Development of a detector for chromatography

Development of a detector for chromatography

Citation for published version (APA):

Willems, G. H. W. (1981). Development of a detector for chromatography. Technische Hogeschool Eindhoven.

https://doi.org/10.6100/IR34922

DOI:

10.6100/IR34922

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Published: 01/01/1981

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DEVELOPMENT OF A DETECTOR FOR

CHROMATOGRAPHY

PROEFSCHRIFT

!er vcrkr(jgin,g van de graad van doctor in de technische wctenschappen aan de Technische

I-logeschool Eindhoven, op gezag van de

rector rnagnif'icus, prof. ir. J. Erkelens, v~~r

een commissie

aangewczcn door het college

Van dekanen in het openbaar Ie verdedigen op

dinsdag 14 april 1981 te 16.00 uur

DOOR

GERARDUS HUBERTUS WILHELMUS WILLEMS

GEBOREN TE VENLQ

Dil proefschrlft is gucdgekeurd door de pWl\"lotoren:

Prol·. dr. .I A. Poulis Ort

vaar

!lSi?

CONTENTS

CONT~NTS

CHAPTER

I GENERAL INTRODUCTION

7

CHAPTER 2

THE FLOW-IMPEDANCE nRIDGE DETECTOR 9

CHAPTER 3

CHAPTER 4

2.1 Introduction

2.2 Principle of the detector 2.3 Detector response for gases 2A Detector response for liquids

VISCOMETER

3.1 Introduction 3.2 Experimental

3.3 Analysis for the binary mixtures 3.4 Results

3.5 Discussion

APPLICATION OF THE FLOW-IMPEDANCE BRIDGE DETECTOR IN CHROMATOGRAPHY 4.1 Introduction 4.2

Gas

chromatography 4_2_1 IImoductio/J

4.2.2 Experimental

4_2.3

Results

4.2.4 Di.~cussion 9 9 II 18 19 19 19 21 23 31 33 33

38

38

40 44 47

4.3 Liquid chromatography

4.3.1 introduaion 4.3.2 Exp('rimental 4.3.3 Results and discussion 4.4 Conclusions REFERENCES SUMMARY SAMENVATTING OANKBETUIGING flJRRICULUM VITAE 6 51 51

51

53 56 58 5'1 60 hi

CHAPTER 1

GENERAL INTRODUCTION

Since the introducHon of chroma tography as an analytical technique there has been a continuous need for improved detectors. A large variety of detectors has been developed for both gas and liquid chromatography. In principle they all respond to a specific property of matter e.g. light ab-sorption, thermal conductivity etc,

One of the ways to classify these detectors, is to distinguish between concentration and mass flow-sensitive detectors, Concentration-sensitive detectors respond to the concentration of a solute in the detector, whereas mass flow-sensitive detectors respond to the mass flow-rate of solute through the detector. Another important difference between various de-tectors is the variety of suhstances to wruch they respond: universal versus selectivE_

The most commonly used detectors in gas chromatography are the name-ionization detector and the therm<ll conductivity detector. For liqUid chromatography the UV-detector is mostly used_ In order to apply these detectors for quantitative analYSiS, a calibration curve must be obtained for each substance. This calibration curve should be measlIrcd under the same experimental conditions that are used for the actual analysis_ Such a calibration can be avoided by using a detector where only knowledge of a physical property of the substances is required.

An universal mas, flow-sensitive detector has been developed which can be used for both gas and liquid chromatographyi,~ _ The detection principle is based on viscosity measurements with a flOW-impedance bridge detector. In contrast with the detector as proposed by Janak and Novak3 ,4, the detector under discussion is a real analogue of the Wheatstone bridge. In order to use this detector for quantitative analysis, only information about the relationship between the viscosity and the composition of the so)ute·carrier mixture that flows through the detector is needed.

Since there is little data on this subject in literature, measurements have been conducted to acquire these viscosity data. With the detector that has been developed accurate measurements of the viscosity of mix-tures as a function of the composition are possible_

!"rom the Chapmalln-E)1skog

theory,

an

expression

can

be derived by

which the

viscosity

of a binary gas mixture can be calculated from the values of some physical pararneters of the compononts of this rtliXt\lrO, ~y reversing this procedu,e it sho\lld be possible to obtain these phydcal para-meters from

accurate

viscosity measurements over a range of temper"-tures_

CHAPTER 2

THE FLOW-lMPEDANCE BRIDGE DETECTOR

2.1 INTRODUCTION

The Wheatstone bridge is a very accurate method for the determina-tion of small variadetermina-tions in the valllC of an electric resistance. The analogue of an electric resistance in fluid dynamics is a capillary, the flow resistance of which is determined by the dimensions of the capUIary and the viscosity of the fluid flowing through it. For a certain capillary the flow resistance is only determined by the viscosity and thus by the nature of the fluid.

A change in the composition of the fluid resulting in a variation in the viscosity can be detected by measuring the change in the flow resistance of the capillary. In order to detect these changes in the flow resistance ac-cura.tely an analogue of the Wheatstone bridge with four equal capUlaries was constructed. With this flow-impedance bridge detector one is able to detect very small variations in the viscosity of a OUid.

A description of the detection principle together with the dynamic be-haviour of the detector follow~. Also a relation is derived that enables one to use the flow-impedance bridge detector for quantitative analysis. 2.2 PRINCIPLE OF THE DETECTOR

In the flow-impedance bridge detector four equal capillaries, together with a differential manQmeter, arc constructed to form a Wheatstone-like bridge. A single variation of the viscosity of the fluid flowing through the detector will result

in

four variations of the pressure difference measured by the differential manometer. These variations, due to the changes in the pressure drop across the various capillaries, are shifted in time. Thls time shift is obtained with the usc of a time delay line in onc of the branches of the bridge.

rig. 2.1 Flow diagram of the dctector.

WI, Wz , W3 and W4 ~re the four equal capillaries, and Pin and P",ut ~re the

pre~sures at the inlN and outlet of the detector respectively. TOL repre-sents the time delay line and DMM the differential manometer nwasuring the difference hetween the pressures P A and P_B. The dlmensiOIlS of the

time delay line and of the connections between WI and

W

2 and between

W.l

and W4 are such that their flow re~istance (g small comp<1red to the

flow impedance of tho capillaries.

L

Fig, ;:,2 Vis<;:<)sity v;iTj~tion at the inlet of the detq't<)T ~s a functiQn of time,

Should the viscosity

or

the fluid entering the inlet of the detector change (see Fig. 2.2), then it is possible to show the variation of the dif-fC1"ontial prc~sure PA PH with time in a schematic diagr<lm <IS eXlnessed in Fig. 2.3.

In Fig. 2.3 t~, represents the time intervallhe front of viscosity varia·

tion needs t() reach capillary W" and 1M stand~ for the time interval the

fluid needs to rass Ihe manometer from WI to W1 and from W3 to W •.

w, w

".

0 t 1M I w,.

_{.. ---i}

"'3

Fig. 2.3 Variation of the pressure difforence P A _. PIl with time in thcidcal situation.

Fig. 2.4 shows

a

typical measured response of the differential mano· meter, and clearly indicates the effects of mixing and of diffusion in the detector.

I.'ig. 2.4 Typical m<;1!.sured response of the diff"r~tJti.1 manometer.

Although in principle four peaks are evident, in practice however. Fig. 2.4 shows that only the peak due to WI is pronounced.

2.3 DETf-:CTOR RESPONSE FOR CASES

In this section the response of the detector wiJI be described, given the following situation;

the composition of the gas flowing through the detector changes from a carrier gas to a gas mixture and then back again to a carr"'! gas.

The gas mixture (viscosity I)", (Pa.~» is a binary mixture of carrier gas (vis· cosity 1)<") and

a

sol\IlC gas with viscosity I)s.

The calculations of the detecto( response will be rostrictod to the varia· tion of t.he viscosity of the gas in W, . That th is ,estriction is j\lst.ified, is

shown in l'ig. 2.4, where it

can

be seen that the viscosity variation of the gas in the other capillaries only results in a smooth variation of the base

line.

The viscosity v~riation at the inlet of the detector as a function of time is shown in hg. 2.5.

'1

flm - - - , - - - ,

<)

rig. 2.5 Yisc<l~ity variation ~t the inlet of the detector as a fUllction of lime.

The timo when the gas mlxture reaches WI, corresponds wilh I = O. The time interval t"., in Fig. 2.5 satisfies the equation

V _m

(2.1)

where Vm represents the volume (m3_{) of the gas )11ixtllre and}

_<PI)

_{the flow·} rate (m'/s) of gas through the detector.

The uiscussic)l1 will be restricted lO tllO~C sit\Jation~ where three reo strictions hold: (I) 1'.

,.,

Wilh P;" ·r

""'H

Po = ... _ - _ ... 2 with 12

(iii) the time intervals teap and

t.

are small compared with all other time intervals involved. leap is the time interval the front of the gas mi:xture needs to pass

a ea

pillary

2 Veap

tell P ..

-;;;;;--where Vcap (m')

is

the volume of

a

capillary, Is is the time interval the gas requires to move from a stationary flow situation to another. According to Schlichting5 _{this time interval can be estimated from the following equation.}

r2

p

t , ,

-S 7J

where r (m) is the radius of the capillary and p (kg,m -~) is the density of the gas with viscosity 7/.

Since the mean pressure in the detector is almost constant (restriction

(i»,

and the Reynolds number is low then the following relation between Dow·rate and pressure drop for

a

capillary can be used.

(2.2)

where 0:

=

ITI'

/8l, ¢,,"P is the flow,rate through and Poop (Pa) the pressure drop acroSS

a

capillary with radius r (m) and length I (m).

As the two compartments of the differential manometer are separated by

a

flexible membrane the volumes of the compartments will depend on the difference between the gas pressures on both sides, For this relation the following equations are used

(2.3") (2.31.»

where ~(m3 Pa-1 _{) represents the VO\L1mctric displacement of the membrane}

per unit of pressure difference, The volume Va includes those volumes that are directly connected to the compartments of tho differential manometer. For the gas pressures at A and B the following equations arc obtained:

0 : . a: "-·(P, .... p ) - - ' ( P -p )=~. tlc In A 17(" A out

+

Vo

dP", +'~.--Po dt (2.4") 13

d(PA-J'll)

{J • ---.~-.,.

cit

Since the fOllr capillaries are equal, the following starting condition is

pertinent:

t~O

Combination of eqns_ 2_4a and 2Ab leads 10:

(2.5)

rtlH 170 (Pill -PO,,!) '1]", '1]"

(Po -PA )· 17", T1/" (FA Fu) 2 . rtm

Tll,~

=

=

7),,,-rt

o

.~:~VoIPn

.

d(FA - PIl)

dt (2.6)

Neglection of th~ lerrll with Po -- P A leads (0 a much simpler differential

equation. Tliis omission is justified because 117m -- 1/" I <{ rtm

+

1/e and

Ip() FA I <i; Pin - Pout. The solLltion of this differential equatioIl reads (2.7)

where I'm is the maximum vahle of the presslire difference, and itself being: '1]", 't1,. Piro --Pout

l' =

-m rt", + fie 2 in)

r

is

the time constant of the detector:

For

those

SitUaliOnS where tm ?- T the detector response R (V),

de-lined

as R = 8_{M •} (P_/1 - P_B) with SM as the sensitivity of the manometer (V . Fa-1

), is given by (see Fig. 2,6)

(2_10')

R =S . F 'e

(t--tm)/'-M tn (2.10")

' ... "l' I I II

/1

"-""----~----. -,.

-

- -

- -

.-

-Fig. 2.6 Calculated detector te~pOnSe upon injection, assuming 1m :<-r.

A typical measured response upon the injection of a large volume of gas

mixture is shown in Fig. 2.7. R

t

Fig. 2.7 Typic.1 measured detector response upon injection under the condition

tm ;.. r.

Another situation where the detector response is easily calculated is

characterised by tm ~ T. The linear approximation ofeqn 2.7 may be used,

and leads to (see Fig. 2.8)

T trn R =SM'

1',." ._-

'e' (/-tm)/T r (2.11 ") (2.11 b)

Fig. 2.9 shows a typical measured response under the condit iOll tm

<

T

lr::===~

_OJ~ ...

Hg, 2,,9 Typical measured detector response upon inj~ctiol1 undur llll': condition

i IH ,,~ To

Returning to l'ig. 2.6 let us ~()t1sider the surface arell O( V.s) of tltc peak, and relate this surface llr~u to the Vol\lme V,(11l·1) of plirc solute with viscosity lis in the gas mixture. I'or t.his calculalion l\ lineHr rciati()11 is a,wlllcd bClwccn tlte concentration of willIe in the gil~ mixture and the viscosity of this mixture

(TIm .. -1),.)' ~." = (77, TI,,)'

v.

(2.12)

For t.lte surface' lnell

0

the following is valid:

0=

f

R.dl (2.13)

And using I", i;> T, then:

o

=

SM . P"., • I", (2.14)

Suhslitlllio[)

ur

lh,' egos 2.1,2.2, 2.R and 2.12 leads to 1/., .... 1/"

( ) = - - _ · S V

40: M ! " (tin ~ r)

(2.15)

This equation indicates that the detector Can be u~ed for quantitative pur-poses when the viscosity of the binary gas mixture is a linear function of

the solute concentration. If the values of the viscosities tI, of pure solute and tI" of pure carrier gas at pressure Po are known then the measured value of the surface area

a

leads to the volume V. which the pure solute

will

have in the mixture at the same pressure.

It

is seen that 0 is indepen-dent of the value of Pin - Pout and therefore of the value of the flow-rate of carrier gas through the detector.

It should be noticed that in case of a non-linear relationship between

composition and viscosity of the gas mixture there are some limitations (sec fig. 2.10). c --;::

~T

~---1~OO% .~

J

Fig. 2.10 Plot of the vi,cosity of soMe carrier mi)(ture~ as a function of the ."lute concentration: a~ as:nlltitd curve: b: actual curve; 0: extrapolation of the: low cuncen-\r~tion data.

The relation for the surface area 0 was derived for a liMar relation (curve a).

In case of a Ilon·linear relationship, for instance curve b, eqn. 2.15 may only be used for small concentrations of solute in the gas mixture. For the calculation of ~ the slope of the CUrve for low concentrations is used and

2.4 DETECTOR Rr:Si'ONSL l"OR LIQUIDS

Fol' the de~cripti()n of the detector respOllse for liquids let us start

from the ~amc assumptions as were made in section 2.3 or this chapter. Since a IiqLtid is nearly incoolpressible the maSS bahlflee for the liquid in

Lfle yol\ltlleS VA ~nd VB leadS to (he following differential equations

(2.16") (x _ . - . 0 (1' ...

p.l

." In H '(m (2.16" )

with·

1\

PI! ~ Ufo!' t";;; 0

The resolution l)f these equations is f()llnd on the analogy of the wlution

given in cqn. 2.7 and reads

0.17)

with

"rim 0 t)c 2[3 7([3

"T = . - - - - . - - "'" - - . (2.1Ci)

1)""l

+

t)c 0: a

Tile only difference with cqn. 2.7 is the exprc~sion COl' the time con·

stant f. This is due to the compressibility ()f gasos. The expression, for the dOrCdOr response R ti)r liquidS arc identic,J! to those round for gases This

is also truc for tlte relation between the lnOaS\lr~d surface area () and the volulIle V, or p\l(~ solute in the mixture.

CHAPTER 3

VISCOMETER

3.1 INTRODUCTION

One of the main problems with the measurement of viscosity is the calibration of the viscomcter.6_{,7 For this calibration a fluid with a known} viscosity is normally used. The uncertainty in the value of this visco~ity causes a systematic error in the experimental determinatlons. This error can be reduced by measuring the viscosity of a substance with respect to the viscosity of a reference fluid.

With the flow.impedance bridge detector described in the previous chapter, measurements to obtain such relative viscosity data can be per· formed, In this chapter the results of these measurements for binary gas mixtures are reported. The composition of the mixtures used was varied, and the lighter component in the mixture Was used as a reference gas.

The experimental results were compared with those found theoretically. Therefore the Chapman-Enskog solution of the Boltzmann equation to-gethe, with the extended law of corresponding states were usCd8,~. 3.2 EXPERIMENTAL

For the determination of the _{relative viscosity tl* "tlm/tlc of a binary} mixture, the flow-impedance bridge detector was used. The lighter compo-nent of the hinary mixture (reference ga~) was ll~ed as a carrier gas. To sim-plify the notation, in the foIlowing equations the heavier compound of the mixture will have a subscript 1 and the lighter component will be de-noted with a SUbscript 2 : i.e. tl*

=

tlmjTi~

For the injection of an amount of gas mlxt\lre into the flow of carrier gas an injection valve (type 772, Packard-Becker, Delft, the Netherlands) was used, as given in Fig, 3.1.

dol~ctor

Fig. 3. I SdlCrnatic ~iagraIl) of the injection v'llw.

The volume VI""p (nr' ) waS hirge enough to ns~ure a platl'au in the d\,(cc(or

response, i.c. tm ;.--'r.

The rnaxinlUm value ur the pressure difference (/\ P/I) iii due to an

injectioll of gas mixture is given hy

1)~' I l'il1 I'olll PI!) 0, = P,."

+

j'(p) '- - - - . - - - .• -

+

f(p)

17"

+

1 :1

(3.1 )

where j'(p) is a correctioll term taking into account the effect of the

den-sity dlfference between the gas mixwre and the carrier gas OIl the head loss 10 This correctiun s~itisries the following equation

./(p) "

(Xu';"

1'''''1)2 -(p, pi) 1671/- (rl" + 1)2 -7r~

(3.2)

where x, is the fractioll (v/v) ()f the heavy cOlllponent in the gas rnixturc.

The experimental cOIlditions were such that thi~ correctiun is ()nly of

in-terest when the vi,c(lsity difference between mixture and carrier bccomes $111(1)) for larger valLl(~s or

x

I .

Measurements have been performed with binary gJS mixtures COli" taining hcliul1l, oxygen ,llld nitrogen (Hoek-Loos, Schiedalll, the Nether-lands). The impurities of tltc gases are listed in table 3.1 . together with the

value's of the viSCOSities as ,Ire given by Touloukian Cl. ltL II.

'l'u,hle 3.1 Tht.:': ln~pllritk:-; ~ll1d the vi~uositic .. of the g.\lSC~ llsed,

fie 0, N, 20 __ ~~~l:'~lrilY

Co

<.0.0 I <.0.1 <: O.OOt

- - _ . _

... _ ...

__

.. . Yf\""sity (10 i Po. <) l~5.9 203.;: 17.).7

The capillaries constituting the bridge are made of stainless steel with an inner diameter of 0.38'10-3 _{m and a Icngth of 0.1095 m, loading to} 0: '" (4.76 ± 0.04)·1O-'~ m". The time delay line consists of a nylon tube with all inner diameter of 4· 10-3 m and a length of 1 nl. This type of wbe was also used to connect WI with W1 and W" with W4 , hoth connections

having a length of 0,5 m. As the volume of each compartment of the dif· ferential manometer is 10-6 _m3

, the volume Vo equals 7.3 .10-6 m3. The value of

ff

of the manometer (model MP-45. Validyne, Northridge, U.S.A.) was measurcd to be gA' 10-11 _mJ _IPa.

POol is atmospheric pressure and

1';"

- Pout has a value of about 260 Pa. This WaS measured with a Baroccll dif-ferential manometer with an accuracy of 0.1 % (model 5810, Datametrics, Wilmington, U.S.A.). P_A - P_E was measured with an accuracy of I

'x,.

For the production of the gas mixtures a gas mixing pump was used, also having an accuracy of 1 % of the adjusted value (modelIM300a-F, Wosthoff, Bo-chum, G.f.R.). All the experiments were performed at room temperature T", 293.7 ± 0.5 K.

3.3 ANALYSIS j·OR TH~; BINARY MIXTURES

for the analysis of the experimental data of binary gas mixtures, the Chapm<ln-Enskog solution of the Boltzmann equation was used. This solu· tion leads to the following expression for the reduced viscosity~.

1)", 1)'" = - = (I +A)j(B

+

C) (3.3) 112 where A ..

~

AIZ

{x~!2

+ 2Xl (I

-Xd

I

M

I2

(~+~)-lJ

5 M,

L

1)1 1)2 + {I

-xd"

M~}

M, 2 1)2 1), B;::x, - +2xI (l--XI)- +(1 ... x_l

?

1'/ I 1) 12 3 { 2 M[ 772 1)12 C=- An x_t- - + 2 x , ( l - · x ,)M,2- - + 5 M~ 1'/, 1)1

In these equatiolls MI and M, arc the molecular weight! (kg/mol) of the

~pcci(;~ and M,~ is defined by

M'2 ,,-,(MI

+M

z

l"/(4M

IM,) (3.4 )

The quantity

A

12 is defined hy

(3.5) wher~

n

(2,2)' and

n (

1 • 1 ). arC universal c(lIH~i()n in tcgrals wh kh ~Ire both 1I 1\IIKtiun of the reduced tcmperalllre Til'

And :q~ being defined a, fulll)wS :

where ('I.,)A is 1I p(ltcnti,\! jlM<ll11ctcr (K).

The viscosity 1) 12 can be expressed by

5 { lkTM[MJ }Y' I 1) ~ - - - . . . ... • - - - - . - . . 12"

Ie) -rrN(M , +M

2)

u;, -

[).(1.2)< 0.6) (37)

wll(:;rC k is the UoiV.m;lnn COllstant, N is Avogadro's nllinber. Tis tht tCIlI· pe['~\tllre (Kl ;111(\ 0

"

, is the collision dbmcter (m).

i\lthough these eqllatioll3 were dofined for l11onatomi,: gases Ke,tin cl. a1. 12·16 h~\ve sh()wn that they can aiso be used for poiyatomic gases. They abo gave cxpressions for the universal colJi!ioll integrals

n ( l , I ) ' =exp{0.347 0.444 (In T*) i"O.093 (In '1'*,)2 .. O.oJO(ln:r*):I} O.S

<

T"

<

25 (3.1l)

~l(2·2)·

=/.

cxp{O.45667-· 0.53955 (In T*)+0.18265 (1n T*~2

·0.03(,92 (In

T''j''

+ 0.00241 (in p)" } I

<

1'*<90

where

I

is a correction factor cuvering higher approximatiom.

13.<))

Silllila,' to eqn. ).7 the rollowing relatiun can be derived for the vis·

co~ity of a pure gas

(3.10)

For the bin~ry oiffusion coefficient Dl~ (ml S~I) at pressure P the following equation is valid

Combination of this expression with the eqns. 3.5 and 3.7 leads to

(3.12)

The values of the three parameters in eqn, 3.3 Le, lJl/lJ~, 1)12/112 and

A II are fitted to the experimental reSLlits of 1')* with a least square fit. There· fore a method based on the Marquandt theorem for fitting non·linear fune-lions with numerical derivatives was used.

The experimental results were al~o compared with predicted values

of 7)*, as calculated with eqns. 3.3.3.10, starting from molecular parameters Elk and (J found in literature.

With 04n. 3.12 and the values of the fitted parameters 7)12/7)2 and A II the values of the diffusion coefficient D12 of the various gas mixtlireS were calculated.

3.4 ){ESlitTS

The experimental values of the reduced viscosity 7)* arc listed in table 3.2 as a function of the fraction Xl' To evaluate the uncertainty of these results, eqn. 3.1 is ,ewritten as

11*- I

a

(Pin - Puut ) ' (Pl - Pl) = -1/-"'-+-1 +

8111

(7)~ +

j-f .

7)~

Since 1/" differs little from unity one can write

(3.13)

(3.14)

The rat.io (I'll. -

PI!)",/(P

i" - p',ut) is measured within 1%, with a systema-t.ic eITO], which is less than 0.1 %. This systematic error is so small hecause the different. i<1 I manometer measuring FA' Ffl is calibrated against the manollletor measuring

p;"

t; .. ,/.

The fract.i()n x I is determined with an accuracy of I %, so the second term on the right hand side has ~ln accuracy of ahollt I % and a systematic error of 2';;" Because the influence c)f this term

on

the reSlllts is less

than a

few percent, the vaillc of

7,'-

I

call hc

determined with an accuracy of 1 % and a systematic error of about 0.2%. hblo 3.2 The rCdllcc,d viscosity n' with various fractions of the lighter ulInpunent for the.": gas mixtures lI:;~d_

._-"", ..•. ,._ ... '.-'., .. " .... _._-, ...

FrudioTlx] Reduced viscosity,,·

-",.".",,'-,-"'" OJ)] 1.00776 i 0.00007 100208, 0.00002 1.00 I 79.! 0.0000 I 0.Q2 1.0143 .0.0001 '1.00381 , 0.00003 1.00351 , 0.00003 0.03 1.0211 ,0.0002 1.00537" 0.00005 1.00516 , 0.00005 004 1.0275 ,0.0002 1.00657 i 0.00006 1.00689 , 0.00006 0.05 1.0334 " 0.0003 1.00766 , 0.00007 1.00844 , 0.00008 0.06 1.0333 .\ 0.0003 j .00350 i 0.00008 1,0100 , 0.0001 0.07 1.0434 , 0.0004 1.00933 , 0.00009 1.0117 , 0.0001 0.08 1.0480 , 0.0004 1.00982 , 0.00009 1.0133 \ O.QOOI 0.09 1.0524 , 0.0005 1.01020, 0.00010 1.0149 ,0.0001 0.10 1.0567 , 0.0005 1.01039 , 0.00010 1.0165 J 0.000"1 0.15 1,0734 ,0.0007 1.0MSl , 0.00009 1.0247 , 0.0002 0.20 1.0836 .\ 0.0008 1.00681, 0.00006 1.0331 ) 0.0(1)3 0.30 1.0944 ,.0.0009 0.99641 , O.OOOOJ 1.0491 ! 0.0004 040 1.0949 ~. 0.0009 0.9832 , 0.0002 1.0647 t 0.0006 0.50 1.0847 , 0.0008 0.9687 ,·0.0003 1.0809 !,0.0008 0.60 1.0817 ,,0.0008 0.9535 , 0.0004 1.0956 , 0.0009 0.70 1.0728 , 0.0007 0.9392 , 0.0006 l.l J 1 , 0.001 0.80 1.0613 .\ 0.0006 O.nsZ ± 0.0007 1.126 , 0.001 0.90 1.0506 ,0.0005 0.9119 ± O.OOOR 1.142 , 0.001 1.00 1,0393 ± 0.0004 0.8982 ± 0.0010 1.156 I 0.001 -""~----. . Gas mixture 0, H,. N, ... 1(,_ 0, -.N., .~',""'--'---'

The result> uf the least square fit applied to the experimcntal data Me

listed in table 3.3.

The vallles of the parameters of tile oxygen·nitrogen mixture werc ohtained

by t1tting the fir~t two parameters i.e. rl,/T], and T]" /T]?" and using A" ,IS

an input paraillctel', whidl vallIe wa~ taken from liter'llure". This had to be dune

!lecallse

uf the almost

linear relatiun

betwee!l17~ and the

Table 3.3 Results of the least square fit applied to the measured values of

7j".

MixttLfC

11,/n,

11" /11, An

O,"'H, 1 ,0394 ± 0.0002 0.a06 ± 0.003 1.06 ± 0.01

N,-II, 0,8989 ± 0.0004 0.747 " 0.003 1.07 ± 0.02 O,-N, 1.1 563 i 0.0002 1,0804 ± 0.0002 1.10 ± 0.05 tration of oxygen in the mixture, not allowing a three p<lrameter nt. As expected the fit appeared to be almost insensitive to the exact value of

A

12·

The influence of the three parameters on the fit is very different. For low concentrations the fit is almost only determined by the value of t)1~

Irr2

<Inci A 12 whereas for high concentrations 171 /112 is dominant.

Fig, 3,2 shows the deviation plots «1/~xj) _. 1/~al,)lrrt"l.

*

10') of the mixtures, where 1/~"le is the reduced visoosity oalculated with eqn. 3.3 and the parameters listed in table 3.3, In this figure the experimental uncer-tainty is also indicated.

103• ''':IIP -Tl~IO~~IC

~.;

r_--+-___ -'----__

---t _ _ _

O_~ -_N_~

_ _ _ ___l -05 -1.0 1.0 uS -0.> -1.0

:: r_+---! ____

--+ __

~O-~--H-e---____1

-OS -1.0 20 40 60 80 100%

X,

In Pig. 3.3 changes in the calculated

vahles

of 7/* (Lln;"I<.)' due to a variation of one of the parameters \1sed to cakubte 1)~;'k' is shown. These parameters wOre varied one by one a.nd the variation was equal to the stan-dard deviation as listed in table 3.3.

to 0.5 10

os

20 40 1 _ ..:::.. (rn /'I'l~J 1= 6!rmlm) J =.6. (Ato!) 60 N,,-He 100% X,

Fig. 3.3 Illtlu"llce of the variatioll in the param<;t<;rs used for the eakulali<m "I'

the valuc. for fI'.

As already mentionod in section 3.3 the reduced viscosity Can also be calculated from potential par"meters i.e. 0"1, 0"2, On and CI, "2, "12. In

table 3.4 some values of thc~e parameters, fO\1nd in literature,N,12 <lre listed. Thc valllcs given hy Ilirschfeldcr CL al. ,He diviJeJ in two series:

H+ is valld for temperatures above 300 K and If- is used for lower tem-peratures.

Since I-lirschfelder et. al. give no vallles for 012 and "12, these val\1es

were calculated from the parameters of the pure gases using the following empiric") combination rules

I

(J12=-(U l +(J1) and

<ll"'..,;e,e:;-2 (3.15)

It should be noticed that since Kestin et. al. give no v<llues for 012 and <:12

of tbe oxygen-helium mixture, these value~ were also calculated with cqn. 3.15,

Table 3.4 Potential parameters given by different authOtS. 1I +: Hirschf~ld~r ct, at

T> 300 K; If -': Hirschfelder ct. at

r

< 300 K. ll+ 1I Kostin G3S e/k(K) .,(10"'· m) c/k(K) 0-(10"" m) </k(K) a(10-00m)

- - -

..

~ fl(! 10,22 2.576 10,n 2.576 11,29 2.556 0, 88,0 3.541 113.0 3.433 137.0 },323 N, 78.8 3.749 91.5 3.681 l13.07 3.568 0, ·-I-Ie 29.99 3.059 33,98 3,005 39,33 2,940 N,-lI,. 28.38 3.163 30,58 3.129 64,32 2.976 O,--N, 83.27 3.645 101.68 3.557 119,58 3.454

With the parameters listed in table 3.4and the eqns. 35-3.10 the values of the viscosities of the pure gases as well a~ the values of the interaction viscosities 1{,1 were calculated. These values arc listed in table 3.5 together with tbe values of these viscosities as determined from the experiments, Since only the relative values of these viscosities were determined, a value Yable 3,5 Calculated and experimental values fOI tile Yiseo~itie, '1 and '1" and for

A",fI+: Hirschfelder et. al. T:> 300 K; JI-: Hirsdlfdder et. aL

r

< 300 K.

Tt" 10' f'a.s ill:l • 1 eJ'l (';:t.. ~

A" ll, o ~ iV, 01-··11~ N,:'-Ha OJ-,·Nl H+ 195,35 204.14 174,61 ISHS 147.64 lSS.54 1110 1.110 1.097 If 195.35 203.13 )74.99 100,17 149.01 IRMO 1.108 LlI0 1.095 Ke~ain 197.96 204,50 175.77 1~>.24 144.52 190.69 1.1l6 1.096 1.082

Thi:;w"rk 195.90 203.62 , 0.Q4 176.09 l 0.08 157.9 ,0,6 146.3 .• O.~ 190,25 , lI.1l4

.18 · 17 • I G I · 15 1 · 11 ·13 1 . 1 ~ I .11 (J~I Q 1 . I ( ) if) '= .. l.rEI CI w _{1 . Of]} U

=J

0 uJ _1·07

".,

J ·06 I. OS 1.04 1 .0.1 .Il? I ·01 02 jN N2 . ~ .

,

o

. I .2 ·3 .4 . S .1)

FRACTION X1

! . . I, J ./ 1/ 11/ ' __ . L ____ . __ L __ .. . B ·9

Fif,. 3.4 Plot of tile ~ed\lced viscosity '1· of o)(ygQn-n.it1'Og~n mixtur"s "3 ~ function of the uxygen cont~nt. _._--JJ +; -.--1/--; ... Kcstin; _ . this Shldy.

.8g .88

87 _ L -.. L -__ ~ ... __ I _ _ '--_L--L_~

o

·1 ·2 ·3 .4 ·5 . 6 7 .8 .9

FRACTION X1

Fig. 3.5 Plot of the redUCed viscosity 71· of nitrogen-h~lium mixtures as a function of the nitrogen content - - -H +; -'.-Ii -; ... Kcstin; - ---. thi,l study.

0'2 IN H F

-Y9

-8R I .... ,." .L._ .. __ L .. L .... ___ .. L._ .. 1

n

• I .2 , j -4 .;, ,Ci . (] Y

FRACTION X1

Fig, 3.6 Plut oHhe redllced vu;cu,ily 71' of oxygcn-helh1.1)1 mixtures as a function M the oxygen contcnt .. ---.. J[ +; ---H -: '" Kc,tin; - -tllig ~tudy_

for the viscosity of one of the pure gases had to bo adopted. Therefore the viscosity of purdwliu)1l was used (table 3.1). Also in table 3.5 the calcu-lated and experimental values of

A

12 are given, except the value of

A

12 for the oxygen-nitrogen mixture for this work, which is an assumed value_

Fig. 3.4-3.6 show the reduced viscosity 1/* of the three mixturcs as a function of

x

I , calculated with eqns. 3.3 and 3.4 and the data listed in

lable 3.5.

The values of the binary diffusion coefficient D [2 were also calculated

from the experimental results. (eqn. 3.12) These values were converted to

273.2 K. using the following expression given by Chapman and Cowlingl~

dlnDl2 5

- - - " , 2 .. · -

c

d T 2 0<c<I/5 (3.16)

The rcslilts are given in table 3.6 together with values givcn by Chapman

Table 3.6 Experimental vatu~s of the diffusion coefficient D" comp<lIcd with values given by Chapntan. )loth at 213.2 K.

C11~plnall Thb work 0.626 0.60, 0.02 N, H,. 0.607 0.57 , 0.02 O,-·N, 0.181 0.178 j, 0.009

- - - . - -

.. ~-3.5 DISCUSSION

As hils been shuwn by the experimental results, it is possible to llse the flow-impedance bridge detector for th~ accurate determination of the rcdllCcd viscosity (1/*) of a binary gas mixture as a function of the com-posHio)). With thc present configuration it is possible to detect relative vis-cosity changes in the order of 1 O-~ --I 0-6 • The only restriction is that the capillaries of the bridge have to be equal. This can be checked within 0.01%, so the systematic error in 1/* dllc to this effect will be less than 0.01%.

The results from the lhcoretical approach

me

quite satisfactory.

The

values

of

the viscosity of the pure

gases

and those

of

the interaction Yis-cosity (7)[1), correspond well with those calculaled from potential para-meters found in literature.

As is shown by table 3.3 and 3.4 variOllS sets (11" potential parameters

load to almost the ~ame value for the viscosity. Since the flow-impedance

bridge detector i~ a very accurate method for tllc dClNmil1otion of the

rc-dllced viscosity. it should be possihle to determine these potential para-meters aCCIlratcly from viscogity measurements over a range of temper,}-tllres_

CHAPTER 4

APPLICATION OF THE FWW·IMPEDANCE BRIDGE DETECfOR IN CHROMATOGRAPHY

4.1 INTRODUCTION

So far it has been assumed that peaks entering the detector had a block shape. [n chromatography however the concentration profile of the solute-carrier mixture leaving the column is normally a Gaussian curve

e=e exp [

~J

m 202 (4.1 )

where em is the maximum concentration (kg.m-3) at the outlet of the column, and (J is the standard deviation. Typical values of

a

for both gas and liquid chromatography are in the order of 5·10 sec. The ma)(imum con-centration em can be expressed by

(4.2)

where

M"

is the maSS (kg) of the injected solute, ~ is the porosity of the column, and

1>

is the flow-rate through the column (m3 _{sol ).}

Since the concentration Cj',j at the inlet of the column equals

Ms

(~, ,= -,-....

,'-'-''') V·

Inl

(4.3)

where

V;"i

is the injected volume, the dilution D by the column is given by C jnj IE

1>

a

..,f2";;

D -- C"I -

Vi"j

(4.4)

In table 4.1 some typical values for the various parameters for both gas (GC) and liquid chromatography (LC) together with the calculated values of the dilution D are listed.

Table 4.] Typk:ul V"hl(:'S ()f ~Ol11e paralIl~t~ts foJ' both g~~s and liquid chromato-graphy. i..~oluml1 < ( ) (j) .t: I Ol'i (11'1,1 ~ I) ('I V;"i

*

10" (m' I j) (.-) cal)ill"ll 1 1.5 I 190 (;C p"ckcd 0.4 ~O 5 [00 40 LC packed 0.4 1.5 5 I 7.1

Table 4.1 $I\Ow3 that the actual valuc~

01"

the 3011lte concontrations in t.hc

detector after the cOIUIlin will be less Thim about 2'

N,

(v/o).

If the respnllse of the lictcctur can be expressed by 1I fi.-st order dif-krentild equlItion ").

dN

d t r

. II

N j (4S)

where R is the response and f is the input signa!. the re~p()nsc upon a peak with a C:"lIssian shape is given by

t

a2 j{ "- /.' c (). eXI) _._--III '-, .I'

f

ex pl··· z

21

LIz ! ()

wjth 11 -, 0 ' h = T • Y ~ (a· h)!

,,/i'

and F is a propoltional factor. The inf1\lcl\(\' of the r,.tio h of the staIldard cicviiltion (el) of the concentration profile to til" tiJlW ,:onst<lIlt (T) of til" JCtC(tof ~)J1 the shape lOr th~ IllCH-smed pe,li( ig SIIllWIl in l'i~. 4, I .

11 caIl be seen fn)11l Fig. 4.1 Ihal not only the height. of the peak changes,

bill that also t.he p()silion of the Illaximuirl i, ,I\iftcd. Thi~ will introdH~e lIB iIlcmrC(\ interpretat.ion of the rGlention time of t.he peak.

In chromatography I/Joro

lire

four

moue,

or

ueto(\or

d'lssificatilln.

20

I. Classificatioll of the dotector ~ccording to the time dependence

or

their r'CS[1()l1S~ :Jilows distinclion between integral and differential de· tectors. The inlcgI'lil detectors signal the total aillount of a sub,lance whid1

has [1ass~d through the device I"rom the sbrt up to a given m()ment. Dif-ferential Lletcc[ors on the ()th~r h,lIlU indicatc tho instantancous quantity

lOr

slll)nance

detected, present at a given moment. 34

R

d

"t u

"0: :

A· 2,35

1\+---1

A-O

lHlr---2 A '"

0,1

l*--~3

A

0=

0,25

4 A

='

D,S

,,, .. +---5 A '"'

1,0

t

Fig. 4.1 Int1uenQ; of the r~t;o (b) of thc time con~t~nt T for tho detector to the

standard deviation" of the concentration plofll0 on the shape of the measured pc~k.

2_ Another classification is destructive versus nondestructive, indio cating whether Qr not the detection d()e~ involve irrevcr~iblc changes of the substance detected_

3_ The most important classification distinguishes between concen· tration- and mass-sensitive detectors_ C()ncentratkm·~ensitivc detectors re-spond to the concentration of solute whereas mass-s~nsitive detectors re-spond to the amount of solute and the r~te of Introduction of this solute

into the detector.

4. The last classification is universal versus selective_ Universal detec-tors respond to almost all substances, whereas selective detecdetec-tors respond only to a certain cla~s of ~lIbstances for which they mostly show a very high sensitivity_

The flame-ionization detector for instance is a selective!mass-sensitive! differential/destructive type of detector, and the katharometer is an uni· versal! concentra lion-sensitive! differential! nO[lde~tructivc ty pc,

The detcctor that kls been developed, ~nd

llnliel'

discu3~ion in this pa-pCI', is of an univcrSiti/di I TertIi tiul/llondcs(I'univc type, and as will he shown, Illass-scnsitiv(~. For this type of detector (110 perforlllancc is chara(:(~rized by five p;trarnctcrs,21 _i.e,

a, sensitivity h. noise level c.

d,

lowesl detecta hlo ]11ilSS Of

mass

flow-rate line~lrit.y

s

'PI) L (V. S kg-] ) (V) (kg) (kg .S-I ) ( )

c. tilllC constant T

(,ec)

In order (0 illustrate WIllC orthcsc paj'~l11eters I-'ig_ 4.2 shows a typi(:ill plot, on a logarithmic scale, of il detector signal R (V) versus the quantity <.(! (kg,s-I ) defined by

.p=¢f)'C (4,7)

where q)f) is the rIow-rilte of carrier through the detectol- and c is thl' con-centration of solute (kg, III :1) entering t.he detector.

<1',"

!,'it., 4.2 Typi~a! p!,-,t 011 lugarithm;(: s",,1e or llle dell'clor ;ir'1ili R versu.' tho ,MSS now-,ate or solute -p,

These five parameters will be discussed in detail in the following section. (ad. a). Th~ ~eilsitivity of the detector is defined as

dR

s=-d<p (4.8)

This parameter depends on a detector quantity, and

a

quantity which only depends upon the combinatioil of carrier and solute.

(ad. b). The noise level

R"

is defined as the standard deviation of the base line t1uctuations. For the determination of this noise level the

av~rage value of the signal R over a period of time comparable with the time interval

4

a

of the concentration profile is used. For qualitative

analy-~is the signal to noise ratjo SNR has to have a valu~ of 3, whereas for quan-titative analysis this value is taken to be 10. Zl •

(ad. c). The lowest detectable mass flow-rate (<Po) can be calcUlated with the following equation (sec i'ig. 4.2).

R,.

'Po

=

S .

SNR

(4.9)

As was noted above the term SNR = 3 is used for qualitative analysis, therofore:

(4.10)

For the lowest detectable mass (Mo) with SNR " 3 the expression (4.11) is equated

3R"oili M,,=----~

S

where

a

is Ihe ~tandard deviation of the concentration profile. (ad. d). The linearity L is defined as (see Fjg. 4.2):

(4.11)

(4.12)

where 'P,,, indic~tes the point where the slope of the line differs 3% from unity.

(ad, 0), The time constant (T) of t.he det.ector follows from the

re-sponse upon ~H\ instantaneous change in t.he inpllt (eqIl. 4.5). The influence of the time constant upon the recorded chromatographic peak is shown in I'ig. 4.1. For qualita tive analysis the ratio OfT has to be in the ord~r of 10. The perfmm;ll1ce of lhis new uctector in ga$ and liq\lid Cht'OlWltO' graphy slI(ces$ivcly will be described, listing the values of thc above dc·

tined parameters for this detector Ht. t.he end of each paragraph.

4.';, (;;\:i ClIROM;\TOld,;\I'HY 4.2.1 /Ilfrodll('fion

i\ t.:hang\~ in the composition ofa gas flowing at a given v01()city t)J!'Ough a Il()w·impedance clcincJlt will ['(suit in ,\ change in the pmssurc drop aCrl)~$ this clemen!. The possibility of Lltilil.ing !l\is phOIlOIl1et1<1 for detecting gas chl\llllutugraphic f"anions was firST. showll by C;ritliths et. a1. in I ')S2,22,2J lIt 19(A Jan{lk and Novuk doscribc(1 u fiow-it1lpcd;ltlce bridge detector,

wll iell wa~ ~uct;e~fully used fot· the detectiou or lllctal vapollrs separated by gas chromat()graphy. ~\,4

i\ Schematic fll)w di;lgr,tt11 oft.hdr CCjuiplllcnl is shown in I'i!l., 43,

!'ill. 4.3 Flow uiagram 01" the uetector by Janak alld Novak.

The variable resistor It;. ~crvcs to coutwl the Iluw-rate~ of carrier gas through the column <Pc \t1l.IS-I₎

_and

_{th),ough the detec(m ¢[) \t11.1S-}1_{). The resistor} Ws serves tl~ a souree of !low if the pneumatic rc~istalwc of WI' i~ substan·

tially grcillcr thall that

()f

the col\lmn,

WI'

W2 , W.l and W" are lh~ capil-laries constituting Ill" bl'jdg~ . WI

=

W4

=

Wo and 1112 = W.J

=

:1

W() !)MM

is the differential manometer measuring the difference between the pres-sures P_A and P_R. The response R of the detector can be expressed by

(4.13)

where SM is the sonsitivity of the differential manometer. It can be SMn fro111 this equation that the response of the detector by Janak and Novak

is effected by two experimental parameters i.e,P_{in - Pout} and <Po" The bridge

can be balanced by adjusting W_r• The change of W4 duc to a change in the composition of the

gas

leaving the GC-colurnn causes a change in R and can be given by

4

- 9

When the bridge is balanced then:

(4.14)

(4.15 )

If this result is compared with the expression that was derived for the new detector (eqn. 2.S)

17_{m '} 17_c

R=SM P " " - - - -_{,~ rtc} (4.16)

it can be ~een that these expressions are very similar. The big difference be-tween the two method~ however is determined by the way the detector is balanced. In the sct-up by Janak and Novak this b<llancing is in fact achieved by adjusting the pressure difference Pin - Pout and the gas flow-rate ¢". and thus will be sensitive for flow variations. The detector under discussion is balanced beCause of the usc of four equal capillaries and thus is independent of the gas flow-rate as in a real Wheatstone bridge.

In the ne)(t ~ectiolls kt us describe some experiments which indicate the possihle LIse of the new detector in gas chromatography.

4.2.2 Fxperimental

III order to explore the possible LIse of the new detectof in ga~ .;hrOIll,\-togruphy (he set-\Ip s)wwn schematically in l'ig. 4.4 was used.

Iii!;, 4,4 Schclll<ltic diagram of th" e>.perirncntal amlJ1gcll1ont.

During the experiments fom types of injection systems werC lIscd to inject a volume

(V;,)

of sO[\1(e or of a mixture of solute ;l.I1c! carrier gas into the flow of carrier gas through the detector. I.e. (see

rig.

4.5)

(i) syringe, _Vinj

<

50'10-')

m;' ;

type 705, 11~l11ilt()n, Bonaduz, Switzer-laml (sec Fig. 4S')

(iil injection valve 230'10-9 _{,;;; I-I,,,,~,}

,,;

_1120'1O-9_{n1'\; typo 772,}

Packard-Beckel', Delft, the Ne(herland~ (see Fig. 4.5")

(iii) syringe in cotllbinaliort with a splitter; type 8(i820, Ila!'lliltort, BOllad\!!', Swill;~rland (see Fig. 4.5")

(iv) injcctiun piston, V_iai

=

10") Ill;' (sec Fig. 4.5,1)

When using injection system (iii) a division factor K must be applied, and is definod as i'ollows (s~c Fig. 4.5")

(4.17) The usc of the tplittcr enables one to inject solute volumes (V,.) int(l the detector much smaller than the syringe volume V_inj

(4.1 il) where xj'\i is the fraction (v/ti) of pLlre solute of the injected gas.

The first experiments were performed with nitrogen as the carrier gas

and oxygen as the solute. This gJS combination was chosen because of the fairly lineM relation. between the viscosity of the oxygeJl-nitrogen mixture ~I\d tile conccntratiull of oxygen (~ce Fig. 3.4). According to cqn. 2.9 for the tiTne constant of the detector

r '"

0.39 sec. is obtained.

lIolulilll

---.

Fig. 4.5 Injection systems used in the experiment..

cietec::tor det~tor

-rel9lrlc~lo:n ¢!o

---.

In order to investigate the influence of a gas combInation with a

non·

linear viscosity relationship, hellum as carrier gas and natural gas as solute

Tabk 4.2 Composition of the ]1at\l~a)

_{---=--_ _ _ _ _ _ _}

gas llsed, _{, . . r} -Compound N,

eli,

C, II, other:; COllCC11tr~ti()n % (o/v) 14.3 81.3 2.9 1.5

[n Fig. 4.6 the viscosity difference (1),,) between helium and Ill.ixtures of hdiuill and natural gas is shllwn as a function of the concentration (%(vlv»

of natural gas in these mixture~.

Xn •

40 60 60 100~.

-20

-60

-80

Fig. 4.6 Plot of the vis("'sjty difference lId bet ween helium and mixture' of i,"I,urn and natural gas as a functi(}n of 1.h" "Oncenltatioll of natural gas.

The uata givcn in Fig. 4,6 wet'e obtained from experiments based on the measuring method described in chapter 3.2. Thc slope

fl.,

of the line for low concentrations of natural gas equals Hv = (--141

±

2) , 10 .. 9 _Pa.s/%. Since the density p of (he natural gas is 0.78 kg.rn"3 this slope is also 42

equal to flm

=

(--·181

±

3) . 10-1 _Pa.s,kg-1 _{m~, When helium is used as} carrier gas then the time constant T is calculated to be OA3 sec.

In o(der to reduce the value of this time constant, a nW8su,ement with hydtogcTl as cattier gas was also conducted which gives a calcu1a.tcd value of T = 0.2 sec. For t.his experiment oxygen as solute was used, Fig. 4,7 shows the viscosity relation for hydrogen-oxygen mixtures as It function of the oxygen content (% (v/v)),

1,0 'ld'10 7 100 (Pit·51 6(J 1.0 20 ... 1 .. :10 40 60 100., Xc, rig. 4,7 I'lot or the viscosity difference 'ld between hyUr<.>gen and oxygen-hydrogen

"'i)(wre~ lIS ~ fu!)ction of the oxygen concentration.

nle

data presented jn Fig, 4,7 were obtained from viscosity measurements, as described in chapter 3.2. The slope of the line for low oxygen Coneen· Ualions equals Hv

=

(402 ± 5) • 10-9 Pa.s!% Or Hm

=

(302 ± 4) - 10-1 h.s kg'"' 1113 (p

=

1.33 kg m~3), The hycltogciluscd in this experiment had an impmity of ahout 1 % air.

In these cases where it was intended to detect very sharp peaks, the detector response was recorded with an UV-rec(lrder (model Visigraph 51., San-fi, Tokyo, Japan). In all othcr exporimcilts the peaks were rcgiHratcd with a x·t-recorder with a response time of about. 0.3 sec, (model BD-41, Kipp & lonen, Delft, the Nethcrlands), as is used typically iTl chromato-graphy.

To test the new detector in combination with a gas chromatographic column, the arrangement shoWTl in [,'ig. 4.8 Was applied.

1"'if;.4.8 Sohcma!k diagram of the cxp~rinwIltal arrangement with a ga, chromato· graphic column_

Helium as carri~r gas was used ,Lnel the CC-column (50 III x 0.02

em

ID) contain~d sq\lalane as tho stationary phasc,

As this work wa~ not concerned with optimi7.ation of the C;C-coILlmn, but rather the exploration of t.he detection principle optim~l conditions from the vicwpoint of

column

efficicncy werC !lot aimed at 111lhoLLgh the flow-rate of carrier ga~ is in the normal range for gas chromat.ogr,Lphic

ap-plicatioIl~. All the experiments were performed ill. room temperature 293.7 ± O.S K.

For the discussion of the results let us use the surface area () of the measured peaks (eqns, 2.13-2,15). This surface area is measured with a

planimeter (type 10.000.115, Ott, Kempten, G.F.R.).

4.2.3 Results

In

r;ig. 4.9 and 4.10 thc illCa$urCd values

of

the $UrfllCC arCa () (V .s) arc plotted as a function of the injected miLSS of pLlre oxygen with nitrogen as carrier gas, I~'or convenience lei liS cxpres~ lhi~ iIlje~lccl mass M_illi in V;ni: Mini = P Villi where p h; the density (kg. 111-3 ) of t.he injected ga~.

20

I~

10

hl W ~ W 9~

V'OL -101m3) Fig. 4.9 Plot of til" m~as\'t~d ~urf"cc arca again,[ the injcdecl volume or oxygen with nitrogen as (Carrier g~$; Ij)o = 10-" TIl; / •.

For these experiments the injection systems (I) and (li) were used respec-tively, in the set-up shown in fig. 4.4. '{'he volume Vu in Fig. 4.10 repre-sents the dead space of the injl>ctlon valve.

o

(vol

200 400 (,00 800

Fig. 4. 10 Plot of th~. mC~S\lrcd surface area again,t the injected volume of OXyg~1l

with JlitrQgcn as catrier gas; <1>0 = 10-0 m' j,.

The experiml>nts with helium as carrier gas and natural gas as solute were performed with the set-up as shown in Fig_ 4.8, where the GC-column was replaced by a capillary with a !low resistance comparable with that of the column. The results of these experiments arC shown in Fig. 4. II, where Mini is also expressed in m3 •

The fact that the line does not pass through the origin, is due to the dead space of the syringe needle wltich has to be taken into account because of the excess preSSure in the splitter (2.5 -lOs Pa). The division factor

K

in these experiments was (7.4 :!: 0.2) - 1O-~. The maximum concentrations of natural gas in the detector, due to mixing and diffusion effects, were below 2% (v/v), so it can be assumed that II linear viscosity relationship exists (sec fig. 4.6). The dilution (about 50 times) compares well with those calculated for GC-colurllns (see table 4.1).

Fig. 4.12 shows the measured response of the detector upon an injcc. tion uf iO-~ nl~ of natural gas through the splitter. This corresponds with the. experiment at the lowest value of

V;"i

in Fig. 4.11. Due to the splitter only 0.08 -

10-

9 _{tn~ of natural gas teaches the detector.}

(v.l

20

Fig. 4.11 Plot of tile measu[l,d sllrface area against tile injocted VDlumc or natural gas wilh helium as carrie! gas; '~l) ~ 10-' In" !s, K = 7.4.10-'.

Fig" 4.12 DNector response "POll injection of 10-' ll\' of nutural g<ls. COllditio,ls:

helium fl!1 carrier gU:l; 'i'f) = lO-H Ill.) j".ll K = 7.4.10-:>.

R·

10 4

(v)

8

0.2s

t

Fig.4.l3 I)erootor rc~pOl1~e upon injection of 10-'J m,t of a mixt.ure OOl1t~llt1i"g

0.1 % of oxygt:.n in hyJrogt;r1. O'::'lldi1iOII~: hydrog.t;n a:-: l,;i.1rricr ga,"i; 1>TJ = 3.1

n-

7 _1Il:~

Is.

The detector response, recorded with the UV-recorder, upon an injec-tion of 10-9 _{m] of}

_a

_{mixture containing 0.1}

_%

_{(vlv) oxygen in hydrogen is} given in Fig. 4.13. FoL' this experiment injection system (iv) waS llsed in the arrangement shown in Fig. 4.4; hydrogen was \lsed as carrier gas.

The chromatogram (see Fig. 4.14) was obtained by injecting 60 ill of a mixture containing air and hydwcarbo))s with helillm as carrier gas. The

hydrocarbon~ were methane, ethane, propane and butane. The arrange·

ment shown in hg. 4.8

was

applied and K was 10-2_.

Pi:;. 4.14 Chromatogram obtained by injecting 6.10'

',tI'

of" mixture oontainin3

air and hydrocarbons. Conditions: helium as carrier gas; K =

ro-',

<i.>D = 10'-' rn' /$,

I ~ ai!, 2 " methane, 3" ethane, 4 0 propane, 5 " butane.

The fact that nitrogen and oxygen were not separated

was

due to the duo-matographic conditions.

4.2.4 Discussion

Let \J~ discuss the results in terms of the surface area O. According to the eqns. 2.15 and 4.18 the surface arCa Can be ex.pressed by

(4.19)

where X_ini is the fraction (v/v) of solute in the injected volume

Vi"j.

In most expcrimcnts pure solute was injected, therefore x_inj = I. In order to express the sllfface area 0 in t~nns ofthe injected solute mass~, '" p • x;".1

, V

_{ioli '} where p is the density of the pure solute, then the following equa-tion is applicable

H",

0=···-· ' M ' 'I _{4& ,. "M} (4.20)

where

Hm

(Pa.s. kg-t m') is the slope oHhe viscosity relation for low solute concentrations.

The theoretical vahle of the slope of t.he lines in Fig. 4.9-4.11 s,ltjsfie~ dO d Villi fl .. p '-~-'K'S '~ .. 4C\' M . "'.I (4.21 )

Bclllw ill lablo 4.3 tho values of the vilrioug parallleters in this eqLliltion

dO ilrc Iistod, together with t.he calculated ami cxpcril)1cntal valLles o f -d

Vj"i

ror buth the experiments with nitrogen Hml with helium a~ (lltrier g;IS.

Tahle 4.3 Valu"" "I' til" parameters for t]10 varioll' "'perilllt'nt; t0gCtl'\('t witl, the

l,.;alcuJal.cd ::l.[lU t:x!~l'ril\lI..:IHi.\l r0:ntlts.

Jlm.ljo: 10' (Pa.s kg'" 111"1) P (k)!, 1lI \) i\. .,. 10' ( ) );'ill i ( ) t.:i.lk " (4.76, O.(H)·lo-'··I11'. r.arti~r gi.\S 1l1lnJglj" h~~Jiu.m 20.7 , 0.1 U3 1000 I iJ,3;l , 0.0'1 C>.4~ , O.(ll) .. ·Ut 3 0.78 7.4

,ru

I ·0,24 . 0.01 ·0.229 • n.003 SM (4.3~, 0,(11)·10 'VII'a

h011! Ihi, lable olle sees all excellent corrdlltion hct.wecii cxpl'riltlClil ,Ind

thoory.

From Fig. 4.12 it can be ,cen that thl~ peak due to an inJcdio!l or lJ.lJe;· I () ,) Ill' Ila III I'll 1 gas into the detector is well above the )1oi~e lovel ilnd thilt (I gil1n in detection of ahout one order of magnitude is po~sib1c. If the standard deviMi()n of the pe~k could abo be redlKed by one order of

lIIagllililllc. onc would h,lveadct~cti()nlil11it ofaboulIO"llm'\ or )0-12 kg

of nalural gas u>ing hclillJl) as cllJ"l'ic( gas.

It is showll in Fig. 4.13 tliat tllis i.letcction limit is also valid for Ihe 1I11lo(lnt

..,f

l)xygCn whic;h (~In be detectctl with itydror,cn il.~ t;;lrrier gBS.

The chromatogram givt:n in !,'ig. 4.14 indicates the possibility to

mell-sure several cilr()lllatognlphit; peah without lilly distlirbalKc due t.o vis-wsity val'i,l1iol)s in cilpilbrics other than WI'

For the ciisclISsion or the performance of the detector in tCflllS

or

tile five paralllekr~ dcrincd in th0 introduction of this dlaptcr, let us take the

situation where hydrogen is used as carrier gas and oxygen as solute, (lim '"

(303 ± 4)-IO-7_Pa.skg-1 _m3_).

The response R of the detector can be written a, (cqn. 2.8)

lim C

R,,.---.~-(P -p

)·s

41ic In out M (4.22)

where

c

is the concentration of wlute (kg m-~). Making use of the fol-lowing ex pression for the flow-rate (¢ I) of carrier gas through the

detec-tor

eqn. 4.22 can be expressed by

SM

R = - - l l _{400 m}

'c"

_';'1)

(4.23)

(4,24)

The sensitivity S

or

the detector i, found by combination of the eqns. 4.7, 4.8 and 4,24, leading to

(4.25)

It can be seen from this equation tflat Lhe sonsitivity of the detector is only determined by an instmmcnt constant i.e, SM/4a and a parameter depending upon the gases involved i.e. lIm' The sensitivity is independent

of the measuring Cil'l;UtllstanCCS.

According to eqIl. 2.9 the time constant 1 of the detector is given by ;

(4.26)

with V_o",7.3-1O-"t11". Po '=I05Pa and fi=;ij.4·1O-t1_m3_jPa.

The maximum mass flow-rate (<pm) up to which the detector main-tains a linear re,ponse (see Fig. 4.2), can be calculated from the following equation

(4.27)

where xI'" is tile cllncentr,ltioJ\ (vlv) at which the slope of the line in Fig. 4.7 records a ;Vi!, (liffcrcnco fronl the vallie at concentration I.em . x,/l

=

5')!,. I;or the flow-rate ¢f) avaJue()fIO"'~ll1)s-l iSLIsed, bcinganormal value in gas chromatography: <{In,

=

(>.7' 10 .. 1<' kg.s-I.

In table 4.4 the vallle:s 0f the parameters are listed, which characterise the det~ctor in lile: present configLlrlllion.

Table 4.4 PnnJ.)11Dtt~r) charactt.)risiIlg tht': ctdcctor in its pH~!jtmt c.uJ\t1gurtltion.

Con-dition; hydrog(11 \I~ carr1cr g:.a;.; and oxygen as _<;c)lutc.

s

7.0' 10' 0.2.1 (). 4 1.\.\0 " 0,9+-10· I ~ 740 0.2 v~ I{]).'·I V k~ kp ., .. ,

II! Drder In estimate the ultimate lowest delcctable i\m()uni kt US be-gin !'rom 0qn. 4.11 and assume lh,\! the standard deviation (I can b,' as ~Illall a~ To I hi~ Icads to tile follOWing expressioll for the lowest dCICd"ble umOllllt:

(4.213)

Suhstitulion ..,1' the vallil's of tile various paralllc[cr, !\iv.:;-s us

/1.'1" "- 1.1 . l 0-11 kg (4.29)

If all lhc$e Cigllre~ together arc t"ken, onc may ~()ndude tilal the de· tector (\)1l1!l11I"es f:Jvourably with tile thermal conductivity detector, al-though there :lrc some differences. The ll1()~t important being Ihe fad that the thermal conductivity detector is c;onecnlrati()n-sen~it.iyc wherl!ils the detect(lr under discLission here i~ mass illlw-scnsitivc. Thi, m~alls t.hat for the thermal condudivity detector the qu,lI1litative a)l"ly~is depend on the gas !low-rate. whereas in this case thG rcwlts are independent of this ex-perimental panLII1C[CI".