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r-n,. _,r î
dGp _ or y
®fn = y _
dv 0 (n-D!
X0^rf- = X^o-Xp
d2Xn _ dX(n_|) dXn dv2 dv dv
in equation (35)
den « y| (y-D
dv (B-1),Zi|_(B-1) r-0
^X(n_i_ r) dX(n-r)] dv dv
d8n a v1 (y-D
dv (B-I)ZjL(B-I) r-0
Ã r-n r
dX(n_i_r) a ÷ò-÷Ã(y-D
dv (B-I)ZjL(B-I) r=0
Now, for the series, Thus,
n _ 0(n-i)_en
— +Ben — y 0(n-i) = Vi)-xe(n-i)-en + P0n
or = (l—y)®(n—1)+ (B_0®n .......................... (36)
From equation (34) and using its expanded form,
v dv (B-1) dv
V òë÷ï U dv
Thus, ('-Y)6(n-l) + (B-1)©n = a-^ ................................................... (37)
Substituting a-^1 from equation (37) for (l-Y)0(n-i) + (B-l)en in equation (36) and rearranging,
^ = a^n_Ben+Y0(n-O ..................................................(38)
it Is seen that equations (37) and (36) are identical which substantiates the validity of equation (35) for (0n). It is also seen from equation (35) that (a),
only effects the magnitude of the curve while (y) and (B) effect its shape as well as its magnitude. Scott (22), assumed practical values for the various physical parameters of the system and calculated the temperature and Integral temperature curves for a series of different practical values of (B) and (y). The results are shown in figure (9). In figure (9) the values of (y) are represented as(6).
Theoretical Temperature and Integral temperature Curves Generated by a Temperature Sensor Situated in the Column
G = 2.66 Â = 2.57 G = 2.66 Â = 2 58 G = 2.66 Â = 2.70 G = 2 66 Â = 2.74 G = 2 66 Â = 2.86
It is seen from the curves in figure (9) that the heat convected into the detector cell or plate also distorts the curves. It is apparent that, unless the heat lost radially is extremely high, so that little heat is convected to the sensor, symmetrical integral peaks will not be obtained This heat loss appears impossible to achieve in practice and thus, the heat of absorption detector does no seem viable for LC.
It is now clear that the plate theory has a wide field of application. Its use, however is not restricted to LC. For example, the plate theory can be used to Investigate temperature changes that take place in a GC column,(3), pressure changes that take place in a GC column, (4), the effect of solute decomposition on band profile and other similar effects that can take place in a chromatographic system. The plate theory has many areas of application that still remain to be explored.
(1) R. P. W. Scott,C. 6. Scott and P. Kucera, Anal. ?7??/??.,44,No1( 1972)100.
(2) R. P. W. Scott, Anal. Chern ., 36,No8( 1964) 1455.
(3) R. P. W. Scott, J. Chromatogr. Sci., July (1973)349.
(4) A. Klinkenberg, in" Gas Chromatography /960"(Û. R.P.W.Scott), Butterworths Scientific Publications<London,England,(1960) 194.
(5) C. N. Reilley.C. P. Hildebrand and J. W. Ashley, AnalChem.,34(1962)1198.
(6) J. H. Purnell, Nature /London),\Ú4,Úìù\. 26(1959)2009.
(7) J. H. Purnell and J.Bohemen, J.Chem.Soc, (1961)2030.
(8) D.H.Desty and A.Goldup," Gas Chromatography 1960"(Û. R.P.W.Scott), Butterworths Scientific Publications<London,England,(i960) 162.
(9) R.P.W.Scott, Nature (LondonI 183(1959)1753.
(10XJ.C.6iddings,“ The Dynamics of Chromatography"?\zvcz\ Dekker,
New York,( 1965)265.
(11) J.C.6iddings, J.Chromatogr. Sci., 12( 1974) 1753.
(12) J.C.Giddings, Anal Chem.Z9 No. 8(1967)1027.
(13) J.KDavis and J.C.Giddings, Anal. Chem. 55(1983)418.
(14) R.PW.bcoll," Liquid Chromatography Detectors" ,Å\úå\1\?ã,/òú\.åøï\ New York, (1986)18.
(15) R.P.W.Scott and C.E.Reese, J.Chromatogr. 138( 1977)283.
(16) G.C.Claxton, J.Chromatogr,2( 1959) 136.
(17) AJ.Groszek, Nature. (London). 182( 1958) 1152.
(18)K.P.Hupe and E.J.Bayer, J.Gas Chromatography.April (1957) 234.
(19) J.L.Cashaw,R.Segura, and A. l\z\.VAs,J.Chromatogr Sci 8(1970)363.
(20) R.H.Perry,C.H.Ch11ton and S.D.Kirkpatrick;' Chem. Eng. Handbook". licGraw Hill (1975)10.
(21) T.W.Smuts.P.W.Rtckter and V.J.Pretorious>J.Chromatog. Sci.9( 1971 )457.
(22) R.P.W.Scott, J.Chromatog.Sci. 11(1973)349
Introduction to the Rate Theory
Solute equilibrium between the mobile and stationary phases is never achieved in the chromatographic column except possibly (as Giddings points out) at the maximum of a peak (1). As stated before, to circumvent this non equilibrium condition and allow a simple mathematical treatment of the chromatographic process, Martin and Synge (2) borrowed the plate concept from distillation theory and considered the column consisted of a series of theoretical plates in which equilibrium could be assumed to occur In fact each plate represented a dwell time' for the solute to achieve equilibrium at that point in the column and the process of distribution could be considered as incremental. It has been shown that employing this concept an equation for the elution curve can be easily obtained and, from that basic equation, others can be developed that describe the various properties of a chromatogram. Such equations will permit the calculation of efficiency, the calculation of the number of theoretical plates required to achieve a specific separation and among many applications, elucidate the function of the heat of absorption detector