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Solvent evaporation rates measured by gas chromatography
Progress in Organic Coatings,
15 (1987)
SOLVENT EVAPORATION CHROMATOGRAPHY REYNALDCi C. CASTELLS* CIDEPINT,
73 - 81
RATES MEASURED
73
BY GAS
and M6NICA L. CASELLA
52 entre 121 y 122,190O
La Plato (Argentina)
(Received July 14,1986)
summary A method to measure solvent evaporation rates under controlled conditions is described. Vapors generated within a thermostated glass cell are swept by a nitrogen current and periodically injected into a chromatographic column and detector by means of an automatic sampling valve. Solvents with evaporation rates equal to or lower than that of cyclohexane may be studied. As the evaporative cooling is negligible, the method offers a definite advantage over classical gravimetric techniques.
Introduction In addition to dissolving or dispersing the solid components of the formulation, adjusting its viscosity to values compatible with the chosen application method and contributing to the wetting of the substrate, the solvent must evaporate at a proper rate and under balanced conditions during each stage of the film-formation process. Film performance is highly dependent on solvent composition, and serious problems can result from too fast, too slow or a differential evaporation of the components in a solvent blend. Solvent evaporation from paint films is a process influenced both by internal factors such as vapor pressures, heats of vaporization, solution activity coefficients, thermal conductivities and diffusivities, and by external factors such as the air flow velocity and direction, relative humidity, the temperature of the film and its surroundings, and the exposed area. A thorough understanding of the mass and energy transport phenomena involved starts from a study of the seemingly simple evaporation of single solvents, follows with the study of solvent blends and concludes by looking into the drying of resin solutions. A detailed review covering these aspects has been written by Kornum [ 11.
*Author to whom all correspondence should be addressed. 0033-0655/87/$3.50
0 Elsevier Sequoia/Printed in The Netherlands
74
The evaporation rates of solvents are measured by gravimetric methods. The best known instrument is the Shell Thin Film Evaporometer; its prototype was first described in 1950 [2 ] and, after several improvements, it has evolved into its present manual and automatic recording versions utilized in the ANSI/ASTM Standard Test Method D3539-76. Saary and Goff [3] have described the Evapocorder built at the Chevron Research Company. Both instruments use an electrobalance to record the change of weight of the sample during its evaporation from a filter paper or a blotter, respectively. The relatively high air flow rates employed with both instruments (21 and 15 1 min-‘, respectively) not only determine conditions which are quite different from those prevailing during the drying of most paints, but also promote the evaporative cooling of the sample [ 41. Yoshida [5] has described a non-gravimetric method: the vapors produced in a small evaporation chamber are conducted to a thermal conductivity detector where a signal proportional to the solvent concentration in the drying gas is continuously generated. A differential curve is recorded with this apparatus, while an integral curve is given by gravimetric instruments. In the present paper, a differential discontinuous gas chromatographic technique using an automatic sample valve and a flame ionization detector (FID) is described. The FID sensitivity is several orders higher than that of the best electrobalance, thus enabling the measurement of the smaller evaporation rates occurring at lower gas flow rates; evaporative cooling is thus minimized, and the evaporation rates can be reliably referred to the working temperature. This paper describes the instrument, the calculation methods, the effects of a series of experimental parameters and the results for a group of single solvents of diverse volatilities.
Experimental Evaporation cell A 34145 conical ground glass joint was used to build the cell, a schematic diagram for which is shown in Fig. 1. Dry nitrogen, at a controlled temperature and flow rate, enters via tube a while b is a fritted disk of coarse porosity. Samples are applied by placing the tip of the needle of a 100 ~1 Hamilton microsyringe on to disk c, which was 2 cm in diameter and cut from a No. 31 Whatman Extra Thick filter paper. This paper disk was supported on a aluminum frame d, -and the syringe needle was inserted through a silicon gum septum f. The solvent vapors only come into contact with glass and metal surfaces, and leave the cell via tube g. Apparatus Measurements were carried out using a Hewlett-Packard 5880 A gas chromatograph with slightly modified flow lines, as shown in Fig. 2. Ana-
75
f
9
I/r e
1
fif
<< a
k-19
c
cm
-I
Fig. 1. Schematic diagram of the evaporation cell; see text for a description of the lettering employed.
a
Fig. 2. Instrument flow sheet; see text for a description of the lettering employed.
lytical grade nitrogen, previously dried by passing through a molecular sieve (Davidson 5A) trap and at a regulated pressure, entered at point a. R is the chromatograph pressure regulator and Fi and Fz are the carrier gas flow regulators. From F, the gas was directed to the Vako automatic sampling valve (V), and thence to the chromatographic column (C) and the detector (D); signals from the FID were fed to the recording and integrating terminal RI. After passing through Fz the gas was fed via copper coil S of l/8” O.D. and 2 m length into the evaporation cell C,; both the coil and the cell were immersed in a water bath. The mixture of gas and solvent vapor emerging from the cell was directed towards the sampling valve and passed through its loop L. Flow rates were measured at point b, using a soap-bubble buret, and ranged between 5 and 60 cm3 min- i in value. The cell temperature was maintained at 25 f 0.06 “C in all the experiments.
The sampling valve was operated with a 1 cm3 loop at 60 “C. The criterion employed in choosing the chromatographic column was the need to attain the separation of the vapors produced by a solvent blend in the minimum amount of time, so as to maximize the sampling frequency. A l/8” 0-D. stainless steel column, 0.5 m in length and packed with 2% OV 101 on Chromosorb W HP lOO/lZO, operated at 60 “C with a nitrogen flow rate of 20 cm3 min-’ was employed in this work; as only single solvents were studied, the sole objective of the column was to widen the peaks to prevent consequent errors in the integration of extremely narrow pulses. Procedure employed All the gas flow rates and temperatures were adjusted to the desired value, and a program operating the sampling valve at constant frequency was introduced into the chromatograph. Time intervals between injections were selected according to the rate of solvent evaporation, and ranged between 1.5 and 5.0 min. The sample, previously thermos~~d at 25 “C, was then introduced and the program commenced. The run was considered to have ended when no detector signal was produced by the injected pulses. The sample size was 100 ~1, the mass of each solvent delivered by the microsyringe being carefully determined by repeated weighing in a microbalance (*lo-$ g) under the same conditions as those prevailing during the application.
The greatest experimental d~ficulty in the development of the method has been the relation of the area under the peak arising from a vapor pulse to a definite mass of the solvent. Initially, the injection into the chromatograph by means of 1 ~1 syringes of dilute solutions of the specimen under study in a reasonable solvent was tried. The results obtained were highly reproducible, but there was no means of reliably estimating the volume injected, and hence the technique was only useful for comparative purposes. Saturation of a nitrogen current with the solvent at controlled temperatures was another possibility considered; this was discarded (a) because of the large volumes of high purity solvents required, (b) because of the extreme complication of the instrument flow diagram involved, and (c) because of the uncertainties associated with the efficiency of any saturator. Hence, a calibration method taking the total mass of solvent applied into the cell, W, as a reference was adopted. Let aj be the area under the peak generated by pulse number i, and II be the total number of pulses during a complete run, Le. up to the point where no solvent peak was produced when the sampling valve was operated. Since the loop volume is 1 cm3, ui is the area produced by the mass of solvent evaporating during l/FL min, where FL (cm3 min-r) is the flow rate of gas through the loop. Then the product ajFr, represents the peak area that the mass of solvent which evaporates during 1 min would produce had it been passed through
77
the FID, and the area under a plot of eilli;l against t, where t is the time elapsed from the beginning of the run, would represent the peak area A corresponding to W g of solvent. Since the time interval between injections, At, is kept constant during a given run, A may be obtain by numerical integration as
where ai is the area under the peak produced by the first pulse. The evaporation rate, u, at the instant of the injection of pulse number i during a given rnn will be given by
(2)
The quantity FL may be computed from Fo, the gas flow rate at the line outlet (point b, Fig. 2) throu~ the use of the equation (3) where p. and T,, are the pressure and temperature at point b, and pL and T,, are the corresponding values within the loop. Experimentally it was found that differences between pL and p. were less than 0.1% at F, = 5 cm3 min-’ and cu. 0.5% at F, = 40 cm3 min- ‘; the temperatures ratio, TL/To, was kept constant in all the runs. In any case, a knowledge of FL is not necessary to calculate u using eqn. (2).
Results and discussion The first experiments, conducted with n-hexane as the solvent, showed an abrupt increase in peak area for the first two or three pulses, followed by an almost exponential decrease; a region of constant peak area was not attainable even at flow rates as low as 2 cm3 min-‘. The calculation of the evaporation rate by means of eqn. (2) was not possible under these circumstances and for this reason the quantity aiF*, proportional to the solvent evaporation rate, has been plotted in Fig. 3 against the run time for several values of F,. The rate of evaporation of n-hexane was too high to be measured by this method. The experimental results obtained with n-octane have been plotted in Fig. 4. In this case a stationary state was rapidly reached, with the signal
50 t
(min)
Fig. 3. A plot of the quantity aiFo (PC cm3 min-I), proportional to the rate of evaporation, against the run time t (min) at several outlet flow rates F. (cm3 min-‘) for nhexane.
50
100
t (mln)
Fig. 4. A plot of the rate of evaporation of n-octane IJ (mg min-I) against the run time t (min) at several outlet flow rates F. (cm3 min-‘).
remaining constant for a period whose length decreased as the gas flow rate increased. A gradual drop in velocity occurs over the final drying stages, obviously as a result of solvent retention within the paper pores. For the purposes of the present report, the plateau value attained is considered as the rate of evaporation of a given solute under specified conditions.
79
In order to extend the scope of the method, solvents with volatilities intermediate between those of n-hexane and n-octane were also studied. According to tables published by the Shell Chemical Co. [6], n-hexane evaporates at a rate l.× faster than cyclohexane; experiments performed with this latter solvent resulted in constant velocity plateaux of 20 min and 10 min in length at flow rates of 5 and 10 cm3 mm-‘, respectively. Since five to 10 vapor samples can be injected during a run time of 10 min, it follows that solvents with volatilities similar to that of cyclohexane (or probably a little higher) determine the upper volatility limit for this method. A series of experiments has been conducted with the object of determining the importance of evaporative cooling. Two copper-con&&an thermocouples were introduced into the cell; one was inserted into the paper disk and the other was placed 1.5 cm above it, in the gas current. Both thermocouples possessed a common wire, the EMF generated being measured by means of a Hewlett-Packard 3456 A digital voltmeter. Using n-hexane as the solvent, temperature differences as high as 5 “C were detected at flow rates of 40 cm3 min-‘; with n-octane, on the other hand, the signal did not exceed the background noise of the instrument even at gas flow rates as high as 60 cm3 min- ‘. The cooling effect is therefore quite small for solvents that evaporate under steady-state conditions, and the measured rates of evaporation can be referred to the cell temperature. In Fig. 5 the evaporation rate of a selected group of solvents has been plotted against the outlet gas flow rate. Some of the experimental points for these solvents, particularly those for n-octane and n-butyl acetate, correspond to runs performed over intervals of several weeks and under different FID conditions. Despite this fact, the reproducibility of the method is very good. The dependence of the rate of evaporation on the flow rate may be expressed by equations of the type u = kl*Fkz, with kz ranging between 0.6 and 0.8. Yoshida [5], who worked at flow rates which were appreciably higher, found a linear relationship between u and F,. Chemical engineering correlations [7] predict that lez is equal to 0.5 at low flow rates and 0.8 at high flow rates; these correlations, however, are hardly valid for a plate of the size employed by us and at the Reynolds number region covered by our experiments. Since evaporation rates are very sensitive to changes in the measurement conditions, it is usual to tabulate the rates of evaporation of solvents relative to that of n-butyl acetate, measured with the same instrument and under identical conditions. The results for the relative evaporation rates (RER) obtained in the present work at several flow rates have been collected in Table 1; values for a given solvent differ by less than 5%, and do not follow any definite trend. Weight-based RER values calculated by Rocklin [ 81 from the volume-based RER values published by the Shell Chemical Co. [6] have also been included. Figure 6 is a plot of the mean of the RER values obtained in this work against the corresponding values measured in the Shell Thin Film Evaporometer. Both sets of data coincide at low RER, but become increasingly divergent as the solvent volatility increases. This
80
Fig. 5. A plot of the evaporation rate u (mg min-‘) for several solvents against the outlet flow rate F0 (cm3 min-‘). (a) Cyclohexanone; (b) n-butyl acetate; (c) n-octane; (d) toluene; and (e) n-heptane. TABLE 1 Weight-based relative evaporation rates at several flow rates Solvent
cyclohexane methylethylketone n-heptane toluene methylisobutylketone n-octane n-butyl acetate n-butanol n-nonane cyclohexanone
Flow rate (cm3 min-l) 5
10
20
6.67 5.43 3.59 2.18
6.48 5.38 3.46 2.14 1.65 1.30 1.00
6.80
1.22 1.00
0.33
40
60
3.49 2.18 1.74 1.28 1.00 0.42 0.47
2.23 1.74 1.28 1.00 0.43 0.45
1.28 1.00
0.32
0.31
0.29
Quoted in ref. 8 3.65 3.53 2.75 1.93 1.51 1.15 1.00 0.41 0.32
effect may be explained by the intense evaporative cooling suffered by solvents in the instrument developed at Shell; their data, therefore, correspond to evaporation rates measured at uncertain and markedly lower temperatures than 25 “C.
81
RER,
Shell
Fig. 6. A plot of the weight-based relative evaporation rates (RER) measured in this work against the corresponding values quoted in ref. 8.
Acknowledgment This work was sponsored by the Consejo National de Investigaciones Cientificas y Thcnicas (CONICET) and by the Cornis& de Investigaciones Cientificas de la Provincia de Buenos Aires (CIC). References 1 2 3 4 5 6 7
L. 0. Kornum, J. Oil Colour Chem. Aseoc., 63 (1980) 103. R. J. Curtis, J. R. Scheibli and T. F. Bradley, Anal. Chem., 22 (1950) 538. Z. Saary and P. L. Goff, J. Paint Technol., 45 (1973) 45. A. L. Rocklin and D. C. Bonner, J. Coat. Technol., 52 (1980) 27. T. Yoshida,Prog. Org. Coat., 1 (1972) 73. Shell Chemical Co., Solvent Properties Chart, SC:48-75 (1975). C. J. Geankoplis, Transport Processes and Unit Operations, Allyn and Bacon, New York, 1975, Chaps. 3 and 7. 8 A. L. Rocklin, J. Gout. Technol., 48 (1976) 45.
15 (1987)
SOLVENT EVAPORATION CHROMATOGRAPHY REYNALDCi C. CASTELLS* CIDEPINT,
73 - 81
RATES MEASURED
73
BY GAS
and M6NICA L. CASELLA
52 entre 121 y 122,190O
La Plato (Argentina)
(Received July 14,1986)
summary A method to measure solvent evaporation rates under controlled conditions is described. Vapors generated within a thermostated glass cell are swept by a nitrogen current and periodically injected into a chromatographic column and detector by means of an automatic sampling valve. Solvents with evaporation rates equal to or lower than that of cyclohexane may be studied. As the evaporative cooling is negligible, the method offers a definite advantage over classical gravimetric techniques.
Introduction In addition to dissolving or dispersing the solid components of the formulation, adjusting its viscosity to values compatible with the chosen application method and contributing to the wetting of the substrate, the solvent must evaporate at a proper rate and under balanced conditions during each stage of the film-formation process. Film performance is highly dependent on solvent composition, and serious problems can result from too fast, too slow or a differential evaporation of the components in a solvent blend. Solvent evaporation from paint films is a process influenced both by internal factors such as vapor pressures, heats of vaporization, solution activity coefficients, thermal conductivities and diffusivities, and by external factors such as the air flow velocity and direction, relative humidity, the temperature of the film and its surroundings, and the exposed area. A thorough understanding of the mass and energy transport phenomena involved starts from a study of the seemingly simple evaporation of single solvents, follows with the study of solvent blends and concludes by looking into the drying of resin solutions. A detailed review covering these aspects has been written by Kornum [ 11.
*Author to whom all correspondence should be addressed. 0033-0655/87/$3.50
0 Elsevier Sequoia/Printed in The Netherlands
74
The evaporation rates of solvents are measured by gravimetric methods. The best known instrument is the Shell Thin Film Evaporometer; its prototype was first described in 1950 [2 ] and, after several improvements, it has evolved into its present manual and automatic recording versions utilized in the ANSI/ASTM Standard Test Method D3539-76. Saary and Goff [3] have described the Evapocorder built at the Chevron Research Company. Both instruments use an electrobalance to record the change of weight of the sample during its evaporation from a filter paper or a blotter, respectively. The relatively high air flow rates employed with both instruments (21 and 15 1 min-‘, respectively) not only determine conditions which are quite different from those prevailing during the drying of most paints, but also promote the evaporative cooling of the sample [ 41. Yoshida [5] has described a non-gravimetric method: the vapors produced in a small evaporation chamber are conducted to a thermal conductivity detector where a signal proportional to the solvent concentration in the drying gas is continuously generated. A differential curve is recorded with this apparatus, while an integral curve is given by gravimetric instruments. In the present paper, a differential discontinuous gas chromatographic technique using an automatic sample valve and a flame ionization detector (FID) is described. The FID sensitivity is several orders higher than that of the best electrobalance, thus enabling the measurement of the smaller evaporation rates occurring at lower gas flow rates; evaporative cooling is thus minimized, and the evaporation rates can be reliably referred to the working temperature. This paper describes the instrument, the calculation methods, the effects of a series of experimental parameters and the results for a group of single solvents of diverse volatilities.
Experimental Evaporation cell A 34145 conical ground glass joint was used to build the cell, a schematic diagram for which is shown in Fig. 1. Dry nitrogen, at a controlled temperature and flow rate, enters via tube a while b is a fritted disk of coarse porosity. Samples are applied by placing the tip of the needle of a 100 ~1 Hamilton microsyringe on to disk c, which was 2 cm in diameter and cut from a No. 31 Whatman Extra Thick filter paper. This paper disk was supported on a aluminum frame d, -and the syringe needle was inserted through a silicon gum septum f. The solvent vapors only come into contact with glass and metal surfaces, and leave the cell via tube g. Apparatus Measurements were carried out using a Hewlett-Packard 5880 A gas chromatograph with slightly modified flow lines, as shown in Fig. 2. Ana-
75
f
9
I/r e
1
fif
<< a
k-19
c
cm
-I
Fig. 1. Schematic diagram of the evaporation cell; see text for a description of the lettering employed.
a
Fig. 2. Instrument flow sheet; see text for a description of the lettering employed.
lytical grade nitrogen, previously dried by passing through a molecular sieve (Davidson 5A) trap and at a regulated pressure, entered at point a. R is the chromatograph pressure regulator and Fi and Fz are the carrier gas flow regulators. From F, the gas was directed to the Vako automatic sampling valve (V), and thence to the chromatographic column (C) and the detector (D); signals from the FID were fed to the recording and integrating terminal RI. After passing through Fz the gas was fed via copper coil S of l/8” O.D. and 2 m length into the evaporation cell C,; both the coil and the cell were immersed in a water bath. The mixture of gas and solvent vapor emerging from the cell was directed towards the sampling valve and passed through its loop L. Flow rates were measured at point b, using a soap-bubble buret, and ranged between 5 and 60 cm3 min- i in value. The cell temperature was maintained at 25 f 0.06 “C in all the experiments.
The sampling valve was operated with a 1 cm3 loop at 60 “C. The criterion employed in choosing the chromatographic column was the need to attain the separation of the vapors produced by a solvent blend in the minimum amount of time, so as to maximize the sampling frequency. A l/8” 0-D. stainless steel column, 0.5 m in length and packed with 2% OV 101 on Chromosorb W HP lOO/lZO, operated at 60 “C with a nitrogen flow rate of 20 cm3 min-’ was employed in this work; as only single solvents were studied, the sole objective of the column was to widen the peaks to prevent consequent errors in the integration of extremely narrow pulses. Procedure employed All the gas flow rates and temperatures were adjusted to the desired value, and a program operating the sampling valve at constant frequency was introduced into the chromatograph. Time intervals between injections were selected according to the rate of solvent evaporation, and ranged between 1.5 and 5.0 min. The sample, previously thermos~~d at 25 “C, was then introduced and the program commenced. The run was considered to have ended when no detector signal was produced by the injected pulses. The sample size was 100 ~1, the mass of each solvent delivered by the microsyringe being carefully determined by repeated weighing in a microbalance (*lo-$ g) under the same conditions as those prevailing during the application.
The greatest experimental d~ficulty in the development of the method has been the relation of the area under the peak arising from a vapor pulse to a definite mass of the solvent. Initially, the injection into the chromatograph by means of 1 ~1 syringes of dilute solutions of the specimen under study in a reasonable solvent was tried. The results obtained were highly reproducible, but there was no means of reliably estimating the volume injected, and hence the technique was only useful for comparative purposes. Saturation of a nitrogen current with the solvent at controlled temperatures was another possibility considered; this was discarded (a) because of the large volumes of high purity solvents required, (b) because of the extreme complication of the instrument flow diagram involved, and (c) because of the uncertainties associated with the efficiency of any saturator. Hence, a calibration method taking the total mass of solvent applied into the cell, W, as a reference was adopted. Let aj be the area under the peak generated by pulse number i, and II be the total number of pulses during a complete run, Le. up to the point where no solvent peak was produced when the sampling valve was operated. Since the loop volume is 1 cm3, ui is the area produced by the mass of solvent evaporating during l/FL min, where FL (cm3 min-r) is the flow rate of gas through the loop. Then the product ajFr, represents the peak area that the mass of solvent which evaporates during 1 min would produce had it been passed through
77
the FID, and the area under a plot of eilli;l against t, where t is the time elapsed from the beginning of the run, would represent the peak area A corresponding to W g of solvent. Since the time interval between injections, At, is kept constant during a given run, A may be obtain by numerical integration as
where ai is the area under the peak produced by the first pulse. The evaporation rate, u, at the instant of the injection of pulse number i during a given rnn will be given by
(2)
The quantity FL may be computed from Fo, the gas flow rate at the line outlet (point b, Fig. 2) throu~ the use of the equation (3) where p. and T,, are the pressure and temperature at point b, and pL and T,, are the corresponding values within the loop. Experimentally it was found that differences between pL and p. were less than 0.1% at F, = 5 cm3 min-’ and cu. 0.5% at F, = 40 cm3 min- ‘; the temperatures ratio, TL/To, was kept constant in all the runs. In any case, a knowledge of FL is not necessary to calculate u using eqn. (2).
Results and discussion The first experiments, conducted with n-hexane as the solvent, showed an abrupt increase in peak area for the first two or three pulses, followed by an almost exponential decrease; a region of constant peak area was not attainable even at flow rates as low as 2 cm3 min-‘. The calculation of the evaporation rate by means of eqn. (2) was not possible under these circumstances and for this reason the quantity aiF*, proportional to the solvent evaporation rate, has been plotted in Fig. 3 against the run time for several values of F,. The rate of evaporation of n-hexane was too high to be measured by this method. The experimental results obtained with n-octane have been plotted in Fig. 4. In this case a stationary state was rapidly reached, with the signal
50 t
(min)
Fig. 3. A plot of the quantity aiFo (PC cm3 min-I), proportional to the rate of evaporation, against the run time t (min) at several outlet flow rates F. (cm3 min-‘) for nhexane.
50
100
t (mln)
Fig. 4. A plot of the rate of evaporation of n-octane IJ (mg min-I) against the run time t (min) at several outlet flow rates F. (cm3 min-‘).
remaining constant for a period whose length decreased as the gas flow rate increased. A gradual drop in velocity occurs over the final drying stages, obviously as a result of solvent retention within the paper pores. For the purposes of the present report, the plateau value attained is considered as the rate of evaporation of a given solute under specified conditions.
79
In order to extend the scope of the method, solvents with volatilities intermediate between those of n-hexane and n-octane were also studied. According to tables published by the Shell Chemical Co. [6], n-hexane evaporates at a rate l.× faster than cyclohexane; experiments performed with this latter solvent resulted in constant velocity plateaux of 20 min and 10 min in length at flow rates of 5 and 10 cm3 mm-‘, respectively. Since five to 10 vapor samples can be injected during a run time of 10 min, it follows that solvents with volatilities similar to that of cyclohexane (or probably a little higher) determine the upper volatility limit for this method. A series of experiments has been conducted with the object of determining the importance of evaporative cooling. Two copper-con&&an thermocouples were introduced into the cell; one was inserted into the paper disk and the other was placed 1.5 cm above it, in the gas current. Both thermocouples possessed a common wire, the EMF generated being measured by means of a Hewlett-Packard 3456 A digital voltmeter. Using n-hexane as the solvent, temperature differences as high as 5 “C were detected at flow rates of 40 cm3 min-‘; with n-octane, on the other hand, the signal did not exceed the background noise of the instrument even at gas flow rates as high as 60 cm3 min- ‘. The cooling effect is therefore quite small for solvents that evaporate under steady-state conditions, and the measured rates of evaporation can be referred to the cell temperature. In Fig. 5 the evaporation rate of a selected group of solvents has been plotted against the outlet gas flow rate. Some of the experimental points for these solvents, particularly those for n-octane and n-butyl acetate, correspond to runs performed over intervals of several weeks and under different FID conditions. Despite this fact, the reproducibility of the method is very good. The dependence of the rate of evaporation on the flow rate may be expressed by equations of the type u = kl*Fkz, with kz ranging between 0.6 and 0.8. Yoshida [5], who worked at flow rates which were appreciably higher, found a linear relationship between u and F,. Chemical engineering correlations [7] predict that lez is equal to 0.5 at low flow rates and 0.8 at high flow rates; these correlations, however, are hardly valid for a plate of the size employed by us and at the Reynolds number region covered by our experiments. Since evaporation rates are very sensitive to changes in the measurement conditions, it is usual to tabulate the rates of evaporation of solvents relative to that of n-butyl acetate, measured with the same instrument and under identical conditions. The results for the relative evaporation rates (RER) obtained in the present work at several flow rates have been collected in Table 1; values for a given solvent differ by less than 5%, and do not follow any definite trend. Weight-based RER values calculated by Rocklin [ 81 from the volume-based RER values published by the Shell Chemical Co. [6] have also been included. Figure 6 is a plot of the mean of the RER values obtained in this work against the corresponding values measured in the Shell Thin Film Evaporometer. Both sets of data coincide at low RER, but become increasingly divergent as the solvent volatility increases. This
80
Fig. 5. A plot of the evaporation rate u (mg min-‘) for several solvents against the outlet flow rate F0 (cm3 min-‘). (a) Cyclohexanone; (b) n-butyl acetate; (c) n-octane; (d) toluene; and (e) n-heptane. TABLE 1 Weight-based relative evaporation rates at several flow rates Solvent
cyclohexane methylethylketone n-heptane toluene methylisobutylketone n-octane n-butyl acetate n-butanol n-nonane cyclohexanone
Flow rate (cm3 min-l) 5
10
20
6.67 5.43 3.59 2.18
6.48 5.38 3.46 2.14 1.65 1.30 1.00
6.80
1.22 1.00
0.33
40
60
3.49 2.18 1.74 1.28 1.00 0.42 0.47
2.23 1.74 1.28 1.00 0.43 0.45
1.28 1.00
0.32
0.31
0.29
Quoted in ref. 8 3.65 3.53 2.75 1.93 1.51 1.15 1.00 0.41 0.32
effect may be explained by the intense evaporative cooling suffered by solvents in the instrument developed at Shell; their data, therefore, correspond to evaporation rates measured at uncertain and markedly lower temperatures than 25 “C.
81
RER,
Shell
Fig. 6. A plot of the weight-based relative evaporation rates (RER) measured in this work against the corresponding values quoted in ref. 8.
Acknowledgment This work was sponsored by the Consejo National de Investigaciones Cientificas y Thcnicas (CONICET) and by the Cornis& de Investigaciones Cientificas de la Provincia de Buenos Aires (CIC). References 1 2 3 4 5 6 7
L. 0. Kornum, J. Oil Colour Chem. Aseoc., 63 (1980) 103. R. J. Curtis, J. R. Scheibli and T. F. Bradley, Anal. Chem., 22 (1950) 538. Z. Saary and P. L. Goff, J. Paint Technol., 45 (1973) 45. A. L. Rocklin and D. C. Bonner, J. Coat. Technol., 52 (1980) 27. T. Yoshida,Prog. Org. Coat., 1 (1972) 73. Shell Chemical Co., Solvent Properties Chart, SC:48-75 (1975). C. J. Geankoplis, Transport Processes and Unit Operations, Allyn and Bacon, New York, 1975, Chaps. 3 and 7. 8 A. L. Rocklin, J. Gout. Technol., 48 (1976) 45.