Anal. Chem. 1987, 59, 23-28
23
Thermal Field-Flow Fractionation Using Supercritical Fluids Judy J. Gunderson, Marcus N. Myers, and J. Calvin Giddings* Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
I n thls paper we have carrled out a prellmlnary lnvestigatlon of supercrltlcal fluids as carrler medla In thermal fleld-flow fractlonatlon (thermal FFF). We show that there are reasonable grounds for expecting supercrltlcal fluids to extend the low molecular welght range of thermal FFF and lead to enhanced mass transport and selectlvlty. An approxlmate theory of solute dlsplacement in the system's temperature gradlent Is based on the SdUMllty parameter theory developed by us earlier to descrlbe supercrltlcai fiuld chromatography. The predlcted levels of retention are compared with experlmental levels using polystyrene samples of molecular welght 10' subjected to channel temperature drops ranglng from 20 to 40 O C . An order of magnltude agreement is found. Retention Is shown to increase, as expected, wlth molecular welght and temperature gradlent. The relatlve retentions observed wlth supercrltical carbon dloxlde and supercrltical ethane are much as predlcted. However, our efforts to proceed to hlgher retention levels, necessary for useful separatlon, have been hampered by peak degradatlon and peak loss. The Importance of thls phenomenon as an obstacle to further development is descrlbed.
-
Thermal field-flow fractionation (FFF) is a major subtechnique of the field-flow fractionation family of methods. Existing thermal FFF systems have been designed to exploit the thermal diffusion of polymers and other large molecules dissolved in liquids which are subjected to a strong temperature gradient impressed across a narrow flow channel (1-4). Because thermal diffusion is a relatively weak secondary effect stemming from a cross term in the general flux equation of irreversible thermodynamics (51, it has been difficult to apply thermal FFF to molecules of low and intermediate molecular weight. Only by pushing temperature increments to 150 OC has it been possible to realize a marginal retention of 600 M w polystyrene (6). The object of this report is to explore the possibility, using both theory and experiment, that supercritical fluids (dense gases) used in place of a liquid solvent might be effective in extending FFF down to intermediate and low molecular weights. Supercritical fluids may also exhibit other advantages such as enhanced solute transport rates to speed the separation process, the ease of separating solvent and solute, and the possibility of combining the FFF effect with a chromatographiceffect by using cold-wall temperatures sufficiently low to condense a thin film of liquid at the cold wall of the FFF channel. We note also the possible value of controlling or programming pressure and cold-wall temperature along with the more conventional parameters of temperature drop and flow rate. The physicochemical factors involved in the mass transport of solute in dense media subjected to a temperature gradient have not been clearly elucidated, and numerical predictions of the magnitude of the effect are not now possible. One approach in describing such transport would utilize Onsager's reciprocity relationships (5) which relate the mass transport induced by a temperature gradient to the transport of heat resulting from a concentration gradient (the Dufour effect). 0003-2700/87/0359-0023$01.50/0
The heat term could be related to the solute-solvent interactions which are ultimately responsible for the induced heat transport. The anticipated advantage of using supercritical fluids in thermal FFF arises in the fact that much higher density gradients can be achieved in such fluids than in liquids when both are subjected to the same temperature gradient. The enhanced density gradient is especially evident near the critical point where theoretically the gradient approaches infinity. With the cold wall of the thermal FFF channel near the critical temperature, it is expected that large density gradients can be realized in the gas near that wall. Nonvolatile or weakly volatile solutes are then expected to seek out the region of highest density (near the cold wall) in order to maximize intermolecular interactions with the dense gas solvent. The accumulation of solvent near the cold wall can then be coupled with flow and used as the basis of an FFF system. In order to estimate the magnitude of the critical FFF parameters when supercritical fluids are used, we employ a previously developed theory describingthe dependence of the solubility (volatility) of a solute on the density of the gaseous solvent (7-10). We may then determine the concentration gradient of the solute as a function of the solvent density gradient.
THEORY In our earlier work on supercritical fluid (dense gas) chromatography we developed a simple theory of solubility in compressed gases based on regular solution theory and the Hildebrand solubility parameter concept. This theory was used to obtain the term l i d which describes the enhancement of solubility caused by densification of the gas; Le., l i d is the ratio of the concentration of the solute in the dense gas to the concentration in the presence of an ideal gas. The term l i d reflects the magnitude of solute-solvent interactions which, as we indicated above, are expected to play a major role in polymeric thermal diffusion. Equation 5 of ref 9, when slightly rearranged, yields
In lid = (V,/RT) 6(26,, - 6 )
(1)
where V, is the molar volume of the solute, R the gas constant, T the temperature, 6 the solubility parameter of the gas, and 6o the solubility parameter of the solute. Theory suggests that the solubility parameter of the dense gas is proportional to the gas density p (6). Thus, we relate 6 to p by the equation where pa, is equal to the density of the gas necessary to make the solubility parameter 6 of the gas equal to the solubility parameter of the solute 6,. The principal assumption of this treatment is that the concentration c of solute in different regions of the dense gas is proportional to lid. Consequently, we can write dIn C --d In l i d (3) dX dx where x is the distance from the cold wall of the FFF channel. The critical FFF parameter 1, which can be described as the 0 1986 American Chemical Society
24
ANALYTICAL CHEMISTRY, VOL. 59, NO. 1, JANUARY 1987
t\
0.9
'
The substitution of eq 7-10 into eq 6 and the latter into eq 5 leads to the 1 expression
1
I
I
I\ \
I
-1
0.8
\\
I
\
0.7
2v0602(P60- P)
--E 0.6 -9 0.5 >-
t v,
0.4 ' 146 atm
4
60/PaO
87 otrn
,
90
60
30
TEMPERATURE ("C)
Flgure 1. Density as a function of temperature and pressure for C02.
mean thickness of the solute layer compressed against the wall, relates to the cuncentration gradient through the equation 1 = - l / ( d In c/dx) (4) The combination of eq 3 and 4 yieIds 1 in terms of the gradient of Ild, 1 = -l/(d In Iid/dx) (5) In view of the form of eq 1and 2 it is most appropriate to write the gradient term in eq 5 in the form d In I j d d In lidd6 d p dT -=---(6) dx d6 dp dT dx Equation 6 contains four terms which require evaluation. The first two terms, obtained directly from eq 1 and 2, assume the form
d 1n l i d -d6
-
2v0(60- 6)
RT
- 2Vob(Pa, - P) R TPa,
db/dp = 6O/Pb,
(7) (8)
The third term (dp/d7') of eq 6 depends on the pressure and temperature conditions in the channel relative to the critical parameters of the gas and will not be evaluated explicitly. The plots of p vs. T for supercritical C02given in Figure 1 show that d p l d T may vary considerably across the channel. For assigning a value to dp/dT, we can choose the cold-wall value of dp/dT or, alternatively, the value at the center of gravity of the solute layer. In the former (and somewhat simpler) case we write dp/dT
(dp/dT),
(12)
where pEq is equal to the density of the gas when condensed to a liquid and P,, is the critical pressure expressed in atmospheres. Equation 12 leads to the form
1 1 0 2otrn I
$c
6 = 1.25Pc,1/2(p/pliq)
0.3
0.2
(- (g)c
(11)
where the negative sign has been absorbed into the density gradient term because dp/dT is negative. Equation 11 can be cast in an alternate form using the following approximate equation for 6 (7):
\
5 a
R TPa:
1=
(9)
where the subscript indicates that the term is to be evaluated at the temperature of the cold wall. The fourth term of eq 6, dT/dx, will also vary across the channel because of the variations in thermal conductivitywith temperature. This term can be written as
(10) where w is the channel thickness and AT is the temperature drop across the channel. The dimensionless factor g compensates for the nonuniformity in temperature gradient across the channel (see later). For numerical purposes we use the temperature gradient at the cold wall, (dTldx),, in place of dT/dx.
= 1.25pc1~~~/Pliq
(13)
which can be substituted back into eq 11. Furthermore, to make eq 11 more explicit, we write T as Tc and p as pc to indicate that these two parameters are to be evaluated at (or near) conditions existing at the cold wall. With these changes, eq 11 becomes 0.32RT~qj~~
I= PcrVO(P6, - Pc)
(- (g)c
(14)
$c
The concentration profile is expressed in terms of 1 by
c/co =
(15)
where co is the concentration at the cold wall. The 1 value of eq 14 can be converted into A = l / w , where A, the retention parameter, governs retention in FFF. The usual FFF equation relating retention parameter R to A,
R = 6h[c0th (1/2A)
- 2x1
(16)
is based on the assumption of a parabolic flow profile. However, the velocity profile in an FFF channel with an applied temperature gradient will deviate from the normal parabolic form due to viscosity variations across the channel. The same effect is observed with liquids. The general approach used for liquid-based thermal FFF may also be used here for examining the velocity profile ( I I , 1 2 ) . The equation of fluid motion is of the form d2u(x)
d&)
du(x)
-= -AP/L o b ) -+ dx dx
dx2
(17)
where u ( x ) is the velocity at position x in the channel, ~ ( x ) is the position-dependent viscosity, and AP/L is the pressure increment per unit length of the channel. In order to determine the position dependence of the viscosity and thus determine the velocity from eq 17, we must do two things: first, we must determine the temperature dependence of the viscosity o ( T ) , and second, we must determine the form of the temperature profile across the channel so that the temperature dependence ~ ( 7 'can ) be converted into the distance dependence ~ ( x ) The . descriptions of these two functions for supercritical fluids can become quite complex because both viscosity and thermal conductivity vary rapidly with temperature near the critical point and they also depend on the pressure of the system. For this paper, we obtain the velocity profile for only one set of experimental conditions, sufficient to compare theoretical predictions of retention with experimentalvalues. The experimental conditions correspond to carbon dioxide subjected to'a pressure of 119 atm and a temperature range from 313 to 353 K.
ANALYTICAL CHEMISTRY. VOL. 59, NO. 1. JANUARY 1987 COARSE PRESSURE GAUGE
-
25
FINE PRWRE
PRESSURE REGULATOR
6
d.3 0.6 d.9 112 115 RELATIVE VELOCITY, v(xV (v(x1)
Flgun 2. Asymmetry of the veloCny profile for CO, at 119 atm wlth a wM wall of 40 OC and A T = 40 OC according 10 eq 21. The isoviscous symmetrical velocity profile is shown for comparison. The temperature dependence of the fluidity (reciprocal viscosity) under the above conditions may be adequately accounted for by fitting fluidity data (13) to a third-order polynomial in temperature T as follows: 1/q = a.
+ alT + a 2 P + a,?O
(18)
The temperature profile T(x) needed to get (l/q)(x) is controlled by the basic heat flux expression
dT/dx = q / r
(19)
where q is the heat flux per unit area and I is the thermal conductivity, which varies with T. The temperature dependence of K is well represented by fitting experimental data (24) to a second-order polynomial function. An exact solution for the temperature profile may then be determined from eq 19, but the result is quite complicated. This results in a very complex expression for (l/q)(x). Instead, we will seek a simpler approximation for the temperature profile by expanding the temperature in a Taylor's series about the cold wall ( x = 0 ) as follows:
(20) The temperature madient dT/& is obtained from eq 19. The higher order derivatives are &o determined from 19 using the second-order polynomial expression r(T). Keeping the first four terms of the expansion is a g o d approximation to the exact solution. The position dependence of the fluidity may now be determined by substituting eq 20 into eq 18. The resulting polynomial is truncated after five terms. The maximum error incurred in truncating the polynomial is 4 % for Cot with a 40 "C cold wall and a 40 OC temperature drop and occurs a t the bot wall. Substituting the polynomial describing the position dependence of the fluidity into eq 17 and performing the necessary integrations give the velocity profile as
4
where each h, is a group of constants (11,12). T h e distortion of the velocity profile, which arises from the thermal gradient and ita resulting distribution of viscosities, is illustrated in Figure 2. Here the symmetric parabolic flow (isoviscous) profile is compared to eq 21 for carbon dioxide at 119 atm pressure with a cold wall of 40 O C and AT = 40 "C.
Flgure 3. Block diagram of suprcritlcal thermal FFF system Once the concentration and velocity profiles are available, the retention parameter R is determined from
R = (~.u)/(c)*(u)
(22)
where the triangular brackets denote average values. By employing eq 15 and 21, this equation yields 7
i-i
With X and the hi values known,R can be obtained by direct numerical means.
EXPERIMENTAL SECTION Apparatus. A block d w a m of the supercriticalthermal FFF system is shown in Figure 3. The pressure of the carrier gas was increased from tank pressure by pumping through a liquid pump Model L P l O (Whitey Research Tool Co., Oakland, CA). To ensure a liquid state during pumping, the pump head was cooled hy circulating ethanol through a coil wrapped around the pump head and through an ice bath. The pressure of the carrier exiting the pump was monitored by a coarse pressure gauge (50 psi increments). Two regulatorswere used to regulate the pressure in the column. The experiments involving carbon dioxide made use of a Consolidated Controls (El Seguudo, CA) Series 1B pressure regulator; for ethane a T w m (ElkRiver, MN) Model 44-1012-24 pressure regulator was used. The two regulators were equally effective at controlling the system's pressure. To accurately measure the pressure in the system, a Heise (Heise, Inc., Newton, CN) Model CM-3012 pressure gauge with 5 psi increments was used. The sample chamber and detector were housed in an oven whose temperature was kept 2 4 O C above the temperature of the cold wall of the column. The oven was a galvanized steel cubical box 24 in. (61em) on a side insulated with 1in. (2.5 cm) of fiberglass. The oven was heated by u8e of a strip heater controlled by a variable transformer. The sample chamber consists of a stainless-steelpressure vessel with a volume of approximately 11 mL within which the sample, deposited on fiberglass, was placed. The high-pressure ultraviolet deteetor is described elsewhere (12). The output was monitored on a twc-pen Servogor 120 chart recorder (MetrawattGMBH,Numberg, Germany). The flow rate through the system was adjusted by using a metering valve. The flow was manually measured hy a huhhle flowmeter and a stopwatch.
28
ANALYTICAL CHEMISTRY, VOL. 59, NO. 1, JANUARY 1987
Table I. Physical Properties of Gases property
Tcl,"C Per, atm Pcr3
g/mL
Pliq,
g/mL
(cal/mL)1/2
C02
C2H6
31.0 72.9 0.468 1.250 10.67
32.3 48.2 0.203 0.574 8.680
Table 11. Comparison of Liquid Ethylbenzene and Supercritical Carbon Dioxide as Solvents in Field-Flow Fractionation for the Analysis of Low Molecular Weight Polystyrene
The channel system is of the same general design as that described before for liquids (15), but with a few changes. It consists of two copper zirconium alloy (Amzirc, Viking Metals, Verdi, NV) bars with highly polished faces. The two bars were sandwiched between two asbestos boards for insulating purposes, and the whole assembly was clamped together with 54 highstrength (SAE 8) finethread 3/8-in.bolts between two 1.0-in. steel plates. The bolts were tightened to 25 f t lb. The channel space was cut out of a sheet of Mylar plastic. The channel is 0.178 mm thick, 1.0 cm in breadth, and 55.1 cm in length from the inlet tip to the outlet tip. In order for the column to seal, 3/ls-in. (0.48-cm) Goretex joint sealant material (W. L. Gore and Associates, Inc., Elkton, MD) was placed around the Mylar spacer. The column was heated by two 1500-Wcartridge heaters. The heat input was regulated by two digitally controlled 25-A relays. The duty cycle and the period were user designated with the period being minimized so as to alleviate temperature fluctuations during the heating and cooling cycles. The maximum period used was 100 ms. Materials. Carbon dioxide and ethane were purchased from Scientific Gas Products (South Plainfield, NJ). The carbon dioxide was provided with a full-length dip tube and was ultra pure grade (99.995%). The ethane was C.P. grade (99.95%). The physical properties of the two gases are listed in Table I. The molecular weights M and polydispersities p = Mw/M,,of the polystyrene standards used in this experiment are as follows: 680, 1.16; 800, 1.3; 955, 1.07; 1152, 1.07; and 1574, 1.06. All the standards were obtained from Pressure Chemical Co. (Pittsburgh, PA). Procedure. The samples were dissolved in spectrograde pentane. The solution was deposited on fiberglass, and the fiberglass was placed in the sample chamber. The solvent was then evaporated. Once the sample chamber was placed in the oven, the entire system was pressurized and allowed to equilibrate. Valves 1and 2 in Figure 3 were left open so that gas would flow through the column and gas in the sample chamber would become saturated with the sample. During this period of time (1-2 h), the temperature drop across the channel was established. The temperatures of the hot wall and of the cold wall were monitored continuously using two Omega (Stamford, CT) type-J thermocouple thermometers. A sample was injected into the system by opening valve 3 and closing valve 1 (see Figure 3) for a short period. The volume of carrier gas injected by this means into the channel is calculated as the duration of this period multiplied by the flow rate. The flow rate may be calculated if the flow rate of the exiting gas past the pressure-reductionvalve is known along with the gas density at the operating temperature and pressure. Note that this procedure cannot be used to calculate the flow rate through the channel because of the large density gradient established across the channel as a result of the imposed temperature drop. The retention time of a sample was taken from the center of the injection period to the center of mass of the zone. Due to a large amount of extra-column tubing between the sample chamber and the column, extra-column contributions could not be ignored. The true retention time of a sample was taken as the measured retention time minus the time spent in the extra tubing. This was calculated from the outlet flow rate and the density of the gas in the extra tubing. The retention ratio of a sample is calculated from
R = to/&
(24)
where t o is the true elution time of a nonretained peak and t, is the true elution time of the sample. Toluene was used t o determine the value of a nonretained peak.
MW
solvent
AT, "C
retention ratio
600 680
ethylbenzene carbon dioxide (114 atm)
158
0.92 0.92
40
Table 111. Retention Ratios of Polystyrene Standards in Supercritical Carbon Dioxide" AT, "C
800MW
20
30 0.85 f 0.02 0.81 f 0.02
40 60
955 MW
1152 MW
0.87 f 0.02 0.82 h 0.02 0.79 f 0.02
0.82 f 0.04 0.74 f 0.04
'Experimental conditions: T, = 40 " C , 122 atm. Table IV. Comparison of Experimental (Rsxptl)and Theoretical (Rl, R,) Retention Ratios for Polystyrene in Supercritical Carbon Dioxide" retention ratio
800 MW
955 MW
Rexptl
0.85 f 0.02 0.53 0.77
0.79 f 0.02 0.46 0.71
R, R2
"Experimental conditions: T, = 40 "C, AT =
40 "C, 122 atm.
RESULTS AND DISCUSSION The main goal of this work was to examine the feasibility of supercritical thermal FFF, particularly as a method of retaining low molecular weight components without the extreme temperature gradients necessary when using normal liquid carriers (6). The consequences of using a supercritical fluid carrier rather than a liquid carrier are illustrated in Table 11. For similar low molecular weight polystyrene standards, the liquid system needed a temperature gradient nearly 4 times that of the supercritical system for comparable levels of retention. This result supports the hypothesis that supercritical fluids can be used to lower the working temperature gradient below that needed with liquid carriers. Despite our success in demonstrating that retention of low molecular weight components is considerably greater in supercritical fluids than in normal liquid solvents, our system could not be pushed to the high retention levels ultimately needed for high resolving power. Attempts to reach useful retention levels ( R I 0.5), either by increasing molecular weight or temperature gradient, provoked a rapid loss of peak area ending in peak disappearance. This phenomenon, whose origins are not clear, will be discussed further on. Comparison of Theoretical and Experimental Results. Retention ratios measured for low molecular weight polystyrene standards in supercritical carbon dioxide are shown in Table 111. The trends present in liquid-based thermal FFF are present here also. At a constant temperature drop, the retention ratio decreases with increasing molecular weight, and for a specified sample, the retention ratio decreases with increasing temperature drop. The large polydispersity of the 800 MW standard prevented accurate determination of the retention ratios at lower temperature drops. The experimental and theoretical retention ratios for a temperature drop across the channel of AT = 40 "C are given in Table IV. The theoretical values were calculated from eq 19. Theoretical molar volumes were calculated as molecular weight divided by solute density. The density used for polystyrene was 1.05 g/mol (16). The values for the retention ratio calculated using these theoretical molar volumes are
ANALYTICAL CHEMISTRY, VOL. 59, NO. 1, JANUARY 1987
Table V. Retention Ratios of Polystyrene Standards in Supercritical Ethane' AT, O C
955 MW
1152 MW
1
40
0.93 0.01 0.89 f 0.01 0.84 f 0.01 0.77 0.01
50 60
70 80
0.90 0.86 0.82 0.78
f 0.01 f 0.01 f 0.02 f 0.02
*
*
"Experimental conditions: T,= 40 "C,
h
1574 MW
0.90
30
6.0
27
*
0.01 0.86 f 0.01 0.84 f 0.02 0.79 f 0.02
122 atm.
designated in Table IV as R1. The agreement between Rerptl and R1 is far from satisfactory. This may be due in part to systematic errors introduced by using the theoretical molar volume. It has been shown (IO) that the effective volumes in supercritical fluids are less than those predicted by theory. Experimental results (IO) indicate that the ratio of the experimental to the theoretical molar volume for these samples should be approximately 0.25. The values of R2 shown in Table IV are the theoretical retention ratios calculated using this correction factor for the molar volumes. These values are closer to the experimentally determined retention ratios, although there is still a discrepancy between experimental and theoretical values. This may be partly due to the evaluation of the terms (temperature, density, temperature gradient, etc.) in the equation for 1, eq 14, at the cold wall. These terms are all functions of channel position, and values at the cold wall were assumed to simplify the equations. The cold-wall evaluation in the present case is highly approximate since the samples are only mildly retained and the cold-wall temperature is no longer representative of the bulk of the zone. The theoretical values may also be incorrect due to the fact that regular solution theory underlies our equations. Regular solution theory neglects density-dependent entropy effects, pressure volume effects, and molecular subtleties which render the theory inexact (10). We have already noted the problem with peak degradation. The peak area/sample size ratio is observed to decrease with increasing temperature gradient. At temperature drops higher than those shown in Table 111, no sample was detected. An example of peak degradation is the behavior of 955 MW polystyrene in C02at 122 atm and T, = 40 "C. As the temperature drop is increased from 20 to 40 "C, there is a corresponding decrease in the peak area/sample size ratio by a factor of 2.6. We have considered solute precipitation as a possible source of peak degradation. However, operation with a cold-wall temperature of 20 "C where solubility is higher than at 40 O C still resulted in the loss of the 955 MW polystyrene peak.
Supercritical Carbon Dioxide and Ethane as Carriers. The retention ratios of low molecular weight polystyrene standards in supercritical ethane are given in Table V. The results follow the same trends as found above for supercritical carbon dioxide; retention increases (retention ratio R decreases) both with increasing temperature gradient and with increasing molecular weight. A comparison of Tables I11 and V shows that a sample in ethane requires a larger temperature gradient than in carbon dioxide for similar levels of retention. For instance, similar results may be achieved by using either a 30 "C temperature drop in carbon dioxide or a 70 "C temperature drop in ethane. If the velocity profiles are assumed similar, then retention in the two systems may be compared by examining 1/1from eq 5 as follows:
The second term on the right side, the gradient in solubility
CHANNEL POSITION, x/w
Flgure 4. The solubility parameter (cal/mL)"2 as a function of channel position for COP with AT = 30 "C and C2H, with AT = 70 "C. The curves were calculated for 122 atm and a cold wall of 40 "C.
parameter 6, may be evaluated from plots of 6 vs. channel position for carbon dioxide with AT = 30 "C and ethane with AT = 70 "C. These plots, presented in Figure 4, show that the solubility gradient of ethane, despite its greater temperature gradient, remaing similar to that of carbon dioxide due to ethane's low critical pressure. For a system pressure of 122 atm, the reduced pressure of ethane is about 2.5, whereas for carbon dioxide it is about 1.7. The density of supercritical fluids becomes less dependent on temperature the greater the reduced pressure. The solubility parameter follows this trend because it is a linear function of density (see eq 2). Thus, the solubility parameter is a weaker function of temperature for ethane than for carbon dioxide. When we write
d6 - -.d6 dT _ dx
dT dx
we see that to achieve the same solubility gradient across the channel, ethane, with a lower dG/dT, requires a higher temperature gradient than carbon dioxide. These results suggest that even in different supercritical solvents, a sample will give similar retention ratios if the solubility parameter at the cold wall is comparable and the solubility parameter gradient is the same, irrespective of other differences.
CONCLUSIONS This study constitutes a preliminary examination of a thermal FFF system in which supercritical fluids replace normal liquid solvents. We have assumed and developed a model based on solubility gradients in supercritical fluids to explain the proposed thermal diffusion process. While this assumption cannot be considered as forming the basis of a rigorous thermal diffusion theory, the results of our study suggest that the postulated thermal diffusion mechanism underlies the retention observed in the system. The degradation and loss of solute peaks at moderate retention levels is a major puzzle unearthed in this study. While it is likely that this phenomenon represents some peculiarity of our system, it cannot be ruled out as endemic to thermal FFF using supercritical fluids. This phenomenon clearly requires further investigation using other channels with other surfaces, other injection techniques, and other supercritical gases. Aside from the problem of peak degradation, the results of this study are encouraging in showing that higher retention levels are possible with supercritical fluids than with liquid solvents. Thus, supercritical fluid technology, in accordance with our original expectations, may be more readily applied
Anal. Chem. 1987, 59, 28-37
28
to low molecular weight components (of the order of magnitude of lo3) than is liquid-based thermal FFF technology. In addition, theory predicts a higher selectivity S for thermal FFF systems using supercritical fluids (S 1) than those using liquids (S 0.6). Theory consequently implies that the selectivity may nearly double using supercritical fluids in place of liquids, thus approaching the selectivity level (unity) found for sedimentation FFF (17),but applicable over a much lower molecular weight range than that accessible to sedimentation FFF.
-
-
LITERATURE CITED (1) Hovingh, M. E.; Thompson, G. H.; Glddings, J. C. Anal. Chem. 1970, 42, 195. (2) Glddings, J. C.; Smith, L. K.; Myers, M. N. Anal. Chem. 1978, 4 8 , 1587. (3) Glddings, J. C.; Martin, M.; Myers, M. N. J . Chromatogr. 1978, 158, 419. (4) Giddings, J. C.; Myers, M. N.; Janca, J. J . Chromatogr. 1979, 186, 37. (5) DeGroot, S. R. Thermodynemics of Irreversible ~ ~ ~ c e s ;sInterscies ence: New York, 1951. (6) Giddings, J. C.; Smith, L. K.; Myers, M. N. Anal. Chem. 1975, 4 7 , 2389.
Giddhgs, J. C.; Myers, M. N.; McLaren, L.; Kelier, R. A. Science (Washlngton, D . C . ) 1908, 162, 67. Myers, M. N.; W i n g s , J. C. I n Progress in Separation and Purification; Perry, E. S.,Van Oss, C. J., Eds.; Wiiey: New York, 1970; Vol. 3, p 133. Giddings. J. C.; Myers, M. N.; King, J. W. J. Chromatogr. Sci. 1969, .7 ,. 276.
Czubryt, J. J.; Myers, M. N.; W i n g s , J. C. J. Phys. Chem. 1970, 7 4 , 4260.
Gunderson, J. J.; Caldwell, K. D.; Giddings, J. C. Sep. Sci. Techno/. 1984, 19. 667. Gunderson, J. J. Doctoral Thesis, University of Utah, Salt Lake City, UT, 1986. Stephan. K.; Lucas, K. Vlscoslty of Dense Fluids; Plenum: New York, 1979.
Varbnik, N. 0. Tables on the Thsrmophysical Properfies of Liquids and Geses; Wlley: New York, 1975. Giddings, J. C.; Caldwell, K. D.; Myers, M. N. Macromolecules 1978, 9, 106. Scott, J. R.; Roff, W. J. Handbook of Common Polymers; Chemical Rubber Co.: Cleveland, OH, 1971. Myers, M. N.; Giddings, J. C. Anal. Chem. 1982, 5 4 , 2284.
RECEIVED for review May 19, 1986. Accepted September 3, This is based work supported by Grant CHE82-18503 from the National Science Foundation.
Fractionating Power in Programmed Field-Flow Fractionation: Exponential Sedimentation Field Decay J. Calvin Giddings* and P. Stephen Williams Department of Chemistry, University of Utah, Salt Lake City, Utah 84112 Ronald Beckett
Water Studies Centre, Chisholm Institute of Technology, Caulfield East, Victoria, Australia
I n order tofill a maJorvoid In the opthrlzaknof programmed fleld-flow fractionation (FFF), we have devdoped general theoretlcal expressions for resdutbn, expremed as fractknating power F d , applkable to essentla#y ail fiekl-programmed FFF systems. The rewklng Integral expressions have then been worked out for a constant fldd/exponentlal Held decay programmlng sequence that Includes the Kbklad-Yau tbnedelay-exponentlal program as a specla1 case. The flnal Fd equation has bean applkd to FFF, yiekwns pkts of F d vs. partlcle dlameter that account for varlatlons In Fd wlth changes In void t h e (or flow veloctty), expmntlal programmlng rate, constant-fkld t h e , InHlal field strength, partkle density, and channel thlcknera Based on the resuits of these plots, we have developed an optlmlzatlon strategy for exponentlally programmed sedlmentatlon FFF.
The importance of programmed operation in field-flow fractionation (FFF) was recognized a t an early stage in the development of sedimentation FFF ( I ) . The philosophy of programming, both in chromatography and field-flow fractionation, has evolved from the recognition that no single set of conditions is suitable for the resolution of each of the components in a mixture of widely variable properties. Consequently, various retention-influencing parameters 0003-2700/87/0359-0028$01.50/0
(temperature, solvent properties, field strength, flow velocity, etc.) are varied in the course of a run in order to expose in an orderly sequence each of the components to effective separation conditions. Sedimentation FFF separates colloidal components on the basis of their effective mass (2). Under ideal conditions, without programming, the retention time or volume is roughly proportionalto particle mass. Thus, a 10-fold range in particle diameter corresponds approximately to a 1000-fold range in retention time. The widely spaced retention times yield a high selectivity leading to very high resolution levels for similar particles, but the process is often impractical because of the inordinate time required for elution of the most massive components. Consequently, programming is invoked. Most commonly, field programming is used. In this technique a high initial field strength is employed for the separation of the small colloidal particles, following which the field strength is programmed downward to provide suitable conditions for the larger particles ( I , 3 ) . Accordingly, the full particle range can be eluted in practical experimental times. The potential and limitations of such programming methods have been discussed in a recent paper (3). Field programming has also been used with other FFF techniques, notably thermal FFF and flow FFF ( 4 , 5 ) . However, selectivity is not as high in these cases as in sedimentation FFF and the need for programming is somewhat blunted by the smaller range in elution time and volume as 0 1986 American Chemical Society
