704
ANALYTICAL CHEMISTRY, VOL 50, NO. 6, MAY 1978
LITERATURE CITED
suggest that both the anion and the alkylating agent are present in the same phase. It is therefore likely that the phenolate anion and the ethyl bromide or ethyl iodide, under our conditions, must also be present in the same phase as the anion, but in these instances, the reaction does not occur. This indicates that the counterion may be more than a simple phase transfer agent (13) and may play a more complex role in the mechanism of action in phase transfer catalysis or extractive alkylation. T h e lack of reactivity of the carboxylate anion can have several explanations. I t is possible that the carboxylate anions do not enter the same phase as the pentafluorobenzyl bromide or they may enter the same phase but may be solvated to a different extent than the phenolate anions. When phenols are determined in physiological matrix via nonspecific derivatization methods, it is necessary to separate these analytes from other organic acids. K i t h classical procedures, this would require a t least one extraction prior t o t h e derivatization step. Even if t h e specific pentafluorobenzylation of phenols and acids reported by Davis (7) mere to be used, the analytes would still have to be isolated from the matrix, thus requiring an extraction step with subsequent evaporation of solLent. Furthermore, the derivatization step itself would require additional workup. The specificity of the present procedure suggests the possibility that phenols can be directly and specifically extracted and derivatized from physiological matrix in one step. The present data also suggest that bs controlling the reaction conditions, different phenols can be extracted and derivatized.
0. Gyllenhaal, H. Brotel, and P. Hartvig, J . Chromatogr.. 129. 295-302 ( 1976), H. Brotell. H. Ehrsson, and 0. Gyllenhaal, J . Chromafogr , 78, 294-301 (1973). H. Ehrsson, Acta Pharm. Suec., 8, 113-118 (1971). A . Arbin and P. Edlund, Acta Pharm. Suec., 12, 119-126 (1975). A. J. F. Wickramasinghe and R. S. Shaw, Biochem. J . , 141, 179-187 (1974). F. A. Fitzpatrick, M. A. Wynalda, and D. G . Kaiser, Anal. Cbem.. 49, 1032-1035 (1977). B. Davis, Anal. Chem., 49, 832-834 (1977). J, Dockx, Synthesis, 441-456 (1973). R. A. Jones, Aldrichim. Acta, 9 (3), 35-45 (1976). E. V. Dehmlow, Agnew. Chem. Int. Ed., 13, 170-179 (1974). C. M. Starks, J . A m . Chem. Soc., 93, 195-199 (1971). C. M. Starks and R. M. Ownes, J . A m . Chem. Soc., 95, 3613-3617 (1973). A. W. Herriott and D. Picker, J . Am. Chem. Soc.. 97 2347-2349 (1975). J. E. Gordon and R. E. Kutina. J. Am. Chem. SOC.,99, 3903-3909 (1977) B. Lindstrom and M. Molander, J . Chromatogr , 101, 219-221 (1974). B. Lindstrom and M. Molander. J . Chromatogr , 114, 459-462 (1975). J. A. F. de Silva and I. Berkersky. J . Chromatogr., 99, 447-460 (1974). H. Ehrsson and A. Tiliy, Ana/. Lett.. 6. 197-210 (1973). J. M. Rosenfeld and V. Taguchi, Anal. Chem., 48, 726-728 (1976). J. M. Rosenfeld, V. Y. Taguchi. B. L. Hillcoat, and M. Kawai, Anal. Chem., 49, 725-727 (1977). J. Rosenfeld, Anal. Lett., 10 (12), 917 (1977). J. Rosenfeld, B. Bowins, J. Roberts, J. Perkins. and A. S. Macpherson, Anal. Chem., 46, 2232-2234 (1974). J. D. Daley, J. M. Rosenfeld, and E. V. Younglai, Steroids, 27, 481-492 (1976). The Merck Index, 8th, Merck & Co., 1968, p 422.
RECEIVED November 18, 197'7. Accepted January 23, 1978. This work was supported by the Medical Research Council of Canada by Grant MRC-GOO7 and by a grant from IBM of Canada.
Influence of the Sample Position in Compensated Scanning Calorimeters Stanislaw L. Randzio' and Stig Sunner" Thermochemistry Laboratory, Chemical Center, University of Lund, S-220 07 Lund, Sweden
because this technique is. in principle, better adapted for calorimetric measurements of good accuracy. In DSC measurements. large quantities of experimental data can easily be collected using an automatic data acquisition system. However, the interpretation of such experimental data is not straightforward which is apparent from the literature uhere one can find considerable discrepancies among results reported (1-3). Many papers are devoted to an analysis of possible causes of these discrepancies. Some papers deal with heat exchange conditions between the calorimetric cell and the sample (3-5). In others the authors try to make a general theory of scanning calorimetric measurements ( 6 , 71, analyse the baseline problem (8-10). study the influence of particular instrumental properties ( 7 , 1 1 , 12) and the kinetics of transitions investigated (13). In the papers cited above, man! suggestions have been put forward on how to correct the obtained experimental information in order to get more precise results referring to the chemical and/ or physical process(es1 studied. Some of the papers deal with the construction of the calorimetric cell ( 1 1 , 14). Main suggestions are to design a system with as small a heat capacity as possible and with a maximal heat transfer between the sample and the calorimetric cell. However, it is evidently not always possible to
A theoretical analysis is made of the influence of sample position on the measured signal in compensated scanning calorimeters (DSC). Equations are derived and block diagrams are constructed for two configurations of the calorimetric cell. It is shown that the signal measured is equal to a thermal signal generated in the sample only under the conditions that the investigated sample is inside the compensation feedback loop and the gain of the amplifier is sufficiently high. When the sample is outside the feedback loop, the signal measured depends also on the time constant of the sample and the heating rate, even if the gain of the amplifier is very high.
Differential scanning calorimetry (DSC) has found broad quantitative applications in measurements of chemical purity, heat capacities, enthalpies and temperatures of transitions. kinetics of condensed phase reactions, etc. Of the two scanning calorimeter techniques available today, heat flux DSC and power compensated DSC, the latter is worth special attention 'On leave from the Institute of Physical Chemistry, Polish Academy of Sciences, PL-01-224 Warsaw 49, Poland. 0003-2700/78/0350-0704$01 O O / O
c'
1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO. 6, M A Y 1978
705
Figure 2. Block diagram of a calorimeter, where the sample is inside the feedback loop
Figure 1. Model configuration of a calorimetric cell, where the sample is inside the feedback IOOD
realize these suggestion5 in practice, especially as the reproducibility of the heat exchange conditions may vary froin experiment to experiment. This paper presents a theoretical analysis of the influence of sample position on the quality of dynamic measurements performed with a compensated DSC instrument LVe will devote ourselves to the problem of the sample position Rith respect to the temperature sensor. heater, and surroundings. T h e study can possibly help to define some of the problems behind observed discrepancies more precisely than has been done before and to give some leads to a better design of calorimetric cells.
ANALYSIS OF A CONFIGURATION WHERE THE SAMPLE IS INSIDE THE FEEDBACK LOOP Let us assume that the power q x is generated in the sample. The sample is located somewhere in the calorimetric cell. With these assumptions we can distinguish two extreme configurations: (1) the sample is inside the compensation feedback loop: (2) the sample is outside the compensation feedback loop. The first arrangement is represented by the diagram in Figure 1. In this model, all power generated in the heater is transfered to the sample, which exchanges heat only with the calorimetric cell. T h e sensor measures the cell temperature. This kind of calorimetric cell can be described by the following equations:
d T s ( t ) + a S c [ T , ( t -) T c ( t ) ]= q , ( t )
dt
+ K[T,(t)
represents the power balance in the calorimetric cell. The heat capacity of the calorimetric cell is C,.il,, is the heat exchange coefficient between the calorimetric cell and the surroundings (W‘ K-’) at temperature T,(t). Equation 3 is a definition of the measured signal q , in LV
qrn(t) = K [ T R ( ~ )T c ( t ) l T h e concept of time constants of the sample orimetric cell T , may be introduced as:
CC and r c =
a,,
where the terms f(T,) and f ( T R )depend on the surroundings and reference temperatures, respectively. Applying Laplace transform, Equations 1. 2 , and 3 can be presented as a block diagram, Figure 2 ( 5 , 15, 16) showing the sample within the compensation feedback loop. If we assume that the temperature is a linear function of time, then it is possible to change variables in Equation 5 and obtain the following form
where b is a heating rate (KSI). Because in this paper we devote ourselves to the analysis of rhe sample position. we omitted the terms / ( T o )and f ( T R ) . R h e n using the relation between the heating rate b, power q , and heat capacity c
q ( T )=
d T c ( t ) + a c , [ T c ( t )- T , ( t ) ]- ct,,[T,(t) d t
-
(5)
-
which represents the power balance in the sample. The heat capacity of the sample is C,, T,(t) and T,(t) are the temperatures of the sample and calorimetric cell, respectively. is the heat exchange coefficient between the sample and the calorimetric cell in \V K-’. q,(t) is the power generated by the sample, K is the amplifier gain in St’ K-’, T R ( t )is the reference temperature.
Ts=
In order to eliminate T,and T,, we differentiate Equation 2. and then introduce both its forms together with Equation 3 into Equation 1. T h e following equation is obtained:
CC Qco +
as,
(3) T~
and cal-
(4)
d Q dT -= cb dT d t
~
(7)
the Equation 6 can be rewritten in the following form:
From the above equations it follows directly that in the calorimetric configuration where the sample is inside the compensation feedback loop, the influence of the time constants of the sample and of the calorimetric cell itself on the measured signal is reduced or eliminated. This is so because the second term of Equations 6 and 8 approaches zero if the gain K is sufficiently high. At the same time, it is shown directly that the influence of the heat exchange coefficients is very much reduced also.
ANALYSIS OF A CONFIGURATION WHERE THE SAMPLE IS OUTSIDE THE FEEDBACK LOOP T h e second configuration is presented in Figure 3. All power generated in the heater is transferred to the calorimetric cell and then partially transferred to the sample and partially to the surroundings. Power q x generated in the sample is
706
ANALYTICAL CHEMISTRY, VOL. 50, NO. 6, MAY 1978
Figure 3. Model configuration of a calorimetric cell, where the sample is outside the feedback loop
partially transferred to the calorimetric cell and partially to the surroundings. As for the previous configuration. power balance equations can be written. Equation 9 presents power balance in the sample:
C
Figure 4. Block diagram of a calorimeter, where the sample is outside the feedback loop
By using Equation 7 we can transform Equation 13 into a heat capacity function
- C , ( T ) = C,(T)
(1 +
-
+
asc
+ aso7sbdCm(T) I dT
CY sc
d T s ( t ) + a s c [ T s ( t-) T c ( t ) ]+ a s o [ T s ( t-) T o ( t ) ]= s
d
t
(9) where a,, is the heat exchange coefficient between the sample and the surrounding in LV K-’. Equation 10 gives the power balance in the calorimetric cell:
C
d T c ( t ) + a c o [ T c ( t-) T , ( t ) ] - a s c [ T s ( t-) T c ( t ) ]= c
d
t
As before, the measured signal q, is defined by Equation 3. T h e time constants of the sample and the calorimetric cell are now defined by
(11) Proceeding as before to eliminate both T , and T,, we differentiate Equation 10 and introduce both its forms together with Equation 3 into Equation 9. T h e following equation is then obtained:
The equivalent block diagram is presented in Figure 4 showing the sample outside the compensation feedback loop. If we again assume that the temperature is a linear function of time we can change variables in Equation 1 2 and obtain
(14) We can see that in the configuration of the compensated scanning calorimeter cell where the sample is outside the feedback loop, the recorded signal depends not only on the signal generated in the sample but also on t h e heating rate and the time constant of the sample, even if the gain K of the amplifier is very high. We can also notice from Equations 12, 13, and 14 that also in adiabatic scanning calorimeters where the heat exchange between the sample and surroundings is by definition negligible (aso= 0), the second term in these equations does not disappear. It means that if the coefficient N,, of heat exchange between the calorimetric cell and the sample has a limited balue, the heat capacity recorded by a compensated adiabatic scanning calorimeter may depend on the heating rate and the time constant of the sample.
CONCLUSIONS Among known compensated scanning calorimeters, one can find some instruments which have arrangements of calorimetric cells and sample holders very similar to the models presented in this paper. Others have arrangements which can be classified somewhere between the two models. I t follows from the equations derived that the investigated sample should be located inside the compensation feedback loop. This presents some difficult technical problems to the designer of a simple, compact, and easily accessible calorimetric cell. And there are some other problems arising: a sample being in a feedback loop may increase the phase shift of the system to such an extent that the system can start to oscillate or even be unstable if usage is made of a proportional amplifier with a high gain. Fortunately, this tendency can be suppressed or even eliminated by using compensation networks ( 1 6 ) . In some compensated scanning calorimeters, the situation can be improved even if the sample is outside the feedback loop. It follows from Equations 13 and 14 that the time constant of the sample should be as small as possible. This can be reached either by decreasing its mass. or by increasing the heat exchange between the sample and the cell, Le., the temperature sensor and the heater, which are in the feedback loop. Heat exchange can be improved for example by increasing the active surface of heat transfer. Some improvements can be obtained by locating t h e heater in a
ANALYTICAL CHEMISTRY, VOL. 50, NO. 6, MAY 1978
po4tion very close t o the sample holder ( 1 4 ) . I n a configuration, where the sample is outside the feedback loop, a calibration of the instrument using a standard substance can be a delicate problem. As follows from Equations 13 and 14 the measured signal is inf'luenced by both the heatiiig rate b and the time constant of the sample 7,. So it is not enoiigh t o use only ihe same heating rate during calihration and measuring runs but also to have the same time coilstants of the samples of both reference and investigated s u bst a n ce. T h e heat exchange between the sample and the surroundings cannot be fully discussed in this paper. To do this, one should more carefully analyze the problem of reference temperature T H in scanning calorimeters. But even if we assume that the direct heat exchange between the sample and surroundings is negligible, the problem of the time constant of the sample does not disappear if the sample is outside the compensation feedback loop. An analysis of ihe ecluivalent problenis connected with a differential mounting in coiiipensated scanning calorimetry !rill be Lreated later.
Ll?'lEHATUHE CTlED (1,
F t. KaidSZ, li. E. B a r , arid J M O'Reilly, J . Po/ymer Sci., Part, 6 , 1141 (1968).
707
S Strella and P. F. Erhardt. J . Appl. Polym. Sci., 13, 1373 (1969) M. J . Richardson and N . G. Savill, Thermochim. Acta, 12, 213 (1975). W . P. Brennan, B. Miller. and J . C. Whitwell, "Analytical Calorimefry", Vol. 2 , R. S. Porter and J. F. Johnson, Ed., Plenum Press, New York, N . Y , . 1970, p 441. M. J. O'Neill, Anal. Chem., 36, 1241 (1964). A. P. Gray, "Anatykal Calorimetry", Vol. 1, R. S. Porter and J. F. Johnson. Ed.. Plenum Press New York, N.Y., 1968, p 209. J. H. Flynn, "Anawical Calorimetry", Vol. 3, R. S. Porter and J. F. Johnson, Ed., Plenum Press, New York, N.Y., 1973, p 17. C. M. Guttman and J. H. Flynn. Anal. Chem., 45, 408 (1973). H. M. Heuvel and K. C. J. B. Lind, Anal. Chem., 42, 1044 (1970). W. P. Brennan, 8. Miller, and J . C. Whitwell. rnd. Eng. Chem., Fundam., 8, 314 (1969). M. J. O'Neill and A. P. say, "Thermal Analysis", Vol. 1, H. G. Wiedemann, Ed., Birkhauser Verlag, Basel and Stuttgart, 1972, p 279 J . H. Flynn, "Thermal Analysis", Vol. 1. H. G. Wiedemann, Ed., Birkhauser Verlag. Basel and Stuttgart, 1972, p 127. J . H. Flynn, Thermochim. Acta, 8, 69 (1974) T Ozawa, Netsusokutei, 4, 45 (1977). S. Randzio and M. Lewandowski, "Fundamentals of Electronic Temperature Control in Diathermic Calorimetry", Ed. Polish Academy of Sciences, Institute of Physical Chemistry, 1973. E. Margas, A. Tabaka, and W. Zielenkiewicz, Bull. Acad. Pol. Sci., Ser. Sci. Chim., 20. 329 (1972). M. J . O'Neill, Anal. Chem., 4 7 , 630 (1975). S. Randzio and M. Lewandowski. 1977, unpublished results
RECEIVED for review October 3, 1977 Accepted January 16. 1978 This paper was presented at the 5th Internationa! Conference on Chemical Thermod>namics, 22-27 August, 1977, Ronneby, Sweden.
Determination of Phosphates in Natural and Waste Waters after Photochemical Decomposition and Acid Hydrolysis of Organic Phosphorus Compounds J. T. H. Goossen and J. G. Kloosterboer* Philips Research L abordtories, Eindhoven, The Netherlands
Total dissolved and suspended phosphate in water samples may be determined after photochemical decomposition of organic phosphorus compounds and thermal hydrolysis of acid-hydrolyzable phosphates, followed by conventional spectrophotometric determination of the liberated orthophosphate as molybdenum blue. With the procedure described, a 75-W medium pressure Zn-Cd-Hg lamp is used for photolysis and hydrolysis. The combined action of UV radiation and heat from the lamp enables the simultaneous conversion of organic phosphates and acid-hydrolyzable phosphates to orthophosphate. I f a thin aluminum sheet is placed between the lamp and the acidified sample solution, only hydrolysis occurs. I n this way ortho, ortho -!- acid-hydrolyzable, and total phosphate may be determined. The method avoids complicated and time-consuming chemical pretreatment and may easily be automated.
I n the analysis of natural and waste water samples, it is of'{en necessary to discriminate between the various forms of
phtrsphorns present. T h e element occiirs almost solely in the form of inorganic and organic phosphate compounds ( 1 ) . Phosphates are commonly classified into orthophosphate, acid-hydrolyzable phosphates, and organically bound phos-
Table I. Simplified Classification of Phosphate Determinations Form of phosphate Totala orthophosphate Totala ortho + acid - h y dr o 1y z a b le phosphate Totala ortho + acid-hydrolyzable + organic phosphate, i.e. to tal phosphate a
Method of analysis N o digestion, direct
spectrophotometric determination of PO, 'Mild acid hydrolysis followed by spectrophotometric determination of PO,'. Wet chemical digestion followed by spectrophotometric determination of PO,'.
Total means suspended and dissolved
-____~___
phates. These categories may be subdivided into filtrable or dissolved and particulate phosphates. The latter distinction can be easily introduced in an analysis by the insertion uf a filtration step in the procedure (0.45 pm membrane filter) and will not be considered here. A simplified scheme of ar,alysis is shown in Table I. Acid-hydrolyzable phosphate and organic phosphate are usually determined by subtraction I I ) . T h e determination of total and organic phosphate requires preliminary digestion, for which several standard methods are being used: perchloric
