I n d . E n g . Chem. Res. 1989, 28, 839-844 Italy; BHRA: Bedford, England, 1988; p 177. Hinze, J. 0. Turbulence; McGraw-Hill: New York, 1975. Naumam, E. B. Mixing in Polymer Reactors. J. Macromol. Sci. 1974, C-10, 75. Sherwood, T. K.; Pigford, R. L.; Wilke, C. R. Mass Transfer;
839
McGraw-Hill: New York, 1977; p 31. Received for review August 23, Revised manuscript receiued November 23, Accepted January 9,
1988 1988 1989
Matrix Method for Correction of Mass Spectra in Deuterium-Exchange Applications Geoffrey L. Price* Department of Chemical Engineering, Louisiana S t a t e University, Baton Rouge, Louisiana 70803
Enrique Iglesia Corporate Research Laboratories, Exxon Research a n d Engineering Company, Route 22 East, Annandale, New Jersey 08801
A matrix method that can be used to correct mass spectra for both isotopic impurities in the skeleton and mass spectral fragmentation has been developed and applied to the computation of deuterium content in hydrocarbons. The method features a single “simulation matrix” that incorporates both types of corrections simultaneously, and all of the elements of the matrix may be obtained from a single equation. A reference spectrum of the nondeuterated molecule must be used in the implementation of the equations, and a n optimization technique that extracts naturally occurring carbon-13 from the reference compound is also reported.
Mass spectroscopy has been widely used for the analysis of deuterium content in hydrocarbons and other hydrogen-containing molecules in the past few decades (Ozaki, 1977). To perform these analyses, two problems, molecular fragmentation and isotopic irregularities in the skeleton, require correction in order to obtain an accurate analysis of deuterium content. With respect to isotopic irregularities, we will focus on naturally occurring 13Cimpurities though the methods presented are general for other isotopic species. Isotopic irregularities such as 13Cimpurities interfere with deuterium exchange analysis because a molecule that contains one 13Catom has (within the resolution of most mass spectrometers) the same mass as a molecule without 13Cbut having one deuterium atom. In the absence of molecular fragmentation, mathematical corrections for 13Care rather simple because the natural abundance of 13Cis usually well-known and can be subtracted easily from the mass spectrum. In this procedure, we begin with the molecular (or parent) ion, Io,for the species containing no deuterium or 13Cand subtract from the Ilion a fraction of the Io ion based on our knowledge of the naturally occurring 13Ccontent. The resulting intensity must be due to molecules that contain one deuterium atom and no 13C.We then successively apply this procedure to the remaining ions to give the corrected spectrum in which the intensities of each resulting ion are proportional to the amount of each deuterium species. If, however, there is molecular fragmentation, particularly abstraction of one or more hydrogen (deuterium) atoms, this procedure cannot be used because the source of any particular ion is not easily recognizable. Generally, researchers have circumvented this problem by one of two methods. The first method involves the reduction of fragmentation voltages to a point such that fragmentation is negligible. However, this cannot always be achieved, particularly with paraffins, and some mass spectrometers do not allow adjustment of fragmentation voltage. Also, the practice of reducing fragmentation
* To whom
correspondence should be addressed.
0888-5885/89/2628-0839$01.50/0
voltage is dangerous since conditions may develop such that ionization of deuterium-containing species may not be as efficient as the ionization of hydrogen-containing species; these isotope effects skew the measured intensities. There is also a reduction in overall sensitivity in the process of reducing fragmentation voltage. The second method involves the measurement of a spectrum of the nondeuterated sample, correcting the nondeuterated spectrum for 13Cor other isotopes, and then applying the results to the unknown deuterium-containing species. We follow this second procedure with a few new twists and have generalized all the procedures for matrix manipulation. Though similar but qualitative descriptions of the correction of mass spectra for deuterium-exchange applications have been reported previously, to our knowledge, there is no general description with detailed equations in the open literature that simultaneously accounts for fine details such as fragmentation of species that contain isotopic irregularities (e.g., carbon-13). We also present a new optimization technique that efficiently extracts isotopic irregularities from the nondeuterated reference material. The method is applicable to a wide range of hydrocarbons and avoids many of the problems discussed earlier. The method is limited to observation of molecules that do not have ions due to methyl group (or other functional group) fragmentation in the molecular ion region. As an example, molecular ions resulting from deuterated nheptane molecules fall in the region 100-116 amu, whereas ions resulting from the removal of a methyl group fall in the region 85-98 amu, which is outside the molecular ion region. In the event that ions from functional group fragmentation occur within our region of interest, we must resort to reducing fragmentation (by lowering the fragmentation voltage) to use the method, though modification could be done to make the necessary corrections. Theory Assuming that we know the fragmentation pattern for each individual D ispecies (more on this later), a measured mass spectrum is simply a linear combination of the in-
1989 American Chemical Society
840
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989
dividual patterns. To put this mathematically, I-, = a-,,oXo + a-,,,X, + ..*+ a-,,,X,
... an+m,OXO+ an+m,lXl + or, in matrix notation, I=AX In+m =
'1.
+ an+m,nXo
A note about the dimensionality of the problem is in order here. For a hydrocarbon that contains n hydrogen (or deuterium) atoms, there are (n + l)Di species (0 through n), so the Xvector is n + 1 dimensional as above. However, because we could theoretically observe a molecule with up to m 13C atoms, there are m extra equations represented by the equations following I,,. These equations are not linearly independent since a spectrum for a species containing 13C is considered identical with a spectrum for a species without 13C multiplied by a factor representing the relative abundance of 13C. Also included in the matrix are equations representing fragmentation by removal of one or more hydrogen or deuterium atoms. These are represented by the equations preceding Io. In the cases we have investigated, removal of more than three hydrogen atoms was insignificant, but we have included all equations up to the removal of all the hydrogen atoms for generality. The equations preceding Ioalso represent equations that are not linearly independent if we assume removal of deuterium is accomplished as easily as removal of hydrogen. We therefore have only n 1independent equations and any (nonzero) n + 1 equations could be picked from these for solution of the problem. The equations from Io through I, should usually be selected because the most intense ions normally reside in this region. This will be true when fragmentation and contributions from isotopic irregularities in the skeleton are minimal. Going back to the problem, the solution is simply x = A-1I or the unknown mole fraction vector may be extracted by multiplying the inverse of A with the measured intensity vector I . We must, naturally, select only n + 1 independent equations in this process. Our task is now to determine matrix A from readily available measurements. If we had pure samples of each Di species, we could measure a mass spectrum for each species and construct A. For example, measuring I, ..., Io,I,, ...,In+mwhen X5 = 1 and Xi,iz5= 0 results in values for ~-,+1,5, ...,~ 0 , 5 ~1,5, , ..., an+m,5,respectively. In order to get equal weighing for each X, we would have to suitably normalize the set of a's for each component (e.g., Ciai,j = constant). However, obtaining suitably pure samples of each species would be tedious if not impossible and overly expensive. We even have trouble obtaining a suitably pure perdeuterated compound. Take, for example, n-hexane-d14,99% isotopic purity. The 1%isotopic impurity generally represents over 10% n-hexane-d,,.by mole percent and a trace of n-hexane-d12and other species. Therefore, we simulate A with probability-based arguments. We assume that there is no deuterium isotope effect in the fragmentation process, though this may not be an appropriate assumption in some circumstances. Schissler et al. (1951) have reported the fragmentation
+
patterns for each of the deuteriomethanes, and an isotope effect in the fragmentation process is apparent. Dibeler et al. (1954) have reported similar effects for the deuterated ethylenes. Lenz and Conner (1985) have developed a method for modeling the cracking patterns of low molecular weight hydrocarbons that includes the isotope effect but requires the measurement of the fragmentation pattern for both the perhydro and perdeuterio molecules and also incorporates one adjustable parameter. Because of the vast number of deuterated species that are possible when the number of hydrogen atoms in a molecule becomes large, it is virtually impossible to obtain all of the information necessary to rigorously model this process for larger molecules. Therefore, the method presented in our paper should be applied with caution when fragmentation ions represent a large fraction of the molecular ion. However, there generally is very little recourse other than reducing the fragmentation voltage. We begin by considering the fragmentation of molecules, but assume for the moment there is no 13C impurity. Clearly, we can measure a fragmentation pattern for the Do species. This results in a parent ion Poand fragmentation ions P-,, P-2,..., P-,, which represent removal of 1, 2, ...,n hydrogen atoms by fragmentation of the parent ion, respectively. We should emphasize that the P vector is a theoretical vector representing the fragmentation pattern of a molecule that contains no 13Cin its skeleton. We will tackle the calculation of this vector from measurements on a Do species that contains 13C later. We detail the arguments for removal of one and two hydrogen atoms and present the final form for removal of more atoms. The fragmentation pattern for the D1 species can be computed as follows: probability of no mass loss: PO probability of loss of one mass unit: loss of H
-p-, n
probability of loss of two mass units: loss of D
-P-,
loss of 2H
-1
1
n
n-ln-2 -p-2 n
n
probability of loss of three mass units: loss of H + D and D + H
In general, for Di, probability of no mass loss:
Po
probability of loss of one mass unit: loss of H
-P_l
probability of loss of two mass units: loss of D
loss of 2H
-i n
i
-P-, n
n-in-i-1 -n n - 1 p-2
probability of loss of three mass units: loss of H + D and D + H probability of loss of four mass units: loss of 2D
+ -i n - i i i--
n n - 1 p-2
Thus, we can compute the spectra of the other species from the Do pattern. All that is left is to construct the rows and columns of A with the appropriate calculated fragment:
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 841 which is the hypergeometric probability distribution. The function
[il
Table I. Raw Mass Spectral Intensities for Benzene and n -Hexane n-hexane benzene nondeu nondeumass terated deuterated mass terated deuterated
-
~~
is given by i!/j!(i - j ) ! . For our purposes, this function is zero when i < 0, j < 0, or i - j < 0. Now, consider the possibility that molecules contain 13C. We introduce the R vector, which contains the information on the relative population of the molecules that contain one or more 13C atoms. ri represents the relative population of the molecules that contain exactly i 13Catoms. For isotopic irregularities other than 13C, i represents the number of mass units shifted up from the parent ion of lowest mass. The spectrum of a 13C-containing molecule is assumed to be identical with the molecule containing no 13C except that intensities are shifted up i mass units. With this modification, A can be calculated from -i+t+k
1
1lj-k
a. . = It1
Pi-t-krt
(1)
The remaining task is to compute P from a measured spectrum of the Do species that contains naturally occurring 13C. A simple method would be to take the spectrum and begin with I-,. Clearly, this ion contains no 13C, so I-, = r&,. We then correct the spectrum for 13C content of ions that have experienced n hydrogen atom fragmentations by subtracting rlP-n from rJ?, from etc. We have now removed all 13Ccontributions from so = r,,P-n+l. We continue this process until all 13C contributions are removed from the spectrum. An alternative procedure that should give a better representation of the P spectrum is to perform a “best fit” procedure. A measured spectrum of the Do species with naturally occurring 13C consists of n + 1 + m measurements. The P vector consists of n + 1 unknowns. We therefore have more measurements than are necessary to solve for P , unless we decide that R is also unknown, in which case we have the same number of measurements as unknowns. However, it would be foolish to solve for R from measurements whenever this vector is well-known from the natural abundance of isotopes. We set up our solution as a minimization of differences between the measured values and computed values. Thus, we require that S(m,n+t)
m
F = C (It t=-n
C riPt-J2
i=L(t,O)
be a minimum. Here, we define S(i,j ) as the smaller of i or j and L ( i , j )as the larger of i or j . To find the minimum, we take the partial derivative with respect to each of the unknowns (P‘s). This yields
for j = -n to 0
Simplifying, we find m S(m,n+t)
m
rirt-jPt-i= CItrt-j
t = j i=L(t,O)
t=j
for j = -n to O ( 2 )
This set of equations (one for each j ) is ( n + 1)X ( n + 1) dimensional and can be solved by matrix inversion for the P vector.
73 74 75 76 77 78 79 80 81 82 83 84 85
4531% 1126390 374 272 1081340 4562940 16760800 1253370 44 032 0 0 0 0 0
35 712 97 792 129 920 192 512 77 568 173 056 415 144 972 800 1953 790 2625 530 2166 780 879616 56 576
82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
10 080 980 25 088 82 560 970 752 56 384 2 556 0 0 0 0 0 0 0 0 0 0 0 0
15 120 4 880 1950 2 928 26 464 3 928 1634 2 720 4 584 7 784 11712 15088 18 048 18 944 18 240 14 544 8 528 3 420 694
This method differs from the simple method but provides P that best fits the experimental data. We can see how this method gives slightly different results from the simple method with the following arguments. During the process of subtracting 13C contributions with the simple method, we eventually correct the Io intensity to yield PO. Multiplying Po by rl, r2,r3,etc., and subtracting from 11, 12,13,etc. (which have already been partially corrected by previous subtractions), should yield exactly zero for PI,Pz, P3, ..., P,. In practice, this does not occur because of measurement errors. The simple procedure provides no means for correcting any errors that may be present. The measurement of I,, 12,13, etc., provides no useful information for the calculation of P. The square difference minimization technique, however, does utilize all of the data and finds the best set of P‘s to satisfy the requirements. Qualitative descriptions covering the main aspects of the overall method have appeared in the open literature in the past. A good example was presented by Koski et al. (1956), who described their calculation procedures for the correction of deuterated samples of pentaborane (B6H9). In this system, corrections were required for loB naturally occurring isotopes (llB is the most abundant isotope) and fragmentation in the parent ion region. Koski et al. (1956) followed a stepwise calculation procedure where the relative abundances of molecules containing isotopic irregularies were first computed. We have called this distribution the R vector. The combined effects of isotopic irregularies and probabilities of fragmentation of the deuterated pentaborane species were then used with a reference spectrum of nondeuterated pentaborane to obtain fragmentation patterns of deuterated pentaborane species. This procedure results in calculations similar to eq 1 in our discussion. Koski et ai. (1956) then subtracted these spectra from their unknown spectra in a stepwise fashion to determine the deuterium distribution. This process can be viewed as a method of solution of the simulation matrix, which we have obtained, by the addition and subtraction of rows of elements. Therefore, the two methods are quite similar. Finally, we would like to suggest the following global approach to solve for both P and X from a measurement of a deuterated sample without having to measure the mass spectrum of the Do species. For a deuterated sample, we can measure 2n + 1 + m ions. Our unknowns are ( n +
842 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 Table 11. Matrix and Vector ( V )Obtained during the Computation of P for Benzene i PO p-1 p-2 p-3 p-4 p-5 0 0.879 63 0.058 59 0.001 59 0.000 00 0.000 00 0.000 00 -1 0.058 59 0.089 63 0.058 59 0.001 59 0.000 00 0.000 00 -2 0.001 59 0.058 59 0.879 63 0.058 59 0.001 59 0.000 00 -3 0.000 00 0.001 59 0.058 59 0.879 63 0.058 59 0.001 59 -4 0.00000 o.oO0 00 0.001 59 0.058 59 0.879 63 0.058 59 -5 0.00000 0.000 00 0.00000 0.001 59 0.058 59 0.879 63 -6 0.000 00 0.000 00 o.oO0oo 0.000 00 0.001 59 0.058 59 Table 111. P Vector, Computed Do Spectrum, and Experimental Do Spectrum for Benzene mass i P Do(computed) Do(exptl) 453 120 -5 484 206 453 120 73 -4 -3 -2 -1 0 1 2
74 75 76 77 78 79 80
1171326 320 839 1 131977 4 799 380 17 598 466
1126 390 374 272 1081348 4 562 554 16 770 530 1108 063 29917
1126390 374 272 1081 340 4 562 940 16 760 800 1253 370 44 032
+
1)P's and (n 1)X's. If we know R ,only 2n + 1 of the measurements are independent; i.e., subtraction of the 13C contributions yields only 2n + 1 remaining ions. This leaves us with 2n + 1measurements and 2n + 2 unknowns. However, one of the P's may be specified arbitrarily since the P vector represents a mass spectrum and only the ratios of the ion intensities are important. Thus, we have 2n 1measurements and 2n + 1nonarbitrary unknowns. The equations that result are
+
6 t=O
j-k
In1
j-0
for i = -n to n
Unfortunately, these equations are nonlinear when both
X and P are considered unknowns as the product XiPj appears. However, it seems feasible to solve these equations by iteration, and we would no longer require the measurement of a Do spectrum.
Example Partially deuterated n-hexane and benzene (among other products) were obtained from the catalytic exchange/reaction of n-hexane in deuterium gas on a Pt/BaKL zeolite catalyst. Reaction conditions were 1atm of total pressure and 460 "C. The products were removed from the reactor, and the mass spectra were recorded by using a Finnigan
lo6 lo5 lo6
lo5 lo'
6
6
CrirtPt-i =
i=t
CZtrt
t=O
or
+
+
lJJ
lo7 lo6
1020 GS/MS system operated with an electron impact source at 70 V. Spectra were obtained by summing all spectra over the width of the chromatographic peak and subtracting a suitable background. Table I lists the spectra for the Do species and for the deuterated samples. We have choosen to discard any intensities less than 0.1% of the major ion in the mass spectrum. We will detail calculation procedures for benzene and simply present final results for n-hexane. First, we compute the R vector using the natural abundance of 13C as 0.011. The binomial distribution gives the following relative probabilities of c6 molecules that contain l3C: zero 13C, 0.9358; one 13C,0.0625; two 13C, 0.0017; three 13C, 2 x W5;four 13C, 2 x lo-'; five 13C, 9 x 10-lo;and six 13C, 2 X 10-l'. We will neglect the contributions of three or more 13Catoms and therefore use ro = 0.9358, r1 = 0.0625, r2 = 0.0017, and r3 = r4 = r5 = r6 = 0. We then set up our minimization function F to compute the P vector. For benzene, m = 6 and n = 6. For j = 0, eq 2 yields
C
P,-kXj = Zi
V 1.5763 X 5.3197 X 1.3256 X 4.2558 X 1.0793 X 4.9507 X 3.0235 X
p-6
0.000 00 O.oO000 0.000 00 0.000 00 0.001 59 0.058 59 0.879 63
+
ro2Po rlr$-l r2r$-' r3r,& + r4r$-4 + r5r,,F5+ r6r$+ + r12Po+ rzrlP-, + r3rlP-2 + r4r1P-3+ r5r1P-4+ r6rlP-5+ rZ2Po+ r3r2P-1+ r4rzP-' + r5r2P-3+ r6r2P-4+ ~3'Po r4r3P-1+ r5r3P-2+ r6r3Pd3+ ~ 4 ~ + P or5r4P-1+ r6r4P-' + r5'Po + r6r5p-1 + r62P0= Ioro + Ilrl + 12r2+ 13r3+ 14r4+ 15r5+ 167-6
+
Plugging in known values for R and I and collecting terms, we obtain 0.87963P0 + O.O5859P_, 0.00159P-2 = 1.5763 X lo7
+
Continuing this process for j = -1, -2, ..., -6, we obtain the matrix given in Table I1 on the left-hand side and the vector (also in Table 11) on the right-hand side. Inversion
Table IV. Simulation Matrix, 34, for Benzene 1
DO
D1
D2
D3
D4
D5
-6 -5 -4 -3 -2
0 453 120 1 126 390 374 272 1081 347 4 562 554 16 770 530 1108063 29917 0 0
0 377 600 831 490 570 031 539 116 1489 292 3 840 790 16 721 255 1106 730 29917 0
0 0
0 0 0 0 0 0 0 0
0 302 080 609 666 684 569 367 966 647 810 1963 140 3 123595 16672 108 1105343 29917 0 0 0 0 0 0
0 226 560 460917 702 873 400071 371 857 674412 2 501 573 2 410 942 16 623 090 1 103984 29917 0 0 0
0 151040 385 243 609 931 538 225 214 500 496 707 597 600 3 103405 1702 804 16 574 199 1 102 624 29917 0 0 0 0 0 0
0 75 520 382 644 390 732 755 840 199590 161474 716 502 400 540 3 767 583 999 153 16 525 437 1101264 29 917 0 0 0
-1
0 1 2 3 4 5 6 7 8 9 10 11 12
0 0 0 0 0 0
0 0
0 0 0 0
D6
0
0
0 0 453 120 30 263 1096 950 73 208 302 232 20 052 1059 850 70 749 4 403 184 299 961 16 476 804 1099 904 29 917 0 0 0 0
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 843 of the matrix and multiplication by the vector yields P given in Table 111. The Do spectrum (containing I3C) computed from P and the experimental Do spectrum are also included in Table 111. We see excellent agreement with masses 73-78. The computed intensity at mass 79 is about 13% off, but the effect will not be significant on the final result since mass 79 is less than an order of magnitude smaller than mass 78. Mass 80 is off by about 50%, but its intensity is less than 2 orders of magnitude smaller than mass 78. Using this P vector, we then compute the simulation matrix A. As an example, we compute three of the points in the column representing the D, molecule. For this case, j = 2, and by use of n = 6 and m = 6, eq 1 becomes 6+i-t-k
xx
ai,2 =
t-0
112-k 161 121
k-0
For i = -5,
[ =
6
-i+t+k
1-t
1-tk
[
a-4.2 =
2-t
2 - t - k][i
k
rL +
+ k]
P-5-t-krt
DO Di Dz D3 D4 D5 D6 D7 DB D9
DlO D11 Diz D13 D14
0.1949 0.0136 0.0065 0.0132 0.0240
0.0447 0.0707 0.0933 0.1148 0.1229 0.1216 0.0979 0.0566 0.0216 0.0037
of A. For this analysis, the equations and intensities representing parent ions were used. Thus, we choose ao,o through a6,6 and Io (mass 78) through 1 6 (mass 84). The resulting X vector, representing the solution, will not sum to 1 unless the complete I vector is made to sum to the same number as a complete column of A (note that all columns of the complete A matrix have identical sums). Generally, it is simpler to normalize X after the computations. The normalized solution is given in Table V along with the solution for hexane. The Do species for benzene is computed to be negative, which means that the measured intensity of mass 78 is smaller than would be expected by fragmentation of heavier ions. This represents an inaccuracy in measurements but is still smaller than 1%which is within our requirements for accuracy.
Acknowledgment
k]
The authors thank Joseph Baumgartner for his assistance in computer programming.
P4-t-krt
1-0 k-0
D6
-0.0019 0.0133 0.0428 0.1916 0.3417 0.3095 0.1150
1
a-5,~= 302080
6
DO Dl D2 D3 D4 D5
Pi-t-krt
t-0 k-0
For i = -4,
Table V. Solution for Benzene and Hexane in Mole Fractions benzene hexane
Nomenclature Matrices A = matrix of simulated spectra Vectors
For i = -3,
a-3,2
=
[
6
3-t
t=O
k=O
x
3-t-k k
][
+k
1 J
P-3-t-krt
I = vector of measured intensities P = theoretical vector of intensities for a molecule containing no deuterium and no 13C R = vector representing the relative ratios of species containing different numbers of I3C atoms V = vector computed in the minimization function F X = vector of moles or mole fraction Scalars a,,, = components of
Continuing this process, we compute the A matrix as given in Table IV. Finally, we choose an appropriate 7 X 7 [ ( n+ 1) X ( n + I)] component of A, take the inverse, and multiply by I , choosing the 7 intensities corresponding to the 7 rows
A ;i represents the difference between the mass of the parent ion containing no deuterium and no I3C and the mass of the corresponding species; j represents the number of deuterium atoms in the molecule D, = molecular species containing i deuterium atoms F = minimization function I, = components of I; i represents the difference between the mass of the ion and the mass of the parent ion that contains no deuterium and no 13C i = index j = index k = index m = number of carbon atoms in a molecule n = number of hydrogen and deuterium atoms in a molecule P, = components of P ; i is the difference between the mass of the ion and the mass of the parent ion containing no deuterium and no 13C
Ind. Eng. Chem. Res. 1989, 28, 844-850
844
R ;i is the number of 13C atoms in the molecule t = index xi = Components Of x;i represents the ~ t d x ofr deuterium atoms in the molecule ri = components of
Functions L ( i , j ) = the larger of i or j S(i,j ) = the smaller of i or j Registry No. D,, 7782-39-0;benzene-d,, 1120-89-4;benzene-d,, 25323-71-1; benzene-4, 25321-35-1; 25321-36-2; benzene-d5,13657-09-5;benzene-d6,1076-43-3;hexane, 110-54-3; hexane-d,, 98821-94-4;hexane-d,, 98821-93-3;hexane-da, 9882192-2; hexane-d,, 120295-95-6;hexane-d,, 120311-04-8;hexane-d6, 120295-96-7: hexane-d,. 120295-97-8: hexane-dn. 120295-98-9: hexane-d9, 120295-99-01 hexane-d,,, 120296-0016; hexane-d,,; 120296-01-7; hexane-d,,, 120296-02-8;hexane-d,,, 120296-03-9; '
hexane-d,,, 120296-04-0.
Literature Cited Dibeler, V. H.; Mohler, F. L.; de Hemptinne, M. Mass Spectra of the Deuteroethylenes. J . Res. Natl. Bur. Stand. 1954, 53(2), 107. Koski, W. S.; Kaufman, J. J.; Friedman, L.; Irsa, A. P. Mass Spectrometric Study of the B,D8-B5H9 Exchange Reaction. J. Chem. Phys. 1956, 24(2), 221-225. Lenz, D. H.; Conner, Wm. C. Computer Analysis of the Cracking Patterns of Deuterated Hydrocarbons. Anal. Chim. Acta 1985, 173, 227-238. Ozaki, A. Isotopic Studies of Heterogeneous Catalysis; Kodonsha Ltd./Academic Press: New York, 1977. Schissler, D,0.; Thompson, S. 0.; Turkevich, J. Behaviour of paraffin Hydrocarbons on Electron Impact: Synthesis and Mass Spectra of some Deuterated Paraffin Hydrocarbons. Discuss. Faraday SOC. 1951, 10, 46.
Received for review March 8, 1988 Revised manuscript received November 28, 1988 Accepted January 24, 1989
Supersaturation and Crystallization Kinetics of Potassium Chloride Ru-Ying Qian,* Xian-Shen Fang, and Zhi-Keng Wang Shanghai Research Institute o f Chemical Industry, Shanghai 200062, People's Republic
of
China
The crystallization kinetics of potassium chloride from its aqueous solution is studied with a novel temperature float method for supersaturation determination. T h e relative supersaturation is with a precision of 1 X The growth rate is proportional t o the measured to be (1.1-2.9) X supersaturation over a wide range of retention times and tip speeds, while the nucleation rate increases rapidly with respect to supersaturation. The supersaturation, growth rate, and nucleation rate are independent of tip speed up to 3 m/s. Beyond 3 m/s, the power index of the tip speed in the kinetic equation increases to 4. A change in the dominant nucleation mechanism is discussed. A slight impeller vibration does not affect the power indexes in the kinetic equation but considerably increases the nucleation rate. A temperature difference of 4-6 K between cooling water and bulk suspension leads to extraordinarily high nucleation rates but does not yet affect growth rates. The crystallization kinetics of potassium chloride has been studied by many investigators (Genck and Larson, 1972; Ploss et al., 1985; Randolph et al., 1981; Qian et al., 1987). However, the width of the metastable zone for this system is so narrow that the supersaturation in crystallizers has not yet been precisely determined. Currently, the supersaturation in crystallizers can be measured accurately only for systems having wide metastable zones. For the potash alum-water system, with the maximum allowable supercooling of 4 K (Mullin, 1972), the supersaturation data are still not precise enough to be correlated with crystallization kinetic data (Garside and JanEiE, 1979). The conventional kinetic equation expresses nucleation rate as a power function of growth rate and operation factors, such as suspension density, agitation speed, and impeller diameter. This empirical equation does not directly include, however, the driving force in the crystallization process, i.e., supersaturation, and cannot be used to correlate kinetic data of different systems. Without supersaturation data, it is impossible to compare the kinetic data of various investigators. The development of crystallization as a unit operation has long been hindered due to the lack of supersaturation data in crystallizers. In this paper, supersaturation of the potassium chloride-water system in a crystallizer was determined precisely by a new method. The corresponding nucleation rate and growth rate were measured simultaneously and were *Present address: 11 Cameron Rd, Wayland, MA 01778.
well correlated with supersaturation. The crystallizer was operated as an MSMPR crystallizer in a wide range of retention times and tip speeds. Excessive nuclei and incrustation were observed at short retention times due to the low cooling water temperature. The effect of impeller vibration on the kinetic equation was studied. The dominant nucleation mechanisms under different operation conditions were discussed. The crystallization kinetics of the KC1-water system was compared with the KC1-brine system.
Apparatus and Procedure In this work, a 2.5-dm3glass crystallizer with a streamlined bottom and a hollow stainless steel draft tube is used. The details of the crystallizer have been reported in our previous work (Qian et al., 1987). The flow system used in that work has been further improved in this study. The system consists of a crystallizer, reservoirs, a saturator, a metering pump, preheaters, a flowmeter, a filter, a sampling bottle, and thermostats. The temperature control of the system has been improved to meet the requirement of precise supersaturation control and measurement, being achieved by using special fine-temperature regulators in thermostats to minimize their temperature fluctuation within K. The crystallization temperature is maintained within jzO.01 K by fine-temperature control of three thermostats, which are used for adjusting the temperatures of the cooling water in the draft tube, the water bath of the crystallizer, and the feed solution, re-
0888-588518912628-0844$01.50/0 0 1989 American Chemical Society
