Process. A setup for dialysis is shown in
diagrammatic form in Fig. 1. Fig. 1(a) represents the situation at the
beginning of the dialysis. In one compartment there is the solution to be
dialyzed containing two solutes of different size, and in the other compart-
ment there is pure solvent. The membrane, M, is a thin sheet of material
placed between the two compartments which will prevent gross mixing by
stirring or convection. It also must have the property of being readily perme-
able to the solvent and the smaller solute and impermeable to the larger
solute. After this system has stood for some time, the change that occurs
is shown in Fig. 1(b). Much of the smaller solute has diffused into the com-
partment at the right, (diffusate) leaving the larger solute in the compart-
ment at the left (dialyzate). If the diffusate is replaced with pure solvent
DIALYSIS 3
from time to time, a complete separation will eventually be obtained. The
volume of the dialyzate will usually increase due to the difference in osmotic
pressure between the two compartments.
Dialysis is a very mild procedure for making separations and in its
simplest form may be looked upon as analogous to separations made by
mechanical sieves. The substances being separated are in a liquid solution,
and a membrane acts as the sieve. The only real difference is in the driving
force. In mechanical sieving, gravity is the driving force which compels the
smaller particles to move through the sieve, whereas in dialysis the driving
force is the concentration gradient. Thus there are two principal factors
which govern the passage of a substance through a membrane, the diffusion
coefficient of the substance and the size of the openings (pores) in the
membrane.
M M
Dialyzate ι
MJ*Î-*ïiDiffusate
~----?-'-7-J
(α) (b)
FIG. 1. Diagrammatic representation of dialysis.
2.1.2. TL· Diffusion Coefficient. The net movement of any substance
in solution is directly proportional to its concentration gradient. This is
expressed quantitatively by Fick's law of diffusion, one form of its expression
being as follows:
^ . ^ - D A^ (1)
dt dx
Q is the quantity of material diffusing in the time, t; D is the diffusion
coefficient; A is the cross-sectional area through which the substance is
diffusing; and dc/dx is the concentration gradient. D is thus a measure of
the quantity of a substance that passes through a plane of unit area in a
unit of time at a unit concentration gradient. It decreases as the molecular
size of the solute increases and is characteristic for each solute. It is not
strictly constant but is somewhat dependent on the absolute concentration
of the solute.
Many attempts have been made to establish a quantitative relationship
between the diffusion coefficient and molecular size, but apparently a simple
relationship does not exist. One of the more recent of these attempts is an
4 CHARLES W. CARR
empirical equation which has been worked out by Poison and van der
Ryden (104). Their equation is
D = -2- + -A- + ± (2)
where M is the molecular weight of the solute, a, 6, and c are empirical
constants, a = 2.74 x 10"5, b = 1.65 x 10"6, and c = 17.0 x 10"5. This
equation has been shown to hold for a series of neutral organic molecules
of compact structure varying in molecular weight from 19 to 294,000. On
the basis of the fit of this equation, Poison and van der Ryden conclude
that the diffusion coefficient is a function of the radius, the area, and the
volume of the diffusing substance.
2.1.3. Dialyzing Mewbranes as Mechanical Sieves. The mechanism by
which a solute goes through a membrane has been discussed since the time
of Graham. It was first suggested that the membranes used in dialysis
behaved like mechanical sieves; i.e., the solvent enters pores in the mem-
branes, and those solutes that are small enough also enter the pores and
diffuse through. Those solutes that are too big are "screened" out and remain
in the original solution. Other mechanisms for membrane permeation have
also been proposed. In the capillary attraction theory, the molecules are
adsorbed on the pore walls and are transmitted by surface mobility. In the
solubility theory, the solute comes out of the solution on one side of the
membrane, enters into a solid solution in the membrane structure, diffuses
through the membrane and re-enters the solution on the other side. At the
present time, however, it has been substantially proven that at least for the
commonly used artificial dialyzing membranes, the fundamental mechanism
of permeation is that of mechanical sieving. (There is a procedure very much
like dialysis in which solubility in the membrane is the mechanism for
permeation; this will be discussed later).
In considering dialyzing membranes as mechanical sieves we are
especially interested in the nature of the pathways or pores through which
solutes may pass. There has been much speculation over the years concern-
ing this point; nevertheless, we are still not able to state with accuracy what
these pores are like. One of the most simple pictures and one that is widely
used is that the membrane is composed of uniform cylindrical pores perpen-
dicular to the plane of the membrane. In reality, however, if we consider
the materials and methods by which dialyzing membranes are formed, it is
to be anticipated that such membranes will not be very regular in their
microstructure. For example, films of cellophane and collodion are essenti-
ally gels, formed by the aggregation of micelles of various shapes and sizes.
According to the "brush heap" concept for the structure of gels, the micelles
align themselves in a more or less random manner. In such an arrangement
DIALYSIS 5
it is readily seen that the pathways available for diffusion will be hetero-
geneous in nature. Each individual pore will be an irregular channel with
cross connections and dead ends and will most likely have a length which is
considerably greater than the thickness of the membrane. Electron micro-
graphs of collodion membranes tend to bear out such a picture for membrane
structure (18, 69).
In a heterogeneous structure as just described the effective pore diameter
of the pores in a membrane will vary considerably, although the extent of
this variation is not easily arrived at. The porosity of a membrane will,
therefore, be the result of the over-all effects of a distribution of pore sizes.
It is presumed that some sort of Gaussian distribution of pore diameters
exists for each membrane, and the porosity of a membrane is referred to in
terms of an "average pore diameter" (A.P.D.).
2.1.4. Restricted Diffusion. When a solute permeates a porous membrane
which has an average pore diameter which is much larger than the diameter
of the solute, the diffusion rate in the pores is the same as in free solution.
For such a case we can write the Fick equation as follows:
§ = DÄA (3)
at x
p
A is the effective total cross-sectional area of the pores, and x is the mean
p p
length of the pores. For reasons indicated above, neither A nor x are
p p
directly measurable in membranes. As a result there have been several
different modifications of this equation used to express the diffusion of
solutes through membranes (30, 36, 89, 102).
When we express the area in terms of the total membrane area and the
pore length as the thickness of the membrane, the diffusion equation then
becomes
^ = kDA^. (4)
dt x
k is a permeability constant which expresses the total restrictive effect of
the membrane on the diffusion of the solute in question. As long as the pore
diameter is much greater than the solute diameter, x will not be much
greater than the thickness of the membrane, and k will be approximately
the fraction of the membrane area that is available pore area. It will be con-
stant for all such small solutes. It has been estimated both from theoretical
deductions (79, 80) and from experimental data (90, 107) that free diffusion
in membranes occurs only when the ratio of pore diameter to solute diameter
is about 30 or greater.
As the diameter of the solute comes closer to the pore diameter, k will
no longer be constant for all solutes. The available pore area will be less for
a larger diffusible solute than for a small solute, and, in a similar way, there