Anal. Chem. 1980, 52,
turning the “balance” potentiometer controls the current through the emitter. This dual mode of operation is convenient when comparing operating characteristics of the constant-temperature vs. constant-current power supplies on one emitter. T e m p e r a t u r e - J u m p Capabilities. This constant-temperature power supply has a very small time constant in achieving the desired temperature. Actually it overdrives the current initially to rebalance the Wheatstone bridge. But since the emitter was initially a t a cooler temperature, this current overdrive acts to set and maintain the emitter temperature at a faster rate. Consequently, by a slight modification to the operating procedure it is possible to produce a very rapid temperature-jump procedure for FD. After balancing, one leaves switch 1 in the balance position and turns up the temperature knob to the desired final average temperature of the wire. Upon turning of the switch from balance to heat, the regulator jumps the temperature to the desired value much faster than a constant-current power supply. In the constant-temperature case, the amplifier will apply and hold almost the entire battery voltage across the reference and emitter resistance until the set point is reached. In the constant current cases, the thermal mass and fzR emitter power are the sole determiners of equilibration time. This emitter temperature regulator is similar to, but in many respects different from, a resistance thermometer. Both employ the temperature coefficient of resistance as the basis of their operation as temperature-sensing transducers. The resistance thermometer (20) typically passes a very small constant current (i.e., no or little Joulean heating) through a wire (usually platinum). A change in ambient temperature changes the resistance of the wire; the ensuing voltage difference is monitored as a temperature change. On the other hand, our constant temperature power supply utilizes a much larger heating current and relies on the heat generated within the wire itself to provide a feedback related to the actual temperature of the wire.
2293-2298
2293
The emitter temperature regulator is basically a regulated power supply. In its present configuration, control of the desired temperature (or milliamperes of heating current) is maintained by manual operation. It would be relatively straightforward to implement either the computer control of Holland and Sweeley (8) or the total ion current feedback system used by Schulten ( 4 , 5).
LITERATURE CITED (1) Beckey. H. D. “Principles of Field Ionization and Fiekl Desorption Mass Spectrometry”; Pergamon Press: Oxford, 1977. (2) Winkler, H. U.; Beckey, H. D. Org. Mass Spectrom. 1972, 6,655. (3) Winkler, H. U.; Linden, B. Org. Mass Spectrom. 1978, 7 7 , 327. (4) Schutten, H. R.; Beckey, H. D. Cancer Treat. Rep. 1978, 60. 501. (5) Schulten, H. R.; Nibbering, N. M. M. Biomed. Mass Spectrorn. 1977, 4 , 55. (6) Winkler, H. U.; Newmann, W.; Beckey, H. D. Int. J . Mass Spectrom. Ion Phvs. 1978. 27, 57. (7) Baroski., D.F.; &cob, L.; Barofsky, E. 23rd Annual Conference on Mass Spectrometry and Allied Topics; Houston, TX, May 1975; Conference Proceedings B-6, pp 60-61. ( 8 ) Maine, J. W.; Soltmann, B.; Holland, J. F.; Young, N. D.; Gerber, J. N.; Sweeley, C. C. Anal. Chem. 1978, 4 8 , 427. (9) Fraley, D. F.; Pedersen, L. G.; Bursey, M. M., unpublished work. (10) Winkler, H. U.; Beckey, H. D. Org. Mass Spectrom. 1973, 7 , 1007. (11) Schutlen, H. R.; Lehmann, W. D.;Haaks. D. Org. Mass Spectrom. 1978, 73, 361. (12) Bursey. M. M.; Rechsteiner, C. E.; Sammons, M. C.; Hinton, D. M.; Colpltts, T. S.;Tvaronas, K. M. J . Phys. €1978, 9 , 145. (13) Beynon, J. H.; Fontaine, A. E.; Job, B. E. Z.Naturforsch A 1966, 27, 766. (14) Rieck, G. D. “Tungsten and Its Compounds”; Pergamon Press: Oxford, 1967; p 25. (15) Beckey, H. D.; Hilt, E.; Schutten, H. R. J. Phys. €1973, 74, 3. (16) Neumann, G. M.; Rogers, D. E.; Derrick, P. J.; Peterson, P. J. K. J. Phys. D 1980, 13, 485. (17) L‘vov, S. N.; Lesnaya, M. I.; ViniWtii. I. M.; Naurnenko, V. Ya High Temp. (€ng/. Trans/.) 1972, TO, 1196. (18) Kummler, D.;Schulten, H. R. Org. Mass Spectrom. 1975, I O , 813. (19) Sweeley, C. C.; SoRmann, B.; Holland, J. F. “High Performance Mass Spectrometry”; Gross, M. L., Ed.; American Chemical Society Symposium Series: Washington, DC, 1978; p 214. (20) “Temperature Measurement Handbook”; Omega Engineering Inc.: Stamford, CT. 1979, p L-2. ~~
RECEIVED for review June 26, 1980. Accepted September 16, 1980.
Polymer Analysis by Thermal Field-Flow Fractionation Michel Martin’ and Ren6 Reynaud Ecole Polytechnique, Laboratoire de Chimie Analytique Physique, 9 7 128 Palaiseau, France
The requirements on the thermal diffusion parameters of polymers for successful thermal fieBflow fractionation (thermal FFF) analysis are establlshed and a literature survey of these parameters Indicates that thermal FFF should be applicable to most of the lipophilic polymers with molecular weight larger than about 10000. Thermal FFF experiments have been conducted with samples d poly(methyl methacrylate) (PMMA). The diffusion and thermal diffusion coefflclents of the polymers have been determined from their thermal FFF behavlor as well as the polydlspersity Index, p, of the samples. The migration of PMMA by thermal diffusion has been shown to occur in the dlrection of the cold temperatures by observing the variations of retention with flow rate In thermogravltational FFF. Collectlng fractions at the outlet of the thermal FFF channel allows a reduction by a factor 2.3-3.8 of the plate height, whlch corresponds to a decrease In the poiydlspersity index from 1.5 to about 1.1.
Field-flow fractionation (FFF) has been introduced as a 0003-2700/80/0352-2293$01 .OO/O
separation method for macromolecules and particules in the 1960s by Giddings. In FFF, external fields or gradients are used to distribute the solutes between the differential velocity regions of a laminar flow in a one-phase, ribbonlike channel, hence the name “one-phase chromatography” or “polarization chromatography” sometimes given to this technique (I). FFF can be divided into several subtechniques depending on the type of field. Up to now, four different fields or gradients have been used, namely: thermal gradient (thermal FFF), centrifugation (sedimentation FFF), electrical field (electrical FFF), and secondary flow through semipermeable membranes (flow FFF). Each subtechnique has its own range of applications more or less overlapping the range of other subtechniques so that the separation capability of FFF can cover almost 15 decades in molecular weight (mol wt) from oligomers (mol wt = io3) to particules of 10-100 pm. In thermal FFF, a temperature gradient is established between two parallel plates to generate solute migration near one wall (usually the cold one) by thermal diffusion (also called in liquids, the Soret effect). The importance of the thermal diffusion, combined with the magnitude of the ordinary dif0 1980 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 52, NO. 14, DECEMBER 1980
fusion, determines how far a given solute will extend in the fast streamlines of the laminar flow, which in turn, determines the solute average axial velocity. Separation of two or more solutes eventually occurs as they elute from the channel if their migration velocities differ sufficiently. In the past few years, thermal FFF has been established as a very powerful separation method for polystyrenes according to the molecular weight with unsurpassed fractionating power (5-20 times more selective than gel permeation chromatography), broad molecular weight range (3-4 decades), fast analysis time, and programming capabilities ( I ) . Recently, thermal FFF experiments have been conducted with samples of polyisoprene, polytetrahydrofuran, and poly(methy1 methacrylate) ( 2 ) . However, the lack of a satisfactory theory of liquid thermal diffusion has restricted the extension of applications of thermal FFF to other polymer types for two reasons. First of all, up to now, in order to obtain the molecular weight distribution curve of an unknown polymer from its elution spectrum, one needed a calibration curve correlating the elution volume with the molecular weight. In the absence of a theory of thermal diffusion, such a curve has to be obtained by observing the retention of several narrowly dispersed standards, which are, most often, not available. Fortunately, it is now possible to get the molecular weight distribution curves without having recourse to calibration curves by coupling the thermal FFF channel to two detectors in series, a classical differential refractometer and a newly developed low-angle laser light scattering photometer ( 3 ) . Second, since it is not possible to predict the thermal diffusion coefficient of a given polymer, the feasibility of its thermal FFF analysis and the operating conditions (solvent and temperature gradient) have to be experimentally determined. In the following, in order to evaluate the possibilities of extension of thermal FFF to polymers, the minimum values of the thermal diffusion parameters of polymers for successful thermal FFF analysis are established and compared with the data available in the literature. Then, the results of the thermal FFF separation of samples of poly(methy1 methacrylate) (PMMA) are shown.
THEORY AND LITERATURE SURVEY The temperature gradient established between the two parallel plates of the thermal FFF channel induces a transport of solute, usually toward the cold wall, with a nearly constant velocity, U. This transport leads to the agglomeration of the solute near the cold wall which is counteracted by the ordinary diffusion so that the flux density, J , of solute is written, for a dilute solution, as ( 4 ) dc dT J = -D- - IU~C- Dy-c
dx
dx
where D is the binary diffusion coefficient of the solutesolvent system, c the solute concentration, y the coefficient of thermal expansion of the solution, T the temperature, x the distance measured from the cold wall on the coordinate along which transport by thermal diffusion occurs (the x axis is perpendicular to the axis of the thermal FFF channel). The last term in the right-hand side of eq 1 accounts for the density variations in the channel. Generally, for polymers D y dT/dx is much smaller than IUI so that eq 1 becomes dc J = -D- - IU~C dx In steady-state conditions, for constant U and D , the solute becomes exponentially distributed across the channel
c = co exp(-x/I)
(3)
where c,, is the concentration at the cold wall, 1 the space
constant (characteristic height) of the solute zone given by
1 = D/lUl
(4)
Each solute is then characterized by a dimensionless parameter = l/w, where w is the channel thickness (distance between the hot and cold plates). The solute retention, measured by the retention factor R, which is the ratio of the solute axial migration velocity to the average flow velocity, is then a function of the basic parameter X and a dimensionless coefficient v, which accounts for the distortion of the parabolic flow profile due to the temperature dependence of the solvent viscosity (5, 6). Thus, R depends on the magnitude of the thermal diffusion of the solute, through X
D
A=-
l Ulw
Three parameters have been used to characterize this magnitude, namely, the thermal diffusion coefficient, DT (cgsu, cmz s-l "C-l), the Soret coefficient, s ("C-'), and the thermal diffusion factor, a (dimensionless). They are given by
s = DT/D
(7)
Here T i s the temperature of the center of gravity of the zone. From these definitions and eq 5, we can express the basic FFF parameter, A, as A =
D DT(dT/dx)w
Assuming a linear temperature gradient, dTldx = AT/w, where AT is the temperature drop between the hot and cold plates, we have A=--
D DTAT
--1 - -SAT
CY
T AT
It has been established that the resolution of two chromatographic or FFF zones, for a constant efficiency and selectivity, is proportional to the factor (1 - R ) , which means that, in order to get sufficient resolution, the retention must reach a certain level. In fact, in FFF, the resolution of a given pair of solutes increases faster than (1- R) as R decreases since both the plate number and the selectivity increase with decreasing R. Thus R must be lower than a maximal value R b , which, in FFF, corresponds to a maximum value for A: X < Xlim, since R is a monotonous function of X (1). Practically one can choose, in FFF, Rh = 0.75. The corresponding X value is Xlim = 0.2. From the relation 10, one can get the minimal values of the thermal diffusion parameters in order to have the required retention level a>-
T
h i mA
T
(11)
In most FFF experiments, the cold plate temperature is around 20 "C and a typical value for the temperature drop is 60 "C. Higher AT can be established when needed.
ANALYTICAL CHEMISTRY, VOL. 52, NO. 14, DECEMBER 1980
2295
Table I. Values of the Thermal Diffusion Parameters of Polymers Reported in the Literature tY Pe polystyrene
solvent various
value (in cgsu) DT = (0.5-2.0) X
poly(4-ethyl1-hexene) polyisobutylene poly(methy1 methacrylate)
isooctane DT = (2.0-20) x 10-7 octane DT = $2 t 0.4) x 10acetone D T = 3.0 X 10-' benzene s = 2.5 x l O - ' [ q ] + 0.17 x i f M = 105,s= 1 2 x 10-3a M = lo6,s = 6 0
ref 7
R
10-7
x
8 9 10
11
10-30
poly(vinyl cyclohex- D T = (1.0-1.2) x chloride) anone 10.l poly(viny1 toluene s = (12-32) x acetate ) for M = 104-10s poly(viny1water D T =(4.1-7.8) X pyrrolidone ) 10-9 a Calculated assuming [ q ] = (15.1 x 10-3),0.70. the intrinsic viscosity of the polymer.
12
13 14 [Q]
is
Thus, the temperature of the zone center of gravity is T = 305 K. With these values and taking A h = 0.2, one obtains for the inequalities 11-13 CY
> 25
(14)
> 83 x 10-3 oc-1 DT > D/12 (cgsu)
(15) (16)
As DT is almost independent of the molecular weight, M , and D is generally related to M through
D = aM-b
(17)
where the typical values of a and b are a = and b = 0.5, combination of expressions 13 and 17 gives the condition on M for sufficient retention.
With the above numerical values, one gets, assuming DT = 10-7 cm2 s-l OC-1
M > 7000
(19)
or for M = 100000
DT > 2.7
X
cm2 s-l
OC-l
(20)
I t is interesting to compare these minimal values with those reported in the literature on thermal diffusion of polymers. Some values are given in Table I. The most numerous data are given for polystyrenes. They have already been compared with data obtained from thermal FFF experiments (7). The data for other polymers are scarce and sometimes conflicting. Values obtained from different methods vary significantly. Nevertheless, the DT values are generally independent of the molecular weight, and i t appears, by comparing the data in Table I and the above required values of the thermal diffusion parameters, that, for most of the polymers, they are high enough to envision successful thermal FFF analyses. The DT value for poly(vinylpyrro1idone) in water is much lower than the value for other polymers. I t is a fact that most of the attempts to fractionate polymers in water by thermal diffusion, for instance, dextrans (I5,I6),poly(acry1ic acids) ( I 7 ) ,poly(vinyl alcohols) ( I O ) , and cellulose ( I O ) , have failed. Beside
20
4
O
60
A
A T ("C) Figure 1. Variation of the retention factor Rfor PMMA 75 and PMMA 160 with the temperature. The cold wall temperatures vary from 23 OC (AT = 10 OC) to 39 OC ( A T = 63 OC).
the polymers listed in Table I, fractionation by thermal diffusion has been observed in some instances like for poly(buty1 methacrylates) (18)and polychloroprenes (19,201 in benzene.
EXPERIMENTAL SECTION The FFF channel used in this study has been previously described (21). The channel space was cut into a Mylar sheet, 0.1 mm in thickness. This space was rectangular with tapered ends. The breadth was 2.05 cm and the void volume of this channel was 0.85 mL, the equivalent length of the channel, L , which is the length of a rectangular channel having the same breadth and volume as the actual one, was 41.6 cm. The solvent was dimethylformamide (DMF) obtained from Prolabo (Paris, France). The pumping system consisted of an Orlita DMP 15-15 pump (Orlita, Giessen, Germany) equipped with a regulator (22) and connected t o a capillary restrictor. A Waters Associates differential refractometer R401 was used as a detector. Two poly(methy1 methacrylate) (PMMA) samples, obtained from Polysciences (Warrington, PA), were used, namely, PMMA 75 ( M = 75000, M,/M, < 1.1) and PMMA 160 ( M = 160000, M J M , < 1.1). A 10-pL sample of 1-1.5% solutions of PMMA in DMF was introduced in a silicone-septum injector with a syringe (Hamilton,no. 701). The temperature of the top (hot) and bottom (cold) plates was controlled by means of a thermocouple (AOIP, Paris, France, Model PN 2). The temperature drop between the two plates was varied from 10 to 64 "C, with cold temperature of 23-38 " C .
RESULTS AND DISCUSSION Effect of the Temperature Drop. The variations of the retention factor R of the two PMMA samples with AT are shown on Figure 1. As expected, R decreases as AT increases. The basic FFF parameter h for each sample can be deduced from the experimental R value, once the Y coefficient is known, which reflects the deviation of the velocity profile from the parabolic one due to the temperature dependence of viscosity. This coefficient has been determined according to an established procedure ( 5 )from the values of the temperature drop AT, the cold wall temperature T c ,and the activation energy for viscosity, which for the DMF solvent has been taken equal to 2.272 kcal mol-' (15). h is plotted vs. l / A T on Figure 2. As expected from eq 10, the curves are straight lines through the origin. The dispersion of the experimental values comes mainly from the difficulty to measure with precision the centers of gravity of the zones on the fractogram, especially for the PMMA 75 peak which is less retained and interferes somewhat with the solvent peak. The slopes of the lines on
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ANALYTICAL CHEMISTRY, VOL. 52, NO.
14, DECEMBER 1980
Table 11. Determination of the Polydispersity Index parameter
PMMA 75
PMMA 160
R
0.618
ha
0.163
H
olyr mm dpn h / d In M d In Rfd In h
4.61
0.407 0,0910 23.2 0.5
P
1.14
x
0.5 0.607
0.817 1.50
a The u coefficients for PMMA 75 and PMMA 160 have been determined to equal - 0.133 ( A T = 37.0 'C, T, = 30.4 " C ) and -0.129 ( A T = 35.9 'C, T, = 30.4 "C), respectively. See ref 5.
1
,
1/ A T
Table 111. Determination of the Diffusion and Thermal Diffusion Coefficients
(T-')
parameter
Flgure 2. Variation of the basic FFF parameter X for PMMA 75 and PMMA 160 with l / A T . The X values are extracted from the R values of Figure 1 after a relationship corresponding to a third degree flow profile (see ref 6)with the values of the Y coefficients (see text) being determined after a procedure described in ref 5 .
c, s X
D , cmz s-' DT,cm2 s-' "C-'
PMMA 75
PMMA 160
4.33 0.0169 3.90 x 10-7 0.57 x lo-'
2.53 0.00738 2.91 x 0.81 x 10.'
of the sample and of the nonequilibrium, respectively. Hpoly is related to the polydispersity index, y, of the polymer (ratio of the weight average molecular weight to the number average molecular weight) by (23) 20
In Table 11, the values of the parameters used to determine are indicated. HWlyis the intercept of the plate height curve, X is deduced from the experimental R using the appropriate value of the v coefficient, which also allows the determination of d In R/d In X (6). The value of d In X/d In M has been assumed to be equal to 0.5, which is a typical value for random coil polymers since, in eq 10 and 17, DT can be assumed to be independent of M and b equal to 0.5. The y values obtained are 1.14 and 1.50 for PMMA 75 and PMMA 160, respectively. This last value is much higher than the one indicated by the manufacturer (p < 1.1).It is worth noting that, for the PMMA 160, this fi value (1.50) is the same as the one obtained from light scattering measurements ( 3 ) . The slope, C, of the plate height curve is used to determine the sample diffusion coefficient, D, according to the relationship y
.u
(mm/5)
Flgure 3. Plate height curves for PMMA 75 and PMMA 160. AT = OC (PMMA 75) and 36 OC (PMMA 160). T, = 30 OC.
37
Figure 2 allow us to determine the Soret coefficients of the polymers, since according to eq 10, we have
s = l/(XA7')
(21)
which give s = 0.146 OC-' and s = 0.279 O C - ' for the PMMA 7 5 and PMMA 160, respectively. The values are higher than the required value of 0.083 OC-' for s (relation 15) since, for the typical value of A T (60 "C), R for both samples is smaller than 0.75. Plate Height Curves. The plate height, H , is a measure of peak broadening in the separation channel. It is equal to L (ut/t&! where t R is the peak retention time and ut the standard deviation of the peak on the fractogram. The plate height curves of the two samples, H vs. u, where u is the average flow velocity, are plotted in Figure 3. They are obtained a t A T = 37 and 36 "C for PMMA 75 and 160, respectively. As previously observed for polystyrene samples (231, these curves are straight lines, the slope reflecting the contribution to peak broadening arising from the flow profile (nonequilibrium contribution) and the intercept being accounted for by the molecular weight inhomogeneity of the polymer samples (polydispersity contribution). Then, it can be written
H
=
Hpoly
+ Hnoneguil
(22)
HWlyand Hnonequil are the contributions of the polydispersity
D = xw2/C
(24)
x is a dimensionless peak broadening coefficient which is calculated from X and the coefficient Y (6),and w is the channel thickness. D values for the two PMMA samples are reported in Table I11 as well as values of the thermal diffusion coefficients DT which are easily determined from D and s after eq 7. DT values are seen to vary slightly from one sample to the other. However, in order to carefully study the dependence of DT on the molecular weight, the peak standard deviations have to be measured with a good precision, which cannot be achieved here with the classical methods valid only for gaussian peaks. Indeed, the bands on the fractogram have a shape relatively far away from the gaussian one, especially when the samples are largely polydisperse, as the one on Figure 4. Thermogravitational Experiments. The transport of polymers by thermal diffusion usually occurs in the direction of the cold plate. However there are some instances where transport toward the hot plate leads to negative Soret coefficients, like for dextran in low saline aqueous solutions (24) or poly(vinylpyrro1idone) in butanol or 2-propanol (25). For poly(methy1 methacrylates), there is some disagreement about
ANALYTICAL CHEMISTRY, VOL. 52,NO. 14,DECEMBER 1980 I
t
2297
I
PMMA 160
R 0.4-
I
'
L'
5
>
10
mtn
25
20
15
Figure 4. Fractogram of PMMA 160. A T = 34 "C. T, = 25 "C. Flow rate = 0.2 mL/min. The negative peak corresponds to the solvent (void volume). PMMA75
0.8L
0.2-
1 4
2
u (mm/s) Figure 6. Same as Figure 5, except that the sample is PMMA 160. Temperatures: A T = 39 "C,T, = 28 "C;A T = 68 OC, T, = 35 "C.
i
I
1
2
I
u (mm/s) Variation of R for PMMA 75 with the solvent velocity u in thermogravitational FFF at two temperature drops ( A T = 39 "C, T, = 29 "C, and A T = 69 "C, T, = 34 "C). Figure 5.
this direction of thermal diffusion sometimes reported to occur toward the hot region (26),while in other experiments, the opposite is true (10,11,27). In order to elucidate this problem, we have taken profit of the thermogravitational effect in the thermal FFF separator, when the channel is oriented vertically, which leads to the so-called thermogravitational FFF technique (28). Indeed, in this case, due to the upward movement of the lighter solution in contact with the hot plate and the downward movement of denser solution near the cold plate, there is a free convection in addition to the forced convection of the pumped flow of solvent. As a result of this combination, if the polymer is concentrated near the cold plate, the retention is higher ( R smaller) than the classical, horizontal thermal FFF retention for an upward solvent flow (injection a t the bottom of the channel) and lower for a downward solvent flow (injection a t the top). The opposite is true if the polymer is concentrated near the hot plate. This shift in retention is more pronounced when the amplitude of the free convection velocity profile relative to the forced convection one is higher, that is, for lower flow rate or average solvent velocity (28). As a consequence, by observing the variations of the retention factor R with the solvent velocity, definitive conclusions about the direction of migration by thermal diffusion can be drawn. These variations are shown in Figure 5 for the PMMA 75 sample and in Figure 6 for PMMA 160. Experiments were done at two temperature drops ( A T = 39 "C and A T = 68-69 "C), in each case, for both upward and downward solvent flows, indicated by corresponding upward or downward arrows on the curves. For the eight curves, R becomes constant a t higher solvent velocities since, then, the thermogravitational effect becomes relatively smaller. Of course, on each figure,
the high flow limiting R value is higher a t A T = 39 "C than a t A T = 68-69 "C and, for a given AT, this limiting value is smaller for PMMA 160 than for PMMA 75. According to eq 10 and 17, this is explained by the fact that the sample zone is more compressed near the wall (hence X is smaller) at higher temperature drops and/or for higher molecular weights. These high-flow limiting R values are the same as the values obtained in the horizontal configuration. In consequence, they should be the same for upward as well as downward flow. This is observed for most of the curves in Figures 5 and 6. The slight difference in these limiting R values at A T = 39 "C for PMMA 75 arises from slightly different actual A T as well as from the dispersion in the measure of R. As expected, on the curves of Figures 5 and 6, the shifts of R from the limiting values are seen to increase with decreasing solvent velocities. When the flow rate is reduced for all A T and samples, R increases for downward solvent flow and decreases for upward solvent flow. All of these observations converge to the conclusion that the poly(methy1 methacrylate) samples, a t least at low concentration, migrate by thermal diffusion in the direction of the cold temperatures. The variations of R with u are seen to persist at a higher velocity for A T = 68-69 "C than for A T = 39 "C. This shows, in agreement with the theory of the thermogravitational column, that the thermogravitational effect is more pronounced in the former case. Fractionation Experiments. In order to evaluate the separation power of thermal FFF for poly(methy1 methacrylates), 50 pL of a 0.867% solution of PMMA 160 was injected in the thermal FFF channel with the classical, horizontal configuration, and the temperature drop was set to 37 "C (T,= 32 "C). Five fractions of the effluent were collected directly a t the outlet of the channel between 11 and 17 min after the injection with a flow rate of 0.176 mL/min. The collected volume was 0.176 mL for each of the four first fractions and 0.352 mL for the fifth fraction. The solvent, DMF, in each fraction was evaporated in vacuo, and then the residual polymer was dissolved in 15 p L of fresh DMF and 10 pL of this solution was reinjected in the thermal FFF channel, at a flow rate of 0.141 mL/min (u = 1.15 mm/s). The retention volume for each fraction was measured as well as the plate height. Peak widths measured a t half-height and a t base line give similar plate height values. The results of the measurements are reported in Figure 7 which shows, in function of the volume of collection of the fractions Cy coordinate), the retention volumes of the reinjected
2298
ANALYTICAL CHEMISTRY, VOL. 52, NO. 14, DECEMBER 1980
-1
._.
L
30
ori XX
28
s
X
'\\\ 2 4
22
I
*r
2 0 1
R e t c n t t o n raturn
(mL)
dtht
I
x x
4.8
