Effect of Stationary Phase Viscosity on Efficiency 01 Gas Chromatography Columns S. J. Hawkes and D. J. Carpenter Brighani Young Unicersify, Proao, Utah
RESISTANCE TO LIQUID FHASE mass transfer has been shown to be proportional to the viscosity v of the stationary phase in tricresyl phosphate arid polypropylene sebacate columns. However, the relationship can be expected to hold only when resistance to flow and resistance to diffusion are caused by the same mechanism. When both are due to polar attraction o r to the inertia of spherical molecules, this is true. I n the long-chain molecules common in gas-liquid chromatography, viscosity is caused mainly by mutual entanglement of the chains which are then dragged along in great clumps. Diffusion o n the contrary, takes place partly by self-diffusion of the solvent which is directly related to viscosity and partly by migration between the chains which have only to be pried apart: this woulc be hindered less by entanglement so that diffusion would be expected to be proportional to some fraction o r fractional exponent of viscosity, and it is the thesis of this paper that it is proportional to a fractional exponent, x, which depends o n the chain length. Taylor’s equation (1) relates diffusivity to the dimensions of the liquid cell, XI, A?, X:,and the Boltzmann constant, k , thus
However in the case of a long-chain solvent, the dimensions of the “liquid cell” halre little meaning and the effective dimension is probably the cross section of the chain modified by its degree of branching and puckering. I n this case D 2 f / T should be approximately constant for all compounds with similar chains. DETERMISATION OF CONSTANTS
Resistance to mass tl,ansfer of samples in columns consisting of 0.5% of squalane, Apiezon L, silicone oil D.C. 550, and silicone elastomer SE30 o n 0.03-cm diameter glass beads was determined and the diffusivities were calculated from the formula proposed by Giddings et al. (2). These conditions are well within the range in which this formula has been found useful ( 2 , 3) so that goad results were expected; however, the equation assumes that the liquid is held almost solely a t the contact points and this could be untrue of the very viscous SE30 and partly account for the anomalies found for it in this work. The apparatus used ior this determination was a Beckman GC-2 gas chromatograph slightly modified t o reduce the dead volumes at the ends clf the columns. To overcome other apparatus limitations, r8amples were chosen with long retention times so that peaks were at least 30 seconds in halfwidth and were usually several minutes; a n accuracy of + 2 0 z was expected. This accuracy was adequate for the original purposes of the work, and provides supporting data (1) H. S. Taylor, J . Phys. Chern., 6, 331 (1938). (2) J. C. Giddings, K. 12. Mallik, and M. Eikelberger, ANAL. CHEW,34, 1026 (1962). (3) S. J. Hawkes, C. P. Russell, and J. C. Giddings, Zbid., 37, 1523
(1965).
for the principal thesis of this paper which is, however, more convincingly demonstrated by the other published data in Table I. The diffusivities were determined a t a number of temperatures for each stationary phase and the value of the exponent, x, which gave the minimum relative standard deviation for the resulting values of DIVZ/Twere calculated by a n iterative technique using a computor. This value of x is recorded in Table I, with the value of D$/T derived from it. The viscosity o f the elastomer SE30 was determined by the falling sphere method and those of squalane and Apiezon L by a cgpillary viscometer. The viscosities of silicone oil D. C. 550 were obtained from the manufacturer’s literature, and those of decane and dinonyl phthalate from references 7 and 5. RESULTS AND DISCUSSION
The experimental results are shown o n Table I together with those from the published literature. The values for SE30 could not be optimized; a n exponent of 0.04 is needed to make the constant for SE30 fall into line with other results. The squalane results were t o o close together for optimization to be meaningful, but if the exponent is a function of chain length it would be between Apiezon L and dinonyl phthalate and hence about 0.6; this figure was used to calculate the constant. The constant was regularly of the same order of magnitude, (0.35 =k 0.15) X for hydrocarbon chains and (0.7 =!= 0.15) X for the methyl-silicone chain. It is mildly surprising that the constant is larger for the silicone chains but it may be caused by the narrow portions around the oxygen atoms offering a diffusion path between the -0CH3 branches. An exponent of 0.7 seems to be the most useful for dinonyl phthalate although it decreases with increasing chain length of the sample as might be expected from the arguments above. The one anomalous exponent is due to the single value for ethane 0.0” C : the constant is nearer the mean value for dinonyl phthalate with a n exponent of 0.75 than with the optimum 0.53. For decane it is clearly 0.8, for silicone oil and Apiezon L, 0.5. These results seem to support the thesis that the exponent is a function of chain length and while it is too early to offer a method of predicting it with any confidence, the system outlined in Table I1 is tentatively suggested. As tricresyl phosphate is not a long-chain molecule it is not expected to conform with the other results but it does d o so reasonably well. It agrees better however, if X,/X,X, is interpreted as (A/V)II3,where Vis the molecular volume and A the Avogadro number; in this case the calculated constant is 0.17 X in good agreement with experiment. Because all the data on diffusivities in stationary phases known to the authors are included in Table I and all give reasonable results using a loose interpretation of Taylor’s equation, it would appear that this is a promising approach to the prediction of these diffusivities, and suggests the general formula VOL. 39, NO. 3, MARCH 1967
a
393
Table I. Diffusivity Parameters T
Sample
X
"C
Dinonyl phthalate
Isobutylene
0.68
0
2.6
15 25
5.5
50
75 Ethane
0.53
0
25 40 60
80 0.75"
0
25 40 60 80 n-Propane
0.75
0 5
20 40 60
80 n-Butane
0.75
0
8 20 40 60
70 80 n-Pentane
0.72
0
20 40
60 80 +Hexane
0.69
0
19 40 60 70
80 4.4 37.8 71.1 104.5 137.8
n-Decane
Methane
0.80
Apiezon Lb
pXylene
0.48
40
0.60.
70 100 130 160 190 220 36
Squalane
n-Hexane
40 70
Silicone D.C. 550
0.50
Toluene
100 34 40 70
0
b
D~ x 107 (cm*/sec)
Solvent
Silicone Elastomer E301
Diethyl phthalate
Tritolyl phosphate
Benzene n-Pentane *Heptane
100 130 190 200 (2) (3) (3)
1.on
Not an optimized value. Purified by solution in hexane and filtration through charcoal.
394
ANALYTICAL CHEMISTRY
50
39 39
8.8 25 61 7.37 19.7 32.3 68.4 98.2 7.37 19.7 32.3 68.4 98.2 2.20 3.21 8.72 20.6 41 .O 81.9 2.11 3.79 7.98 20.4 44.2 56.6 68.9 2.59 8.06 20.0 39.8 82.4 3.29 8.12 20.1 41.6 58.0 71.7 432 690 1120 1570 2025 7 23 46 75 83 110 140 16 19 27 27 19 24 47 45 49 68 54 33 15.2 11.9
4
(poise) 6.82 1.54 0.813 0.234 0.0927 6.82 0.81 0.35 0.15 0.08
6.82 0.81 0.35 0.15 0.08
6.82 3.55 0.81 0.35 0.15 0.08 6.82 2.65 1.10 0.35 0.15 0.11 0.08 6.82 1.10 0.35 0.15 0.08 6.82 1.15 0.35 0.15 0.11 0.08 0.01207 0.00725 0,00490 0.00357 0.00273 4.15 0.68 0.24 0.10 0.06 0.036 0,023 0.20 0.16 0.06 0.03 1.05 0.80 0.36 0.21 26600 14100 11800 0.18 0.26 0.26
DrqZ/T X 108
0.35 0.26 0.25 0.29 0.35 0.75 0.59 0.59 0.75 0.73 1.14 0.56 0.47 0.50 0.42 0.34 0.30 0.31 0.30 0.30 0.35 0.33 0.28 0.29 0.30 0.32 0.32 0.29 0.38 0.22 0.30 0.30 0.38 0.45 0.29 0.31 0.34 0.52 0.35 0.45 0.43 0.46 0.46 0.44 0.44
0.56 0.62 0.62 0.50
0.48 0.40 0.20 0.20 0.15 0.09 0.63 0.68
0.82 0.55
0.18 0.13 0.10
when c is the constart term, 0.35 X loW8for hydrocarbon for methyl-silicones and (V/A)*‘3 for nonchains, 0.7 X linear molecules such as tricresyl phosphate. Effect of Viscosity 011 Nonpolar Column Efficiencies. Using the above equation together with the equations previously cited by Hawkes and hfooney ( 4 ) it can be shown that a viscosity of 0.5 poise in a long-chain solvent with a n exponent of 0.5 will keep C l below 10-3 second in packed o r capillary columns with usual loadings. This is comparable to the values of C, found by Sternberg and Poulson (5) so that a viscosity limit of 0.5 poise for these oils will usually be adequate for analytical :olumns. However a more stringent viscosity limit is needed for glass bead columns: for 0.25 % loading, a particle diameter of 0,015 cm (100-mesh) and k = 10, a limit of 0.2 poise I S found, which is not difficult to achieve but requires some wat1:hfulness. No values of C Llower than 5 x have been r1:ported for glass bead columns, and it (4) S. J. Hawkes and E. F. Mooney, Ibid., 36, 1473 (1964). ( 5 ) J. C. Sternberg and I
