RHEOLOGICAL PROPERTIES O F BITUMENS
149
REFERENCES (1) I.: J. Am. Chem. SOC.39. 1848 (1917). . . LANGMUIR. (2) NELLENSTEYN, F. J. : Bereiding en constitutie'van asphalt (Manufacture and constitution of asphaltic bitumen); Dissertatie Technische Hoogeschool, Delft, 1923. (3) PFEIFFER, J. PH.: De Ingenieur 64, P4-P10 (1939). J. PH.: De Ingenieur 64, Mk41-Mk47 (1939). (4) PFEIFFER, ( 5 ) PEFIFFER, J. PH.,AND DOORMAAL, P. M.VAN:J. Inst. Petroleum Tech. 22, 414 (1936). 16) SAAL,R. X , J., AND LABOUT, J. W. A.: J Phys. Chem. 43, 149 (1939).
RHEOLOGICAL PROPERTIES OF ASPHALTIC BITUMENS' R. N. J. SAAL
AND
J. W. A. LABOUT
Laboratoraum N . V . de Bataafsche Petroleum Maatschappij, Amsterdam, Holland Received August 7, 1959 I. INTRODUCTION
In numerous investigations, the rheological properties of asphaltic bitumens have been found to vary widely in elastic deformability and thixotropy (5, 6). From the point of view of their thixotropic properties, they may be divided arbitrarily into two groups-those of the sol type and those of the gel type (3). Elasticity may be due to the elastic deformability either of the separate micelles or of a structure built up by coherent micelles; it may therefore occur both in bitumens of the sol type and in those of the gel type (4). The wide and continuous range of chemical composition observed in all asphaltic bitumens makes it likely that free (sol) micelles or isolated small agglomerates of micelles, which may themselves be considered free micelles, may be present in bitumens of the gel type as well as in those of the sol type. Among the technical asphaltic bitumens, therefore, many representatives of mixed gel-sol types may be expected. In order to be able to judge in how far the rheological properties of asphaltic bitumens may be explained by regarding them either as sols or as gels, a close study was made of the rheological properties of two quite different bitumens, not only the deformation under constant shearing stress being investigated, but also the elastic recovery or the relaxation of the stress. The measurements were carried out in a concentric rotation viscometer with a conical bottom. Presented a t the Sixteenth Colloid Symposium, held a t Stanford University, California, July 6-8, 1939.
150
. R . N . J. a u L AND J.
w.
A. LABOUT
The chief characteristics of the bitumens used in this investigation are given in table 1. The rheological measurements were made at 35”C.,a temperature at which the deformations could be accurately observed. On the strength of the penetration index bitumen A would seem to belong to the gel type, bitumen B to the sol type (3). The low C/H ratio of the asphaltenes should be expected to give both of these bitumens a high elastic deformability (4). The following rheological measurements were made: (1) The change in deformation with time under constant shearing stress (subsequently referred to here as “deformation”). (2) The degree of elastic recovery after various deformations. (3) The relaxation of the internal stress with time after various deformations. The internal stress will be referred to here &s the relaxation stress. (4) The recovery with time after defor-
TABLE 1 Chief chamten’slics of bitumens A and B ~~
Penetration at 25°C.. ............................. R & B melting point, “C.. ........................ Penetration index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Insoluble in eO/M gasoline, per cent by weight. . . . C/H ratio of asphaltenes. . . . . . . . . . . . . . . . . . . . . . . . . Penetration at 35°C.. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
~
~
64
17
68 3.2 25.0 0.90
62.5
100
-0.7 25.3 0.85 50
mation and partial relaxation of the stress. (5) The relaxation of the internal stress with time after deformation and partial recovery. 11. THEORETICAL CONSIDERATIONS
For mathematical analysis asphaltic bitumens or colloidal systems in general may be typified as (1) pure sols in which each micelle is independently mobile, (2) pure gels in which all the micelles are interconnected to form a structure, or (9) gel-sols in which part of the micelles form a structure, but others are independently mobile. Using a rough theoretical model somewhat different from that of Burgers (l),flow equations for the mixed gel-sol type may be derived. Figure 1 represents in two dimensions a unit of volume containing one free micelle. The dimensions of the free micelle, the elasticity of which is indicated by GI,are given by p and q. The deformation of the element is indicated by s, that of the free micelle by s’. Further, there is an elastic element of the structure Gp, to which, for the sake of simplicity, no vulume has been sssigned. Rotations of the free micelle are left out of consideration. The theoretical analyses of the five types of rheological measurements reported are here indicated briefly.
151
RHEOLOGICAL PROPERTIES OF BITUMENS
1. Deformation For the deformation of this model system the following equations may be set up: ds which says that the stress resisting deformation of the element is equal to the sum of the viscous stress in compartments I1 and I and the elastic stress Gas; and s’ -GI = -.! ds - ds’ Q 1--q dt
(- -;ii)
which says that the elastic stress in the micelle is equal t o the viscous stress in compartment I above it. 8
I I
I
Liquid ‘ O f Viscositk
q
I
v’
,’
I = --G
Fme Micelle
4 GI P
E’IO.
I+
1.
When solved for the case of a particular value of the constant equations give
in which XI and X I = -3{(1 Here
and
-q
+ pq)a + a ) f $7
7
these
152
R. N. J. SAAL AND J. W. A. LABOUT
As elements with different properties must be combined to obtain a real material, the dependence of the deformation on time becomes more complicated. The integral values of the deformation, however, probably will be proportional to the stress whenever time is taken to be constant making s =
(14
7fl(t)
At large deformations real structures will be destroyed and the applicability of equation l a is, therefore, limited. 2. Recovery
Recovery phenomena may be derived from differential equations similar to those used above:
and
If these differential equations are solved for the case in which recovery follows immediately upon a deformation with shearing strPss 70 during time to, an equation of the same type as equation 1 is obtained, which can be reduced to se =
70(fl(tO
+ t) -
.fi(t)}
(2)
where se is the part of the total recovery se0 which the bitumen still has to cover a t the end of the time of recovery t. Referred to the previous deformation so or to the total recovery ss0, equation 2 becomes
3. Relaxation
Relaxation is possible only with free micelles. Therefore thc formula cannot be of type 1 or 2. If the relaxation follows immediately after a deformation during t o under 7 0 , then
+ ?EY
=~~s,,
(e'l'o
- e's'o)"''
where 6
= (1
- p)
(1
- q)a
(3)
RHEOLOGICAL PROPERTIE8 OF BITUMENS
153
I n more general forms this equation is 7,/r0 =
Gzfl(to) - fdto)e-"
(34
- .f3s(tO,t)
(3b)
or even 78/70
=
Gzfi(t0)
Therefore relative relaxation stress-time curves must coincide with equal times of previous deformation, and it should further be possible to make relaxation curves with differing to, but with equal SO, coincide by shifting them in the direction of the time axis.
4 Recovery ajter partial relaxation If,after deformation s!, a certain relaxation to the stress ~~0 takes plhce, followed by recovery, a recovery curve will have to be found coinciding with one after a deformation of so under a smaller shearing stress, of such a magnitude that its relaxation stress at the first moment equals rR0. 5. Relaxation after partial recovery
In deformations to so by r0during to and partial recovery to s, during t, followed by relaxation, the value of the elastic deformation of the free micelle after the partial recovery must first be calculated. With large enough recoveries this deformation can be negative, in which case during the relaxation following, the stress will rise. For this case the following formula can be obtained: 7 B
=
TR(t0
+ te) -
781,
(4)
This equation says that the relaxation stress in question is equal to the difference between the relaxation stresses after deformations with the same shearing stress during times (to te) and t,, if the three values of r g are taken after equal relaxation time. The above formulas are derived for mixed gel-sol type systems and therefore also comprise the separate cases of the pure sol and pure gel type. Since the particular bitumens we examined showed pronounced relaxation which occurs only with free micelles, only the equations for the pure sol type need to be deduced. (1) Deformation in connection with time is then found to be
+
154
H. N. J. SAAL AND J. W. A. LABOUT
(8) The recovery is represented by
and the total recovery is therefore given by =
Seo
~0f3(t0)
so that formula 5a can also be written as s
-
s0 .
=
rAt
Furthermore, formula 6 may be reduced to
so that for the sol type we must always refer the recovery to the total recovery. (3) For the relaxation
so that the generalized form 78
=
TO.f4(tO,
t)
becomes analogous to equation 3b. (4) When after deformation partial relaxation is followed by recovery, the relationships are the same for the sol type as for the more general gel-sol type. (5) When after deformation partial recovery is followed by relaxation, for the pure sol type no rise in the relaxation stress is possible but only a regular decrease to zero. It is not quite certain, however, that this will continue to apply with a more generalized model. Before ascertaining in how far measurements are in agreement with the formulas, the following remarks have to be made: Owing to the continuous transition in chemical nature between the components that form the bitumen, it cannot be expected that there should be a sharp distinction between free and bound micelles in the mixed gel-sol type. Continuous transition may also be expected in the force with which the micelles are bound together. If loosely bound micelles are present, the theories given above may not fully apply. The theory is based on the contrast between free and bound micelles. A similar mathematical analysis might be based on differences in the rate of mutual binding of micelles.
RHEOLOGICAL PROPERTIES OF BITUMENS
155
111. MEASUREMENTS
I. Deformation In figures 2 and 3 curves for deformations under constant shearing stress have been drawn for bitumen A and bitumen B by plotting the logarithm of the deformation (log s) against the logarithm of the time of deformation (log t ) , s being expressed in centimeters qf shear per centimeter of layer thickness and t in seconds. It appears that with small deformations the distances between the lines at the same times are approximately equal to the logarithms of the ratios of the shearing stresses applied, which is in agreement with formula 1 or formula 5.
FIG. 2. Relation between deformation and time. Bitumen A
With greater deformations this rule no longer holds for bitumen A. When the rate of deformation for different values of t is calculated, it further appears for curves DI and DZfor bitumen A that the rate of deformation increases with the time for greater deformations, which in the graph is clear from the slope of the curves. This is in agreement with the assumption that bitumen A contains a skeleton which is broken down a t a certain deformation. It has further appeared that after a sufficient time of rest (1 t o 3 days) the curve can be completely reproduced, whereas this is not possible a t once, which indicates that this bitumen has the property of self-healing or thixotropy. Beyond the deformation a t which structure is temporarily destroyed the curves cannot be derived from the model.
156
R. M. J. BAAL AND J. W. A. LABOUT
For small deformations the curves for bitumen A are practically straight and can therefore be represented by s = Tat"
(8)
Hence in formula la, fl(t) = at", where a = 1.38 X 10-6 and n = 0.38. Curves for bitumen B have been found to display a distinct curvature a t small deformations, but after great deformations the slope becomes practically 1, so that ds/dt is constant. Hence there are here no indications for skeleton breakdown.
FIQ.3. Relation between deformation and time. Bitumen B 2. Recovery
In figures 2 and 3 are also plotted the curves el, e2, and e3,which indicate the total elastic recovery observed on releasing the external stress immediately after deformation during the period indicated on the abscissa. The distance between the corresponding lines D and e therefore gives for each time of deformation that part of the deformation which is permanent. It is clear that for bitumen A the total recovery after small deformation is complete, whereas this is not true in the case of great deformations. This makes it probable in the case of small deformation bitumen A must be considered to have a coherent structure. In the case of bitumen B such a structure seems to be absent from the start. With bitumen A the e lines display a distinct maximum near the defor-
that
RHEOLOGICAL PROPERTIES OF BITUMENS
157
mation at which the D lines display the greatest curvature, indicating that after breakdown of the skeleton the total recovery becomes smaller. The order of magnitude at which serious breakdown occurs corresponds with that calculated by Kratky (2). With bitumen B also the e lines afford indications of a breakdown either of a weak structure or of structures in small agglomerates, although for this asphalt the D lines do not disclose this property. In any case the behavior of bitumen B seems to approach that of the sol type, and for this reason we have further plotted, in figure 3, log (s - sea) against log time (curves D'), obtaining straight lines of slopes very close to 1 which approximately satisfy equation 5b. The secondary effects which account for the small deviations have been treated in previous publications (5). It may further be noted that also in the case of bitumen A, log (s - sea) plotted against log time gives practically a straight line but the slope of this line is not always 1, and it is therefore described by the equation s
- S.O
= bt"
(9)
where m may be > 1 and can to a certain extent be used as a measure for thixotropy (4). In figure 2 the first parts of the e lines coincide with the D lines and can therefore be represented, for these or even greater deformations, by the formula Seo
=
Toat;
(10)
In figure 3 the first part of the e lines, unlike that of the D lines, is straight and hence can also be represented by formula 10, where a = and n = 0.50. 0.49 X It is important to define the conditions under which no skeleton breakdown occurs. I t was found that immediately after one experiment good duplicate results could be obtained as long as the previous deformation did not exceed s = 0.6 to 1.0 a t most. For bitumens A and B the rates of recovery are given in figures 4 and 5 by plotting se/se0against time. This permits comparison of the results with the theoretical recovery equation (2a), into which it has now become possible to introduce the specific form of the function as given by equations 8 and 10, so that we have
In figures 4 and 5 there is a regular displacement of the lines dependent upon the duration of the preceding deformation as shown on the graphs, and apparently independent of other conditions. Quantitatively there is reasonable agreement, points of equal t / t o which according to equation 11
158
R. N. J. S M L AND J. W. A. LABOUT
should have equal values of s./seO1 and which in a few cases have been connected by lines, displaying differences between maxima and minima of 0.05. Direct calculation of s,/scp by means of formula 11 gives values for bitumen A that are somewhat lower than those found experimentally,
1"
FIG.4. ltelation between S./S.O and time after various deformations at different shearing stresses. Bitumen A. Times on curves refer to duration of previous defjrmation. Horizontal dotted lines connect points of equal t/to.
t
NO.
+O
ec&
0.30 0.75 1.27 27.5 0.255 0.55 0.87 0.135 0.375
0.30 0.64 0.87 0.615 0.245 0.46
0.625 0.12 0.255
dynar per rg.cm.
30 240 600
s,m
6Ooo
58,OOo 28,700 28,700 28,700 7,080 7,080
120 600 1500
360 2400
58,m
s,m
the maximum difference being 0.10; for bitumen B the equation applies within the limits of error of our experiments. There therefore appears to be satisfactory agreement with the model. With values of so greater than 1, on the contrary, no agreement is found, probably owing t o breakdown of structure.
RHEOLOGICAL PROPERTIES OF BITUMENS
159
t
FIG.5. Relation between se/sCo and time after various deformations a t different shearing stresses. Bitumen B. Times on curves refer to duration of previous deformation. Horizontal dotted lines connect points of equal t l t a . CAICULATED
NO. SeUWIds
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0.090 0.24 0.382 0.69 1.51 3.37 45.4 0.161 0.438 2.40 15.8 0.225 0.945 4.22 7.5
0.071 0.146 0.21 0.32 0.465 0.473 0.38 0.094 0.195 0.356 0.282 0.064 0.128 0.131 0.135
5 20 40
90 240
600 7740 30 120 900
6ooo 270 1500 7200 14100
!gnu per sq.cm.
66,700 66,700 66,700 66,700 66,700 66,700 66,700 33,000 33,000 33,000 33,000 8,130 8,130 8,130 8,130
S. Relaxation In figures 6 and 7 the relaxation stress after various previous deformations under different shearing stresses have been plotted against time as
160
R. N. J. SAAL AND J. W. A. LABOUT
Q/TO. Here, too, the phenomenon discussed in the previous section is observed: up to deformations of SO = about 1 the curves fall in the expected order in accordance with the theoretical relaxation equation (3b), but a t greater deformations these curves again lie in reversed order. A second possibility of checking the relaxation equation is to compare the relaxation curves at equal values of so but different values of to, since by displacing them in a 7R-t diagram in the direction of the time axis it should be possible to make them coincide in accordance with equation 3. A few cases have been illustrated in figures 6 and 7, which must now be read as ~ - diagrams t according t o the scale division a t the right-hand side of the diagrams. In these figures relaxation curves for a low shearing stress have been laid with their first points on a curve of higher shearing stress with the same previous deformation so. The agreement proves to be satisfactory.
4. Recovery after partial relaxation In figure 8 the curves A and D are ordinary recovery curves of bitumen A, while curves E to G represent recoveries after partial relaxation. In all cases so is about 1. It appears that the curves are of the same shape for both groups. The relaxation stress a t the beginning of recovery agrees with that predicted by the model. The conditions of the deformation in experiment B are practically the same as those employed in the experiment represented by curve 14 of figure 6, for which by extrapolation a relaxation stress at t = 0 is obtained of about 26,000 to 28,000 dynes per square centimeter. It will be seen that this recovery curve B coincides fairly well with curve F , representing an experiment where a higher stress was released to 29,000 dynes per square centimeter before recovery started. Similar results were obtained using bitumen B. 5. Relaxation after partial recovery
This type of experiment has little accuracy, since calculation of the results by means of the model involves a difference between two measurements of relaxation stress. In figure 9 is given the result of a single experiment using bitumen A. In agreement with the model it is found that the relaxation stress can rise a t first. Calculation of the relaxation stresses by means of equation 4, using the data of figure 6, gives reasonable agreement with the observations indicated by figure 9. The gradual decrease of the stress shown by the bitumen after longer relaxation time is not in agreement with the model, for according to the model the relaxation stress must approach a constant value Gzs,. Here again the discrepancy may be attributed to skeleton breakdown, and better agreement would be expected at lower deformations.
161
RHEOLOGICAL PROPERTIES O F DITUMENS
2
FIG.6. Relation between m / r Oand time after various deformations a t different, shearing stresses. Bitumen A . Times on curves refer to duration of previous deformation. NO.
1
2 3 4 5
6 7
8 9 10 11 12 13 14 15 16 17 18
'a
0.176 0.203 0.225 0.247 0.262 0.53 0.75 1.27 3.26 27.2 0.083 0.247 0.53 0.90 3.86 16.9 0.13 1.50
srconda
dunu pcr aq.cm.
5 10 15 20 30 147 242 546 1559 6660 5 120 600 1500 7200 21720 499 24000
58,000 58,000 58,000 58,000 58,m 58,000 58,000
58,OOo 58,000
58,000 28,700 28,700 28,700 28,700 28,700 28,700 7,080 7,080
In the case of bitumen B similar phenomena are observed, as shown by figure 10. Here, too, a maximum occurs in the relaxation stress-time curve after which, however, the relaxation stress decreases in the normal
162
R. S . J. SAAI, AND J. W. A . LAROIJT
L . r. 04
-+ESP*& f l d - m ' l P c m p d h e x p ~ 0 ...e . - 46: .. .. c
..
02
0
FIG.7. Relation between T R / T ~and time after various deformations a t different shearing stresses. Bitumen B. Times on curves refer to duration of previous deformation. NO.
aecondi
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
0.097 0.24 0.375 0.68 1.50 3.34 8.4 44.2 0.052 0.24 0.68 2.24 16.1 40.3 0.24 2.68 7.5
5 23 42.4 92.4 242 603 1481 7525 10 58 208 900 6Ooo
15600 280 5100 13780
dunw per S Q . C ~ .
66,700 66,700 F.6,700 66,700 66,700 66,700 66,700 66,700 33,000 33,000 33,000 33,000 33,000 33,000 8,130 8,130 8,130
way. These results indicate a weak structure for bitumen B as contrasted to a stronger structure for bitumen A.
From the foregoing discussions it has become clear that there is a satisfactory agreement between material and model.
163
RHEOLOGICAL PROPERTIEB OF BITUMENS
From the data given it appears that in the two bitumens examined there must be a certain amount of coherence between the micelles. In the case
., .
..
.. . . . . . . . . I"
..con&!
FIG.8. Relation between elastic recovery and time after partial relaxation. Bitumen A
I
8 3-
0
FIG. 9. Changes in relaxation stress after partial elastic recovery. Bitumen A
of bitumen A this follows from the complete recovery after small deformations, from the maximum in the curve for the total recovery and from the higher rate of deformation, recovery, and relaxation at high deformations,
164
R. N. J. S M L AND J. W. A. LABOUT
the last four factors pointing to breakdown of structure. In the case of bitumen B only the maximum in the curve for the total recovery and the higher rate of recovery and relaxation at high deformations were observed. At deformations small enough to show no serious breakdown of the skeleton, a satisfactory agreement with the model system, representing a mixed gel-sol system, was found in the five different ways of investigation used. From this we conclude that the model in the main represents the constitution of the bitumen. I
6
3
r'
I I
I
II
I
4 0
1
0
0
.
0
0
I
I
I
I
400
I
I
I
I
.oo
I
I
I
I
ma
I
I
I
I
I
IOW
I1w
t. +(. (*cord.)
FIQ. 10. Changes in relaxation stress after partial elastic recovery. Bitumen B
As bitumen A showed complete recovery at small deformation and pronounced skeleton breakdown at larger deformations, this bitumen must possess a marked gel structure. As bitumen B showed incomplete recovery and skeleton breakdown to only a slight degree, this product must be considered as containing either free agglomerates of micelles or very slight coherence throughout the material and is therefore more in the nature of a sol. This is in agreement with the theories formerly given by Pfeiffer and van Doormaal (3). It will not be possible, however, always to account for still more complicated treatment. The following experiment may serve as an instance: The bitumen was deformed to s = 1, then by an opposite stress to s = -0.4, and then released. There was at first recovery to s = +0.15, when
RHEOLOGICAL PROPERTIES OF BITUMENS
165
the movement was reversed. After rcaching s = +0.10 it was again reversed, reaching a final position of s = $0.12. To explain such phenomena it will be necessary to assume coupling of differently formed elementary systems (1). 1V. SUMMARY
1. Rheological measurements in a conicylindrical rotation viscometer
were carried out on two asphaltic bitumens of different types, employing methods of investigation involving deformations under constant stress, elastic recovery, relaxation, and combinations of these. 2. The experimental results were found to be in satisfactory agreement with the properties of a theoretical model representing the simplest iorm of a mixed gel-sol system. 3. It is concluded, in accordance with the views of Pfeiffer and van Doormaal, that asphaltic bitumens must be considered such mixed gel-sol systems and that the degrees of structure exhibited can vary widely with composition. The authors are indebted to +heManagement of the N. V. de Bataafsche Petroleum Maatschappij for their permission to publish this paper and to their collaborators in these investigations. REFERENCES (1) BURGERS,J. M.:First Report on Viscosity and Plasticity. Academy of Sciences, Amsterdam (1935). (2) KRATKY, 0.:Kolloid-Z. 70, 14 (1935). (3) PFEIFFER,J. Pa., AND DOORMAAL, P. M. VAN: J. Inst. Petroleum Tech. 22,414 (1936). (4) PFEIFFER, J. PH.,AND SAAL,R. N . J.: J. Phys. Chem. 43, 139 (1939). (5) SAAL,R. N . J . : J. Inst. Petroleum Tech. 19, 176 (1933);Proc. World Petroleum Congr., London, 1939, 11, 515. R. N.,AND COLLABORATORS, a . 0 . : J. Applied Phys. 8, 291 (1937); J. (6) TRAXLER, Phys. Chem. 40, 1133 (1936).
