STUDIES ON GLASS
IT. Some T’iscosity Data on Liquid Glucose and Glucose-Glycerol Solutions B Y GEORGE S. PARKS A S D WALLACE A . GILKEY
Up to a few years ago a glass was generally regarded as a liquid oi great viscosity. Recent studies, however, have demonstrated that in a number of properties, such as specific heat, coefficient of thermal expansion and dielectric constant, the glassy state more closely resembles the crystalline than the liquid state out of which it has been formed by cooling. Therefore, it is perhaps preferable to regard a glass as an amorphous solid rather than as an undercooled liquid. Severtheless, the viscosity of a glass-forming liquid is of theoretical interest and in some cases, those of commercial inorganic glasses for instance, niay also prove of great practical importance. In the present investigation, which is essentially an outgrowth of previous studies’ on organic glasses, we have measured the viscosity of liquid glucose over a temperature range of almost 80’. In this connection we have also studied the viscosity of a series of glucose-glycerol solutions, all of which liquids, when properly cooled, form clear, reasonably stable organic glasses.
Method and Apparatus The method employed was by no means new in principle, its essential features having been used in the past by numerous workers.* The liquid which %-as to be studied was placed in a stationary, cylindrical cont’ainer and a second cylinder! smaller and co-axial with this, was next introduced to a certain depth of immersion. The inner cylinder was then caused to rotate under the influence of a given torque and the rate of rotation was measured. From the dimensions of the apparat,us the viscosity of the liquid could then be calculated. Two different instruments, based upon this method, were used in the course of the measurements. For viscosities in excess of 106 poises we constructed our own viscometer. The outer cylinder, containing the liquid, consisted of a stout Pyrex test-tube ( 2 . 2 cm. internal diameter) which was tightly clamped to an iron stand and was thus held stationary. A long steel or glass rod (about 0.7 cm. in diameter) served as the inner, rotating cylinder. This rod rotated in a bearing which held it in a central, vertical position in the test-tube and maintained a constant depth of immersion (about 7 . 5 cm.) in the liquid under investigation. Above the bearing the rod was bent outward at a right angle for a distance of I j cm., and a brass weight, operating upon the Parks and Huffman: J. Phys. Chem., 31, 1842 (19271; Parks, Huffman and Cattoir: 32, 1366 (1928); Cattoir and Parks: 33, 879 (1929). * Couette: Ann. Chim. Phvs., (6) 21, 433 (1890); Searle: Proc. Camb. Phil. SOC., 16, 7 (1912). See also Hatschek: “The Viscosity of Liquids,” 50 (1928).
STUDIES ON GLASS
1429
free end thru a pulley, thereby provided a suitable moment of force for rotating the inner cylinder of the viscometer. A needle pointer, attached to this lever arm and moving along a millimeter scale, served to determine the amount of rotation, the corresponding time, when brief, being measured by a stop-watch and, when longer, by a good ordinary timepiece. The test-tube and contents were placed in a Dewar jar, which served as a small adjustable thermostat. For measurements below 0°C.the bath liquid was ethyl alcohol cooled with carbon dioxide snow or liquid air, and the temperatures were measured with a copper-constantan thermocouple, accurate to within 0 . 3 O C . Above 0°C. water was the bath liquid in the Dewar jar and temperatures were determined to 0.I O with a mercury thermometer. For such an apparatus, if the viscous effects due to the liquid between the eo-axial cylindrical surfaces be given sole consideration, the viscosity can be calculated by the formula,
'
C (Rz? - Rj2) =
2
w AR1 Rz2
(111
where C is the torque or moment of force' producing rotation of the movable rod, o is its resulting angular velocity, h and R1 are, respectively, its lateral area and radius, and R2 is the inside radius of the Pyrex tube. From a theoretical standpoint the viscous effect on the lower end of the moving rod should have been taken into consideration also. However, this quantity could not be exactly calculated; and we therefore neglected it, since owing to the dimensions of our apparatus it was undoubtedly very small. Experimentally we were fully justified in such a procedure, because the substitution of a rod of double the diameter and the use of various depths of immersion, etc. gave fairly concordant results as calculated by equation I . For viscosities smaller than 106 poises we employed a Stormer viscometer which we modified slightly because it has been originally designed for use with less viscous liquids. In this instrument the brass inner cylinder was 2.46 cm. in diameter and was immersed to a depth of 2.11 cm. The outer cylinder was a brass cup 4.85 cm. in diameter] which contained about 6 0 cc. of the liquid under investigation. I n this case the inner, co-axial cylinder was also the one which rotated but the rate of rotation was always small enough to avoid appreciable centrifugal effects. For temperature control the brass cup and contents were immersed in a paraffin bath which could be heated by a small gas burner. The entire viscometer outfit was then placed in a small closet, provided with a glass window. This closet served as an adjustable air thermostat, the temperature of wyhich could be varied over the range from 40' to 17oOC. The temperatures of the liquid under investigation were determined immediately after each viscosity measurement by a mercury therA certain small torque was found necessary to overcome the friction in the bearings and pulleys of the apparatus when no liquid was present in the Pyrex tube. Hence, when a liquid was being studied, this value was always subtractedfrom the total torque employed; C then represents the net torque required to overcome the viscosity of the liquid.
I330
GEORGE S. PARKS A S D TVALLACE A. GILKEY
mometer. The times for ten rotations were measured by a stop-watch. K i t h this Stornier viscometer the viscosities were calculated by the equation,
where A. as before, is thcx lateral area of the inner cylinder and B represents approximately the correction for the end effect. The viscosity results obtained by the use of these two inst,ruments, while not of extreme precision, were undoubtedly as accurate as the reproducibility of the glucose samples warranted.
Preparation of the Liquids As in the earlier studies, the samples of liquid glucose were prepared by heating crystalline a-glucose (Pfanstiehl Chernical Company) in a flask immersed in a paraffin bath. The glucose crystals melted at about 146’C and were then maintained under a vacuum a t a somewhat higher temperature for a short time, usually about five minutes, in order to eliminate bubbles of air or water vapor. Khen the liquid had become fairly clear, air was admitted and t,he sample was allowed to cool; it v a s usually straw-colored. Considerably longer periods of heating at 1 6 j 0 or above led to noticeable decomposition and a product which was dark brown in color. The glycerol employed in some of the early work was a C. P. “Pfanstiehl” product, which had a density corresponding to a water content of about 3 5 . Hereafter in this paper it will be referred to as “97%‘, glycerol.” I n our final work some of this mat’erial was subjected to distillation under a pressure of 5 to I O mm. Rejecting the first and last quarters, we employed the middle portion in the present research. It had a specific gravity corresponding to 99.95; glycerol on the basis of the recent data of Bosart and Snoddy.1 The various two-component liquids containing glycerol and glucose were prepared by mixing the proper amounts of the two components and then heating until complete solution had taken place. The resulting liquids were either colorless or a light straw-color. Experimental Results Very early in the course of the present investigation the question arose as to whether we were dealing with true viscosity or with plasticity as the temperatures approached the region of the glassy state. With a case of true viscosity the velocity gradient, dv, dx, between a unit plane surface moving parallel t o a stationary plane is directly proportional to the shearing force, F, as shown in the following equation: dv,/dx = @F (31, where @ is the fluidity, the reciprocal of the viscosity. On the other hand, the corresponding equation* for a plastic material is dvjdx = p(F - f ) (41, 1
2
Bosart and Snoddy: Ind. Eng. Chem., 19, 509 (1927). Bingham: J. Phys. Chem., 29, 1203 (1925).
‘43‘
STUDIES O S GLASS
where p is the “mobility” and j” is the “yield-value.” For viscometers such as ours, if velocities of shear be plot,ted as ordinates against’the corresponding shearing forces as abscissas, the resulting curve is a straight line passing thru the origin in any case of true viscosity, while in a case of plasticity the straight line should cut the X-axis a t some distance to the right of the origin. Thus the distinction between the two phenomena can be readily made. To answer this question the rate of rot,ation of the rod in our first viscometer was determined for a series of different torques in the case of liquid glucose at 44°C. and also in the case of a solution consisting of S2yc glucose
FIG.I 1-elocity of viscometer pointer. T’,,plotted against IT, the weight used for producing rotation.
and 1872glycerol at the respective temperatures, zoo, 16’, IZ’, So, oo, and -4T. The data thus obtained for the glucose-glycerol solution at 12.0’ are given in Table I and are represented graphically in Fig. I . They are typical of the other data as well. In all cases the results indicated that we were dealing with true viscosity and not with plasticity. 1-iscosity Data f o r Liquid Glucose.--Using the first viscometer, which by its dimensions was specially adapted for the measurement of very high viscosities, we next determined the viscosity-temperature curve between about 60‘ and 3 0 T . for five different samples of liquid glucose. The essential data arc given in Table I1 and are represented graphically in Fig. 2 . All these five curves are very similar in character, altho they do not coincide. Thus the temperatures a t which the viscosity is 1oio poises are, respectively, 36.1’, 33.6O, 34.9‘, 34.6”, and 31.4.T. Evidently no two samples of the liquid glucose were exactly alike. This situation may be due in part to two different .+O1
GEORGE S. PARKS A S D WALLACE
I432
T.4BLE
A.
GILKEY
1
Viscosity Test made at I 2 .o"C. upon a Two-Component Liquid containing 82% (by weight) Glucose and 18% Glycerol Velocity of viscometer pointer in em. per see.
Weight used to produce rotation, in grams
v
Ratio: v /XV
\v
0.OOjI
20
0.00025
o ,0141
50
o ,000282
0.0282
IO0
0.000282
0.0582
200
0.000291
0,IIjj
400
0.000289
0.1667
600
0,ZTj
o .OOOZ j 8
+-
0.0002 7 j
1000
I
I
1
4
111ll
I
r
n
m 0
X
F
I 50
T e m p . "G.
FIG.2 Viscosity curves for five different samples of liquid glucose as the hardening temperature is approached
factors: via., (I) differences in the character of the glucose in the various samples, as evidenced by different degrees of mutarotation, and ( 2 ) the presence of varying amounts of impurities incurred in the preparation of the liquids. Polarimetric measurements were made on aqueous solutions of the glucose used in preparing the samples. The results indicated that the crystalline material was about 955a and jYc P-glucose. On the other hand, six dif-
I433
STUDIES O S GLASS
ferent samples of liquid glucose gave specific rotations varying from + 4 z 0 to +49O; and their rotary powers showed practically no change with temperature as the samples were cooled over a range of IOO’C. and the glassy state was attained. Similarly the various liquids in the glucose-9jT glycerol system showed specific rotations ranging from +48’ to j 8 ” . As the specific rotations of aqueous solutions of pure a and pure @glucose were found by Hudson and Tanovsky’ to be +113.4’ and +19’, respectively, we are
+
TABLE I1 Viscosity Data for Five Samples of Liquid Glucose below 60°C Temp ‘C
28 o 29 .o 3 0 .o 32 . o 34 0
I
I1
-
-
Viscosity,
-
1.37
(IO”)
-
(IOIO)
1.30
(10~’)
6.83 1.79
3.63
(IOIO)
1.08
I.0j
;’
3.16
‘’
2.44
”
1.12
”
3.84
44.0
3.63 ( I o 8 )
7.17 (10’)
48 .o j2 .o
7.50
1.68
j6.0
’‘
-
’’ ”
-
(10’~)
-
3.j7
(IO”)
3.69 1.42
(IOIO)
8.08
109)
”
3.01
”
i.41
(109)
1.21
)’
2.oj 9.20
(10~)
-
3.90 (IO”)
(10~)
9.78
v 1.13
-
(109)
2.12
(10~)
-
(10~)
4.10(109)
1.66
IV
-
1.95 j.30
“
36 0 38.0 40 .o
))
in poises I11
7,
I’
2.09 3.26
(10~)
1.6j
(10’)
2.83
8.3 j
(10~)
j.84 (106)
2.24
I’
2.63
”
4.70 108)
2.06
(10~) 9 . j o
”
”
4.52 (IO7) 2.62 6.2
(10~) ”
(10~)
justified in concluding that our several liquids contained varying proportions of the 01 and p forms, with the latter predominating in all instances. Differences in the temperature and in the duration of heating incident to the preparation of the various samples may have produced, therefore, these appreciable differences in the relative quantities of the two forms and likewise somewhat different viscosity curves. Earlier observations on the effect of heating liquid glucose for considerable periods at 16 j”C. or above had indicated t o us that more orless chemicalchange took place. There was a noticeable darkening of the color of the sample, and water appeared to be formed and evolved as vapor. Accordingly, in the present investigation we measured the viscosities, as the liquid was cooled to a glass, of a glucose sample which had been prepared in the usual way and then redetermined the viscosities after heating the liquid a t 16 j0-17o”C. for twenty minutes This heating procedure was repeated twice. The four viscosity-temperature curves thus obtained were similar; but in each case, after reheating, the curve was shifted about 4’ along the temperature axis in the direction of the origin. h similar shift toward lower temperatures, this time of about 8‘ in magnitude, was observed when 1‘lC of water was dissolved in another liquid glucose sample. It was found that both these experiments Hudson and I-anovsky: J. .im Chem. ~ o c . 39, , 103j (1917:.
‘434
GEORGE S. PARKS .4SD WALLACE A. GILKEY
were reproducible. Thus it may well be that the prolonged heating a t 165’ decomposed the sugar and produced water a t a faster rate than it was evolved; the observed shift in the viscosity curves can then be accounted for by an increase of 0.57~ in the water content of the liquid glucose for each twentyminute heating period. While the time of heating in preparing the five different samples of Fig. 2 was never over four or five minutes, it is quite possible that part of the observed differences are due to a small amount of decomposition’ in some cases with a resulting increase in the water content. Sone of the measured viscosities go above I O I I poises and no measurements on pure liquid glucose were made below z 8 O C . However, extrapolations can easily be carried beyond these values, since the curve obtained by plotting the logarithms of the viscosities against the corresponding temperatures is regular and, over a short temperature interval, does not deviate greatly from a straight line. Using the data of sample I11 as fairly representative of liquid glucose, we have found by this means a viscosity value of 1oI3,Opoises a t zj°C. This is the middle point in the temperature interval, 2o0-3ooC., within which a sharp 2 0 0 7 ~increase in the coefficient of thermal expansion takes place and the values for the refractive index2 and dielectric constant3 begin to change rapidly. For purposes of brevity it may well be termed the hardening point of liquid glucose or the softening point of the glass. While its location at zs0C. and a viscosity of 1ol3,Opoises is admittedly very arbitrary, the fact that the temperature of this viscosity value is reproducible t o within 1 2 ’ in the case of five samples, coupled with the fact that the other properties just, mentioned show marked changes around this point, justifies in a sense the adoption of some such temperature as a crude division mark between the liquid and glassy states. Tammann and Hesse‘ in a very interesting paper have recently come to essentially the same conclusion with respect to the hardening point, and others who have studied the viscosities of glass-forming liquids have roughly checked this value of 1013poises. Thus Samsoen5 states that the sharp change in the coefficient of thermal expansion of several amorphous substances comes at a viscosity of 1 0 ~ ~Likewise . in the case of a number of silicate glasses English6 has obtained a ilscosity value of approximately IO'*.^ for the “annealing temperature,” while Stott’ suggests “that the change occurring in the constitution of glass should happen when the viscosity is in the neighborhood of 1oX3.’poises.” In this connection, however, it should be noted that for both propylene glycol and glucose the sharp Further evidence of the decomposition of liquid glucose i n this way was obtained bv heating a sample weighing 26.16 gm. for over ninety minutes under a-vacuum at The material lost about 44; of its initial weight during the process. Khile the heat treatment of the liquid in this test was undoubtedly more severe than that incidental to the preparation of the other samples, the result again indicates the possible existence of some decomposition products in the several liquids employed in the viscosity determinations. *Parks, Huffman and Cattoir: J. Phys. Chem., 32, 1374 (1928). Cattoir and Parks: 3. Phys. Chem., 33, 882 (1929). Tammann and Hesse: Z. anorg. allgem. Chem., 156, 256 (1926). Samsoen: Compt. rend., 182, 51; i(1926j. Society of Glass Technology: “The Constitution of Glass,” (1927). Society of Technology: “The Constitution of Glass,” 75 (1927).
170’c.
I435
STUDIES O S GLASS
rise in the heat capacity curx-r is completed at a temperature somewhat below the “softening point,” as here defined. While this situation is rather surprising, me are inclined to regard it as real, altho it might be explained a m y by the statement that the various kinds of measurements were never made upon precisely the same sample of material. K i t h the modified Stormer viscometer measurements were made upon a sample of liquid glucose over the temperature range from 60’ to I I O ” ~ . -kt about 105’ the liquid began t o show signs of devitrification and above
FIG.3
TABLE I11 T’iscosity for Liquid Glucose above 60°C Temp. “C. 7 (poisesj 5.89 (105) 60.0 62 . o 3 ‘94 ” 64 . o 2.11 ” 66 . o I .03 ” 70.0
74.0 78.0
82 . o
3.84 1.67
(10~)
7.49
(10~)
3.15
”
”
Temp., “C.
(poises)
log10 71
j.770
86.0
1.77 ( l o 3 )
5.596
90.0 94.0 98.0
8.00 (IO*)
3.248 2.903 2.767
Log,,
71
5.324 5.013 4.584 4.223 3.875
102.0
106.0 110.0
r)
j.8j
”
3.27 ” 2.45 ” 2.09 ” 2.45)’
2 . j I j
2.389 2.320 2.389
3.498
I 10’ this tendency toward crystallization became so pronounced as to prevent further measurements. The viscosity data are given in Table 111. In Fig. 3 me have plotted the logarithms of the viscosities against the corresponding temperatures and for purposes of completeness we have also
1436
GEORGE S. PARKS AND WALLACE A. GILKEY
included the data for Sample I11 obtained with the first viscometer. The two sets of data are in good agreement and thus give us an experimental curve for a liquid range of about 80’. 17zscosity Data f o r Glucose-Glycerol Soluhwx-Viscosity measurements in the range between 106 and ~ o l lpoises were made upon various twocomponent liquids in the two systems, glucose-glycerol and glucose-“9; % glycerol.” The essential data for the first system are given brieflyin Table IT.’. I n Column I are the various viscosity values in even numbers, while in the
C 0
-20
9 Q-40
E
IO b
0)
/--60
IO8
IO’O
-80
IO“
iot3
I M o l F r a c t i o n of Glucose. FIG. 4
The high-viscosity isokoms for the binary system, glucose-glycerol.
succeecmg columns appear the temperatures corresponding to these values for the several liquids of the system In the case of each liquid these results were derived from a graph in which log 11 was plotted against the temperatures of the measurements. The “hardening point,” corresponding to a viscosity of 1013 poises, was obtained by extrapolation. The isokoms (Le. lines of constant viscosity) for this system are represented graphically in Fig. 4, where temperatures are plot’ted as ordinates against the mol fractions as abscissas. The very heavy line for a value of 1013 poises might be called the “hardening line” or boundary between the
1437
STUDIES ON GLASS
liquid and glassyregions. It falls far below the broken line abc which represents approximately the position of the equilibrium lines between the liquid phase and phases of pure crystalline glucose and pure crystalline glycerol, respectively. This last line has not been realized experimentally but was sketched into the figure after the eutectic temperature had been calculated for this system by the method of Washburn and Read.‘
TABLE Is’ Viscosity Data for the Glucose-Glycerol System yiscosity in poises I 106 I 0’
.oo
58.4OC. j1.6 ” ”
I010
45.6 40.0 35.1
10‘1
31.0
”
1013
2j.
!’
I08 I o9
” If
Mol Fraction of Glucose in Solution 0.80 o 60 0.40 0.20 38.0”C. 14.ooC. -16.0”C. -37.OC. 8.0 ” -22 -42 *’ 33.0 ‘’ 27.6 ” 3.0 ” -28. ” -47. ” 2 2 . 5 !! - 2.0 ” -33. ” -53. ” - i,j” -38. ” - 59. ’’ 13.0 ” - 12.0 ” -43. ” -63. ” ) *
6.
”
-20.
”
- 50.
-j2.
”
0.00
- 52.OC. - 5 8 . ’I -64. ” -70.
_ -i 3.-
!’ ))
-80.
”
-87.
’!
Essentially similar results were obtained in a study of the system glucoseAs compared with the first system containing anhydrous glycerol, the only effect of 3’3 water in the glycerol was to lower the temperatures corresponding to the various viscosity values, the effect being greatest, of course, for the sample of 97% glycerol itself. In this particular case the “hardening point” was lowered about 5’. “97 7 glycerol.”
summary The viscosities of undercooled liquid glucose have been measured over a temperature range of almost 80‘. Five different samples of glucose gave slightly different curves as the “hardening point’‘ 71-as approached, probably owing to varying proportions of the CL and /3 forms in these samples as well as to small but variable amounts of water. From a study of the data the hardenzng point was rather arbitrarily defined as the temperature a t which an extrapolated viscosity value of 1 0 ’ ~ ’poises was found. For glucose it is about 2 5 O C . The viscosities and “hardening points” for various liquids in the two binary systems, glucose-glycerol and glucose-“g7 % glycerol,’’ have been determined. Department of Chemrstru. S t a n j m d Unzcersity, California. Aprd 1.6, 1928.
‘IYashburn and Read: Proc. T a t . Acad. Sci. 1, 191 (1915). In this calculation the binarv svstem r a s assumed to be ideal and the heats of fusion of glucose and glycerol were taken a i 7,800 and 4,370 cal. per mol, respectivelv. The eutectic temperature and mol fraction of glucose thus obtained were 17.0‘C. and 0016, respectively.
