摘要:

Enthalpic Exclusion Chromatography BY JOHNH. KNOX,ROMANKALISZAN~ J. KENNEDY AND (IN PART) GORDON Department of Chemistry University of Edinburgh West Mains Road Edinburgh EH9 3JJ Received 31st July 1980 Enthalpic exclusion of solutes from a porous matrix arises if the energetic environment within the matrix is unfavourable when compared with that outside. Two forms of enthalpic exclusion are demonstrated (a)exclusion of non-polar solutes from a matrix with a polar surface (Corning porous glass) when eluted by a polar eluent ; (b)exclusion of anionic solutes from a reversed-phase packing material (ODs Hypersil) when eluted by water + ethanol mixtures. Type (a) is considered to be one of negative adsorption where AH,, is positive rather than nega- tive.In type (b) fixed charges due to residual 35-0-groups are considered to be responsible. These produce a Donnan potential step at the surface of the particle. Exclusion of acids can be ex-plained quantitatively on this basis when allowance is made for the effect of pH on the ratio of ionized to un-ionized forms of the acids. The term " exclusion chromatography " is normally associated with the separation of polymers or other large molecules.1 The sample of polymer dissolved in a suitable solvent is eluted through a column containing a microporous packing material or matrix whose pores are of similar dimensions to those of the solute molecules. A simple but nonetheless realistic model for the process regards the solute molecules 2-4 as rigid spheres with a certain radius r.Correlation of experimental data with theo- retical predictions shows that this radius is close to the hydrodynamic radius of the polymer molecules. The centre of such a molecule cannot approach closer to any part of the internal surface of the matrix than this distance r. Thus if a surface is drawn parallel to the original internal surface of the matrix but at a distance r away from it the volume from which a solute molecule of radius r is excluded is the volume between this new surface and the original surface of the matrix. This simple idea is illustrated in fig. 1 for 2 dimensions. This volume can be expressed as a fraction of the pore volume of the matrix Vp or as a fraction of the total volume of the column other than that of the solid part of the matrix V,.In thermodynamic terms this exclusion effect is normally considered as resulting from a lower configurational en- tropy of the solute within the pores of the matrix than outside the matrix. However one could regard a molecule of radius r within the matrix as being constrained within a square-well potential the floor of the well being at the same potential as that outside the matrix while the walls of the well rise to infinite potential energy at a distance r from the internal surface of the matrix. In this way exclusion can be regarded as arising from energetic rather than steric effects. The square-well potential is of course simply a special case of a more general potential function but is evidently adequate for polymers in this context.Small molecules can also be excluded from matrices if their potential energy within the matrix is higher than that outside the matrix. In such a case we might envisage a t Present address Institute of Technology and Analysis of Drugs Medical Academy 80-416 Gdansk K. Marksa 107 Poland. ENTHALPIC EXCLUSION CHROMATOGRAPHY outer particle surface gion of exclusion solid matrix r FIG.'1.-Two-dimensional analogue for exclusion of a spherical molecule of radius r from a matrix composed of colloidal spherical particles (such as a silica gel for instance). series of surfaces drawn at different distances from the internal surface of the matrix each representing a potential-energy contour with the energy increasing as the distance from the original surface is reduced.Exclusion so described is essentially enthalpic rather than entropic and might be thought of as " negative adsorption ". All forms of exclusion both entropic and enthalpic may in fact be embraced by the general eqn (1) for the ratio of molecular concentration within the pores of the matrix Cp,to the molecular concentration outside the matrix CO5 where pxyzis the excess molecular free energy at any point (x,y z)within the pores of the matrix and the integral is taken over the entire pore volume. In the case of purely geometric exclusion (as proposed in the simple model for polymers) pxVzis zero within the accessible volume and infinite everywhere else so that the ratio Cp/Co is the fraction of pore volume accessible to the polymer molecule.non-entrant contours AJ solid matrix -equipotential lines FIG.2.-Two-dimensional analogue showing equipotential contours in a matrix composed of colloidal spherical particles and illustrating the existence of non-entrant contours. J. H. KNOX R. KALISZAN AND G. J. KENNEDY There are two straightforward situations under which enthalpic exclusion will occur. The first is exemplified by the partial or total exclusion of a non-polar sub-stance such as pentane from a column containing silica gel when eluted with a highly polar eluent such as ethanol. Because of hydrogen bonding between the silanol groups of the gel and ethanol there will be a unimolecular layer of strongly adsorbed ethanol at the surface of the matrix (see for example Scott and Kucera6).This will be overlaid by further layers which are progressively less strongly adsorbed but never- theless have a significantly lower molar free energy than bulk ethanol. Whereas in the bulk phase and at the centre of wide pores in the matrix molecules of pentane will have an equal statistical probability of replacing ethanol molecules volume for volume they will have a much lower probability of replacing ethanol molecules in the ad- sorbed surface layer owing to the positive enthalpy change in the displacement re- action (2) a(c5H12) + P(C2H50Hads) *a(C2H12ads) + P(C2HSOH) (2) (where a and p are inversely proportional to the molar volumes of pentane and ethanol respectively). In effect C5H12 molecules will be partially or completely ex- cluded from the adjacent and surface layers.Accordingly the probability per unit volume of finding a pentane molecule in any volume element within the pores of the matrix will be lower the closer that volume element is to the surface of the matrix. The second situation arises with charged species since any surface will possess a charge due to fixed ions or ions adsorbed from the surrounding liquid and conse- quently an electrical potential relative to the liquid with which it is in contact. In the same way as surfaces corresponding to different free energies may be drawn parallel to the internal surface of the matrix surfaces of equal electrical potential can also be drawn as shown for two dimensions in fig. 2. The position of such contour-surfaces will be governed by theories such as the Stern Gouy and Chapman7 theory for the electrical double layer.For typical materials used in h.p.1.c. the pores of the matrix will be of similar dimensions to the thickness of an electrical double layer K-I. For example in a typical silica gel the pores may have a mean radius of ca. 50 A while IC-I for a uni-univalent electrolyte in water is approximately given in A by 3/(C/mol dm-3)'t. Evidently at low values of C the lower-energy contour-surfaces may never in fact enter the particles. We can therefore envisage that a potential step must be overcome before an ion of similar charge to the particle can enter the pores and that once inside it will experience an increasingly repulsive potential as it tries to approach the surface of the matrix.In general for a trace concentration of an ion X,with a charge z (where z may be a positive or negative integer) the total electrochemical potential throughout the system (both inside and outside the matrix) must remain constant. That is taking the outside electrical potential as zero Po = Pv + ZSVF (34 RT lna = RT lna + zyF (3b) where p0and a. are the chemical potential and activity of Xz+in the bulk eluent while pwand a are the corresponding quantities in a region where the electrical potential is w. Eqn (3) makes it clear that ions with a positive charge (z positive) will have lower chemical potentials and activities in regions of positive potential and so will be excluded from such regions while ions of negative charge will be attracted into such regions.A special case arises where a potential-determining ion is confined or largely con- ENTHALPIC EXCLUSION CHROMATOGRAPHY fined to one side of a surface either by a physical membrane which it cannot penetrate or as a result of adsorption onto the surface of a porous matrix of high internal surface area while other counter- and co-ions are not so restricted. This is the situation resulting in the classic Donnan membrane equilibrium. The potential which results is a function of the concentrations of the various species in the system being larger the more dilute the external solution. If a trace concentration of a salt is now introduced into such a system the ions of the salt will be distributed between the two regions according to eqn (3).In the present context we therefore envisage that a Donnan membrane in effect exists at the outer surface of any particle of packing material and that superimposed on this will be effects resulting from the varying potential throughout the pores of the matrix close to its internal surface. As the ionic strength of the bulk liquid outside the particles is increased both the Dorinan effect and that arising from the double layer at the internal surface of the matrix will be reduced. Thus for an excluded ion (with the same charge as the particles of matrix) the degree of exclusion should be reduced as the ionic strength of the eluent is increased. in this paper we establish the existence of both types of exclusion namely exclusion of neutral species by " negative adsorption " and exclusion of ions by like-charpe repulsion.EXPERIMENTAL EQUIPMENT AND CHEMICALS For the work on the exclusion of non-polar solutes from silica gel the equipment was as described by Kennedy and Knox.8 Columns were 480 x 2.1 mm and packed with 44-53 pm Corning porous glass CPG 70 (surface area 300 m2 g-I). For the work on the exclusion of ionized solutes from a reversed-phase bonded silica gel a conventional h.p.1.c. system was used comprising an Orlita DMP 1515 microdosing pump (Orlita Giessen GFR) a Shandon pattern 250 mm long 5 nim bore column with a septum injector (Shandon Southern Products Runcorn) and a Cecil 212 U.V. photometer (Cecil Instruments Cambridge). The column was slurry packed with 5 pm ODs-Hypersil (Shandon Southern Products).Solvents were either h.p.1.c. grade from Rathburn Chemicals Walkerburn or A.R. grade (B.D.H. Chemicals Poole). Retention volumes were determined directly by weighing the eluent emerging from the column between the moment of injection and the emergence of the peak allowance being made for the density of the eluent which was independently measured. An Oertling F22TD Balance (Oertling) was used for this purpose. The output from both the detector and the balance were passed to a Servoscribe 2 twin pen recorder (Smiths Industries London). pH was measured by a Pye model 290 pH meter (Pye Unicam Cam- bridge) fitted with a CF72 glass electrode (Russel pH Auchtermuchty). The volume of eluent in the column V,, was determined by a method to be described in detail el~ewhere.~ In summary the method involves determining the retention times of radio-labelled components of eluent.V is then precisely obtained from the equation V" = xAVA* $-xBVa* f -.. .-(4) where xA,xa . . . are the volume fractions of components A B . . in the eluent and VA* V,* . . . are the retention volumes of radio-labelled samples of A B . . .. The radio-labelled chemicals were obtained from the Radiochemical Centre Amersham. Their retention volumes were determined by collecting single drops of eluate and counting these after dilution with scintillation counting fluid (B.D.H. Poole) using a Beckniann LS 133 scintillation coun- ter (Beckmann Instruments Fullerton U.S.A.). The drop volume was obtained in a separate experiment by weighing a given number of drops.Using this technique with three pure radio-labelled eluents V for the column packed with CPG 75 material was found to be J. H. KNOX R. KALISZAN AND G. J. KENNEDY 117 1.27 f 0.02 cm3. Using the same techni-que but with 19 eluent mixtures Vm for the ODS- Hypersil column was found to be 2.85 & 0.01 cm3 the error limit being the standard deviation of the mean. For the second column the weight of the packing determined after completing the experiments was 2.440 g and the volume of the empty tube was 4.10 cm3. Other details of the parameters for the two columns are given in table 1. TABLE 1.-COLUMN PARAMETERS Directly determined parameters are italicised. packing material CPG 75 ODs-Hypersil particle size dp/pm 44-53 5 (nominal) column length,”L/mm 480 250 column borelmm dJmm 2.17 5.00 empty column volume Vc/cm3 1.78 4.10 wt.of packing/g not determined 2.440 volume of eluent Vm/cm3 1.27 $ 0.02 ’ 2.85 5 0.01 volume of silica Vs/cm3 0.51 1.01 = volume of organic material Voto/cm3 nil 0.24 volume of mobile zone Vo/crn3 0.76 1.76 pore volume Vp/cm3 0.51 1.09 k’ for complete exclusion -0.40 -0.38 (1 -Vo/Vm) Determined by radio-tracer method see text. Calculated from known pore volume of 0.45 cm3 g-’ assumed density of matrix of 2.20 g cm-3 and assumed porosity of packing VJVC = 0.43 (see Knox and McLennan).” Calculated from weight of packing manufacturer’s data on %C and 0.90 g ~m-~ assumed density of matrix of 2.20 g cn~-~ for ODS bonded layer.“ Vo/VCassumed 0.43.” The degree of exclusion (or retention) of any solute is measured by the column capacity ratio k’ which is defined by eqn (5) column capacity ratio k’ VR -v (5:) = __II-Vm where Vmis the volume of the eluent phase within the column and VRthe retention volume of the solute. For excluded solutes k’ is negative. In this paper k’ is preferred to the alterna- tive parameter the zone capacity ratio k” defined in eqn (6) where Yois the volume of the mobile zone outside the particles since there is a well-defined method of determining V, whereas Yocan be inferred only by assuming it equal to VR for the most excluded solute available. Measurements of the zeta potential of ODs-Hypersil were made with a Rank microelectro- phoresis equipment Mark I1 (Rank Bros.Bottisham Cambridge). The electrophoretic velocity u, was determined in a quartz cell 0.80 mm deep 9.7 mm wide and ca. 50 mm long at different distances Y from the lower face of the cell. A voltage of 50 V was applied across the two platinum electrodes. The true electrophoretic velocity id, relative to the liquid was then obtained from the measurements of u by the standard procedure (see Overbeek)’’ and the zeta potential c found by application of the Helmholtz-Smoluchowski equation where = viscosity E = field strength = dimensionless dielectric constant or relative permittivity of medium E* = permittivity of a vacuum = 8.85 x C m-’. ENTHALPIC EXCLUSION CHROMATOGRAPHY RESULTS I.ENTHALPIC EXCLUSION OF NEUTRAL SPECIES Values of k’ for a variety of solutes are shown in fig. 3 from which it is clear that there is a substantial degree of exclusion of a non-polar solute such as pentane when eluted with a highly polar eluent such as ethanol. The degree of exclusion closely follows the eluotropic series as established by Snyder.ll The most extreme exclusion was found for the elution of pentane by ethanol where k’ = -0.25. This compares with a value of ca. -0.40 for complete exclusion. CPG 75 is a material with a mean eluent CCI MeCOOEt EtOH EO I 0.18 I 0;58I‘ 0.88 0.0 soIute E0 k’ -0.1 Me NO2 0.64 PhCl 0.30 -0.2 c CI 0-18 -0.3 I I I I I I J . ‘5 H12 0.00 0.0 0.2 0.4 0.6 0.8 1.0 E’ of eluent FIG.3.-Exclusion of non-polar solutes eluted by polar eluents from an adsorbent.Packing material 44-53 pm chips of Corning porous glass CPG 75. Values of E’ are taken from ref. (1 1). For other details see table 1. pore diameter of ca. 70 and one therefore envisages that the intense adsorption of ethanol on the surface extends some way beyond the first monolayer so that the value of AH for the exchange reaction (2) is still significant even at the centre of a pore. Averaged over the pore volume the mean AG for transfer from the bulk eluent to the pore-liquid is +2.5 kJ mo1-’. It may be noted that the results depicted in fig. 3 invalidate a widely advocated method for determining V,12913 in adsorption chromatography which for any eluent advocates that V be taken as the elution volume of the most non-polar solute avail- able.It is clear that in many cases such solutes will be significantly excluded. The correct version of this recipe for determining V should identify V as the elution volume of a solute having the same eluotropic strength as the eluent. 11. ENTHALPIC EXCLUSION OF CHARGED SPECIES The exclusion of three organic acids from ODs-Hypersil was examined under a wide range of conditions. The acids and their pK valuesI4 are listed in table 2. Fig. 4 shows the dependence of k’ upon volume fraction of water in water-ethanol mixtures containing mol dm’3 sodium nitrate. The measured pH of the un-buffered solutions were from 5.5 to 7 indicating negligible concentration of either H+ or OH-. Under these conditions all acids involved were fully ionized at the con- J.H. KNOX R. KALISZAN AND G. J. KENNEDY TABLE 2.-vALUES OF k' FOR UN-IONIZED AND IONIZED ACIDS AND THEIR APPARENT PK,VALUES IN WATER~ETHANOL50/50 v/v PKJ3 acid kLA" k'Ab eluent" pure waterb sulphanilicbenzoic -0.03 0.60 -0.29 -0.26 3.25 5.48 (1; 3.25 4.20 salicylic 0.87 -0.29 4.05 3.10 Values which give curves drawn through data points of fig. 7. Taken from ref. (14). centrations used for chromatography ( mol dm-3 and below). Sulphanilic acid shows the greatest degree of exclusion with a minimum k' of almost -0.4 correspond-ing to complete exclusion (see table 1) from the pores of the packing material. Tn general a high degree of exclusion is exhibited over the entire composition range.The other two organic acids are partially excluded in the composition range 10-80%. Maximal exclusion occurs at a composition of ca. 50% water. With more than 80% water both acids become retained. The effect of ionic strength on the exclusion of the three acids in an eluent com- prising 30/70 by volume water + ethanol is shown in fig. 5. The variation of k' with concentration of sodium nitrate follows the curve expected from the Donnan equili- brium as discussed in detail below. In fig. 6 corresponding curves are shown for sulphanilic acid with water as eluent containing various concentrations of sodium nitrate. The dependence of zeta poten- tial is also shown and closely follows the degree of exclusion. Fig. 7 shows the dependence of k' upon pH for 50/50 by volume water + ethanol containing 5 x mol dmq3 sodium nitrate and buffered by 5 x potassium 60 40 k' c -20 0 0.2 0.4 0.6 0.8 1 volume fraction H20 FIG.4.-Dependence upon composition of k'-values for acids eluted from ODs-Hypersil by water + ethanol mixtures. For column details see table 1. Eluents contain mol dm- Na NO, 0 zeta potential in mV (right-hand scale); (3 k' for benzoic acid (left-hand scale); 0,k' for salicylic acid (left-hand scale); e,k' for sulphanilic acid (left-hand scale). 120 ENTHALPIC EXCLUSION CHROMATOGRAPHY I I 1 I I 0 - - k’ 0 0 . acetate HCl being added to adjust the pH. The degree of retention is progressively reduced as the pH is increased and the acids pass from the un-ionized to ionized forms.The data are in close agreement with prediction assuming that the un-ionized and ionized forms of the acids have individual k’ values which are independent of pH. The zeta potential increases markedly with pH. Detailed discussion is presented below. DISCUSSION EXCLUSION THROUGH THE DONNAN EFFECT Exclusion of co-ions arises whenever charged species are confined to a particular region within a thermodynamic system and this is accompanied by a corresponding 60 40 k‘ 20 --0.4 I I I I I 0 -5 -4 -3 -2 -1 0 log (INaN03]/mol drn-j) FIG. 6.-Dependence upon ionic strength of zeta potential and k‘ oEphanilic acid. Eluent water. Curve for k’ dependence drawn according to eqn (16) with [X-]= lW2a5mol dm-’.J. H. KNOX R. KALISZAN AND G. J. KENNEDY electrical potential difference between the two regions. In the present case we suppose that the packing material (ODs Hypersil) which zeta-potential measurements show to be negatively charged contains a certain number of fixed charges X- whose con- centration is denoted by [X-]. In general quantities with bars will apply to the region within the particles of packing material. In the presence of eluent containing 60 e k‘ 5 40 20 PH FIG.7.-Dependence upon pH of zeta potential and k’-values of acids. Eluent 50/50 by volume water + ethanol containing 5 x mol dm-3 NaNO and 5 x mol dm-3 K CH3CO0 pH adjusted by addition of HCl. For symbols see fig. 4. Lines calculated according to eqn (20) with values listed in table 2.added salt for example sodium nitrate the thermodynamic system shown in fig. 8 will exist. If it is assumed that S-is present in trace quantities equalities (8) and (9) are then required for overall electrical neutrality “a+] = [NO-,] (8) and equalities (10) and (1 1) for thermodynamic equilibrium aNa OINOa = aNa %NO3 aNa as = ENS as* As a first approximation it is reasonable to replace activities by concentrations in eqn (10). However in eqn (11) while ascan be set equal to [S-1 the activity coeffi- cient of S-within the particles of packing g,cannot be taken as unity because of ENTHALPIC EXCLUSION CHROMATOGRAPHY likelihood of strong hydrophobic interactions between the organic groups in S-and the hydrocarbon-bonded stationary phase.Eqn (10) and (1 1) can be approximated by eqn (12) and (13) [Na+][S-] = [Na+][S-] ys . Simple elimination then yields eqn (14) for the zone-capacity ratio k” for S-where Eqn (14) provides a minimum value k’lmin= 0 when “a+] tends to zero (ie. Z -+ GO) and a maximum value k”,, = plys when “a+] is high (Le.,Z -f 0). Eqn (14) can thus be recast as In fig. 5 and 6 the lines are drawn to give the best fit of eqn (16) to the data. The fit is seen to be within experimental error. The optimum values of [X-] are mol dm-3 for fig. 5 (30/70 by volume water + ethanol) and 10-2*5mol dme3 for fig. 6 (water). It may be supposed that the fixed charges X are 3%-0- groups at the internal Outside Particle inside Particle Surface Particle -Fixed charges [X-] .X Background “a+] Electrolyte } {m -Solute ions [S-] ccs Solute ions [S-] .S FIG.8.-Thermodynamic system for discussion of Donnan equilibrium.surface of the packing material. Hypersil before bonding has a specific surface area of 170 m2 g-’. Taken with data from table 1 it is readily shown that this is equivalent to 350 m2 per cm3 of pore volume in ODS-Hypersil. Concentrations of 10-1.5 mol dm-3 and mol dm-3 then correspond to 0.09 and 0.01 pmol m-2 if localized at the original internal surface of the silica gel. These concentrations are low when com- pared to the total concentration of octadecyl groups bonded to the surface (2.5 pmol m-’) or of underivitized silanol groups (6 pmol m-2) or of the maximum concentra- tion of hydrophobic ion-pairing agent which can be adsorbed by ODS Hypersil (up to 5 pmol m-2).15 The electrical potential between the exterior and interior of the particles (see fig.8) containing fixed charges X-will be given by J. H. KNOX R. KALISZAN AND G. J. KENNEDY Applying eqn (14)-( 16) then gives Thus changes in In kffshould be reflected in changes in v. If w is identified as the zeta potential then by changing “a+] there should be corresponding changes in In k” which are mirrored by changes in c. The data in fig. 6 provide a test of this hypo- thesis. Table 3 lists relevant data. It is seen that although the c-values are of the correct magnitude [does not fall to zero at high “a+] but to a more or less constant value of 15 mV.However the amount by which 6 exceeds 15 mV does follow the theoretical relationship fairly well. We may therefore conclude that the major cause for exclusion of sulphanilic acid and presumably of the other acids from ODs-Hypersil arises from the Donnan effect that is from a potential step at the surface of each particle which discourages the entry TABLE 3.-CORRELATION OF ZETA POTENTIAL WITH EXCLUSION Packing ODs-Hypersil ; eluent water containing NaN03. - 10-4 -0.33 0.12 0.10 2.30 -59 -55 -40 -0.45 0.43 0.37 0.99 -25 -43 -28 lo-* 0.45 0.91 0.78 0.25 -6.4 -23 -8 lo-‘ 1 0.26 0.28 1.10 1.13 0.94 0.97 0.06 0.03 -1.5 -0.8 -417) -(W -2 -1 a k” calculated assuming that the completely excluded solute (k” = 0) has k‘ = -0.4. k” max Bracketed values areextrapolated all values of [ are negative.c0 assumed -15 assumed 1.17. mV. of ions of the same charge as the particles of packing material. There does not appear to be any significant effect attributable to selective exclusion within the pores of the packing material and resulting from the double layer close to the internal surface of the matrix. The situation is closely parallel to that observed with ion-exchange resins.16 EFFECT OF pH ON k‘ For any acid the ratio W,of the un-ionized to the ionized forms is given by where K is the hydrolysis constant of HA. If the capacity ratios for HA and A-are respectively kIHAand klAthen the observable value of k’ for a partially ionized sample of acid will be given by eqn (20) By fitting the experimental dependence of k’ upon pH to eqn (20) pKa may be found.The values so obtained are listed in table 2 along with values of k’HAand kfA. The curves in fig. 7 are theoretical curves drawn according to eqn (20) from which it is seen that an excellent fit is obtained. As expected the molecular forms of the acids ENTHALPIC EXCLUSION CHROMATOGRAPHY are either fully permeating (sulphanilic acid) or retained (benzoic and salicylic acids) while the ionized forms are all excluded. The pK of sulphanilic acid in Sol50 by volume water + ethanol is the same as in water but those of the carboxylic acids are increased by about one unit. The dependence of zeta potential upon pH is shown in fig. 7. The potential rises in a concave fashion as pH is increased from 2 to 8.In constructing the curves for fig. 7 it was assumed that k’ was unaffected by pH. However in the light of the discussion of the Donnan effect k’ should be closely linked to [. Only when [ is fairly large will klA be near its minimum value of ca. -0.3 to -0.4. It will however be noted that for both benzoic and salicylic acids the major part of the change in k’ with pH occurs at pH exceeding 4 when the zeta potential is in the range 25-55 mV. Over this range the function exp [-Fc/RT] which governs the extent of exclusion falls in the range 0.38-0.12 so that S-is fairly well excluded over this range. The major cause of the fall in k’ is the change in the proportion of un-ionized to ionized forms rather than the precise value of klA.Only when the pH exceeds ca. 5 and c exceeds ca. 40 mV is the observed value of k’ dominated by the value of klAwhen the exponential factor is more or less constant between 0.2 and 0.12. For sulphanilic acid the situation is different for the change from high to low k’ occurs over a range of pH where the zeta potential is low and changing rapidly from 0 to 30 mV. In this region the change in k’may result as much from the change in as from the change in the ratio of un-ionized to ionized forms. More extensive experi- mental data would be required to establish which factor was dominant here. CONCLUSIONS Solutes may be excluded from typical packing materials used in h.p.1.c. on the basis of unfavourable enthalpy changes. Two types of enthalpic exclusion are demonstrated (a) exclusion of non-polar solutes when eluted by polar eluents from a polar adsorbent (Corning porous glass) and (b) exclusion of anionic solutes eluted from a reversed-phase packing material (ODS-Hypersil) by water + ethanol mixtures.Exclusion of the first type arises because of the difficulty which a non-polar solute finds in displacing a strongly adsorbed polar molecule from the surface of the polar adsorbent. This is an example of negative adsorption in which AHadsis positive rather than negative. Further work is desirable to determine the value of AHadsand to establish the relative importance of enthalpy and entropy effects. Exclusion of the second type arises from the presence of fixed negative charges probably due to 3Si-0- groups within the matrix of the packing material at a concentration of 0.01-0.09 pmol m-2.The degree of exclusion of anionic solutes correlates well with the zeta potential and can be explained quantitatively by the Don- nan effect. The effect of pH on the degree of exclusion or retention of acids is ex-plained by the change in the ratio of ionized to un-ionized forms. W. W. Yau J. J. Kirkland and D. D. Bly Modern Size-Exclusion Liquid Chromatography (John Wiley New York 1979). E. F. Cassassa and Y. Tagami Macromolecules 1969 2 14. J. H. Knox and H. P. Scott to be published. M. E. van Krefeld and N. van den Hoed J. Chromatogr. 1973 83 111. J. C. Giddings E. Kucera C. P. Russell and M. N. Meyers J. Phys. Chem. 1968 72 4397. R. P. W. Scott and P.Kucera J. Chromatogr. 1978 149 93. ’J. T. G. Overbeek in Colloid Science ed. H. R. Kruyt (Elsevier Amsterdam 1952) vol. 1. G. J. Kennedy and J. H. Knox J. Chromatogr. Sci. 1972,10 549. J. H. Knox and P. Kaliszan to be published. J. H. KNOX R. KALISZAN AND G. J. KENNEDY lo J. H. Knox and F. McLennan J. Chromqtogr. 1979 185 289. l1 L. R. Snyder Principles of Adsorption Chromatography (Marcel Dekker New York 1968). l2 R. P. W.Scott Contemporary Liquid Chromatography (John Wiley New York 1976) p. 260. l3 L. R. Snyder and J. J. Kirkland Zntroduction to Modern Liquid Chromatography (John Wiley New York 2nd edn 1979) p. 24. l4 Landolt-Bornstein Zahlenwerte und Fuctionen (Springer-Verlag Berlin 1959) band 11 p. 775. l5 R. A. Hartwick and J. H. Knox J. Chromatogr. 1980 in press. l6 F. Helfferich Zon Exchange (McGraw Hill New York 1972).

ISSN:0301-5696    

DOI:10.1039/FS9801500113

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

Macromolecular Separations by Liquid Exclusion Chromatography BY JOHN V. DAWKINS YEADON? AND GRAHAM Department of Chemistry Loughborough University of Technology Loughborough Leicestershire LE11 3TU Received 7th July 1980 High-performance separations of macromolecules by liquid exclusion chromatography have been performed with silica microspheres (particle diameter M 8 pm) having a bonded phase resulting from reaction with y-glycidoxypropyltrimethoxysilane. Experimental retention data for dextrans and several proteins e.g. ovalbumin and myoglobin in aqueous media suggest that the separation mechanism is steric exclusion. For other proteins secondary mechanisms which may be either adsorption or partial exclusion owing to ionic repulsion occur and may be interpreted in terms of a thermodynamic representation of a mixed mechanism.When interactions between solute and sta- tionary phase are not involved solute diameter is a reasonable universal size parameter for dextrans and proteins in aqueous media and for polystyrenes in tetrahydrofuran. Experimental plate-height data for proteins and polystyrenes indicate a considerable increase in the contribution from solute mass-transfer in the stationary phase as the eluent flow-rate is raised. Diffusion coefficients for macromolecules in the stationary phase determined from experimental plate-height data by a method proposed for high polymers are far below (ca. one tenth) the values for the solutes in free solution. The same method also permits the evaluation of the polydispersity from experimental plate-height data demonstrating that ovalbumin may be regarded as monodisperse.Many theoretical models have been proposed for the size separation of macro- molecules with a porous packing in liquid exclusion chromatography which describes more accurately the separation process than the more common terms gel-filtration and gel-permeation chromatography. The theories are conveniently classified under two headings equilibrium models and flow models. There is abundant evidence indicat- ing that size-exclusion separations performed at practical eluent velocities of ca. 0.1 cm s-l operate close to equilibrium conditions.lP2 The first theories of steric exclu- sion considered simple geometrical models from which the fraction of pore volume accessible to a solute of given size may be ~alculated.~ This steric-exclusion model is equivalent to the statistical mechanical treatment of the loss in conformational entropy when a macromolecule approaches an inert surface.These thermodynamic theo- ries1V4-’ calculate the accessible pore volume in terms of pore size for various models of pore shape and in terms of solute size for both rigid and flexible-coil polymers. Consequently flow mechanisms such as the restricted-diffusion model proposed by Ackers8 are assumed to have no role in determining the fundamental separation relation between solute size and retention volume V, except possibly as a secondary effect at high eluent velocities above 1 cm However the suggestion that diffusion of molecules in porous media is hindered due to tortuosity and constriction effects is important in the detailed interpretation of the dispersion mechanisms which influence the peak width of a chromatogram.In the first thorough theoretical treat- ment of chromatogram-broadening in liquid exclusion chromatography Giddings and Mallik l1 indicated from experimental evidence for small molecules separating in t Present Address National Adhesives and Resins Braunston Daventry Northants. MACROMOLECULAR SEPARATIONS soft gels that the diffusion coefficient of a solute D,in a porous gel was ca. 2DJ3 where D is the solute diffusion coefficient in the mobile phase. Values of D,may be determined by evaluating from the total plate height of an experimental chromato- gram the contribution arising from solute mass-transfer in the stationary phase.For polystyrene standards values of D,are much less than D, results in the range 0,/20 to D,/5 being typical.12-14 In this paper we report retention-volume and plate-height data for monodisperse proteins separating in aqueous media by liquid exclusion chromatography with porous silica particles having a bonded phase resulting from reaction with y-glycid- oxypropyltrimethoxysilane (abbreviated here to 7-G). Since 1976,15-18there has been considerable interest in microparticulate inorganic packings modified by this silylation treatment for high-speed and high-resolution size-exclusion separations of biological macromolecules. Because the column packing consists of rigid particles our size separations of proteins and dextrans with an aqueous eluent may be compared with results for polystyrene standards in tetrahydrofuran.The proposal that the extent of solute permeation in a steric-exclusion mechanism is dependent on the mean external length or molecular projection for various types of molecules6~' has been studied and the occurrence of secondary mechanisms arising from interactions between solute and stationary phase has been considered. From the dependence of plate height for monodisperse proteins on eluent flow rate the mass-transfer contribu- tion arising from solute diffusion in the stationary phase may be evaluated permitting the determination of D,. The same procedure has been used for polystyrene stan- dards also showing how the polydispersity may be evaluated from plate-height data.EXPERIMENTAL The sample of SG30 silica was kindly provided by Dr. J. D. F. Ramsay and Dr. D. C. Sammon of AERE Harwell. Examination of the silica particles by scanning electron micro- scopy and Coulter counter suggested that the mean particle diameter was 8 pm. Before reaction with the silylating agent siloxane groups on the silica surface were converted to silanol groups by refluxing the SG30 silica sample in hydrochloric acid (2.5 mol dm- 3 for 1.5 h and then leaving the sample to cool for a further 2 h. The silica was washed with distilled water followed by acetone (AR) and then dried under vacuum at 150 "C for 24 h in order to remove physically-bound water. The silica having a y-G bonded phase was prepared by reacting SG30 silica (10 g) with y-glycidoxypropyltrimethoxysilanein aqueous media according to the method described by Regnier and Noel.Is After the packing had been washed with water it was further washed with 0.1 mol dm-3 hydrochloric acid (50 cm3) water and acetone (AR) before drying under vacuum.From elemental analysis the carbon content of the silylated SG30 silica was estimated to be 3.Ox. Scanning electron micrographs before and after silylation indicated no breakdown of the particles. A column (25 cm X 0.8 cm internal diameter) was packed by pumping a methanol slurry of the silylated silica at 5.86 x lo6 N rnv2 according to the method of Bristow et aI.I9 At the top of the column the silica packing was covered by a stainless-steel mesh above which was placed Ballotini which in turn was covered by a porous Teflon plug.A syringe injection head was then attached at the top of the column. Separations were performed with a Perkin-Elmer model 1220positive displacement syringe pump. Detection of solutes was performed with a variable-wavelength Pye-Unicam 1.c.-U.V. detector (215 nm cell volume 8 x 10-6dm3 single beam) for proteins (various sources) an LDC RefractoMonitor model 1107 (cell volume 0.5 X dm3) for dextrans (Sigma and Phar- macia) and an ARL U.V. detector (254 nni cell volume 8 X dm3 air reference) for poly- styrene standards (Waters Associates). The polystyrene standards are designated PS with a number which is the molecular weight. Water doubly distilled from glass was employed as eluent for dextran standards and was used to prepare 0.1 mol dmT3phosphate buffer (pH 6.3) for the elutions of the proteins.For separations of polystyrene standards the eluent J. V. DAWKINS AND G. YEADON was tetrahydrofuran (B.D.H.) which was destabilized stored over calcium hydride for 4 h and then distilled from calcium hydride and copper(1) chloride. Calibration curves were established at an eluent flow rate of 1 cm3 min-I as follows proteins 0.1% w/v in lo-' dm3 injection volume; dextrans 0.25% w/v in 25 x dm3; polystyrene standards d 0.2% w/v in lo-' dm3. Column efficiencies at varying flow rates for albumin ovalbumin myoglobin and acetamide (A.R.) in aqueous phosphate buffer were established with a solute concentration of 0.1% w/v in Cn injection volume of 5 x dm3 and for tetrahydrofuran elutions with injections (lo+ dm3)of polystyrene standards at 0.2% w/v tetraphenylethylene (Aldrich) at 0.01% w/v and A.R.toluene (B.D.H.)at 0.2% wjv. The plate height was calculated from an experimental chromatogram by the width at half-height method. RESULTS AND DISCUSSION SEPARATION MECHANISM The experimental dependence of the molecular weight M of proteins on retention volume is shown in fig. 1. When the separation mechanism is dominated by steric exclusion the distribution coefficient KDlies in the range 0-1 and is given by where V is the interstitial (or void) volume and Vi is the internal pore volume. The 106 A \ \ \ 0 \ M 1 0' .. \ \ 0 \ rn '\ \ A 1 04 V L 6 a 10 V&m3 FIG.1.-Molecular weight calibration for proteins eluted from y-G SG30 silica.A,thyroglobulin; 0,catalase; 0,albumin; m ovalbumin; 0,pepsin; A myoglobin; 'J cytochrome c. total volume of solvent in the column V + Vi may be estimated with a totally per- meating solute and V for acetamide was found to be 10.05 cm3. Consequently thyroglobulin (A4 = 670 000) may be regarded as a totally-excluded solute which is consistent with retention-volume data for polystyrene standards for H4 silica2o having MACROMOLECULAR SEPARATIONS a similar pore size distribution to SG30 silica. Furthermore myoglobin (M = 17800) and cytochrome c (M = 12 400) are almost totally permeating solutes. We shall as- sume that ovalbumin (M = 45 000) in fig.1 separates solely by steric exclusion. Schmidt et al." have shown that ovalbumin separating in aqueous media at pH 5.0 with y-G silica shows no change in VRas the ionic strength of the eluent is changed. Regnier and Noells demonstrated by dynamic recovery studies that no adsorption of ovalbumin occurred with y-G porous glass. The results in fig. 1 suggest that the separation of albumin (M = 67 000) is determined mainly by steric exclusion and satisfactory separations of albumin with y-G porous glass and silica have been re- ported by other w~rkers.'~*''*~~,~~ A high recovery of albumin from y-G porous glass was reported by Regnier and Noel.ls The displacement of catalase (M = 250 000) and pepsin (M = 35 500) from the curve in fig.1 suggests a mixed mechanism involving steric exclusion and interactions between solute and stationary phase. Then the mechanism may be considered as a network-limited separation. For separations in which VRis higher than expected from steric exclusion Dawkins and Hemming 24 proposed network-limited partition and network-limited adsorption mechanisms and derived the retention relation where Kpis the distribution coefficient for interactions between solute and stationary phase. For a steric exclusion separation with an inert stationary phase eqn (1) and (2) are identical with Kp= 1.0. For separations operating close to equilibrium con- ditions at constant temperature T the distribution coefficient is related to the free- energy change for the transfer of solute molecules from the mobile phase to the stationary phase.The retention volume is determined by the entropy change AS and the enthalpy change AH in the equation2' VR= V + Viexp (-AH/kT) exp (AS/k) (3) where k is Boltzmann's constant. Since steric exclusion is dominated by an entropy c~ntribution,'-~ it was proposed that interaction effects as represented by Kp are It follows from eqn (2) and (3) that Kp> dominated by an enthalpy contributi~n.~~ 1.0 for an attractive interaction and that Kp < 1.0 for a repulsive interaction. The early elution of some polymers has been interpreted in terms of Kpbelow unity corres- ponding to a secondary mechanism of partial exclusion by polymer incompatibility with the stationary phase.26 The retention data in fig.1 may be interpreted with the aid of eqn (2). Values of VR for pepsin (Kp< l.O) catalase (Kp> 1.0) and lysozyme (Kp9 1.0) for which we were unable to obtain a chromatogram may be considered in terms of ionic effects as suggested by Schmidt et aL21 It might be expected that unreacted silanol groups which may be present on the silica surface dissociate in aqueous media at pH 6.3 giving a net negative charge on the silica s~rface.~'*~~ The ionic strength of our eluent lies in the range investigated by Schmidt et aL2'and so interactions between charged proteins and the silica surface may not be completely neutralised. The behaviour of lysozyme in particular is very dependent on the ionic strength of the eluent. At pH 6.3 lyso- zyme is positively charged and pepsin is negatively ~harged,~'.~~ so that these two pro- teins will be subjected to attractive and repulsive interactions respectively.This ionic explanation is less satisfactory for catalase which is close to a neutral protein at pH 6.3.27 However of the 16 proteins subjected by Regnier and NoelI5 to dynamic recovery studies catalase exhibited the worst recovery with <SO% of the protein eluting from the column containing y-G porous glass. An increased interaction J. V. DAWKINS AND G. YEADON 131 (Kp> 1.0) at high ionic strength giving higher values of V has been demonstrated for several proteins which is interpreted in terms of hydrophobic interactions.21*28 The molecular-weight calibrations for proteins and dextrans in aqueous media and for polystyrenes in tetrahydrofuran are compared in fig.2. The polydispersity defined as the ratio of weight-average and number-average molecular weights &fw/an, of a calibration standard will determine the accuracy of a calibration curve. For proteins and polystyrene standards there should be little error in assigning the mole- cular weight at the peak retention volume of a chromatogram. The dextran stan- dards have values of aw/Bn in the range 1.35-1.50 and so data for a,,,were used to establish the calibration curve in fig. 2 for reasons discussed elsewhere.29 In fig. 2 the dextran and polystyrene data give good agreement for V for y-G SG30 silica but elutions of acetamide (VR = 10.05cm3) and toluene (V = 9.55 cm3) suggest different a 0 a 0.X + lo 41 6 8 10 VR/cm3 FIG.2.-Molecular-weight calibrations for proteins dextrans and polystyrenes eluted from y-G SG30 silica; A,thyroglobulin; 0,albumin; u,ovalbumin; A myoglobin; V,cytochrome c; V protamine sulphate; 0,dextrans; 0, polystyrene standards; + acetamide; x ,toluene. accessible pore volumes. An alternative explanation is that interactions between solute and stationary phase which are more prevalent for small molecules than for macromolecules [see for example ref. (29)] may be occurring and may differ for aceta- mide and toluene. In order to demonstrate that the macromolecules shown in fig. 2 are separating predominantly by steric exclusion retention data must be interpreted in terms of 132 MACROMOLECULAR SEPARATIONS solute size rather than molecular weight.Giddings et aZ6proposed that separations of rigid molecules are determined by the mean external length or molecular projection which is equal to the diameter D of a spherical solute. Consequently for proteins D has been evaluated from tabulated data for the Stokes' radius.30 Casassa7 has proposed that should also be regarded as an acceptable size parameter for flexible- chain polymers. If it is assumed that dextrans and polystyrenes may be represented by the model of an equivalent hydrodynamic then the diameter D (cm) of this sphere is given by D3 = 2.4 K MI+"In N (4) where N is Avogadro's number and K and a are constants in the equation for the intrinsic viscosity [q](cm3 g-') for the polymer solution [q]= KM".Values of these constants were assumed to be K = 1.164 x cm3 g-l a = 0.73 for polystyrene in tetrahydrofuran at 25 "C as reported by Spychaj et uZ.,~~and K = 0.1 cm3g-l a = 0.5 for dextrans in water at 25 "C as reported by Senti et aZ.33 Values of KD for each solute were determined from V data with eqn (1) in which V,was assumed 0 0 c A V. 0 t3 11 0 0.25 0.50 0.75 I.o KD FIG.3.-Universal calibration plot of solute diameter against the distribution coefficient for steric exclusion for y-G SG30 silica. Solutes and symbols as in fig. 2. to be 4.9 cm3 for excluded solutes (KD= 0) in fig. 2 and Vi was calculated from values of VRfor acetarnide and toluene (KD= 1). A semilogarithmic plot of D against KD is shown in fig.3. The results for proteins and dextrans in aqueous media lie almost on the same curve suggesting that the hydrodynamic diameter of the equivalent sphere is a reasonable choice of size parameter for a flexible-coil polymer and that these sepa- rations operate by steric exclusion without perturbations from interaction effects. J. V. DAWKINS AND G. YEADON Good agreement is also observed between the aqueous separation data and the results for polystyrene in tetrahydrofuran in the low range of K, the range which is less easy The slight deviation between the curves for the aqueous to work out theoreti~ally.~-~ and tetrahydrofuran separations at high K, in particular at KDNN 0.8 may arise from differences between Vi for the two eluents and/or interaction effects between small molecules (toluene and acetamide) and the stationary phase which are dependent on small molecule and eluent.DISPERSION MECHANISMS Curves showing the dependence of plate height H for proteins and acetamide on the linear flow rate u of the eluent are shown in fig. 4. Linear velocity was calculated with V which was determined from fig. 2. The low values of H for ovalbumin and I I I 0 2.5 5.O u/mm s-' FIG.4.-Dependence of experimental plate height on eluent flow rate for proteins eluted from 7-G SG30 silica 0,albumin; m,ovalbumin; A,myoglobin; 0,acetamide. myoglobin which is almost a neutral protein at pH 6.3,27arise from narrow chromato- grams suggesting no interactions between solute and stationary phase.Values of H for albumin were much higher and tailing was observed on the chromatograms which together with the displacement of the retention volume for albumin from the curve in fig. 1 to high VR,indicates an interaction between albumin and the stationary phase. Curves showing the dependence of H on u for polystyrene standards tetraphenyl- MACROMOLECULAR SEPARATIONS ethylene and toluene are shown in fig. 5. Data for PS-110000 for u > 2 mm s-result from peaks having pronounced asymmetry. It is evident in fig. 2 that th polystyrene standard has VRclose to the exclusion limit so peak asymmetry at high may occur because part of the solute is excluded whilst the remainder permeates som pores. Experimental data for H for a solute having constant VR over the range of u ma 0.5 A 0.4 0.3 E E z 0.2 0.1 X X f + I I 0 2.5 5 .O u/mm s-I FIG.5.-Dependence of experimental plate height on eluent flow rate for polystyrene standards eluted from y-G SG30 silica.A PS-110 000; 0,PS-35 000; a PS-9800; 0,PS-3600; x PS-600; + tetraphenylethylene; 0,toluene. be interpreted in terms of the dispersion mechanisms occurring in the mobile and sta- tionary phases. Giddings and Mallik" proposed an expression for H for separations by liquid exclusion chromatography which for a monodisperse solute we shall write in the form H = (B/u)+ Csu + 2 l/[(l/A) + (l/Crn~)I (6) in which A B C,and C are coefficients depending on several parameters (see later) where the first term results from dispersion owing to molecular diffusion in the longi- tudinal direction in the mobile phase the second term results from solute dispersion owing to mass transfer in the stationary phase and the third term containing contribu- tions from eddy diffusion (A) and mass transfer (CmU) results from solute dispersion in the mobile phase.The minima for acetamide toluene tetraphenylethylene and 135 J. V. DAWKINS AND G. YEADON PS-600in fig. 4 and 5 indicate the importance of the term for longitudinal molecular diffusion for small molecules. No minima are observed for high polymers and because of the low diffusion coefficients of high polymers the first term in eqn (6) at u > 1 mm s-l may be neglected as discussed el~ewhere.~~.~~ We turn now to the third term in eqn (6) which from the treatment of Giddings and Mallikll may be written in the form where A (close to unity) is a constant characteristic of the packing dp is the particle diameter D is the diffusion coefficient of the solute in the mobile phase assumed to be the diffusion coefficient of a molecule in free solution at infinite dilution and wiis a geometrical factor of order unity.For a macromolecule with M z 20 000 having a value of D around cm2s-l [see ref. (34)],the second term in the denominator in relation (7) at u = 2.5 mm s-l and with dp= 8 pm will be ca. 1 % of the first term in the denominator. We may conclude that for high polymers the eddy-diffusion term dominates mobile phase dispersion and there is abundant experimental evidence that non-permeating macromolecules exhibit little or no change in Has u is rai~ed.~~~~~ Consequently for a monodisperse high polymer eqn (6) simplifies to H = 2Adp + R(1 -R)dP2u/30D (8) in which the term for mass transfer in the stationary phase corresponds to the one given by Giddings and Mallik" where R is the retention ratio defined by V,/V which may be found from the calibration data in fig.2 and D is the diffusion coeffi- cient of the solute in the stationary phase. Eqn (8) was employed to evaluate D for proteins from the straight-line plots in fig. 4. The data are shown in table 1 assuming dp = 8 pm. For a polydisperse solute eqn (8) must be extended to include the true polydispersity [i@4&?JT.A general procedure for incorporating a polydispersity term into the expression for H has been proposed by Knox and McLennan.14p3' A simplified procedure involving the assumption that the true molecular-weight distribution of polystyrene standards may be represented by a logarithmic-normal distribution has been discussed pre- viou~ly.~~*~~ The polydispersity term from our treatment may be incorporated in eqn (8) giving H = 2Adp + R(l -R) d,2u/30 D + (L ln[&?w/i@n]T/D2 VR2) (9) where L is the column length (25 cm) and D2 is the slope of the calibration curve of In M against V in the partial permeation range (see fig. 2). Consequently D for polystyrenes may be evaluated from the straight-line plots in fig. 5 and values are pre- sented in table 1.Literature data of D for protein~~~.~' are given in table 1 and values of D for polystyrene standards included in table 1 were determined from the Wilke-Chang eq~ation~~-~~ and from the expression proposed by Rudin and John- ~ton.~O The derived data for D in table 1 are much less than values of D, and our results suggest that DJD is below 0.1. Giddings et aZ.I2studied the chromatogram broadening of low-molecular-weight polystyrenes (M < 4000) separated with porous- glass particles having diameters in the range 44-74 pm and found that D,was ca. D,/6. Van Kreveld and van den Hoed13 evaluated the dispersion term for mass transfer in the stationary phase for polystyrene standards (A4= 20 000-160 000) separating with porous silica particles (dp= 75-124 pm) finding DJD to decrease from 0.31 to 0.12 as M increased.Knox and McLennan14 have also determined D values for polystyrene standards (M = 2000-33 000) separating with porous silica MACROMOLECULAR SEPARATIONS (dp "N 7.5 pm) by evaluating the mass-transfer term quoting data for D,lDm in the range 0.045-0.104 (or 0.059-0.167 depending on the method of calculating 0,). Despite the scatter of the literature data it is clear that macromolecular diffusion in the stationary phase in liquid exclusion chromatography is likely to be restricted. TABLE COEFFICIENTSa 1 .-DIFFUSION macromolecule &J10-7 em2s-I R O,/lO-* em2 S-' DJDm myoglobin ovalbumin 10.3 7.8 0.53 0.60 7.8 7.5 0.076 0.096 albumin 6.0 0.63 4.5 0.075 PS-3600 28.9 0.57 30.6 0.106 PS-9800 15.8 0.63 15.4 0.098 PS-35 000 7.4 0.75 5.3 0.072 (I Data for D are for solutes in free solution and values of D are calculated from slopes in fig.4 and fig. 5. Although our calculation procedure is simpler than that employed by Knox and Mc- Leniian,14 our results for polystyrene standards with a similar column packing are in reasonable agreement. Our results also indicate that restricted diffusion occurs not only for flexible-chain molecules but also for rigid macromolecules. POLYDISPERSITY From the data in fig. 5 values of [&!fW/n& may be evaluated with eqn (9) pro-vided the first term for mobile-phase dispersion is known accurately. One procedure would be to assume ;? = 1.0 when the plate height for mobile-phase dispersion H would be 16 pm.A second procedure would be the direct determination of H with a non-permeating high-molecular-weight polystyrene and results for porous silicas (dp 2i 15-20 pm) are reported elsewhere.20 It was observed that H (PS-1 987 000) was not very different from H for toluene. We may evaluate theoretically H for toluene with eqn (6) using the expressions for B C, A and C proposed by Giddings and Mallik," giving H = 16.3pm at u = 0.25 cm s-l and H = 17.35 pm at u = 0.50 cm s-' with dp = 8 pm D = 2.3 x cm2 s-I from ref. (38) and (39) and D,= 20,/3. The major contribution to these H values arises from the eddy-diffusion term and of course there is no need to consider the polydispersity term for toluene. The experimental values of H for toluene in fig.5 are 18 and 25 pm at u = 0.17 and 0.50 cm s-l respectively. Consequently a third procedure for the evaluation of [i@,,,/nn] involves the assumption as proposed previously,20 that the plate-height data for toluene in fig. 5 can represent the first term in eqn (9) for a high polymer. With this third method for H, values of [A7w/A7n]Tfor polystyrene standards given in table 2 were determined from experimental plate-height data. Apart from PS-3600 the data for polydispersity are reasonable being higher than theoretical values cal- culated for polystyrenes prepared by a " living " anionic p~lymerisation.~~ The theoretical value of [i@w/a"]T for PS-3600 is 1.029 indicating that the value in table 2 is too low. This probably arises because the calibration curve in fig.2 suggests that PS-3600 is separating close to the total permeation volume so that fractionation of the chains in this polystyrene standard may be incomplete. The results in table 2 do suggest that the permeating polystyrene standards have narrow distributions. The theoretical values of [i@,,,/&fJT for PS-9800 and PS-35 000 are 1.011 and 1.003 res- 137 J. V. DAWKINS AND G. YEADON pe~tively,~~ but higher values will occur in practice because of the rigorous conditions required in the experimental polymerisation technique. The values of [h?,JH,JTfor ovalbumin in table 2 determined by using plate-height data for acetamide in fig. 4 for the first term in eqn (9) are much lower than the data for polystyrene standards con- firming that this protein may be regarded as monodisperse.The values of [i@w/mn]T for myoglobin also indicate a narrow distribution although the agreement between the two values is poor. No values of [i@w/i@n]T are quoted for albumin because the plate heights in fig. 4 and therefore polydispersities from eqn (9) are raised artificially TABLE 2.-POLYDISPERSITIES OBTAINED FROM PLATE HEIGHTS AT VARIOUS ELUENT FLOW RATES wfw/~IIl* macromolecule u = 1.7 mm s-' u = 3.4 mm s-' u = 5.1 mm s-' PS-3600 1.012 1.012 1.010 PS-9800 1.035 1.036 1.034 PS-35 000 1.011 1.013 1.009 myoglobin ovalbumin 1.004 - 1.011 - 1.0 a 1.008 -~~~ a Plate-height contribution from polydispersity was negative. by the adsorption effect which was discussed earlier.In summary our simple method gives reasonable estimates of polydispersity ; a more involved procedure has been investigated by Knox and M~Lennan.l'*'~ CONCLUSIONS Our studies with porous silica having a y-G bonded phase indicate that separations of non-ionic macromolecules in aqueous media are determined by a steric-exclusion mechanism operating close to equilibrium conditions. For charged macromolecules the composition of the aqueous eluent must be adjusted e.g. by careful selection of pH and ionic strength to minimise interactions between the solute and the stationary phase. If secondary interaction effects e.g. adsorption or partial exclusion owing to ionic repulsion do occur the retention data may be interpreted in terms of a thermo- dynamic representation of a mixed mechanism.A comparison of retention data for proteins e.g. ovalbumin and myoglobin which do not participate in interaction effects with the stationary phase dextrans and polystyrenes suggests that solute diameter is a reasonable universal size parameter for the representation of macromolecules separ- ating by steric exclusion. The general expression proposed for the plate height of small molecules may be simplified for high polymers which have a mobile-phase contribution to plate height from the eddy-diffusion dispersion mechanism. Consequently the contribution to plate height from mass transfer in the stationary phase which is considerable at fast eluent velocities may be evaluated from experimental data for plate height.The diffusion coefficients of proteins and flexible-coil polystyrenes during mass transfer in the stationary phase are low and our data for polystyrene are in fair agreement with the results reported by other workers. The simplified expression for plate height may be extended to include a polydis- persity term. Provided the mobile-phase contribution to plate height from eddy diffusion can be estimated polydispersity may be determined from experimental data for plate height. Proteins separating solely by steric exclusion may be regarded as MACROMOLECULAR SEPARATIONS monodisperse. Values of the polydispersity of polystyrene standards were in reason- able agreement with theoretical expectation. We thank Dr. D. C. Sammon Dr. J. D. F. Ramsay and Dr.R. L. Nelson of A.E.R.E. 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Chromatogr. 1979 185 259. l5 F. E. Regnier and R. Noel J. Chromafogr. Sci. 1976 14 316. l6 S. Ho. Chang K. M. Gooding and F. E. Regnier J. Chromatogr. 1976 125 103. l7 C. Persiani P. Cukor and K. French J. Chromatogv. Sci. 1976 14 417. la H. D. Crone and R. M. Dawson J. Chromatogr. 1976 129 91. l9 P. A. Bristow P. N. Brittain C. M. Riley and B. F. Williamson J. Chronzatogr. 1977 131 57. 2o J. V. Dawkins and G. Yeadon J. Chromatogr. 1980 188 333. 21 D. E. Schmidt R. W. Giese D. Conron and B. L. Karger Anal.Chem. 1980 52 177. 22 N. Becker and K. K. Unger Chromatographia 1979 12 539. 23 P. Roumeliotis and K. K. Unger J Chromatogr. 1979 185 289. 24 J. V. Dawkins and M. Hemming Makromol. Chem. 1975 176 1777 1795 1815. 25 J. V. Dawkins J. Polym. Sci. Polym. Phys. Ed. 1976 14 569. 26 J. V. Dawkins Polymer 1978 19 705. 27 A. White P. Handler E. L. Smith R. L. Hill and I. R. Lehman Principles of Biochemistry (McGraw-Hill New York 6th edn 1978) p. 97. 28 R. A. Barford B. J. Sliwinski and H. L. Rothbert Chromatographia 1979 12 285. 29 J. V. Dawkins J. W. Maddock and A. Nevin Eur. Polym. J. 1973 9 327. 30 P. Andrews Methods of Biochemical Analysis ed. D. Glick (Wiiey-Interscience New York 1970) vol. 18 p. 22 23. 31 P. J. Flory Principles of Polymer Chemistry (Cornell University Press Ithaca N.Y.1953) chap. XIV. 32 T. Spychaj D. Lath and D. Berek Polymer 1979 20 437. 33 F. R. Senti N. N. Hellman N. H. Ludwig G. E. Babcock R. Tolin C. A. Glass and B. J. Lamberts J. Polym. Sci. 1955 17 527. 34 J. V. Dawkins and G. Yeadon Polymer 1979 20 981. 35 J. H. Knox and F. McLennan Chromatographia 1977 10 75. 36 C. Tanford Physical Cheniistry of Macromolecules (Wiley New York 1961) p. 358. 37 Handbook of Biochemistry Selected Data for Molecular Biology ed. H. A. Sober (The Chemi- cal Rubber Co. Cleveland Ohio 1968) sect. C. 38 C.R. Wilke and P. Chang AZChE J. 1955 1 264. 39 R. C. Reid and T. K. Sherwood The Properties of Gases and Liquids (McGraw-Hill NewYork 1965) chap. 8. 40 A. Rudin and H. K. Johnston J. Polym. Sci.,Polyrn. Lett. Ed. 1971 9 55. 41 L. H. Peebles Molecular Weight Distributions in Polymers (Wiley-Interscience New York 1971) chap. 1.

ISSN:0301-5696    

DOI:10.1039/FS9801500127

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

Study of the Influence of Sodium Dodecyl Sulphate on Warfarin-Human Serum Albumin Binding -Using Chromatographic Retention Data BY BERNARD SEBILLE AND NICOLETHUAUD Laboratoire de Physico-chimie des Biopolymkres U.E.R. de Sciences Universitd de Paris Val-de-Marne Avenue de GCnCral du Gaulle 94010 Creteil CCdex France AND JEAN-PAUL TILLEMENT Ddpartment de Pharmacologie FacultC de MCdecine UniversitC de Paris Val-de-Marne Avenue du GCnCral Sarrail 94000 Creteil CCdex France Received 22nd July 1980 The equilibrium saturation chromatographic method has been applied to the study of the influence of sodium dodecyl sulphate (SDS) on warfarin-human serum albumin binding. The ligand retention volume depends upon the association and gives 7 the number of bound ligands per mole of macro-molecule.Another method for evaluating the influence of SDS upon drug-protein binding is intro- duced. We have reported 1-4 the use of high-performanceliquid chromatography for measur- ing drug-human serum albumin binding parameters. When a polymer forms rever- sible complexes with a ligand the association parameters cannot in general be ob- tained by injecting the component mixture on a column eluted by the solvent. Indeed if the column is able to separate the different compounds by a size-exclusion mechanism the complex is partially or completely dissociated during the transfer. A simple way for preventing this dissociation is the method of Hummel and Dreyer,’ in which the eluent is a ligand solution thus maintaining an unaffected equilibrium.We have also described an equilibrium saturation method2 in which the eluent is a solution of protein and ligand. By injecting a small volume of solvent the unbound ligand can be measured from the ligand peak negative area. In the present work we show that the variation of the retention volume of a drug with different eluent compositions can be used to measure the influence of a competitor like SDS on the drug-protein affinity. We also describe a very simple process for a qualitative evaluation of this influence. EXPERIMENTAL EQUIPMENT Chromatographic equipment A 6000 A pump U6K injector and a 440U.V. detector all from Waters Associates (Milford Mass.) were used for all the experiments. The monitoring wave-length was 313 nm.The stainless-steel column (15 cm length 4.7 mm i.d) is filled by a slurry-packing technique with Lichrosorb Diol support (Merck Darmstadt R.F.A.) 10 pm particle diameter. WARFARIN-SERUM ALBUMIN INTERACTIONS MATERIALS Warfarin was a gift of Merell-Toraude Lab. (Paris). SDS obtained from B.D.H. (Poole) was dissolved directly in the phosphate buffers. Human serum albumin (HSA) was obtained from Sigma (A 1887essentially fatty-acid-free albumin). All products were dissolved in a 0.067 mol dm-3 phosphate buffer pH 7.4. RESULTS AND DISCUSSION The binding of a drug to serum albumin can be influenced by other ligands able to bind either on the same site (competitive inhibition) or on a different site (uncom- petitive inhibition). Sometimes the binding can be enhanced by a co-operative effect.In human plasma albumin is generally associated with fatty acids the presence of which modifies the drug binding. We preferred to study the influence of SDS on warfarin-HSA affinity because of the chemical similarity of this compound to fatty acids and its better solubility in aqueous media. With respect to physiological condi- tions we have chosen to work with a constant ratio R = [SDS]/[HSA] by using the equilibrium saturation method. Fig. 1 represents the chromatograin obtained when a small volume of solvent is 2 4 FIG.1 .-Equilibrium saturation method eluents buffered (pH 7.4 phosphate 0.067 mol dm-3) mixtures of warfarin (2.5 pmol dm-3) HSA (0.4 g drnw3) and SDS for different ratios R = [SDSll [HSA] = 0 4 10 20.Injection 50 cm3 of buffer. injected on a size-exclusion column eluted by a solution of protein SDS and warfarin. The chromatogram profile has two negative peaks the first corresponds to the bound protein while the second represents the free drug. As SDS has a negligible optical density at this wavelength (313 nm) it gives no signal. For low values of the ratio R = [SDS]/[HSA] the warfarin retention volume decreases as does the peak area. For R > 4 we notice in contrast an increase in the ligand retention volume and peak area. At the same time the bound-protein peak area changes in the opposite way. It has previously been shown that surface measure- ment can lead to an evaluation of the bound warfarin.2 The retention volume also B.SEBILLE N. THUAUD AND J. P. TILLEMENT provides a simple method for the evaluation of r‘ the mean number of bound ligands per mole of macromolecule VR == V + KUf (1) where V is the retention volume of the solute V the void volume vf the stationary- phase volume and K the partition coefficient. When the eluent contains a polymer totally excluded by the pores (such as is virtually the case for HSA with the support used6) the drug retention volume becomes Vi = V + K’Vf in which K’= K(1 -a) where a is the ratio [A]b/[A], [AIb and [A] being respectively the bound and total drug concentrations. We also have r‘ = [A]b/cP1o (4) with [PI as the total polymer concentration. By combining eqn (1)-(4) one obtains This equation shows clearly that F can be determined from Vi VR and V if [A] and [PIn are known.We have represented in fig. 2 the results obtained for F as evaluated from eqn (5) with those previously reported from the ligand surface peak measurement. There is good agreement between the two sets of data. By combining eqn (3) and (5),we can write Vi -V = (1 -a)(VR-V,) . (6) This equation predicts a linear relationship between Vi and (1 -a) with a slope V -V,. In fig. 3 are plotted the experimental values of VI; as a function of (I -a)measured 0.3 c I I 1 0.1 L I 0 5 10 15 20 R FIG.2.-Mean number U of bound ligand as a function of R = [SDS]/[HSA]. Same conditions as in fig. 1 0,F from peak surface measurement; x ,F from retention volume. WARFARIN-SERUM ALBUMIN INTERACTIONS 5- 2 I-“E 3-9 1-.’* /*A.I 1 I I I 1 I 1 I I 1-a FIG.3.-Retention volume of free warfarin as a function of (1 -a). a = [A]J[A1 evaluated by surface measurement. from ligand peak area observe that the results confirm the validity of eqn (6). When a decreases by changing the relative proportions of drug protein and SDS the lig- and retention volume VA varies linearly between V and VR. Then the experimental value of Vk gives directly the fraction of bound ligand a and the r‘ parameter [eqn (5)]. A different process for studying the influence of SDS on warfarin-HSA binding is now presented. In this method the eluent is a mixture of protein and drug and one injects on the column a small volume of a solution of SDS dissolved in the eluent.Fig. 4 represents the chromatogram obtained. Because SDS has no optical density at the chosen wavelength it cannot be directly detected. But as the presence of SDS begins to modify the warfarin-HSA complexa- tion there appears first a positive peak fdlowed by a negative peak at the ligand retention volume. The two peaks have the same surface area. Because the amount m -m V&m3 W d 0 FIG.4.-Qualitative evaluation of SDS influence on warfarin HSA binding eluent buffered (pH 7.4,0.067 on phosphate); solution of warfarin 5 pmol dm-3 and HSA (0.4g dm-3); injection 10 mm3 of a 2 x mol dm-3 SDS solution in the eluent. B. SEBILLE N. THUAUD AND J. P. TILLEMENT of SDS is very low the ratio R = [SDS]/[HSA] is small and corresponds to a zone where SDS increases warfarin-HSA binding.Accordingly when SDS elutes out of the column the mixture has an optical density higher than that of the eluent because of the higher warfarin complexation and thus leads to a positive peak. The second peak represents the deficit of warfarin eluted in the peak as in the method of Hummel and Dreyer. The two peaks must have equal areas since in this method optical density sterns only from the warfarin concentration variations. This process does not permit a detailed study of the influence of SDS since the SDS concentration is not constant during its transfer through the column and the ratio R is not precisely known. However this method gives a very simple way of measuring the effect of a second ligand on the fixation of the first ligand on a protein.The present results confirm those previously reported for a low value of the ratio R,the presence of SDS increases the warfarin binding with HSA. This effect arises from a conformational modification of the warfarin fixation site as has been observed using circular dichroism measurement^.^ For ratio R > 4 there is a de- crease in warfarin complexation because of a displacement of the drug by the SDS exactly as for short-chain fatty acids.2 CONCLUSION The influence of SDS on warfarin-HSA binding can be studied by an equilibrium saturation chromatographic method. The drug-retention volume on a column eluted by a mixture of protein warfarin and SDS provides a simple way of measuring the extent of association.The results are in a good agreement with those given by surface- area evaluation and are obtained more simply. Low values of [SDS]/[HSA] lead to an increase of warfarin binding while a higher value of R gives a decrease of this bind- ing. We also present another method for evaluating the influence of a second ligand on a drug-protein binding. This new method gives information on the kind of SDS action but cannot be used for a quantitative determination since the SDS concentra-tion is not constant during the experiments. B. Sebille N. Thuaud and J. P. Tillement J. Chromatogr. 1978 167,159. B. Sebille N. Thuaud and J. P. Tillement J. Chromatogr. 1979 180 103. B. Sebille and N. Thuaud J. Liquid Chromatogr. 1980 3 299. B. Sebille N. Thuaud and J. P. Tillement Spectra 2000 1980 60 55. J. P. Hummel and W. J. Dreyer Biochim. Biophys. Actu 1962 63 530. D. E. Schmidt R. W. Giese D. Conron and B. L. Karger Anal. Chem. 1980 52 177. ’N. Thuaud Thbe de Doctorat d’Etut (University Paris XII 1980).

ISSN:0301-5696    

DOI:10.1039/FS9801500139

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

Diffusion Coefficient Measurements by the Chromatographic Method BY WILLIAM A. WAKEHAM Department of Chemical Engineering and Chemical Technology Imperial College London SW7 2AY Receiued 11th July 1980 This paper reviews advances in the theory and implementation of the chromatographic method for diffusion-coefficient measurements in the liquid phase. It is shown that by means of a proper design an instrument can be constructed which conforms very nearly to the simplest model of it so the remain- ing small departures from the model can be taken into account. An instrument for the measurement of liquid-phase diffusion coefficients with an accuracy of f1% is described and some results for the mutual diffusion coefficients of normal alkane mixtures are presented which confirm the correct operation of the instrument.Exploratory work on the application of the chromatographic method to self-diffusion coefficient measurements of ions in solution and mutual-diffusion coefficients near a liquid-liquid critical point is briefly discussed. The measurement of diffusion coefficients in fluids has been until recently a time-consuming and error-prone activity. In view of the importance of diffusion in both naturally occurring and industrial processes 1-3 the lack of reliable diffusion co- efficients is regrettable. In the last few years new methods such as holographic interferometry4 and photon-correlation ~pectroscopy,~ have been developed for the measurement of the diffusion coefficients of special kinds of system and one somewhat older method the chromatographic technique which is more widely applicable has received a new stimulus.The chromatographic method was first employed for diffusion-coefficient measure- ments by Taylor6 in the course of his studies of the dispersion of a solute in a solvent flowing in laminar flow through an empty circular-section tube. Taylor also provided an approximate mathematical analysis of the dispersion process which satisfactorily described his observations of the dispersion of potassium permanganate solution in water. Subsequently the development of the technique followed two distinct paths. On the one hand the process of dispersion of solutes in pipelines of various geometries was studied by chemical and on the other hand the phenomenon was employed by several workers to determine diffusion coefficients in the gas phase.lo*ll It is from the latter studies that the name of the technique has been derived since in the early work the apparatus employed was invariably a standard gas chromatograph which provided all that was necessary for the performance of the measurements.lO*ll However because no absorption processes are involved in the empty “chromato-graphic column” and no separation of components occurs the name is somewhat misleading.In this paper some of the recent advances in the chromatographic method of diffusi-vity determination in the liquid phase are reviewed which now permit rapid and accu- rate measurements to be performed. The application of the technique to a number of different systems is illustrated.DIFFUSION-COEFFICIENT MEASUREMENTS THEORY OF THE EXPERIMENTAL METHOD Fig. 1 illustrates the principle of the chromatographic technique for diffusivity measurements. A fluid mixture of components 1 and 2 whose physical properties are composition-independent and which has molar concentrations C, and Czf,flows in laminar flow (with a parabolic velocity profile and mean velocity tio) through an infinitely long straight circular-section tube of radius a,. At time t =0 a delta- function pulse of a fluid mixture of the same two components with concentrations Cli t=t ftO i parabolic I // *. velocity I L profile z=o FIG.1.-Ideal chromatographic method for diffusion coefficient measurements. and C2iis injected into the flowing stream at the axial position z =0 in such a way that it completely fills the cross-section of the tube and is uniformly distributed across it.The number of moles of component 1 injected into the flowing stream in excess of those already present N, is then The perturbation to the composition of the flowing stream is subsequently dispersed by the combined action of molecular diffusion and the parabolic velocity profile. The eluted concentration averaged over a cross-section and denoted by ACI, is observed at the axial position z =L. The first temporal moment of the distribution and the variance defined by the equations and are related7J2 to the velocity of the fluid the radius of the tube and the mutual-diffu- sion coefficient for the system B12.In particular it may be shown based on the analysis of Aris7*12*13 that provided tio >700.9,,/a0 (4) and 91zfid,/ai>10 (5) W. A. WAKEHAM the moments fid and a&may be used to obtain the diffusion coefficient from the work- ing equation l2 where Sa = 0.266 66 iiga;/Lgl2. The conditions (4) and (5) are imposed to simplify the working equations and to them must be added the requirement for laminar flow that 2a0pii,/p < 2000 (7) where p is the fluid mixture viscosity and p its density. Conditions (4) (5) and (7) are easily satisfied in practice for liquids by the use of sufficiently large values of L and sufficiently small values of a,. However for gases where the diffusion coefficient is very much larger the same conditions are more difficult to satisfy.We therefore confine ourselves to the liquid state in the discussion which follows. The subscript (id) attached to the moments f and o2in the foregoing equations indicates that these are the moments which would be observed in the ideal experiment. In practice of course the instrument must depart from this ideal model of it in several respects. However by proper design it is possible to render the effects of some of these departures negligible and others sufficiently small that an approximate analysis is adequate for their estimation. In this context we use the word negligible to mean that the residual correction to the diffusion coefficient amounts to <&0.05%. An analysis of the departures of a real instrument from the ideal model has been given by Alizadeh et a1.12 It has been possible to express all the non-negligible effects of de- partures from the ideal model as small corrections to be added to the moments ob- served in a practical instrument so as to recover the ideal moments.That is we write and where f and a2are the moments of the distribution observed in a real instrument. The departures from the ideal model can be classified under four headings and analytic expressions for the significant corrections St;and So;have been obtained.12 (a) CON CE NTR A TI ON DISTR I B U TI ON DETERMINATION It is not possible to determine the concentration distribution in an infinitesimally thin cross-section of the tube. Instead it is necessary either to observe the concentra- tion distribution in a finite length of the tube as shown in fig.2(a) or to employ a detector of finite volume at the exit of the tube as shown in fig. 2(b). In either case the method of observation perturbs the measured moments of the distribution from their ideal values. The corrections to be applied to the observed moments when the detector is a finite length of the tube SL are12 6f-_-6L 1- 2iio and where DIFFUSION-COEFFICIENT MEASUREMENTS On the other hand if the detector is a perfectly mixed volume V at the end of the diffusion tube the corrections are l2 All of these corrections may be readily estimated for a particular instrument. (b) SAMPLE INTRODUCTION The introduction of the solute pulse cannot practically be performed as a &function.However it is relatively straightforward to introduce a square-pulse of volume Vi detection zone (. I ( *I-10 I I i \ I detector volume Yo diffuse tube I 1 I z=L Z FIG.2.-Detection of the dispersed pulse. (a)A finite length of the diffusion tube. (6)A perfectly mixed volume at the end of the diffusion tube. with the aid of an injection valve. In which case the corrections to be applied to the observed moments are l2 and (C) DIFFUSION-TUBE GEOMETRY The lengths of diffusion tube required to ensure satisfaction of conditions (4) (5)and (7) are generally of the order of 10 m so that it is impractical to maintain the tube straight if it is to be satisfactorily thermostatted.For this reason the diffusion tube is normally coiled in the form of a helix of radius.&. The coiling causes secondary W. A. WAKEHAM flows in the tube which in general influence the dispersion However provided that R,lao >100 (17) and the effect of coiling on the measured diffusion coefficient is negligible.8*9*12 This may be confirmed experimentally because the effects of coiling are velocity-dependent so that only if coiling effects are negligible will the observed diffusion coefficients be independent of the fluid velocity used for the measurements. Of course it is also impossible to ensure perfect uniformity of the tube cross-section over a length of 10 m. However provided that the non-uniformities lie within pre- scribed bounds,” which may.be satisfied by high-quality tubing their effect upon the diffusion coefficient evaluated from eqn (6) is negligible though their effect on the individual moments is small but significant. Even more remarkably even if the cross- section of the tube is not circular but for example elliptical the evaluation of the diffu- sion coefficient with the aid of eqn (6) is still correct to a very high order of accuracy12 provided that the a which enters it is defined by the equation a =A/n (19) where A is the average cross-sectional area of the tube. This average may of course be determined by measurement of the volume and length of the diffusion tube. Finally it is often necessary to join the diffusion tube to the detector with a short length Z of tubing of a different radius a,.The modifications to the ideal moments introduced on this account are12 l sr = (-=-)(-J2[1 a +$($)~(1+ $1 and (d) CONCENTRATI0N -DEPENDENT FLUID PROPERTIES In general both the diffusion coefficient and the density of the fluid mixture depend upon composition unlike the assumptions of the ideal model. So far as the com- position dependence of the diffusion coefficient is concerned the working eqn (6) remains unchangedI2 but the composition to which the measured coefficient refers is not that of the flowing stream but rather the composition Clr,given by theexpression12 when iVlextra moles of component 1 are introduced. The composition dependence of the density of the fluid mixture leads to buoyancy driven contributions to the dispersion process not included in the ideal rn0de1.l~ To date no complete solution of this problem is available although there have been a number of attempts at partial ~olutions.~~J~ These attempts show that the buoyancy effects if significant lead to an observed diffusion coefficient dependent on the fluid DIFFUSION-COEFFICIENT MEASUREMENTS velocity used for the measurement.Again this provides the basis for an experimental verification that buoyancy effects are negligible. EXPERIMENTAL The experimental studies which have been undertaken with the chromatographic technique are of two types. On the one hand an instrument has been designed with the foregoing theory in mind so as to yield the most accurate possible data.On the other hand investiga- tions have been carried out into the possible applications of the technique and have therefore been of an exploratory nature. A brief description of both of these activities is included here to illustrate the range of systems amenable to study in this way. (a) ACCURATE MEASUREMENTS Fig. 3 contains a schematic diagram of an instrument designed to satisfy all the conditions (4) (9,(7) (17) and (18) arising from the theory of the method. The apparatus has also been constructed so that none of the corrections di or 60 amounts to more than &0.5% of the ideal moments and so that they may be estimated to within 5%. The residual uncertainty FIG.3.-Schematic diagram of the chromatographic diffusion apparatus. arising from each correction is therefore no more than &0.025%.The diffusion tube itself @ is made from 0.8 mm nominal-internal-diameter steel tubing wound on a copper former @ and embedded in lead @ to provide thermal stability. The tube and a liquid chroma- tograph injection valve @) (Analytical Accessories) are contained in a copper isothermal enclosure fitted with pipes @ for the circulation of a heating fluid. The temperature of the W. A. WAKEHAM diffusion tube is measured with the aid of iron-constantan thermocouples @I inserted into the lead support. The temperature stability and uniformity is ca. f0.05 K over a period of several hours. The fluid flow is maintained by a gravity feed @ which is arranged so that the liquid-level change during the course of a single measurement is negligible.The liquid flows to the injection valve through a preheater @ to ensure thermal equilibrium before injection of the solute sample. The efFluent from the diffusion tube is fed to a differential refractometer @ (Waters Associates) employed for detection of the eluted distribution. For the measurements reported here on some mixtures of normal alkanes the diffusion tube employed had a length of 13.218 i-0.005 m and an average cross-sectional area of 52.80 f 0.05 mm2. The volume of sample injected and the volume of the refractive index detector were both 10 mm3. The analogue output signal of the refractometer was digitized and re- corded on magnetic tape at 2-s intervals during the course of the measurement which usually extended over a period of at least 1 h.The recorded data were subsequently analysed to determine the moments of the efiluent distribution. Although the eluted distribution is not exactly a normal one the deviations from normality under the conditions of operation are usually insignificant.17 Consequently the moments of the distribution have been determined by fitting the recorded data to a normal distribution by means of a non-linear least-squares technique. In general this procedure allowed determination of the moments of the eluted distributions with a reproducibility of -k0.5% which we take as a measure of the precision of the measurements. These experimental moments were then corrected according to the pre- ceding analysis to yield the ideal moments for use in eqn (6) to determine the diffusion co- efficient.Full details of the analysis of the experimental data and of the apparatus construc- 2 0 3750 4000 4250 4500 time t/s FIG.4.-Coniparison of the recorded distribution of the dispersion peak 0 with a fitted normal distribution (-). tion are given e1sewhere.l’ Here it is sufficient to report that the design of the instrument together with the theory of its operation ensure that systematic errors are negligible. Ac-counting for the errors in the measurement of the geometry of the diffusion tube the accuracy of the reported data is estimated to be one of i-1.Ox. Fig. 4 contains a comparison of the recorded concentration distribution for a typical measurement with the fitted normal distri- bution.The deviation between the two distributions does not exceed the statistical uncer- tainty of the recorded signal which confirms the theoretical analysis of the experimental method and justifies the use of the normal distribution for the fitting procedure. Mutual-diffusion-coefficient measurements have been carried out on mixtures of n-hexane and n-heptane both supplied by B.D.H. The liquids were purified and degassed before use DIFFUSION-COEFFICIENT MEASUREMENTS first moment fld/ks FIG.5.-Measured diffusion coefficient as a function of flowvelocity for the n-hexane + n-heptane system Xc6 = 1.0 at 28.6 "C. and mixtures for the flowing stream were manufactured gravimetrically. The samples for injection were manufactured volumetrically and usually differed in mole fraction from the composition of the flowing stream by <0.1.It is an essential feature of the theoretical description of the experimental method that if the instrument operates in accordance with tlic theory the observed diffusion coefficient should be independent of the flow velocity employed for the measurements or equivalently the first moment of the measurements. To demonstrate that the present instrument conforms to this 12% temperature T/"C FIG.6.-Mutual-diffusion coefficients for the n-hexane + n-heptane system as a function of tempera-ture. 0 xc6 = 0.0; 0xc6 = 1.0. W. A. WAKEHAM requirement we have carried out measurements of the mutual-diffusion coefficient of the n-hexane + n-heptane system at 28.6 "Cfor the limit &6 = 1.0 over a range of flow VelOCi- ties.Fig. 5 shows the results of these measurements as a function of flow velocity. Within the experimental uncertainty the observed diffusion coefficient is indeed independent of flow rate. Fig. 6 contains a plot of the experimental diffusion coefficients for the n-hexane + n-heptane system as a function of temperature in the limits of pure n-hexane and pure n-hep- tane. The observed linear dependence on temperature is typical of that observed for inter- mediate compositions and other normal hydrocarbon systems.'* The estimated accuracy of the present experimental data is superior to that of the earlier measurements on similar liquid mixtures and the chromatographic technique now offers both speed and accuracy for the determination of liquid-phase diffusion coefficients.(b) EX P LOR AT 0RY M E A SUREM E N T S In addition to measurements of the mutual diffusion coefficients of liquid mixture^^^-^^ the chromatographic technique has already been employed for preliminary measurements of the mutual-diffusion coefficients of gases in liq~ids,~~*~~ of the self-diffusion coefficients of water and monohydric and of lipoproteins in blood serum.24 Two new applica- tions of the technique which have been explored are the measurement of the self-diffusion coefficients of ions in electrolyte solutions and the behaviour of the mutual-diffusion coefi- cient of a liquid mixture in the neighbourhood of a liquid-liquid critical point. For the first of these investigations measurements of the self-diffusion coefficient of thal- lous ions in aqueous solutions of thallous sulphate have been performed.In order to carry I 1 10 20 30 40 50 temperature T/"C FIG.7.-Mutual-diffusion coefficient of the system 2-n-butoxy-ethanol J -water near the lower critical solution point. out these measurements the flowing stream was an aqueous solution of thallous sulphate (T12S04) whereas the injected solute was a solution of the same concentration of T12S04manu-factured with radioactive thallium TlZo4 which is a beta-emitter. In this case the diffusion process involved in the dispersion is that of self-diffusion of the thallous ion in the solution. The dispersed pulse of radioactive thallous ions was detected by passing a short length of the diffusion tube through a section of scintillation plastic optically coupled to a photo- multiplier.The only experimental measurements so far carried out yield a value for the DIFFUSION-COEFFICIENT MEASUREMENTS self-diffusion coefficient for the thallous ion in infinite dilution in water of 1.39 i0.09 x m2s-' at 30 "C. The large experimental uncertainty of 16%reflects the preliminary nature of the measurements and further work is currently in progress. At a liquid-liquid critical point the mutual-diffusion coefficient of the system is known on theoretical grounds to become zero.25 There have been only a few practical demonstrations of this effect owing to the extreme difficulty of performing measurements in the critical region.The chromatographic technique has been applied to the measurement of the mutual-diffusion coefficient of the system 2-n-butoxy-ethanol + water which exhi bits a lower critical solution temperature at ca. 50 "C for a water mole fraction xHIO= 0.9387. The results of the measurements of the diffusion coefficient are shown in fig. 7 for the mixture of this composition and it can be seen that the diffusion coefficient does indeed approach zero as the critical solution temperature is approached. These preliminary investigations indicate that the chromatographic method may turn out to be a technique of wide applicability for the measurement of diffusion coefficients in liquid- phase systems. The accuracy of the measurements of mutual-diffusion coefficients in ordi- nary liquid mixtures has now been made comparable with that of other techniques but con- siderably more effort is required to achieve the same accuracy in more exotic systems.The author is grateful to Mr. A. Alizadeh Mrs. S. Kalicinski and Professor C. A. Nieto de Castro for their contributions to this work and to I.C.I. Mond Division for some financial support. K. H. Keller Biomaterials ed. L. Stark and G. Agarwal (Plenum Press New York 1969) p. 103. 'W. A. Wakeham and E. A. Mason Ind. Eng. Chem. Fundam. 1979 18 301. R. F. Treybal Mass Transfer Operations (McGraw-Hill New York 2nd edn 1968). C. Durou C. Moutou and J. Mackenc J. Chim. Phys. 1974 71 2171. E. R. Pike Photon Correlation and Light Beating Spectroscopy ed. H. Z. Cummins and E.R. Pike NATO Advanced Study Institute Series (Plenum Press London 1974) p. 5. G. I. Taylor Proc. R. SOC. London Ser. A 1953 219,186. R. Ark Proc. R. Soc. London Ser. A 1956 235 67. R. J. Nunge T. S. Lin and W. N. Gill J. Fluid Mech. 1972 51 363. L. A. M. Janssen Chem. Eng. Sci. 1976 31 215. J. C. Giddings and S. L. Seager J. Chem. Phys. 1960 33 1579. l1 W. A. Wakeham and D. H. Slater J. Phys. B 1974 7 297. l2 A. Alizadeh C. A. N. de Castro and W. A. Wakeham Int. J. Thermophys. in press. l3 R. T. Ferrell Ph. D. Thesis (University of Texas 1966). l4 M. E. Erdogan and P. C. Chatwin J. Fluid Mech. 1967 29 465. l5 N. G.Barton J. Fluid Mech. 74 81 91. l6 R. Smith J. Fluid Mech. 1978 88 323. l7 A. Alizadeh and W. A. Wakeham to be published. l8 A. Alizadeh Ph.D.Thesis (Imperial College London 1980). l9 A. C. Ouano Ind. Eng. Chem. Fundam. 1972 11 268. 'O K. C. Pratt and W. A. Wakeham Proc. R. SOC. London Ser. A 1974,336 393. 21 E. Grushka and E. J. Kikta J. Phys. Chem. 1974,78 2297. 22 K. C. Pratt D. H. Slater and W. A. Wakeham Chem. Eng. Sci. 1973 28 1901. 23 K. C.Pratt and W. A. Wakeham J. Chem. Soc. Faraday Trans. 2 1977,73 997. 24 W. A. Wakeham N. H. Salpadoru and C. G.Caro Atherosclerosis 1976 25 225. 2s J. V. Sengers Critical Phenomena Varenna Lectures Course LI ed. M. S. Green (Academic Press New York 1971) p. 445.

ISSN:0301-5696    

DOI:10.1039/FS9801500145

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

Chromatography of Atomic Hydrogen A. CLIFFORD, BY ANTHONY PETERGRAY,RODS. MASON?AND JOHN I. WADDICOR Department of Physical Chemistry University of Leeds Leeds LS2 9JT Received 9th July 1980 During experiments to measure the diffusion of hydrogen atoms using a flow system chromato- graphic retention of hydrogen atoms on the walls of the quartz tube was observed possibly the first example of the chromatography of a highly chemically reactive species. In these experiments the rate of adsorption and desorption can be obtained (and consequently the chromatographic partition coefficient,k’) as well as the diffusion coefficients and the rate of loss of H atoms by chemical reaction on the walls. The results show that the reversible adsorption of H atoms on a quartz surface is a more probable event than loss by reaction.This has important implications for the understanding of surface effects on gas-phase reactions in both static and flowing systems and could significantly effect the values of rate constants obtained experimentally. The diffusion coefficients of chemically reactive intermediates are important para- meters in the analysis of reacting systems under certain conditions such as high tem- perature and low pressure. Examples of such systems are (a)combustion and flames,l (b)the upper atmosphere2 and (c) surface reactions3 Hydrogen atoms are of parti-cular interest because of their high diffusion coefficients and importance in many flames. Consequently a number of measurements on diffusion have been made using a variety of techniques and detection methods.Most of these techniques are applicable to only a small number of systems mainly because the atoms are produced in the carrier gas. Furthermore the results obtained are not usually very consistent. In an attempt to develop a method to measure directly the diffusion coefficients of different reactive species in a wide variety of gases we have adapted the gas-chroma- tographic technique which has been widely used for chemically inert molecules. The main features necessary for unstable species are (a) the experiment must be carried out quickly and flow rates must be high (b)the pressure needs to be low so that diffu- sion is fast and turbulence is avoided and (c) the diameter of the tube must be large to minimise the loss of atoms by chemical reaction on the walls.It is also necessary to find a technique for detecting atoms which will respond sensitively and rapidly. The detection technique chosen was resonance fluorescence used in conjunction with photon-counting methods. In developing the method it was discovered that (a)the velocity of the pulses of H atoms was less than the mean gas velocity and (b)the diffusion coefficients obtained were apparently dependent on gas velocity. A large number of experiments was carried out with the H + Ar system to characterise these effects which were ascribed to reversible adsorption of H atoms on the walls of the quartz tube occurring at a rate slow enough to contribute to the dispersion of the pulse of atoms. The experiment has been analysed theoretically following the methods of G.I. Tayl~r,~ ArkS and Golay6 and these results will be presented later. In their most approximate form t Present address School of Chemistry and Molecular Sciences University of Warwick Coventry CV4 7AL. CHROMATOGRAPHY OF ATOMIC HYDROGEN many of the expressions obtained will be familiar to students of chromatography and only the method of analysis of results will be presented here in outline. EXPERIMENTAL Fig. 1 is a schematic diagram of the apparatus which shows the four main components the flow tube F the atom source S and the two observation points A and B. The flow tube is made of quartz washed with chromic and hydrofluoric acids of internal diameter 18.54 mni and length of ca.2.5 m. Atoms are injected through a pinhole P ca. 1 m from the end of the tube and observed at points A and B. The distances P-A and A-B are 0.35 m and 1.10 m respectively. The gas velocity is of the order of 10 m s-I and the pressure is rather less than 1 kPa (8 mmHg). The tube is at present kept at room temperature ca. 295 K. S FIG.1.-Schematic diagram of the apparatus. F is the main flow tube S is the H atom source with M the microwave discharge C the chopper and P the pinhole through which the atoms enter the tube. A and B are observation points with hydrogen lamps L seen in cross-section and photo- multipliers PM. The atom source S has the carrier gas containing some H2 flowing through it. On the inlet side is a microwave discharge M which produces H atoms in the source.These leak through the pinhole P but are interrupted by a metal chopper C. The chopper revolves at ca. 1 Hz and allows in H atoms for ca. 10 ms per revolution. The edges of the cut-out sector are shaped to pass close to the pinhole and also inject a pulse of nearly Gaussian shape simplifying the analysis of results. The maximum concentration of H atoms in the injected pulses is ca. 10'' m-3. Greater concentrations can cause self-reversal (reabsorption of the fluorescence). The observation points each have a hydrogen discharge lamp L above the tube produced by a microwave discharge and a solar-blind photomultiplier PM in the horizontal plane (EMR 541 3). LiF windows are used and an oxygen filter which has a window at the Lyman- awavelength of 121.7 nm cuts out U.V.light of other frequencies. The photomultipliers are used in aphoto-counting mode with low-noise FET amplifiers and an Ortec discriminator and multichannel analyser which is connected via an intelligent v.d.u. to the University Amdahl computer. The data-collection system is triggered by the chopper a preset number of times typically 2000. In between pulse injections the background signal is subtracted from the channels to give a zero baseline. The eventual output of the data-collection system is a digitized profile of the averaged pulses on the same time-base. The pulses are nearly Gaussian in shape and in a typical experiment widen from 20 to 35 ms in width at half height and fall in area by a factor of 2 between points A and B.Mainly because the intensities of the two lamps at points A and B are not identical it is necessary'to measure the rate of loss of total concentra- tion of H atoms between points A and B by titration. This is carried out by feeding in NO2 diluted in argon just above the observation points. CLIFFORD GRAY MASON AND WADDICOR 157 ANALYSIS OF RESULTS To the accuracy required for the analysis of the results of these experiments the following model system is used. Streamline flow is assumed without slip at c-mean velocity v. The H atoms are assumed to be subject to diffusion characterized by a coefficient D inversely proportional to pressure p. They are assumed to be lost by reaction on the walls at a rate koper unit area per unit concentration in the gas.They are assumed to be adsorbed at a rate k1per unit area per unit concentration in the gas and desorbed at a rate k per unit area per unit surface concentration. The normal chromatographic partition coefficient k’ is related to kl and k2by k’ = 2kl/k2r (1) where r is the tube radius. It can be shown that the following expressions apply approximately. If n is the total number of atoms in the pulse at time t and no is the number at a nominal t = 0 then n = noexp(-ut) where cc = 2ko/(l + k’)r. (3) If v’ is the pulse velocity as measured by the transit time of the centroid of the pulse from point A to B then V‘ 1 -=-v l+k” (4) Finally if a is an effective diffusion coefficient obtained from the increase of the pulse width with time then [1 + 6k’ + 11(k’)2]v2r2 krv2 (5) a=D+ 48(1 + k‘I2D (1 +k’)’k2 ’ The second term in this equation is the effect of the velocity profile as originally ob- tained by Golay.6 The third term is the contribution to the dispersion caused by the variation in residence time on the tube walls and is similar in form to expressions for the effect of slow diffusion through the stationary phase in g.l.~.~ It is thus possible to obtain all the parameters ko,kl,k2 (k‘) and D from the experi- ment.k‘ is obtained from the transit time. kois obtained from the rate of loss of atoms. k2(and hence k,) can be obtained from the velocity dependence of the effec- tive diffusion coefficient. And D can be obtained by extrapolating line effective dif- fusion coefficient to zero velocity.RESULTS AND DISCUSSION Results are presented for the H + Ar system at 295 K in the order in which they are obtained from the data i.e. the partition coefficient for H atoms on quartz the rate of loss of H atoms on quartz by reaction the diffusion coefficient for H atoms in argon and finally the rates of adsorption and desorption. EQUILIBRIUM CONSTANT FOR ADSORPTION OF H ON QUARTZ Table 1 shows results obtained for the time taken for pulses of H atoms to travel 1.10m from A to B for a range of argon velocities and pressures. From these values CHROMATOGRAPHY OF ATOMIC HYDROGEN ratios of the pulse velocity to the gas velocity are calculated and given in the last column. These are all seen to be within 2% of the value 0.90 giving a value for k' of 0.11.The related equilibrium constant k,/k2is 5.5 x m at 295 K. Mohnke and Saffert' have separated the isotopes of molecular hydrogen and their nuclear-spin isomers using an uncoated glass tubular column of more conventional dimensions. From their results the equilibrium constant kl/k2,for the adsorption of ortho-hydrogen molecules on the column surface can be calculated to be 3.3 x m. TABLECHROMATOGRAPHIC RETENTION OF PULSES OF HYDROGEN ATOMS IN AN ARGON CARRIER GAS AND A QUARTZ TUBE AT 295 K mean argon velocity argon pressure pulse transit time A -+ B pulse velocity argon velocity /m s-l /Pa /ms 5.20 686 233 0.91 5.30 746 231 0.90 5.35 648 228 0.90 5.51 671 221 0.90 6.02 580 201 0.91 6.02 607 204 0.90 6.39 493 191 0.91 6.39 528 190 0.91 6.42 601 188 0.90 6.88 600 180 0.89 6.89 585 176 0.91 7.03 557 174 0.90 7.05 493 173 0.91 7.55 475 163 0.89 7.55 501 165 0.89 7.76 445 157 0.91 8.03 469 153 0.90 8.46 406 145 0.90 9.07 374 135 0.90 9.38 380 131 0.90 11.18 328 112 0.88 i.e.of the same order of magnitude as hydrogen atoms on a quartz surface. How-ever these experiments were carried out at liquid-nitrogen temperatures and the inside of the glass tube had to be etched to increase its surface area. It is therefore clear that hydrogen atoms have a much stronger tendency to be adsorbed than hydrogen mole- cules. RATE OF LOSS OF H ATOMS ON THE QUARTZ WALLS Table 2 shows the results of several experiments carried out under different condi- tions of pressure and velocity and with different concentrations of H atoms for the exponential decay constant.This is found to have an average value of 8.6 s-l with a range of ca. I s-l. Thus about half the H atoms are lost by reaction between points A and B. The value k,,is 0.044 m s-l. The rate of wall reaction is often expressed in terms of a wall efficiency y the fraction of collisions with the wall which result in loss by reaction. CLIFFORD GRAY MASON AND WADDICOR TABLE 2.-MEASUREMENTS OF THE EXPONENTIAL DECAY CONSTANT tc ,FOR THE QUARTZ FLOW TUBE [HI = [HlOexp(at),AT VARIOUS ARGON VELOCITIES AND PRESSURES AND H ATOM CON-CENTRATIONS (GIVEN BY OBSERVATIONEPOINT B) mean argon velocity /m s-‘ argon pressure /Pa 10-17[H] at B /atoms m-3 number of experiments OL is-’ 6.59 535 2.6 5 8.9 6.59 535 1.4 5 8.9 5.68 599 6.5 4 9.6 5.68 599 7.2 5 7.1 5.68 599 6.9 4 8.3 y for the H/quartz system is found in these experiments to be 5.0 x at room temperature.This compares with values published by Sancier and Wise’ of 1.8 x and Linnett et aZ.I0 of between 4.0 x and 1.0 x DIFFUSION COEFFICIENTS OF H ATOMS IN ARGON AT 295 K The effective diffusion coefficients a were corrected for the velocity profile effect [the second term in eqn (5)] using an estimate for D of sufficient accuracy. The cor-rected values a’ were plotted on fig. 2 as a’p against v2p where p is the pressure in 2 .o 1.6 1 *41 I I I 0 0.l 0.2 0.3 v”pm’ s-’ atm FIG.2.-Extrapolation of the effective diffusion coefficient a’ corrected for the dispersion effect of velocity multiplied by pressure p in atm to obtain the true diffusion coefficient for H atoms in argon at 295 K and 1 atm pressure.standard atmospheres. The intercept gives a value of D at 1 atm and 295 K of 1.6 & 0.15 x m2s-I. This compares with a value obtained by Schiff and co-workers,ll from measurements on the ternary H + H + Ar system and corrected to 295 K of 1.4 & 0.2 x m2 s-l at 1 atm. CHROMATOGRAPHY OF ATOMIC HYDROGEN RATE OF ADSORPTION AND DESORPTION OF H ATOMS The slope of the plot in fig. 3 gives using eqn (5) the rate constant for desorption k2,as 810 5 150 S-'. From the value of the equilibrium coefficient kl/k2,a value of 0.45 -J=0.1 m s-' can be obtained for the rate constant for adsorption k,.From k the average time of attachment of the H atoms to the quartz wall is seen to be 1.2 & 0.2 ms. k is seen to be in an order of magnitude greater than k,, indicat-ing that reversible adsorption is statistically a more important event than loss on the wall by reaction. SUMMARY An experiment originally designed to measure diffusion coefficients for hydrogen atoms has demonstrated chromatographic retention of a highly reactive species and shown itself capable of measuring rates of adsorption and desorption of H atoms on quartz. The reversible adsorption of H atoms on quartz is shown to be an order of magnitude more probable an event than loss of H atoms by reaction. The results obtained at 295 K are as follows k, the rate of adsorption per unit area per concentra- tion in the gas phase 0.45 & 0.1 m s-'; k2the rate of desorption per unit area per unit concentration 810 & 150 s-,; y the wall efficiency 5 x and the diffusion coefficient for H atoms in argon at one atmosphere 1.6 & 0.15 x m2 s-l.We gratefully acknowledge financial support from the S.R.C. in the form of a research grant and a studentship for J. I. W. G. Dixon-Lewis and D. J. Williams Comprehensive Chemical Kinetics ed. G. H. Bamford and C. F. H. Tipper (Elsevier Amsterdam 1977) vol. 17 chap. 1. M. R. Bowman L. Thomas and J. E. Geisler J. Atmos. Terr. Phys. 1970 32 1661. H. Wise and B. J. Wood Adu. Atom. Mol. Phys. 1967 3 291. G. I. Taylor Proc. R. SOC.London Ser. A 1953 219 186; 1954 223 446; 1953 225 473. R. Aris Proc. R. SOC.London Ser. A 1956 235 67. M. Golay Gas Chromatography ed. D. H. Desty (Butterworth London 1958) p. 35. 'H. Purnell Gas Chromatography (Wiley New York 1962) p. 127. M. Mohnke and W. Saffert Gas Chromatography ed. M. van Swaay (Butterworth Washington D.C. 1962) p. 216. 'K. M. Sancier and H. Wise J. Chem. Phys. 1969 51 1434. lo M. G. Green K. R. Jennings J. W. Linnett and D. Schofield Trans. Faraday SOC.,1959 55 2152. B. Khouw J. E. Morgan and H. I. Schiff J. Chem. Phys. 1969 50 66.

ISSN:0301-5696    

DOI:10.1039/FS9801500155

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr. P. F. Tiley (Bath University) (communicated) Dr. Phillips' account of the chromatographic use of molecules as probes to study the nature of solid surfaces brings to mind that some thirty years ago Stone and 11v2 used physically adsorbed krypton to investigate the chemisorbed state of carbon monoxide and oxygen on cop- per oxide. In those days we naturally used a static-equilibrium apparatus but there are obvious analogies with the dynamic chromatographic technique. F. S. Stone and P. F. Tiley Nature (London) 1951 167 654. * P. F. Tiley Nature (London) 1951 168 434. Dr. A. A. Clifford(Leeds University) and Dr. W. A. Wakeham (Imperial College London) said The determination of structural parameters seems to place impossible demands on the accuracy of the model forces between the molecule and the surface which are required to predict the Henry's Law constant.In the case of indane for example the angle to be determined affects the interaction of only one of the nine atoms in the molecule with the surface so that even a large change in the angle can only alter the molecule-surface interaction by a few percent. Furthermore from studies in the gas phase it is known that the "theoretical and combinatorial " methods employed by the authors cannot predict intermolecular forces to this precision. Thus even if the experimental data were perfectly accurate uncertainties in the model inter- actions assumed would not allow the structural angle to be determined. Prof. A. V. Kiselev (University of Moscow) (communicated) This comment is con- nected with some misunderstanding.The model of intermolecular interactions of course is not precise enough. However we used the semi-empirical atom-atom poten- tial functions in the parameters of which we introduced a correction factor found from a comparison of the calculated and experimental chromatographic values of Henry's constant for the adsorption of reference molecules of the same class of hydro- carbons [see ref. (2) (9) and (10) in our paper]. We indicated in our paper that the possibility of extrapolating the atom-atom potential functions obtained for reference molecules of a given class to other molecules of the same class was subsequently checked [see ref. (2) (9) (lo) (1 6)-(18) ;the last will appear in 198 11.The sensitivity of the reverse chromatoscopic method is obvious for example from fig. 2 of our paper in which the Kt value is of course influenced by all the atoms of the indane molecule. Dr. 2. Elkoshi (Hebrew University Jerusalem) said This remark is related to fig. 3 of Prof. Kiselev's paper which demonstrates the correspondence between theory and experiment and suggests the angle a to be 19". For this demonstration to be more convincing it is recommended that one draw theoretical lines corresponding to several values of a different from 19". This might demonstrate whether the line is sensitive to a change in a. If such proves not to be fig. 3 is then not a proof that a is 19". Prof. A. V. Kiselev (University of Moscow) (communicated) The dependence of Kl on a for 5-methylindane is quite similar to that for indane (see fig.2 of our paper); only the values of Kl for 5-methylindane are higher respectively. Dr. 2. Elkoshi (Hebrew University of Jerusalem) (communicated) I calculate that changing a from 19 to 10" changes the slope of the theoretical line in fig. 3 by < 2%. GENERAL DISCUSSION Prof. J. S. Rowlinson (Oxford University) said The coefficients kAB in table 2 of the paper of Prof. Findenegg and his colleagues should be related to the relative strengths of the like (A-A and B-B) and unlike (A-B) intermolecular energies if the molecules are all the same size. Is it possible to refine these quantities and correct for the size difference? If so it should be possible to see if the set reflects the well- known weakness of aliphatic-aromatic interactions when compared with a mean of aliphatic-aliphatic and aromatic-aromatic.Prof. G. H. Findenegg (Ruhr Uniuersity Bochum) said As Prof. Rowlinson has pointed out the lateral interaction of adsorbed molecules is proportional to the energy parameter e a a//3 rather than a alone. For single adsorbates the analysis of our ex- perimental data (gravimetric as well as gas-chromatographic) yields ci and pi (or Tm, J as independent parameters; we find that the intermolecular energy for like mole- cules ei increases in the order hexane < methylpentanes < dimethylbutanes < cyclo-hexane and that the value for benzene is considerably smaller than that for hexane. For mixed adsorbates our gas-chromatographic measurements yield the cross-para- meter EAB if the parameters aA,PA and pRare known [cf.eqn (8) and (IS)]. By ana- logy with ei the intermolecular energy of an A-B pair is then EAB = 2mA4PA + Ad-’. and we may express the deviation of EAB from the geometric mean of and E~ by kkB kkB = 1 -EAB(EA&B)-~’~. Generally kkB is larger than kAB; for hexane + benzene where the difference in mole- cular size is largest kkB = 0.08 as compared with kAB = 0.04. However in order to evaluate kAB and kkB we had to take aB from the gravimetric study. As the para- meters ai and pi obtained by the two methods agree only within ca. 80/ the values of kAB presented at this meeting may be unreliable. We are now extending the scope of the gas-chromatographic measurements in such a way that both components of a binary mixture are being used as component A and B.All parameters which are needed for the evaluation of kkB can then be determined by the same method and the consistency of the results can be checked by comparing the two values of kkBobtained when either of the two substances is used as component A. Dr. C. S. G. Phillips (Oxford University) said With reference to fig. 3 of the paper by Prof. Findenegg and his co-workers are the effective surface areas as mea- sured by benzene and by cyclohexane the same? Prof. J. H. Purnell (Uniuersity College of Swansea) said Is the absence of a maxi- mum in the plot for benzene in fig. 3 as well as the anomalously low value of E quoted by Prof.Findenegg in discussion in any way indicative of the possibility that benzene lies flat on the surface at all xAwhile the others do not and may vary in orientation with xA?(See p. 192.) Prof. R J. Laub (Ohio State Uniuersity) said Would Prof. Findenegg care to speculate on the discrepancy between static and gas-chromatographic measurements of the adsorption isotherm shown in fig. 5 of his paper? As stated in the paper the difference is ca. 8% i.e. is not inconsiderable which seems to cast some doubt upon the chromatographic method or for that matter upon the manner in which the g.c. and/or static experiments were here carried out. Dr. J. R. Conder (University College of Swansea) said The paper by Findenegg and co-workers provides an excellent example of the capabilities of finite-concentra-tion gas chromatography.The method used is elution on a plateau (EP) one of several alternative techniques which were developed in their present refined form by GENERAL DISCUSSION 163 Helfferich Kobayashi and Purnell and myself.l*' Purnell and I dealt with a gas phase containing a sorbed component and an inert-carrier component Helfferich and Kobayashi also worked with the multicomponent case where the gas phase contains two or more sorbed components but no carrier. Prof. Findenegg and his colleagues have now completed the picture by using a gas phase containing both two sorbed components and a carrier. The chromatogram however is puzzling. In this case when a single pulse of B is injected onto a plateau of A theory3 permits only two peaks in the chromatogram and not three as appear in fig.2 of the paper. The first peak (peak 1) should involve simultaneous depletion of A and enrichment of car- rier the second peak (peak 2) enrichment of A and depletion of carrier. One but not both of these peaks (presumably the second when A = cyclohexane and B = n-hexane) should also contain the component B. The relative enrichment or depletion of the various components in the two peaks is governed by the condition of mass balance. It is not necessary to invoke a third peak in order to satisfy the mass- balance condition. It seems reasonable to identify peak 2 with the one marked hB,pin fig. 2. Peak 1 must be either the one marked hA,por the negative peak immediately following it.One of these latter two peaks must therefore be an artefact produced by some secondary effect such as a pressure pulse produced by the injection which could temporarily perturb the gas composition at a pressure-sensitive point such as the satu- rator or diffusion cell. I recall observing similar effects when injecting onto a concen- tration plateau. Did the authors observe the same pattern of fig. 2 for all cases studied ? One wonders which of the first two peaks in fig. 2 is the false one. The authors give a good reason (agreement with retention of A on A) for supposing that peak 1 is the positive one marked IZ~,~, though the other reason (retention independent of nature of B) could apply to the false peak too. The direction of the signal for peak 1 is difficult to use for diagnosis because of the complexity of the response of a thermal conductivity detector to a mixed gas.Because of its makeup however peak I is much more likely to give a negative than a positive signal when R > RA,though this need not be so when RA > RB. It is therefore difficult to say with any certainty which of the first two peaks in fig. 2 is to be identified as peak 1. I should like to make one other point about the supposed problem of column- pressure drop in finite-concentration work. Reference has been made to Valentin and Guiochon's view that the experimental conditions under which low pressure gra- dients can be achieved lead to poor accuracy of the results. This is fallacious since conditions can easily be chosen to avoid loss of accuracy.By using packing of par- ticle size say 20-30 mesh instead of 80-100 one can reduce the pressure drop tc around 0.01 bar m-' at typical gas velocities. The number of plates in the column is maintained by doubling the column length. The overall effect is to reduce the pres- sure gradient by two orders of magnitude without any loss in precision of retention measurement. The pressure correction terms can then be taken outside the integrals in eqn (3) and (4) allowing the isotherm to be derived directly from the experimental data as was done by Conder and P~rnell.~ Valentin and Guiochon's approach using a large pressure drop is less satisfactory in that the isotherm is never obtained directly as Prof. Findenegg and his colleagues point out.Instead the accuracy one achieves is at the mercy of the mathematical model for the isotherm used to fit the chromatogram and so is highly variable and unpredictable. J. R. Conder and C. L. Young Physicochemical Measurement by Gas Chromatography (John Wiley London 1979) chap. 9. I).L. Peterson and F. Helfferich J. Phys. Chem. 1965 69 1283. F. Helfferich and G. Kelin Multicomponent Chromatography (Marcel Dekker New York 1970) pp. 207-209. J. R. Conder and J. H. Purnell Trans. Faraday SOC., 1968,64 1505 3100; 1969,65 824 839. GENERAL DISCUSSION Prof. J. H. Knox (Edinburgh University) said As Dr. Conder stated when there are n components in a chromatographic mobile phase the injection of a sample of different composition to the eluant (but containing no extra components) should pro- duce (n -1) peaks.I do not therefore understand how three peaks can be produced as shown in your fig. 2 for as I understand it there are only three substances present helium hexane and cyclohexane. Therefore only two peaks should be obtained. Would you have obtained two peaks if a pulse of cyclohexane had been injected (but with no hexane present) or only one peak'? Prof. G. H. Findenegg (Ruhr Uniuersity Bochum) said :With regard to Prof. Laub's question we believe that the discrepancy between our static and gas-chromatographic adsorption isotherms is not caused by deviations from local sorption equilibrium as our adsorbent (graphitized carbon black) is non-porous and has an inert highly homo- geneous surface.Major sources of systematic error of the g.c. method are (i) The determination of the concentration xAof vapour A in the mobile phase from the total pressure and temperature in the cell using the Antoine equation. (ii) The large pressure gradient along the column (PI =~(~)/p(') up to ca. 2 for the work reported in the paper); as the experimental R(xA)values are related to an average value of the derivative dr,/dpA from p(i) to p(A) errors may arise when dT,/dp varies strongly over that section of the isotherm. This happens to be the case with the adsorption isotherm of n-hexane. It has been shown that the deviation between the static and g.c. isotherms in fig. 5 of our paper can be attributed mainly to the section around the point of inflection of the adsorption isotherm.Recently we have achieved a much smaller pressure drop (P z 1.1) and we expect to improve the consistency between the static and g.c. results in this way. Further developments will show whether it is possible in our case to reduce the pressure gra- dient down to 0.01 bar m-' as suggested by Dr. Conder. In that case we could de- rive the isotherm directly from the experimental R(xA)data and more important account for the non-ideality of the mobile phase by the formalism given by Conder and Purnell. However so long as PI>I. 1the method of evaluation which we used in our paper seems to introduce smaller systematic errors than the method of Conder and Purnell. W. von Rybinski Ph.D. Dissertation (Ruhr University Bochum 1980).Prof. G. H. Findenegg and Mr. M. Albrecht (Ruhr Uniuersity Bochum) (partly communicated) Dr. Conder and Prof. Knox have raised some interesting ques- tions concerning the nature of the chromatogram in fig. 2 of our paper. Let us point out at first that the analysis of the mixed-gas adsorption given in our paper is based on the retention of peak 2 (marked hB,J,which contains the component B. In order to clarify the nature of the first two signals in this chromatogram we have now made some additional measurements. Incidentally all experiments of our work were made using a flame-ionization detector; thus the positive signals in fig. 2 are to be attri- buted to an enrichment of the hydrocarbons A and/or B and the negative signal to a depletion of A.If a pulse of the sorbable vapour A is added to a step of A plus carrier gas only one peak (retention R0.A) is obtained. When a pulse of vapour B is injected on a step of A the chromatograms exhibit two or three peaks depending on the extent of pre- coverage of the adsorbent with component A and on the relative affinities of A and B. If RA z R (e.g. cyclohexane and 2,2-dimethylbutane) only two signals appear first a negative peak and then a larger positive peak; this pattern seems to agree with When RR the theoretical prediction mentioned by Dr. C0nder.l :> RAa positive sig- nal appears immediately before the negative peak and its area increases with increasing GENERAL DI$CUsSION affinity of B (hence fig. 2 shows an extreme case as n-hexane is much more strongly adsorbed than cyclohexane).Here we have to modify two statements made in our paper (i) in all cases the peak area of the first positive signal seems to be less than that of the subsequent negative signal; (ii) the retention time of the first positive peak tAf (tA in fig. 2) is always less than the retention time of a pulse of A on a step of A tA,O. When a positive signal appears t; is less than tA,O and tA becomes larger than tA,O; however the arithmetic mean of ti and ti becomes approximately equal to tA,O as can be seen in table 1. TABLERETENTION TIMES tz AND ti OF THE POSITIVE AND NEGATIVE SIGNAL OF PEAK 1 FOR PULSES OF COMPONENT B ON A PLATEAU OF CYCLOHEXANE (A) tA,O= 3.88 min; xA= 4.5 x lop3;Pi = 1.1; T= 353.2 K.B ti /min t,/min +(t -tti)/min 2,2-dimethylbu tane 2,3-dimet hylbutane a a - 3.42 3.90 - 3-methylpentane 3.58 4.03 3.81 n-hexane 3.63 4.12 3.88 * No positive signal detectable. When RB< RA (e.g. A = n-hexane) the first peak represents tB and the second peak consists of a positive signal (ti) immediately followed by a negative signal (ti). In both cases it seems neither t nor ti but (t + t~)/2 corresponds roughly to the retention time tA,O. The arguments of Conder and Knox seem to be based on the assumption that the total amount adsorbed per unit area of the stationary phase remains constant (i.e. a " stoichiometric '' exchange equilibrium in the terminology of Helfferich and Klein).' This condition may apply to systems for which RB N RA and it is indeed this case in which we observedjust two peaks.However in other cases we may expect that the amount adsorbed is altered by the exchange equilibrium (" non-stoichiometric " ex-change) e.g. when two adsorbed molecules A are displaced by one more strongly adsorbed larger molecule B. According to theory1 a system with n sorbable com- ponents exhibiting non-stoichiometric sorption is formally equivalent to an (n 4-1)-component system with stoichiometric exchange and constant total concentrations in both phases. Therefore it seems reasonable to find a chromatogram with three peaks in that case. However a detailed theoretical analysis of the two peaks not containing component B should be difficult. F. Helfferich and G. Klein Multiconiponent Chrornarography (Marcel Dekker New York 1970) p.207. F. Helfferich and G. Klein Multicomponent Chromatography (Marcel Dekker New York 1970) p. 283. Prof. J. H. Knox (Edinburgh University) said I address my remarks to Prof. Roberts. (a)Amino-bonded phases are often made by the supposed reaction OEt I 3Si-OH + (EtO),Si(CH2)3 NH,+ -/ SiO Si -(CH,),NH2+ C,H,OH I OEt GENERAL DISCUSSION The existence of two different environments for the N atom in the p.e.s. spectrum of Spherisorb-5-amino suggests that some of the aminopropyl-triethoxysilane (if this was the reagent actually used) might have reacted at the NH2 group. 2 SiOH+NH,(CH,),Si(OEt) _t =SiNH(CH,),Si(OEt),+ H,O 4 (b) The presence of a significant amount of surface sodium in the permaphase materials is probably due to the fact that these are pellicular.That is they consist of a thin surface layer deposited on a solid glass bead. The sodium presumably arises from the glass of the bead. (c) The concentrations of N found listed in table 3 of your paper are equivalent to ca. 6 pmol m-2 of bonded groups. This is about twice the quantity found by CHN analysis. Is this the sort of discrepancy which one might expect from p.e.s.? If so could this kind of experiment provide a means of calibrating p.e.s. measurements of surface concentrations ? Prof. M. W. Roberts (University College Cardzfl)said I thank Prof. Knox for his helpful comments. It is indeed a problem that we know so little about how the bonded phases are formed.I think the way to proceed in this area would be to carry out what I like to describe as “Dynamic Photoelectron Spectroscopy ” where the chemistry taking place is monitored in situ. This is a much preferred experimental strategy from the more usual approach of studying the surface as it were after the event and one we have found most useful in our surface chemistry studies using p.e.s. Regarding the last point (c)I would not be surprised that our quantitative estima- tions of surface concentrations of “ N ” species may be “ in error ” by as much as &30%. We have of course calibrated our p.e.s. approach to estimating surface concentrations on well-defined metal surfaces in various ways and problems mainly arise from accurate knowledge of photoionisation cross-sections.Generally how- ever we believe that with metals the error is no more than &15%. When we are dealing with topographicalIy undefined (rough) surfaces as we have in the present work the accuracy could be significantly less. Prof. C. L. de Ligny (Analytical Chemistry Laboratory Utrecht) said The authors conclude that in the substrates Spherisorb-5-nitrile and Spherisorb-5-amino two nitrogen species are present a free nitrile (or amino) nitrogen and nitrogen present in a nitrile (or amino) group that is adsorbed at the silica surface. We have drawn the same conclusion for two analogous surface-modified silicas with surface groups =Si-N(CH3)-(CH2),-CN (I) and rSi-(CH2)4-NH2 (11) respectively from a study of their properties as adsorbents in high-performance liquid chromatography .9 In short an analysis of our data by Snyder’s semi-empirical approach showed that the strength cc of the adsorbents was abnormally low as compared with that of octa- decyl silica. We could explain this fact by assuming that some of the cyano groups in (I) and of the amino groups in (11) adsorb at the silica surface presumably by hydro- gen bonding with surface rSiOH groups. When the silica is immersed in hexane the fractions of the surface groups that are adsorbed at the silica surface are calculated to be 0.88 and 0.95 for the substrates (I) and (11) respectively. W. E. Hammers C.H. Kos W. K. Brederode and C. L. de Ligny J. Chromatogr. 1979,168,9. W. E. Hammers M. C. Spanjer and C. L. de Ligny J.Chrornatogr. 1979 174 291. GENERAL DISCUSSION Prof. M. W. Roberts (University College Cardzf) said What of course should be attempted is to study in situ the molecular processes occurring during surface modifi- cation of the silica substrate. This may indeed be possible with our recently deve- loped “ high-pressure ” photoelectron spectrometer where the advantages of “ dyna-mic ” studies can be realised. This is the way we were able to assign our observed N (1s) spectra using N2H4 N2 NO and NH3 but with metal surfaces. On reflection I would also add that your comments are most relevant to our photoelectron spectroscopic data in that we have assigned N (1s) peaks to CN and NH surface species and C (1s) peaks to CN species. We also have X.P.S.for the role of hydrogen bonding in systems analogous to those discussed in your paper. C. T. Au and M. W. Roberts Chern. Phys. Left.,1980 74 472. L. Moroney S. Rassias and M. W. Roberts Surf. Sci. in press. Dr. G. B. Cox [Du Pont Co. (UK) Ltd. Stevenage] said I wish to make three points. (1) The differences observed in behaviour between the PermaphaseTM ODS and Spherisorb packings is probably due to the difference in nature of the bonded phase materials. The PermaphaseTM material consists of a glass bead surrounded by a thin (1 pm) layer of porous silica on which an octadecylsiloxane polymer has been formed. The Spherisorb material has essentially a monomolecular layer of bonded phase material on its surface. Presumably the polymer on the PermaphaseTM surface masks the remainder of the particle thus giving the relatively small silica signals.(2) Two types of chemical environment were seen for carbon in the PermaphaseTM ETH material. It is reasonable to suppose that one type comprises the methylene chain the other the glycidoxy residue. Given that these differences are observable it is surprising to note that only one type of carbon environment was observed for the Spherisorb CN material. This contains some 25% of its carbon in a cyano group which one might expect to be detected by virtue of different binding energy resulting from its chemical environment. (3) The appearance of two types of amino group in the Spherisorb-5-amino could arise through its method of synthesis since the chain length is short enough to cast doubt on the possibility of adsorption of the amino group on the silica surface.These materials are conventionally prepared by reaction of triethoxy aminopropyl silane with silica. It is not inconceivable that triethoxy silyl groups could react with an amino function already bonded to give a carbon-nitrogen-silicon linkage thus giv- ing rise to the secondary amine. It is less likely that the amino group will react directly with the silica surface since reactions used to carry out such an addition in the past have necessitated the initial chlorination of the silica surface. It is difficult to postulate how a CN group could be formed in the synthesis of the cyano phase but it is equally difficult to explain the observed two-component spectrum in any other way.Prof. M. W. Roberts (University College Cardifl) said Dr. Cox’s comments on the preparative methods used are most relevant to the interpretation of the spectra. I agree with the second comment and just note that the C (1s) profile in that case is over 3 eV wide and may therefore be composite. Prof. M. W. Roberts (University College Cardif) said I was most interested in Dr. Scott’s informally presented model for the silica surface and in particular the role GENERAL DISCUSSION of hydrogen bonding in determining the multilayer structure. On the basis of the thermal stability of the hydrogen-bonded water layer I would guess that the strength of the bonding must be ca. 100 kJ mol-I. Recently we have observed by X-ray photoelectron spectroscopy interaction between H20(a) and chemisorbed oxygen pre- sent on a Cu(ll1) surface which we have interpreted as “hydroxylation ” induced by strong 0--H interaction.We have similar behaviour in the case of HCl OH(a) formation followed by H20(a) and desorption was observed the end-result being that O(a) is “replaced ” by Cl(a). This occurs at 150 K. With “CuO ” a simi-lar interaction is observed with the replacement of O(a) by NH(a). Dr. P. F. Tiley (Bath Uniuersity) said I address my remarks to Dr. Scott. With reference to the simple distribution law concerning the distribution of solute A be-tween two immiscible liquid phases I and 11 thermodynamically K= (a similar treatment applies if concentrations are used). If K is sensibly constant over a finite concentration range it does not necessarily follow that the individual y values are themselves constant i.e.that the phases are ideal-dilute solutions. The concentration range over which Henry’s Law applies within experimental limits varies from one system to another. Henry’s Law would have been better named “ Henry’s Approximation ” since unlike Raoult’s Law or the Ideal Gas Laws there can be no hypothetical model of a binary system conforming to Henry’s Law over a finite concentration range. The conceptual value of Henry’s Law in defining a ther- modynamic reference state for the solute in a dilute solution should not blind us to the fact that Henry’s Law is nothing other than a mathematical approximation when used in the form of a linear (p x) or (p c) relation and the degree of approximation is a variable quantity.Dr. P. F. Tiley (Bath University) (partly communicated) Dr. Scott’s experimental results on the distribution of small quantities of a polar solute between water and a mixture of heptane + heptyl acetate are indeed a close parallel of g.1.c. studies on mixed-solvent columns and could provide a relatively simple technique for studying the ternary liquid mixtures involved in chromatography. Two warnings are neces- sary. The first concerns experimental accuracy. Some years ago there were hopes that g.1.c. “head-space ” analysis would provide a simple technique for studying isothermal vapour-liquid equilibrium in multicomponent systems. Alas as I know from personal experience the experimental accuracy of this method is not good enough.The second point is that theoretically completely immiscible liquid com- ponents do not exist. One needs to be sure that the solubility in water of the organic solvents is sufficiently small as to have no effect whatsoever on the activity of the distributed solute in the aqueous phase. Let us assume that both these points have been satisfactorily met then Dr. Scott’s results imply that in the ternary mixture X + RCH3 + RY where X is a polar com- ponent at high dilution l/y is a linear function of the concentration of the polar sol- vent RY. From thermodynamic theory there is no a priori reason why this should be so but equally well there is no reason why it may not be a good approximation for certain systems.Further consideration of this type of system is certainly merited if it has relevance to liquid chromatography. It would however be most surprising if this simplistic approach were applicable to all ternary systems of the type X + A + B where A is any non-polar solvent and B any polar solvent. In fact the g.1.c. results of Littlewood and Willmott where A = squalane B = dodecanol or lauronitrile showed that linearity only occurred for certain classes of polar solute. GENEkAL DISCUSSION Dr. P. J. Schoenmakers (Laboratory for Analytical Chemistry Delft) said I have three points to make concerning Dr. Scott’s paper. (1) Dr. Scott discusses the adsorption of water on the silica surface in a highly quantized way taking the adsorption of one water molecule per silanol group at the surface as a unit quantity.The different layers are supposed to be completed (or almost completed) before the next layer starts to build up. This suggests a very large difference in potential energy for molecules present in successive adsorption layers. Hence it suggests a very strong long-range interaction effect caused by silanol groups. I consider this to be unlikely certainly beyond the second adsorbed layer. Hence I think the adsorption occurs in a less ordered way and any conclusions drawn from the assumption of quantized adsorption of water should be approached with care. (2) The discussion following fig. 14 of Dr. Scott’s paper concerns concentration of This is considered to be an polar solvents in a non-polar one of 0.03-0.15 g ~m-~.example of a complete monolayer adsorption. This is in sharp contrast to fig. 7 where already at 0.03 g cm-3 a considerable deviation from this assumption is observed. (3) In eqn (1)-(4) the distribution coefficient is related to the interactive forces in the solution. Now the distribution coefficient is known to be exponentially related to free energies K = exp (AGIRT) rather than linearly to forces. Hence the summation of forces in the way des- cribed in eqn (1)-(4) appears to be incorrect. Also the similarity between eqn (4) and (5) seems to be very limited. Prof. J. H. Purnell (University College of Swansea) said The data shown in fig. 2 do not agree with those of table 1. Does this mean that they come from different experiments and if so which do you favour in the context of the present discussion? Dr.R. P. W. Scott (Perkin-Elmer Inc. Norwalk Connecticut) said I must certainly agree with Dr. Tiley when he states “if K is sensibly constant over a finite concentra- tion range it does not necessarily follow that the individual values are themselves con- stant.” In my paper I state “ linear curves are obtained relating the concentration of the solute in each phase and the curves extrapolated to the origin within experimental error”. Both these points have to be taken into account. As a result K will be constant down to infinite dilution where the system can indeed be considered ideal. It follows that the system having same value for K at higher concentrations as that at infinite dilution behave in an ideal manner at the higher concentrations.I can certainly sympathize with Dr. Tiley’s problems in obtaining precise analyses of vapour samples by gas chromatography. I have met the same problem myself but found it due to sampling problems involving surface absorption on the walls of the sampling vessel. The gas-chromatographic analyses of liquid samples however can be very precise. In table 2 the ratio of the areas of ethyl acetate to a standard decane is given for six replicate samples of the same solution each one carried out in duplicate. It is seen that the overall data have a mean of 1.5251 with standard deviation 0.003 86 which is equivalent to 0.253% of the mean. Such precision is more than adequate to be confident of the relationships pre- sented.Finally I would agree that further consideration of this type of system is GENERAL DISCUSSION TABLE 2.-RESULTS OBTAINED FROM THE REPLICATE ANALYSIS OF A SOLVENT MIXTURE BY GAS CHROMATOGRAPHY solvent mixture 1.0%each of n-decane and n-propanol in n-heptane sample size 0.5 mm3 column packing 15% PEG on Chromasorb column length 6 ft column temperature 65 "C (isothermal) flow rate 20 cm3 min-I area of n-decane peak/area of n-propanol peak sample duplicates 1 2 1 1.526 67 1.530 1 2 1.523 8 1.523 9 3 1.521 3 1.517 1 4 1.526 3 1.524 4 5 1.522 0 1.527 4 6 1.526 9 1.531 0 mean 1.525 1 d 0.003 86 % of mean 0.253 certainly merited. . .' So far we have confirmed the linear relationships shown in fig.17 of my paper for the following systems solute phase 1 phase 2 ethyl acetate water butyl chloride + heptane mixtures (0-100%) ethyl ace tat e water heptyl chloride + heptane mixtures (0-100%) isopropanol water butyl chloride + heptane mixtures (0-100%) n-propanol water butyl chloride + heptane mixtures (C-1CGx) n-pro pano water 1 ,Zdichlorethane + heptane mixtures (O-lOO%) These data together with others will be published in due course. I turn now to Dr. Schoenmakers. There is indeed a large difference in potential energy for molecules present in successive adsorption layers. This is because the first layer is held by hydrogen-bonding forces between the solvent and the silanol groups and the second layer is merely held by polar interactions between the solvent molecules themselves.These latter interactions are those that permit the solvent to exist as a liquid up to its boiling point. I agree that long-range interactions by silanol groups are extremely unlikely and certainly do not and have not postulated their existence. Fig. 7 and 8 of my paper both confirm that the monolayer absorption is virtually complete and subsequent to 0.03 g ~rn-~ the second layer is being formed. Fig. 7 shows no deviation from this concept. The answer to the conflict of my results with those expected from thermodynamic reasoning is best covered by the point made by Dr. Tiley with which I entirely agree. I quote "from thermodynamic theory there is no apriori reason why the linear rela- tionship should be so but equally well there is no reason why it may not be a good approximation for certain systems." We have now examined five further solvent systems and have found the relationships shown in fig.17 to be precisely confirmed for every system so far examined where the two phases have high mutual insolubility. GENERAL DISCUSSION 171 Prof. C. L. de Ligny (Analytical Chemistry Laboratory Utrecht) said Dr. Scott and his collaborators have presented a very interesting series of papers on the adsorp- tion of solutes and of solvent components in straight-phase and reverse-phase chroma- tography in the last few years. However in our opinion the calculations that they present in the paper under dis- cussion are beset with two errors.(1) The authors conclude that the adsorption isotherms of the investigated solutes on the adsorbent ODS 2 are strongly curved (see their fig. 4). In that case the ob-served retention volume of the solute is given by the equation1 dT v= v,+ V'= vm+-ql dcm where V is the observed retention volume of the solute r is its surface excess concen- tration at the adsorbent surface and the other symbols are the same as used by Scott and Simpson. Eqn (1) holds for the diffuse boundary of the solute in elution chroma- tography and in the case of continuous introduction of a mixture of solvent and solute (=moderator) into the column for the retention volume of a minor disturbance of the solute (=moderator) concentration (fig.1). For the retention volume of a major disturbance of the solute concentration in the case of continuous introduction the following equation holds v= v la) positive adsorption [b)negative adsorption adsorption is0ther.m derivative of adsorption isotherm V sample vm volume elution I chroma togra PhY V vnl con t inu ous Crn introduction Crn FIG.1.-Relationship between adsorption isotherm and retention volume in the case of elution chromatography and continuous introduction. GENERAL DISCUSSION For a step from zero solute concentration to c or vice versa i.e. for the sharp boun- dary in elution chromatography it holds analogously that In all cases Vdepends on c,. Scott and Simpson use eqn (3) (formulated as Y' = Kq) to calculate the corrected retention volume of a disturbance of the moderator concentration in the case of con-tinuous introduction of a mixture of solvent and moderator into the column.This is not correct in this case either eqn (1) or eqn (2) holds depending on whether the disturbance of the moderator concentration is infinitesimally small or large. (2) A correct way to determine V is to fill the column successively with two sol- vents of different densities to weigh the column and to divide the difference in the weights by the difference in the densities. In principle Vmcannot be found from the retention volume of a sample of a salt solution. The retention of the peak is governed by eqn (1) and (3) and as a very polar substance like a salt is negatively adsorbed at a non-polar adsorbent like ODS 2 the observed retention volume Y is smaller than V,, [fig.I@)]. Moreover if the adsorbent has a surface charge caused by ionization of residual silanol groups ion exclusion may occur. According to Berendsen,2 the effect can be very large (table 3). Thus our criticism of the calculations of Scott and Simpson is twofold (i) their estimates of V, obtained from the retention volume of the peak maximum of NaCl samples are probably low; (ii) the corrected retention volume of the peak maximum of moderator samples does not yield the adsorption isotherm but its derivative with respect to the moderator concentration (if the injected amounts are so low that they give rise to minor disturbances of the moderator concentration).TABLE3.-POROSITY OF TWO REVERSE-PHASE PACKINGS I AND 11 DETERMINED BY WEIGHT MEASUREMENTS (E,) AND FROM THE ELUTION VOLUMES OF SAMPLES OF SALT SOLUTIONS (EKB~ AND &K1) Ew &KI * I EUI IU 0.72 0.46-0.66 I1 0.72 0.42-0.72 0.42-0.66 I is a home-made octadecyl silica surface coverage 3.04 pmol m-2. I1 is Merck RP-18 octadecyl silica. E~~~ was calculated from the retention volume of the peak maxima obtained by injecting various amounts of KBr ranging from 1 mm3 of a mol dm-3 solution to 15 mm3of a 5 mol dm-3 solution. Eluent water. EK~was determined by injecting 10 mm3 of KI solutions of concentrations ranging from mol dm-3 to 1 mol dm-3. Eluent water. e/KIwas determined with methanol as the eluent. D. de Vault J.Am. Chem. SOC.,1940 62 1583. G. E. Berendsen Ph.D. Thesis (Technical University Delft 1980). Dr. G. B. Cox [DuPunt Cu. (UK)Ltd. Stevenage] said The void-volume results shown in tables 2-10 of the paper by Scott and Simpson have values ranging from 41 to 49% of the total column volume. Most estimates of void volume in relation to total column volume range between 70 and 85%. The measured porosity for RP18 for example is 72%. The discrepancy between the observed and expected values may be explained by an ion-exclusion mechanism since the void-volume measurements were made by intro- duction of a small amount of sodium chloride into the aqueous methanol mobile GENERAL DISCUSSION phase. Ion exclusion is a phenomenon well-known in the field of aqueous size-exclu- sion chromatography and is usually countered by use of a salt added to the mobile phase to increase the ionic strength.This is demonstrated by the work of Berendsen’ where an injection of 100 pg potassium iodide gave a porosity of ca. 49% without added salt but approached 70% when sodium bromide was added to the mobile phase. The errors in measurement of void volume are obviously of vital importance to the accuracy with which thermodynamic parameters may be obtained by chromatographic techniques. It is clear that the method used for measurement of V must be very carefully chosen and verified prior to calculation. G. Berendsen Ph.D. Thesis (Technical University Delft 1980). Prof. J. H. Knox (Edinburgh University) said (a) MEASUREMENTS OF DEAD VOLUME V,.Following the comment by Dr. Cox I would like to support the view that a dilute sample of NaCl eluted by aqueous mixtures containing no electrolyte would be com- pletely or almost completely excluded from the pores of a reversed-phase material such as Partisil-ODS 2 and so would not give V,. The reason for exclusion is the following (for a fuller explanation see paper by Knox and Kaliszan) ODs-bonded phases exhibit a negative zeta potential and apparently contain fixed negative charges at the internal surface of the material. These must be accompanied within the pores by an equal concentration of mobile positively charged ions-probably Na+. In the ab- sence of an external electrolyte trace quantities of anions such as Cl- will be unable to enter the pores of the particles and although Na+ ions which may accompany the C1- ions can exchange freely a small sample of NaCl will appear to migrate at the same speed as the Cl- ions.It will thus emerge in a volume equal to the volume of the mobile zone outside the particles. Normally this occupies ca. 42% of the volume of the packed tube in this case 1.75 cm3. Allowing for some extra-column dead volume this is fairly close to the observed values of 1.7-2.0cm3. For a column packed with an ODS loaded silica gel the volume of eluent in the column would be expected to be ca. 70% of the tube volume in this case 2.9 cm3. As has been pointed out in my joint comment with Dr. Kovats the isotopic method is the only method which correctly gives V,.In general (as shown in the paper by Knox and Kaliszan) with a mixed eluent V is given by the equation Vm = qAVA* + qBvB* + * -* where qA,pB,etc. are the volume fractions of A B etc.in the eluent and V,* VB*,etc. are the retention volumes of radio-labelled A B etc. This equation assumed only that the partial molar volumes of A B etc. are independent of composition and of adsorption. (b) DETERMINATION OF ISOTHERMS While I agree with the derivation of the eqn (1)-(8) and in particular with eqn (4) and (71 which essentially express the Langmuir isotherm I do not believe that the experimental method used provides a measure of V’ the net retention volume of the moderator. In terms of the adsorption isotherm (ix.the plot of C,against C,) the value of K given by eqn (3) represents the gradient of the chord of the isotherm drawn through the origin.Experiments using the pulse-plateau method (or steppulse method as described for example by Rybinski Albrecht and Findenegg) provide information on the gradient of the isotherm. Thus what has been measured is not in fact Y’ as required by eqn (4) but rather V” given by V”= qdC,/dC = vg(g + NSCm/M)2 174 GENERAL DISCUSSION from which it is readily deduced that a plot of (V’’)-* against C should be linear. The value of g is then no longer related by the simple relationships (5) and (6) to the gradient and intercept of the plots. While the linearity of the plots in fig. 1-3 and of fig. 5 is impressi\.e this must regrettably be fortuitous in view of the two errors made in the interpretation of the experimental data.Alternatively a different isotherm may be involved. Prof. J. H. Purnell (University College of Swansea) said I would like to make one observation and ask one question. First the column dead volumes recorded in the tables appear very small indeed for the column dimensions given. Further they seem to vary within a given set to rather more than the specified accuracy of flow measurement with rather spectacular differences for n-butanol + water mixtures. Would Drs. Scott and Simpson care to comment on these observations? One notes also that in fig. 4 a monolayer line is drawn which is presumably meant to be common to all the alkanols. Since the ordinate is in g this appears to mean that the alkanol molecules are not disposed vertically since then the common monolayer line would be at constant mol cmW3.The realistic alternative is a horizon- tal orientation in which case as the alkyl chain increases to match the results quoted each adsorbate molecule covers an increasing number of sites. Have they taken any account of this in their interpretation? Dr. P. J. Schoenmakers (Laboratoryfor Analytical Chemistry Delft) said (1) From the experimental data on the sorption behaviour of n-alcohols (tables 2-5) a Langmuir type adsorption isotherm for monolayer adsorption is concluded. However no data are taken above concentrations of 0.02 g cme3 of n-alcohols in water. The discussion in the experimental section suggests that data points at higher concentrations do not follow the same behaviour.Therefore fig. 4 seems to be a considerable and highly optimistic extrapolation. It seems a dubious practice to derive conclusions from such a limited part of the iso- therm. The suggested complete coverage is never approached in the experiments. (2) In the discussion following table 12on the retention behaviour of homologous series it is stated that the interactions between the functional group and the stationary phase will be “ largely dispersive in nature ”. It is suggested that there is a direct rela- tion between the dispersion characteristics of the functional group and the intercept from eqn (9). The authors state that the dispersive interactions between the hydro- carbon chains of the solute molecules and the stationary phase is proved to be similar because of the equal values of the slope in eqn (9).Both statements are incorrect. The question whether eqn (9) is obeyed as well as the value of the parameters is for RPLC systems mainly determined by the mobile phase. Hence the intercept A should rather be related to polar than to dispersive interactions and the equality of the B values indicates equal hydrophobicity of the hydrocarbon chains in the different molecules. Finally it was remarked by Dr. Scott that the linearity of the curves in fig. 5 indi-cates that the correct value for the dead volume of the system had been applied. However the absolute values for the distribution coefficient are so large that there will be no influence of the V value upon the curvature in this case.Dr. W. E. Hammers (Laboratory for Analytical Chemistry Utrecht) said The rather low effective ODs-2 adsorbent surface area has been ascribed to blocking of the micropore regions of the starting silica. However in addition to that cause it may be questioned whether a close monolayer of organic modifier can be formed in this case. GENERAL DISCUSSION We applied TMS silicas at maximum coverage of TMS groups in g.s.c. and 1.s.c. columns the latter with n-hexane as eluent. The logarithm of the net retention vo- lumes of nionosubstituted benzenes could be described very well by means of the So values of the adsorption model by Snyder. This result points to polar interaction forces due to residual silanol groups and/ or force fields of the silica beneath the TMS groups.The same may apply to ODs-2. Therefore it cannot be ruled out that water molecules block out part of the ODs-2 layer preventing the complete coverage of organic modifier in aqueous solutions. Dr. R. P. W. Scott (Perkin-Elmer Inc. Norwalk Connecticut) and Dr. C.F. Simpson (Chelsea College London) said We have considered the comments made on our paper with interest but before answering the individual points raised it might be use- ful to summarise the rationale of the paper. (1) We assumed that a solvent is adsorbed on the surface of a reversed-phase material according to a Langmuir adsorption isotherm and if this is so then we could calculate the exposed area at any given concentration from a knowledge of the distri- bution coefficient.(2) We considered that if a solute (which in these experiments is the same as the solvent) was retained on a column that was partially covered according to the Lang- rnuir adsorption isotherm the retention volume would be proportional to the product of the distribution coefficient of the solvent between the exposed area of the reversed phase and water. (3) By simple algebra we could relate the corrected retention volume to the con- centration of the solvent in the mobile phase and predict a particular reciprocal rela- tionship. (4) From this relationship employing the slope and intercept of the resulting linear curve we could calculate the distribution coefficient of the solvent and the effective chromatographic surface area in a given column.(5) Although the proven reciprocal relationship confirmed our assumptions per se we could further validate our theory by demonstrating that Martin’s equation held and the plot of the log of the distribution coefficient against carbon number for a homologous series of solvents would be a straight line. (6) Finally if such a straight line was produced the lines obtained for different homologous series should be parallel but with different intercepts and this was also demonstrated. To reply specifically to Dr. Cox and Prof. Knox We measured the required cor- rected retention volumes by taking them to be the difference between the measured retention volume and the dead volume obtained using salt solution as the dead-volume marker.These data produced the linear relationships given in our paper and sup-ported entirely our original theoretical assumption. However employing values for the dead volume obtained from either the retention volume of D,O (2.53 cm3) or by weighing the water content of a column (2.61 cm3) pro- duced an obvious curve in the graphs relating l/Vi against solvent concentration which if force fitted to a linear function provided a slope and intercept giving a value of the distribution coefficient for methanol having a 12% error relative to the curve presented for the alkanols. Various procedures have been suggested for measuring the dead volume and recently we have measured the “ dead volume ” of various ODs-2 columns using a variety of methods including those suggested.The results obtained are given below in table 4. GENERAL DISCUSSION TABLE 4.-DEAD VOLUMES OF VARIOUS ODs-2 COLUMNS IN PURE WATER column marker vm 1 (original) 2 NaCl 0.1 %w/v K2Cr207 2.05 2.39 2 NaN02 1.97 2 3 gravimetrically D20 2.61 2.53 3 3 NaCl 0.1 %w/v NaClO.1 mol 1.94 dm-3 in 1% ionic solvent 2.16 3 NaClO.1 mol dmV3in 5% ionic solvent 2.18 From these data it would appear that one can get a range of" dead volumes " to choose from so that it is necessary to define the dead volume that one requires to know. The dead volume in which we are interested in this work is the chromatographic dead volume and that is the volume which when subtracted from the total retention volume provides the corrected solvent retention volume which reflects the true reten- tion characteristics of the solvent.Such a volume may or may not have anything to do with the loss in weight from a column on evaporating the mobile phase from it or conversely the retention volume of an isotope of a component of the mobile phase. The values for the dead volume that we obtained using a salt solution provided the linear curves that were predicted by the theory and the linear log K against carbon number according to the Martin equation. Thus we maintain that the use of sodium chloride at the 0.1% level gives a true value for the chromatographic dead volume. Therefore before our results can be gainsaid an alternative theory must be put forward to account for the relationships we have demonstrated.Prof. Knox suggests that our results may be fortuitous. This will mean that the results obtained from over 150 experiments (each measurement in triplicate) are all fortuitous together with the nine linear curves relating the reciprocal of the corrected retention volume with mobile phase composition and three linear curves relating log K against carbon number for three homologous series and the parallel nature of these curves. The likelihood of these results being all fortuitous we leave to the judgement of the reader. With regard to Prof. Knox's second point regarding the validity of eqn (3) it must be pointed out that this equation gives the eflectiue distribution at a specific solvent concentration. It does not give the absolute distribution coefficient of the solvent between water and the reversed phase-and this is the ultimate value we are interested in.The latter part of this second point we feel is covered by our remarks about the measurement of dead volume. In reply to Dr. Schoenmakers' comments it is true that we do not make measure- ments above solvent levels of 2% but in all cases with the C3 and C4 solvents each homologous series has been examined over a range of at least 70% surface coverage and for the C,compounds ca. 60% coverage. Only for methanol does the range of concentrations examined account for ca. 30% coverage. Therefore the GENERAL DISCUSSION curves given in fig. 4 of our paper are valid as the curve for methanol can rationally be compared with those of the higher alcohols; hence the extrapolation for methanol is acceptable.With regard to Dr. Schoenmakers’ second point about the dispersive interactions with the functional groups we agree that there can be polar interactions involved (as stated in the paper) but these will be restricted to the residual silanols on the surface of the reversed phase. However we cannot agree with the last two points regarding the nature of reten- tion because we consider that this is due to dispersive interactions between the hydro- carbon chains on the stationary phase and those in the various solvents. We cannot therefore accept the concept of water repelling the solvent molecules on to the station- ary phase as molecular repulsion between any molecules could only occur when they are within the van der Wads radii of the species involved.Dr. Hammers comments that the low chromatographic dead volume using sodium chloride could be due to obstruction of the pores by the water and we agree that this may be so. However we doubt this explanation because subsequent experiments have shown that the dead volume measured in pure water and 75% methanol + 25% water using sodium chloride (0.1 mol ~lm’~) as the marker gave dead volumes of 1.94 and 1.99cm3 respectively on an ODs-2 column (column 3 in table 4 of this comment). It would be expected that in the latter mobile phase any “ blocking ” of the pore structure by water would not be present. To summarise we have found certain experimental relationships which were pre- dicted accurately on a rational theoretical basis.We are confident that the experi- mental data presented in the paper are precise. We would be interested to consider any alternative theory which predicts the same relationships that we have established employing the data we have presented. Prof. J. H. Knox (Edinburgh University) and Prof. E. sz. Kovits (EPFL-Ecublens Lausanne) said In adsorption/liquid chromatography the retention volume of a marked substance A * in the non-marked substance used as eluent is equal to the dead volume of the column if following conditions are satisfied (i) The physical properties of marked and non-marked substances are exactly the same with the exception of one allowing for the detection of A* in A at minute concentrations.(ii) The molar volume of the substance A (or A *) is the same throughout the column i.e. also in the adsorbed state. These conditions are certainly met at the proximity of low-energy surfaces such as used in reversed-phase chromatography and Karger showed that by this technique dead volumes are easily determined.’ Regarding the question of the determination of the dead volumes in binary eluants composed of solvents A and B our two research (Edinburgh and Lausanne) groups arrived independently at the same conclusions. Let us suppose that the same conditions are valid as in the case of the pure eluent. If A is preferentially adsorbed at the solid surface B must be negatively adsorbed therefore the retention volume of A * VR(A *) is higher and that of B * VR(B *) is smaller than the dead volume of the column.There is a simple relation between these quantities (see Symposium paper by Knox and Kaliszan) where qAand tpB are the volume fractions of A and B respectively7 (J. H. Knox and C t Theoretically V = C (pIVR(I*)for a C-component mixture. 1 GENERAL DISCUSSION Kaliszhn; I;. Riedo and E. sz. Kovhts). This relationship has been verified in a large experimental domain and it has been shown that the precision of' the determination of the dead volume is very good if qA or qB are not too low (0.03 < a < 0.97) (J. H. Knox and Kaliszan; Ha -Ngoc Le and E. sz. Kovhts). Extensive theoretical and experimental material will be published in the near future. R. M.McCormick and B.L. Karger Anal. Chem. 1980 52 2249. Dr. 2.Elkoshi (Hebrew University Jerusalem) said This remark is related to the procedure of calculating the effective areas of moderator molecules. The calculation assumes equal probabilities for each of the three possible axial positions for each molecule. Such a procedure might lead to large errors. For instance suppose that for n-butanol position 1 (table 1 of the paper by Scott and Simpson) prevails. The calculated mean area would then be ca. 30% of the real effective area and the error is as large as that. This error will diminish for spherically symmetrical molecules. For such mole- cules the mean effective area is not far from the effective areas calculated for each position. Nevertheless even if the molecule is not spherically symmetrical there is some- times a way to decide which position prevails.For instance it was found that' [AGO (toluene) -AGO (benzene)] = + [AGO (xylene) -AGO (benzene)] = -5 [AGO( mesitylene) -AGO (benzene)] where AGo(x) is the standard free-energy change for the transfer of molecule x from the mobile to the stationary phase in reverse-phase chromatography (the mobile phase was a 50/50 water -+ methanol mix- ture and the stationary phase was some alkyl-bonded phase). Such behaviour is expected only if the benzene molecule and its alkyl derivatives are adsorbed in a symmetrical way with respect to the stationary-phase surface i.e. such that the molecular plane is parallel to the stationary-phase surface. This of course might indicate which position has to be preferred for calculation of the effective surface area in this specific example.C. H. Lochmuller and D. R. Wilder f. Chromatogr. Sci. 1979 17 574. Dr. P. F. Tiley (Bath University) said Now that we all have computers on our desk-tops and regression routines in our pocket calculators I would like to issue a warning about the statistic called " correlation coefficient " or "index of determina- tion ". Useful as this statistic may be in the analysis of cause and effect in relatively unstructured situations (e.g. smoking and lung cancer) its utility is much less in the physical sciences in the testing of precisely-formulated hypothetical relationships. For example if data on the vapour pressure of a pure liquid are tested against a linear (In p 1/T) relation correlation coefficients in excess of 0.999 are obtained and yet the approximate nature of this relationship is well-known.Examination of a table of residuals is generally far more revealing together with a calculation of a standard deviation of the fit. This can then be followed if necessary by a significance test such as the F-test. And when it comes to non-linear regression the generation of sets of pseudo-experimental data as described under data set (0) in my paper can give a reasonable idea of the precision to be expected in the best estimates of the adjustable parameters. Prof. J. H. Purnell (University College of Swansea) said In response to Dr. Tiley's statement regarding linearity or otherwise of (n',,~) plots for binary solvents and an infinitely dilute third component is it not also true to say that no approach GENERAL DISCUSSION based on conventional theory has yet satisfactorily dealt with a case where significant curvature is seen? Dr.P. F. Tiley (Bath University) said In reply to Prof. Purnell’s informally posed question as to whether any existing theory can account for the g.1.c. results on mixed- solvent columns the answer on a trivial level is that the quadratic (In KR p) relation nearly always gives a better fit than the linear (KR,9)relation. At a deeper level if the question is whether any theory can reliably predict KR values in the mixed solvent from measured KR values on the pure solvents for all possible solutes and solvents the answer is certainly no.Prediction of vapour-liquid data for ternary (1-2-3) systems from measurements on the associated binaries (1-2 1-3 2-3) has met with some success in the chemical engineering field. But in this particular g.1.c. problem we are trying to predict the behaviour of the ternary system (even though one com- ponent is always at infinite dilution) from a knowledge of only two of the binaries (1-2 and 1-3). Thermodynamically this is not possible. However if we introduce extrathermodynamic concepts such as solubility-parameter theory then as I have shown elsewhere,l a value of 3/23 can be estimated from values of KR(~) and &(3) and this value of xZ3can be used to calculate KR in the mixed solvent. This method is reasonably successful (within 5%) for alkane solutes in a number of solvent systems but is unreliable for solutes where polar solute-solvent interactions may occur.The disadvantage of the mixed-solvent linear approximation is that it seems diffi- cult to predict when it will be a poor approximation and a number of the sets of data I have cited show examples of deviations in excess of 20%. One particular case arises from the work of Vernier et al. For the solvent system benzonitrile + dimethyl-sulphoxide benzene (within 5%) and isoprene (within 2%) give linear relations but in the same solvent system hexane and heptane show deviations from linearity of 50-60%! P.F. Tiley J. Chrornaiogr. 1979 179,247. Prof. R. J. Laub (Ohio State University) (communicated) Despite the controversy surrounding theoretical models pertaining to non-electrolyte solutions,l there are several advantages2 to the use of mechanical mixtures of pure-solvent packings in analytical g.~.~*~ Stationary phases comprising intimately blended solvents have not however been utilized commonly with op m- tubular (capillary) column systems presumably because of the supposed practical difficulties associated with fabrication of columns even of pure liquids (let alone blends).Recent studies in our laboratory have in contrast provided illustration of the benefits to be derived from the use of mixed phases with such columns these including inter aka control of the selectivity of the (binary) stationary liquid reduction of the partial pressure (“ bleed ”) of each of the mixture components in approximate accordance with Raoult’s law and preser- vation for the most part of the chromatographic “ efficiency ” (kinetic band-broaden- ing characteristics) of the diluent liq~id.~,~ Fig.2 shows for example the separations of seven polycyclic aromatic hydro- carbons obtained with open-tubular columns containing blends of a liquid crystal (poor efficiency; high selectivity) with a silicone gum (high efficiency; poor selecti- vity) of 0% (w/w) 2% 5% 10% and 20% respectively of the former in the latter.7 Of particular interest is the variation of retentions (here in terms of capacity factors k’)with column composition illustration of which is provided in fig. 3 for ten (as-yet unidentified) nanogram-level impurities surrounding phenanthrene (no.1) and anthra- cene (no. 2) solutes. The question obviously arises as to whether the mesogen is dissolved or dispersed in the silicone gum matrix even though the stationary phases were here deposited in each GENERAL DISCUSSION lal lb) 5,7 34 12 I 7 2 34 5 67 .I In1 inj 1 1 L I -0481 6 04 8121 t ime/min ld) id 2 12 b I 34 5 6 7 0 4 8 12 16 20 24 0 4 8 12 16 18 20 24 timelmin FIG.2-Chromatograms ' of phenanthrene (l) anthracene (2) fluoranthene (3) pyrene (4) tri-phenylene (3,benzo[a]anthracene (6),and chrysene (7) with stationary phases comprising respec- tively pure SE-52 silicone gum (a); 2% (w/w) NN'-bis(p-butoxybenzylidene)-cr,cr'-bis-~-toluidine (BBBT m.p.159°C; 188"-+nematic+303" isotropic) + 9So/ SE-52 (b); 5% BBBT + 95% SE-52 (c); 10% BBBT + 90% SE-52 (d); and 20% BBBT + 80% SE-52 (e). Columns 20 m by 0.25 mm i.d. glass; temperature 220 "Cisothermal. of the columns from common solution (methylene chloride solvent). In the former instance rationalization of the experimental data in terms of conventional treatments of solutions is clearly precluded since at the present time mixtures of even the sim- plest of species other than n-alkanes cannot be dealt with in other than semi-empirical terms. If on the other hand dispersion obtains the retention data are predicted to GENERAL DISCUSSION 1 . 4 3) L I 4 2) 1 ‘ 1) I I I 0.5 % (w/w)BBBT FIG.3-Dependence of capacity factors (k’) of ten impurities (nos.l’-lO’) surrounding phen- anthrene (no. 1) and anthracene (no. 2) on stationary-phase composition. Columns and con-ditions as in fig. 2. vary linearly with column composition since the situation then conforms precisely to that wherein solvent compositions exhibit macroscopic immiscibility.8 The matter is now under further study with a variety of mixtures comprising in part compounds which exhibit nematic and cholesteric phase transitions since the easily-detected variation of the unique properties of solutions of these substances provides unequivo- cal information regarding their molecular state of aggregation in the presence of diluents. Mesogens can hence be regarded in this context as solvent probes. In any event the approximation of linear variation of retentions with liquid-phase composition is borne out for the systems considered here which promises considerable utility of the mixed-solvent approach in analytical separations with open-tubular g.c.column systems. R. J. Laub and C. A. Wellington Study of Complexation Phenomena by Gas-Liquid Chromato- graphy in Molecular Association ed. R. Foster (Academic Press London 1979) vol. 2 chap. 3. R. J. Laub and J. H. Purnell J. Chromatogr. 1975 112 71. C-F. Chien M. M. Kopecni and R. J. Laub Anal. Chem. 1980 52 1402. C-F. Chien M. M. Kopecni and R. J. Laub Anal. Chem. 1980 52 1407. R. J. Laub and W. L. Roberts Use of Mixed Phases for Enhanced Gas-Chromatographic Separa- tion of Polycyclic Aromatic Hydrocarbons Preliminary Studies with Liquid Crystals in Poly-nuclear Aromatic Hydrocarbons Chemistry and Biological Efects ed.A. Bjorseth and A. J. Dennis (Battelle Press Columbus Ohio 1980) vol. IV p. 25. R. J. Laub W. L. Roberts and C. A. Smith J. High Resolution Chromatogr. Chromatogr. Commun. 1980 3 355. R. J. Laub W. L. Roberts and C. A. Smith Use of Mixed Phases for Enhanced Gas-Chromafo- graphic Separation of Polycyclic Aromatic Hydrocarbons. II. Prediction of Retentions with Open-Tubular Columns of High Eficiency with Liquid-Crystal Solvents in Polynuclear Aromatic Hydrocarbons Chemistry and Biological Efects ed. M. W. Cooke and A. J. Dennis (Battelle Press Columbus Ohio 1980) vol. V in press. R. J. Laub J. H. Purnell and D. M. Summers J. Chem. Soc. Faraday Trans.I 1980,76 362. GENERAL DISCUSSION Dr. Z. Elkoshi (Hebrew Uniuersity Jerusalem) said Prof. Letcher has used the mole-fraction scale for defining the activity coefficient. It is more advantageous to use the molarity scale for defining standard thermodynamic quantities of transfer as was suggested by Ben-Naim.l For instance if the standard chemical potential of a solute A is defined using the molarity scale then (1) it is the simplest and least ambiguous quantity; (2) it is the quantity that directly probes the difference in the solvation properties of the two solvents with respect to the solute; (3) it can be used without any change of notation in any solution not necessarily a dilute one and including even pure A; (4) by straightforward thermodynamic manipulation one obtains the entropy the enthalpy volume changes etc.for the same process. A. Ben-Naim J. Phys. Chem. 1978,82,792. Dr J. R. Conder (Uniuersity CoZZege of Swansea) said In determining activity coefficients one often encounters complications from adsorption effects which contri- bute to retention according to the equation where the K are the solute distribution coefficients between the gas and liquid (L) gas-liquid interface (I) and solid-support surface (S) ; V denotes volume and A area. The two adsorption terms can be separated from the liquid partitioning term by varying the liquid loading and plotting VN/VL against l/VL. To reduce the adsorption con- tribution and improve the accuracy of measurement of the activity coefficient silan- ised supports have often been advocated but there has been much debate about the size of the resulting adsorption contribution KIAI.This depends on the nature of the distribution of liquid on the support which controls the area AI of the gas-liquid inter- face. Mrs. N. Ibrahim at the university College of Swansea has recently obtained some results which help to throw light on this distribution. The retention of acetone on a column of squalane on silanised Chromosorb P has been measured for various 5.O 10.0 15.0 loading (%) FIG.4.-Plot of total adsorption contribution to retention of acetone against liquid loading of squa- lane on silanised Chromosorb Pat 58.8 "C. r is the surface excess concentration of solute at the gas- liquid interface qs the solute concentration on the support surface and c the concentration of solute in the gas phase.GENERAL DISCUSSION liquid loadings at 58.8 "C. When the data are processed' to plot VN/VLagainst l/VL for a constant gas-phase mole fraction of 1.28 x the plot of the adsorption con- tribution shown in fig. 4 is obtained. The unusual feature of this plot is the sharp rise and peak at 7.7% loading. We believe that this is due to the transition from a non-wetting droplet distribution of liquid at low loadings to a coalesced film at higher loadings. A simple model shows that coalescence is to be associated with a sharp rise in Anpreceding the peak and not as might otherwise be expected a fall in AI. The adsorption contribution thus depends on liquid loading but is far from negligible for the system studied on a silanised support.Further work is in progress. J. R. Conder J. Chi-omotogr..,1969 39 273. Prof. V. Mathot (University of Brussels) said Infinite-dilution activity coefficients are very useful to solution thermodynamicists in so far as activity coefficients are one-parameter functions of mole fractions i.e. the excess functions are symmetric para- bolic functions of mole fractions. In most case of interest for g.1.c. (volatile solute in long-chain non-volatile solvent) these excess functions are asymmetrical which implies more than one parameter in the activity coefficients. Does then the determination of activity coefficients at j3zite concentration not involve more work of a less accurate nature? Dr.J. R. Conder (University College of Swansea) said There are several gas- chromatographic methods of measuring activity coefficients in solution at finite solute concentrations. The main ones are based on generalising the infinite-dilution reten- tion equation VN = VLk; to the finite-concentration form' where qLand c are the concentrations of solute in liquid and gas phases yois the mole fraction of solute in the gas phase at the column outlet j is the pressure gradient cor- rection factor and a is a parameter which can usually be taken as 1. The activity coefficients can be calculated once the partition isotherm qL(c)has been obtained by measuring VN at a series of values of solute concentration. This concentration how- ever has to remain constant along the column for dqJdc to have a definite value and the four main chromatographic methods differ in the way this constant concentration is achieved.The method of Frontal Analysis by Characteristic Point (FACP) depends upon replacing the pure carrier-gas stream flowing into the column by a stream of mixed carrier and solute vapour. With the concentration change in this positive direction a gas-liquid isotherm (for which normally d2qJdc2 > 0) gives a chromatogram in which the boundary breaks through over a period of time according to eqn (1). A point or the boundary has passed through the column with a characteristic concentrz- tion and has a retention given by eqn (1). Provided certain experimental con-dition~'-~ are satisfied qL(c)can therefore be obtained by integration.In the Frontal '4nalysis (FA) method the change in influent concentration is made in the reverse direction leading to a virtually instantaneous breakthrough of the boundary at the column outlet. Here qL(c)is again obtained by integration but only for the particular solute concentration plateau used. GENERAL DISCUSSION Elution by Characteristic Point (ECP) involves a large elution peak which can be regarded as two frontal boundaries one of which is analysed as for FACP. Elution on a Plateau (EP) requires that the column is first equilibrated with a stream of mixed carrier and solute whose concentration is essentially constant along the column. On this plateau is then injected a small positive or negative peak of solute whose retention is given by eqn (1).Repetition at different plateau concentra- tions yields qL(c)after integration. The method is sometimes described4 as the “ step and pulse ” method but the term “ elution on a plateau ” is more descriptive since it is the plateau rather than a step which is characteristic of the method. A method using elution of an isotope on a platea~~.~ has advantages for niulticomponent systems. The chromatographic methods for finite concentration are capable of the same precision as their infinite-dilution counterpart ca. 0.53%. This compares satis- factorily with static methods particularly at the low end of the concentration range. They are also much faster than static methods and avoid the sampling problems of other techniques but are limited to maximum liquid-phase mole fractions of solute in the region of 0.6-0.95.3 J.R. Conder and J. H. Purnell Trans. Faraduy Soc. 1968 64 3100. J. R. Conder and J. H. Purnell Trans. Faraduy Soc. 1969 65 824 839. J. R. Conder and C. L. Young Physicocheniical Measurement by Gus Chromatography (John Wiley London 1979) chap. 9. P. Valentin and G. Guiochon J. Chromatogr. Sci. 1976 14 56. K. T. Koonce H. A. Deans and R. Kobayashi AIChE J. 1965 11 259. Prof. V. Mathot (University of Brussels) said The terms enthalpic or entropic ex-clusion instead of interaction or dimension exclusion used by Prof. Knox seem to me rather unfortunate as long the phenomena have not been studied as function of tem- perature. Such a study would add the guarantee of experimental thermodynamics to an otherwise very interesting but rather unwarranted interpretation.Prof. J. H. Knox (Edinburgh University) said I agree that we now need measure- ments of the temperature dependence of the degree of exclusion in the cases of small molecules excluded from silica gel by polar solvents and of ionic species excluded from particles by virtue of a hostile electric charge. I still think it is useful to draw the attention of chromatographers to the fact that exclusion can arise from enthalpic as well as entropic (or steric) effects and am personally convinced that the effects we have studied do in fact arise from enthalpic effects. Perhaps our claims are pre- mature. Dr. P. J. Schoenmakers (Laboratoryfor Analytical Cheniistry Delft> said In the experimental section the authors state that an exact estimate of the eluent volume in the column can be obtained from a weighted average of the retention volumes of radio-labelled eluent molecules.This experiment yields the total volume of eluent present in the column which is essentially the same as the volume measured by pyk- nometry. In this definition all the eluent present in the column is assumed to be part of the mobile phase i.e. adsorbed molecules are not considered to belong to the sta- tionary phase. The important question is whether this definition when applied to Prof. Knox’s eqn (9,will yield k’-values that are of fundamental significance. As long as there are many definitions of V in use it is very hard to interpret experimental data from the literature.According to the discussion of enthalpic exclusion due to the electric charge at the GENERAL DISCUSSION surface of the stationary phase the exclusion should drop to zero for high ionic strength eluents. The same effect can be obtained by simply injecting large quantities of sa1t.l If the ionic species are taken to be small inorganic molecules the limiting value turns out to be constant but generally smaller than the total eluent volume as described above. Would this limiting value be a more realistic estimate of the actual mobile phase volume? G. E. Berendsen P. J. Schoenmakers,L. de Galan Gy. Vigh Z. Varga-Puchony and J. InczCdy J. Liq. Chrornatogr. 1980 3 1669.Prof. J. H. Knox (Edinburgh Uniuersity) said The method proposed by us for determining V undoubtedly determines the volume of all molecules of the solvent species in the column whether positively or negatively adsorbed and it assumes that the partial molar volume is the same within the column packing as in the bulk eluent. This latter assumption may be slightly erroneous. Unfortunately it is difficult to define clearly the amount of each component adsorbed and to distinguish between an ad- sorbed molecule and one which is not adsorbed. It does not therefore seem to us to be useful to try to define V in terms of unadsorbed species. A definition such as ours has the great merit that a unique value for V is obtained whatever the eluent used. Regarding exclusion arising from charge it would be correct to say that the ex- cluding effect of an electrical potential difference will be reduced to zero in a solvent of infinite ionic strength.Unfortunately this does not mean that an ion eluted by such a solution will have a retention volume V, equal to V, because the ion may be positively or negatively adsorbed by the surface of the packing material (the internal surface). This effect can be seen in our fig. 5 and 6. Negative adsorption is parti- cularly likely to occur with small hydrophilic ions eluted from reversed-phase packings by aqueous/organic eluents. The organic component is adsorbed and the ion is par- tially excluded from this region so VRis slightly less than V,. This type of additional exclusion is demonstrated by our fig.3. I do not therefore think that VRfor a small ion eluted by a strong salt solution gives a good measure of V,. Dr. M. E. Van Kreveld (KonlShell Laboratorium Amsterdam) said A first remark relates to our determination of diffusion coefficients of polystyrene in pores (J. Chrorna-togr. 1978 149 71). Our values are not equal to those found by other authors not only as was suggested by Dr. Dawkins because we used silicas that differed from the ones used by others but probably mainly because we applied a different theoretical description of the mass-transfer process. Secondly it is rather difficult if not impossible from Dr. Davkins’ paper to derive an impression about the accuracy of the determined values. To serve this purpose it would be very useful if he had published an experimental chromato- gram.This can give an idea of the accuracy that can be achieved in this kind of ex- periment. But in addition one also needs the actual uncertainties of the experimental points to evaluate the experiments properly. The third point I want to put forward relates to formula (9). The third term on the right-hand side of this equation shows no velocity dependence whatsoever. Thus in my opinion the third term cannot be determined as such from the (H u) curve. Only the sum of this third term together with the first term can be determined from the cut-off of the H-axis when u = 0. One value of (aW/i@,,) for each sample can be cal- culated from this cut-off if the value of the first term is already known.So what is the meaning of calculating (Gw/nn) values at different speeds of the mobile phase as is presented in table 2? GENERAL DISCUSSION The next comment stems from the suggestion of Dr. Dawkins that an impression of the accuracy of the experiments could be gathered from the excellent repeatability of the experiments. Diffusion coefficients are derived from the width of a peak or what is theoretically much more justified from the second moment p2 of a peak. One has to be extremely careful because the greater part of the value of p2 is contributed by the wings of the peak. By cutting off the wings one is making a considerable sacrifice. However removing the wings of a peak is most useful if one has as sole objective increasing the repeatability.In its turn measuring the peak width at half-height is the most effective procedure to remove the contribution of the wings thus reversing that line of reason- ing very repeatable values of peak widths mean very inaccurate diffusion coefficients. Dr. J. V. Dawkins (Loughborough Uniuersity) said I agree with the comment made by Dr. Van Kreveld that the accuracy of the method for determining values of diffusion coefficients should be considered. The experimental chromatograms from which plate-height data are derived are observed to be reproducible in position and shape. The major assumption in the use of eqn (9) in our paper is that the experimental chromatogram corresponds to a Gaussian distribution function so that plate height may be calculated by the width at half-height method.Therefore errors will arise when chromatograms exhibit non-Gaussian tailing. Dr. Van Kreveld is correct in stating that a single value of [nw/M,,ITfor each sample should be calculated from a plot of H against u. This procedure assumes that the value of the eddy diffusion term in eqn (9) is known. Our evaluation of this eddy diffusion contribution follows from the experimental observation that a constant value of H for a non-permeating polystyrene over a range of u was close to the curve of H against u for to1uene.l However H for small molecules such as acetamide and toluene does change with u as shown in fig. 4 and 5 of our paper. Therefore the values of [A?w/&fn]r for each sample in table 2 are calculated with values of the eddy diffusion term estimated at u = 1.7 3.4 and 5.1 mm s-' from the curves of H against u for acetamide and toluene.J. V. Dawkins and G. Yeadon J. Chromatogr. 1980 188 333. Dr. M. E. Van Kreveld (KonlShell Laboratorium Amsterdam) said I have my doubts about the use of introducing the concept of an SWP (Square Well Potential) in the case of exclusion of solute molecules by solvent molecules absorbed on the wall of the pores. This SWP picture is commonly accepted as a rough model for intermolecu- lar potential energy with a long-range attractive force combined with the rigid-sphere behaviour at short distances. It serves often as a rough approximation of the well- known Lennard-Jones potential that is quite often a much better approximation for intermolecular potential energy.Rigid spheres do not behave as though they were in an SWP because they lack the long-range attraction. If one wants to calculate the distribution coefficient from a priori calculated partitions functions both in pores and bulk solution by statistical mechanics one has of course to use an intermolecular PO-tential-energy function. If one carries out this type of calculation it is not helpful to mix up the concepts of energy and entropy for both are needed to calculate the total free enthalpy. First the concept is not used in a proper way as compared with the generally accepted theory; secondly the author does not apply statistical mechanics. This causes confusion in two ways. It is probably much better here to leave out the con- cept of the SWP.GENERAL DISCUSSION Prof. J. H. Knox (Edinburgh Uniuersity) said While I agree completely with the main part of Dr. Van Kreveld’s comment I think it arises from a misunderstanding of our reference to the SWP. This was applied in our paper specifically to the exclusion of a polymer molecule regarded as a rigid sphere from the pores of a matrix such as silica gel it was not meant to apply to the exclusion of (small) “ solute molecules by solvent molecules adsorbed on the walls of the pores ”. In this case of course the comments of Dr. Van Kreveld apply. In the case of the rigid-sphere polymer mole- cule no attractive forces are involved the two sides of the SWP well go off to infinite potential energy and arise from the presence of the pore walls.They are separated by a distance which is 2r less than the pore diameter (where r is the radius of the spherical molecule). Dr. J. E. Newbery (Goldsmiths’ College London) said In fig. 2 of Prof. Sebille’s paper a plot of the mean bound ligand Fis made as a function of the SDS/HSA ratio. This graph shows an initial increase in binding followed by a steady decrease with a maximum at a ratio of ca. 3.8. With the HSA set at 0.4 g dm-3 this corresponds to 1.52 g dm-3 of SDS or 5.3 x mol dm-3. It is well-known’ that SDS acts as a denaturing agent for proteins enabling the coiled structure to unfold into a rod-like shape. The observed maximum may thus represent the attainment of some specific stage in the unfolding process but it seems worth considering whether the position is somehow related to the critical micelle con- centration (c.m.c.) of SDS.This is found2 in the vicinity of 8 x lom3 mol dm-3 for pure aquo systems and decreases with rise of ionic strength. Thus a value of 5.3 x in 0.067 mol dm-3 phosphate buffer would by no means be unexpected. Oakes reports3 that SDS will bind to bovine serum albumin and n.m.r. suggests that the subsequent proton environment is similar to that found in a micelle. For a coiled species using published values4 of the diffusion coefficient and sedimentation coefficient it is possible to estimate an approximate “ hard-sphere ” radius of 2.7 nm or a hydrated radius of 3.5 nm for an HSA particle. These are not so distinct from the micellar size that some correlation between the maximum binding point and the c.m.c.must be ruled out. A. G. Marshall Biophysical Chemistry (J. Wiley New York 1978). R. J. Williams J. N. Phillips and K. J. Mysels Trans. Favaday Soc. 1955 51 728. J. Oakes J. Chem. SOC.,Faraday Trans. 1 1974 70 2200. A. L. Lehninger Biochemistry (Worth Publishers 1975). Prof. B. Sebille (Universite‘ de Paris) said I thank Dr. Newbery for his comment. In fig. 2 the SDS/HSA ratio mentioned is the molar ratio. It means that the maxi- mum of warfarin binding occurs at an SDS concentration equal to 20 pmol dme3. Such a concentration is lower than the critical micelle concentration (c.m.c.) and its denaturing effect for HSA is probably weak. We have noticed by c.d.measurements only a small change of the residual ellip- ticity of HSA occurring between 250 and 300 nm for molar ratios SDS/HSA = 3-4. On the other hand in the presence of warfarin we noted an important increase in the c.d. signal at 315 nm (for molar ratio SDS/HSA = 3) greater than expected from the change of warfarin-HSA binding (measured by chromatography). We interpret this phenomenon as a conformational modification of the drug binding site in presence of low molar ratios of SDS. (B. Sebille N. Thuaud and J. P. Tillement unpublished results.) Prof. P. Gray (Leeds Uniuersity) said I should like to congratulate Dr. Wakeham on his brilliantly executed experiments. I might also highlight two contrasts be- GENERAL DISCUSSION ween his study and ours.We both use the chromatographic method i.e. Taylor dispersion to determine diffusivities but there is a difference in time-scale of 104-105 between his pulse widths or elution times in liquids and ours in dilute gases (from 5000 to 0.1 s) and a similar or larger factor of 106-107in the values of the diffusivities of the species as studied under the conditions of the two experiments. (Communicated) Believing we had mastered the history if not the science I was going to suggest that one should eventually drop the name “chromatographic method ” which arose naturally because the early work on the method for gases was done with chromatographic equipment and use “Taylor dispersion method ’’ in its place. I have since found that Taylor’s highly original studies’ in 1953 and 1954 are not the earliest analysis.In 1947 J. W. Westhaver2 gave a lucid analysis of the prob- lem of dispersion for different velocity profiles deriving the term &(uo2r02/D)for laminar flow. The dispersion of a narrow pulse of positive holes travelling down a potential gradient along a germanium rod has also been studied and has yielded3 values for their diffusion constant. A11 the above relate to dispersion which is not complicated by irreversible removal of unstable species at the walls and by the temporary adsorption and desorption at the walls that constitutes true chromatography. The theories of these combined effects are presented elsewhere. G. I. Taylor Proc. R. SOC.London Ser. A 1953 219 186; 223,446; 1954 225 473.J. W. Westhaver J. Rex Natl. Bur. Stand. U.S.A. 1947 38 169. J. R. Haynes and W. Shockley Phys. Rev. 1951 81 835. T. Boddington and A. A. Clifford in press. Prof. J. H. Knox (Edinburgh Uniuersity) said I should like to ask four questions in relation to the elegant experiments described by Dr. Wakeham. (a)Was the absence of adsorption established? The Taylor-Golay equation shows that 0is strongly dependent upon the degree of retention k’. (b) How accurate is the Taylor equation when the surface is rough? (c) How does coiling of the tube affect the accuracy of the equation? (d)Was the experiment calibrated against a system with an accurately known diffu- sion coefficient? Dr. W.A. Wakeham (Imperial College London) said (a)The first point raised by Prof.Knox may be answered by reference to fig. 5 and eqn (6) of the original paper. If adsorption were to occur during the diffusion mea- surements both the first and second moments of the eluted distribution would be affected in a manner not accounted for in the derivation of eqn (6). In that case the diffusion coefficient derived from experimental measurements of the two moments through eqn (6) would not be a true diffusion coefficient and would depend for example on the average velocity of the carrier liquid. Fig. 5 indicates that this is not the case for these measurements so that the possible contribution of adsorption can be discounted. (b)The surface roughness of the diffusion tube on a microscopic scale has a negli- gible effect upon the Taylor equation describing the dispersion process.This is because under the conditions of laminar flow employed the effect of the roughness is only to perturb the velocity profile near to the wall where the velocity of the fluid is in any event small. For this reason the effect is that of a second-order perturbation. The effects caused by non-uniformities in the diffusion tube bore on a macroscopic scale have been examined by Alizadeh et al. in ref. (12) of the paper and have been GENERAL DISCUSSION shown to be rendered negligible by proper design. (c) Coiling of the diffusion tube can have a profound effect upon the diffusion pro- cess and hence upon the accuracy of the Taylor equation. The effect may be such as to change the apparent diffusion coefficient by an order of magnitude.The magni- tude of the effect is characterized by the Dean number for the flow which involves the Reynolds number for the flow and the ratio of the tube internal radius to the coil radius. There have been a number of numerical solutions of the equations describing the dispersion process in coiled tubes. All of these studies indicate that at sufficiently small Dean numbers the effect of the coiling of the diffusion tube becomes negligible. Quantitative limits for the Dean number for accurate diffusion coefficient measure- ments have been given by Alizadeh et al. and the present measurements have all been conducted under conditions where the coiling of the tube contributes (0.1% to the observed dispersion.If the effects of coiling are significant the diffusion coefficient observed depends strongly on the average velocity used for its measurements as has been shown in ref. (12) and (20) of the paper. No such effects are visible in the re- sults of the present work shown in fig. 5. (d) Inasmuch as the diffusion-coefficient measurements made with this technique are absolute it is not necessary to calibrate the instrument against a standard. Never-theless to establish the veracity of the experimental results several measurements have been performed which may be directly compared with results obtained by other methods. On every occasion for systems as widely different as sodium chloride in aqueous solution and mixtures of the normal alkanes the agreement has been far within the mutual uncertainty of the various results.Prof. J. H. Knox (Edinburgh University) (communicated) In reply to my first question Dr. Wakeham states that if adsorption of solute onto the walls of the tube occurred his eqn (6) would not correctly give D1,. With this I agree and this was the reason for my question. He then states that if adsorption occurred the value of DI2 would depend upon flow velocity. This is incorrect and accordingly flow inde- pendence of D, as determined by eqn (6) cannot be used to discount adsorption. Eqn (6) may be approximated when ojd/fid is small by eqn (A) Golay' showed that if the solute was adsorbed at the walls of the tube and if the ad- sorption/desorption process was sufficiently fast a condition analogous to eqn (5) the simplified eqn (A) was modified to (B) ao2ti (1 + 6K + llK2) D --2-24 oid2 (I $-K) where K = (<-$/to and where cis the elution time (first moment) of an unretained solute moving at a speed u, while ti,is the elution time of the retained solute.Since the function of K ranges from unity (K=0) to 11 (Klarge) it is essential that either K is known or preferably it is established by experiment to be zero. M. J. E. Golay Gas Chromatography 1958 ed. D. H. Desty (Butterworth Scientific Publications London 1959) p. 36. Dr. W.A. Wakeham (Imperial College London) (communicated) Golay's analysis which leads to eqn (B) given by Prof. Knox is founded on the supposition that the rates of adsorption and desorption are rapid compared with the dispersion process.GENERAL DISCUSSION In the gas phase this may be a reasonable supposition because the dispersion process is dominated by molecular diffusion which is slow. In the liquid phase the process of dispersion is not dominated by molecular diffusion but by the very much faster Taylor dispersion mechanism. I can see no certainty that the rates of adsorption and desorption are much more rapid than this dispersion process-which would imply that Golay's analysis is not appropriate. In the case when the rates of adsorption and desorption are relatively slow they surely most influence the dispersion process. If Golay's analysis were accepted as a basis for discussion then it also provides a further test for freedom from adsorption effects which I mentioned at the meeting.This is because if the third central moment of the distribution resulting from his model is adopted it is found to be directly proportional (in first order) to the partition coefficient K introduced by Prof. Knox. Thus asymmetry of the eluted distribution would be a sure sign of adsorption. This was never detected in any experiments within their resolution. The result for the third moment has already been demon- strated for a packed chromatographic column by Kubin.' Finally a comparison of experimental results obtained by this method with those obtained by other techniques is tantamount to a determination of K. It has been found to be zero within experimental error for every system studied where a compari-son has been possible.M. Kubin Coll. Czech. Cham. Commun. 1965 30 1104. Prof. G. H. Findenegg (Ruhr University Bochum) said In connection with Dr. Wakeham's paper on diffusion-coefficient measurements in the liquid phase by the chromatographic method I should like to draw attention to the work by Prof. G. M. Schneider and his coworkers on the determination of binary diffusion coefficients D12 by supercritical fluid chromatography (s.f.c.).' In s.f.c. a compressed gas (component 1) at near-critical densities and temperatures above the critical temperature is used as the mobile phase. For several aromatic molecules (component 2) in C02or ethane Ol2was found to have values between and lo-' m2 s-'. Thus these values are about two or three orders of magnitude smaller than in gases at normal pressure and about two orders of magnitude larger than in the normal liquid range.I. Swaid and G. M. Schneider Ber. Bunsenges. Phys. Chem. 1979 83 969; U. van Wasen I. Swaid and G. M. Schneider Ber. Bunsenges. Phys. Chem. 1979 83 1130; see also U. van Wasen I. Swaid and G. M. Schneider Angew. Chem. I&. Ed. Engl. 1980 19 575. Prof. P. Gray (Leeds University) said Since our paper was submitted precision has been improved and the parallel measurements of diffusion in a nitrogen carrier have been made. At 294 K and 1 atm we have D(H,Ar)/cm2 s-l = 1.61 0.04 D(H,N2)/cm2s-l = 1.35 j-0.03. That is to say the method is capable of yielding precision similar to that (&2%) generally regarded as restricted to stable species.Of course the very best work on stable species can surpass this Dunlop claiming precision of &0.2%in H2 + N2and He + Ar systems. The chromatographic results have implications for discharge-flow kineticists. Our conditions are not untypical and they suggest that 10% corrections may need to be made to yield true gas-phase atom concentrations from total numbers of atoms in a discharge-flow tube. They also raise the question how are the atoms held on to the surface and at what sites. Clean and washed quartz must have adsorbed water as well as hydroxyl groups and oxygen atoms. GENERAL DISCUSSION Prof. R. J. Laub (Ohio State University) said It is amusing to speculate that in this instance a mass spectrometer would serve as a useful inlet system for the gas chromatograph.Prof. P. Gray (Leeds University) said The speculation is an interesting one since the ion-source of a mass spectrometer produces the kinds of species that offer the kinds of challenge we should like to take up. In principle the present method would make it possible not only to study various surfaces various temperatures other atoms of importance (e.g. N 0 Cl and so on) and maybe many of the species that can be generated by titration methods but it also opens the door to looking at excited states. Dr. 2. Elkoshi (Hebrew University Jerusalem) said Hydrogen atoms (or any other atoms) adsorbed on a chromatographic surface comprise a powerful device for a study of the atomic motion of the adsorbent on the surface. Such an information can be extracted from the temperature dependence of k’ using statistical thermo- dynamics.The advantage of such a system for the investigation of the adsorbent motion on the surface lies in the fact that the adsorbent has no internal degree of free- dom which might be affected during adsorption. This facilitates the calculations to a great extent. Dr. A. A. Clifford and Prof. P. Gray (Leeds University) said We do indeed intend to conduct studies at different temperatures so as to separate energy and entropy effects in the light of the temperature dependence of k’ (the equilibrium property) and so as to evaluate activation energies of desorption from the temperature-depen- dence of k (the kinetic property). As Dr. Elkoshi’s question implies there is no difficulty in representing the partition function for free gaseous hydrogen atoms and also for hydrogen atoms on the surface if one assumed a simple model of atoms attached to a fixed number of identical sites of infinite mass.It is only lack of know- ledge about the total number of such sites which precludes us from making an absolute calculation at one temperature. We also intend to carry out studies with deuterium atoms and this should also give us information on binding energies using the simple model described. In our reversible adsorption we believe the atoms reside on the surface for ca. 1 ms. Their maximum surface concentration is ca. 1015m-, i.e. of the order of lom4 atoms per surface atom of the silica. How are they adsorbed? They cannot reasonably form strong covalent H-0 bonds to be able to eventually escape from the surface.They may be physically attached or hydrogen-bonded to (i) 0 in ad- sorbed water (ii) 0 in OH groups on the silica surface or (iii) 0 attached to silicon. All these features of the silica surface are discussed by Linnett and coworkers (Trans. Faraday Suc. 1959 55,2152) although in the context of H-atom recombination on a silica surface. Less likely possibilities are that they are mobile on the surface or per- form more complex vibrational motions. Dr. A. A. Clifford (Leeds University) said Speaking as one of the authors of the paper whose field of study is transport properties of gases and who discovered a chromatographic effect for hydrogen atoms by accident I would like to suggest to the experts in chromatography present that the possibility of separating and analysing reactive intermediates in complex reacting systems by chromatography should be investigated.One could imagine an experiment where samples from a reacting gaseous system such as a hydrocarbon flame could be rapidly eluted in fast-flowing gas through a wide tube and the intermediates detected by a catalytic detector with a rapid response such as a very fine thermocouple.

ISSN:0301-5696    

DOI:10.1039/FS9801500161

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

AUTHOR INDEX* Albrecht M. 25 164 Carley A. F. 39 Clifford A. A. 155 161 191 Conder J. R. 162 182 183 Cox G. B. 167 172 Dawkins J. V. 127 186 Elkoshi Z. 161 178 182 191 Findenegg G. H. 25 162 164 190 192 Gray P. 155 187 190 191 Hammers W. E. 174 Kalizan R. 113 Kennedy G. J. 113 Kiselev A. V. 13 161 192 Knox J. H. 113 164 165 173 177 184 185 187 188 189 Kovats F. sz 177 Laub R. J. 162 179 191 Letcher T. M. 103 de Ligny C. L. 166 171 Mason R. S. 155 Mathot V. 183 184 McCann M. 83 Moroney L. 39 Newbery J. E. 187 Phillips C. S. G. 7,162 Poshkus D. P. 13 Purnell J. H. 83 162 169 174 178 Roberts M. W. 39 166 167 Rowlinson J. S. 162 von Rybinski W. 25 Schoenmakers P. J. 169 174 184 Scott R. P. W. 49 69 169 175 Sebille B. 139 187 Simpson C. F. 69 175 Thuaud N. 139 Tiley P. F. 93 161 168 178 179 Tillement J. P. 139 Van Kreveld M. E. 185 186 Waddicor J. I. 155 Wakeham W. A. 145 161 188 189 Wellington C. A. 83 Yeadon G. 127 * The page numbers in heavy type indicate papers submitted for discussion.

ISSN:0301-5696    

DOI:10.1039/FS980150192b

出版商:RSC    

年代:1980

数据来源: RSC