FRACTIONAL PRECIPITATION O F POLYMERS
THE
721
FRACTIONAL PRECIPITATION OF MOLECULAR-WEIGHT SPECIES FROM HIGH POLYMERS
THEORIES OF
THE
PROCESS AND SOME EXPERIMEXTAL EVIDENCE^
D. R . MOREY
AND
J. W. TAIIIBLYNZ
Kodak Research Laboratories, Rochester, .Veto York Received January 8 , 1947
The phenomenon of longer chains being less soluble than shorter ones of like structure has been known for some time, and has been utilized for the separation of chains on a length basis. The reasons for such behavior have been much less known and understood than the empirical applications, and it is only recently that theoretical frameworks have been found which coordinate the facts. We limit our discussion here to the case when the chains differ in length but not in over-all composition. Chains of differing chemical structure will have differing solubility properties on this account, and these two effects may, for certain solvents, oppose each other; for other solvents they may act in the same dire~tion.~ At the present time there are three distinct theories accounting for the selective precipitation of different molecular-weight species from solution.4 The earliest theory is that proposed by Schulz (25), who treated the problem by considering the distribution of polymer between solution and precipitate to be governed by Communication S o . 1133 from the Kodak Research Laboratories. Present address : Tennessee Eastman Corporation, Kingsport, Tennessee. 3 When it is known t h a t the polymer varies in composition (as, for example, in degree of esterification), then fractions obtained by a precipitation fractionation should be analyzed t o shoa. that there is no progressive change in composition, and hence separation on a length basis only. Otherwise, conclusions as to molecular-weight distribution are in error. In this paper, some reverse-order precipitation effects are described. We base their explanation upon the differential solubility of end groups, as compared to inner segments. If this is correct, tben these effects in a way might be classed as due t o differences in composition. But this is a difference of composition which is itself a direct function of chain length, whereas other compositional differences so far recognized are not necessarily related to chain length. Several other methods of fractionating polymers have been used, but the standard and most widely used method remains t h a t of fractional precipitation and is the method specifically considered in the three theories. The various methods, and the uses to which they have been applied, are described in a comprehensive review of the literature on high-poly. mer fractionation, recently published by Cragg and Hammerschlag (4). Some rather estravagant claims for fractionation by extraction from a “coacervate” have been made by Gavoret and Duclaus (10) on a fractionation of polyvinyl acetate. However, there seems to be a confusion, in the stating of their concentration units, between “grams” and“grundmo1s”. Correcting for this, we note t h a t their separation of molecular weights is like t h a t which a-e have obtained on several fractionations of polyvinyl acetate, using the precipitation method. On a different polymer a.e have carried out parallel fractionations, using the standard method and the “coacervate” method of these authors. Besides finding this latter technique very time consuming, we found the resultant fractions t o be less well separated than those from fractional precipitation. 1
2
‘
722
D. R. MOREY AND J. W. TAMBLYN
the relative energies in the two phases and the Boltzmann probability for such energies. The thermodynamic approach has been developed by Flory (7), Gee (ll),and Huggins (14). Both entropies and heats of mixing are calculated for the solution and precipitate phases; these are then used in the thermodynamics of equilibrium between two phases. A treatment which considers the mechanics of the start of aggregation of precipitation as a reversible reaction in equilibrium was recently proposed by Morey (18) and is further elaborated in this paper. The theory of Schulz, while open to criticism, also deserves a favorable word for being the first vigorous attack on the problem, and for stimulating interest in the theoretical aspects of polymer fractionation. The basis of the theory is laid in a Brgnsted-Boltzmann expression for the distribution of a substance in two immiscible solvents. Representing by E the energy difference per molecule of the material on passing from the first solvent to the second, and by ul and u2 the activities in the two liquids, a1 = -
K!
--BlkT
a2
Schulz assumes that the activities may be replaced by the actual concentrations, C1and C2. This is reasonable a t lorn concentrations, but is questionable a t higher concentrations and when the polymer is no longer molecularly dispersed, but aggregated. It is further assumed that the two immiscible solvents may be replaced, in theory, by the solution and precipitate, considering the latter as a fluid. The specific application to high polymers comes in defining E as proportional to the number of monomer units in the chain, and the proportionality factor to be a linear function of the per cent of precipitant, P , which has been added to the solvent. Hence:
For the study of precipitation and fractionation phenomena, a very convenient parameter is the per cent of precipitant just at the moment of precipitation; put in another way, the saturated state and the values of concentration, precipitant, and temperature which produce the saturated state form a readily measurable set of parameters. We shall henceforth designate the concentration of polymer (of a given molecular weight) in solution which produces saturation as C,, and the per cent of precipitant which corresponds to this same state of saturation as PY. One more assumption is now made by Schulz,-namely, that the concentration of polymer in the precipitated phase, C?, is constant. This is known to be in error to some extent; the lower-molecular-weight precipitates are less swollen than the precipitates of longer chains. Fortunately for the theory, the error in this assumption is counterbalanced by the opposing error introduced when concentrations are made to replace activities. Schulz thus arrives a t :
c 7 -
Ke-(A+BP7)(M/kT)
(1)
FRACTIOXAL PRECIPITATIOX O F POLYhIERS
723
wherein K , .4,and B are constants. At constant temperature, this expression leads to two consequences which may be tested experimentally: ( a ) for constant molecular weight, P, is linearly related to log C,; ( h ) with the concentration at saturation the same, for each different species precipitated, P, is linearly related to l/M. Experiments xi11 be presented later in the paper, but a t this point we may note some of the results: Deduction ( a ) is found to be true, while ( b ) is only approximated. Aside from the explicit assumptions already cited, there are two which are implicit. It will be noted that the energy difference between solution and gel is made proportional to the molecular weight. This has the effect of stating, when the equation is applied to the very start of precipitation, that in the precipitate, the longer the chain, the greater the number of secondary links to other chains. This is certainly the case for large-size particles or aggregates, but in the initial coalescence only a few secondary cross links are required to establish a nucleus or embryo aggregate, this number being nearly independent of chain length. Indeed, the probability of establishing these first links is related to the chain length, but this probability is not to be confused with the number of links required for initial coalescence. This latter factor is the one which must be considered if phase separations are to be noted experimentally by the first signs of optical haze. The other implicit assumption has already been noted by Flory and Huggins, and is the neglect of effects due t o the entropy of mixing of polymer and solvent. THERMODYXAVIC THEORY
The thermodynamic approach is a quite general study of phase relationships out of which as particular cases can be derived both fractionation by successive precipitation from solution, and fractionation by extraction from a highly swollen gel. The outline is as follows: The partial molal free energy of the solvent, AF,, and its activity, al, are expressed by the fundamental relation: A & = RT In al = AR1 - TAS1
(2)
and similarly for the polymer:
AF,
=
RT In a2
=
AR2 - T A &
(3)
To predict a separation of phases requires a knoivledge of these partial molal free energies; hence, the partial molal heats of mixing and the partial molal entropy changes, on passing from one phase t o another, must be calculated. For the heat term, those who use the thermodynamic approach take the form as given by Scatchard (23), and by differentiating ii-ith respect to the mole fraction of solvent or polymer, obtain: AH1 = BL’1+:
A H , = BV,+i
(4)
and & are the volume fractions which the solvent and polymer occupy in the whole system, and B is a constant. The entropy term is obtained from the Boltzmann definition of entropy as the T’, and T7z are the molar volumes,
+I
724
D. R. MOREY AND J. W. TAMBLYS
logarithm of probability. The problem then becomes one of counting all the different ways in which polymer and solvent molecules can be arranged. This is a somewhat difficult procedure, and requires a number of assumptions as to the randomness of m Xing, the absence of aggregation, the degree of flexibility of the chains, etc. Some of these assumptions have been further considered by Flory (9), Alfrey and Doty (l), and by Schuchoivitzky (24). The counting method is based upon the regarding of the system of solvent and polymer as an assembly of lattice points or holes into each of which may be placed a solvent molecule or an equal-sized polymer segment. The segments of a chain must be placed in neighboring lattice points, although not in a straight line. For rubber, one might expect free bending a t each union between monomer units, but for cellulose derivatives, one must assume that, on the average, 6 monomer units must be placed in a straight line before a kink occurs. By this means, variations in chain flexibility are recognized and incorporated into the theory. These entropy calculations result finally in the expressions for the partial molal free energies :
The coefficient BT’JRT is, following Huggins, denoted by p . The effect of p is to emphasize the heat term at the expense of the entropy term. For solutions of rubber in toluene, Flory (8) indicates that a value of p = 5 brings agreement with experiment, while a value of 8 is found for polystyrene in toluene. On the basis of a folloiving discussion on the lack of flexibility found for cellulose acetate, a value of 6 = 50 for cellulose derivatives seems like a reasonable guess. Having obtained equations 5 and 6, the next problem is to calculate the amounts of the components which bring about t,he appearance of a precipitate. Because of the complexity of equations 5 and 6 this is not simple analytically, but the method is graphically illustrated in figure 1. If a solution phase and a gel phase are in equilibrium, then the partial molal free energy (activity) of the solvent which is present in the solution equals the partial molal free energy (activity) of the solvent irhich finds itself in the gel. If AF1 is plotted against the volume fraction of solvent, it \vi11 be found to increase \vith larger amounts of the solvent. If this curve rises continuously, then two phases are not found, for there are not tmo different values on the volume fraction asis for which the same partial molal free energy exists. But for certain values of fig, the cuwes show a maximum and a minimum. Then two phases can appear, and a t different values of the volume fraction, equal partial molal free energies are found. A similar curve can be plotted for AF,, as shown in figure I, and the same equilibrium condition must be met for two stable phases to appear; that is, a horizontal line must cut this curve also a t more than one point. In one and the %me solution, these equilibrium conditions must also begin simultaneously ;
725
FRACTIO3-AL PRECIPITATION O F POLYAXERS
this condition requires drawing vertical lines. It n-ill be found that there is only one place in which the two horizontal and the two vertical lines can be put together to form a rectangle with corners on the curves. The compositions determined by the positions of the two vertical lines then give the “critical” compositions a t which a phase first appears or disappears. These critical compositions can then be plotted against f i p or against the per cent of precipitant
-Gel
F:,
Phase+-Liquld+
0
Volume
I
-
Precipitate
-
-Liquid n a s e -
Fraction of Solvent Vdume Froctton of Polymer
L
O
1. Appearance of phases in relation t o the partial molal free energies of the components
added t o the solution, as in figure 2. (It can be shown that the percentage of precipitant is approximately proportional to log p p . ) Such a curve gives the limiting compositions a t nhich a change in the number of phases takes place. This curve represents the case xhen the polymer is considered to be of only one molecular weight; for each different molecular weight there is a characteristic curve, as shown in figure 3, and as determined by the ratio V,/V,, appearing in equations 5 and 6. With the aid of figure 3, the essential features of fractionation can be deduced. For fractionation by precipitation, we deal with the portions of the curves in figure 3 which are below the peaks or extreme left parts of the curves. Put in
726
D. R. MOREY LVD J. W. TAYBLYX
another way, if one species forms a precipitate, it must be denser and richer in polymer than the phase from which it came. This means entering the two-
Percent Reclpdonl+Log
p
-
FIG.2. Region of single and double phases in relation t o the amount of precipitant. Phases for a single molecular weight: A , one phase only; B, two coexisting phases. the compositions of which are given a t intersection points such as I,, I?.
Perccnl Precipltont+
LO^
FIG.3. Double phase regions for varying molecular weights. Possible courses of fracall species present inequal amounts, 0-, a possible mass distributionation. 0-, tion.
phase region from below rather than from above the left-sided peak; otherwise the process is more a syneresis than a precipitation. The inclined straight lines on figure 3 show the order in which the various species would begin precipitating, as one continuously added precipitant. They are not quite horizontal,
FRbCTIOS.IL PRECIPITATIOX O F POLYMERS
727
since the concentration of polymer decreases as precipitant is added. (They would be horizontal if the experiment were carried out by lowering the temperature.) If the species in the polymer were all present in the same amount, precipitation would proceed as indicated by the solid line. But if the species have a non-uniform distribution, which is generally the case, then precipitation takes place by following the various dashed lines, which start out from different concentration values, on the Jf curves. (The values of molecular weights shown in figure 3 have no quantitative significance; they indicate the direction of dependence on M.) It is seen that the concentration, as well as the identity, of a species determines the precipitation point, and that a species of low molecular weight may start precipitating before one of higher molecular veight if the former is present in much greater amounts. The starting distribution thus plays a part in determining the purity of fractions, and necessitates a refractionation when abrupt changes in distribution are present. This effect of a low species precipitating before a higher one, owing to distribution, is not to be confused nith the true reverse-order effect (20), which is still found when the species are made to have equal concentrations. As to fractionation by extraction, this too is predicted by this outline of phase relationships, as has been pointed out by Scott (26). This comes about by starting, on figure 3, on the right-hand side, and drawing lines approximately horizontal, cutting across the phase separation boundaries. The line proceeds to the left as more solvent ia added, and the lon-molecular-weight fraction is seen to enter the solution phasr first Returning to fractional precipitation, and the use of the loner portions of the phase separation boundaries, the authors have constructed such curves from experimental data and have used them to deduce the distribution curves of cellulose acetate butyrate polymers (19). The distribution was obtained both by a graphical use of the phase boundary curves and by an analytical procedure. Figure 4 s h o w one of the nomograms used. The curved lines, plotted for molecular-weight intervals of 10,000, show where each particular species will begin to precipitate. The diagram is calculated for a fixed value of initial concentration of the n-hole polymer, including all species. The straight lines fix the precipitation point for a given species when present in varying fractions of the total polymer. Thus, if a molecular weight of 100,000 was the only species present, the line C , w / C ~ = M 1would fix the per cent precipitant. If the amount of that species present was only 0.1 of the total, then the line C.w/C,,w = 1 n-ould be folloned Since figure 4 is constructed using a loir value of polymer concentration, it may be regarded as a high magnification of the lower part of figure 3. Phase-change boundary curves for polyethylene in various solvents have been published recently by Richards (21), showing the shape of curve to be dependent upon solvent power. THE RELATI YE IMPORTASCE O F THE ESTROPY COSTRIBUTIOX
We have seen that a large portion of the thermodynamic development has been concerned with including entropy effects. The size of error which may
728
D. R. MOREY AND J. W. TAMBLYN
result from such a lack of entropy terms must depend, however, upon the type of polymer molecule, and one can make a rough separation of polymer solutions
i
06
0 ,
09
03
0.e 0.15
0.125
0.10 0.075 0.05 0.025 0.01
FIG.4 . Phase separation limits for cellulose acetate butyrate. cipitant, 3:1 (by volume) mixture of ethyl alcohol and water.
Solvent, acetone; pre-
into t r y 0 classes: (1) Relatively uncross-linked rubber and other hydrocarbons with large flexibility a t each segment; ( 2 ) cellulose esters and other relatively rigid chains, for which entropy effects are less pronounced and interaction effects strong. Rubber molecules in solution may have such high kinking that the
FRACTIONAL PRECIPITATION OF POLYMERS
729
distance between ends may be only one-tenth the extended length, but considering cellulose esters, recent evidence is that the entropy effects must be much smaller. Thus, in a study of cellulose acetate in acetone, Stein and Doty (29) conclude that “the smaller molecules of cellulose acetate are approximately fully extended in acetone solution, but that the longer ones are bent in gentle waves.” From other optical measurements, Doty and Kaufmann (5) conclude that cellulose acetate chains are relatively rigid, and mention calculations by R. M. Simha indicating that such chains in solution have approximately half the extended length. Further evidence that specific interaction effects, rather than entropy effects, play the chief rBle for the solutions of cellulose esters is given by the large differences in fractionating behavior obtained by the use of varied types of precipitants (20). Recent work of Doty, Wagner, and Singer (6) shows that association may take place before the visual turbidity point is reached, and that such associations may be quite stable. This condition gives a different statistical counting than an idealIy random solution, and a lowered entropy contribution. We must not, therefore, expect Schulz’s theory to hold for rubber, but when applied to cellulose derivatives, its shortcomings as regards a lack of entropy terms are not so significant. On the other hand, the thermodynamic treatment needs a careful weighting of the entropy contribution before it is applied specifically to cellulose derivatives. In the equilibrium rate theory which is now discussed, entropy is not calculated directly. Its effects are not completely ignored, however, since the probability of collision enters into the calculations. PRECIPITATION
AS A REVERSIBLE
REACTIOS
COSSIDERED
FROM T H E K I S E T I C
VIETPOIXT
A step common to the three theories is that of defining precisely the state of saturation. The measurable factors which define such a state are the per cent of precipitant (P,), the temperature ( T ) ,the concentration (C?),and the molecular weight (M,) of the dissolved polymer. In actual practice, a measure of this state is best obtained by carrying a little beyond saturation, so that precipitation has proceeded enough to give a measurable turbidity. We inquire, therefore, into the mechanics of the process of forming the first small aggregates. The initial step of aggregation consists in two chains coming together and remaining attached for a t least a time, until two other chains shall have formed a similar union. We assume that for such a union it is not necessary that the chains be completely joined through all the possible secondary links, but that only a relatively few junction points, n in number, suffice for such an embryo aggregate. The rate a t which one chosen chain will be able to find another and establish with it the necessary n bonds is inversely proportional to n , and since the n bonds must all be between the same two chains, not simply n bonds anywhere in solution, then the rate is proportional to the chain lengths M , and M, of the pair of molecules ~ n i t i n g . ~The rate will also be proportional to the number of other This number n is not to be confused with the total number of bonds which may develop upon subsequent further growth of the aggregate; it represents a minimum number of link-
730
D. R. 310REY AND
J. W. TAMBLYN
chains in solution from which one particular M , can choose a partner. The number of such chains is proportional to the weight concentration of polymer, Cy,divided by the average molecular weight. Then the rate of aggregation for a particular chain molecule is: (rate), = D / n . X , M , C,/Ma (7) where is a constant, including a diffusion coefficient. The rate for all possible pairs of chains thus is: (rate),, = D/n.Jft.M?.C?,/Mi (8) We shall now assume that all the different .If values indicated may be replaced . may be further defined as proportional to the by the number average, J V ~ I) square root of the absolute temperature, and inversely proportional t o both chain length and viscosity of the solvent, since both factors result in lessened mobility.6 Since the viscosity factor is temperature dependent, this would require further evaluation if the theory is tested by temperature experiments. However, most available data are taken a t fixed temperature. Thus (rate)r, =
B T M. ~ C; ~
11%
(91
B being a constant. This rate is calculated on the assumption that all bondings are equallyeffective, whether arising from segments within the chain or from end groups. But there is a growing body of evidence showing that end groups, while few in number, may exert, under proper conditions, appreciable influence. In considering the solubility of a long chain, it is not to be considered as a homogeneous unit. Just as with the fatty acids, wherein some of the valuable lubricating and surfaceactive properties are due to different behaviors of carboxyl and hydrocarbon ends, so also the action of end groups can be differentiated from that of inner segments of a polymer chain. This has been recognized by others; for example, Highfield (12) showed that solvents for cellulose nitrate contain polar and nonpolar groups, and considered that each was necessary to solvate different parts of the polymer. Staudinger and Heuer (28) considered that the aromatic and paraffinic portions of polystyrene retain their own characteristic solubility when polymerized. I t is reported (15) that the use of potassium persulfate as catalyst in the polymerization of polyethylene forms associative end groups ; when these were hydrolyzed off, the polymer had a much lower melting point. The marked ages which create a nucleus capable of further growth and sharing in the turbidity by which P , is detected. There may well be long portions of chains in this embryo nucleus which float freely in the solution without a t first being linked t o each other. For these reasons, n is t o a first approximation independent of molecular weight, although the probability of attaznzng n is related t o molecular weight. It was pointed out earlier in the paper t h a t Schulz’s theory contains a confusion of these considerations. 6 D is inversely proportional to the first power of chain length for chains of slight kinking, but to a fractional power between and 1 if the chains show much coiling.
+
FRACTIOXAL PRECIPITATIOh- O F POLYYERS
73 1
influence of traces of metallic ions (calcium, magnesium) present in water used for washing newly acetylated cellulose is well recognized commercially (31). The increased viscosity which is known to result (“salt effect”) has been ascribed to calcium bridges forming complexes of chains (22). This increased viscosity appears with acetone as solvent, but not with acetic acid, according to Lohmann (17). This requirement of particular groups and particular solvating medium has also been found necessary for the reverse-order precipitation effect (20). We therefore return to the calculation of the aggregation rate, to include a separate term for end groups. Since the size of a linear chain determines the number of inner segments but has nothing to do with the number of ends of the chain, the quantities X , and A f j , which appear in equations 7 , 8, and 9, do not affect the contribution of end groups to the aggregation rate. The combined rate thus becomes : Aggregation rate = BT‘C; M.
+ fBT‘C;Mz3 ?n
where f is a weighting factor which weighs the relative bonding strength or importance of end-containing bonds, as compared to segment-segment bonds, in imparting stability to the embryo aggregate; f thus varies with the solvent-precipitant system chosen. We nom equate the rate of aggregation to the rate of solution,’ the latter being due to secondary bonds receiving excess thermal energies :
B may be further defined a t this point to absorb the additional constants introduced. The weighting factor f appears on the right-hand side also, since if it is concluded that end groups are important in forming an aggregate, then the breaking of an end-containing bond T d l be equally important for the disappearance of the aggregate. The terms E, and E. are the dissociation energies of the segment-segment and the end-containing bonds. These energies are dependent upon the kind of neighbors which surround the segments in question; when, for example, the neighbors are all solvent molecules, this energy drops below a value necessary 7 A similar theoretical approach, applied to the theory of melting of fatty acids, has already been used by King and Garner (16). These authors equate the probability that a molecule will collide with and join to the solid surface, t o the probability that it will be removed by receiving thermal activation energy equal to the heat of crystallization. The probability of adsorption is placed in inverse relation t o the chain length, so that
K/,W = e - Q i R T is obtained. The second paper deals with the question of the molecule being rod-shaped or kinked, and for the latter case the probability of adsorption is a more complicated function of ,W. These authors have also assigned a different effectiveness to terminal groups, as compared to inner groups, in holding chains together, and show that these have different values of heats of solution.
732
D. R. MOREY AND J. W. TAMBLYN
for the continued existence of the bond. As precipitant molecules enter the sphere of neighbors, the bond energy rises. We shall assume that E. is linear with P,:
E, = sP,- U. where U,is a constant related to the energy of association between segment and solvent. The proportionality function s could be further defined in terms of cohesive energy densities of polymer, solvent, and precipitant. This is not essential to the present development of this theory, and we shall amplify s only to account for its dependence upon concentration. For low polymer concentrations, the bonds in the embryo aggregate are surrounded for the most part by small-molecule material. As the concentration increases, however, we must take into account the fact that segments from still other chains form part of the shell of neighbors around the secondary link in question. This will have the effect of aiding the precipitation, so that we shall assume
u,
(13)
+ C,/lOO) - u.
(14)
E, = S8P,(1 f C,/100)
-
and similarly
E. = S.P,(l
expressing Cyin grams per 100 g. of solution. Equations 11, 13, and 14 may now be applied to specific conditions. Considering normal-order precipitation, in which end groups play no significant pa-t, f is assigned a very small value. Then c 2
= t/R
e-S,P7(l+Ctl100)lkT
e U,IkT
BT'M.
for concentrations below 10 per cent. In agreement with common experimental knowledge, equation 15 predicts: ( a ) with increasing molecular weight, a decrease in the concentration a t which precipitation begins; ( b ) with increasing amount of precipitant, a decrease in the concentration needed for saturation; ( e ) for some (but not all) systems, an increase in the concentration needed for saturation, with increasing temperature. Two other predictions are made, for which the experimental evidence is less well known: (d) At a fixed molecular weight, there is a linear relation between log Cy and P,. (It is not the initial concentration, but the actual concentration a t each precipitation point which must be used.) SchuIz has already established the validity of prediction (d), and with a few exceptions, we have confirmed it in numerous examples, two of which are illustrated in figures 5 and 6. ( e ) At a fixed value of Cy, there is a linear relation between log I / M and P,. To test ( e ) , one must adjust Cy to come out the same a t each precipitation point, or else calculate what the value of P, would be a t the chosen Cy. Predic-
733
FRACTIOXAL P R E C I P I T h T I O S O F POLYMERS
tion ( e ) is important for determining the correctness of this theory as compared to that of Schuls, the latter predicting linearity between 1/M and P,. We have carefully examined the available data, tyhich are presented graphically in
Y
LO*
Cq
(C,
I Y UNITS
OF
~/lOOSCl
(a,,
FIG 5. P,-log C, relation for cellulose acetate butyrate. 0 , uniractionated = 71,000); A, fraction B1 (A@,, = 126,000); 0 , fraction D2 (27" = 54,000). Solvent, acetone; precipitant, 3 : l (by volume) mixture of ethylalcohol and water. 31
Solvent' Pyridine 37°C.
-
29-
c z
-
&I
g 27n a
25-
' I
U
-
-
23-
0
-
-
$021
'a
-
19-
I I I -20
Solvent: Glacial aceiic acid I
-16
I
"
I
'
-12 - 0 8 L O G C,
I
'
-04
,
'
0
- 2 0 -16 LOG C,(C,
,
,
,
,
,
28'C ,
,
I
I
-08 - 0 4 0 +I 4 IN GRAMS PER IOOcc)
-12
FIG.6. P,-log C, relation for cellulose acetate butyrate fractions. X , 164,000;
0,
48,000.
figures 7 to 14. In figure 7 are presented the data which are the most favorable to the 1/31 relation. Good straight lines, over the range covered, are seen. However, the range of 1/M is limited, and when data covering a wider range are plotted, as in figure 8, then the linearity is seen to exist only for higher molecular
734
D. R. MOREY AND J. W. TAMBLYN
weights, while the log 1 / M form gives linearity for the lower range. It may be concluded that for the polystyrene-benzene-methyl alcohol system, an inter-
Ed &* 5
3:y) 26 27 28
25
-
I
I
I
I
1
I
/,/
IO
20
30
I
4 n ap* L
1614-
!:/ 12 IO-.
0
I
04
I
l
I
I
08
I
1
I
,
I
l
12
FIG.7. P 7 - 1 / M and log 1/M relations for polystyrene and nitrocellulose. Top: polystyrene; solvent, benzene; precipitant, methyl alcohol. D a t a of Schula and Jirgensons (Z. physik. Chem. B46, 114 (1940)). Bottom: nitrocellulose; solvent, acetone; precipitant, water. Data of Schuls and Jirgensons.
mediate degree of dependence on 1/&1 is correct. Later data of Schulz and Jirgensons (25) also deviated from the 1/M form, and these authors suggested as a modification that Pyshould be linear with l / M 2 ’ 3 . This form does, in fact, fit the data of figures 9 and 10, both of which show 1/31 and log 1/M to be approaching a fit from opposite directions.
735
FRACTIOXAL PRECIPITATION O F POLY?dERS
POLYSTYRENE ; SOLVENT: BENZENE PRECIPITANT : METHYL ALCOHOL
: 11
SOLVENT: METHYL ETHYL KETONE PRECIPITANT : METHYL ALCOHOL -D
24
/
/*
2 I/M x 10'
LOG W M x IC
Combined data of Schulz (Z. FIG.8. P7-l/.ld and log I/M relations for:polystyrene. physik. Chem. A179, 321 (1937)) and of Staudinger and Heuer (Z. physik. Chem. A171, 144 (1934)).
FIG.0. P,-l/.lI and log l / M relations for polymethyl methacrylate. Solvent, benzene ; precipitant, cyclohesane. Data of Schulz and Jirgensons ( Z . phyaik. Chem. B46, 114 (1940)).
736
D. R. MOREY AND J. W. TAMBLYN
Figures 11 and 12 show a marked superiority of the log 1/M form. Figure 13, plotted with the aid of additional data on the effect of concentration, kindly furnished us by Dr. W. 0. Baker, shows again a departure from linearity a t low
56 0
g
'?
-
5452-
5048-
u' 1
.a-
4644-
42
-
40-
38
I
I
I
I
IO
20
30
40
I
I
I
I
50 04 06 00
I
I
I
I
IO
I2
14
I6
B
FIG.11. P7-1/M and log 1I.V relations for polyoxyethylenes. Solvent, methyl alcohol; precipitant, ether. Data of Love11 and Hibbert (J. Am. Chem. SOC.61, 1916 (1939)).
molecular weights m-hen using the l / M form, while the log form fits reasonably well. In figure 14 the log form is only approximately correct, but obviously gives a better fit than does l/X. I t may be concluded that the linearity of P-, with log 1 / M is approximated sufficiently well to establish the first-order correctness of the rate theory.
737
FRACTIOS.4L PRECIPITATION OF POLYMERS
bMx
Log
I06
Ch 'X 101
FIG.12. P,-l/M and log l/M relations for cellulose acetate (40.4per cent acetyl) fractions. Solvent, acetone; precipitant, water.
8
12
16
20
24
28
32
36
40
10
I1
I / M x IO5
12
13
15
14
LOG [ VM
1051
FIG.13. P,-l/V and log l/M relations for polyundecanoates. Solvent, chloroform; precipitant, methyl alcohol. D a t a of Baker, Fuller, and Heiss (J. Am. Chem. Soc. 63, 2142 (1941)).
B E
0.N
"8 3 2
80
6810
20 I/M x 10'
30
08
09
10
I1
I2
13
14
15
LOG [I/M x IO6)
FIG. 14. P,-l/JI and log 1/.M relations for cellulose acetate butyrate fractions. Solvent, acetone; p.recipitant, 3 : l (by volume) mixture of ethyl alcohol a n d water.
738
D. R. MOREY AND
J. W. TAMBLYX
REVERSE-ORDER PRECIPITATIOK
We now inquire into the consequencesof choosing a system of polymer, solvent, and precipitant in which the end groups are particularly active. This corresponds, in the general equation (equation ll),to making the weighting factor f large. In the extreme case, we neglect terms not containing j and obtain, for lower concentrations :
We see that with increasing molecular weight, the concentration required for saturation increases; put another way, the shortest chains will precipitate first. That there are rather unique cases of this has already been reported (20). Fur-
- 7
4
7
a
$68w
>
66-
a >
64-
m
-
-62-
-
av 60
1
1
1
1
1
-2.4 -2.0 -1.6
1
1
1
1
1
1
1
-1.2 - 0 8 -0.4
LOG C, FIG.15. Reverse-order precipitation as a function of concentration. Cellulose acetate butyrate fractions; glacial acetic acid-isopropyl ether system; 11°C. 0 , M , = 48,000; X,
Y, =
164,000.
ther study of the effect, as it appears with cellulose acetate butyrate solutions and isopropyl ether as precipitant, has shown that it is not a temperaturedependent phenomenon, but does depend strongly upon the concentration of the polymer solution used. This is illustrated in figure 15. At a quite dilute concentration, approximately 0.03 per cent, the two lines, each corresponding to a different molecular-weightfraction, cross. At this point, both species precipitate a t the same value of P?. For concentrations lower than this, the fractions precipitate in normal manner. For concentrations higher than this, however, the low-molecular-weightcomponent precipitates before the higher, and indeed the divergence is more and more marked as higher concentrations are used.* The two graphs in figure 15 refer to different optical means of detecting the These same two fractions and solvent are shown i n figure 6, wherein with water as precipitant, normal-order precipitation is seen for all concentrations.
739
FRACTIOKAL PRECIPITATIOS O F POLYMERS
initial turbidity. Figure 16 shows that an increase of temperature, for both the normal- and the reverse-order regions, increases the over-all solubility, but does not destroy the reverse-order effect nor its dependence upon concentration. Figure 17 again illustrates the r81e of concentration, this time with acetone as solvent and using additional fractions. Before accepting an explanation of this reverse-order effect based upon a more abstruse matter such as the end-group hypothesis advanced here, it is desirable to know that no other analytic factor is responsible. We have determined (30)
50°C
-2.4 -2.0 -1.6
-1.2
-0.8.-0.4
LOG Cd FIG.16. Reverse-order precipitation independent of temperature. Cellulose acetate butyrate fractions; glacial acetic acid-isopropyl ether system. 0 , M , = 48,000; X , M , = 164,000.
that the acetyl and butyryl contents of the fractions employed were the same within the accuracy of analysis, approximately 0.5 per cent. Ash analysis, made on another set of fractions of the same polymer, gave the results in table 1. It is seen that with the exception of the higher ash content collected in the first fraction, the ash content is essentially independent of molecular weight; hence the reverse-order effect is hardly to be ascribed to a progressive change in total ash content. This is more apparent when it is recalled that the reverse-order effect was obtained on several pairs of fractions taken from the range encompassed by fractions 2 and 7 of table 1. Accepting the vieiv that end groups are
740
D. R . YOREY Ahm J. W. TAMBLYN
responsible, then there should be some change of analysis with molecular weight, but its detection would require still more precise analytic procedure, and not
pr z
o
5
t-
0
W
a
-NORMAL
ORDER
To-
REVERSE ORDER-
66-
-
a c U
62-
a W
I
L
58-
-I
r n 0
g
54-
0
II t
E
50-
0
a W
n
- 2.0
-3.0
FRACTION NO.
1
C
-1.0
L O G Ct Cr I N GMS. P E R 100
CC.
VISCOSITY
-PENT
i 11
INOPGAhTC MAIEBIAL I C -0.21
m i g h t per emf
l..... ..................... 2 . . . . . .................... 3. . . . . . . . . . . . . . . . . . . . . . . . . . . 4.......................... 5........................... 8........................... ?...........................
8. . . . . . . . . . . . . . . . . . . . . . . . . . . Unfractionated original. . . . .
,
2.84 2.64 2.49 2.32 1.98 1.57 0.84 0.75 1.70
0.092 *0.002 0.031 f O . 0 0 6 0.029 rt0.002 0.030 *0.002
0.028 rt0.002 0.028 f 0 . 0 0 2 0.034 rt0.002 0.016 rt0.006 0.036 f O . 0 0 2
LL
0
62-
-
$ 60 -II
pr from initial scatter rise
% from P, from start initial transmission drop of rapid precipitation
742
D. R. M O R E S AND J. W. TbMBLYN
preference as to molecular weight. Such a case has recently been reported by Battista and Sisson (2). In such cases, it is evident that any computation of a “distribution” curve of molecular weights is in gross error. The evidence so far presented on the appearance of reverse-order precipitation has been on dilute solutions, examined optically. I t would, therefore, be more convincing if an actual physical separation of fractions were accomplished, with first fractions being examined and found to be of lower molecular weight. This has been done, with the results given in tables 2 and 3. We have seen that the appearance of reverse order is associated with high concentrations. SeveraI fractionations were therefore carried out, a t varying concentrations, with typical results shown in table 2. At lower concentrations, the fractions appear normally, and a separation is obtained similar t o that which holds when a more
k
Go=
O.O167g/1OOcc.
a W I-
t0 v)
w v)
a
W
> cn z a U
I - .
FIG.19. Course of precipitation, in a reverse-order system, for various concentrations Cellulose acetate butyrate fractions. Solvent, pyridine. 0 , M, = 48,000; X, M , = 164,000.
usual precipitant, such as water, is used. At 10 per cent starting concentration, lower fractions are found to separate first, and then as fractionation proceeds, normal order again sets in. Further examples of this are given in table 3, wherein results on fractionating from other solvents, but still using a precipitant specific for reverse order, are shown. EFFICIESCY O F FRACTIONATION
These data again illustrate the importance of careful choice of solvent and precipitant, for efficiency in separation. The use of a higher concentration, if a system with reverse-order tendencies were chosen, would thus lead to an apparently less efficient normal-order fractionation. The lower efficiency would be due not to higher concentrations per se as the prime cause, but to enhancement of the end-group effect. Efficiency is of practical importance, and it is proper
743
FRACTIONAL PRECIPITATION O F POLYMERS
that in the course of the development of theories. this should be examined. However. it is striking that in the discussion of efficiencies. so much attention TABLE 2 Fractionation of cellulose acetate butyrate Solvent. acetone; prec itant. isopropyl ether STAXIEiG CONCENTRAIION
1.25 O./lW CC
Fraction No .
Weight per cent
1 .......... 2. . . . . . . . . . . . . . 3 ............ 4. . . . . . . . . . . . . . 5 ............. 6. . . . . . . . . . . 7. . . . . . . . . . . . . . 8. . . . . . . . . . . . . . 9. . . . . . . . . . . . .
4.3 4.1 14.9 17.9 19.9 13.3 9.7 6.9 9.0
{n
le
.
SIAPIINO CONCENTBATlON:
.
0.25
2.88 2.76 2.48 2.11 1.80 1.40 1.08 0.78 0.43
Fraction No .
10.0 0./100
CC
.
Weight per cent
1. . . . . . . . . . . 2. . . . . . . . 3. . . . . . . . . . . 4 ........ ' 5. . . . . . . . . . . 6.,......... 7. . . . . . . . . . 8. . . . . . . . . . 9. . . . . . . . . . . 10. . . . . . . . . . . 11. . . . . . . . . . 12 . . . . . . . . . 13. . . . . . . . . . .
4.7 2.1 1.9 11.1 9.9 12.5 12.6 10.0 8.7 8.0 5.0 3.5 3.5
1.70 1.83 2.12 2.30 2.10 1.98 1.87 1.82 1.69 1.54 1.36 1.16 0.97 0.69
TABLE 3 Fractionation o f cellulose acetate butvrate
.
PROY 5 PEP. CENI SOLUIION I N PyPu)INE PRECIPITANT ISOPPOPYL ETKER
Fraction S o
.
1+2 ...... 3. . . . . . . . . . . . 4. . . . . . . . . . . . 5. . . . . . . . . 6. . . . . . . . . . . . 7. . . . . . . . . . . 8 .......... 9. . . . . . . . . . . 10. . . . . . . . . 11 . . . . . . 12. . . . . . . . . . . . 13. . . . . . . . . . . 14 . . . . . .
Weight per cent
1.1 1.1 3.3 9.3 13.6 15.7 15.6 12.1 8.1 5.4 5.1 4.4
5.2
11).-0.26
1.61 2.03 2.99 2.65 2.28 2.03 1.79 1.50 1.24 1.11 0.94 0.74 0.52
FPOY
5 P E P CENT SOLUTION IN GLACIAL ACETIC
ACID
PRECIPITANT. ISOPROPYL ETHER
Fraction No .
1
1. . . . . . . . . . 2. . . . . . . . . . 3 ........ 4 ......... 5 ......... 6. . . . . . . . . . 7. . . . . . . . . 8. . . . . . . . . . . 9 ..........
Weight per cent
Inlc-o.zs
1.0 .7 .9 .8 2.8 6.7 17.5 15.8 16.2
1.63 1.78 1.58 1.48 2.06 2.67 2.21 1.93 1.71 1.34 1.17 0.95 0.69
has been paid to the concentration. while the importance of the proper choice of system has not been understood . Howlett and Urquhart (13) examined a number of solvent-precipitant combinations. for cellulose acetate. and chose the
744
D. R. KOREY AND J. W. TAMBLYh‘
system which spread out the fractions over the greatest range of per cent precipitant; this has the advantage that less precision is required in adding the proper amount for approximately equal fractions. Similar considerations influenced the choice made by Blease and Tuckett (3) for their fractionation of polyvinyl acetate. But this goal of spreading the fractions over a wide range of precipitant, while desirable in itself, still leaves unanswered and unproved the crux of the matter: to obtain fractions which are spaced in molecular weights. As Battista and Sisson have shown, there is a distinction to be drawn between mere mass separations and species separations. As to the use of low concentrations, one must critically determine whether or not the gains predicted by approximate theory are really of such magnitude as to justify the attendant disadvantages, and this should be done by experiment, It has been our opinion, expressed earlier, that too much emphasis has been laid on extremely low concentrations (20). I t is of interest to note that a fractionation of nitrocellulose was carried out by S p u r h (27) from a 10 per cent acetone solution, and a good degree of molecular weight separation reported. Further experimental evidence dealing with the fractionation of butyl rubbers has been reported to us by Dr. J. Rehner, Jr. With his kind permission the following passage is quoted from one of his communications to us: “We have on several occasions carried out fractionations in parallel starting with polymer concentrations ranging from about 0.25 per cent t o about 2 per cent, and have found little or no difference in the results. While emphasis has been placed for some years on the necessity of employing high dilutions for good fractionation, our results showed t h a t , a t least for the polymers worked with, this did not appear t o be a vital factor; we found careful temperature control t o be far more important. The relatively minor importance of concentration on efficiency of fractionation agrees with your recently reported findings with cellulose acetate.”
The expressions for denoting efficiency, as deduced by Schulz and Flory, are not so much concerned with the concentration as they are with the volume fraction of the precipitated phase; these efficiency measures state that the separability rises with the log of the ratio of solution to precipitate volumes. In other words, efficiency is concerned more with taking small cuts or fractions, and hence a larger number of fractions, than it is with the over-ail concentration. Referring again to figures 3 and 4,it is seen that if one of the dashed lines is followed corresponding to increasing the amount of precipitant, but followed for only a short distance (small cut), then one particular species is most active in precipitation. But if the same line is followed a long distance (large cut), then so many phase boundaries are crossed that the net result is an average composition of lesser homogeneity. Our physical means of distinguishing one chain length from another do not permit us to go on indefinitely recognizing length differences; we soon come to a point where we consider neighboring chains to be identical. This means, on the basis of figures 3 and 4,that letting P7vary over a still shorter range (smaller cut) does not produce any recognizable
FRACTIOKAL PRECIPITATION O F POLYMERS
745
increase in homogeneity, and hence there is a practical limit to the number of fractions to be taken out. Diagrams such as figure 3 show the left-hand peaks to occur a t rather low concentrations. There is a tendency to regard this as additional evidence for the idea that only a t very low concentrations can efficient fractionation be obtained. It must be kept in mind, however, that the ordinate scale of volume fraction (or concentration) of such diagrams applies to each particular molecular species being considered a t the moment, not to the mixture of all species. In precipitation, it is true that a species is not one pure molecular weight, but a band of neighboring sizes which are not distinguishable; these can then be considered to interact. But when the molecular weights are far enough apart, then, for reasonably low concentrations, such separated species act quite independentl~.~Therefore, in a broad distribution, a concentration of say 10 per cent for the whole mixture means something like 1 pnr cent on each particular curve of figure 3. Concentrations which are above the left-hand peaks of these curves are too high, but it is hardly a valid argument against the efficiency of a precipitation process to point to conditions where such a process is no longer taking place and where actually syneresis is occurring. SUMMARY
Existing theories accounting for the selective precipitation of increasing chain lengths are reviewed. These theories are: ( a ) that of G. V. Schulz, a treatment based upon considering the potential energy of a chain molecule when in the solution or in the precipitate phase; ( b ) a thermodynamic treatment, developed by Flory, Gee, and Huggins, in which a calculation of activities is made and used to predict phase separation conditions; and ( c ) a theory in which the precipitate phase is considered as a consequence of the opposing rates of solution and aggregation. With this last theory, by including a 'separate term for the influence of end groups, the type of fractionation in which short chains are less soluble than the long ones can be accounted for. This reverse-order effect is further studied and shown to be independent of temperature but dependent upon concentration. The opposing rate theory is shown to be in accord also with experimental data on normal-order precipitations. The efficiency of fractionation is also discussed from the viewpoint of these studies. 9 I n a n experimental proof of this, the concentration of the high fraction must be adjusted t o the same value, upon the addition of a low fraction, t h a t it had in the comparison titration. It is incorrect t o take the same concentration for the mixed species. This would lead to a n apparent enhancement of long-chain solubility by the presence of short chains, when the effect is actually one of variation of titration point with concentration. I n a study of such mixtures by thermodynamic theory, the same precautions hold; the volume fraction of the species being considered t o precipitate must not be confused with the combined volume fraction of all polymer components.
746
D. R. MOREY AND J. W. TAMBLYX REFERENCES
(1) ALFREY,T . , AND DOTY,P . M.: J. Chem. Phys. 13, 77 (1945). 0. A., AND SISSON,W. A,: J. Am. Chem. SOC.68, 915 (1946). (2) BATTISTA, R . F.: Trans. Faraday SOC.37,571 (1941). (3) BLEASE,R . A., AND TUCKETT, (4) CRAGG,L. H., AND HAMMERSCHLAG, H . : Chem. Rev. 39, 79 (1946). (5) DOTY,P . M., AND KAUFMAN, H. S.: J. Phys. Chem. 49, 583 (1945). II., AND SINGER,S.: J. Phys. Colloid Chem. 61, 32 (1947). (6) DOTY,P. M., WAGNER, , ~ J.Chem.Phys.9,660 . (1941);10,51 (1942);12,425 (1944). (7) F L O R YJ.: P . J.: J. Chem. Phys. 10, 57 (1942). (8) FLORY, P. J.: J. Chem. Phys. 13, 453 (1945). (9) FLORY, J.: J. chim. phys. 42,41 (1945). (10) GAVORET, G., AND DUCLAUX, (11) GEE, G.: Trans. Faraday SOC.38, 276 (1942). (12) HIGHFIELD, A.: Trans. Faraday SOC.22,57 (1926). F., AND URQUHART, A. R.: J. Textile Inst. 37, T89 (1946). (13) HOWLETT, (14) HUGGINS, M. L.: J. Chem. Phys. 9, 440 (1941); J . Phys. Chem. 46, 151 (1942); Chap. 9B of Cellulose and its Derivatives, Emil O t t (Editor), Interscience Publishers, Inc., New York (1943). (15) I. G. Report: Modern Plastics 23, 153 (1946). (16) KING,A.M., AND GARNER, W. E . : J. Chem. SOC.1934,1449; 1936,1368. (17) LOHMANN, H . : J. prakt. Chem. 166, 301 (1940). (18) MOREY,D . R . : A.A.A.S. Conference on High Polymers, Gibson Island, Maryland, July, 1946. J. W.: Meeting of the Division of High-Polymer Phy(19) MOREY, D . R., AND TAMBLYN, sics, Rochester, Kew York, 1944; J. Applied Phys. 16,419 (1945). (20) MOREY, D . R., AND TADIBLYX, J. W.: J. Phys. Chem. 60, 12 (1946). (21) RICHARDS, R . B . : Trans. Faraday SOC.42, 10 (1946). S., AND SCHLACHOVER, M.: Kolloid-Z. 78, 224 (1937). (22) ROGOVIN, (23) SCATCHARD, G.: Chem. Rev. 8, 321 (1931). 8.:Acta Physicochim. U.R.S.S. 20, 887 (1945). (24) SCHUCHOWITZKY, (25) SCHULZ, G. V.: Z. physik. Chem. A179,321 (1937) (with B. Jirgensons); B46,122 (1940). (26) SCOTT,R . L . : J. Chem. Phys. 13, 178 (1945). (27) SPURLIN, H . M.: Ind. Eng. Chem. 30, 538 (1938). H . , AND HEUER,W.: Z. physik. Chem. A171.146 (1934). (28) STAUDINGER, (29) STEIN,R . S., AND DOTY,P. M . : J . Am. Chem. SOC.68,166 (1946). J. W., MOREY, D . R., AND WAGNER, R . H.: Ind. Eng. Chem. 37,573 (1945). (30) TAMBLYN, (31) U. S. patents 2,126,488-9.
