JOURNAL OF POLYMER SCIENCE VOL. XXV, PAGES 325-331 (1957)

Dependence of Mechanical Shear Degradation of Polymers in Solution on Rate of Energy Application

and on Concentration*

PHILIP GOODMAN,? National Bureau of Standards, Wushington, D. C.

1. INTRODUCTION

Several papers1V2 have appeared concerning the kinetics of the degrada- tion of polyisobutene molecules while undergoing mechanical shearing in a capillary. The degradation has been treated as resulting from a focalization of mechanical energy into some of the chemical bonds of the polymer chain by means of the molecular entanglements present in concentrated solution. When sufficient energy is concentrated in this manner into a given bond, this bond breaks, resulting in a decrease in the average molecular weight. This molecular weight reduction after shearing is evidenced by a change in intrinsic viscosity. A quantitative determination of the number of bonds broken by the mechanical shearing action requires the use of the number- average molecular weight. As an expedient approximation, the viscosity- average molecular weight has been used for this calculation and the number of moles of bonds broken per gram of solution, B, is then given by:

B = w(l/M - l/Mo) (1)

where w is the weight concentration of polymer in solution, and Mo and M are, respectively, the initial molecular weight and the molecular weight at any time. The rate of the mechanical degradation reaction can be repre- sented by a plot of B us. the average time of residence in the capillary, as cal- culated from the volume rate of flow through the capillary. The degrada- tion rate constant, k , obtained as the initial slope of such a plot, has been treated in terms of an equation of the form:

k = C exp { -E*/aJ] (2)

E* represents the activation energy required for bond rupture and C is a * Presented a t the meeting of the Division of High Polymer Physics, American Physi-

cal Society, Detroit-Ann Arbor, Michigan, March, 1954. This work was performed as part of a research project sponsored by the Reconstruc-

tion Finance Corporation, Office of Synthetic Rubber, in connection with the Govern- ment Synthetic Rubber Program.

t Present address: Corning Glaas Works, Corning, N. Y . 325

326 P. GOODMAN

proportionality constant. J , the average rate of shear energy per unit volume supplied to the polymer solution, is obtained as the product of the average shearing stress, 213 of the shearing stress at the wall, and the average rate of shear. Since the velocity for the non-Newtonian flow of these solutions is not known, the average rate of shear has been approximated by that for Newtonian flow, that is, 2/3 of the nominal rate of shear, D. The factor, a, relates J to the average amount of mechanical energy temporarily stored in a mole of chain bonds largely as a result of the molecular entangle- ments in the solution. In this paper, studies are reported of the dependence of the kinetics and energy requirements for mechanical shear degradation upon the rate of shear energy application and upon the concentration of polymer in the solution.

U. EXPERIMENTAL

Measurements have been made on solutions of Vistanex B-100 polyiso- butene having a viscosity-average molecular weight of 1,740,000 in cetane (n-hexadecane) . These solutions were sheared in a McKee Consistometer,3 which is essentially a capillary viscometer in which a single sample can be repeatedly passed through the capillary. The capillary used was 0.635 cm. long and had a radius of 0.01913 cm. The apparatus was air-thermo- stated at 40 f 0.5"C. Intrinsic viscosities of the unsheared solution and of the solution sheared after two, four, and six passes through the capillary were converted to viscosity-average molecular weights using the relation- ships of Fox and Flory.* In addition, the intrinsic viscosity of the solu- tions was determined after no further degradation was occurring.

In. DEPENDENCE UPON THE RATE OF ENERGY APPLICATION

Previous studies' have indicated that, for a particular solution at con- stant temperature, the logarithm of the initial rate constant for the deg- radation is a linear function of the reciprocal of the rate of energy ap- plication. It seemed advisable to examine this linearity more critically and to determine whether it existed over a wider range of J than had previ- ously been studied. Further measurements were therefore made on a 10% solution of Vistanex B-100 a t rates of shear of 50,400, 33,000, 25,100, and 14,300 set.-'. For each of these fixed rates of shear, the course followed by the shearing load, which is proportional to the shearing stress, is shown in Figure 1 as the solution is repeatedly passed through the capillary.

The intrinsic viscosities of the solutions sheared for varying amounts of time and the viscosity-average molecular weights of polyisobutene in these solutions are shown in Table I. From the initial slope of a plot of tbe number of bonds broken per gram of solution, as calculated from the vis- cosity-average molecular weights, against the average total time of resi- dence of a molecule in the capillary, values for the reaction rate constant, k, were calculated. The assumption has been made that this is a first-order reaction dependent only upon the concentration of bonds present.

MECHANICAL SHEAR DEGRADATION 327

Rate of shear, sec. -l

14,300

25,100

33,000

50,400

60

50

40 B z 6 4 30

20

I0

0

I 1

D. SEC? 0 14,300

u 33,000 25,100

I I 1

0 I0 20 30 40 WSS NUMBER

Fig. 1. Shearing load variation with amount of shearing.

TABLE I Dependence upon Rate of Shear Energy Application at 40°C.

(Initial Viscosity-Average Molecular Weight 1,740,000)

Av. Cap. residence time, sec.

x 102 0.00 1.85 3.70 5.55

1.06 2.11 3.17

0.80 1.60 2.41

0.53 1.05 1.58 9.46

18.5

13.7

12.0

Intrinsic viscosity,

dl./g.

2.88 2.84 2.82 2.80 2.74 2.78 2.64 2.60 2.57 2.73 2.63 2.58 2.44 2.74 2.63 2.53 2.29

Visc.-av. mol. wt. x 10-6 1.74 1.70 1.69 1.67 1.61 1.64 1.53 1.50 1.46 1.61 1.52 1.47 1.34 1.62 1.52 1.43 1.24

Rate const., Bonds k, moles

g. soh., ruptured/g. moles polymer/ X lo8 sec. X 106

0.0 0.62 1.4 1.9 2.6 4.5 3.4 3.50 8.0 9.4 10.9 4.8 5.95 8.3 10.5 17.4 4.5 8.05 8.3 12.3 23.3

ruptured/ bonds J, ergD, g.

set.-' x 10-11 0.134

0.391

0.464

0.840

328 P. GOODMAN

1 I I I I I

I l R A T E OF ENERGY APPLICATION P E R GRAM POLYMER. d. SEC. /ERG. 10"

Fig. 2. Rate constant dependence upon 1 /J : ( 0 ) this paper, (0) reference (1).

The values of log k are shown in Figure 2 plotted against the reciprocal of J . The open points represent the data previously reported by Bestu1.I Although there is some scatter from the straight line shown, there appears to be no systematic deviation from this line. The value of log k at the low- est value of J deviates more than others, but, since the extent of degrada- tion here is least, the errors in this determination are greatest. According to equation (2), the slope of this straight line is given by E*/a. Since there is little reason to believe that E* varies, the existence of a linear relation- ship indicates that a does not vary over the range of J studied. Therefore, a appears to be a constant for a particular chemical system at one tempera-

Fig. 3. Rate constant d e r d e n a e upon 1/J for solutions of different concentration. Data or 5-15% solutions from reference (1).

MECHANICAL SHEAR DEGRADATION 329

ture, rather than a function of one or more of the variables associated with the shearing action.

IV. DEPENDENCE UPON CONCENTRATION

Shear degradation has also been previously investigated' as a function of the concentration of the polymer in cetane solution. The range over which this dependence has been studied has been extended in both directions by studying the process in 3 and 20y0 solutions. The same polymer as above, Vistanex B-100, was used and the temperature was maintained at 40°C. Treating the data in the same manner as before, the results are shown in Table I1 and are plotted in Figure 3, wherein the data previously obtained by Bestul' in the t?i--15y0 concentration range are also included. Consider- ing the accuracy of the data, those for the 5-20y0 solutions can all be reason- ably well represented by the single straight line shown. The two points for

TABLE I1 Dependence upon Concentration at 4OOC.

(Initial Viscosity-Average Molecular Weight 1,740,000)

Concn., wt. yo

:5

20

Rate of shear, sec. -l

66,000

100,OOO

19,000

33,000

66,000

Bonds Av. cap. ruptured / residence Vim.-av. g. soln.,

time, mol. wt. moles sec. X lo2 X 10-6 X 100

0.403 1.71 0.31 0.806 1.67 0.77 1.209 1.63 1.15 6.045 1.56 1.94 0.266 1.73 0.10 0.532 1.59 1.65 0.798 1.53 2.34 3.989 1.42 3.93 1 ,408 1.62 8.64 2.816 1.54 14.8 4.224 1.49 19.1 0.802 1.62 8.64 1 .603 1.55 14.1 2.405 1.45 22.9 0 403 1.62 8.64 0 806 1.57 12.6 1.209 1.50 18.4

Rate const., k, moles bonds J ,

ruptured/g. ergJ, g.-l polymer/ set.-' sec. X 10B X lo-"

3.03 1.004

10.3 1,918

2 . 8 0.305

4.75 0.582

8.15 1.360

the 3% solutions do, however, give a line with a much greater negative slope. It would be desirable to have more data for the 3% solution. How- ever, intermediate rates of shear were not available and a t the next lower available rate of shear no measurable degradation was observed to occur in this solution. Higher rates of shear than 100,OOO set.-' are not attainable in the present apparatus.

330 P. GOODMAN

However, the fact that no degradation was observed for the 3% solutions a t the next lower available rate of shear, 50,000 sec.-l, can be used to check the data represented. By present methods a degradation in 3% solution which is governed by a rate constant below about 6 X lo-' sec.-l could not be detected. Taking the initial load as that which was observed, the value of J a t 50,OOO sec.-l would be 3.06 X 1O'O (1/J = 3.3 X and the rate constant as given by Figure 3 would be about 8 X Since this rate constant would govern a degradation too small to be detected, the data are in agreement with the experimental observation of the lack of degradation a t 50,000 sec.-l.

As above there is no reason to expect that E* will change with concentra- tion. Thus the change in E*/a at low concentrations may probably be at- tributed to a decrease in a with decreasing concentration. The coefficient a has been found' to remain essentially constant in the temperature range from 30 to 50" but to decrease with increasing temperature above 50°C. This behavior has been interpreted as resulting from a decreased efficiency of the intermolecular entanglements in temporarily focalizing the me- chanical energy into the polymer molecular bonds. That a smaller value of a should be found in less concentrated solutions is to be expected. Degrada- tion is probably not observed in dilute solutions at these rates of shear and there should be some intermediate region in which the value of a diminishes. This decrease is found to commence in the neighborhood of 301, concentra- tion for this polyisobutene-cetane system.

References 1. A. B. Bestul, J . Appl. Phya., 25,1069 (1954); J . C h a . Phys., 24,1196 (1956). 2. P. Goodman and A. B. Bestul, J . Polyrter Sci., 18,235 (1955). 3. S. A. McKee and H: S. White, ASTM Bull. No. 153, 90 (1948); J . Research Natl.

4. T. G. Fox, Jr., and P. J. Flory, J. Am. Chem. Soe., 73,1904,1909 (1951). Bur. Standards, 46,18 (1951).

Synopsis The kinetics of the degradation of polyisobutene in cetane solutions produced by

mechanical shearing action in a capillary has been studied as a function of rate of shear energy application and of concentration. The initial rate constant, k, for the degrada- tion was determined as the initial rate of bond cleavage per unit concentration by weight. Log k wm found to be a linear function of the reciprocal of the rate of shear energy appli- cation per unit volume, J. At all ooncentrations studied in the range 5-20 weight per cent, log k was the same function of 1/J, but auch a plot for 3% solutions had a much greater negative slope. This indicates a decreased efficiency for the concentration of meohanical energy by the polymer molecules in less concentrated solutions.

R6sum6 La cin6tique de degradation du polyisobutbne en solution dans le chtane, produite par

cisaillement mhanique dans un capillaire, a B t B Btudiee en fonction de la tension de cis- aillement et de I s concentration. La constante de vitesse initiale de ddgradation, k, a Bt6 determine6 c o m e &ant la vitesse initiale de rupture de liaison par unit4 de poids. La log k Btait une fonction linesire de l'inverse de la tension de cisaillement par unit6 de volume J. A tout- les concentrations Btudibes, variant de 5 A 20% en poids, le log k

MECHANICAL SHEAR DEGHADAI’ION 331

h i t une fonction identique de 1/J, mais le diagramme obtenu pour des solutions B 3% pr6sente une tangente n6gative beaucoup plus prononcb. Ceci indque une efficacitb r6duite de l’bnergie mbcanique h1’6gard des mol6culea polym6riquea lorsque les solutions sont moins concentrbes.

Zusammenfassung Die Kinetik des Abbaus von Polyisobutylen in Cetanlosungen, der durch mechanische

Schubwirkung in einer Kapillare hervorgerufen wurde, wurde als Funktion der Schub- geschwindigkeits-Energieanwendung und der Konzentration untersucht. Die anfang- liche Geschwindigkeitskonstante k fur den Abbau wurde als die anfangliche Gesch- windigkeit von Bindungsspaltung pro Einheitskonzentration nach Gewicht bestimmt. Es wurde gefunden, dass log k eine lineare Funktion des reziproken Wertes der Schub- geschwindigkeits-Energieanwendung pro Einheitsvolumen J ist. Bei allen unter- suchten Konzentrationen im Bereich von 5-20 Gewichtsprozent war log k die gleiche Funktion von 1/J, aber eine solche Darstellung fur 3%ige Liisungen hatte eine vie1 grossere negative Neigung. Dies zeigt eine verminderte Wirkeamkeit fur die Konzen- tration von mechanischer Energie durch die Polymermolekule in weniger konzentrierten Losungen.

Received May 11, 1956